From c71c008945f67f3bbb8a647ce855ac801f15b1db Mon Sep 17 00:00:00 2001
From: mhjensen <morten.hjorth-jensen@fys.uio.no>
Date: Fri, 12 Oct 2018 04:55:15 +0200
Subject: [PATCH] updating splines

---
 doc/pub/NeuralNet/ipynb/NeuralNet.ipynb       | 124 ++----
 doc/pub/Splines/html/._Splines-bs000.html     | 173 ++++----
 doc/pub/Splines/html/._Splines-bs001.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs002.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs003.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs004.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs005.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs006.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs007.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs008.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs009.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs010.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs011.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs012.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs013.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs014.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs015.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs016.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs017.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs018.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs019.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs020.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs021.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs022.html     | 171 ++++----
 doc/pub/Splines/html/._Splines-bs023.html     | 209 +++++----
 doc/pub/Splines/html/._Splines-bs024.html     | 217 +++++-----
 doc/pub/Splines/html/._Splines-bs025.html     | 259 ++++++-----
 doc/pub/Splines/html/._Splines-bs026.html     | 237 ++++++----
 doc/pub/Splines/html/._Splines-bs027.html     | 203 +++++----
 doc/pub/Splines/html/._Splines-bs028.html     | 203 +++++----
 doc/pub/Splines/html/._Splines-bs029.html     | 195 +++++----
 doc/pub/Splines/html/._Splines-bs030.html     | 186 ++++----
 doc/pub/Splines/html/._Splines-bs031.html     | 212 +++++----
 doc/pub/Splines/html/._Splines-bs032.html     | 237 +++++-----
 doc/pub/Splines/html/._Splines-bs033.html     | 206 +++++----
 doc/pub/Splines/html/._Splines-bs034.html     | 234 +++++-----
 doc/pub/Splines/html/._Splines-bs035.html     | 243 ++++++-----
 doc/pub/Splines/html/._Splines-bs036.html     | 231 ++++++----
 doc/pub/Splines/html/._Splines-bs037.html     | 222 +++++-----
 doc/pub/Splines/html/._Splines-bs038.html     | 221 ++++++----
 doc/pub/Splines/html/._Splines-bs039.html     | 201 +++++----
 doc/pub/Splines/html/._Splines-bs040.html     | 192 +++++----
 doc/pub/Splines/html/._Splines-bs041.html     | 214 +++++-----
 doc/pub/Splines/html/._Splines-bs042.html     | 225 +++++-----
 doc/pub/Splines/html/._Splines-bs043.html     | 207 +++++----
 doc/pub/Splines/html/._Splines-bs044.html     | 211 ++++-----
 doc/pub/Splines/html/._Splines-bs045.html     | 212 +++++----
 doc/pub/Splines/html/._Splines-bs046.html     | 192 +++++----
 doc/pub/Splines/html/._Splines-bs047.html     | 193 +++++----
 doc/pub/Splines/html/._Splines-bs048.html     | 199 +++++----
 doc/pub/Splines/html/._Splines-bs049.html     | 198 +++++----
 doc/pub/Splines/html/._Splines-bs050.html     | 206 ++++-----
 doc/pub/Splines/html/._Splines-bs051.html     | 208 +++++----
 doc/pub/Splines/html/._Splines-bs052.html     | 224 +++++-----
 doc/pub/Splines/html/._Splines-bs053.html     | 373 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs054.html     | 404 ++++++++++++++++++
 doc/pub/Splines/html/._Splines-bs055.html     | 330 ++++++++++++++
 doc/pub/Splines/html/._Splines-bs056.html     | 356 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs057.html     | 344 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs058.html     | 353 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs059.html     | 358 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs060.html     | 362 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs061.html     | 356 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs062.html     | 355 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs063.html     | 364 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs064.html     | 363 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs065.html     | 358 ++++++++++++++++
 doc/pub/Splines/html/._Splines-bs066.html     | 334 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs067.html     | 343 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs068.html     | 341 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs069.html     | 348 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs070.html     | 342 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs071.html     | 334 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs072.html     | 343 +++++++++++++++
 doc/pub/Splines/html/._Splines-bs073.html     | 326 ++++++++++++++
 doc/pub/Splines/html/Splines-bs.html          | 173 ++++----
 doc/pub/Splines/html/Splines-reveal.html      | 286 +++++++++++--
 doc/pub/Splines/html/Splines-solarized.html   | 348 +++++++++++----
 doc/pub/Splines/html/Splines.html             | 348 +++++++++++----
 doc/pub/Splines/ipynb/Splines.ipynb           | 364 +++++++++++++++-
 .../Splines/ipynb/ipynb-Splines-src.tar.gz    | Bin 209 -> 209 bytes
 doc/pub/Splines/pdf/Splines-minted.pdf        | Bin 419239 -> 452393 bytes
 doc/src/Splines/Splines.do.txt                | 159 +++++++
 83 files changed, 14530 insertions(+), 4991 deletions(-)
 create mode 100644 doc/pub/Splines/html/._Splines-bs053.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs054.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs055.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs056.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs057.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs058.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs059.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs060.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs061.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs062.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs063.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs064.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs065.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs066.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs067.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs068.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs069.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs070.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs071.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs072.html
 create mode 100644 doc/pub/Splines/html/._Splines-bs073.html

diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
index 0c42fc8c4..d97039c78 100644
--- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
+++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb
@@ -597,9 +597,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -1520,9 +1518,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# import necessary packages\n",
@@ -1589,9 +1585,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from sklearn.model_selection import train_test_split\n",
@@ -1713,9 +1707,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# building our neural network\n",
@@ -1792,9 +1784,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# setup the feed-forward pass, subscript h = hidden layer\n",
@@ -1957,9 +1947,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# to categorical turns our integer vector into a onehot representation\n",
@@ -2061,9 +2049,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "class NeuralNetwork:\n",
@@ -2186,9 +2172,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "epochs = 100\n",
@@ -2222,9 +2206,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "eta_vals = np.logspace(-5, 1, 7)\n",
@@ -2259,9 +2241,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# visual representation of grid search\n",
@@ -2321,9 +2301,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
@@ -2354,9 +2332,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2439,9 +2415,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "pip3 install tensorflow"
@@ -2457,9 +2431,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "conda install tensorflow"
@@ -2475,9 +2447,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# import necessary packages\n",
@@ -2527,9 +2497,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from keras.utils import to_categorical\n",
@@ -2559,9 +2527,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import tensorflow as tf\n",
@@ -2707,9 +2673,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "epochs = 100\n",
@@ -2724,9 +2688,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "DNN_tf = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
@@ -2749,9 +2711,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2790,9 +2750,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2816,9 +2774,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "conda install keras"
@@ -2834,9 +2790,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "pip3 install keras"
@@ -2852,9 +2806,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from keras.models import Sequential\n",
@@ -2877,9 +2829,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
@@ -2902,9 +2852,7 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2941,7 +2889,25 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.0"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 2
 }
diff --git a/doc/pub/Splines/html/._Splines-bs000.html b/doc/pub/Splines/html/._Splines-bs000.html
index bece1e921..8625c257e 100644
--- a/doc/pub/Splines/html/._Splines-bs000.html
+++ b/doc/pub/Splines/html/._Splines-bs000.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -272,7 +293,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 6, 2018</h4></center> <!-- date -->
+<center><h4>Oct 12, 2018</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -296,7 +317,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs008.html">9</a></li>
   <li><a href="._Splines-bs009.html">10</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs001.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs001.html b/doc/pub/Splines/html/._Splines-bs001.html
index 5dcab7015..de70d2fa8 100644
--- a/doc/pub/Splines/html/._Splines-bs001.html
+++ b/doc/pub/Splines/html/._Splines-bs001.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -282,7 +303,7 @@ some approximative/numerical method to compute the minimum.
   <li><a href="._Splines-bs009.html">10</a></li>
   <li><a href="._Splines-bs010.html">11</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs002.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs002.html b/doc/pub/Splines/html/._Splines-bs002.html
index d04d8f945..530190f6f 100644
--- a/doc/pub/Splines/html/._Splines-bs002.html
+++ b/doc/pub/Splines/html/._Splines-bs002.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -290,7 +311,7 @@ where \( \hat{\beta} \) are the weights we wish to extract from data, in our cas
   <li><a href="._Splines-bs010.html">11</a></li>
   <li><a href="._Splines-bs011.html">12</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs003.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs003.html b/doc/pub/Splines/html/._Splines-bs003.html
index b39e9900e..e3fa4abba 100644
--- a/doc/pub/Splines/html/._Splines-bs003.html
+++ b/doc/pub/Splines/html/._Splines-bs003.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -295,7 +316,7 @@ This defines what is called  the Hessian matrix.
   <li><a href="._Splines-bs011.html">12</a></li>
