From 8467a2a9a24be7437c7e59ff1575b944ea17e6c7 Mon Sep 17 00:00:00 2001
From: mhjensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 26 Oct 2020 08:08:50 +0100
Subject: [PATCH] updating pca

---
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 doc/pub/week43/html/week43.html              | 385 ++++++++---------
 doc/pub/week43/ipynb/ipynb-week43-src.tar.gz | Bin 190 -> 191 bytes
 doc/pub/week43/ipynb/week43.ipynb            | 427 +++++--------------
 doc/src/week43/week43.do.txt                 |  64 +--
 84 files changed, 12944 insertions(+), 13284 deletions(-)

diff --git a/doc/pub/week43/html/._week43-bs000.html b/doc/pub/week43/html/._week43-bs000.html
index 5b34a0ba8..67ebb8e8e 100644
--- a/doc/pub/week43/html/._week43-bs000.html
+++ b/doc/pub/week43/html/._week43-bs000.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -323,7 +325,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 23, 2020</h4></center> <!-- date -->
+<center><h4>Oct 26, 2020</h4></center> <!-- date -->
 <br>
 <p>
 
diff --git a/doc/pub/week43/html/._week43-bs001.html b/doc/pub/week43/html/._week43-bs001.html
index 4714db0d4..18029d21e 100644
--- a/doc/pub/week43/html/._week43-bs001.html
+++ b/doc/pub/week43/html/._week43-bs001.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
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                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
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                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,6 +306,8 @@ MathJax.Hub.Config({
 <a name="part0001"></a>
 <!-- !split -->
 
+<h2 id="___sec0" class="anchor">Plans for week 43 </h2>
+
 <ul>
 <li> Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage" target="_self">Video of Lecture October 22</a></li>
 <li> Friday: Principal Component Analysis and Dimensionality Reduction. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober23.mp4?vrtx=view-as-webpage" target="_self">Video of Lecture October 23</a></li>
diff --git a/doc/pub/week43/html/._week43-bs002.html b/doc/pub/week43/html/._week43-bs002.html
index 3ae833796..e8d257ebe 100644
--- a/doc/pub/week43/html/._week43-bs002.html
+++ b/doc/pub/week43/html/._week43-bs002.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
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-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
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+              ('The final step', 2, None, '___sec68'),
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
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+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0002"></a>
 <!-- !split -->
 
-<h2 id="___sec0" class="anchor">Recurrent Neural Networks </h2>
+<h2 id="___sec1" class="anchor">Recurrent Neural Networks </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini" target="_self">Overview video</a>.
diff --git a/doc/pub/week43/html/._week43-bs003.html b/doc/pub/week43/html/._week43-bs003.html
index 9c2adb8d4..32b2bc0dd 100644
--- a/doc/pub/week43/html/._week43-bs003.html
+++ b/doc/pub/week43/html/._week43-bs003.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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                2,
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-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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                2,
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+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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+               '___sec52'),
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
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+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0003"></a>
 <!-- !split -->
 
-<h2 id="___sec1" class="anchor">Solving ODEs with Deep Learning </h2>
+<h2 id="___sec2" class="anchor">Solving ODEs with Deep Learning </h2>
 
 <p>
 The Universal Approximation Theorem states that a neural network can
diff --git a/doc/pub/week43/html/._week43-bs004.html b/doc/pub/week43/html/._week43-bs004.html
index 39cf34075..0efbb055e 100644
--- a/doc/pub/week43/html/._week43-bs004.html
+++ b/doc/pub/week43/html/._week43-bs004.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
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               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0004"></a>
 <!-- !split -->
 
-<h2 id="___sec2" class="anchor">Ordinary Differential Equations </h2>
+<h2 id="___sec3" class="anchor">Ordinary Differential Equations </h2>
 
 <p>
 An ordinary differential equation (ODE) is an equation involving functions having one variable.
diff --git a/doc/pub/week43/html/._week43-bs005.html b/doc/pub/week43/html/._week43-bs005.html
index 61d6bd835..c8a60d28c 100644
--- a/doc/pub/week43/html/._week43-bs005.html
+++ b/doc/pub/week43/html/._week43-bs005.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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+               '___sec51'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0005"></a>
 <!-- !split -->
 
-<h2 id="___sec3" class="anchor">The trial solution </h2>
+<h2 id="___sec4" class="anchor">The trial solution </h2>
 
 <p>
 Let the trial solution \( g_t(x) \) be
diff --git a/doc/pub/week43/html/._week43-bs006.html b/doc/pub/week43/html/._week43-bs006.html
index 82f9aa18e..c9d00a0b0 100644
--- a/doc/pub/week43/html/._week43-bs006.html
+++ b/doc/pub/week43/html/._week43-bs006.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0006"></a>
 <!-- !split -->
 
-<h2 id="___sec4" class="anchor">Minimization process </h2>
+<h2 id="___sec5" class="anchor">Minimization process </h2>
 
 <p>
 For the minimization to be defined, we need to have a cost function at hand to minimize.
diff --git a/doc/pub/week43/html/._week43-bs007.html b/doc/pub/week43/html/._week43-bs007.html
index f867887a5..3487488fd 100644
--- a/doc/pub/week43/html/._week43-bs007.html
+++ b/doc/pub/week43/html/._week43-bs007.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0007"></a>
 <!-- !split -->
 
-<h2 id="___sec5" class="anchor">Minimizing the cost function using gradient descent and automatic differentiation </h2>
+<h2 id="___sec6" class="anchor">Minimizing the cost function using gradient descent and automatic differentiation </h2>
 
 <p>
 To perform the minimization using gradient descent, the gradient of \( C\left(\boldsymbol{x}, P\right) \) is needed.
diff --git a/doc/pub/week43/html/._week43-bs008.html b/doc/pub/week43/html/._week43-bs008.html
index 53beb5a0b..b17a842a1 100644
--- a/doc/pub/week43/html/._week43-bs008.html
+++ b/doc/pub/week43/html/._week43-bs008.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0008"></a>
 <!-- !split -->
 
-<h2 id="___sec6" class="anchor">Example: Exponential decay </h2>
+<h2 id="___sec7" class="anchor">Example: Exponential decay </h2>
 
 <p>
 An exponential decay of a quantity \( g(x) \) is described by the equation
diff --git a/doc/pub/week43/html/._week43-bs009.html b/doc/pub/week43/html/._week43-bs009.html
index d731e390f..93ca9cbdb 100644
--- a/doc/pub/week43/html/._week43-bs009.html
+++ b/doc/pub/week43/html/._week43-bs009.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
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-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0009"></a>
 <!-- !split -->
 
-<h2 id="___sec7" class="anchor">The function to solve for </h2>
+<h2 id="___sec8" class="anchor">The function to solve for </h2>
 
 <p>
 The program will use a neural network to solve
diff --git a/doc/pub/week43/html/._week43-bs010.html b/doc/pub/week43/html/._week43-bs010.html
index 2438c3260..817974cd1 100644
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+++ b/doc/pub/week43/html/._week43-bs010.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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                2,
                None,
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-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0010"></a>
 <!-- !split -->
 
-<h2 id="___sec8" class="anchor">The trial solution </h2>
+<h2 id="___sec9" class="anchor">The trial solution </h2>
 To begin with, a trial solution \( g_t(t) \) must be chosen. A general trial solution for ordinary differential equations could be
 
 $$
diff --git a/doc/pub/week43/html/._week43-bs011.html b/doc/pub/week43/html/._week43-bs011.html
index dd39cdf93..2dce366b0 100644
--- a/doc/pub/week43/html/._week43-bs011.html
+++ b/doc/pub/week43/html/._week43-bs011.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0011"></a>
 <!-- !split -->
 
-<h2 id="___sec9" class="anchor">Setup of Network </h2>
+<h2 id="___sec10" class="anchor">Setup of Network </h2>
 
 <p>
 In this network, there are no weights and bias at the input layer, so \( P = \{ P_{\text{hidden}},  P_{\text{output}} \} \).
diff --git a/doc/pub/week43/html/._week43-bs012.html b/doc/pub/week43/html/._week43-bs012.html
index 1ad0f8a89..cbd958a4d 100644
--- a/doc/pub/week43/html/._week43-bs012.html
+++ b/doc/pub/week43/html/._week43-bs012.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0012"></a>
 <!-- !split -->
 
-<h2 id="___sec10" class="anchor">Reformulating the problem </h2>
+<h2 id="___sec11" class="anchor">Reformulating the problem </h2>
 
 <p>
 We wish that our neural network manages to minimize a given cost function.
diff --git a/doc/pub/week43/html/._week43-bs013.html b/doc/pub/week43/html/._week43-bs013.html
index 3a49a07c6..820c8344c 100644
--- a/doc/pub/week43/html/._week43-bs013.html
+++ b/doc/pub/week43/html/._week43-bs013.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
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                2,
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0013"></a>
 <!-- !split -->
 
-<h2 id="___sec11" class="anchor">More technicalities </h2>
+<h2 id="___sec12" class="anchor">More technicalities </h2>
 
 <p>
 The left hand side and right hand side of <a href="._week43-bs012.html#mjx-eqn-8">(8)</a> must be computed separately, and then the neural network must choose weights and biases, contained in \( P \), such that the sides are equal as best as possible.
diff --git a/doc/pub/week43/html/._week43-bs014.html b/doc/pub/week43/html/._week43-bs014.html
index 0da56dce0..50b88fe00 100644
--- a/doc/pub/week43/html/._week43-bs014.html
+++ b/doc/pub/week43/html/._week43-bs014.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
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+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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+              ('Towards the PCA theorem', 2, None, '___sec59'),
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-              ('Compute the sample covariance', 3, None, '___sec62'),
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-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0014"></a>
 <!-- !split -->
 
-<h2 id="___sec12" class="anchor">More details </h2>
+<h2 id="___sec13" class="anchor">More details </h2>
 
 <p>
 If the neural network evaluates \( g_t(x, P) \) at more values for \( x \), say \( N \) values \( x_i \) for \( i = 1, \dots, N \), then the <em>total</em> error to minimize becomes
diff --git a/doc/pub/week43/html/._week43-bs015.html b/doc/pub/week43/html/._week43-bs015.html
index 46cc77e10..2f1707d77 100644
--- a/doc/pub/week43/html/._week43-bs015.html
+++ b/doc/pub/week43/html/._week43-bs015.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
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               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0015"></a>
 <!-- !split -->
 
-<h2 id="___sec13" class="anchor">A possible implementation of a neural network </h2>
+<h2 id="___sec14" class="anchor">A possible implementation of a neural network </h2>
 
 <p>
 For simplicity, it is assumed that the input is an array \( \boldsymbol{x} = (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural network should find \( P \) such that it fulfills <a href="._week43-bs014.html#mjx-eqn-9">(9)</a>.
diff --git a/doc/pub/week43/html/._week43-bs016.html b/doc/pub/week43/html/._week43-bs016.html
index 885aa95bb..4d6435e03 100644
--- a/doc/pub/week43/html/._week43-bs016.html
+++ b/doc/pub/week43/html/._week43-bs016.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
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                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Correlation Matrix with Pandas and the Franke function',
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+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
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-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0016"></a>
 <!-- !split -->
 
-<h2 id="___sec14" class="anchor">Technicalities </h2>
+<h2 id="___sec15" class="anchor">Technicalities </h2>
 
 <p>
 For the \( i \)-th in the hidden layer with weight \( w_i^{\text{hidden} } \) and bias \( b_i^{\text{hidden} } \), the weighting from the \( j \)-th neuron at the input layer is:
diff --git a/doc/pub/week43/html/._week43-bs017.html b/doc/pub/week43/html/._week43-bs017.html
index 0dd5c4161..9981c6ffc 100644
--- a/doc/pub/week43/html/._week43-bs017.html
+++ b/doc/pub/week43/html/._week43-bs017.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0017"></a>
 <!-- !split -->
 
-<h2 id="___sec15" class="anchor">Final technicalities I </h2>
+<h2 id="___sec16" class="anchor">Final technicalities I </h2>
 
 <p>
 The result after weighting the inputs at the \( i \)-th hidden neuron can be written as a vector:
diff --git a/doc/pub/week43/html/._week43-bs018.html b/doc/pub/week43/html/._week43-bs018.html
index f68d4ab27..ba83a99b8 100644
--- a/doc/pub/week43/html/._week43-bs018.html
+++ b/doc/pub/week43/html/._week43-bs018.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0018"></a>
 <!-- !split -->
 
-<h2 id="___sec16" class="anchor">Final technicalities II </h2>
+<h2 id="___sec17" class="anchor">Final technicalities II </h2>
 
 <p>
 The vector \( \boldsymbol{p}_{i, \text{hidden}}^T \) constitutes each row in \( P_{\text{hidden} } \), which contains the weights for the neural network to minimize according to <a href="._week43-bs014.html#mjx-eqn-9">(9)</a>.
diff --git a/doc/pub/week43/html/._week43-bs019.html b/doc/pub/week43/html/._week43-bs019.html
index 5c42f6b3e..c68d54609 100644
--- a/doc/pub/week43/html/._week43-bs019.html
+++ b/doc/pub/week43/html/._week43-bs019.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0019"></a>
 <!-- !split -->
 
-<h2 id="___sec17" class="anchor">Final technicalities III </h2>
+<h2 id="___sec18" class="anchor">Final technicalities III </h2>
 
 <p>
 The procedure of weighting the output neuron \( j \) in the hidden layer to the \( i \)-th neuron in the output layer is similar as for the hidden layer described previously.
diff --git a/doc/pub/week43/html/._week43-bs020.html b/doc/pub/week43/html/._week43-bs020.html
index 3fd6c690c..fa092a70e 100644
--- a/doc/pub/week43/html/._week43-bs020.html
+++ b/doc/pub/week43/html/._week43-bs020.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0020"></a>
 <!-- !split -->
 
-<h2 id="___sec18" class="anchor">Final technicalities IV </h2>
+<h2 id="___sec19" class="anchor">Final technicalities IV </h2>
 
 <p>
 Expressing \( z_{1,j}^{\text{output}} \) as a vector gives the following way of weighting the inputs from the hidden layer:
diff --git a/doc/pub/week43/html/._week43-bs021.html b/doc/pub/week43/html/._week43-bs021.html
index 6536855d8..a53d66669 100644
--- a/doc/pub/week43/html/._week43-bs021.html
+++ b/doc/pub/week43/html/._week43-bs021.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0021"></a>
 <!-- !split -->
 
-<h2 id="___sec19" class="anchor">Back propagation </h2>
+<h2 id="___sec20" class="anchor">Back propagation </h2>
 
 <p>
 The next step is to decide how the parameters should be changed such that they minimize the cost function.
diff --git a/doc/pub/week43/html/._week43-bs022.html b/doc/pub/week43/html/._week43-bs022.html
index 9192d9756..de6cdbb4b 100644
--- a/doc/pub/week43/html/._week43-bs022.html
+++ b/doc/pub/week43/html/._week43-bs022.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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                2,
                None,
-               '___sec42'),
+               '___sec43'),
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0022"></a>
 <!-- !split -->
 
-<h2 id="___sec20" class="anchor">Gradient descent </h2>
+<h2 id="___sec21" class="anchor">Gradient descent </h2>
 
 <p>
 The idea of the gradient descent algorithm is to update parameters in
diff --git a/doc/pub/week43/html/._week43-bs023.html b/doc/pub/week43/html/._week43-bs023.html
index 0bad80e07..84a302189 100644
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@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-               '___sec13'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
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+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0023"></a>
 <!-- !split -->
 
-<h2 id="___sec21" class="anchor">The code for solving the ODE </h2>
+<h2 id="___sec22" class="anchor">The code for solving the ODE </h2>
 
 <p>
 
diff --git a/doc/pub/week43/html/._week43-bs024.html b/doc/pub/week43/html/._week43-bs024.html
index a20407e5d..a783fddf0 100644
--- a/doc/pub/week43/html/._week43-bs024.html
+++ b/doc/pub/week43/html/._week43-bs024.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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                2,
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0024"></a>
 <!-- !split -->
 
-<h2 id="___sec22" class="anchor">The network with one input layer, specified number of hidden layers, and one output layer </h2>
+<h2 id="___sec23" class="anchor">The network with one input layer, specified number of hidden layers, and one output layer </h2>
 
 <p>
 It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.
diff --git a/doc/pub/week43/html/._week43-bs025.html b/doc/pub/week43/html/._week43-bs025.html
index 32c4027f0..ec93ce5e7 100644
--- a/doc/pub/week43/html/._week43-bs025.html
+++ b/doc/pub/week43/html/._week43-bs025.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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-               '___sec5'),
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-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
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-               '___sec13'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
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                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
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+               '___sec57'),
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0025"></a>
 <!-- !split -->
 
-<h2 id="___sec23" class="anchor">Example: Population growth </h2>
+<h2 id="___sec24" class="anchor">Example: Population growth </h2>
 
 <p>
 A logistic model of population growth assumes that a population converges toward an equilibrium.
diff --git a/doc/pub/week43/html/._week43-bs026.html b/doc/pub/week43/html/._week43-bs026.html
index 5009c0dc5..a70407947 100644
--- a/doc/pub/week43/html/._week43-bs026.html
+++ b/doc/pub/week43/html/._week43-bs026.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0026"></a>
 <!-- !split -->
 
-<h2 id="___sec24" class="anchor">Setting up the problem </h2>
+<h2 id="___sec25" class="anchor">Setting up the problem </h2>
 
 <p>
 Here, we will model a population \( g(t) \) in an environment having carrying capacity \( A \).
diff --git a/doc/pub/week43/html/._week43-bs027.html b/doc/pub/week43/html/._week43-bs027.html
index fad0a913d..9e4abf48e 100644
--- a/doc/pub/week43/html/._week43-bs027.html
+++ b/doc/pub/week43/html/._week43-bs027.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0027"></a>
 <!-- !split -->
 
-<h2 id="___sec25" class="anchor">The trial solution </h2>
+<h2 id="___sec26" class="anchor">The trial solution </h2>
 
 <p>
 We will get a slightly different trial solution, as the boundary conditions are different
diff --git a/doc/pub/week43/html/._week43-bs028.html b/doc/pub/week43/html/._week43-bs028.html
index fd7b7de13..f8c0afd00 100644
--- a/doc/pub/week43/html/._week43-bs028.html
+++ b/doc/pub/week43/html/._week43-bs028.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0028"></a>
 <!-- !split -->
 
-<h2 id="___sec26" class="anchor">The program using Autograd </h2>
+<h2 id="___sec27" class="anchor">The program using Autograd </h2>
 
 <p>
 The network will be the similar as for the exponential decay example, but with some small modifications for our problem.
diff --git a/doc/pub/week43/html/._week43-bs029.html b/doc/pub/week43/html/._week43-bs029.html
index 5fdcc43de..1b3903e99 100644
--- a/doc/pub/week43/html/._week43-bs029.html
+++ b/doc/pub/week43/html/._week43-bs029.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0029"></a>
 <!-- !split -->
 
-<h2 id="___sec27" class="anchor">Using forward Euler to solve the ODE </h2>
+<h2 id="___sec28" class="anchor">Using forward Euler to solve the ODE </h2>
 
 <p>
 A straightforward way of solving an ODE numerically, is to use Euler's method.
diff --git a/doc/pub/week43/html/._week43-bs030.html b/doc/pub/week43/html/._week43-bs030.html
index 26e10ace3..82ebfda96 100644
--- a/doc/pub/week43/html/._week43-bs030.html
+++ b/doc/pub/week43/html/._week43-bs030.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0030"></a>
 <!-- !split -->
 
-<h2 id="___sec28" class="anchor">Example: Solving the one dimensional Poisson equation </h2>
+<h2 id="___sec29" class="anchor">Example: Solving the one dimensional Poisson equation </h2>
 
 <p>
 The Poisson equation for \( g(x) \) in one dimension is
diff --git a/doc/pub/week43/html/._week43-bs031.html b/doc/pub/week43/html/._week43-bs031.html
index 9cae8f8ab..7752a47e3 100644
--- a/doc/pub/week43/html/._week43-bs031.html
+++ b/doc/pub/week43/html/._week43-bs031.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0031"></a>
 <!-- !split -->
 
-<h2 id="___sec29" class="anchor">The specific equation to solve for </h2>
+<h2 id="___sec30" class="anchor">The specific equation to solve for </h2>
 
 <p>
 Here, the function \( g(x) \) to solve for follows the equation
diff --git a/doc/pub/week43/html/._week43-bs032.html b/doc/pub/week43/html/._week43-bs032.html
index e9f705002..1775691d3 100644
--- a/doc/pub/week43/html/._week43-bs032.html
+++ b/doc/pub/week43/html/._week43-bs032.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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                None,
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-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0032"></a>
 <!-- !split -->
 
-<h2 id="___sec30" class="anchor">Solving the equation using Autograd </h2>
+<h2 id="___sec31" class="anchor">Solving the equation using Autograd </h2>
 
 <p>
 
diff --git a/doc/pub/week43/html/._week43-bs033.html b/doc/pub/week43/html/._week43-bs033.html
index 69ba54e02..5c5fb5133 100644
--- a/doc/pub/week43/html/._week43-bs033.html
+++ b/doc/pub/week43/html/._week43-bs033.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0033"></a>
 <!-- !split -->
 
-<h2 id="___sec31" class="anchor">Comparing with a numerical scheme </h2>
+<h2 id="___sec32" class="anchor">Comparing with a numerical scheme </h2>
 
 <p>
 The Poisson equation is possible to solve using Taylor series to approximate the second derivative.
diff --git a/doc/pub/week43/html/._week43-bs034.html b/doc/pub/week43/html/._week43-bs034.html
index a3fee85b7..f912c3c26 100644
--- a/doc/pub/week43/html/._week43-bs034.html
+++ b/doc/pub/week43/html/._week43-bs034.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
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+              ('Gradient descent', 2, None, '___sec21'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0034"></a>
 <!-- !split -->
 
