From 9d2bcb57ab589b727f0d341160cbe95a57335f3c Mon Sep 17 00:00:00 2001
From: mhjensen <morten.hjorth-jensen@fys.uio.no>
Date: Wed, 22 Nov 2017 14:45:03 +0100
Subject: [PATCH] Update on neural networks

---
 doc/pub/NeuralNet/html/._NeuralNet-bs000.html |  14 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs001.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs002.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs003.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs004.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs005.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs006.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs007.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs008.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs009.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs010.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs011.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs012.html |  12 +-
 doc/pub/NeuralNet/html/._NeuralNet-bs013.html |  12 +-
 doc/pub/NeuralNet/html/NeuralNet-bs.html      | 393 ++++++++++--
 doc/pub/NeuralNet/html/NeuralNet-reveal.html  |   7 +-
 .../NeuralNet/html/NeuralNet-solarized.html   |   8 +-
 doc/pub/NeuralNet/html/NeuralNet.html         |   6 +-
 doc/pub/NeuralNet/ipynb/NeuralNet.ipynb       |   7 +-
 .../ipynb/ipynb-NeuralNet-src.tar.gz          | Bin 215 -> 211 bytes
 .../pdf/NeuralNet-beamer-handouts2x3.pdf      | Bin 185697 -> 185707 bytes
 doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf    | Bin 184164 -> 184164 bytes
 doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf    | Bin 252797 -> 252799 bytes
 .../Regression/html/._Regression-bs000.html   |  14 +-
 .../Regression/html/._Regression-bs001.html   |  12 +-
 .../Regression/html/._Regression-bs002.html   |  12 +-
 .../Regression/html/._Regression-bs003.html   |  12 +-
 .../Regression/html/._Regression-bs004.html   |  12 +-
 .../Regression/html/._Regression-bs005.html   |  12 +-
 .../Regression/html/._Regression-bs006.html   |  12 +-
 .../Regression/html/._Regression-bs007.html   |  12 +-
 .../Regression/html/._Regression-bs008.html   |  12 +-
 .../Regression/html/._Regression-bs009.html   |  12 +-
 .../Regression/html/._Regression-bs010.html   |  12 +-
 .../Regression/html/._Regression-bs011.html   |  12 +-
 .../Regression/html/._Regression-bs012.html   |  12 +-
 .../Regression/html/._Regression-bs013.html   |  12 +-
 .../Regression/html/._Regression-bs014.html   |  12 +-
 .../Regression/html/._Regression-bs015.html   |  12 +-
 .../Regression/html/._Regression-bs016.html   |  12 +-
 .../Regression/html/._Regression-bs017.html   |  12 +-
 .../Regression/html/._Regression-bs018.html   |  12 +-
 doc/pub/Regression/html/Regression-bs.html    | 568 ++----------------
 .../Regression/html/Regression-reveal.html    |   2 +-
 .../Regression/html/Regression-solarized.html |   5 +-
 doc/pub/Regression/html/Regression.html       |   5 +-
 .../ipynb/ipynb-Regression-src.tar.gz         | Bin 210 -> 212 bytes
 .../pdf/Regression-beamer-handouts2x3.pdf     | Bin 197535 -> 197535 bytes
 doc/pub/Regression/pdf/Regression-beamer.pdf  | Bin 185221 -> 185221 bytes
 doc/pub/Regression/pdf/Regression-minted.pdf  | Bin 224600 -> 224600 bytes
 doc/src/NeuralNet/make.sh                     |   4 +-
 doc/src/Regression/make.sh                    |   4 +-
 52 files changed, 617 insertions(+), 792 deletions(-)

diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html
index 9deb68ceb..cfffb676d 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs000.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs000.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -137,7 +137,7 @@ 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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -168,8 +168,8 @@ MathJax.Hub.Config({
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html
index 70078cb9c..80a1f940d 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs001.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs001.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -156,8 +156,8 @@ found applications in a wide variety of other areas, including bioinformatics, e
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html
index 342fc1408..bca771bb8 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs002.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs002.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -163,8 +163,8 @@ Some of the most common tasks are:
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html
index 5bf0c6769..7126463dc 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs003.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs003.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -167,8 +167,8 @@ a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neuron
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html
index f135f4674..2d4cbb22b 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs004.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs004.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -154,8 +154,8 @@ is associated with a weight variable.
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs005.html b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html
index cf35cda0d..2377ef139 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs005.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs005.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -169,8 +169,8 @@ which gathers all the local data and produces the outputs. They have wide applic
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html
index 842a54015..bbd2ff0fd 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs006.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs006.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -153,8 +153,8 @@ sentences, making recurrent NNs especially well-suited for handwriting and speec
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs007.html b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html
index 0650c1789..6fc8d5f9a 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs007.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs007.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -157,8 +157,8 @@ of how a fully-connected FFNN works, and how it can be used to interpolate data
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs008.html b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html
index 83cfe1dac..0145387c7 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs008.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs008.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -156,8 +156,8 @@ which means that each neuron receives a weighted sum of the outputs of <em>all</
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs009.html b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html
index 5bfc977c7..34a1eebc1 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs009.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs009.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -67,8 +67,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -177,8 +177,8 @@ the values of the subsequent layer can be calculated and so forth until the outp
 
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-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
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index 7ce27473f..adb0065c3 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs010.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs010.html
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-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
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diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html
index c3647be3b..3523b4833 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs011.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs011.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
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 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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@@ -159,8 +159,8 @@ which illustrates a basic property of MLPs: The only independent variables are t
 
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-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
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index 4ef54b9e6..8a028540a 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs012.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs012.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Elements of machine learning</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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@@ -172,8 +172,8 @@ $$
 
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-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html
index 649680dd1..a1e542a34 100644
--- a/doc/pub/NeuralNet/html/._NeuralNet-bs013.html
+++ b/doc/pub/NeuralNet/html/._NeuralNet-bs013.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
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 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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@@ -192,8 +192,8 @@ and vector additions that are used as input to the activation functions. For eac
 
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-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
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 <footer>
diff --git a/doc/pub/NeuralNet/html/NeuralNet-bs.html b/doc/pub/NeuralNet/html/NeuralNet-bs.html
index 9deb68ceb..c286d1928 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-bs.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-bs.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
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 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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+<script type="text/javascript" async
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 </script>
 
 
@@ -90,19 +90,19 @@ 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="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Neural network types</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Mathematical model</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Mathematical model</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
-     <!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;"><b>Neural network types</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;"><b>Mathematical model</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;"><b>Mathematical model</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation</a></li>
 
         </ul>
       </li>
@@ -115,7 +115,6 @@ MathJax.Hub.Config({
 
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-<a name="part0000"></a>
 <!-- ------------------- main content ---------------------- -->
 
 
@@ -137,39 +136,349 @@ 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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
-
-
-<p><a href="._NeuralNet-bs001.html" class="btn btn-primary btn-lg">Read &raquo;</a></p>
-
-
+<!-- potential-jumbotron-button -->
 </div> <!-- end jumbotron -->
 