   <li><a href="._Splines-bs012.html">13</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs004.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs004.html b/doc/pub/Splines/html/._Splines-bs004.html
index e63ef43ad..ded6d78cf 100644
--- a/doc/pub/Splines/html/._Splines-bs004.html
+++ b/doc/pub/Splines/html/._Splines-bs004.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -296,7 +317,7 @@ If we can compute these matrices, in particular the Hessian, the above is often
   <li><a href="._Splines-bs012.html">13</a></li>
   <li><a href="._Splines-bs013.html">14</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs005.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs005.html b/doc/pub/Splines/html/._Splines-bs005.html
index aaec6aa73..96b97c1d8 100644
--- a/doc/pub/Splines/html/._Splines-bs005.html
+++ b/doc/pub/Splines/html/._Splines-bs005.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -288,7 +309,7 @@ normally discourage the use of this method.
   <li><a href="._Splines-bs013.html">14</a></li>
   <li><a href="._Splines-bs014.html">15</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs006.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs006.html b/doc/pub/Splines/html/._Splines-bs006.html
index 1edaf8466..73992aa61 100644
--- a/doc/pub/Splines/html/._Splines-bs006.html
+++ b/doc/pub/Splines/html/._Splines-bs006.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -308,7 +329,7 @@ $$
   <li><a href="._Splines-bs014.html">15</a></li>
   <li><a href="._Splines-bs015.html">16</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs007.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs007.html b/doc/pub/Splines/html/._Splines-bs007.html
index 65a1cd9a2..83c300073 100644
--- a/doc/pub/Splines/html/._Splines-bs007.html
+++ b/doc/pub/Splines/html/._Splines-bs007.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -291,7 +312,7 @@ vanishes, then Newton-Raphson may fail totally
   <li><a href="._Splines-bs015.html">16</a></li>
   <li><a href="._Splines-bs016.html">17</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs008.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs008.html b/doc/pub/Splines/html/._Splines-bs008.html
index e4b0d0150..0382bcc0c 100644
--- a/doc/pub/Splines/html/._Splines-bs008.html
+++ b/doc/pub/Splines/html/._Splines-bs008.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -329,7 +350,7 @@ more than two non-linear equations. In our case, the Jacobian matrix is given by
   <li><a href="._Splines-bs016.html">17</a></li>
   <li><a href="._Splines-bs017.html">18</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs009.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs009.html b/doc/pub/Splines/html/._Splines-bs009.html
index 95b7b9fde..891834392 100644
--- a/doc/pub/Splines/html/._Splines-bs009.html
+++ b/doc/pub/Splines/html/._Splines-bs009.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -299,7 +320,7 @@ we are always moving towards smaller function values, i.e a minimum.
   <li><a href="._Splines-bs017.html">18</a></li>
   <li><a href="._Splines-bs018.html">19</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs010.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs010.html b/doc/pub/Splines/html/._Splines-bs010.html
index 930254831..e27d4cb66 100644
--- a/doc/pub/Splines/html/._Splines-bs010.html
+++ b/doc/pub/Splines/html/._Splines-bs010.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -295,7 +316,7 @@ the learning rate within the context of Machine Learning.
   <li><a href="._Splines-bs018.html">19</a></li>
   <li><a href="._Splines-bs019.html">20</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs011.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs011.html b/doc/pub/Splines/html/._Splines-bs011.html
index a2d29ef4d..e7d36fffb 100644
--- a/doc/pub/Splines/html/._Splines-bs011.html
+++ b/doc/pub/Splines/html/._Splines-bs011.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -302,7 +323,7 @@ Note that the gradient is a function of \( \mathbf{x} =
   <li><a href="._Splines-bs019.html">20</a></li>
   <li><a href="._Splines-bs020.html">21</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs012.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs012.html b/doc/pub/Splines/html/._Splines-bs012.html
index de3759975..a45c5522f 100644
--- a/doc/pub/Splines/html/._Splines-bs012.html
+++ b/doc/pub/Splines/html/._Splines-bs012.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -295,7 +316,7 @@ randomness. One such method is that of Stochastic Gradient Descent
   <li><a href="._Splines-bs020.html">21</a></li>
   <li><a href="._Splines-bs021.html">22</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs013.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs013.html b/doc/pub/Splines/html/._Splines-bs013.html
index 288107e02..187387ea6 100644
--- a/doc/pub/Splines/html/._Splines-bs013.html
+++ b/doc/pub/Splines/html/._Splines-bs013.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -296,7 +317,7 @@ regular polygons (triangles, rectangles, pentagons, etc...).