-<h2 id="___sec32" class="anchor">Setting up the code </h2>
+<h2 id="___sec33" class="anchor">Setting up the code </h2>
 
 <p>
 We can then compare the result from this numerical scheme with the output from our network using Autograd:
diff --git a/doc/pub/week43/html/._week43-bs035.html b/doc/pub/week43/html/._week43-bs035.html
index 726ad43a0..767d63038 100644
--- a/doc/pub/week43/html/._week43-bs035.html
+++ b/doc/pub/week43/html/._week43-bs035.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
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+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0035"></a>
 <!-- !split -->
 
-<h2 id="___sec33" class="anchor">Partial Differential Equations </h2>
+<h2 id="___sec34" class="anchor">Partial Differential Equations </h2>
 
 <p>
 A partial differential equation (PDE) has a solution here the function
diff --git a/doc/pub/week43/html/._week43-bs036.html b/doc/pub/week43/html/._week43-bs036.html
index 4da3dba65..2069800a9 100644
--- a/doc/pub/week43/html/._week43-bs036.html
+++ b/doc/pub/week43/html/._week43-bs036.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
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-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
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+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
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-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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+               '___sec48'),
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+               '___sec51'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0036"></a>
 <!-- !split -->
 
-<h2 id="___sec34" class="anchor">Type of problem </h2>
+<h2 id="___sec35" class="anchor">Type of problem </h2>
 
 <p>
 The problem our network must solve for, is similar to the ODE case.
diff --git a/doc/pub/week43/html/._week43-bs037.html b/doc/pub/week43/html/._week43-bs037.html
index 43bf2f3ae..e89ab0d0f 100644
--- a/doc/pub/week43/html/._week43-bs037.html
+++ b/doc/pub/week43/html/._week43-bs037.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0037"></a>
 <!-- !split -->
 
-<h2 id="___sec35" class="anchor">Network requirements </h2>
+<h2 id="___sec36" class="anchor">Network requirements </h2>
 
 <p>
 The network tries then the minimize the cost function following the
diff --git a/doc/pub/week43/html/._week43-bs038.html b/doc/pub/week43/html/._week43-bs038.html
index c4552ab87..e995f6151 100644
--- a/doc/pub/week43/html/._week43-bs038.html
+++ b/doc/pub/week43/html/._week43-bs038.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
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+               '___sec51'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
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               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
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               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0038"></a>
 <!-- !split -->
 
-<h2 id="___sec36" class="anchor">More details </h2>
+<h2 id="___sec37" class="anchor">More details </h2>
 
 <p>
 If we let \( \boldsymbol{x} = \big( x_1, \dots, x_N \big) \) be an array containing the values for \( x_1, \dots, x_N \) respectively, the cost function can be reformulated into the following:
diff --git a/doc/pub/week43/html/._week43-bs039.html b/doc/pub/week43/html/._week43-bs039.html
index 1e3d4d217..46aa3df4b 100644
--- a/doc/pub/week43/html/._week43-bs039.html
+++ b/doc/pub/week43/html/._week43-bs039.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
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-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0039"></a>
 <!-- !split -->
 
-<h2 id="___sec37" class="anchor">Example: The diffusion equation </h2>
+<h2 id="___sec38" class="anchor">Example: The diffusion equation </h2>
 
 <p>
 In one spatial dimension, the equation reads
diff --git a/doc/pub/week43/html/._week43-bs040.html b/doc/pub/week43/html/._week43-bs040.html
index 6a597ed03..96326c426 100644
--- a/doc/pub/week43/html/._week43-bs040.html
+++ b/doc/pub/week43/html/._week43-bs040.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0040"></a>
 <!-- !split -->
 
-<h2 id="___sec38" class="anchor">Defining the problem </h2>
+<h2 id="___sec39" class="anchor">Defining the problem </h2>
 
 <p>
 For this case, we want to find \( g(x,t) \) such that
diff --git a/doc/pub/week43/html/._week43-bs041.html b/doc/pub/week43/html/._week43-bs041.html
index 29365503d..36219dfce 100644
--- a/doc/pub/week43/html/._week43-bs041.html
+++ b/doc/pub/week43/html/._week43-bs041.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0041"></a>
 <!-- !split -->
 
-<h2 id="___sec39" class="anchor">Setting up the network using Autograd </h2>
+<h2 id="___sec40" class="anchor">Setting up the network using Autograd </h2>
 
 <p>
 The only change to do here, is to extend our network such that
diff --git a/doc/pub/week43/html/._week43-bs042.html b/doc/pub/week43/html/._week43-bs042.html
index bb30c8c32..5e70b842b 100644
--- a/doc/pub/week43/html/._week43-bs042.html
+++ b/doc/pub/week43/html/._week43-bs042.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0042"></a>
 <!-- !split -->
 
-<h2 id="___sec40" class="anchor">Setting up the network using Autograd; The trial solution </h2>
+<h2 id="___sec41" class="anchor">Setting up the network using Autograd; The trial solution </h2>
 
 <p>
 The cost function must then iterate through the given arrays
diff --git a/doc/pub/week43/html/._week43-bs043.html b/doc/pub/week43/html/._week43-bs043.html
index d7f62e5c4..aeac8278b 100644
--- a/doc/pub/week43/html/._week43-bs043.html
+++ b/doc/pub/week43/html/._week43-bs043.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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                None,
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-              ('Technicalities', 2, None, '___sec14'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0043"></a>
 <!-- !split -->
 
-<h2 id="___sec41" class="anchor">Why the jacobian? </h2>
+<h2 id="___sec42" class="anchor">Why the jacobian? </h2>
 
 <p>
 The Jacobian is used because the program must find the derivative of
diff --git a/doc/pub/week43/html/._week43-bs044.html b/doc/pub/week43/html/._week43-bs044.html
index 29cae84ea..7d53260ed 100644
--- a/doc/pub/week43/html/._week43-bs044.html
+++ b/doc/pub/week43/html/._week43-bs044.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
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                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0044"></a>
 <!-- !split -->
 
-<h2 id="___sec42" class="anchor">Setting up the network using Autograd; The full program </h2>
+<h2 id="___sec43" class="anchor">Setting up the network using Autograd; The full program </h2>
 
 <p>
 Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.
diff --git a/doc/pub/week43/html/._week43-bs045.html b/doc/pub/week43/html/._week43-bs045.html
index 43e6de5a1..db71ecc87 100644
--- a/doc/pub/week43/html/._week43-bs045.html
+++ b/doc/pub/week43/html/._week43-bs045.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
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-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('The specific equation to solve for', 2, None, '___sec30'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
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-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0045"></a>
 <!-- !split -->
 
-<h2 id="___sec43" class="anchor">Example: Solving the wave equation with Neural Networks </h2>
+<h2 id="___sec44" class="anchor">Example: Solving the wave equation with Neural Networks </h2>
 
 <p>
 The wave equation is
diff --git a/doc/pub/week43/html/._week43-bs046.html b/doc/pub/week43/html/._week43-bs046.html
index 49c16ace5..0cd0a41bf 100644
--- a/doc/pub/week43/html/._week43-bs046.html
+++ b/doc/pub/week43/html/._week43-bs046.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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               ('Introducing the Covariance and Correlation functions',
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0046"></a>
 <!-- !split -->
 
-<h2 id="___sec44" class="anchor">The problem to solve for </h2>
+<h2 id="___sec45" class="anchor">The problem to solve for </h2>
 
 <p>
 The wave equation to solve for, is
diff --git a/doc/pub/week43/html/._week43-bs047.html b/doc/pub/week43/html/._week43-bs047.html
index b854166ad..ba58aa617 100644
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@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
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+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
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+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
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                None,
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-              ('The specific equation to solve for', 2, None, '___sec29'),
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-              ('Setting up the code', 2, None, '___sec32'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
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-               '___sec40'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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+               '___sec48'),
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-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0047"></a>
 <!-- !split -->
 
-<h2 id="___sec45" class="anchor">The trial solution </h2>
+<h2 id="___sec46" class="anchor">The trial solution </h2>
 Setting up the network is done in similar matter as for the example of solving the diffusion equation.
 The only things we have to change, is the trial solution such that it satisfies the conditions from <a href="._week43-bs046.html#mjx-eqn-20">(20)</a> and the cost function.
 
diff --git a/doc/pub/week43/html/._week43-bs048.html b/doc/pub/week43/html/._week43-bs048.html
index 49f067277..2f2252fba 100644
--- a/doc/pub/week43/html/._week43-bs048.html
+++ b/doc/pub/week43/html/._week43-bs048.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0048"></a>
 <!-- !split -->
 
-<h2 id="___sec46" class="anchor">The analytical solution </h2>
+<h2 id="___sec47" class="anchor">The analytical solution </h2>
 
 <p>
 The analytical solution for our specific problem, is
diff --git a/doc/pub/week43/html/._week43-bs049.html b/doc/pub/week43/html/._week43-bs049.html
index ccc1c8dc7..d563d365a 100644
--- a/doc/pub/week43/html/._week43-bs049.html
+++ b/doc/pub/week43/html/._week43-bs049.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-               '___sec42'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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                None,
-               '___sec51'),
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-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0049"></a>
 <!-- !split -->
 
-<h2 id="___sec47" class="anchor">Solving the wave equation - the full program using Autograd </h2>
+<h2 id="___sec48" class="anchor">Solving the wave equation - the full program using Autograd </h2>
 
 <p>
 
diff --git a/doc/pub/week43/html/._week43-bs050.html b/doc/pub/week43/html/._week43-bs050.html
index 98a20ffc8..2ff34c66e 100644
--- a/doc/pub/week43/html/._week43-bs050.html
+++ b/doc/pub/week43/html/._week43-bs050.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
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-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
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                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0050"></a>
 <!-- !split -->
 
-<h2 id="___sec48" class="anchor">Resources on differential equations and deep learning </h2>
+<h2 id="___sec49" class="anchor">Resources on differential equations and deep learning </h2>
 
 <ol>
 <li> <a href="https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf" target="_self">Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al</a></li>
diff --git a/doc/pub/week43/html/._week43-bs051.html b/doc/pub/week43/html/._week43-bs051.html
index 36081a7bb..9c7b84c94 100644
--- a/doc/pub/week43/html/._week43-bs051.html
+++ b/doc/pub/week43/html/._week43-bs051.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
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-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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                None,
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
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+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
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 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0051"></a>
 <!-- !split -->
 
-<h2 id="___sec49" class="anchor">Friday, Principal Component Analysis </h2>
+<h2 id="___sec50" class="anchor">Friday, Principal Component Analysis </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=fkf4IBRSeEc&ab_channel=SteveBrunton" target="_self">Overview video</a>
diff --git a/doc/pub/week43/html/._week43-bs052.html b/doc/pub/week43/html/._week43-bs052.html
index a985322ba..d06f0460e 100644
--- a/doc/pub/week43/html/._week43-bs052.html
+++ b/doc/pub/week43/html/._week43-bs052.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0052"></a>
 <!-- !split -->
 
-<h2 id="___sec50" class="anchor">Basic ideas of the Principal Component Analysis (PCA) </h2>
+<h2 id="___sec51" class="anchor">Basic ideas of the Principal Component Analysis (PCA) </h2>
 
 <p>
 The principal component analysis deals with the problem of fitting a
diff --git a/doc/pub/week43/html/._week43-bs053.html b/doc/pub/week43/html/._week43-bs053.html
index 04b559612..30f60d019 100644
--- a/doc/pub/week43/html/._week43-bs053.html
+++ b/doc/pub/week43/html/._week43-bs053.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
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                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-               '___sec51'),
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               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Back to the Cancer Data', 2, None, '___sec71'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0053"></a>
 <!-- !split -->
 
-<h2 id="___sec51" class="anchor">Introducing the Covariance and Correlation functions  </h2>
+<h2 id="___sec52" class="anchor">Introducing the Covariance and Correlation functions  </h2>
 
 <p>
 Before we discuss the PCA theorem, we need to remind ourselves about
diff --git a/doc/pub/week43/html/._week43-bs054.html b/doc/pub/week43/html/._week43-bs054.html
index cae1130d6..6953bf1a3 100644
--- a/doc/pub/week43/html/._week43-bs054.html
+++ b/doc/pub/week43/html/._week43-bs054.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0054"></a>
 <!-- !split -->
 
-<h2 id="___sec52" class="anchor">Correlation Function and Design/Feature Matrix </h2>
+<h2 id="___sec53" class="anchor">Correlation Function and Design/Feature Matrix </h2>
 
 <p>
 In our derivation of the various regression algorithms like <b>Ordinary Least Squares</b> or <b>Ridge regression</b>
diff --git a/doc/pub/week43/html/._week43-bs055.html b/doc/pub/week43/html/._week43-bs055.html
index 5f4b1c09f..8c4c9906f 100644
--- a/doc/pub/week43/html/._week43-bs055.html
+++ b/doc/pub/week43/html/._week43-bs055.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Rewriting the Covariance and/or Correlation Matrix',
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                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
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+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0055"></a>
 <!-- !split -->
 
-<h2 id="___sec53" class="anchor">Covariance Matrix Examples </h2>
+<h2 id="___sec54" class="anchor">Covariance Matrix Examples </h2>
 
 <p>
 The Numpy function <b>np.cov</b> calculates the covariance elements using
diff --git a/doc/pub/week43/html/._week43-bs056.html b/doc/pub/week43/html/._week43-bs056.html
index 9ce214653..6c05a923b 100644
--- a/doc/pub/week43/html/._week43-bs056.html
+++ b/doc/pub/week43/html/._week43-bs056.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
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+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
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+              ('Reformulating the problem', 2, None, '___sec11'),
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+              ('More details', 2, None, '___sec13'),
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-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
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+              ('Partial Differential Equations', 2, None, '___sec34'),
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+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
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-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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-               '___sec47'),
+               '___sec48'),
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-               '___sec48'),
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                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0056"></a>
 <!-- !split -->
 
-<h2 id="___sec54" class="anchor">Correlation Matrix  </h2>
+<h2 id="___sec55" class="anchor">Correlation Matrix  </h2>
 
 <p>
 The previous example can be converted into the correlation matrix by
diff --git a/doc/pub/week43/html/._week43-bs057.html b/doc/pub/week43/html/._week43-bs057.html
index e9a9386d4..199e51dac 100644
--- a/doc/pub/week43/html/._week43-bs057.html
+++ b/doc/pub/week43/html/._week43-bs057.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
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               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0057"></a>
 <!-- !split -->
 
-<h2 id="___sec55" class="anchor">Correlation Matrix with Pandas </h2>
+<h2 id="___sec56" class="anchor">Correlation Matrix with Pandas </h2>
 
 <p>
 We whow here how we can set up the correlation matrix using <b>pandas</b>, as done in this simple code
diff --git a/doc/pub/week43/html/._week43-bs058.html b/doc/pub/week43/html/._week43-bs058.html
index 86d386b42..2b219f27d 100644
--- a/doc/pub/week43/html/._week43-bs058.html
+++ b/doc/pub/week43/html/._week43-bs058.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
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+              ('Gradient descent', 2, None, '___sec21'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
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-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
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-               '___sec40'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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                None,
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+               '___sec48'),
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-               '___sec48'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
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+              ('Towards the PCA theorem', 2, None, '___sec59'),
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-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
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-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0058"></a>
 <!-- !split -->
 
-<h2 id="___sec56" class="anchor">Correlation Matrix with Pandas and the Franke function </h2>
+<h2 id="___sec57" class="anchor">Correlation Matrix with Pandas and the Franke function </h2>
 
 <p>
 
diff --git a/doc/pub/week43/html/._week43-bs059.html b/doc/pub/week43/html/._week43-bs059.html
index 77a753ec9..ed6efeea8 100644
--- a/doc/pub/week43/html/._week43-bs059.html
+++ b/doc/pub/week43/html/._week43-bs059.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0059"></a>
 <!-- !split -->
 
-<h2 id="___sec57" class="anchor">Rewriting the Covariance and/or Correlation Matrix </h2>
+<h2 id="___sec58" class="anchor">Rewriting the Covariance and/or Correlation Matrix </h2>
 
 <p>
 We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix \( \boldsymbol{X} \) as 
diff --git a/doc/pub/week43/html/._week43-bs060.html b/doc/pub/week43/html/._week43-bs060.html
index 61c87c892..6e15e3a04 100644
--- a/doc/pub/week43/html/._week43-bs060.html
+++ b/doc/pub/week43/html/._week43-bs060.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
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                None,
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+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
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-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0060"></a>
 <!-- !split -->
 
-<h2 id="___sec58" class="anchor">Towards the PCA theorem </h2>
+<h2 id="___sec59" class="anchor">Towards the PCA theorem </h2>
 
 <p>
 We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as
diff --git a/doc/pub/week43/html/._week43-bs061.html b/doc/pub/week43/html/._week43-bs061.html
index 6b7d165f9..f7f785824 100644
--- a/doc/pub/week43/html/._week43-bs061.html
+++ b/doc/pub/week43/html/._week43-bs061.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0061"></a>
 <!-- !split -->
 
-<h2 id="___sec59" class="anchor">The Algorithm before theorem </h2>
+<h2 id="___sec60" class="anchor">The Algorithm before theorem </h2>
 
 <p>
 Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. 
@@ -327,7 +329,7 @@ $$
 
 <ul>
 <li> Center the data by subtracting the mean value for each column. This leads to a new matrix \( \boldsymbol{X}\rightarrow \overline{\boldsymbol{X}} \).</li>
-<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}\overline{\boldsymbol{X}}^T] \).</li>
+<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}^T\overline{\boldsymbol{X}}] \).</li>
 <li> Find the eigenpairs of \( \boldsymbol{C} \) with eigenvalues \( [\lambda_0,\lambda_1,\dots,\lambda_{p-1}] \) and eigenvectors \( [\boldsymbol{s}_0,\boldsymbol{s}_1,\dots,\boldsymbol{s}_{p-1}] \).</li>
 <li> Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.</li>
 <li> Keep only those \( l \) eigenvalues larger than a selected threshold value, discarding thus \( p-l \) features since we expect small variations in the data here.</li>
diff --git a/doc/pub/week43/html/._week43-bs062.html b/doc/pub/week43/html/._week43-bs062.html
index 899900e74..f82fa366d 100644
--- a/doc/pub/week43/html/._week43-bs062.html
+++ b/doc/pub/week43/html/._week43-bs062.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
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                None,
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,11 +306,11 @@ MathJax.Hub.Config({
 <a name="part0062"></a>
 <!-- !split -->
 
-<h2 id="___sec60" class="anchor">Writing our own PCA code </h2>
+<h2 id="___sec61" class="anchor">Writing our own PCA code </h2>
 
 <p>
 We will use a simple example first with two-dimensional data
-drawn from a multivariate normal distribution with the following mean and covariance matrix:
+drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):
 $$
 \mu = (-1,2) \qquad \Sigma = \begin{bmatrix} 4 & 2 \\
 2 & 2
@@ -316,8 +318,8 @@ $$
 $$
 
 Note that the mean refers to each column of data. 
-We will generate \( n = 1000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
-this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \).
+We will generate \( n = 10000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
+this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \). This is our design matrix where we have forced the covariance and mean values to take specific values.
 
 <p>
 The following Python code aids in setting up the data and writing out the design matrix.
@@ -337,7 +339,7 @@ X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>r
 <p>
 Now we are going to implement the PCA algorithm. We will break it down into various substeps.
 
-<h3 id="___sec61" class="anchor">Compute the sample mean and center the data </h3>
+<h3 id="___sec62" class="anchor">Compute the sample mean and center the data </h3>
 
 <p>
 The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is
@@ -352,7 +354,7 @@ $$
 
 When you are done with these steps, print out \( \mu_n \) to verify it is
 close to \( \mu \) and plot your mean centered data to verify it is
-centered at the origin! Compare your code with the functionality from <b>Scikit-Learn</b> discussed above.
+centered at the origin! 
 The following code elements perform these operations using <b>pandas</b> or using our own functionality for doing so. The latter, using <b>numpy</b> is rather simple through the <b>mean()</b> function. 
 <p>
 
@@ -374,7 +376,7 @@ variance. The diagonal covariance matrix elements will then be one,
 while the non-diagonal ones need to be divided by \( 2\sqrt{2} \) for our
 specific case.
 
-<h3 id="___sec62" class="anchor">Compute the sample covariance </h3>
+<h3 id="___sec63" class="anchor">Compute the sample covariance </h3>
 
 <p>
 Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation
@@ -414,9 +416,9 @@ plt<span style="color: #666666">.</span>show()
 </pre></div>
 <p>
 Depending on the number of points \( n \), we will get results that are close to the covariance values defined above.
-The plot shows how the data are clustered around a line with slope close to one. Is this expected?
+The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed.
 
-<h3 id="___sec63" class="anchor">Diagonalize the sample covariance matrix to obtain the principal components </h3>
+<h3 id="___sec64" class="anchor">Diagonalize the sample covariance matrix to obtain the principal components </h3>
 
 <p>
 Now we are ready to solve for the principal components! To do so we
diff --git a/doc/pub/week43/html/._week43-bs063.html b/doc/pub/week43/html/._week43-bs063.html
index 8bcc8f0d4..b53560b7d 100644
--- a/doc/pub/week43/html/._week43-bs063.html
+++ b/doc/pub/week43/html/._week43-bs063.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0063"></a>
 <!-- !split -->
 
-<h2 id="___sec64" class="anchor">Classical PCA Theorem   </h2>
+<h2 id="___sec65" class="anchor">Classical PCA Theorem   </h2>
 
 <p>
 We assume now that we have a design matrix \( \boldsymbol{X} \) which has been
@@ -313,15 +315,6 @@ overline symbol. The matrix is defined in terms of the various column
 vectors \( [\boldsymbol{x}_0,\boldsymbol{x}_1,\dots, \boldsymbol{x}_{p-1}] \) each with dimension
 \( \boldsymbol{x}\in {\mathbb{R}}^{n} \).
 