+<!-- !split -->
+
+<h2 id="___sec0" class="anchor">What is Machine Learning? </h2>
+
 <p>
-<!-- navigation buttons at the bottom of the page -->
-<ul class="pagination">
-  <li class="active"><a href="._NeuralNet-bs000.html">1</a></li>
-  <li><a href="._NeuralNet-bs001.html">2</a></li>
-  <li><a href="._NeuralNet-bs002.html">3</a></li>
-  <li><a href="._NeuralNet-bs003.html">4</a></li>
-  <li><a href="._NeuralNet-bs004.html">5</a></li>
-  <li><a href="._NeuralNet-bs005.html">6</a></li>
-  <li><a href="._NeuralNet-bs006.html">7</a></li>
-  <li><a href="._NeuralNet-bs007.html">8</a></li>
-  <li><a href="._NeuralNet-bs008.html">9</a></li>
-  <li><a href="._NeuralNet-bs009.html">10</a></li>
-  <li><a href="">...</a></li>
-  <li><a href="._NeuralNet-bs013.html">14</a></li>
-  <li><a href="._NeuralNet-bs001.html">&raquo;</a></li>
+Machine learning is the science of giving computers the ability to learn without being explicitly programmed. 
+The idea is that there exist generic algorithms which can be used to find patterns in a broad class of data sets without 
+having to write code specifically for each problem. The algorithm will build its own logic based on the data.
+
+<p>
+Machine learning is a subfield of computer science, and is closely related to computational statistics. 
+It evolved from the study of pattern recognition in artificial intelligence (AI) research, and has made contributions to
+AI tasks like computer vision, natural language processing 
+and speech recognition. It has also, especially in later years, 
+found applications in a wide variety of other areas, including bioinformatics, economy, physics, finance and marketing.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec1" class="anchor">Types of Machine Learning </h2>
+
+<p>
+The approaches to machine learning are many, but are often split into two main categories. 
+In <em>supervised learning</em> we know the answer to a problem,
+and let the computer deduce the logic behind it. On the other hand, <em>unsupervised learning</em>
+is a method for finding patterns and relationship in data sets without any prior knowledge of the system.
+Some authours also operate with a third category, namely <em>reinforcement learning</em>. This is a paradigm 
+of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, 
+solely from rewards and punishment.
+
+<p>
+Another way to categorize machine learning tasks is to consider the desired output of a system.
+Some of the most common tasks are:
+
+<ul>
+  <li> Classification: Outputs are divided into two or more classes. The goal is to   produce a model that assigns inputs into one of these classes. An example is to identify  digits based on pictures of hand-written ones. Classification is typically supervised learning.</li>
+  <li> Regression: Finding a functional relationship between an input data set and a reference data set.   The goal is to construct a function that maps input data to continuous output values.</li>
+  <li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand.  It is thus a form of unsupervised learning.</li>
 </ul>
+
+<!-- !split -->
+
+<h2 id="___sec2" class="anchor">Artificial neurons  </h2>
+The field of artificial neural networks has a long history of development, and is closely connected with 
+the advancement of computer science and computers in general. A model of artificial neurons 
+was first developed by McCulloch and Pitts in 1943  to study signal processing in the brain and 
+has later been refined by others. The general idea is to mimic neural networks in the human brain, which
+is composed of billions of neurons that communicate with each other by sending electrical signals. 
+Each neuron accumulates its incoming signals, 
+which must exceed an activation threshold to yield an output. If the threshold is not overcome, the neuron
+remains inactive, i.e. has zero output.
+
+<p>
+This behaviour has inspired a simple mathematical model for an artificial neuron.
+
+$$
+\begin{equation}
+ y = f\left(\sum_{i=1}^n w_ix_i\right) = f(u)
+\label{artificialNeuron}
+\end{equation}
+$$
+
+Here, the output \( y \) of the neuron is the value of its activation function, which have as input
+a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neurons.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec3" class="anchor">Neural network types </h2>
+
+<p>
+An artificial neural network (NN), is a computational model that consists of layers of connected neurons, or <em>nodes</em>. 
+It is supposed to mimic a biological nervous system by letting each neuron interact with other neurons
+by sending signals in the form of mathematical functions between layers. 
+A wide variety of different NNs have
+been developed, but most of them consist of an input layer, an output layer and eventual layers in-between, called
+<em>hidden layers</em>. All layers can contain an arbitrary number of nodes, and each connection between two nodes
+is associated with a weight variable.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec4" class="anchor">Feed-forward neural networks </h2>
+The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, 
+the information moves in only one direction: forward through the layers.
+
+<p>
+Nodes are represented by circles, while the arrows display the connections between the nodes, including the 
+direction of information flow. Additionally, each arrow corresponds to a weight variable, not displayed here. 
+We observe that each node in a layer is connected to <em>all</em> nodes in the subsequent layer, 
+making this a so-called <em>fully-connected</em> FFNN.
+
+<p>
+A different variant of FFNNs are <em>convolutional neural networks</em> (CNNs), which have a connectivity pattern
+inspired by the animal visual cortex. Individual neurons in the visual cortex only respond to stimuli from
+small sub-regions of the visual field, called a receptive field. This makes the neurons well-suited to exploit the strong
+spatially local correlation present in natural images. The response of each neuron can be approximated mathematically 
+as a convolution operation.
+
+<p>
+CNNs emulate the behaviour of neurons in the visual cortex by enforcing a <em>local</em> connectivity pattern
+between nodes of adjacent layers: Each node
+in a convolutional layer is connected only to a subset of the nodes in the previous layer, 
+in contrast to the fully-connected FFNN.
+Often, CNNs 
+consist of several convolutional layers that learn local features of the input, with a fully-connected layer at the end, 
+which gathers all the local data and produces the outputs. They have wide applications in image and video recognition
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec5" class="anchor">Recurrent neural networks </h2>
+
+<p>
+So far we have only mentioned NNs where information flows in one direction: forward. <em>Recurrent neural networks</em> on
+the other hand, have connections between nodes that form directed <em>cycles</em>. This creates a form of 
+internal memory which are able to capture information on what has been calculated before; the output is dependent 
+on the previous computations. Recurrent NNs make use of sequential information by performing the same task for 
+every element in a sequence, where each element depends on previous elements. An example of such information is 
+sentences, making recurrent NNs especially well-suited for handwriting and speech recognition.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec6" class="anchor">Other types of networks </h2>
+
+<p>
+There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation
+in multidimensional space is the radial basis function (RBF) network. RBFs are typically made up of three layers: 
+an input layer, a hidden layer with non-linear radial symmetric activation functions and a linear output layer (''linear'' here
+means that each node in the output layer has a linear activation function). The layers are normally fully-connected and 
+there are no cycles, thus RBFs can be viewed as a type of fully-connected FFNN. They are however usually treated as
+a separate type of NN due the unusual activation functions.
+
+<p>
+Other types of NNs could also be mentioned, but are outside the scope of this work. We will now move on to a detailed description
+of how a fully-connected FFNN works, and how it can be used to interpolate data sets.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec7" class="anchor">Mathematical model  </h2>
+
+$$
+\begin{equation}
+ y = f\left(\sum_{i=1}^n w_ix_i + b_i\right) = f(u)
+\label{artificialNeuron2}
+\end{equation}
+$$
+
+In an FFNN of such neurons, the <em>inputs</em> \( x_i \)
+are the <em>outputs</em> of the neurons in the preceding layer. Furthermore, a MLP is fully-connected, 
+which means that each neuron receives a weighted sum of the outputs of <em>all</em> neurons in the previous layer.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec8" class="anchor">Mathematical model  </h2>
+
+<p>
+First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \),
+
+$$
+\begin{equation}
+ u_i^1 = \sum_{j=1}^2 w_{ij}^1 x_j  + b_i^1 
+\label{_auto1}
+\end{equation}
+$$
+
+This value is the argument to the activation function \( f_1 \) of each neuron \( i \),
+producing the output \( y_i^1 \) of all neurons in layer 1,
+
+$$
+\begin{equation}
+ y_i^1 = f_1(u_i^1) = f_1\left(\sum_{j=1}^2 w_{ij}^1 x_j  + b_i^1\right)
+\label{outputLayer1}
+\end{equation}
+$$
+
+where we assume that all nodes in the same layer have identical activation functions, hence the notation \( f_l \)
+
+$$
+\begin{equation}
+ y_i^l = f_l(u_i^l) = f_l\left(\sum_{j=1}^{N_{l-1}} w_{ij}^l y_j^{l-1} + b_i^l\right)
+\label{generalLayer}
+\end{equation}
+$$
+
+where \( N_l \) is the number of nodes in layer \( l \). When the output of all the nodes in the first hidden layer are computed,
+the values of the subsequent layer can be calculated and so forth until the output is obtained.
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec9" class="anchor">Mathematical model  </h2>
+
+<p>
+The output of neuron \( i \) in layer 2 is thus,
+
+$$
+\begin{align}
+ y_i^2 &= f_2\left(\sum_{j=1}^3 w_{ij}^2 y_j^1 + b_i^2\right) 
+\label{_auto2}\\
+ &= f_2\left[\sum_{j=1}^3 w_{ij}^2f_1\left(\sum_{k=1}^2 w_{jk}^1 x_k + b_j^1\right) + b_i^2\right]
+\label{outputLayer2}
+\end{align}
+$$
+
+where we have substituted \( y_m^1 \) with. Finally, the NN output yields,
+
+$$
+\begin{align}
+ y_1^3 &= f_3\left(\sum_{j=1}^3 w_{1m}^3 y_j^2 + b_1^3\right) 
+\label{_auto3}\\
+ &= f_3\left[\sum_{j=1}^3 w_{1j}^3 f_2\left(\sum_{k=1}^3 w_{jk}^2 f_1\left(\sum_{m=1}^2 w_{km}^1 x_m + b_k^1\right) + b_j^2\right)
+  + b_1^3\right]
+\label{_auto4}
+\end{align}
+$$
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec10" class="anchor">Mathematical model  </h2>
+
+<p>
+We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form
+is,
+$$
+\begin{align}
+&y^{l+1}_1\! = \!f_{l+1}\!\left[\!\sum_{j=1}^{N_l}\! w_{1j}^3 f_l\!\left(\!\sum_{k=1}^{N_{l-1}}\! w_{jk}^2 f_{l-1}\!\left(\!
+ \dots \!f_1\!\left(\!\sum_{n=1}^{N_0} \!w_{mn}^1 x_n\! + \!b_m^1\!\right)
+ \!\dots \!\right) \!+ \!b_k^2\!\right)
+ \!+ \!b_1^3\!\right] &&
+\label{completeNN}
+\end{align}
+$$
+
+which illustrates a basic property of MLPs: The only independent variables are the input values \( x_n \).
+
+<p>
+<!-- !split -->
+
+<h2 id="___sec11" class="anchor">Mathematical model  </h2>
+
+<p>
+This confirms that an MLP,
+despite its quite convoluted mathematical form, is nothing more than an analytic function, specifically a 
+mapping of real-valued vectors \( \vec{x} \in \mathbb{R}^n \rightarrow \vec{y} \in \mathbb{R}^m \). 
+In our example, \( n=2 \) and \( m=1 \). Consequentially, 
+the number of input and output values of the function we want to fit must be equal to the number of inputs and outputs of our MLP.
+
+<p>
+Furthermore, the flexibility and universality of a MLP can be illustrated by realizing that 
+the expression  is essentially a nested sum of scaled activation functions of the form
+
+$$
+\begin{equation}
+ h(x) = c_1 f(c_2 x + c_3) + c_4
+\label{_auto5}
+\end{equation}
+$$
+
+where the parameters \( c_i \) are weights and biases. By adjusting these parameters, the activation functions
+can be shifted up and down or left and right, change slope or be rescaled 
+which is the key to the flexibility of a NN. 
+
+$$
+\begin{equation}
+ f_o = f(u_o) = u_o
+\label{outputActivation}
+\end{equation}
+$$
+
+<p>
+<!-- !split -->
+
+<h3 id="___sec12" class="anchor">Matrix-vector notation </h3>
+
+We can introduce a more convenient notation for the activations in a NN.
+
+<p>
+Additionally, we can represent the biases and activations
+as layer-wise column vectors \( \vec{b}_l \) and \( \vec{y}_l \), so that the \( i \)-th element of each vector 
+is the bias \( b_i^l \) and activation \( y_i^l \) of node \( i \) in layer \( l \) respectively.
+
+<p>
+We have that \( \mathrm{W}_l \) is a \( N_{l-1} \times N_l \) matrix, while \( \vec{b}_l \) and \( \vec{y}_l \) are \( N_l \times 1 \) column vectors. 
+With this notation, the sum in  becomes a matrix-vector multiplication, and we can write
+the equation for the activations of hidden layer 2 in
+
+$$
+\begin{equation}
+ \vec{y}_2 = f_2(\mathrm{W}_2 \vec{y}_{1} + \vec{b}_{2}) = 
+ f_2\left(\left[\begin{array}{ccc}
+    w^2_{11} &w^2_{12} &w^2_{13} \\
+    w^2_{21} &w^2_{22} &w^2_{23} \\
+    w^2_{31} &w^2_{32} &w^2_{33} \\
+    \end{array} \right] \cdot
+    \left[\begin{array}{c}
+           y^1_1 \\
+           y^1_2 \\
+           y^1_3 \\
+          \end{array}\right] + 
+    \left[\begin{array}{c}
+           b^2_1 \\
+           b^2_2 \\
+           b^2_3 \\
+          \end{array}\right]\right)
+\label{_auto6}
+\end{equation}
+$$
+
+and we see that the activation of node \( i \) in layer 2 is
+
+$$
+\begin{equation}
+ y^2_i = f_2\Bigr(w^2_{i1}y^1_1 + w^2_{i2}y^1_2 + w^2_{i3}y^1_3 + b^2_i\Bigr) = 
+ f_2\left(\sum_{j=1}^3 w^2_{ij} y_j^1 + b^2_i\right)
+\label{_auto7}
+\end{equation}
+$$
+
+which is in accordance with. Note that
+This is not just a convenient and compact notation, but also 
+a useful and intuitive way to think about MLPs: The output is calculated by a series of matrix-vector multiplications
+and vector additions that are used as input to the activation functions. For each operation 
+\( \mathrm{W}_l \vec{y}_{l-1} \) we move forward one layer.
+
+<p>
+
 <!-- ------------------- end of main content --------------- -->
 