   <li><a href="._Splines-bs021.html">22</a></li>
   <li><a href="._Splines-bs022.html">23</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs014.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs014.html b/doc/pub/Splines/html/._Splines-bs014.html
index 5e10bd7e7..141407dc8 100644
--- a/doc/pub/Splines/html/._Splines-bs014.html
+++ b/doc/pub/Splines/html/._Splines-bs014.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -284,7 +305,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs022.html">23</a></li>
   <li><a href="._Splines-bs023.html">24</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs015.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs015.html b/doc/pub/Splines/html/._Splines-bs015.html
index 91adb73aa..ad49b99ec 100644
--- a/doc/pub/Splines/html/._Splines-bs015.html
+++ b/doc/pub/Splines/html/._Splines-bs015.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -320,7 +341,7 @@ This condition is particularly useful since it gives us an procedure for determi
   <li><a href="._Splines-bs023.html">24</a></li>
   <li><a href="._Splines-bs024.html">25</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs016.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs016.html b/doc/pub/Splines/html/._Splines-bs016.html
index 707c47a6c..1e6629e86 100644
--- a/doc/pub/Splines/html/._Splines-bs016.html
+++ b/doc/pub/Splines/html/._Splines-bs016.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -307,7 +328,7 @@ This result means that if we know that the cost/loss function is convex and we a
   <li><a href="._Splines-bs024.html">25</a></li>
   <li><a href="._Splines-bs025.html">26</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs017.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs017.html b/doc/pub/Splines/html/._Splines-bs017.html
index efe5d542e..370c62d6e 100644
--- a/doc/pub/Splines/html/._Splines-bs017.html
+++ b/doc/pub/Splines/html/._Splines-bs017.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -303,7 +324,7 @@ Using the definition of convexity, try to show that a function satisfying the pr
   <li><a href="._Splines-bs025.html">26</a></li>
   <li><a href="._Splines-bs026.html">27</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs018.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs018.html b/doc/pub/Splines/html/._Splines-bs018.html
index d6f43e6d8..b785e0140 100644
--- a/doc/pub/Splines/html/._Splines-bs018.html
+++ b/doc/pub/Splines/html/._Splines-bs018.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -312,7 +333,7 @@ When we have found the exact solution, \( \hat{r}=0 \).
   <li><a href="._Splines-bs026.html">27</a></li>
   <li><a href="._Splines-bs027.html">28</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs019.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs019.html b/doc/pub/Splines/html/._Splines-bs019.html
index 2664f2e41..3f75c1a00 100644
--- a/doc/pub/Splines/html/._Splines-bs019.html
+++ b/doc/pub/Splines/html/._Splines-bs019.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -293,7 +314,7 @@ symmetric.  This defines also the Hessian and we want it to be  positive definit
   <li><a href="._Splines-bs027.html">28</a></li>
   <li><a href="._Splines-bs028.html">29</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs020.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs020.html b/doc/pub/Splines/html/._Splines-bs020.html
index d51c26820..94926845c 100644
--- a/doc/pub/Splines/html/._Splines-bs020.html
+++ b/doc/pub/Splines/html/._Splines-bs020.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -299,7 +320,7 @@ instead.
   <li><a href="._Splines-bs028.html">29</a></li>
   <li><a href="._Splines-bs029.html">30</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs021.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs021.html b/doc/pub/Splines/html/._Splines-bs021.html
index d41a12c70..01a05f1bd 100644
--- a/doc/pub/Splines/html/._Splines-bs021.html
+++ b/doc/pub/Splines/html/._Splines-bs021.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -307,7 +328,7 @@ and
   <li><a href="._Splines-bs029.html">30</a></li>
   <li><a href="._Splines-bs030.html">31</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs022.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs022.html b/doc/pub/Splines/html/._Splines-bs022.html
index da6752d42..92d7b66f4 100644
--- a/doc/pub/Splines/html/._Splines-bs022.html
+++ b/doc/pub/Splines/html/._Splines-bs022.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -320,7 +341,7 @@ $$
   <li><a href="._Splines-bs030.html">31</a></li>
   <li><a href="._Splines-bs031.html">32</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs023.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs023.html b/doc/pub/Splines/html/._Splines-bs023.html
index 3d49a5bef..37f424a2f 100644
--- a/doc/pub/Splines/html/._Splines-bs023.html
+++ b/doc/pub/Splines/html/._Splines-bs023.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,43 +274,7 @@ MathJax.Hub.Config({
 <a name="part0023"></a>
 <!-- !split -->
 