-<p>
-We assume also that we have an orthogonal transformation \( \boldsymbol{W}\in {\mathbb{R}}^{p\times p} \).  We define the reconstruction error (which is similar to the mean squared error we have seen before) as
-$$
-J(\boldsymbol{W},\boldsymbol{Z}) = \frac{1}{n}\sum_i (\boldsymbol{x}_i - \overline{\boldsymbol{x}}_i)^2,
-$$
-
-with \( \overline{\boldsymbol{x}}_i = \boldsymbol{W}\boldsymbol{z}_i \), where \( \boldsymbol{z}_i \) is a row vector with dimension \( {\mathbb{R}}^{n} \) of the matrix
-\( \boldsymbol{Z}\in{\mathbb{R}}^{p\times n} \).  When doing PCA we want to reduce this dimensionality.
-
 <p>
 The PCA theorem states that minimizing the above reconstruction error
 corresponds to setting \( \boldsymbol{W}=\boldsymbol{S} \), the orthogonal matrix which
diff --git a/doc/pub/week43/html/._week43-bs064.html b/doc/pub/week43/html/._week43-bs064.html
index 3b3488d30..1817841ba 100644
--- a/doc/pub/week43/html/._week43-bs064.html
+++ b/doc/pub/week43/html/._week43-bs064.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,25 +306,10 @@ MathJax.Hub.Config({
 <a name="part0064"></a>
 <!-- !split -->
 
-<h2 id="___sec65" class="anchor">Proof of the PCA Theorem  </h2>
+<h2 id="___sec66" class="anchor">Proof of the PCA Theorem  </h2>
 
 <p>
-To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{w}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)= \frac{1}{n}\sum_i (\boldsymbol{x}_i - z_{i0}\boldsymbol{w}_0)^2=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2\boldsymbol{w}_0^T\boldsymbol{w}_0),
-$$
-
-which we can rewrite due to the orthogonality of \( \boldsymbol{w}_i \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2).
-$$
-
-Minimizing \( J \) with respect to the unknown parameters \( z_{0i} \) we obtain that
-$$
-z_{i0}=\boldsymbol{w}_0^T\boldsymbol{x}_i,
-$$
-
-where the vectors on the rhs are known.
+To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{s}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
 
 <p>
 <p>
diff --git a/doc/pub/week43/html/._week43-bs065.html b/doc/pub/week43/html/._week43-bs065.html
index f1fad3bc5..9c436aef5 100644
--- a/doc/pub/week43/html/._week43-bs065.html
+++ b/doc/pub/week43/html/._week43-bs065.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,37 +306,7 @@ MathJax.Hub.Config({
 <a name="part0065"></a>
 <!-- !split -->
 
-<h2 id="___sec66" class="anchor">PCA Proof continued </h2>
-
-<p>
-We have now found the unknown parameters \( z_{i0} \). These correspond to the projected coordinates and we can write
-$$
-J(\boldsymbol{w}_0)= \frac{1}{p}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - z_{i0}^2)=\mathrm{const}-\frac{1}{n}\sum_i z_{i0}^2.
-$$
-
-<p>
-We can show that the variance of the projected coordinates defined by \( \boldsymbol{w}_0^T\boldsymbol{x}_i \) are given by
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2,
-$$
-
-since the expectation value of
-$$
-\mathbb{E}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \mathbb{E}[z_{i0}]= \boldsymbol{w}_0^T\mathbb{E}[\boldsymbol{x}_i]=0,
-$$
-
-where we have used the fact that our data are centered.
-
-<p>
-Recalling our definition of the covariance as 
-$$
-\boldsymbol{C}[\boldsymbol{x}] = \frac{1}{n}\boldsymbol{X}\boldsymbol{X}^T=\mathbb{E}[\boldsymbol{X}\boldsymbol{X}^T],
-$$
-
-we have thus that
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2=\boldsymbol{w}_0^T\boldsymbol{C}[\boldsymbol{x}]\boldsymbol{w}_0.
-$$
+<h2 id="___sec67" class="anchor">PCA Proof continued </h2>
 
 <p>
 We are almost there, we have obtained a relation between minimizing
diff --git a/doc/pub/week43/html/._week43-bs066.html b/doc/pub/week43/html/._week43-bs066.html
index 9e07f1869..7a6563d95 100644
--- a/doc/pub/week43/html/._week43-bs066.html
+++ b/doc/pub/week43/html/._week43-bs066.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0066"></a>
 <!-- !split -->
 
-<h2 id="___sec67" class="anchor">The final step </h2>
+<h2 id="___sec68" class="anchor">The final step </h2>
 
 <p>
 We could trivially maximize the variance of the projection (and
diff --git a/doc/pub/week43/html/._week43-bs067.html b/doc/pub/week43/html/._week43-bs067.html
index d496369c2..5476031d8 100644
--- a/doc/pub/week43/html/._week43-bs067.html
+++ b/doc/pub/week43/html/._week43-bs067.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
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                None,
-               '___sec42'),
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               ('Example: Solving the wave equation with Neural Networks',
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                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0067"></a>
 <!-- !split -->
 
-<h2 id="___sec68" class="anchor">Geometric Interpretation and link with Singular Value Decomposition </h2>
+<h2 id="___sec69" class="anchor">Geometric Interpretation and link with Singular Value Decomposition </h2>
 
 <p>
 For a detailed demonstration of the geometric interpretation, see <a href="https://www.springer.com/gp/book/9780387878102" target="_self">Vidal, Ma and Sastry, section 2.1.2</a>.
diff --git a/doc/pub/week43/html/._week43-bs068.html b/doc/pub/week43/html/._week43-bs068.html
index acb68c7d3..1643e64a0 100644
--- a/doc/pub/week43/html/._week43-bs068.html
+++ b/doc/pub/week43/html/._week43-bs068.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
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                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0068"></a>
 <!-- !split -->
 
-<h2 id="___sec69" class="anchor">Principal Component Analysis </h2>
+<h2 id="___sec70" class="anchor">Principal Component Analysis </h2>
 
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
diff --git a/doc/pub/week43/html/._week43-bs069.html b/doc/pub/week43/html/._week43-bs069.html
index 76f663a70..450940c24 100644
--- a/doc/pub/week43/html/._week43-bs069.html
+++ b/doc/pub/week43/html/._week43-bs069.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0069"></a>
 <!-- !split  -->
 
-<h2 id="___sec70" class="anchor">PCA and scikit-learn </h2>
+<h2 id="___sec71" class="anchor">PCA and scikit-learn </h2>
 
 <p>
 Scikit-Learn&#8217;s PCA class implements PCA using SVD decomposition just like we did before. The
diff --git a/doc/pub/week43/html/._week43-bs070.html b/doc/pub/week43/html/._week43-bs070.html
index 7b30fc5c6..900a91d69 100644
--- a/doc/pub/week43/html/._week43-bs070.html
+++ b/doc/pub/week43/html/._week43-bs070.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0070"></a>
 <!-- !split -->
 
-<h2 id="___sec71" class="anchor">Back to the Cancer Data </h2>
+<h2 id="___sec72" class="anchor">Back to the Cancer Data </h2>
 We can now repeat the above but applied to real data, in this case our breast cancer data.
 Here we compute performance scores on the training data using logistic regression.
 <p>
diff --git a/doc/pub/week43/html/._week43-bs071.html b/doc/pub/week43/html/._week43-bs071.html
index 9f925d170..f8b29450e 100644
--- a/doc/pub/week43/html/._week43-bs071.html
+++ b/doc/pub/week43/html/._week43-bs071.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0071"></a>
 <!-- !split -->
 
-<h2 id="___sec72" class="anchor">More on the PCA </h2>
+<h2 id="___sec73" class="anchor">More on the PCA </h2>
 
 <p>
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
diff --git a/doc/pub/week43/html/._week43-bs072.html b/doc/pub/week43/html/._week43-bs072.html
index 16bf363db..758953a69 100644
--- a/doc/pub/week43/html/._week43-bs072.html
+++ b/doc/pub/week43/html/._week43-bs072.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0072"></a>
 <!-- !split -->
 
-<h2 id="___sec73" class="anchor">Incremental PCA </h2>
+<h2 id="___sec74" class="anchor">Incremental PCA </h2>
 
 <p>
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
diff --git a/doc/pub/week43/html/._week43-bs073.html b/doc/pub/week43/html/._week43-bs073.html
index 60c2b4630..7b2c6f576 100644
--- a/doc/pub/week43/html/._week43-bs073.html
+++ b/doc/pub/week43/html/._week43-bs073.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
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-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
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-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
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-               '___sec42'),
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-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
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                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0073"></a>
 <!-- !split -->
 
-<h2 id="___sec74" class="anchor">Randomized PCA </h2>
+<h2 id="___sec75" class="anchor">Randomized PCA </h2>
 
 <p>
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
diff --git a/doc/pub/week43/html/._week43-bs074.html b/doc/pub/week43/html/._week43-bs074.html
index 0517159e2..ae16d5662 100644
--- a/doc/pub/week43/html/._week43-bs074.html
+++ b/doc/pub/week43/html/._week43-bs074.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
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                2,
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-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Correlation Matrix with Pandas and the Franke function',
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               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0074"></a>
 <!-- !split -->
 
-<h2 id="___sec75" class="anchor">Kernel PCA </h2>
+<h2 id="___sec76" class="anchor">Kernel PCA </h2>
 <div class="panel panel-default">
 <div class="panel-body">
 <p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
diff --git a/doc/pub/week43/html/._week43-bs075.html b/doc/pub/week43/html/._week43-bs075.html
index de8009f41..cdfbe4448 100644
--- a/doc/pub/week43/html/._week43-bs075.html
+++ b/doc/pub/week43/html/._week43-bs075.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
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- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
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-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
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-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
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+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
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-              ('Solving the equation using Autograd', 2, None, '___sec30'),
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-              ('Setting up the code', 2, None, '___sec32'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
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+              ('Partial Differential Equations', 2, None, '___sec34'),
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+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
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-               '___sec40'),
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+              ('The problem to solve for', 2, None, '___sec45'),
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+               '___sec48'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
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+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
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+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0075"></a>
 <!-- !split -->
 
-<h2 id="___sec76" class="anchor">LLE </h2>
+<h2 id="___sec77" class="anchor">LLE </h2>
 
 <p>
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
diff --git a/doc/pub/week43/html/._week43-bs076.html b/doc/pub/week43/html/._week43-bs076.html
index 020800275..0c39e5bfa 100644
--- a/doc/pub/week43/html/._week43-bs076.html
+++ b/doc/pub/week43/html/._week43-bs076.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
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+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
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-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
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               ('Introducing the Covariance and Correlation functions',
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-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
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               ('Correlation Matrix with Pandas and the Franke function',
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                None,
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               ('Rewriting the Covariance and/or Correlation Matrix',
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
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+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
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-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
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+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -304,7 +306,7 @@ MathJax.Hub.Config({
 <a name="part0076"></a>
 <!-- !split -->
 
-<h2 id="___sec77" class="anchor">Other techniques </h2>
+<h2 id="___sec78" class="anchor">Other techniques </h2>
 
 <p>
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
diff --git a/doc/pub/week43/html/week43-bs.html b/doc/pub/week43/html/week43-bs.html
index 5b34a0ba8..67ebb8e8e 100644
--- a/doc/pub/week43/html/week43-bs.html
+++ b/doc/pub/week43/html/week43-bs.html
@@ -41,139 +41,140 @@ Automatically generated HTML file from DocOnce source
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
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-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
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                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
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-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
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+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
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-               '___sec40'),
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-              ('The trial solution', 2, None, '___sec45'),
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+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
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               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
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                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
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-              ('Correlation Matrix', 2, None, '___sec54'),
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+              ('Covariance Matrix Examples', 2, None, '___sec54'),
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                None,
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               ('Rewriting the Covariance and/or Correlation Matrix',
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                None,
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-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
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-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
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-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -211,84 +212,85 @@ MathJax.Hub.Config({
       <li class="dropdown">
         <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
         <ul class="dropdown-menu">
-     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec0" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec1" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec2" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec3" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec4" style="font-size: 80%;"><b>Minimization process</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec5" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec6" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec7" style="font-size: 80%;"><b>The function to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec8" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec9" style="font-size: 80%;"><b>Setup of Network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec10" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec11" style="font-size: 80%;"><b>More technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec12" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec13" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec14" style="font-size: 80%;"><b>Technicalities</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec15" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec16" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec17" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec18" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec19" style="font-size: 80%;"><b>Back propagation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec20" style="font-size: 80%;"><b>Gradient descent</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec21" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec22" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec23" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec24" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec25" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec26" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec27" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec28" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec29" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec30" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec31" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec32" style="font-size: 80%;"><b>Setting up the code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec33" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec34" style="font-size: 80%;"><b>Type of problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec35" style="font-size: 80%;"><b>Network requirements</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec36" style="font-size: 80%;"><b>More details</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec37" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec38" style="font-size: 80%;"><b>Defining the problem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec39" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec41" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec42" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec43" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec44" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec45" style="font-size: 80%;"><b>The trial solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec46" style="font-size: 80%;"><b>The analytical solution</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec47" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec48" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec49" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec50" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec51" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec52" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec53" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec54" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec57" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec58" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec59" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec60" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec64" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec65" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec66" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec67" style="font-size: 80%;"><b>The final step</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec68" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec69" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec70" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec71" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec72" style="font-size: 80%;"><b>More on the PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec73" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec74" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec75" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec76" style="font-size: 80%;"><b>LLE</b></a></li>
-     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec77" style="font-size: 80%;"><b>Other techniques</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Recurrent Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Solving ODEs with Deep Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>Ordinary Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Minimization process</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs007.html#___sec6" style="font-size: 80%;"><b>Minimizing the cost function using gradient descent and automatic differentiation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>Example: Exponential decay</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>The function to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Setup of Network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs013.html#___sec12" style="font-size: 80%;"><b>More technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>A possible implementation of a neural network</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Technicalities</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>Final technicalities I</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Final technicalities II</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Final technicalities III</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs020.html#___sec19" style="font-size: 80%;"><b>Final technicalities IV</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Back propagation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Gradient descent</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>The code for solving the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>The network with one input layer, specified number of hidden layers, and one output layer</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Example: Population growth</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Setting up the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>The program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>Using forward Euler to solve the ODE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Example: Solving the one dimensional Poisson equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>The specific equation to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>Solving the equation using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs033.html#___sec32" style="font-size: 80%;"><b>Comparing with a numerical scheme</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Setting up the code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Partial Differential Equations</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>Type of problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs037.html#___sec36" style="font-size: 80%;"><b>Network requirements</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>More details</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Example: The diffusion equation</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs040.html#___sec39" style="font-size: 80%;"><b>Defining the problem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>Setting up the network using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Setting up the network using Autograd; The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Why the jacobian?</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>Setting up the network using Autograd; The full program</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Example: Solving the wave equation with Neural Networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>The problem to solve for</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>The trial solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>The analytical solution</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Solving the wave equation - the full program using Autograd</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs050.html#___sec49" style="font-size: 80%;"><b>Resources on differential equations and deep learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>Friday, Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs052.html#___sec51" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec55" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs057.html#___sec56" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs058.html#___sec57" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs059.html#___sec58" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs060.html#___sec59" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs061.html#___sec60" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec61" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec62" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec63" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs062.html#___sec64" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs063.html#___sec65" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs064.html#___sec66" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs065.html#___sec67" style="font-size: 80%;"><b>PCA Proof continued</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs066.html#___sec68" style="font-size: 80%;"><b>The final step</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs067.html#___sec69" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs068.html#___sec70" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs069.html#___sec71" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs070.html#___sec72" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs071.html#___sec73" style="font-size: 80%;"><b>More on the PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs072.html#___sec74" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs073.html#___sec75" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs074.html#___sec76" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs075.html#___sec77" style="font-size: 80%;"><b>LLE</b></a></li>
+     <!-- navigation toc: --> <li><a href="._week43-bs076.html#___sec78" style="font-size: 80%;"><b>Other techniques</b></a></li>
 
         </ul>
       </li>
@@ -323,7 +325,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 23, 2020</h4></center> <!-- date -->
+<center><h4>Oct 26, 2020</h4></center> <!-- date -->
 <br>
 <p>
 
diff --git a/doc/pub/week43/html/week43-reveal.html b/doc/pub/week43/html/week43-reveal.html
index 0b372e64c..8caa40010 100644
--- a/doc/pub/week43/html/week43-reveal.html
+++ b/doc/pub/week43/html/week43-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Oct 23, 2020</h4></center> <!-- date -->
+<center><h4>Oct 26, 2020</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -159,6 +159,7 @@ MathJax.Hub.Config({
 
 
 <section>
+<h2 id="___sec0">Plans for week 43 </h2>
 
 <ul>
 <p><li> Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture October 22</a></li>
@@ -171,7 +172,7 @@ We will also study the usage of <a href="https://www.youtube.com/watch?v=fRf4l5q
 
 
 <section>
-<h2 id="___sec0">Recurrent Neural Networks </h2>
+<h2 id="___sec1">Recurrent Neural Networks </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini" target="_blank">Overview video</a>.
@@ -186,7 +187,7 @@ See also lecture on Thursday October 22 and examples from <a href="https://compp
 
 
 <section>
-<h2 id="___sec1">Solving ODEs with Deep Learning </h2>
+<h2 id="___sec2">Solving ODEs with Deep Learning </h2>
 
 <p>
 The Universal Approximation Theorem states that a neural network can
@@ -196,7 +197,7 @@ and output layer to any given precision.
 
 
 <section>
-<h2 id="___sec2">Ordinary Differential Equations </h2>
+<h2 id="___sec3">Ordinary Differential Equations </h2>
 
 <p>
 An ordinary differential equation (ODE) is an equation involving functions having one variable.
@@ -225,7 +226,7 @@ for the solution to be unique.
 
 
 <section>
-<h2 id="___sec3">The trial solution </h2>
+<h2 id="___sec4">The trial solution </h2>
 
 <p>
 Let the trial solution \( g_t(x) \) be
@@ -258,7 +259,7 @@ As described previously, an optimization method could be used to minimize the pa
 
 
 <section>
-<h2 id="___sec4">Minimization process </h2>
+<h2 id="___sec5">Minimization process </h2>
 
 <p>
 For the minimization to be defined, we need to have a cost function at hand to minimize.
@@ -294,7 +295,7 @@ The neural net should then find the parameters \( P \) that minimizes the cost f
 
 
 <section>
-<h2 id="___sec5">Minimizing the cost function using gradient descent and automatic differentiation </h2>
+<h2 id="___sec6">Minimizing the cost function using gradient descent and automatic differentiation </h2>
 
 <p>
 To perform the minimization using gradient descent, the gradient of \( C\left(\boldsymbol{x}, P\right) \) is needed.
@@ -307,7 +308,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
 
 
 <section>
-<h2 id="___sec6">Example: Exponential decay </h2>
+<h2 id="___sec7">Example: Exponential decay </h2>
 
 <p>
 An exponential decay of a quantity \( g(x) \) is described by the equation
@@ -341,7 +342,7 @@ Having an analytical solution at hand, it is possible to use it to compare how w
 
 
 <section>
-<h2 id="___sec7">The function to solve for </h2>
+<h2 id="___sec8">The function to solve for </h2>
 
 <p>
 The program will use a neural network to solve
@@ -363,7 +364,7 @@ In this example, \( \gamma = 2 \) and \( g_0 = 10 \).
 
 
 <section>
-<h2 id="___sec8">The trial solution </h2>
+<h2 id="___sec9">The trial solution </h2>
 To begin with, a trial solution \( g_t(t) \) must be chosen. A general trial solution for ordinary differential equations could be
 
 <p>&nbsp;<br>
@@ -378,7 +379,7 @@ with \( h_1(x) \) ensuring that \( g_t(x) \) satisfies some conditions and \( h_
 
 
 <section>
-<h2 id="___sec9">Setup of Network </h2>
+<h2 id="___sec10">Setup of Network </h2>
 
 <p>
 In this network, there are no weights and bias at the input layer, so \( P = \{ P_{\text{hidden}},  P_{\text{output}} \} \).
@@ -405,7 +406,7 @@ $$
 
 
 <section>
-<h2 id="___sec10">Reformulating the problem </h2>
+<h2 id="___sec11">Reformulating the problem </h2>
 
 <p>
 We wish that our neural network manages to minimize a given cost function.
@@ -443,7 +444,7 @@ is fulfilled as <em>best as possible</em>.
 
 
 <section>
-<h2 id="___sec11">More technicalities </h2>
+<h2 id="___sec12">More technicalities </h2>
 
 <p>
 The left hand side and right hand side of <a href="#mjx-eqn-8">(8)</a> must be computed separately, and then the neural network must choose weights and biases, contained in \( P \), such that the sides are equal as best as possible.
@@ -477,7 +478,7 @@ for an input value \( x \).
 