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diff --git a/doc/pub/NeuralNet/html/NeuralNet-reveal.html b/doc/pub/NeuralNet/html/NeuralNet-reveal.html
index c5784ccd4..6e4dcb45b 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-reveal.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-reveal.html
@@ -1,3 +1,4 @@
+\
 <!DOCTYPE html>
 
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
@@ -116,8 +117,8 @@ MathJax.Hub.Config({
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 </script>
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- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -147,7 +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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 
diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html
index f64ff50ad..fa48edec1 100644
--- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html
+++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html
@@ -15,7 +15,7 @@ Automatically generated HTML file from DocOnce source
 <script src="https://cdn.rawgit.com/hplgit/doconce/master/bundled/html_styles/style_solarized_box/js/highlight.pack.js"></script>
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-<link href="http://thomasf.github.io/solarized-css/solarized-light.min.css" rel="stylesheet">
+<link href="https://thomasf.github.io/solarized-css/solarized-light.min.css" rel="stylesheet">
 <style type="text/css">
 h1 {color: #b58900;}  /* yellow */
 /* h1 {color: #cb4b16;}  orange */
@@ -61,8 +61,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -88,7 +88,7 @@ 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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
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index 98b14ca0b..04804c9c2 100644
--- a/doc/pub/NeuralNet/html/NeuralNet.html
+++ b/doc/pub/NeuralNet/html/NeuralNet.html
@@ -66,8 +66,8 @@ MathJax.Hub.Config({
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+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -93,7 +93,7 @@ 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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
index 7bffb3c01..3b424cdc9 100644
--- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
+++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
@@ -7,9 +7,10 @@
     "<!-- dom:TITLE: Data Analysis and Machine Learning: Elements of machine learning -->\n",
     "# Data Analysis and Machine Learning: Elements of machine learning\n",
     "<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
-    "<!-- Author: --> **Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
+    "<!-- 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: **Nov 2, 2017**\n",
+    "Date: **Nov 22, 2017**\n",
     "\n",
     "Copyright 1999-2017, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
@@ -485,5 +486,5 @@
  ],
  "metadata": {},
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 2
 }
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diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf
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diff --git a/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf b/doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf
index b7081b0c24133b604852a26ee9eed7adc41856d9..b621586f761b3c297ffaef520b58f0a520c8dd1e 100644
GIT binary patch
delta 2529
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diff --git a/doc/pub/Regression/html/._Regression-bs000.html b/doc/pub/Regression/html/._Regression-bs000.html
index 618248fe1..a83d203fa 100644
--- a/doc/pub/Regression/html/._Regression-bs000.html
+++ b/doc/pub/Regression/html/._Regression-bs000.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -168,7 +168,7 @@ 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>Nov 2, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -199,8 +199,8 @@ MathJax.Hub.Config({
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs001.html b/doc/pub/Regression/html/._Regression-bs001.html
index 12e540f11..c81ba9755 100644
--- a/doc/pub/Regression/html/._Regression-bs001.html
+++ b/doc/pub/Regression/html/._Regression-bs001.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -196,8 +196,8 @@ A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \)
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs002.html b/doc/pub/Regression/html/._Regression-bs002.html
index 1089f3fad..10dc65f7a 100644
--- a/doc/pub/Regression/html/._Regression-bs002.html
+++ b/doc/pub/Regression/html/._Regression-bs002.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -193,8 +193,8 @@ where \( \epsilon_i \) is the error in our approximation.
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs003.html b/doc/pub/Regression/html/._Regression-bs003.html
index 4e884bbec..5e6306041 100644
--- a/doc/pub/Regression/html/._Regression-bs003.html
+++ b/doc/pub/Regression/html/._Regression-bs003.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -193,8 +193,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs004.html b/doc/pub/Regression/html/._Regression-bs004.html
index 6e8d158aa..9973fbb92 100644
--- a/doc/pub/Regression/html/._Regression-bs004.html
+++ b/doc/pub/Regression/html/._Regression-bs004.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -213,8 +213,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs005.html b/doc/pub/Regression/html/._Regression-bs005.html
index 00e069e82..24b7bcd7b 100644
--- a/doc/pub/Regression/html/._Regression-bs005.html
+++ b/doc/pub/Regression/html/._Regression-bs005.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -198,8 +198,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs006.html b/doc/pub/Regression/html/._Regression-bs006.html
index ac4176515..69895fadb 100644
--- a/doc/pub/Regression/html/._Regression-bs006.html
+++ b/doc/pub/Regression/html/._Regression-bs006.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -204,8 +204,8 @@ The left-hand side of this equation forms know. Our error vector \( \hat{\epsilo
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs007.html b/doc/pub/Regression/html/._Regression-bs007.html
index 6af425469..f9afa4984 100644
--- a/doc/pub/Regression/html/._Regression-bs007.html
+++ b/doc/pub/Regression/html/._Regression-bs007.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -199,8 +199,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs008.html b/doc/pub/Regression/html/._Regression-bs008.html
index de8ef0d4f..96f32fd16 100644
--- a/doc/pub/Regression/html/._Regression-bs008.html
+++ b/doc/pub/Regression/html/._Regression-bs008.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -202,8 +202,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs009.html b/doc/pub/Regression/html/._Regression-bs009.html
index ba39d1674..b6cd7c750 100644
--- a/doc/pub/Regression/html/._Regression-bs009.html
+++ b/doc/pub/Regression/html/._Regression-bs009.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -216,8 +216,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs010.html b/doc/pub/Regression/html/._Regression-bs010.html
index 0358670d0..cbaf161da 100644
--- a/doc/pub/Regression/html/._Regression-bs010.html
+++ b/doc/pub/Regression/html/._Regression-bs010.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -203,8 +203,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs011.html b/doc/pub/Regression/html/._Regression-bs011.html
index 2071ec61d..1caf7ed62 100644
--- a/doc/pub/Regression/html/._Regression-bs011.html
+++ b/doc/pub/Regression/html/._Regression-bs011.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -204,8 +204,8 @@ meaning that the solution for \( \hat{\beta} \) is the one which minimizes the r
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs012.html b/doc/pub/Regression/html/._Regression-bs012.html
index 8309bbc13..1ec83a2b5 100644
--- a/doc/pub/Regression/html/._Regression-bs012.html
+++ b/doc/pub/Regression/html/._Regression-bs012.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -198,8 +198,8 @@ where the matrix \( \hat{\Sigma} \) is a diagonal matrix with \( \sigma_i \) as
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs013.html b/doc/pub/Regression/html/._Regression-bs013.html
index 7d35cf836..77c242f3b 100644
--- a/doc/pub/Regression/html/._Regression-bs013.html
+++ b/doc/pub/Regression/html/._Regression-bs013.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -202,8 +202,8 @@ where we have defined the matrix \( \hat{A} =\hat{X}/\hat{\Sigma} \) with matrix
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs014.html b/doc/pub/Regression/html/._Regression-bs014.html
index 8398bdffa..ac088ce9d 100644
--- a/doc/pub/Regression/html/._Regression-bs014.html
+++ b/doc/pub/Regression/html/._Regression-bs014.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -199,8 +199,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs015.html b/doc/pub/Regression/html/._Regression-bs015.html
index 9a9b947e1..ad3973d74 100644
--- a/doc/pub/Regression/html/._Regression-bs015.html
+++ b/doc/pub/Regression/html/._Regression-bs015.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -203,8 +203,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs016.html b/doc/pub/Regression/html/._Regression-bs016.html
index 741ec340c..3537d2b01 100644
--- a/doc/pub/Regression/html/._Regression-bs016.html
+++ b/doc/pub/Regression/html/._Regression-bs016.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -195,8 +195,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs017.html b/doc/pub/Regression/html/._Regression-bs017.html
index f66f408e2..5e6198107 100644
--- a/doc/pub/Regression/html/._Regression-bs017.html
+++ b/doc/pub/Regression/html/._Regression-bs017.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -215,8 +215,8 @@ The LSM suffers often from both being underdetermined and overdetermined in the
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
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 <footer>
diff --git a/doc/pub/Regression/html/._Regression-bs018.html b/doc/pub/Regression/html/._Regression-bs018.html
index 51bbfd9b7..ad3eed9ae 100644
--- a/doc/pub/Regression/html/._Regression-bs018.html
+++ b/doc/pub/Regression/html/._Regression-bs018.html
@@ -11,9 +11,9 @@ Automatically generated HTML file from DocOnce source
 <title>Data Analysis and Machine Learning: Linear Regression and more Advanced Regression Analysis</title>
 