-<h2 id="___sec22" class="anchor">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-<p>
-
-<!-- code=c++ (!bc cppcod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;cmath&gt;</span><span style="color: #BC7A00"></span>
-<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;iostream&gt;</span><span style="color: #BC7A00"></span>
-<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;fstream&gt;</span><span style="color: #BC7A00"></span>
-<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;iomanip&gt;</span><span style="color: #BC7A00"></span>
-<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&quot;vectormatrixclass.h&quot;</span><span style="color: #BC7A00"></span>
-<span style="color: #008000; font-weight: bold">using</span> <span style="color: #008000; font-weight: bold">namespace</span>  std;
-<span style="color: #408080; font-style: italic">//   Main function begins here</span>
-<span style="color: #B00040">int</span> <span style="color: #0000FF">main</span>(<span style="color: #B00040">int</span>  argc, <span style="color: #B00040">char</span> <span style="color: #666666">*</span> argv[]){
-  <span style="color: #B00040">int</span> dim <span style="color: #666666">=</span> <span style="color: #666666">2</span>;
-  Vector x(dim),xsd(dim), b(dim),x0(dim);
-  Matrix A(dim,dim);
-
-  <span style="color: #408080; font-style: italic">// Set our initial guess</span>
-  x0(<span style="color: #666666">0</span>) <span style="color: #666666">=</span> x0(<span style="color: #666666">1</span>) <span style="color: #666666">=</span> <span style="color: #666666">0</span>;
-  <span style="color: #408080; font-style: italic">// Set the matrix</span>
-  A(<span style="color: #666666">0</span>,<span style="color: #666666">0</span>) <span style="color: #666666">=</span>  <span style="color: #666666">3</span>;    A(<span style="color: #666666">1</span>,<span style="color: #666666">0</span>) <span style="color: #666666">=</span>  <span style="color: #666666">2</span>;   A(<span style="color: #666666">0</span>,<span style="color: #666666">1</span>) <span style="color: #666666">=</span>  <span style="color: #666666">2</span>;   A(<span style="color: #666666">1</span>,<span style="color: #666666">1</span>) <span style="color: #666666">=</span>  <span style="color: #666666">6</span>;
-  b(<span style="color: #666666">0</span>) <span style="color: #666666">=</span> <span style="color: #666666">2</span>; b(<span style="color: #666666">1</span>) <span style="color: #666666">=</span> <span style="color: #666666">-8</span>;
-  cout <span style="color: #666666">&lt;&lt;</span> <span style="color: #BA2121">&quot;The Matrix A that we are using: &quot;</span> <span style="color: #666666">&lt;&lt;</span> endl;
-  A.Print();
-  cout <span style="color: #666666">&lt;&lt;</span> endl;
-  xsd <span style="color: #666666">=</span> SteepestDescent(A,b,x0);
-  cout <span style="color: #666666">&lt;&lt;</span> <span style="color: #BA2121">&quot;The approximate solution using Steepest Descent is: &quot;</span> <span style="color: #666666">&lt;&lt;</span> endl;
-  xsd.Print();
-  cout <span style="color: #666666">&lt;&lt;</span> endl;
-}
-</pre></div>
-<p>
-</div>
-</div>
-
+<h2 id="___sec22" class="anchor">Code examples for steepest descent </h2>
 