 
 <section>
-<h2 id="___sec12">More details </h2>
+<h2 id="___sec13">More details </h2>
 
 <p>
 If the neural network evaluates \( g_t(x, P) \) at more values for \( x \), say \( N \) values \( x_i \) for \( i = 1, \dots, N \), then the <em>total</em> error to minimize becomes
@@ -511,7 +512,7 @@ $$
 
 
 <section>
-<h2 id="___sec13">A possible implementation of a neural network </h2>
+<h2 id="___sec14">A possible implementation of a neural network </h2>
 
 <p>
 For simplicity, it is assumed that the input is an array \( \boldsymbol{x} = (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural network should find \( P \) such that it fulfills <a href="#mjx-eqn-9">(9)</a>.
@@ -524,7 +525,7 @@ The input layer will consist of \( N_{\text{input} } \) neurons, passing its ele
 
 
 <section>
-<h2 id="___sec14">Technicalities </h2>
+<h2 id="___sec15">Technicalities </h2>
 
 <p>
 For the \( i \)-th in the hidden layer with weight \( w_i^{\text{hidden} } \) and bias \( b_i^{\text{hidden} } \), the weighting from the \( j \)-th neuron at the input layer is:
@@ -548,7 +549,7 @@ $$
 
 
 <section>
-<h2 id="___sec15">Final technicalities I </h2>
+<h2 id="___sec16">Final technicalities I </h2>
 
 <p>
 The result after weighting the inputs at the \( i \)-th hidden neuron can be written as a vector:
@@ -573,7 +574,7 @@ $$
 
 
 <section>
-<h2 id="___sec16">Final technicalities II </h2>
+<h2 id="___sec17">Final technicalities II </h2>
 
 <p>
 The vector \( \boldsymbol{p}_{i, \text{hidden}}^T \) constitutes each row in \( P_{\text{hidden} } \), which contains the weights for the neural network to minimize according to <a href="#mjx-eqn-9">(9)</a>.
@@ -615,7 +616,7 @@ it is assumes that the number of neurons in the output layer is one.
 
 
 <section>
-<h2 id="___sec17">Final technicalities III </h2>
+<h2 id="___sec18">Final technicalities III </h2>
 
 <p>
 The procedure of weighting the output neuron \( j \) in the hidden layer to the \( i \)-th neuron in the output layer is similar as for the hidden layer described previously.
@@ -638,7 +639,7 @@ $$
 
 
 <section>
-<h2 id="___sec18">Final technicalities IV </h2>
+<h2 id="___sec19">Final technicalities IV </h2>
 
 <p>
 Expressing \( z_{1,j}^{\text{output}} \) as a vector gives the following way of weighting the inputs from the hidden layer:
@@ -662,7 +663,7 @@ In this case we seek a continuous range of values since we are approximating a f
 
 
 <section>
-<h2 id="___sec19">Back propagation </h2>
+<h2 id="___sec20">Back propagation </h2>
 
 <p>
 The next step is to decide how the parameters should be changed such that they minimize the cost function.
@@ -685,7 +686,7 @@ Here, gradient descent with a constant step size has been chosen.
 
 
 <section>
-<h2 id="___sec20">Gradient descent </h2>
+<h2 id="___sec21">Gradient descent </h2>
 
 <p>
 The idea of the gradient descent algorithm is to update parameters in
@@ -732,7 +733,7 @@ $$
 
 
 <section>
-<h2 id="___sec21">The code for solving the ODE </h2>
+<h2 id="___sec22">The code for solving the ODE </h2>
 
 <p>
 
@@ -886,7 +887,7 @@ $$
 
 
 <section>
-<h2 id="___sec22">The network with one input layer, specified number of hidden layers, and one output layer </h2>
+<h2 id="___sec23">The network with one input layer, specified number of hidden layers, and one output layer </h2>
 
 <p>
 It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.
@@ -1060,7 +1061,7 @@ The number of neurons within each hidden layer are given as a list of integers i
 
 
 <section>
-<h2 id="___sec23">Example: Population growth </h2>
+<h2 id="___sec24">Example: Population growth </h2>
 
 <p>
 A logistic model of population growth assumes that a population converges toward an equilibrium.
@@ -1087,7 +1088,7 @@ Here, we stay with a more simple approach and implement for comparison, the simp
 
 
 <section>
-<h2 id="___sec24">Setting up the problem </h2>
+<h2 id="___sec25">Setting up the problem </h2>
 
 <p>
 Here, we will model a population \( g(t) \) in an environment having carrying capacity \( A \).
@@ -1110,7 +1111,7 @@ In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).
 
 
 <section>
-<h2 id="___sec25">The trial solution </h2>
+<h2 id="___sec26">The trial solution </h2>
 
 <p>
 We will get a slightly different trial solution, as the boundary conditions are different
@@ -1140,7 +1141,7 @@ $$
 
 
 <section>
-<h2 id="___sec26">The program using Autograd </h2>
+<h2 id="___sec27">The program using Autograd </h2>
 
 <p>
 The network will be the similar as for the exponential decay example, but with some small modifications for our problem.
@@ -1316,7 +1317,7 @@ The network will be the similar as for the exponential decay example, but with s
 
 
 <section>
-<h2 id="___sec27">Using forward Euler to solve the ODE </h2>
+<h2 id="___sec28">Using forward Euler to solve the ODE </h2>
 
 <p>
 A straightforward way of solving an ODE numerically, is to use Euler's method.
@@ -1454,7 +1455,7 @@ extending the program that uses the network using Autograd:
 
 
 <section>
-<h2 id="___sec28">Example: Solving the one dimensional Poisson equation </h2>
+<h2 id="___sec29">Example: Solving the one dimensional Poisson equation </h2>
 
 <p>
 The Poisson equation for \( g(x) \) in one dimension is
@@ -1489,7 +1490,7 @@ In addition, it could be interesting to see how a typical method for numerically
 
 
 <section>
-<h2 id="___sec29">The specific equation to solve for </h2>
+<h2 id="___sec30">The specific equation to solve for </h2>
 
 <p>
 Here, the function \( g(x) \) to solve for follows the equation
@@ -1535,7 +1536,7 @@ $$
 
 
 <section>
-<h2 id="___sec30">Solving the equation using Autograd </h2>
+<h2 id="___sec31">Solving the equation using Autograd </h2>
 
 <p>
 
@@ -1695,7 +1696,7 @@ $$
 
 
 <section>
-<h2 id="___sec31">Comparing with a numerical scheme </h2>
+<h2 id="___sec32">Comparing with a numerical scheme </h2>
 
 <p>
 The Poisson equation is possible to solve using Taylor series to approximate the second derivative.
@@ -1805,7 +1806,7 @@ which makes it possible to solve for the vector \( \boldsymbol{g} \).
 
 
 <section>
-<h2 id="___sec32">Setting up the code </h2>
+<h2 id="___sec33">Setting up the code </h2>
 
 <p>
 We can then compare the result from this numerical scheme with the output from our network using Autograd:
@@ -2008,7 +2009,7 @@ We can then compare the result from this numerical scheme with the output from o
 
 
 <section>
-<h2 id="___sec33">Partial Differential Equations </h2>
+<h2 id="___sec34">Partial Differential Equations </h2>
 
 <p>
 A partial differential equation (PDE) has a solution here the function
@@ -2033,7 +2034,7 @@ where \( f \) is an expression involving all kinds of possible mixed derivatives
 
 
 <section>
-<h2 id="___sec34">Type of problem </h2>
+<h2 id="___sec35">Type of problem </h2>
 
 <p>
 The problem our network must solve for, is similar to the ODE case.
@@ -2058,7 +2059,7 @@ The role of the function \( h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P)) \), is to ensu
 
 
 <section>
-<h2 id="___sec35">Network requirements </h2>
+<h2 id="___sec36">Network requirements </h2>
 
 <p>
 The network tries then the minimize the cost function following the
@@ -2083,7 +2084,7 @@ $$
 
 
 <section>
-<h2 id="___sec36">More details </h2>
+<h2 id="___sec37">More details </h2>
 
 <p>
 If we let \( \boldsymbol{x} = \big( x_1, \dots, x_N \big) \) be an array containing the values for \( x_1, \dots, x_N \) respectively, the cost function can be reformulated into the following:
@@ -2106,7 +2107,7 @@ $$
 
 
 <section>
-<h2 id="___sec37">Example: The diffusion equation </h2>
+<h2 id="___sec38">Example: The diffusion equation </h2>
 
 <p>
 In one spatial dimension, the equation reads
@@ -2135,7 +2136,7 @@ with \( u(x) \) being some given function.
 
 
 <section>
-<h2 id="___sec38">Defining the problem </h2>
+<h2 id="___sec39">Defining the problem </h2>
 
 <p>
 For this case, we want to find \( g(x,t) \) such that
@@ -2171,7 +2172,7 @@ First, we will look into how Autograd could be used in a network tailored to sol
 
 
 <section>
-<h2 id="___sec39">Setting up the network using Autograd </h2>
+<h2 id="___sec40">Setting up the network using Autograd </h2>
 
 <p>
 The only change to do here, is to extend our network such that
@@ -2234,7 +2235,7 @@ network at each possible pair \( (x,t) \), given an array for the desired
 
 
 <section>
-<h2 id="___sec40">Setting up the network using Autograd; The trial solution </h2>
+<h2 id="___sec41">Setting up the network using Autograd; The trial solution </h2>
 
 <p>
 The cost function must then iterate through the given arrays
@@ -2267,7 +2268,7 @@ since \( (0) = u(1) = 0 \) and \( u(x) = \sin(\pi x) \).
 
 
 <section>
-<h2 id="___sec41">Why the jacobian? </h2>
+<h2 id="___sec42">Why the jacobian? </h2>
 
 <p>
 The Jacobian is used because the program must find the derivative of
@@ -2335,7 +2336,7 @@ mixed derivatives of \( g(x,t) \).
 
 
 <section>
-<h2 id="___sec42">Setting up the network using Autograd; The full program </h2>
+<h2 id="___sec43">Setting up the network using Autograd; The full program </h2>
 
 <p>
 Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.
@@ -2589,7 +2590,7 @@ Using TensorFlow results in a much better execution time. Try it!
 
 
 <section>
-<h2 id="___sec43">Example: Solving the wave equation with Neural Networks </h2>
+<h2 id="___sec44">Example: Solving the wave equation with Neural Networks </h2>
 
 <p>
 The wave equation is
@@ -2622,7 +2623,7 @@ where \( \frac{\partial g(x,t)}{\partial t} \Big |_{t = 0} \) means the derivati
 
 
 <section>
-<h2 id="___sec44">The problem to solve for </h2>
+<h2 id="___sec45">The problem to solve for </h2>
 
 <p>
 The wave equation to solve for, is
@@ -2656,7 +2657,7 @@ In this example, let \( c = 1 \) and \( u(x) = \sin(\pi x) \) and \( v(x) = -\pi
 
 
 <section>
-<h2 id="___sec45">The trial solution </h2>
+<h2 id="___sec46">The trial solution </h2>
 Setting up the network is done in similar matter as for the example of solving the diffusion equation.
 The only things we have to change, is the trial solution such that it satisfies the conditions from <a href="#mjx-eqn-20">(20)</a> and the cost function.
 
@@ -2684,7 +2685,7 @@ Note that this trial solution satisfies the conditions only if \( u(0) = v(0) =
 
 
 <section>
-<h2 id="___sec46">The analytical solution </h2>
+<h2 id="___sec47">The analytical solution </h2>
 
 <p>
 The analytical solution for our specific problem, is
@@ -2698,7 +2699,7 @@ $$
 
 
 <section>
-<h2 id="___sec47">Solving the wave equation - the full program using Autograd </h2>
+<h2 id="___sec48">Solving the wave equation - the full program using Autograd </h2>
 
 <p>
 
@@ -2928,7 +2929,7 @@ $$
 
 
 <section>
-<h2 id="___sec48">Resources on differential equations and deep learning </h2>
+<h2 id="___sec49">Resources on differential equations and deep learning </h2>
 
 <ol>
 <p><li> <a href="https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf" target="_blank">Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al</a></li>
@@ -2940,7 +2941,7 @@ $$
 
 
 <section>
-<h2 id="___sec49">Friday, Principal Component Analysis </h2>
+<h2 id="___sec50">Friday, Principal Component Analysis </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=fkf4IBRSeEc&ab_channel=SteveBrunton" target="_blank">Overview video</a>
@@ -2948,7 +2949,7 @@ $$
 
 
 <section>
-<h2 id="___sec50">Basic ideas of the Principal Component Analysis (PCA) </h2>
+<h2 id="___sec51">Basic ideas of the Principal Component Analysis (PCA) </h2>
 
 <p>
 The principal component analysis deals with the problem of fitting a
@@ -2974,7 +2975,7 @@ A good read is for example <a href="https://www.springer.com/gp/book/97803878781
 
 
 <section>
-<h2 id="___sec51">Introducing the Covariance and Correlation functions  </h2>
+<h2 id="___sec52">Introducing the Covariance and Correlation functions  </h2>
 
 <p>
 Before we discuss the PCA theorem, we need to remind ourselves about
@@ -3047,7 +3048,7 @@ In the above example this is the function we constructed using <b>pandas</b>.
 
 
 <section>
-<h2 id="___sec52">Correlation Function and Design/Feature Matrix </h2>
+<h2 id="___sec53">Correlation Function and Design/Feature Matrix </h2>
 
 <p>
 In our derivation of the various regression algorithms like <b>Ordinary Least Squares</b> or <b>Ridge regression</b>
@@ -3118,7 +3119,7 @@ $$
 
 
 <section>
-<h2 id="___sec53">Covariance Matrix Examples </h2>
+<h2 id="___sec54">Covariance Matrix Examples </h2>
 
 <p>
 The Numpy function <b>np.cov</b> calculates the covariance elements using
@@ -3164,7 +3165,7 @@ C = np.cov(W)
 
 
 <section>
-<h2 id="___sec54">Correlation Matrix  </h2>
+<h2 id="___sec55">Correlation Matrix  </h2>
 
 <p>
 The previous example can be converted into the correlation matrix by
@@ -3209,7 +3210,7 @@ The above procedure with <b>numpy</b> can be made more compact if we use <b>pand
 
 
 <section>
-<h2 id="___sec55">Correlation Matrix with Pandas </h2>
+<h2 id="___sec56">Correlation Matrix with Pandas </h2>
 
 <p>
 We whow here how we can set up the correlation matrix using <b>pandas</b>, as done in this simple code
@@ -3236,7 +3237,7 @@ We expand this model to the Franke function discussed above.
 
 
 <section>
-<h2 id="___sec56">Correlation Matrix with Pandas and the Franke function </h2>
+<h2 id="___sec57">Correlation Matrix with Pandas and the Franke function </h2>
 
 <p>
 
@@ -3296,7 +3297,7 @@ matrix without them.
 
 
 <section>
-<h2 id="___sec57">Rewriting the Covariance and/or Correlation Matrix </h2>
+<h2 id="___sec58">Rewriting the Covariance and/or Correlation Matrix </h2>
 
 <p>
 We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix \( \boldsymbol{X} \) as 
@@ -3349,7 +3350,7 @@ It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\t
 
 
 <section>
-<h2 id="___sec58">Towards the PCA theorem </h2>
+<h2 id="___sec59">Towards the PCA theorem </h2>
 
 <p>
 We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as
@@ -3408,7 +3409,7 @@ features/predictors.
 
 
 <section>
-<h2 id="___sec59">The Algorithm before theorem </h2>
+<h2 id="___sec60">The Algorithm before theorem </h2>
 
 <p>
 Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. 
@@ -3432,7 +3433,7 @@ $$
 
 <ul>
 <p><li> Center the data by subtracting the mean value for each column. This leads to a new matrix \( \boldsymbol{X}\rightarrow \overline{\boldsymbol{X}} \).</li>
-<p><li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}\overline{\boldsymbol{X}}^T] \).</li>
+<p><li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}^T\overline{\boldsymbol{X}}] \).</li>
 <p><li> Find the eigenpairs of \( \boldsymbol{C} \) with eigenvalues \( [\lambda_0,\lambda_1,\dots,\lambda_{p-1}] \) and eigenvectors \( [\boldsymbol{s}_0,\boldsymbol{s}_1,\dots,\boldsymbol{s}_{p-1}] \).</li>
 <p><li> Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.</li>
 <p><li> Keep only those \( l \) eigenvalues larger than a selected threshold value, discarding thus \( p-l \) features since we expect small variations in the data here.</li>
@@ -3441,11 +3442,11 @@ $$
 
 
 <section>
-<h2 id="___sec60">Writing our own PCA code </h2>
+<h2 id="___sec61">Writing our own PCA code </h2>
 
 <p>
 We will use a simple example first with two-dimensional data
-drawn from a multivariate normal distribution with the following mean and covariance matrix:
+drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):
 <p>&nbsp;<br>
 $$
 \mu = (-1,2) \qquad \Sigma = \begin{bmatrix} 4 & 2 \\
@@ -3455,8 +3456,8 @@ $$
 <p>&nbsp;<br>
 
 Note that the mean refers to each column of data. 
-We will generate \( n = 1000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
-this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \).
+We will generate \( n = 10000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
+this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \). This is our design matrix where we have forced the covariance and mean values to take specific values.
 
 <p>
 The following Python code aids in setting up the data and writing out the design matrix.
@@ -3476,7 +3477,7 @@ X = np.random.multivariate_normal(mean, cov, n)
 <p>
 Now we are going to implement the PCA algorithm. We will break it down into various substeps.
 
-<h3 id="___sec61">Compute the sample mean and center the data </h3>
+<h3 id="___sec62">Compute the sample mean and center the data </h3>
 
 <p>
 The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is
@@ -3495,7 +3496,7 @@ $$
 
 When you are done with these steps, print out \( \mu_n \) to verify it is
 close to \( \mu \) and plot your mean centered data to verify it is
-centered at the origin! Compare your code with the functionality from <b>Scikit-Learn</b> discussed above.
+centered at the origin! 
 The following code elements perform these operations using <b>pandas</b> or using our own functionality for doing so. The latter, using <b>numpy</b> is rather simple through the <b>mean()</b> function. 
 <p>
 
@@ -3517,7 +3518,7 @@ variance. The diagonal covariance matrix elements will then be one,
 while the non-diagonal ones need to be divided by \( 2\sqrt{2} \) for our
 specific case.
 
-<h3 id="___sec62">Compute the sample covariance </h3>
+<h3 id="___sec63">Compute the sample covariance </h3>
 
 <p>
 Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation
@@ -3559,9 +3560,9 @@ plt.show()
 </pre></div>
 <p>
 Depending on the number of points \( n \), we will get results that are close to the covariance values defined above.
-The plot shows how the data are clustered around a line with slope close to one. Is this expected?
+The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed.
 
-<h3 id="___sec63">Diagonalize the sample covariance matrix to obtain the principal components </h3>
+<h3 id="___sec64">Diagonalize the sample covariance matrix to obtain the principal components </h3>
 
 <p>
 Now we are ready to solve for the principal components! To do so we
@@ -3626,7 +3627,7 @@ This code does not contain all the above elements, but it shows how we can use <
 
 
 <section>
-<h2 id="___sec64">Classical PCA Theorem   </h2>
+<h2 id="___sec65">Classical PCA Theorem   </h2>
 
 <p>
 We assume now that we have a design matrix \( \boldsymbol{X} \) which has been
@@ -3635,17 +3636,6 @@ overline symbol. The matrix is defined in terms of the various column
 vectors \( [\boldsymbol{x}_0,\boldsymbol{x}_1,\dots, \boldsymbol{x}_{p-1}] \) each with dimension
 \( \boldsymbol{x}\in {\mathbb{R}}^{n} \).
 
-<p>
-We assume also that we have an orthogonal transformation \( \boldsymbol{W}\in {\mathbb{R}}^{p\times p} \).  We define the reconstruction error (which is similar to the mean squared error we have seen before) as
-<p>&nbsp;<br>
-$$
-J(\boldsymbol{W},\boldsymbol{Z}) = \frac{1}{n}\sum_i (\boldsymbol{x}_i - \overline{\boldsymbol{x}}_i)^2,
-$$
-<p>&nbsp;<br>
-
-with \( \overline{\boldsymbol{x}}_i = \boldsymbol{W}\boldsymbol{z}_i \), where \( \boldsymbol{z}_i \) is a row vector with dimension \( {\mathbb{R}}^{n} \) of the matrix
-\( \boldsymbol{Z}\in{\mathbb{R}}^{p\times n} \).  When doing PCA we want to reduce this dimensionality.
-
 <p>
 The PCA theorem states that minimizing the above reconstruction error
 corresponds to setting \( \boldsymbol{W}=\boldsymbol{S} \), the orthogonal matrix which
@@ -3658,76 +3648,15 @@ eigenvectors of the covariance(correlations matrix).
 
 
 <section>
-<h2 id="___sec65">Proof of the PCA Theorem  </h2>
+<h2 id="___sec66">Proof of the PCA Theorem  </h2>
 
 <p>
-To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{w}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
-<p>&nbsp;<br>
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)= \frac{1}{n}\sum_i (\boldsymbol{x}_i - z_{i0}\boldsymbol{w}_0)^2=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2\boldsymbol{w}_0^T\boldsymbol{w}_0),
-$$
-<p>&nbsp;<br>
-
-which we can rewrite due to the orthogonality of \( \boldsymbol{w}_i \) as
-<p>&nbsp;<br>
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2).
-$$
-<p>&nbsp;<br>
-
-Minimizing \( J \) with respect to the unknown parameters \( z_{0i} \) we obtain that
-<p>&nbsp;<br>
-$$
-z_{i0}=\boldsymbol{w}_0^T\boldsymbol{x}_i,
-$$
-<p>&nbsp;<br>
-
-where the vectors on the rhs are known.
+To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{s}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
 </section>
 
 
 <section>
-<h2 id="___sec66">PCA Proof continued </h2>
-
-<p>
-We have now found the unknown parameters \( z_{i0} \). These correspond to the projected coordinates and we can write
-<p>&nbsp;<br>
-$$
-J(\boldsymbol{w}_0)= \frac{1}{p}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - z_{i0}^2)=\mathrm{const}-\frac{1}{n}\sum_i z_{i0}^2.
-$$
-<p>&nbsp;<br>
-
-<p>
-We can show that the variance of the projected coordinates defined by \( \boldsymbol{w}_0^T\boldsymbol{x}_i \) are given by
-<p>&nbsp;<br>
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2,
-$$
-<p>&nbsp;<br>
-
-since the expectation value of
-<p>&nbsp;<br>
-$$
-\mathbb{E}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \mathbb{E}[z_{i0}]= \boldsymbol{w}_0^T\mathbb{E}[\boldsymbol{x}_i]=0,
-$$
-<p>&nbsp;<br>
-
-where we have used the fact that our data are centered.
-
-<p>
-Recalling our definition of the covariance as 
-<p>&nbsp;<br>
-$$
-\boldsymbol{C}[\boldsymbol{x}] = \frac{1}{n}\boldsymbol{X}\boldsymbol{X}^T=\mathbb{E}[\boldsymbol{X}\boldsymbol{X}^T],
-$$
-<p>&nbsp;<br>
-
-we have thus that
-<p>&nbsp;<br>
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2=\boldsymbol{w}_0^T\boldsymbol{C}[\boldsymbol{x}]\boldsymbol{w}_0.
-$$
-<p>&nbsp;<br>
+<h2 id="___sec67">PCA Proof continued </h2>
 
 <p>
 We are almost there, we have obtained a relation between minimizing
@@ -3738,7 +3667,7 @@ of the projected data.
 