 <!-- Bootstrap style: bootstrap -->
-<link href="http://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
 <!-- not necessary
-<link href="http://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
 -->
 
 <style type="text/css">
@@ -93,8 +93,8 @@ MathJax.Hub.Config({
   }
 });
 </script>
-<script type="text/javascript"
- src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
 </script>
 
 
@@ -183,8 +183,8 @@ $$
 
 </div>  <!-- end container -->
 <!-- include javascript, jQuery *first* -->
-<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
-<script src="http://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
+<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
+<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
 
 <!-- Bootstrap footer
 <footer>
diff --git a/doc/pub/Regression/html/Regression-bs.html b/doc/pub/Regression/html/Regression-bs.html
index 57bafe39d..a83d203fa 100644
--- a/doc/pub/Regression/html/Regression-bs.html
+++ b/doc/pub/Regression/html/Regression-bs.html
@@ -46,8 +46,7 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                '___sec2'),
-              ('Rewriting the fitting procedure as a linear algebra problem, '
-               'follows',
+              ('Rewriting the fitting procedure as a linear algebra problem, follows',
                2,
                None,
                '___sec3'),
@@ -89,7 +88,7 @@ end of tocinfo -->
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
   TeX: {
-     equationNumbers: {  autoNumber: "AMS"  },
+     equationNumbers: {  autoNumber: "none"  },
      extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
   }
 });
@@ -117,24 +116,24 @@ 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%;">Regression analysis, overarching aims</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;">General linear models</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem, follows</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">Optimizing our parameters</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">Optimizing our parameters, more details</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec13" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;">The singular value decompostion</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs001.html#___sec0" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs002.html#___sec1" style="font-size: 80%;">General linear models</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs003.html#___sec2" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs004.html#___sec3" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem, follows</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs005.html#___sec4" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs006.html#___sec5" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs007.html#___sec6" style="font-size: 80%;">Optimizing our parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs008.html#___sec7" style="font-size: 80%;">Optimizing our parameters, more details</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs009.html#___sec8" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs010.html#___sec9" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs011.html#___sec10" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs012.html#___sec11" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs013.html#___sec12" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs014.html#___sec13" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs015.html#___sec14" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs016.html#___sec15" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs017.html#___sec16" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
+     <!-- navigation toc: --> <li><a href="._Regression-bs018.html#___sec17" style="font-size: 80%;">The singular value decompostion</a></li>
 
         </ul>
       </li>
@@ -147,6 +146,7 @@ MathJax.Hub.Config({
 
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
+<a name="part0000"></a>
 <!-- ------------------- main content ---------------------- -->
 
 
@@ -168,517 +168,33 @@ 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>Nov 21, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
-<!-- potential-jumbotron-button -->
+
+
+<p><a href="._Regression-bs001.html" class="btn btn-primary btn-lg">Read &raquo;</a></p>
+
+
 </div> <!-- end jumbotron -->
 