 <p>
 <p>
@@ -317,7 +302,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs031.html">32</a></li>
   <li><a href="._Splines-bs032.html">33</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs024.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs024.html b/doc/pub/Splines/html/._Splines-bs024.html
index 62b53c6d0..e98f55f27 100644
--- a/doc/pub/Splines/html/._Splines-bs024.html
+++ b/doc/pub/Splines/html/._Splines-bs024.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,33 +274,37 @@ MathJax.Hub.Config({
 <a name="part0024"></a>
 <!-- !split -->
 
-<h2 id="___sec23" class="anchor">The routine for the steepest descent method </h2>
+<h2 id="___sec23" class="anchor">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
 <div class="panel panel-default">
 <div class="panel-body">
 <p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
 <p>
 
 <!-- code=c++ (!bc cppcod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>Vector <span style="color: #0000FF">SteepestDescent</span>(Matrix A, Vector b, Vector x0){
-  <span style="color: #B00040">int</span> IterMax, i;
-  <span style="color: #B00040">int</span> dim <span style="color: #666666">=</span> x0.Dimension();
-  <span style="color: #008000; font-weight: bold">const</span> <span style="color: #B00040">double</span> tolerance <span style="color: #666666">=</span> <span style="color: #666666">1.0e-14</span>;
-  Vector x(dim),f(dim),z(dim);
-  <span style="color: #B00040">double</span> c,alpha,d;
-  IterMax <span style="color: #666666">=</span> <span style="color: #666666">30</span>;
-  x <span style="color: #666666">=</span> x0;
-  r <span style="color: #666666">=</span> A<span style="color: #666666">*</span>x<span style="color: #666666">-</span>b;
-  i <span style="color: #666666">=</span> <span style="color: #666666">0</span>;
-  <span style="color: #008000; font-weight: bold">while</span> (i <span style="color: #666666">&lt;=</span> IterMax){
-    z <span style="color: #666666">=</span> A<span style="color: #666666">*</span>r;
-    c <span style="color: #666666">=</span> dot(r,r);
-    alpha <span style="color: #666666">=</span> c<span style="color: #666666">/</span>dot(r,z);
-    x <span style="color: #666666">=</span> x <span style="color: #666666">-</span> alpha<span style="color: #666666">*</span>r;
-    r <span style="color: #666666">=</span>  A<span style="color: #666666">*</span>x<span style="color: #666666">-</span>b;
-    <span style="color: #008000; font-weight: bold">if</span>(sqrt(dot(r,r)) <span style="color: #666666">&lt;</span> tolerance) <span style="color: #008000; font-weight: bold">break</span>;
-    i<span style="color: #666666">++</span>;
-  }
-  <span style="color: #008000; font-weight: bold">return</span> x;
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;cmath&gt;</span><span style="color: #BC7A00"></span>
+<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;iostream&gt;</span><span style="color: #BC7A00"></span>
+<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;fstream&gt;</span><span style="color: #BC7A00"></span>
+<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&lt;iomanip&gt;</span><span style="color: #BC7A00"></span>
+<span style="color: #BC7A00">#include</span> <span style="color: #408080; font-style: italic">&quot;vectormatrixclass.h&quot;</span><span style="color: #BC7A00"></span>
+<span style="color: #008000; font-weight: bold">using</span> <span style="color: #008000; font-weight: bold">namespace</span>  std;
+<span style="color: #408080; font-style: italic">//   Main function begins here</span>
+<span style="color: #B00040">int</span> <span style="color: #0000FF">main</span>(<span style="color: #B00040">int</span>  argc, <span style="color: #B00040">char</span> <span style="color: #666666">*</span> argv[]){
+  <span style="color: #B00040">int</span> dim <span style="color: #666666">=</span> <span style="color: #666666">2</span>;
+  Vector x(dim),xsd(dim), b(dim),x0(dim);
+  Matrix A(dim,dim);
+
+  <span style="color: #408080; font-style: italic">// Set our initial guess</span>
+  x0(<span style="color: #666666">0</span>) <span style="color: #666666">=</span> x0(<span style="color: #666666">1</span>) <span style="color: #666666">=</span> <span style="color: #666666">0</span>;
+  <span style="color: #408080; font-style: italic">// Set the matrix</span>
+  A(<span style="color: #666666">0</span>,<span style="color: #666666">0</span>) <span style="color: #666666">=</span>  <span style="color: #666666">3</span>;    A(<span style="color: #666666">1</span>,<span style="color: #666666">0</span>) <span style="color: #666666">=</span>  <span style="color: #666666">2</span>;   A(<span style="color: #666666">0</span>,<span style="color: #666666">1</span>) <span style="color: #666666">=</span>  <span style="color: #666666">2</span>;   A(<span style="color: #666666">1</span>,<span style="color: #666666">1</span>) <span style="color: #666666">=</span>  <span style="color: #666666">6</span>;
+  b(<span style="color: #666666">0</span>) <span style="color: #666666">=</span> <span style="color: #666666">2</span>; b(<span style="color: #666666">1</span>) <span style="color: #666666">=</span> <span style="color: #666666">-8</span>;
+  cout <span style="color: #666666">&lt;&lt;</span> <span style="color: #BA2121">&quot;The Matrix A that we are using: &quot;</span> <span style="color: #666666">&lt;&lt;</span> endl;
+  A.Print();
+  cout <span style="color: #666666">&lt;&lt;</span> endl;
+  xsd <span style="color: #666666">=</span> SteepestDescent(A,b,x0);
+  cout <span style="color: #666666">&lt;&lt;</span> <span style="color: #BA2121">&quot;The approximate solution using Steepest Descent is: &quot;</span> <span style="color: #666666">&lt;&lt;</span> endl;
+  xsd.Print();
+  cout <span style="color: #666666">&lt;&lt;</span> endl;
 }
 </pre></div>
 <p>
@@ -313,7 +338,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs032.html">33</a></li>
   <li><a href="._Splines-bs033.html">34</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs025.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs025.html b/doc/pub/Splines/html/._Splines-bs025.html
index 9face255c..24f29b77e 100644
--- a/doc/pub/Splines/html/._Splines-bs025.html
+++ b/doc/pub/Splines/html/._Splines-bs025.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,72 +274,40 @@ MathJax.Hub.Config({
 <a name="part0025"></a>
 <!-- !split -->
 
-<h2 id="___sec24" class="anchor">Steepest descent example </h2>
-
+<h2 id="___sec24" class="anchor">The routine for the steepest descent method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
 <p>
 