 
 <section>
-<h2 id="___sec67">The final step </h2>
+<h2 id="___sec68">The final step </h2>
 
 <p>
 We could trivially maximize the variance of the projection (and
@@ -3800,7 +3729,7 @@ For more details, see for example <a href="https://www.springer.com/gp/book/9780
 
 
 <section>
-<h2 id="___sec68">Geometric Interpretation and link with Singular Value Decomposition </h2>
+<h2 id="___sec69">Geometric Interpretation and link with Singular Value Decomposition </h2>
 
 <p>
 For a detailed demonstration of the geometric interpretation, see <a href="https://www.springer.com/gp/book/9780387878102" target="_blank">Vidal, Ma and Sastry, section 2.1.2</a>.
@@ -3808,7 +3737,7 @@ For a detailed demonstration of the geometric interpretation, see <a href="https
 
 
 <section>
-<h2 id="___sec69">Principal Component Analysis </h2>
+<h2 id="___sec70">Principal Component Analysis </h2>
 
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
@@ -3864,7 +3793,7 @@ X2D = X_centered.dot(W2)
 
 
 <section>
-<h2 id="___sec70">PCA and scikit-learn </h2>
+<h2 id="___sec71">PCA and scikit-learn </h2>
 
 <p>
 Scikit-Learn&#8217;s PCA class implements PCA using SVD decomposition just like we did before. The
@@ -3896,7 +3825,7 @@ variance that lies along the axis of each principal component.
 
 
 <section>
-<h2 id="___sec71">Back to the Cancer Data </h2>
+<h2 id="___sec72">Back to the Cancer Data </h2>
 We can now repeat the above but applied to real data, in this case our breast cancer data.
 Here we compute performance scores on the training data using logistic regression.
 <p>
@@ -3937,7 +3866,7 @@ We see that our training data after the PCA decomposition has a performance simi
 
 
 <section>
-<h2 id="___sec72">More on the PCA </h2>
+<h2 id="___sec73">More on the PCA </h2>
 
 <p>
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -3968,7 +3897,7 @@ X_reduced = pca.fit_transform(X)
 
 
 <section>
-<h2 id="___sec73">Incremental PCA </h2>
+<h2 id="___sec74">Incremental PCA </h2>
 
 <p>
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -3980,7 +3909,7 @@ instances arrive).
 
 
 <section>
-<h2 id="___sec74">Randomized PCA </h2>
+<h2 id="___sec75">Randomized PCA </h2>
 
 <p>
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -3991,7 +3920,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
 
 
 <section>
-<h2 id="___sec75">Kernel PCA </h2>
+<h2 id="___sec76">Kernel PCA </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -4017,7 +3946,7 @@ X_reduced = rbf_pca.fit_transform(X)
 
 
 <section>
-<h2 id="___sec76">LLE </h2>
+<h2 id="___sec77">LLE </h2>
 
 <p>
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -4029,7 +3958,7 @@ these local relationships are best preserved (more details shortly).
 
 
 <section>
-<h2 id="___sec77">Other techniques </h2>
+<h2 id="___sec78">Other techniques </h2>
 
 <p>
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
diff --git a/doc/pub/week43/html/week43-solarized.html b/doc/pub/week43/html/week43-solarized.html
index 898b21c21..094fa80c7 100644
--- a/doc/pub/week43/html/week43-solarized.html
+++ b/doc/pub/week43/html/week43-solarized.html
@@ -61,139 +61,140 @@ div { text-align: justify; text-justify: inter-word; }
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -235,11 +236,13 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 23, 2020</h4></center> <!-- date -->
+<center><h4>Oct 26, 2020</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
+<h2 id="___sec0">Plans for week 43 </h2>
+
 <ul>
 <li> Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture October 22</a></li>
 <li> Friday: Principal Component Analysis and Dimensionality Reduction. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober23.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture October 23</a></li>
@@ -250,7 +253,7 @@ We will also study the usage of <a href="https://www.youtube.com/watch?v=fRf4l5q
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec0">Recurrent Neural Networks </h2>
+<h2 id="___sec1">Recurrent Neural Networks </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini" target="_blank">Overview video</a>.
@@ -265,7 +268,7 @@ See also lecture on Thursday October 22 and examples from <a href="https://compp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec1">Solving ODEs with Deep Learning </h2>
+<h2 id="___sec2">Solving ODEs with Deep Learning </h2>
 
 <p>
 The Universal Approximation Theorem states that a neural network can
@@ -275,7 +278,7 @@ and output layer to any given precision.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec2">Ordinary Differential Equations </h2>
+<h2 id="___sec3">Ordinary Differential Equations </h2>
 
 <p>
 An ordinary differential equation (ODE) is an equation involving functions having one variable.
@@ -302,7 +305,7 @@ for the solution to be unique.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec3">The trial solution </h2>
+<h2 id="___sec4">The trial solution </h2>
 
 <p>
 Let the trial solution \( g_t(x) \) be
@@ -333,7 +336,7 @@ As described previously, an optimization method could be used to minimize the pa
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec4">Minimization process </h2>
+<h2 id="___sec5">Minimization process </h2>
 
 <p>
 For the minimization to be defined, we need to have a cost function at hand to minimize.
@@ -365,7 +368,7 @@ The neural net should then find the parameters \( P \) that minimizes the cost f
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec5">Minimizing the cost function using gradient descent and automatic differentiation </h2>
+<h2 id="___sec6">Minimizing the cost function using gradient descent and automatic differentiation </h2>
 
 <p>
 To perform the minimization using gradient descent, the gradient of \( C\left(\boldsymbol{x}, P\right) \) is needed.
@@ -378,7 +381,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec6">Example: Exponential decay </h2>
+<h2 id="___sec7">Example: Exponential decay </h2>
 
 <p>
 An exponential decay of a quantity \( g(x) \) is described by the equation
@@ -408,7 +411,7 @@ Having an analytical solution at hand, it is possible to use it to compare how w
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec7">The function to solve for </h2>
+<h2 id="___sec8">The function to solve for </h2>
 
 <p>
 The program will use a neural network to solve
@@ -428,7 +431,7 @@ In this example, \( \gamma = 2 \) and \( g_0 = 10 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec8">The trial solution </h2>
+<h2 id="___sec9">The trial solution </h2>
 To begin with, a trial solution \( g_t(t) \) must be chosen. A general trial solution for ordinary differential equations could be
 
 $$
@@ -441,7 +444,7 @@ with \( h_1(x) \) ensuring that \( g_t(x) \) satisfies some conditions and \( h_
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec9">Setup of Network </h2>
+<h2 id="___sec10">Setup of Network </h2>
 
 <p>
 In this network, there are no weights and bias at the input layer, so \( P = \{ P_{\text{hidden}},  P_{\text{output}} \} \).
@@ -466,7 +469,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec10">Reformulating the problem </h2>
+<h2 id="___sec11">Reformulating the problem </h2>
 
 <p>
 We wish that our neural network manages to minimize a given cost function.
@@ -500,7 +503,7 @@ is fulfilled as <em>best as possible</em>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec11">More technicalities </h2>
+<h2 id="___sec12">More technicalities </h2>
 
 <p>
 The left hand side and right hand side of \eqref{nnmin} must be computed separately, and then the neural network must choose weights and biases, contained in \( P \), such that the sides are equal as best as possible.
@@ -530,7 +533,7 @@ for an input value \( x \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec12">More details </h2>
+<h2 id="___sec13">More details </h2>
 
 <p>
 If the neural network evaluates \( g_t(x, P) \) at more values for \( x \), say \( N \) values \( x_i \) for \( i = 1, \dots, N \), then the <em>total</em> error to minimize becomes
@@ -558,7 +561,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec13">A possible implementation of a neural network </h2>
+<h2 id="___sec14">A possible implementation of a neural network </h2>
 
 <p>
 For simplicity, it is assumed that the input is an array \( \boldsymbol{x} = (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural network should find \( P \) such that it fulfills \eqref{min}.
@@ -571,7 +574,7 @@ The input layer will consist of \( N_{\text{input} } \) neurons, passing its ele
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec14">Technicalities </h2>
+<h2 id="___sec15">Technicalities </h2>
 
 <p>
 For the \( i \)-th in the hidden layer with weight \( w_i^{\text{hidden} } \) and bias \( b_i^{\text{hidden} } \), the weighting from the \( j \)-th neuron at the input layer is:
@@ -593,7 +596,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec15">Final technicalities I </h2>
+<h2 id="___sec16">Final technicalities I </h2>
 
 <p>
 The result after weighting the inputs at the \( i \)-th hidden neuron can be written as a vector:
@@ -616,7 +619,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec16">Final technicalities II </h2>
+<h2 id="___sec17">Final technicalities II </h2>
 
 <p>
 The vector \( \boldsymbol{p}_{i, \text{hidden}}^T \) constitutes each row in \( P_{\text{hidden} } \), which contains the weights for the neural network to minimize according to \eqref{min}.
@@ -654,7 +657,7 @@ it is assumes that the number of neurons in the output layer is one.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec17">Final technicalities III </h2>
+<h2 id="___sec18">Final technicalities III </h2>
 
 <p>
 The procedure of weighting the output neuron \( j \) in the hidden layer to the \( i \)-th neuron in the output layer is similar as for the hidden layer described previously.
@@ -675,7 +678,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec18">Final technicalities IV </h2>
+<h2 id="___sec19">Final technicalities IV </h2>
 
 <p>
 Expressing \( z_{1,j}^{\text{output}} \) as a vector gives the following way of weighting the inputs from the hidden layer:
@@ -697,7 +700,7 @@ In this case we seek a continuous range of values since we are approximating a f
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec19">Back propagation </h2>
+<h2 id="___sec20">Back propagation </h2>
 
 <p>
 The next step is to decide how the parameters should be changed such that they minimize the cost function.
@@ -718,7 +721,7 @@ Here, gradient descent with a constant step size has been chosen.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec20">Gradient descent </h2>
+<h2 id="___sec21">Gradient descent </h2>
 
 <p>
 The idea of the gradient descent algorithm is to update parameters in
@@ -761,7 +764,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec21">The code for solving the ODE </h2>
+<h2 id="___sec22">The code for solving the ODE </h2>
 
 <p>
 
@@ -914,7 +917,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec22">The network with one input layer, specified number of hidden layers, and one output layer </h2>
+<h2 id="___sec23">The network with one input layer, specified number of hidden layers, and one output layer </h2>
 
 <p>
 It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.
@@ -1087,7 +1090,7 @@ The number of neurons within each hidden layer are given as a list of integers i
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec23">Example: Population growth </h2>
+<h2 id="___sec24">Example: Population growth </h2>
 
 <p>
 A logistic model of population growth assumes that a population converges toward an equilibrium.
@@ -1112,7 +1115,7 @@ Here, we stay with a more simple approach and implement for comparison, the simp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec24">Setting up the problem </h2>
+<h2 id="___sec25">Setting up the problem </h2>
 
 <p>
 Here, we will model a population \( g(t) \) in an environment having carrying capacity \( A \).
@@ -1133,7 +1136,7 @@ In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec25">The trial solution </h2>
+<h2 id="___sec26">The trial solution </h2>
 
 <p>
 We will get a slightly different trial solution, as the boundary conditions are different
@@ -1159,7 +1162,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec26">The program using Autograd </h2>
+<h2 id="___sec27">The program using Autograd </h2>
 
 <p>
 The network will be the similar as for the exponential decay example, but with some small modifications for our problem.
@@ -1334,7 +1337,7 @@ The network will be the similar as for the exponential decay example, but with s
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec27">Using forward Euler to solve the ODE </h2>
+<h2 id="___sec28">Using forward Euler to solve the ODE </h2>
 
 <p>
 A straightforward way of solving an ODE numerically, is to use Euler's method.
@@ -1463,7 +1466,7 @@ extending the program that uses the network using Autograd:
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec28">Example: Solving the one dimensional Poisson equation </h2>
+<h2 id="___sec29">Example: Solving the one dimensional Poisson equation </h2>
 
 <p>
 The Poisson equation for \( g(x) \) in one dimension is
@@ -1494,7 +1497,7 @@ In addition, it could be interesting to see how a typical method for numerically
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec29">The specific equation to solve for </h2>
+<h2 id="___sec30">The specific equation to solve for </h2>
 
 <p>
 Here, the function \( g(x) \) to solve for follows the equation
@@ -1532,7 +1535,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec30">Solving the equation using Autograd </h2>
+<h2 id="___sec31">Solving the equation using Autograd </h2>
 
 <p>
 
@@ -1691,7 +1694,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec31">Comparing with a numerical scheme </h2>
+<h2 id="___sec32">Comparing with a numerical scheme </h2>
 
 <p>
 The Poisson equation is possible to solve using Taylor series to approximate the second derivative.
@@ -1789,7 +1792,7 @@ which makes it possible to solve for the vector \( \boldsymbol{g} \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec32">Setting up the code </h2>
+<h2 id="___sec33">Setting up the code </h2>
 
 <p>
 We can then compare the result from this numerical scheme with the output from our network using Autograd:
@@ -1991,7 +1994,7 @@ We can then compare the result from this numerical scheme with the output from o
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec33">Partial Differential Equations </h2>
+<h2 id="___sec34">Partial Differential Equations </h2>
 
 <p>
 A partial differential equation (PDE) has a solution here the function
@@ -2014,7 +2017,7 @@ where \( f \) is an expression involving all kinds of possible mixed derivatives
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec34">Type of problem </h2>
+<h2 id="___sec35">Type of problem </h2>
 
 <p>
 The problem our network must solve for, is similar to the ODE case.
@@ -2037,7 +2040,7 @@ The role of the function \( h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P)) \), is to ensu
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec35">Network requirements </h2>
+<h2 id="___sec36">Network requirements </h2>
 
 <p>
 The network tries then the minimize the cost function following the
@@ -2060,7 +2063,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec36">More details </h2>
+<h2 id="___sec37">More details </h2>
 
 <p>
 If we let \( \boldsymbol{x} = \big( x_1, \dots, x_N \big) \) be an array containing the values for \( x_1, \dots, x_N \) respectively, the cost function can be reformulated into the following:
@@ -2079,7 +2082,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec37">Example: The diffusion equation </h2>
+<h2 id="___sec38">Example: The diffusion equation </h2>
 
 <p>
 In one spatial dimension, the equation reads
@@ -2104,7 +2107,7 @@ with \( u(x) \) being some given function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec38">Defining the problem </h2>
+<h2 id="___sec39">Defining the problem </h2>
 
 <p>
 For this case, we want to find \( g(x,t) \) such that
@@ -2136,7 +2139,7 @@ First, we will look into how Autograd could be used in a network tailored to sol
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec39">Setting up the network using Autograd </h2>
+<h2 id="___sec40">Setting up the network using Autograd </h2>
 
 <p>
 The only change to do here, is to extend our network such that
@@ -2198,7 +2201,7 @@ network at each possible pair \( (x,t) \), given an array for the desired
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec40">Setting up the network using Autograd; The trial solution </h2>
+<h2 id="___sec41">Setting up the network using Autograd; The trial solution </h2>
 
 <p>
 The cost function must then iterate through the given arrays
@@ -2227,7 +2230,7 @@ since \( (0) = u(1) = 0 \) and \( u(x) = \sin(\pi x) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec41">Why the jacobian? </h2>
+<h2 id="___sec42">Why the jacobian? </h2>
 
 <p>
 The Jacobian is used because the program must find the derivative of
@@ -2294,7 +2297,7 @@ mixed derivatives of \( g(x,t) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec42">Setting up the network using Autograd; The full program </h2>
+<h2 id="___sec43">Setting up the network using Autograd; The full program </h2>
 
 <p>
 Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.
@@ -2545,7 +2548,7 @@ Using TensorFlow results in a much better execution time. Try it!
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec43">Example: Solving the wave equation with Neural Networks </h2>
+<h2 id="___sec44">Example: Solving the wave equation with Neural Networks </h2>
 
 <p>
 The wave equation is
@@ -2574,7 +2577,7 @@ where \( \frac{\partial g(x,t)}{\partial t} \Big |_{t = 0} \) means the derivati
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec44">The problem to solve for </h2>
+<h2 id="___sec45">The problem to solve for </h2>
 
 <p>
 The wave equation to solve for, is
@@ -2604,7 +2607,7 @@ In this example, let \( c = 1 \) and \( u(x) = \sin(\pi x) \) and \( v(x) = -\pi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec45">The trial solution </h2>
+<h2 id="___sec46">The trial solution </h2>
 Setting up the network is done in similar matter as for the example of solving the diffusion equation.
 The only things we have to change, is the trial solution such that it satisfies the conditions from \eqref{condwave} and the cost function.
 
@@ -2628,7 +2631,7 @@ Note that this trial solution satisfies the conditions only if \( u(0) = v(0) =
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec46">The analytical solution </h2>
+<h2 id="___sec47">The analytical solution </h2>
 
 <p>
 The analytical solution for our specific problem, is
@@ -2640,7 +2643,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec47">Solving the wave equation - the full program using Autograd </h2>
+<h2 id="___sec48">Solving the wave equation - the full program using Autograd </h2>
 
 <p>
 
@@ -2869,7 +2872,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec48">Resources on differential equations and deep learning </h2>
+<h2 id="___sec49">Resources on differential equations and deep learning </h2>
 
 <ol>
 <li> <a href="https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf" target="_blank">Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al</a></li>
@@ -2880,7 +2883,7 @@ $$
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec49">Friday, Principal Component Analysis </h2>
+<h2 id="___sec50">Friday, Principal Component Analysis </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=fkf4IBRSeEc&ab_channel=SteveBrunton" target="_blank">Overview video</a>
@@ -2888,7 +2891,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec50">Basic ideas of the Principal Component Analysis (PCA) </h2>
+<h2 id="___sec51">Basic ideas of the Principal Component Analysis (PCA) </h2>
 
 <p>
 The principal component analysis deals with the problem of fitting a
@@ -2913,7 +2916,7 @@ A good read is for example <a href="https://www.springer.com/gp/book/97803878781
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec51">Introducing the Covariance and Correlation functions  </h2>
+<h2 id="___sec52">Introducing the Covariance and Correlation functions  </h2>
 
 <p>
 Before we discuss the PCA theorem, we need to remind ourselves about
@@ -2974,7 +2977,7 @@ In the above example this is the function we constructed using <b>pandas</b>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec52">Correlation Function and Design/Feature Matrix </h2>
+<h2 id="___sec53">Correlation Function and Design/Feature Matrix </h2>
 
 <p>
 In our derivation of the various regression algorithms like <b>Ordinary Least Squares</b> or <b>Ridge regression</b>
@@ -3035,7 +3038,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec53">Covariance Matrix Examples </h2>
+<h2 id="___sec54">Covariance Matrix Examples </h2>
 
 <p>
 The Numpy function <b>np.cov</b> calculates the covariance elements using
@@ -3078,7 +3081,7 @@ C = np.cov(W)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec54">Correlation Matrix  </h2>
+<h2 id="___sec55">Correlation Matrix  </h2>
 
 <p>
 The previous example can be converted into the correlation matrix by
@@ -3123,7 +3126,7 @@ The above procedure with <b>numpy</b> can be made more compact if we use <b>pand
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec55">Correlation Matrix with Pandas </h2>
+<h2 id="___sec56">Correlation Matrix with Pandas </h2>
 
 <p>
 We whow here how we can set up the correlation matrix using <b>pandas</b>, as done in this simple code
@@ -3150,7 +3153,7 @@ We expand this model to the Franke function discussed above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec56">Correlation Matrix with Pandas and the Franke function </h2>
+<h2 id="___sec57">Correlation Matrix with Pandas and the Franke function </h2>
 
 <p>
 
@@ -3210,7 +3213,7 @@ matrix without them.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec57">Rewriting the Covariance and/or Correlation Matrix </h2>
+<h2 id="___sec58">Rewriting the Covariance and/or Correlation Matrix </h2>
 
 <p>
 We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix \( \boldsymbol{X} \) as 
@@ -3253,7 +3256,7 @@ It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\t
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec58">Towards the PCA theorem </h2>
+<h2 id="___sec59">Towards the PCA theorem </h2>
 
 <p>
 We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as
@@ -3304,7 +3307,7 @@ features/predictors.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec59">The Algorithm before theorem </h2>
+<h2 id="___sec60">The Algorithm before theorem </h2>
 
 <p>
 Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. 
@@ -3327,7 +3330,7 @@ $$
 
 <ul>
 <li> Center the data by subtracting the mean value for each column. This leads to a new matrix \( \boldsymbol{X}\rightarrow \overline{\boldsymbol{X}} \).</li>
-<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}\overline{\boldsymbol{X}}^T] \).</li>
+<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}^T\overline{\boldsymbol{X}}] \).</li>
 <li> Find the eigenpairs of \( \boldsymbol{C} \) with eigenvalues \( [\lambda_0,\lambda_1,\dots,\lambda_{p-1}] \) and eigenvectors \( [\boldsymbol{s}_0,\boldsymbol{s}_1,\dots,\boldsymbol{s}_{p-1}] \).</li>
 <li> Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.</li>
 <li> Keep only those \( l \) eigenvalues larger than a selected threshold value, discarding thus \( p-l \) features since we expect small variations in the data here.</li>
@@ -3335,11 +3338,11 @@ $$
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec60">Writing our own PCA code </h2>
+<h2 id="___sec61">Writing our own PCA code </h2>
 
 <p>
 We will use a simple example first with two-dimensional data
-drawn from a multivariate normal distribution with the following mean and covariance matrix:
+drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):
 $$
 \mu = (-1,2) \qquad \Sigma = \begin{bmatrix} 4 & 2 \\
 2 & 2
@@ -3347,8 +3350,8 @@ $$
 $$
 
 Note that the mean refers to each column of data. 
-We will generate \( n = 1000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
-this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \).
+We will generate \( n = 10000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
+this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \). This is our design matrix where we have forced the covariance and mean values to take specific values.
 