-<!-- !split -->
-
-<h2 id="___sec0" class="anchor">Regression analysis, overarching aims  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
 <p>
-Regression modeling deals with the description of  the sampling distribution of a given random variable \( y \) varies as function of another variable or a set of such variables \( \hat{x} =[x_0, x_1,\dots, x_p]^T \). 
-The first variable is called the <b>dependent</b>, the <b>outcome</b> or the <b>response</b> variable while the set of variables \( \hat{x} \) is called the independent variable, or the predictor variable or the explanatory variable.
-
-<p>
-A regression model aims at finding a likelihood function \( p(y\vert \hat{x}) \), that is the conditional distribution for \( y \) with a given \( \hat{x} \). The estimation of  \( p(y\vert \hat{x}) \) is made using a data set with 
-
-<ul>
-<li> \( n \) cases \( i = 0, 1, 2, \dots, n-1 \)</li> 
-<li> Response (dependent or outcome) variable \( y_i \) with \( i = 0, 1, 2, \dots, n-1 \)</li> 
-<li> \( p \) Explanatory (independent or predictor) variables \( \hat{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip}] \) with \( i = 0, 1, 2, \dots, n-1 \)</li>   
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+  <li class="active"><a href="._Regression-bs000.html">1</a></li>
+  <li><a href="._Regression-bs001.html">2</a></li>
+  <li><a href="._Regression-bs002.html">3</a></li>
+  <li><a href="._Regression-bs003.html">4</a></li>
+  <li><a href="._Regression-bs004.html">5</a></li>
+  <li><a href="._Regression-bs005.html">6</a></li>
+  <li><a href="._Regression-bs006.html">7</a></li>
+  <li><a href="._Regression-bs007.html">8</a></li>
+  <li><a href="._Regression-bs008.html">9</a></li>
+  <li><a href="._Regression-bs009.html">10</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Regression-bs018.html">19</a></li>
+  <li><a href="._Regression-bs001.html">&raquo;</a></li>
 </ul>
-
- The goal of the regression analysis is to extract/exploit relationship between \( y_i \) and \( \hat{x}_i \) in or to infer causal dependencies, approximations to the likelihood functions, functional relationships and to make predictions .
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec1" class="anchor">General linear models  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-Before we proceed let us study a case from linear algebra where we aim at fitting a set of data \( \hat{y}=[y_0,y_1,\dots,y_{n-1}] \). We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables \( \hat{x}=[x_0,x_1,\dots,x_{n-1}] \), that is \( y_i = y(x_i) \) with \( i=0,1,2,\dots,n-1 \). The variables \( x_i \) could represent physical quantities like time, temperature, position etc. We assume that \( y(x) \) is a smooth function.
-
-<p>
-Since obtaining these data points may not be trivial, we want to use these data to fit a function which can allow us to make predictions for values of \( y \) which are not in the present set. The perhaps simplest approach is to assume we can parametrize our function in terms of a polynomial of degree \( n-1 \) with \( n \) points, that is
-$$
-y=y(x) \rightarrow y(x_i)=\tilde{y}_i+\epsilon_i=\sum_{j=0}^{n-1} \beta_i x_i^j+\epsilon_i,
-$$
-
-where \( \epsilon_i \) is the error in our approximation.
-
-<p>
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec2" class="anchor">Rewriting the fitting procedure as a linear algebra problem  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-For every set of values \( y_i,x_i \) we have thus the corresponding set of equations
-$$
-\begin{align*}
-y_0&=\beta_0+\beta_1x_0^1+\beta_2x_0^2+\dots+\beta_{n-1}x_0^{n-1}+\epsilon_0\\
-y_1&=\beta_0+\beta_1x_1^1+\beta_2x_1^2+\dots+\beta_{n-1}x_1^{n-1}+\epsilon_1\\
-y_2&=\beta_0+\beta_1x_2^1+\beta_2x_2^2+\dots+\beta_{n-1}x_2^{n-1}+\epsilon_2\\
-\dots & \dots \\
-y_{n-1}&=\beta_0+\beta_1x_{n-1}^1+\beta_2x_{n-1}^2+\dots+\beta_1x_{n-1}^{n-1}+\epsilon_{n-1}.\\
-\end{align*}
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec3" class="anchor">Rewriting the fitting procedure as a linear algebra problem, follows  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-Defining the vectors
-$$
-\hat{y} = [y_0,y_1, y_2,\dots, y_{n-1}]^T,
-$$
-
-$$
-\hat{\beta} = [\beta_0,\beta_1, \beta_2,\dots, \beta_{n-1}]^T,
-$$
-
-$$
-\hat{\epsilon} = [\epsilon_0,\epsilon_1, \epsilon_2,\dots, \epsilon_{n-1}]^T,
-$$
-
-and the matrix
-$$
-\hat{X}=
-\begin{bmatrix} 
-1& x_{0}^1 &x_{0}^2& \dots & \dots &x_{0}^{n-1}\\
-1& x_{1}^1 &x_{1}^2& \dots & \dots &x_{1}^{n-1}\\
-1& x_{2}^1 &x_{2}^2& \dots & \dots &x_{2}^{n-1}\\                      
-\dots& \dots &\dots& \dots & \dots &\dots\\
-1& x_{n-1}^1 &x_{n-1}^2& \dots & \dots &x_{n-1}^{n-1}\\
-\end{bmatrix} 
-$$
-
-we can rewrite our equations as
-$$
-\hat{y} = \hat{X}\hat{\beta}+\hat{\epsilon}.
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec4" class="anchor">Generalizing the fitting procedure as a linear algebra problem  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-We are obviously not limited to the above polynomial. We could replace the various powers of \( x \) with elements of Fourier series, that is, instead of \( x_i^j \) we could have \( \cos{(j x_i)} \) or \( \sin{(j x_i)} \), or time series or other orthogonal functions.
-For every set of values \( y_i,x_i \) we can then generalize the equations to 
-$$
-\begin{align*}
-y_0&=\beta_0x_{00}+\beta_1x_{01}+\beta_2x_{02}+\dots+\beta_{n-1}x_{0n-1}+\epsilon_0\\
-y_1&=\beta_0x_{10}+\beta_1x_{11}+\beta_2x_{12}+\dots+\beta_{n-1}x_{1n-1}+\epsilon_1\\
-y_2&=\beta_0x_{20}+\beta_1x_{21}+\beta_2x_{22}+\dots+\beta_{n-1}x_{2n-1}+\epsilon_2\\
-\dots & \dots \\
-y_{i}&=\beta_0x_{i0}+\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_{n-1}x_{in-1}+\epsilon_i\\
-\dots & \dots \\
-y_{n-1}&=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_1x_{n-1,n-1}+\epsilon_{n-1}.\\
-\end{align*}
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec5" class="anchor">Generalizing the fitting procedure as a linear algebra problem  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-We redefine in turn the matrix \( \hat{X} \) as
-$$
-\hat{X}=
-\begin{bmatrix} 
-x_{00}& x_{01} &x_{02}& \dots & \dots &x_{0,n-1}\\
-x_{10}& x_{11} &x_{12}& \dots & \dots &x_{1,n-1}\\
-x_{20}& x_{21} &x_{22}& \dots & \dots &x_{2,n-1}\\                      
-\dots& \dots &\dots& \dots & \dots &\dots\\
-x_{n-1,0}& x_{n-1,1} &x_{n-1,2}& \dots & \dots &x_{n-1,n-1}\\
-\end{bmatrix} 
-$$
-
-and without loss of generality we rewrite again  our equations as
-$$
-\hat{y} = \hat{X}\hat{\beta}+\hat{\epsilon}.
-$$
-
-The left-hand side of this equation forms know. Our error vector \( \hat{\epsilon} \) and the parameter vector \( \hat{\beta} \) are our unknow quantities. How can we obtain the optimal set of \( \beta_i \) values?
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec6" class="anchor">Optimizing our parameters  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-We have defined the matrix \( \hat{X} \)
-$$
-\begin{align*}
-y_0&=\beta_0x_{00}+\beta_1x_{01}+\beta_2x_{02}+\dots+\beta_{n-1}x_{0n-1}+\epsilon_0\\
-y_1&=\beta_0x_{10}+\beta_1x_{11}+\beta_2x_{12}+\dots+\beta_{n-1}x_{1n-1}+\epsilon_1\\
-y_2&=\beta_0x_{20}+\beta_1x_{21}+\beta_2x_{22}+\dots+\beta_{n-1}x_{2n-1}+\epsilon_1\\
-\dots & \dots \\
-y_{i}&=\beta_0x_{i0}+\beta_1x_{i1}+\beta_2x_{i2}+\dots+\beta_{n-1}x_{in-1}+\epsilon_1\\
-\dots & \dots \\
-y_{n-1}&=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_1x_{n-1,n-1}+\epsilon_{n-1}.\\
-\end{align*}
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec7" class="anchor">Optimizing our parameters, more details  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-We well use this matrix to define the approximation \( \hat{\tilde{y}} \) via the unknown quantity \( \hat{\beta} \) as
-$$
-\hat{\tilde{y}}= \hat{X}\hat{\beta},
-$$
-
-and in order to find the optimal parameters \( \beta_i \) instead of solving the above linear algebra problem, we define a function which gives a measure of the spread between the values \( y_i \) (which represent hopefully the exact values) and the parametrized values \( \tilde{y}_i \), namely
-$$
-Q(\hat{\beta})=\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2=\left(\hat{y}-\hat{\tilde{y}}\right)^T\left(\hat{y}-\hat{\tilde{y}}\right),
-$$
-
-or using the matrix \( \hat{X} \) as
-$$
-Q(\hat{\beta})=\left(\hat{y}-\hat{X}\hat{\beta}\right)^T\left(\hat{y}-\hat{X}\hat{\beta}\right).
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec8" class="anchor">Interpretations and optimizing our parameters  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-The function 
-$$