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy.linalg</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">la</span>
-
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scipy.optimize</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sopt</span>
-
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pt</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> axes3d
-
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">0.5*</span>x[<span style="color: #666666">0</span>]<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">2.5*</span>x[<span style="color: #666666">1</span>]<span style="color: #666666">**2</span>
-
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">df</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>array([x[<span style="color: #666666">0</span>], <span style="color: #666666">5*</span>x[<span style="color: #666666">1</span>]])
-
-fig <span style="color: #666666">=</span> pt<span style="color: #666666">.</span>figure()
-ax <span style="color: #666666">=</span> fig<span style="color: #666666">.</span>gca(projection<span style="color: #666666">=</span><span style="color: #BA2121">&quot;3d&quot;</span>)
-
-xmesh, ymesh <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mgrid[<span style="color: #666666">-2</span>:<span style="color: #666666">2</span>:<span style="color: #666666">50j</span>,<span style="color: #666666">-2</span>:<span style="color: #666666">2</span>:<span style="color: #666666">50j</span>]
-fmesh <span style="color: #666666">=</span> f(np<span style="color: #666666">.</span>array([xmesh, ymesh]))
-ax<span style="color: #666666">.</span>plot_surface(xmesh, ymesh, fmesh)
+<!-- code=c++ (!bc cppcod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>Vector <span style="color: #0000FF">SteepestDescent</span>(Matrix A, Vector b, Vector x0){
+  <span style="color: #B00040">int</span> IterMax, i;
+  <span style="color: #B00040">int</span> dim <span style="color: #666666">=</span> x0.Dimension();
+  <span style="color: #008000; font-weight: bold">const</span> <span style="color: #B00040">double</span> tolerance <span style="color: #666666">=</span> <span style="color: #666666">1.0e-14</span>;
+  Vector x(dim),f(dim),z(dim);
+  <span style="color: #B00040">double</span> c,alpha,d;
+  IterMax <span style="color: #666666">=</span> <span style="color: #666666">30</span>;
+  x <span style="color: #666666">=</span> x0;
+  r <span style="color: #666666">=</span> A<span style="color: #666666">*</span>x<span style="color: #666666">-</span>b;
+  i <span style="color: #666666">=</span> <span style="color: #666666">0</span>;
+  <span style="color: #008000; font-weight: bold">while</span> (i <span style="color: #666666">&lt;=</span> IterMax){
+    z <span style="color: #666666">=</span> A<span style="color: #666666">*</span>r;
+    c <span style="color: #666666">=</span> dot(r,r);
+    alpha <span style="color: #666666">=</span> c<span style="color: #666666">/</span>dot(r,z);
+    x <span style="color: #666666">=</span> x <span style="color: #666666">-</span> alpha<span style="color: #666666">*</span>r;
+    r <span style="color: #666666">=</span>  A<span style="color: #666666">*</span>x<span style="color: #666666">-</span>b;
+    <span style="color: #008000; font-weight: bold">if</span>(sqrt(dot(r,r)) <span style="color: #666666">&lt;</span> tolerance) <span style="color: #008000; font-weight: bold">break</span>;
+    i<span style="color: #666666">++</span>;
+  }
+  <span style="color: #008000; font-weight: bold">return</span> x;
+}
 </pre></div>
 <p>
-And then as countor plot
-<p>
+</div>
+</div>
 
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
-pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh)
-guesses <span style="color: #666666">=</span> [np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">2./5</span>])]
-</pre></div>
-<p>
-Find guesses
-<p>
 
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>x <span style="color: #666666">=</span> guesses[<span style="color: #666666">-1</span>]
-s <span style="color: #666666">=</span> <span style="color: #666666">-</span>df(x)
-</pre></div>
-<p>
-Run it!
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1d</span>(alpha):
-    <span style="color: #008000; font-weight: bold">return</span> f(x <span style="color: #666666">+</span> alpha<span style="color: #666666">*</span>s)
-
-alpha_opt <span style="color: #666666">=</span> sopt<span style="color: #666666">.</span>golden(f1d)
-next_guess <span style="color: #666666">=</span> x <span style="color: #666666">+</span> alpha_opt <span style="color: #666666">*</span> s
-guesses<span style="color: #666666">.</span>append(next_guess)
-<span style="color: #008000; font-weight: bold">print</span>(next_guess)
-</pre></div>
-<p>
-What happened?
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
-pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh, <span style="color: #666666">50</span>)
-it_array <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array(guesses)
-pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666">.</span>T[<span style="color: #666666">0</span>], it_array<span style="color: #666666">.</span>T[<span style="color: #666666">1</span>], <span style="color: #BA2121">&quot;x-&quot;</span>)
-</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -345,7 +334,7 @@ pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666"
   <li><a href="._Splines-bs033.html">34</a></li>
   <li><a href="._Splines-bs034.html">35</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs026.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs026.html b/doc/pub/Splines/html/._Splines-bs026.html
index 94a0a1fc8..160569e29 100644
--- a/doc/pub/Splines/html/._Splines-bs026.html
+++ b/doc/pub/Splines/html/._Splines-bs026.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,8 +274,72 @@ MathJax.Hub.Config({
 <a name="part0026"></a>
 <!-- !split -->
 
-<h2 id="___sec25" class="anchor">Conjugate gradient </h2>
+<h2 id="___sec25" class="anchor">Steepest descent example </h2>
 