 <p>
 The following Python code aids in setting up the data and writing out the design matrix.
@@ -3368,7 +3371,7 @@ X = np.random.multivariate_normal(mean, cov, n)
 <p>
 Now we are going to implement the PCA algorithm. We will break it down into various substeps.
 
-<h3 id="___sec61">Compute the sample mean and center the data </h3>
+<h3 id="___sec62">Compute the sample mean and center the data </h3>
 
 <p>
 The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is
@@ -3383,7 +3386,7 @@ $$
 
 When you are done with these steps, print out \( \mu_n \) to verify it is
 close to \( \mu \) and plot your mean centered data to verify it is
-centered at the origin! Compare your code with the functionality from <b>Scikit-Learn</b> discussed above.
+centered at the origin! 
 The following code elements perform these operations using <b>pandas</b> or using our own functionality for doing so. The latter, using <b>numpy</b> is rather simple through the <b>mean()</b> function. 
 <p>
 
@@ -3405,7 +3408,7 @@ variance. The diagonal covariance matrix elements will then be one,
 while the non-diagonal ones need to be divided by \( 2\sqrt{2} \) for our
 specific case.
 
-<h3 id="___sec62">Compute the sample covariance </h3>
+<h3 id="___sec63">Compute the sample covariance </h3>
 
 <p>
 Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation
@@ -3445,9 +3448,9 @@ plt.show()
 </pre></div>
 <p>
 Depending on the number of points \( n \), we will get results that are close to the covariance values defined above.
-The plot shows how the data are clustered around a line with slope close to one. Is this expected?
+The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed.
 
-<h3 id="___sec63">Diagonalize the sample covariance matrix to obtain the principal components </h3>
+<h3 id="___sec64">Diagonalize the sample covariance matrix to obtain the principal components </h3>
 
 <p>
 Now we are ready to solve for the principal components! To do so we
@@ -3511,7 +3514,7 @@ This code does not contain all the above elements, but it shows how we can use <
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec64">Classical PCA Theorem   </h2>
+<h2 id="___sec65">Classical PCA Theorem   </h2>
 
 <p>
 We assume now that we have a design matrix \( \boldsymbol{X} \) which has been
@@ -3520,15 +3523,6 @@ overline symbol. The matrix is defined in terms of the various column
 vectors \( [\boldsymbol{x}_0,\boldsymbol{x}_1,\dots, \boldsymbol{x}_{p-1}] \) each with dimension
 \( \boldsymbol{x}\in {\mathbb{R}}^{n} \).
 
-<p>
-We assume also that we have an orthogonal transformation \( \boldsymbol{W}\in {\mathbb{R}}^{p\times p} \).  We define the reconstruction error (which is similar to the mean squared error we have seen before) as
-$$
-J(\boldsymbol{W},\boldsymbol{Z}) = \frac{1}{n}\sum_i (\boldsymbol{x}_i - \overline{\boldsymbol{x}}_i)^2,
-$$
-
-with \( \overline{\boldsymbol{x}}_i = \boldsymbol{W}\boldsymbol{z}_i \), where \( \boldsymbol{z}_i \) is a row vector with dimension \( {\mathbb{R}}^{n} \) of the matrix
-\( \boldsymbol{Z}\in{\mathbb{R}}^{p\times n} \).  When doing PCA we want to reduce this dimensionality.
-
 <p>
 The PCA theorem states that minimizing the above reconstruction error
 corresponds to setting \( \boldsymbol{W}=\boldsymbol{S} \), the orthogonal matrix which
@@ -3541,60 +3535,15 @@ eigenvectors of the covariance(correlations matrix).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec65">Proof of the PCA Theorem  </h2>
+<h2 id="___sec66">Proof of the PCA Theorem  </h2>
 
 <p>
-To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{w}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)= \frac{1}{n}\sum_i (\boldsymbol{x}_i - z_{i0}\boldsymbol{w}_0)^2=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2\boldsymbol{w}_0^T\boldsymbol{w}_0),
-$$
-
-which we can rewrite due to the orthogonality of \( \boldsymbol{w}_i \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2).
-$$
-
-Minimizing \( J \) with respect to the unknown parameters \( z_{0i} \) we obtain that
-$$
-z_{i0}=\boldsymbol{w}_0^T\boldsymbol{x}_i,
-$$
-
-where the vectors on the rhs are known.
+To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{s}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec66">PCA Proof continued </h2>
-
-<p>
-We have now found the unknown parameters \( z_{i0} \). These correspond to the projected coordinates and we can write
-$$
-J(\boldsymbol{w}_0)= \frac{1}{p}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - z_{i0}^2)=\mathrm{const}-\frac{1}{n}\sum_i z_{i0}^2.
-$$
-
-<p>
-We can show that the variance of the projected coordinates defined by \( \boldsymbol{w}_0^T\boldsymbol{x}_i \) are given by
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2,
-$$
-
-since the expectation value of
-$$
-\mathbb{E}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \mathbb{E}[z_{i0}]= \boldsymbol{w}_0^T\mathbb{E}[\boldsymbol{x}_i]=0,
-$$
-
-where we have used the fact that our data are centered.
-
-<p>
-Recalling our definition of the covariance as 
-$$
-\boldsymbol{C}[\boldsymbol{x}] = \frac{1}{n}\boldsymbol{X}\boldsymbol{X}^T=\mathbb{E}[\boldsymbol{X}\boldsymbol{X}^T],
-$$
-
-we have thus that
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2=\boldsymbol{w}_0^T\boldsymbol{C}[\boldsymbol{x}]\boldsymbol{w}_0.
-$$
+<h2 id="___sec67">PCA Proof continued </h2>
 
 <p>
 We are almost there, we have obtained a relation between minimizing
@@ -3605,7 +3554,7 @@ of the projected data.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec67">The final step </h2>
+<h2 id="___sec68">The final step </h2>
 
 <p>
 We could trivially maximize the variance of the projection (and
@@ -3659,7 +3608,7 @@ For more details, see for example <a href="https://www.springer.com/gp/book/9780
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec68">Geometric Interpretation and link with Singular Value Decomposition </h2>
+<h2 id="___sec69">Geometric Interpretation and link with Singular Value Decomposition </h2>
 
 <p>
 For a detailed demonstration of the geometric interpretation, see <a href="https://www.springer.com/gp/book/9780387878102" target="_blank">Vidal, Ma and Sastry, section 2.1.2</a>.
@@ -3667,7 +3616,7 @@ For a detailed demonstration of the geometric interpretation, see <a href="https
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec69">Principal Component Analysis </h2>
+<h2 id="___sec70">Principal Component Analysis </h2>
 
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
@@ -3722,7 +3671,7 @@ X2D = X_centered.dot(W2)
 <p>
 <!-- !split  -->
 
-<h2 id="___sec70">PCA and scikit-learn </h2>
+<h2 id="___sec71">PCA and scikit-learn </h2>
 
 <p>
 Scikit-Learn&#8217;s PCA class implements PCA using SVD decomposition just like we did before. The
@@ -3754,7 +3703,7 @@ variance that lies along the axis of each principal component.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec71">Back to the Cancer Data </h2>
+<h2 id="___sec72">Back to the Cancer Data </h2>
 We can now repeat the above but applied to real data, in this case our breast cancer data.
 Here we compute performance scores on the training data using logistic regression.
 <p>
@@ -3795,7 +3744,7 @@ We see that our training data after the PCA decomposition has a performance simi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec72">More on the PCA </h2>
+<h2 id="___sec73">More on the PCA </h2>
 
 <p>
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -3825,7 +3774,7 @@ X_reduced = pca.fit_transform(X)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec73">Incremental PCA </h2>
+<h2 id="___sec74">Incremental PCA </h2>
 
 <p>
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -3837,7 +3786,7 @@ instances arrive).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec74">Randomized PCA </h2>
+<h2 id="___sec75">Randomized PCA </h2>
 
 <p>
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -3848,7 +3797,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec75">Kernel PCA </h2>
+<h2 id="___sec76">Kernel PCA </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3877,7 +3826,7 @@ X_reduced = rbf_pca.fit_transform(X)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec76">LLE </h2>
+<h2 id="___sec77">LLE </h2>
 
 <p>
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -3889,7 +3838,7 @@ these local relationships are best preserved (more details shortly).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec77">Other techniques </h2>
+<h2 id="___sec78">Other techniques </h2>
 
 <p>
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
diff --git a/doc/pub/week43/html/week43.html b/doc/pub/week43/html/week43.html
index 7091c4c39..4810cb2ca 100644
--- a/doc/pub/week43/html/week43.html
+++ b/doc/pub/week43/html/week43.html
@@ -66,139 +66,140 @@ div { text-align: justify; text-justify: inter-word; }
 
 <!-- tocinfo
 {'highest level': 2,
- 'sections': [('Recurrent Neural Networks', 2, None, '___sec0'),
-              ('Solving ODEs with Deep Learning', 2, None, '___sec1'),
-              ('Ordinary Differential Equations', 2, None, '___sec2'),
-              ('The trial solution', 2, None, '___sec3'),
-              ('Minimization process', 2, None, '___sec4'),
+ 'sections': [('Plans for week 43', 2, None, '___sec0'),
+              ('Recurrent Neural Networks', 2, None, '___sec1'),
+              ('Solving ODEs with Deep Learning', 2, None, '___sec2'),
+              ('Ordinary Differential Equations', 2, None, '___sec3'),
+              ('The trial solution', 2, None, '___sec4'),
+              ('Minimization process', 2, None, '___sec5'),
               ('Minimizing the cost function using gradient descent and '
                'automatic differentiation',
                2,
                None,
-               '___sec5'),
-              ('Example: Exponential decay', 2, None, '___sec6'),
-              ('The function to solve for', 2, None, '___sec7'),
-              ('The trial solution', 2, None, '___sec8'),
-              ('Setup of Network', 2, None, '___sec9'),
-              ('Reformulating the problem', 2, None, '___sec10'),
-              ('More technicalities', 2, None, '___sec11'),
-              ('More details', 2, None, '___sec12'),
+               '___sec6'),
+              ('Example: Exponential decay', 2, None, '___sec7'),
+              ('The function to solve for', 2, None, '___sec8'),
+              ('The trial solution', 2, None, '___sec9'),
+              ('Setup of Network', 2, None, '___sec10'),
+              ('Reformulating the problem', 2, None, '___sec11'),
+              ('More technicalities', 2, None, '___sec12'),
+              ('More details', 2, None, '___sec13'),
               ('A possible implementation of a neural network',
                2,
                None,
-               '___sec13'),
-              ('Technicalities', 2, None, '___sec14'),
-              ('Final technicalities I', 2, None, '___sec15'),
-              ('Final technicalities II', 2, None, '___sec16'),
-              ('Final technicalities III', 2, None, '___sec17'),
-              ('Final technicalities IV', 2, None, '___sec18'),
-              ('Back propagation', 2, None, '___sec19'),
-              ('Gradient descent', 2, None, '___sec20'),
-              ('The code for solving the ODE', 2, None, '___sec21'),
+               '___sec14'),
+              ('Technicalities', 2, None, '___sec15'),
+              ('Final technicalities I', 2, None, '___sec16'),
+              ('Final technicalities II', 2, None, '___sec17'),
+              ('Final technicalities III', 2, None, '___sec18'),
+              ('Final technicalities IV', 2, None, '___sec19'),
+              ('Back propagation', 2, None, '___sec20'),
+              ('Gradient descent', 2, None, '___sec21'),
+              ('The code for solving the ODE', 2, None, '___sec22'),
               ('The network with one input layer, specified number of hidden '
                'layers, and one output layer',
                2,
                None,
-               '___sec22'),
-              ('Example: Population growth', 2, None, '___sec23'),
-              ('Setting up the problem', 2, None, '___sec24'),
-              ('The trial solution', 2, None, '___sec25'),
-              ('The program using Autograd', 2, None, '___sec26'),
-              ('Using forward Euler to solve the ODE', 2, None, '___sec27'),
+               '___sec23'),
+              ('Example: Population growth', 2, None, '___sec24'),
+              ('Setting up the problem', 2, None, '___sec25'),
+              ('The trial solution', 2, None, '___sec26'),
+              ('The program using Autograd', 2, None, '___sec27'),
+              ('Using forward Euler to solve the ODE', 2, None, '___sec28'),
               ('Example: Solving the one dimensional Poisson equation',
                2,
                None,
-               '___sec28'),
-              ('The specific equation to solve for', 2, None, '___sec29'),
-              ('Solving the equation using Autograd', 2, None, '___sec30'),
-              ('Comparing with a numerical scheme', 2, None, '___sec31'),
-              ('Setting up the code', 2, None, '___sec32'),
-              ('Partial Differential Equations', 2, None, '___sec33'),
-              ('Type of problem', 2, None, '___sec34'),
-              ('Network requirements', 2, None, '___sec35'),
-              ('More details', 2, None, '___sec36'),
-              ('Example: The diffusion equation', 2, None, '___sec37'),
-              ('Defining the problem', 2, None, '___sec38'),
-              ('Setting up the network using Autograd', 2, None, '___sec39'),
+               '___sec29'),
+              ('The specific equation to solve for', 2, None, '___sec30'),
+              ('Solving the equation using Autograd', 2, None, '___sec31'),
+              ('Comparing with a numerical scheme', 2, None, '___sec32'),
+              ('Setting up the code', 2, None, '___sec33'),
+              ('Partial Differential Equations', 2, None, '___sec34'),
+              ('Type of problem', 2, None, '___sec35'),
+              ('Network requirements', 2, None, '___sec36'),
+              ('More details', 2, None, '___sec37'),
+              ('Example: The diffusion equation', 2, None, '___sec38'),
+              ('Defining the problem', 2, None, '___sec39'),
+              ('Setting up the network using Autograd', 2, None, '___sec40'),
               ('Setting up the network using Autograd; The trial solution',
                2,
                None,
-               '___sec40'),
-              ('Why the jacobian?', 2, None, '___sec41'),
+               '___sec41'),
+              ('Why the jacobian?', 2, None, '___sec42'),
               ('Setting up the network using Autograd; The full program',
                2,
                None,
-               '___sec42'),
+               '___sec43'),
               ('Example: Solving the wave equation with Neural Networks',
                2,
                None,
-               '___sec43'),
-              ('The problem to solve for', 2, None, '___sec44'),
-              ('The trial solution', 2, None, '___sec45'),
-              ('The analytical solution', 2, None, '___sec46'),
+               '___sec44'),
+              ('The problem to solve for', 2, None, '___sec45'),
+              ('The trial solution', 2, None, '___sec46'),
+              ('The analytical solution', 2, None, '___sec47'),
               ('Solving the wave equation - the full program using Autograd',
                2,
                None,
-               '___sec47'),
+               '___sec48'),
               ('Resources on differential equations and deep learning',
                2,
                None,
-               '___sec48'),
-              ('Friday, Principal Component Analysis', 2, None, '___sec49'),
+               '___sec49'),
+              ('Friday, Principal Component Analysis', 2, None, '___sec50'),
               ('Basic ideas of the Principal Component Analysis (PCA)',
                2,
                None,
-               '___sec50'),
+               '___sec51'),
               ('Introducing the Covariance and Correlation functions',
                2,
                None,
-               '___sec51'),
+               '___sec52'),
               ('Correlation Function and Design/Feature Matrix',
                2,
                None,
-               '___sec52'),
-              ('Covariance Matrix Examples', 2, None, '___sec53'),
-              ('Correlation Matrix', 2, None, '___sec54'),
-              ('Correlation Matrix with Pandas', 2, None, '___sec55'),
+               '___sec53'),
+              ('Covariance Matrix Examples', 2, None, '___sec54'),
+              ('Correlation Matrix', 2, None, '___sec55'),
+              ('Correlation Matrix with Pandas', 2, None, '___sec56'),
               ('Correlation Matrix with Pandas and the Franke function',
                2,
                None,
-               '___sec56'),
+               '___sec57'),
               ('Rewriting the Covariance and/or Correlation Matrix',
                2,
                None,
-               '___sec57'),
-              ('Towards the PCA theorem', 2, None, '___sec58'),
-              ('The Algorithm before the Theorem', 2, None, '___sec59'),
-              ('Writing our own PCA code', 2, None, '___sec60'),
+               '___sec58'),
+              ('Towards the PCA theorem', 2, None, '___sec59'),
+              ('The Algorithm before the Theorem', 2, None, '___sec60'),
+              ('Writing our own PCA code', 2, None, '___sec61'),
               ('Compute the sample mean and center the data',
                3,
                None,
-               '___sec61'),
-              ('Compute the sample covariance', 3, None, '___sec62'),
+               '___sec62'),
+              ('Compute the sample covariance', 3, None, '___sec63'),
               ('Diagonalize the sample covariance matrix to obtain the '
                'principal components',
                3,
                None,
-               '___sec63'),
-              ('Classical PCA Theorem', 2, None, '___sec64'),
-              ('Proof of the PCA Theorem', 2, None, '___sec65'),
-              ('PCA Proof continued', 2, None, '___sec66'),
-              ('The final step', 2, None, '___sec67'),
+               '___sec64'),
+              ('Classical PCA Theorem', 2, None, '___sec65'),
+              ('Proof of the PCA Theorem', 2, None, '___sec66'),
+              ('PCA Proof continued', 2, None, '___sec67'),
+              ('The final step', 2, None, '___sec68'),
               ('Geometric Interpretation and link with Singular Value '
                'Decomposition',
                2,
                None,
-               '___sec68'),
-              ('Principal Component Analysis', 2, None, '___sec69'),
-              ('PCA and scikit-learn', 2, None, '___sec70'),
-              ('Back to the Cancer Data', 2, None, '___sec71'),
-              ('More on the PCA', 2, None, '___sec72'),
-              ('Incremental PCA', 2, None, '___sec73'),
-              ('Randomized PCA', 2, None, '___sec74'),
-              ('Kernel PCA', 2, None, '___sec75'),
-              ('LLE', 2, None, '___sec76'),
-              ('Other techniques', 2, None, '___sec77')]}
+               '___sec69'),
+              ('Principal Component Analysis', 2, None, '___sec70'),
+              ('PCA and scikit-learn', 2, None, '___sec71'),
+              ('Back to the Cancer Data', 2, None, '___sec72'),
+              ('More on the PCA', 2, None, '___sec73'),
+              ('Incremental PCA', 2, None, '___sec74'),
+              ('Randomized PCA', 2, None, '___sec75'),
+              ('Kernel PCA', 2, None, '___sec76'),
+              ('LLE', 2, None, '___sec77'),
+              ('Other techniques', 2, None, '___sec78')]}
 end of tocinfo -->
 
 <body>
@@ -240,11 +241,13 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 23, 2020</h4></center> <!-- date -->
+<center><h4>Oct 26, 2020</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
+<h2 id="___sec0">Plans for week 43 </h2>
+
 <ul>
 <li> Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture October 22</a></li>
 <li> Friday: Principal Component Analysis and Dimensionality Reduction. <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober23.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture October 23</a></li>
@@ -255,7 +258,7 @@ We will also study the usage of <a href="https://www.youtube.com/watch?v=fRf4l5q
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec0">Recurrent Neural Networks </h2>
+<h2 id="___sec1">Recurrent Neural Networks </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini" target="_blank">Overview video</a>.
@@ -270,7 +273,7 @@ See also lecture on Thursday October 22 and examples from <a href="https://compp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec1">Solving ODEs with Deep Learning </h2>
+<h2 id="___sec2">Solving ODEs with Deep Learning </h2>
 
 <p>
 The Universal Approximation Theorem states that a neural network can
@@ -280,7 +283,7 @@ and output layer to any given precision.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec2">Ordinary Differential Equations </h2>
+<h2 id="___sec3">Ordinary Differential Equations </h2>
 
 <p>
 An ordinary differential equation (ODE) is an equation involving functions having one variable.
@@ -307,7 +310,7 @@ for the solution to be unique.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec3">The trial solution </h2>
+<h2 id="___sec4">The trial solution </h2>
 
 <p>
 Let the trial solution \( g_t(x) \) be
@@ -338,7 +341,7 @@ As described previously, an optimization method could be used to minimize the pa
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec4">Minimization process </h2>
+<h2 id="___sec5">Minimization process </h2>
 
 <p>
 For the minimization to be defined, we need to have a cost function at hand to minimize.
@@ -370,7 +373,7 @@ The neural net should then find the parameters \( P \) that minimizes the cost f
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec5">Minimizing the cost function using gradient descent and automatic differentiation </h2>
+<h2 id="___sec6">Minimizing the cost function using gradient descent and automatic differentiation </h2>
 