-Q(\hat{\beta})=\left(\hat{y}-\hat{X}\hat{\beta}\right)^T\left(\hat{y}-\hat{X}\hat{\beta}\right),
-$$
-
-can be linked to the variance of the quantity \( y_i \) if we interpret the latter as the mean value of for example a numerical  experiment. When linking below with the maximum likelihood approach below, we will indeed interpret \( y_i \) as a mean value
-$$
-y_{i}=\langle y_i \rangle = \beta_0x_{i,0}+\beta_1x_{i,1}+\beta_2x_{i,2}+\dots+\beta_{n-1}x_{i,n-1}+\epsilon_i,
-$$
-
-where \( \langle y_i \rangle \) is the mean value. Keep in mind also that till now  we have treated \( y_i \) as the exact value. Normally, the response (dependent or outcome) variable \( y_i \) the outcome of a numerical experiment or another type of experiment and is thus only an approximation to the true value. It is then always accompanied by an error estimate, often limited to a statistical error estimate given by the standard deviation discussed earlier. In the discussion here we will treat \( y_i \) as our exact value for the response variable.
-
-<p>
-In order to find the parameters \( \beta_i \) we will then minimize the spread of \( Q(\hat{\beta}) \) by requiring
-$$
-\frac{\partial Q(\hat{\beta})}{\partial \beta_j} = \frac{\partial }{\partial \beta_j}\left[ \sum_{i=0}^{n-1}\left(y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}\right)^2\right]=0, 
-$$
-
-which results in
-$$
-\frac{\partial Q(\hat{\beta})}{\partial \beta_j} = -2\left[ \sum_{i=0}^{n-1}x_{ij}\left(y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}\right)\right]=0, 
-$$
-
-or in a matrix-vector form as
-$$
-\frac{\partial Q(\hat{\beta})}{\partial \hat{\beta}} = 0 = \hat{X}^T\left( \hat{y}-\hat{X}\hat{\beta}\right).  
-$$
-
-<p>
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec9" class="anchor">Interpretations and optimizing our parameters  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-We can rewrite
-$$
-\frac{\partial Q(\hat{\beta})}{\partial \hat{\beta}} = 0 = \hat{X}^T\left( \hat{y}-\hat{X}\hat{\beta}\right),  
-$$
-
-as
-$$
-\hat{X}^T\hat{y} = \hat{X}^T\hat{X}\hat{\beta},  
-$$
-
-and if the matrix \( \hat{X}^T\hat{X} \) is invertible we have the solution
-$$
-\hat{\beta} =\left(\hat{X}^T\hat{X}\right)^{-1}\hat{X}^T\hat{y}.
-$$
-
-<p>
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec10" class="anchor">Interpretations and optimizing our parameters  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-The residuals \( \hat{\epsilon} \) are in turn given by
-$$
-\hat{\epsilon} = \hat{y}-\hat{\tilde{y}} = \hat{y}-\hat{X}\hat{\beta},
-$$
-
-and with 
-$$
-\hat{X}^T\left( \hat{y}-\hat{X}\hat{\beta}\right)= 0, 
-$$
-
-we have
-$$
-\hat{X}^T\hat{\epsilon}=\hat{X}^T\left( \hat{y}-\hat{X}\hat{\beta}\right)= 0, 
-$$
-
-meaning that the solution for \( \hat{\beta} \) is the one which minimizes the residuals.  Later we will link this with the maximum likelihood approach.
-
-<p>
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec11" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
-<p>
-Normally, the response (dependent or outcome) variable \( y_i \) the outcome of a numerical experiment or another type of experiment and is thus only an approximation to the true value. It is then always accompanied by an error estimate, often limited to a statistical error estimate given by the standard deviation discussed earlier. In the discussion here we will treat \( y_i \) as our exact value for the response variable.
-
-<p>
-Introducing the standard deviation \( \sigma_i \) for each measurement \( y_i \), we define now the \( \chi^2 \) function as  
-$$
-\chi^2(\hat{\beta})=\sum_{i=0}^{n-1}\frac{\left(y_i-\tilde{y}_i\right)^2}{\sigma_i^2}=\left(\hat{y}-\hat{\tilde{y}}\right)^T\frac{1}{\hat{\Sigma^2}}\left(\hat{y}-\hat{\tilde{y}}\right),
-$$
-
-where the matrix \( \hat{\Sigma} \) is a diagonal matrix with \( \sigma_i \) as matrix elements.
-
-<p>
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec12" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
-<p>
-In order to find the parameters \( \beta_i \) we will then minimize the spread of \( \chi^2(\hat{\beta}) \) by requiring
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \beta_j} = \frac{\partial }{\partial \beta_j}\left[ \sum_{i=0}^{n-1}\left(\frac{y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}}{\sigma_i}\right)^2\right]=0, 
-$$
-
-which results in
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \beta_j} = -2\left[ \sum_{i=0}^{n-1}\frac{x_{ij}}{\sigma_i}\left(\frac{y_i-\beta_0x_{i,0}-\beta_1x_{i,1}-\beta_2x_{i,2}-\dots-\beta_{n-1}x_{i,n-1}}{\sigma_i}\right)\right]=0, 
-$$
-
-or in a matrix-vector form as
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \hat{\beta}} = 0 = \hat{A}^T\left( \hat{b}-\hat{A}\hat{\beta}\right).  
-$$
-
-where we have defined the matrix \( \hat{A} =\hat{X}/\hat{\Sigma} \) with matrix elements \( a_{ij} = x_{ij}/\sigma_i \) and the vector \( \hat{b} \) with elements \( b_i = y_i/\sigma_i \).
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec13" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
-<p>
-We can rewrite
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \hat{\beta}} = 0 = \hat{A}^T\left( \hat{b}-\hat{A}\hat{\beta}\right),  
-$$
-
-as
-$$
-\hat{A}^T\hat{b} = \hat{A}^T\hat{A}\hat{\beta},  
-$$
-
-and if the matrix \( \hat{A}^T\hat{A} \) is invertible we have the solution
-$$
-\hat{\beta} =\left(\hat{A}^T\hat{A}\right)^{-1}\hat{A}^T\hat{b}.
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec14" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
-<p>
-If we then introduce the matrix
-$$
-\hat{H} =  \hat{A}^T\hat{A},
-$$
-
-we have then the following expression for the parameters \( \beta_j \) (the matrix elements of \( \hat{H} \) are \( h_{ij} \))
-$$
-\beta_j = \sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}\frac{y_i}{\sigma_i}\frac{x_{ik}}{\sigma_i} = \sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}b_ia_{ik}
-$$
-
-We state without proof the expression for the uncertainty  in the parameters \( \beta_j \) as
-$$
-\sigma^2(\beta_j) = \sum_{i=0}^{n-1}\sigma_i^2\left( \frac{\partial \beta_j}{\partial y_i}\right)^2, 
-$$
-
-resulting in 
-$$
-\sigma^2(\beta_j) = \left(\sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}a_{ik}\right)\left(\sum_{l=0}^{p-1}h_{jl}\sum_{m=0}^{n-1}a_{ml}\right) = h_{jj}!
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec15" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-The first step here is to approximate the function \( y \) with a first-order polynomial, that is we write
-$$
-y=y(x) \rightarrow y(x_i) \approx \beta_0+\beta_1 x_i.
-$$
-
-By computing the derivatives of \( \chi^2 \) with respect to \( \beta_0 \) and \( \beta_1 \) show that these are given by
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \beta_0} = -2\left[ \sum_{i=0}^{1}\left(\frac{y_i-\beta_0-\beta_1x_{i}}{\sigma_i^2}\right)\right]=0,
-$$
-
-and
-$$
-\frac{\partial \chi^2(\hat{\beta})}{\partial \beta_0} = -2\left[ \sum_{i=0}^{1}x_i\left(\frac{y_i-\beta_0-\beta_1x_{i}}{\sigma_i^2}\right)\right]=0.
-$$
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec16" class="anchor">The \( \chi^2 \) function  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-
-<p>
-We define then
-$$
-\gamma =  \sum_{i=0}^{1}\frac{1}{\sigma_i^2},
-$$
-
-
-$$
-\gamma_x =  \sum_{i=0}^{1}\frac{x_{i}}{\sigma_i^2},
-$$
-
-$$
-\gamma_y = \sum_{i=0}^{1}\left(\frac{y_i}{\sigma_i^2}\right),
-$$
-
-$$
-\gamma_{xx} =  \sum_{i=0}^{1}\frac{x_ix_{i}}{\sigma_i^2},
-$$
-
-$$
-\gamma_{xy} = \sum_{i=0}^{1}\frac{y_ix_{i}}{\sigma_i^2},
-$$
-
-and show that
-$$
-\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
-$$
-
-$$
-\beta_1 = \frac{\gamma_{xy}\gamma-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2}.
-$$
-
-<p>
-The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \).  A better approach is to use the Singular Value Decomposition (SVD) method discussed below.
-</div>
-</div>
-
-
-<p>
-<!-- !split -->
-
-<h2 id="___sec17" class="anchor">The singular value decompostion  </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-How can we use the singular value decomposition to find the parameters \( \beta_j \)? More details will come. We first note that a general \( m\times n \) matrix \( \hat{A} \) can be written in terms of a diagonal matrix \( \hat{\Sigma} \) of dimensionality \( n\times n \) and two orthognal matrices \( \hat{U} \) and \( \hat{V} \), where the first has dimensionality \( m \times n \) and the last dimensionality \( n\times n \). We have then
-$$
-\hat{A} = \hat{U}\hat{\Sigma}\hat{V}
-$$
-</div>
-</div>
-
-
-<p>
-
 <!-- ------------------- end of main content --------------- -->
 
 </div>  <!-- end container -->
diff --git a/doc/pub/Regression/html/Regression-reveal.html b/doc/pub/Regression/html/Regression-reveal.html
index 5653f2d53..98d95cd62 100644
--- a/doc/pub/Regression/html/Regression-reveal.html
+++ b/doc/pub/Regression/html/Regression-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>Nov 21, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 
diff --git a/doc/pub/Regression/html/Regression-solarized.html b/doc/pub/Regression/html/Regression-solarized.html
index 79d8f0338..0fb7548ac 100644
--- a/doc/pub/Regression/html/Regression-solarized.html
+++ b/doc/pub/Regression/html/Regression-solarized.html
@@ -66,8 +66,7 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                '___sec2'),
-              ('Rewriting the fitting procedure as a linear algebra problem, '
-               'follows',
+              ('Rewriting the fitting procedure as a linear algebra problem, follows',
                2,
                None,
                '___sec3'),
@@ -141,7 +140,7 @@ 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>Nov 21, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
diff --git a/doc/pub/Regression/html/Regression.html b/doc/pub/Regression/html/Regression.html
index 497beb44d..e474ec469 100644
--- a/doc/pub/Regression/html/Regression.html
+++ b/doc/pub/Regression/html/Regression.html
@@ -71,8 +71,7 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                '___sec2'),
-              ('Rewriting the fitting procedure as a linear algebra problem, '
-               'follows',
+              ('Rewriting the fitting procedure as a linear algebra problem, follows',
                2,
                None,
                '___sec3'),
@@ -146,7 +145,7 @@ 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>Nov 21, 2017</h4></center> <!-- date -->
+<center><h4>Nov 22, 2017</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
diff --git a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz
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diff --git a/doc/pub/Regression/pdf/Regression-beamer.pdf b/doc/pub/Regression/pdf/Regression-beamer.pdf
index c344916dd7b02b0a87addb4e31da85c3c8684a9c..85264c5f1c0e1998dd8e8bb0cb76594b29ddcec9 100644
GIT binary patch
delta 301
zcmZo&&fU74dqWyiy@iyF;%esPnIe3rFHO>1cgpedX2(8%qekxbng?7wi~i~@vAl5U
zW6<oqI!lZDmfqxSYu=*k^>+KwlXtg0xb)|ySeyZ~(Df40n(5QbLUSM4Y}uJ$bh2#D
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Y;$&=TVQgw<Vy9q3NXd59i%bbj0H$Md_5c6?