 <p>
 To perform the minimization using gradient descent, the gradient of \( C\left(\boldsymbol{x}, P\right) \) is needed.
@@ -383,7 +386,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec6">Example: Exponential decay </h2>
+<h2 id="___sec7">Example: Exponential decay </h2>
 
 <p>
 An exponential decay of a quantity \( g(x) \) is described by the equation
@@ -413,7 +416,7 @@ Having an analytical solution at hand, it is possible to use it to compare how w
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec7">The function to solve for </h2>
+<h2 id="___sec8">The function to solve for </h2>
 
 <p>
 The program will use a neural network to solve
@@ -433,7 +436,7 @@ In this example, \( \gamma = 2 \) and \( g_0 = 10 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec8">The trial solution </h2>
+<h2 id="___sec9">The trial solution </h2>
 To begin with, a trial solution \( g_t(t) \) must be chosen. A general trial solution for ordinary differential equations could be
 
 $$
@@ -446,7 +449,7 @@ with \( h_1(x) \) ensuring that \( g_t(x) \) satisfies some conditions and \( h_
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec9">Setup of Network </h2>
+<h2 id="___sec10">Setup of Network </h2>
 
 <p>
 In this network, there are no weights and bias at the input layer, so \( P = \{ P_{\text{hidden}},  P_{\text{output}} \} \).
@@ -471,7 +474,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec10">Reformulating the problem </h2>
+<h2 id="___sec11">Reformulating the problem </h2>
 
 <p>
 We wish that our neural network manages to minimize a given cost function.
@@ -505,7 +508,7 @@ is fulfilled as <em>best as possible</em>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec11">More technicalities </h2>
+<h2 id="___sec12">More technicalities </h2>
 
 <p>
 The left hand side and right hand side of \eqref{nnmin} must be computed separately, and then the neural network must choose weights and biases, contained in \( P \), such that the sides are equal as best as possible.
@@ -535,7 +538,7 @@ for an input value \( x \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec12">More details </h2>
+<h2 id="___sec13">More details </h2>
 
 <p>
 If the neural network evaluates \( g_t(x, P) \) at more values for \( x \), say \( N \) values \( x_i \) for \( i = 1, \dots, N \), then the <em>total</em> error to minimize becomes
@@ -563,7 +566,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec13">A possible implementation of a neural network </h2>
+<h2 id="___sec14">A possible implementation of a neural network </h2>
 
 <p>
 For simplicity, it is assumed that the input is an array \( \boldsymbol{x} = (x_1, \dots, x_N) \) with \( N \) elements. It is at these points the neural network should find \( P \) such that it fulfills \eqref{min}.
@@ -576,7 +579,7 @@ The input layer will consist of \( N_{\text{input} } \) neurons, passing its ele
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec14">Technicalities </h2>
+<h2 id="___sec15">Technicalities </h2>
 
 <p>
 For the \( i \)-th in the hidden layer with weight \( w_i^{\text{hidden} } \) and bias \( b_i^{\text{hidden} } \), the weighting from the \( j \)-th neuron at the input layer is:
@@ -598,7 +601,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec15">Final technicalities I </h2>
+<h2 id="___sec16">Final technicalities I </h2>
 
 <p>
 The result after weighting the inputs at the \( i \)-th hidden neuron can be written as a vector:
@@ -621,7 +624,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec16">Final technicalities II </h2>
+<h2 id="___sec17">Final technicalities II </h2>
 
 <p>
 The vector \( \boldsymbol{p}_{i, \text{hidden}}^T \) constitutes each row in \( P_{\text{hidden} } \), which contains the weights for the neural network to minimize according to \eqref{min}.
@@ -659,7 +662,7 @@ it is assumes that the number of neurons in the output layer is one.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec17">Final technicalities III </h2>
+<h2 id="___sec18">Final technicalities III </h2>
 
 <p>
 The procedure of weighting the output neuron \( j \) in the hidden layer to the \( i \)-th neuron in the output layer is similar as for the hidden layer described previously.
@@ -680,7 +683,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec18">Final technicalities IV </h2>
+<h2 id="___sec19">Final technicalities IV </h2>
 
 <p>
 Expressing \( z_{1,j}^{\text{output}} \) as a vector gives the following way of weighting the inputs from the hidden layer:
@@ -702,7 +705,7 @@ In this case we seek a continuous range of values since we are approximating a f
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec19">Back propagation </h2>
+<h2 id="___sec20">Back propagation </h2>
 
 <p>
 The next step is to decide how the parameters should be changed such that they minimize the cost function.
@@ -723,7 +726,7 @@ Here, gradient descent with a constant step size has been chosen.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec20">Gradient descent </h2>
+<h2 id="___sec21">Gradient descent </h2>
 
 <p>
 The idea of the gradient descent algorithm is to update parameters in
@@ -766,7 +769,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec21">The code for solving the ODE </h2>
+<h2 id="___sec22">The code for solving the ODE </h2>
 
 <p>
 
@@ -919,7 +922,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec22">The network with one input layer, specified number of hidden layers, and one output layer </h2>
+<h2 id="___sec23">The network with one input layer, specified number of hidden layers, and one output layer </h2>
 
 <p>
 It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.
@@ -1092,7 +1095,7 @@ The number of neurons within each hidden layer are given as a list of integers i
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec23">Example: Population growth </h2>
+<h2 id="___sec24">Example: Population growth </h2>
 
 <p>
 A logistic model of population growth assumes that a population converges toward an equilibrium.
@@ -1117,7 +1120,7 @@ Here, we stay with a more simple approach and implement for comparison, the simp
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec24">Setting up the problem </h2>
+<h2 id="___sec25">Setting up the problem </h2>
 
 <p>
 Here, we will model a population \( g(t) \) in an environment having carrying capacity \( A \).
@@ -1138,7 +1141,7 @@ In this example, we let \( \alpha = 2 \), \( A = 1 \), and \( g_0 = 1.2 \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec25">The trial solution </h2>
+<h2 id="___sec26">The trial solution </h2>
 
 <p>
 We will get a slightly different trial solution, as the boundary conditions are different
@@ -1164,7 +1167,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec26">The program using Autograd </h2>
+<h2 id="___sec27">The program using Autograd </h2>
 
 <p>
 The network will be the similar as for the exponential decay example, but with some small modifications for our problem.
@@ -1339,7 +1342,7 @@ The network will be the similar as for the exponential decay example, but with s
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec27">Using forward Euler to solve the ODE </h2>
+<h2 id="___sec28">Using forward Euler to solve the ODE </h2>
 
 <p>
 A straightforward way of solving an ODE numerically, is to use Euler's method.
@@ -1468,7 +1471,7 @@ extending the program that uses the network using Autograd:
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec28">Example: Solving the one dimensional Poisson equation </h2>
+<h2 id="___sec29">Example: Solving the one dimensional Poisson equation </h2>
 
 <p>
 The Poisson equation for \( g(x) \) in one dimension is
@@ -1499,7 +1502,7 @@ In addition, it could be interesting to see how a typical method for numerically
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec29">The specific equation to solve for </h2>
+<h2 id="___sec30">The specific equation to solve for </h2>
 
 <p>
 Here, the function \( g(x) \) to solve for follows the equation
@@ -1537,7 +1540,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec30">Solving the equation using Autograd </h2>
+<h2 id="___sec31">Solving the equation using Autograd </h2>
 
 <p>
 
@@ -1696,7 +1699,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec31">Comparing with a numerical scheme </h2>
+<h2 id="___sec32">Comparing with a numerical scheme </h2>
 
 <p>
 The Poisson equation is possible to solve using Taylor series to approximate the second derivative.
@@ -1794,7 +1797,7 @@ which makes it possible to solve for the vector \( \boldsymbol{g} \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec32">Setting up the code </h2>
+<h2 id="___sec33">Setting up the code </h2>
 
 <p>
 We can then compare the result from this numerical scheme with the output from our network using Autograd:
@@ -1996,7 +1999,7 @@ We can then compare the result from this numerical scheme with the output from o
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec33">Partial Differential Equations </h2>
+<h2 id="___sec34">Partial Differential Equations </h2>
 
 <p>
 A partial differential equation (PDE) has a solution here the function
@@ -2019,7 +2022,7 @@ where \( f \) is an expression involving all kinds of possible mixed derivatives
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec34">Type of problem </h2>
+<h2 id="___sec35">Type of problem </h2>
 
 <p>
 The problem our network must solve for, is similar to the ODE case.
@@ -2042,7 +2045,7 @@ The role of the function \( h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P)) \), is to ensu
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec35">Network requirements </h2>
+<h2 id="___sec36">Network requirements </h2>
 
 <p>
 The network tries then the minimize the cost function following the
@@ -2065,7 +2068,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec36">More details </h2>
+<h2 id="___sec37">More details </h2>
 
 <p>
 If we let \( \boldsymbol{x} = \big( x_1, \dots, x_N \big) \) be an array containing the values for \( x_1, \dots, x_N \) respectively, the cost function can be reformulated into the following:
@@ -2084,7 +2087,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec37">Example: The diffusion equation </h2>
+<h2 id="___sec38">Example: The diffusion equation </h2>
 
 <p>
 In one spatial dimension, the equation reads
@@ -2109,7 +2112,7 @@ with \( u(x) \) being some given function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec38">Defining the problem </h2>
+<h2 id="___sec39">Defining the problem </h2>
 
 <p>
 For this case, we want to find \( g(x,t) \) such that
@@ -2141,7 +2144,7 @@ First, we will look into how Autograd could be used in a network tailored to sol
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec39">Setting up the network using Autograd </h2>
+<h2 id="___sec40">Setting up the network using Autograd </h2>
 
 <p>
 The only change to do here, is to extend our network such that
@@ -2203,7 +2206,7 @@ network at each possible pair \( (x,t) \), given an array for the desired
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec40">Setting up the network using Autograd; The trial solution </h2>
+<h2 id="___sec41">Setting up the network using Autograd; The trial solution </h2>
 
 <p>
 The cost function must then iterate through the given arrays
@@ -2232,7 +2235,7 @@ since \( (0) = u(1) = 0 \) and \( u(x) = \sin(\pi x) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec41">Why the jacobian? </h2>
+<h2 id="___sec42">Why the jacobian? </h2>
 
 <p>
 The Jacobian is used because the program must find the derivative of
@@ -2299,7 +2302,7 @@ mixed derivatives of \( g(x,t) \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec42">Setting up the network using Autograd; The full program </h2>
+<h2 id="___sec43">Setting up the network using Autograd; The full program </h2>
 
 <p>
 Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.
@@ -2550,7 +2553,7 @@ Using TensorFlow results in a much better execution time. Try it!
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec43">Example: Solving the wave equation with Neural Networks </h2>
+<h2 id="___sec44">Example: Solving the wave equation with Neural Networks </h2>
 
 <p>
 The wave equation is
@@ -2579,7 +2582,7 @@ where \( \frac{\partial g(x,t)}{\partial t} \Big |_{t = 0} \) means the derivati
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec44">The problem to solve for </h2>
+<h2 id="___sec45">The problem to solve for </h2>
 
 <p>
 The wave equation to solve for, is
@@ -2609,7 +2612,7 @@ In this example, let \( c = 1 \) and \( u(x) = \sin(\pi x) \) and \( v(x) = -\pi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec45">The trial solution </h2>
+<h2 id="___sec46">The trial solution </h2>
 Setting up the network is done in similar matter as for the example of solving the diffusion equation.
 The only things we have to change, is the trial solution such that it satisfies the conditions from \eqref{condwave} and the cost function.
 
@@ -2633,7 +2636,7 @@ Note that this trial solution satisfies the conditions only if \( u(0) = v(0) =
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec46">The analytical solution </h2>
+<h2 id="___sec47">The analytical solution </h2>
 
 <p>
 The analytical solution for our specific problem, is
@@ -2645,7 +2648,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec47">Solving the wave equation - the full program using Autograd </h2>
+<h2 id="___sec48">Solving the wave equation - the full program using Autograd </h2>
 
 <p>
 
@@ -2874,7 +2877,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec48">Resources on differential equations and deep learning </h2>
+<h2 id="___sec49">Resources on differential equations and deep learning </h2>
 
 <ol>
 <li> <a href="https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf" target="_blank">Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al</a></li>
@@ -2885,7 +2888,7 @@ $$
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec49">Friday, Principal Component Analysis </h2>
+<h2 id="___sec50">Friday, Principal Component Analysis </h2>
 
 <p>
 <a href="https://www.youtube.com/watch?v=fkf4IBRSeEc&ab_channel=SteveBrunton" target="_blank">Overview video</a>
@@ -2893,7 +2896,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec50">Basic ideas of the Principal Component Analysis (PCA) </h2>
+<h2 id="___sec51">Basic ideas of the Principal Component Analysis (PCA) </h2>
 
 <p>
 The principal component analysis deals with the problem of fitting a
@@ -2918,7 +2921,7 @@ A good read is for example <a href="https://www.springer.com/gp/book/97803878781
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec51">Introducing the Covariance and Correlation functions  </h2>
+<h2 id="___sec52">Introducing the Covariance and Correlation functions  </h2>
 
 <p>
 Before we discuss the PCA theorem, we need to remind ourselves about
@@ -2979,7 +2982,7 @@ In the above example this is the function we constructed using <b>pandas</b>.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec52">Correlation Function and Design/Feature Matrix </h2>
+<h2 id="___sec53">Correlation Function and Design/Feature Matrix </h2>
 
 <p>
 In our derivation of the various regression algorithms like <b>Ordinary Least Squares</b> or <b>Ridge regression</b>
@@ -3040,7 +3043,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec53">Covariance Matrix Examples </h2>
+<h2 id="___sec54">Covariance Matrix Examples </h2>
 
 <p>
 The Numpy function <b>np.cov</b> calculates the covariance elements using
@@ -3083,7 +3086,7 @@ C <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec54">Correlation Matrix  </h2>
+<h2 id="___sec55">Correlation Matrix  </h2>
 
 <p>
 The previous example can be converted into the correlation matrix by
@@ -3128,7 +3131,7 @@ The above procedure with <b>numpy</b> can be made more compact if we use <b>pand
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec55">Correlation Matrix with Pandas </h2>
+<h2 id="___sec56">Correlation Matrix with Pandas </h2>
 
 <p>
 We whow here how we can set up the correlation matrix using <b>pandas</b>, as done in this simple code
@@ -3155,7 +3158,7 @@ We expand this model to the Franke function discussed above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec56">Correlation Matrix with Pandas and the Franke function </h2>
+<h2 id="___sec57">Correlation Matrix with Pandas and the Franke function </h2>
 
 <p>
 
@@ -3215,7 +3218,7 @@ matrix without them.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec57">Rewriting the Covariance and/or Correlation Matrix </h2>
+<h2 id="___sec58">Rewriting the Covariance and/or Correlation Matrix </h2>
 
 <p>
 We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix \( \boldsymbol{X} \) as 
@@ -3258,7 +3261,7 @@ It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\t
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec58">Towards the PCA theorem </h2>
+<h2 id="___sec59">Towards the PCA theorem </h2>
 
 <p>
 We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as
@@ -3309,7 +3312,7 @@ features/predictors.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec59">The Algorithm before theorem </h2>
+<h2 id="___sec60">The Algorithm before theorem </h2>
 
 <p>
 Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. 
@@ -3332,7 +3335,7 @@ $$
 
 <ul>
 <li> Center the data by subtracting the mean value for each column. This leads to a new matrix \( \boldsymbol{X}\rightarrow \overline{\boldsymbol{X}} \).</li>
-<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}\overline{\boldsymbol{X}}^T] \).</li>
+<li> Compute then the covariance/correlation matrix \( \mathbb{E}[\overline{\boldsymbol{X}}^T\overline{\boldsymbol{X}}] \).</li>
 <li> Find the eigenpairs of \( \boldsymbol{C} \) with eigenvalues \( [\lambda_0,\lambda_1,\dots,\lambda_{p-1}] \) and eigenvectors \( [\boldsymbol{s}_0,\boldsymbol{s}_1,\dots,\boldsymbol{s}_{p-1}] \).</li>
 <li> Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.</li>
 <li> Keep only those \( l \) eigenvalues larger than a selected threshold value, discarding thus \( p-l \) features since we expect small variations in the data here.</li>
@@ -3340,11 +3343,11 @@ $$
 
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec60">Writing our own PCA code </h2>
+<h2 id="___sec61">Writing our own PCA code </h2>
 
 <p>
 We will use a simple example first with two-dimensional data
-drawn from a multivariate normal distribution with the following mean and covariance matrix:
+drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):
 $$
 \mu = (-1,2) \qquad \Sigma = \begin{bmatrix} 4 & 2 \\
 2 & 2
@@ -3352,8 +3355,8 @@ $$
 $$
 
 Note that the mean refers to each column of data. 
-We will generate \( n = 1000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
-this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \).
+We will generate \( n = 10000 \) points \( X = \{ x_1, \ldots, x_N \} \) from
+this distribution, and store them in the \( 1000 \times 2 \) matrix \( \boldsymbol{X} \). This is our design matrix where we have forced the covariance and mean values to take specific values.
 
 <p>
 The following Python code aids in setting up the data and writing out the design matrix.
@@ -3373,7 +3376,7 @@ X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>r
 <p>
 Now we are going to implement the PCA algorithm. We will break it down into various substeps.
 
-<h3 id="___sec61">Compute the sample mean and center the data </h3>
+<h3 id="___sec62">Compute the sample mean and center the data </h3>
 
 <p>
 The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is
@@ -3388,7 +3391,7 @@ $$
 
 When you are done with these steps, print out \( \mu_n \) to verify it is
 close to \( \mu \) and plot your mean centered data to verify it is
-centered at the origin! Compare your code with the functionality from <b>Scikit-Learn</b> discussed above.
+centered at the origin! 
 The following code elements perform these operations using <b>pandas</b> or using our own functionality for doing so. The latter, using <b>numpy</b> is rather simple through the <b>mean()</b> function. 
 <p>
 
@@ -3410,7 +3413,7 @@ variance. The diagonal covariance matrix elements will then be one,
 while the non-diagonal ones need to be divided by \( 2\sqrt{2} \) for our
 specific case.
 
-<h3 id="___sec62">Compute the sample covariance </h3>
+<h3 id="___sec63">Compute the sample covariance </h3>
 
 <p>
 Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation
@@ -3450,9 +3453,9 @@ plt<span style="color: #666666">.</span>show()
 </pre></div>
 <p>
 Depending on the number of points \( n \), we will get results that are close to the covariance values defined above.
-The plot shows how the data are clustered around a line with slope close to one. Is this expected?
+The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed.
 
-<h3 id="___sec63">Diagonalize the sample covariance matrix to obtain the principal components </h3>
+<h3 id="___sec64">Diagonalize the sample covariance matrix to obtain the principal components </h3>
 
 <p>
 Now we are ready to solve for the principal components! To do so we
@@ -3516,7 +3519,7 @@ This code does not contain all the above elements, but it shows how we can use <
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec64">Classical PCA Theorem   </h2>
+<h2 id="___sec65">Classical PCA Theorem   </h2>
 
 <p>
 We assume now that we have a design matrix \( \boldsymbol{X} \) which has been
@@ -3525,15 +3528,6 @@ overline symbol. The matrix is defined in terms of the various column
 vectors \( [\boldsymbol{x}_0,\boldsymbol{x}_1,\dots, \boldsymbol{x}_{p-1}] \) each with dimension
 \( \boldsymbol{x}\in {\mathbb{R}}^{n} \).
 