delta 301
zcmZo&&fU74dqWyieWi(oQyBX(BTboUOI3qorZz82Z<d*#!X(c3^MI&?%kNl^;sr||
zFEy)<^m;Diy;+!tJu`aBt^DrEyK@gN{kd6pPXe3Dx|do%^mKDq-8xd4QG76E(p!tE
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diff --git a/doc/pub/Regression/pdf/Regression-minted.pdf b/doc/pub/Regression/pdf/Regression-minted.pdf
index d710633b33cb2e1c2105cd50b784d6f9a367e63d..b5b602d88e4f3a2cd433402b41834b24955d0662 100644
GIT binary patch
delta 161
zcmca{i}%JY-VLryjK!PXn6_}RJao=n*!+*H{T~-25HoH6$Hg2UrDbGjVq|1wscm4W
zZeXCU$))d`pW>2OlB%HLVr67tXl`g|1XZ%VJ(YO@tFxhnvzv>ViHoDDfs475g{iZP
erJJ*vv7>>Dk-4*hp|PEU4Iw4lv$C1rF#-VL@GYtU

delta 161
zcmca{i}%JY-VLryjK-VYn6_}R?B&Z`(EN|9{T~-25HoH6$Hg2UrDbSnZenU^sBK`V
zZeXCU$))d`pW>2OlB%HLVr67tXl`g|1XZ%VJ(YO@tFx)4sjHijk&C&pfs=`gtEG#R
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diff --git a/doc/src/NeuralNet/make.sh b/doc/src/NeuralNet/make.sh
index edfed7c87..cd6f9422e 100755
--- a/doc/src/NeuralNet/make.sh
+++ b/doc/src/NeuralNet/make.sh
@@ -1,4 +1,4 @@
-#!/bin/sh
+v#!/bin/sh
 set -x
 
 function system {
@@ -44,7 +44,7 @@ system doconce split_html $html.html --method=space10
 # Bootstrap style
 html=${name}-bs
 system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
-system doconce split_html $html.html --method=split --pagination --nav_button=bottom
+#system doconce split_html $html.html --method=split --pagination --nav_button=bottom
 
 # IPython notebook
 system doconce format ipynb $name $opt
diff --git a/doc/src/Regression/make.sh b/doc/src/Regression/make.sh
index d73ef27fc..0671a98d3 100755
--- a/doc/src/Regression/make.sh
+++ b/doc/src/Regression/make.sh
@@ -44,10 +44,10 @@ system doconce split_html $html.html --method=space10
 # Bootstrap style
 html=${name}-bs
 system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
-#system doconce split_html $html.html --method=split --pagination --nav_button=bottom
+system doconce split_html $html.html --method=split --pagination --nav_button=bottom
 
 # IPython notebook
-system doconce format ipynb $name $opt
+#system doconce format ipynb $name $opt
 
 # LaTeX Beamer slides
 beamertheme=red_plain