-<p>
-We assume also that we have an orthogonal transformation \( \boldsymbol{W}\in {\mathbb{R}}^{p\times p} \).  We define the reconstruction error (which is similar to the mean squared error we have seen before) as
-$$
-J(\boldsymbol{W},\boldsymbol{Z}) = \frac{1}{n}\sum_i (\boldsymbol{x}_i - \overline{\boldsymbol{x}}_i)^2,
-$$
-
-with \( \overline{\boldsymbol{x}}_i = \boldsymbol{W}\boldsymbol{z}_i \), where \( \boldsymbol{z}_i \) is a row vector with dimension \( {\mathbb{R}}^{n} \) of the matrix
-\( \boldsymbol{Z}\in{\mathbb{R}}^{p\times n} \).  When doing PCA we want to reduce this dimensionality.
-
 <p>
 The PCA theorem states that minimizing the above reconstruction error
 corresponds to setting \( \boldsymbol{W}=\boldsymbol{S} \), the orthogonal matrix which
@@ -3546,60 +3540,15 @@ eigenvectors of the covariance(correlations matrix).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec65">Proof of the PCA Theorem  </h2>
+<h2 id="___sec66">Proof of the PCA Theorem  </h2>
 
 <p>
-To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{w}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)= \frac{1}{n}\sum_i (\boldsymbol{x}_i - z_{i0}\boldsymbol{w}_0)^2=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2\boldsymbol{w}_0^T\boldsymbol{w}_0),
-$$
-
-which we can rewrite due to the orthogonality of \( \boldsymbol{w}_i \) as
-$$
-J(\boldsymbol{w}_0,\boldsymbol{z}_0)=\frac{1}{n}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - 2z_{i0}\boldsymbol{w}_0^T\boldsymbol{x}_i+z_{i0}^2).
-$$
-
-Minimizing \( J \) with respect to the unknown parameters \( z_{0i} \) we obtain that
-$$
-z_{i0}=\boldsymbol{w}_0^T\boldsymbol{x}_i,
-$$
-
-where the vectors on the rhs are known.
+To show the PCA theorem let us start with the assumption that there is one vector \( \boldsymbol{s}_0 \) which corresponds to a solution which minimized the reconstruction error \( J \). This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of \( \boldsymbol{w}_0 \) and \( \boldsymbol{z}_0 \) as
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec66">PCA Proof continued </h2>
-
-<p>
-We have now found the unknown parameters \( z_{i0} \). These correspond to the projected coordinates and we can write
-$$
-J(\boldsymbol{w}_0)= \frac{1}{p}\sum_i (\boldsymbol{x}_i^T\boldsymbol{x}_i - z_{i0}^2)=\mathrm{const}-\frac{1}{n}\sum_i z_{i0}^2.
-$$
-
-<p>
-We can show that the variance of the projected coordinates defined by \( \boldsymbol{w}_0^T\boldsymbol{x}_i \) are given by
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2,
-$$
-
-since the expectation value of
-$$
-\mathbb{E}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \mathbb{E}[z_{i0}]= \boldsymbol{w}_0^T\mathbb{E}[\boldsymbol{x}_i]=0,
-$$
-
-where we have used the fact that our data are centered.
-
-<p>
-Recalling our definition of the covariance as 
-$$
-\boldsymbol{C}[\boldsymbol{x}] = \frac{1}{n}\boldsymbol{X}\boldsymbol{X}^T=\mathbb{E}[\boldsymbol{X}\boldsymbol{X}^T],
-$$
-
-we have thus that
-$$
-\mathrm{var}[\boldsymbol{w}_0^T\boldsymbol{x}_i] = \frac{1}{n}\sum_i z_{i0}^2=\boldsymbol{w}_0^T\boldsymbol{C}[\boldsymbol{x}]\boldsymbol{w}_0.
-$$
+<h2 id="___sec67">PCA Proof continued </h2>
 
 <p>
 We are almost there, we have obtained a relation between minimizing
@@ -3610,7 +3559,7 @@ of the projected data.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec67">The final step </h2>
+<h2 id="___sec68">The final step </h2>
 
 <p>
 We could trivially maximize the variance of the projection (and
@@ -3664,7 +3613,7 @@ For more details, see for example <a href="https://www.springer.com/gp/book/9780
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec68">Geometric Interpretation and link with Singular Value Decomposition </h2>
+<h2 id="___sec69">Geometric Interpretation and link with Singular Value Decomposition </h2>
 
 <p>
 For a detailed demonstration of the geometric interpretation, see <a href="https://www.springer.com/gp/book/9780387878102" target="_blank">Vidal, Ma and Sastry, section 2.1.2</a>.
@@ -3672,7 +3621,7 @@ For a detailed demonstration of the geometric interpretation, see <a href="https
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec69">Principal Component Analysis </h2>
+<h2 id="___sec70">Principal Component Analysis </h2>
 
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
@@ -3727,7 +3676,7 @@ X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666"
 <p>
 <!-- !split  -->
 
-<h2 id="___sec70">PCA and scikit-learn </h2>
+<h2 id="___sec71">PCA and scikit-learn </h2>
 
 <p>
 Scikit-Learn&#8217;s PCA class implements PCA using SVD decomposition just like we did before. The
@@ -3759,7 +3708,7 @@ variance that lies along the axis of each principal component.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec71">Back to the Cancer Data </h2>
+<h2 id="___sec72">Back to the Cancer Data </h2>
 We can now repeat the above but applied to real data, in this case our breast cancer data.
 Here we compute performance scores on the training data using logistic regression.
 <p>
@@ -3800,7 +3749,7 @@ We see that our training data after the PCA decomposition has a performance simi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec72">More on the PCA </h2>
+<h2 id="___sec73">More on the PCA </h2>
 
 <p>
 Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -3830,7 +3779,7 @@ X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec73">Incremental PCA </h2>
+<h2 id="___sec74">Incremental PCA </h2>
 
 <p>
 One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -3842,7 +3791,7 @@ instances arrive).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec74">Randomized PCA </h2>
+<h2 id="___sec75">Randomized PCA </h2>
 
 <p>
 Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -3853,7 +3802,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec75">Kernel PCA </h2>
+<h2 id="___sec76">Kernel PCA </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -3882,7 +3831,7 @@ X_reduced <span style="color: #666666">=</span> rbf_pca<span style="color: #6666
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec76">LLE </h2>
+<h2 id="___sec77">LLE </h2>
 
 <p>
 Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -3894,7 +3843,7 @@ these local relationships are best preserved (more details shortly).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec77">Other techniques </h2>
+<h2 id="___sec78">Other techniques </h2>
 
 <p>
 There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
diff --git a/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz b/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz
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diff --git a/doc/pub/week43/ipynb/week43.ipynb b/doc/pub/week43/ipynb/week43.ipynb
index ec3fcba20..04536e6ab 100644
--- a/doc/pub/week43/ipynb/week43.ipynb
+++ b/doc/pub/week43/ipynb/week43.ipynb
@@ -10,12 +10,13 @@
     "<!-- Author: -->  \n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
     "\n",
-    "Date: **Oct 23, 2020**\n",
+    "Date: **Oct 26, 2020**\n",
     "\n",
     "Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
     "\n",
     "\n",
+    "## Plans for week 43\n",
     "\n",
     "* Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. [Video of Lecture October 22](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage)\n",
     "\n",
@@ -672,7 +673,9 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -837,7 +840,9 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1091,7 +1096,9 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1351,7 +1358,9 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
@@ -1552,7 +1561,9 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1860,7 +1871,9 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2283,7 +2296,9 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "def sigmoid(z):\n",
@@ -2382,7 +2397,9 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "# Set up the trial function:\n",
@@ -2449,7 +2466,9 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2807,7 +2826,9 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -3335,7 +3356,9 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "# Importing various packages\n",
@@ -3366,7 +3389,9 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -3410,7 +3435,9 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -3439,39 +3466,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0         1         2         3         4         5         6         7  \\\n",
-      "0  0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1  0.0  0.070063  0.069533  0.067085  0.068151  0.069193  0.057333  0.058540   \n",
-      "2  0.0  0.069533  0.069368  0.066521  0.067744  0.068951  0.056953  0.058268   \n",
-      "3  0.0  0.067085  0.066521  0.068521  0.069618  0.070705  0.061297  0.062609   \n",
-      "4  0.0  0.068151  0.067744  0.069618  0.070847  0.072071  0.062332  0.063755   \n",
-      "5  0.0  0.069193  0.068951  0.070705  0.072071  0.073435  0.063371  0.064907   \n",
-      "6  0.0  0.057333  0.056953  0.061297  0.062332  0.063371  0.056744  0.057998   \n",
-      "7  0.0  0.058540  0.058268  0.062609  0.063755  0.064907  0.057998  0.059350   \n",
-      "8  0.0  0.059802  0.059641  0.063981  0.065242  0.066511  0.059310  0.060763   \n",
-      "9  0.0  0.061119  0.061072  0.065414  0.066793  0.068183  0.060681  0.062239   \n",
-      "\n",
-      "          8         9  \n",
-      "0  0.000000  0.000000  \n",
-      "1  0.059802  0.061119  \n",
-      "2  0.059641  0.061072  \n",
-      "3  0.063981  0.065414  \n",
-      "4  0.065242  0.066793  \n",
-      "5  0.066511  0.068183  \n",
-      "6  0.059310  0.060681  \n",
-      "7  0.060763  0.062239  \n",
-      "8  0.062282  0.063866  \n",
-      "9  0.063866  0.065561  \n"
-     ]
-    }
-   ],
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -3504,7 +3503,7 @@
     "\n",
     "\n",
     "# Making meshgrid of datapoints and compute Franke's function\n",
-    "n = 3\n",
+    "n = 4\n",
     "N = 100\n",
     "x = np.sort(np.random.uniform(0, 1, N))\n",
     "y = np.sort(np.random.uniform(0, 1, N))\n",
@@ -3726,7 +3725,7 @@
    "source": [
     "* Center the data by subtracting the mean value for each column. This leads to a new matrix $\\boldsymbol{X}\\rightarrow \\overline{\\boldsymbol{X}}$.\n",
     "\n",
-    "* Compute then the covariance/correlation matrix $\\mathbb{E}[\\overline{\\boldsymbol{X}}\\overline{\\boldsymbol{X}}^T]$.\n",
+    "* Compute then the covariance/correlation matrix $\\mathbb{E}[\\overline{\\boldsymbol{X}}^T\\overline{\\boldsymbol{X}}]$.\n",
     "\n",
     "* Find the eigenpairs of $\\boldsymbol{C}$ with eigenvalues $[\\lambda_0,\\lambda_1,\\dots,\\lambda_{p-1}]$ and eigenvectors $[\\boldsymbol{s}_0,\\boldsymbol{s}_1,\\dots,\\boldsymbol{s}_{p-1}]$.\n",
     "\n",
@@ -3737,7 +3736,7 @@
     "## Writing our own PCA code\n",
     "\n",
     "We will use a simple example first with two-dimensional data\n",
-    "drawn from a multivariate normal distribution with the following mean and covariance matrix:"
+    "drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):"
    ]
   },
   {
@@ -3756,8 +3755,8 @@
    "metadata": {},
    "source": [
     "Note that the mean refers to each column of data. \n",
-    "We will generate $n = 1000$ points $X = \\{ x_1, \\ldots, x_N \\}$ from\n",
-    "this distribution, and store them in the $1000 \\times 2$ matrix $\\boldsymbol{X}$.\n",
+    "We will generate $n = 10000$ points $X = \\{ x_1, \\ldots, x_N \\}$ from\n",
+    "this distribution, and store them in the $1000 \\times 2$ matrix $\\boldsymbol{X}$. This is our design matrix where we have forced the covariance and mean values to take specific values.\n",
     "\n",
     "The following Python code aids in setting up the data and writing out the design matrix.\n",
     "Note that the function **multivariate** returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$."
@@ -3765,8 +3764,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -3775,7 +3776,7 @@
     "from IPython.display import display\n",
     "n = 10000\n",
     "mean = (-1, 2)\n",
-    "cov = [[3.0, 2.0], [2.0, 2.5]]\n",
+    "cov = [[4, 2], [2, 2]]\n",
     "X = np.random.multivariate_normal(mean, cov, n)"
    ]
   },
@@ -3821,14 +3822,16 @@
    "source": [
     "When you are done with these steps, print out $\\mu_n$ to verify it is\n",
     "close to $\\mu$ and plot your mean centered data to verify it is\n",
-    "centered at the origin! Compare your code with the functionality from **Scikit-Learn** discussed above.\n",
+    "centered at the origin! \n",
     "The following code elements perform these operations using **pandas** or using our own functionality for doing so. The latter, using **numpy** is rather simple through the **mean()** function."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "df = pd.DataFrame(X)\n",
@@ -3876,21 +3879,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "          0         1\n",
-      "0  2.983691  1.981141\n",
-      "1  1.981141  2.466534\n",
-      "[[2.98369133 1.98114104]\n",
-      " [1.98114104 2.46653391]]\n"
-     ]
-    }
-   ],
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
    "source": [
     "print(df.cov())\n",
     "print(np.cov(X_centered.T))"
@@ -3906,31 +3899,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Centered covariance using own code\n",
-      "[[2.98369133 1.98114104]\n",
-      " [1.98114104 2.46653391]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
    "source": [
     "# extract the relevant columns from the centered design matrix of dim n x 2\n",
     "x = X_centered[:,0]\n",
@@ -3952,7 +3925,7 @@
    "metadata": {},
    "source": [
     "Depending on the number of points $n$, we will get results that are close to the covariance values defined above.\n",
-    "The plot shows how the data are clustered around a line with slope close to one. Is this expected?\n",
+    "The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed. \n",
     "\n",
     "### Diagonalize the sample covariance matrix to obtain the principal components\n",
     "\n",
@@ -3996,25 +3969,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Eigenvalues of Covariance matrix\n",
-      "4.723057254133826\n",
-      "0.7271679895800756\n",
-      "First eigenvector\n",
-      "[0.75147267 0.65976422]\n",
-      "Second eigenvector\n",
-      "[-0.65976422  0.75147267]\n",
-      "Eigenvector of largest eigenvalue\n",
-      "[-0.75147267 -0.65976422]\n"
-     ]
-    }
-   ],
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
    "source": [
     "# diagonalize and obtain eigenvalues, not necessarily sorted\n",
     "EigValues, EigVectors = np.linalg.eig(Cov)\n",
@@ -4053,24 +4012,7 @@
     "vectors $[\\boldsymbol{x}_0,\\boldsymbol{x}_1,\\dots, \\boldsymbol{x}_{p-1}]$ each with dimension\n",
     "$\\boldsymbol{x}\\in {\\mathbb{R}}^{n}$.\n",
     "\n",
-    "We assume also that we have an orthogonal transformation $\\boldsymbol{W}\\in {\\mathbb{R}}^{p\\times p}$.  We define the reconstruction error (which is similar to the mean squared error we have seen before) as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{W},\\boldsymbol{Z}) = \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - \\overline{\\boldsymbol{x}}_i)^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "with $\\overline{\\boldsymbol{x}}_i = \\boldsymbol{W}\\boldsymbol{z}_i$, where $\\boldsymbol{z}_i$ is a row vector with dimension ${\\mathbb{R}}^{n}$ of the matrix\n",
-    "$\\boldsymbol{Z}\\in{\\mathbb{R}}^{p\\times n}$.  When doing PCA we want to reduce this dimensionality. \n",
+    "\n",
     "\n",
     "The PCA theorem states that minimizing the above reconstruction error\n",
     "corresponds to setting $\\boldsymbol{W}=\\boldsymbol{S}$, the orthogonal matrix which\n",
@@ -4084,141 +4026,12 @@
     "\n",
     "## Proof of the PCA Theorem\n",
     "\n",
-    "To show the PCA theorem let us start with the assumption that there is one vector $\\boldsymbol{w}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\\boldsymbol{w}_0$ and $\\boldsymbol{z}_0$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)= \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - z_{i0}\\boldsymbol{w}_0)^2=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2\\boldsymbol{w}_0^T\\boldsymbol{w}_0),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which we can rewrite due to the orthogonality of $\\boldsymbol{w}_i$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Minimizing $J$ with respect to the unknown parameters $z_{0i}$ we obtain that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "z_{i0}=\\boldsymbol{w}_0^T\\boldsymbol{x}_i,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where the vectors on the rhs are known. \n",
-    "\n",
+    "To show the PCA theorem let us start with the assumption that there is one vector $\\boldsymbol{s}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\\boldsymbol{w}_0$ and $\\boldsymbol{z}_0$ as\n",
     "\n",
     "## PCA Proof continued\n",
     "\n",
-    "We have now found the unknown parameters $z_{i0}$. These correspond to the projected coordinates and we can write"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0)= \\frac{1}{p}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - z_{i0}^2)=\\mathrm{const}-\\frac{1}{n}\\sum_i z_{i0}^2.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can show that the variance of the projected coordinates defined by $\\boldsymbol{w}_0^T\\boldsymbol{x}_i$ are given by"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "since the expectation value of"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathbb{E}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\mathbb{E}[z_{i0}]= \\boldsymbol{w}_0^T\\mathbb{E}[\\boldsymbol{x}_i]=0,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where we have used the fact that our data are centered.\n",
     "\n",
-    "Recalling our definition of the covariance as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T=\\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T],\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "we have thus that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2=\\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
+    "\n",
     "We are almost there, we have obtained a relation between minimizing\n",
     "the reconstruction error and the variance and the covariance\n",
     "matrix. Minimizing the error is equivalent to maximizing the variance\n",
@@ -4330,7 +4143,9 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -4375,7 +4190,9 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "W2 = V.T[:, :2]\n",
@@ -4397,7 +4214,9 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "#thereafter we do a PCA with Scikit-learn\n",
@@ -4419,7 +4238,9 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "pca.components_.T[:, 0]"
@@ -4440,33 +4261,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Train set accuracy from Logistic Regression: 0.95\n",
-      "Train set accuracy scaled data: 0.99\n",
-      "Train set accuracy scaled and PCA data: 0.96\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/MortenImac/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  extra_warning_msg=_LOGISTIC_SOLVER_CONVERGENCE_MSG)\n"
-     ]
-    }
-   ],
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -4517,7 +4316,9 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "pca = PCA()\n",
@@ -4538,7 +4339,9 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "pca = PCA(n_components=0.95)\n",
@@ -4583,7 +4386,9 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "metadata": {},
+   "metadata": {
+    "collapsed": false
+   },
    "outputs": [],
    "source": [
     "from sklearn.decomposition import KernelPCA\n",
@@ -4621,25 +4426,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.8"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 4
 }
diff --git a/doc/src/week43/week43.do.txt b/doc/src/week43/week43.do.txt
index eecacf57c..5f63992a0 100644
--- a/doc/src/week43/week43.do.txt
+++ b/doc/src/week43/week43.do.txt
@@ -2827,7 +2827,7 @@ x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \dots & \dots x_{n-1,p-1}\\
 \]
 !et
 * Center the data by subtracting the mean value for each column. This leads to a new matrix $\bm{X}\rightarrow \overline{\bm{X}}$.
-* Compute then the covariance/correlation matrix $\mathbb{E}[\overline{\bm{X}}\overline{\bm{X}}^T]$.
+* Compute then the covariance/correlation matrix $\mathbb{E}[\overline{\bm{X}}^T\overline{\bm{X}}]$.
 * Find the eigenpairs of $\bm{C}$ with eigenvalues $[\lambda_0,\lambda_1,\dots,\lambda_{p-1}]$ and eigenvectors $[\bm{s}_0,\bm{s}_1,\dots,\bm{s}_{p-1}]$.
 * Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.
 * Keep only those $l$ eigenvalues larger than a selected threshold value, discarding thus $p-l$ features since we expect small variations in the data here.
@@ -2997,14 +2997,7 @@ overline symbol. The matrix is defined in terms of the various column
 vectors $[\bm{x}_0,\bm{x}_1,\dots, \bm{x}_{p-1}]$ each with dimension
 $\bm{x}\in {\mathbb{R}}^{n}$.
 
-We assume also that we have an orthogonal transformation $\bm{W}\in {\mathbb{R}}^{p\times p}$.  We define the reconstruction error (which is similar to the mean squared error we have seen before) as
-!bt
-\[
-J(\bm{W},\bm{Z}) = \frac{1}{n}\sum_i (\bm{x}_i - \overline{\bm{x}}_i)^2,
-\]
-!et
-with $\overline{\bm{x}}_i = \bm{W}\bm{z}_i$, where $\bm{z}_i$ is a row vector with dimension ${\mathbb{R}}^{n}$ of the matrix
-$\bm{Z}\in{\mathbb{R}}^{p\times n}$.  When doing PCA we want to reduce this dimensionality. 
+
 
 The PCA theorem states that minimizing the above reconstruction error
 corresponds to setting $\bm{W}=\bm{S}$, the orthogonal matrix which
@@ -3019,63 +3012,12 @@ eigenvectors of the covariance(correlations matrix).
 !split
 ===== Proof of the PCA Theorem  =====
 
-To show the PCA theorem let us start with the assumption that there is one vector $\bm{w}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\bm{w}_0$ and $\bm{z}_0$ as
-!bt
-\[
-J(\bm{w}_0,\bm{z}_0)= \frac{1}{n}\sum_i (\bm{x}_i - z_{i0}\bm{w}_0)^2=\frac{1}{n}\sum_i (\bm{x}_i^T\bm{x}_i - 2z_{i0}\bm{w}_0^T\bm{x}_i+z_{i0}^2\bm{w}_0^T\bm{w}_0),
-\]
-!et
-which we can rewrite due to the orthogonality of $\bm{w}_i$ as
-!bt
-\[
-J(\bm{w}_0,\bm{z}_0)=\frac{1}{n}\sum_i (\bm{x}_i^T\bm{x}_i - 2z_{i0}\bm{w}_0^T\bm{x}_i+z_{i0}^2).
-\]
-!et
-Minimizing $J$ with respect to the unknown parameters $z_{0i}$ we obtain that
-!bt
-\[
-z_{i0}=\bm{w}_0^T\bm{x}_i,
-\]
-!et
-where the vectors on the rhs are known. 
-
+To show the PCA theorem let us start with the assumption that there is one vector $\bm{s}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\bm{w}_0$ and $\bm{z}_0$ as
 
 !split
 ===== PCA Proof continued =====
 
-We have now found the unknown parameters $z_{i0}$. These correspond to the projected coordinates and we can write
-!bt
-\[
-J(\bm{w}_0)= \frac{1}{p}\sum_i (\bm{x}_i^T\bm{x}_i - z_{i0}^2)=\mathrm{const}-\frac{1}{n}\sum_i z_{i0}^2.
-\]
-!et
 
-We can show that the variance of the projected coordinates defined by $\bm{w}_0^T\bm{x}_i$ are given by
-!bt
-\[
-\mathrm{var}[\bm{w}_0^T\bm{x}_i] = \frac{1}{n}\sum_i z_{i0}^2,
-\]
-!et
-since the expectation value of
-!bt
-\[
-\mathbb{E}[\bm{w}_0^T\bm{x}_i] = \mathbb{E}[z_{i0}]= \bm{w}_0^T\mathbb{E}[\bm{x}_i]=0,
-\]
-!et
-where we have used the fact that our data are centered.
-
-Recalling our definition of the covariance as 
-!bt
-\[
-\bm{C}[\bm{x}] = \frac{1}{n}\bm{X}\bm{X}^T=\mathbb{E}[\bm{X}\bm{X}^T],
-\]
-!et
-we have thus that
-!bt
-\[
-\mathrm{var}[\bm{w}_0^T\bm{x}_i] = \frac{1}{n}\sum_i z_{i0}^2=\bm{w}_0^T\bm{C}[\bm{x}]\bm{w}_0.
-\]
-!et
 
 We are almost there, we have obtained a relation between minimizing
 the reconstruction error and the variance and the covariance