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy.linalg</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">la</span>
+
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">scipy.optimize</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sopt</span>
+
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pt</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> axes3d
+
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">0.5*</span>x[<span style="color: #666666">0</span>]<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">2.5*</span>x[<span style="color: #666666">1</span>]<span style="color: #666666">**2</span>
+
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">df</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>array([x[<span style="color: #666666">0</span>], <span style="color: #666666">5*</span>x[<span style="color: #666666">1</span>]])
+
+fig <span style="color: #666666">=</span> pt<span style="color: #666666">.</span>figure()
+ax <span style="color: #666666">=</span> fig<span style="color: #666666">.</span>gca(projection<span style="color: #666666">=</span><span style="color: #BA2121">&quot;3d&quot;</span>)
+
+xmesh, ymesh <span style="color: #666666">=</span> np<span style="color: #666666">.</span>mgrid[<span style="color: #666666">-2</span>:<span style="color: #666666">2</span>:<span style="color: #666666">50j</span>,<span style="color: #666666">-2</span>:<span style="color: #666666">2</span>:<span style="color: #666666">50j</span>]
+fmesh <span style="color: #666666">=</span> f(np<span style="color: #666666">.</span>array([xmesh, ymesh]))
+ax<span style="color: #666666">.</span>plot_surface(xmesh, ymesh, fmesh)
+</pre></div>
+<p>
+And then as countor plot
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
+pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh)
+guesses <span style="color: #666666">=</span> [np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">2./5</span>])]
+</pre></div>
+<p>
+Find guesses
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>x <span style="color: #666666">=</span> guesses[<span style="color: #666666">-1</span>]
+s <span style="color: #666666">=</span> <span style="color: #666666">-</span>df(x)
+</pre></div>
+<p>
+Run it!
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1d</span>(alpha):
+    <span style="color: #008000; font-weight: bold">return</span> f(x <span style="color: #666666">+</span> alpha<span style="color: #666666">*</span>s)
+
+alpha_opt <span style="color: #666666">=</span> sopt<span style="color: #666666">.</span>golden(f1d)
+next_guess <span style="color: #666666">=</span> x <span style="color: #666666">+</span> alpha_opt <span style="color: #666666">*</span> s
+guesses<span style="color: #666666">.</span>append(next_guess)
+<span style="color: #008000; font-weight: bold">print</span>(next_guess)
+</pre></div>
+<p>
+What happened?
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">&quot;equal&quot;</span>)
+pt<span style="color: #666666">.</span>contour(xmesh, ymesh, fmesh, <span style="color: #666666">50</span>)
+it_array <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array(guesses)
+pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666">.</span>T[<span style="color: #666666">0</span>], it_array<span style="color: #666666">.</span>T[<span style="color: #666666">1</span>], <span style="color: #BA2121">&quot;x-&quot;</span>)
+</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -281,7 +366,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs034.html">35</a></li>
   <li><a href="._Splines-bs035.html">36</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs027.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs027.html b/doc/pub/Splines/html/._Splines-bs027.html
index b5ed4f3ab..5bbe32891 100644
--- a/doc/pub/Splines/html/._Splines-bs027.html
+++ b/doc/pub/Splines/html/._Splines-bs027.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,37 +272,9 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0027"></a>
-<!-- !split  -->
+<!-- !split -->
 
-<h2 id="___sec26" class="anchor">Revisiting our first homework </h2>
-
-<p>
-We will use linear regression as a case study for the gradient descent
-methods. Linear regression is a great test case for the gradient
-descent methods discussed in the lectures since it has several
-desirable properties such as:
-
-<ol>
-<li> An analytical solution (recall homework set 1).</li>
-<li> The gradient can be computed analytically.</li>
-<li> The cost function is convex which guarantees that gradient descent converges for small enough learning rates</li>
-</ol>
-
-We revisit the example from homework set 1 where we had 
-$$
-y_i = 5x_i^2 + 0.1\xi_i, \ i=1,\cdots,100
-$$
-
-with \( x_i \in [0,1]  \) chosen randomly with a uniform distribution. Additionally \( \xi_i \) represents stochastic noise chosen according to a normal distribution \( \cal {N}(0,1) \). 
-The linear regression model is given by 
-$$
-h_\beta(x) = \hat{y} = \beta_0 + \beta_1 x,
-$$
-
-such that 
-$$
-\hat{y}_i = \beta_0 + \beta_1 x_i.
-$$
+<h2 id="___sec26" class="anchor">Conjugate gradient </h2>
 
 <p>
 <p>
@@ -309,7 +302,7 @@ $$
   <li><a href="._Splines-bs035.html">36</a></li>
   <li><a href="._Splines-bs036.html">37</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs028.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs028.html b/doc/pub/Splines/html/._Splines-bs028.html
index 9a3ebf016..187c6b180 100644
--- a/doc/pub/Splines/html/._Splines-bs028.html
+++ b/doc/pub/Splines/html/._Splines-bs028.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,27 +274,35 @@ MathJax.Hub.Config({
 <a name="part0028"></a>
 <!-- !split  -->
 
-<h2 id="___sec27" class="anchor">Gradient descent example </h2>
+<h2 id="___sec27" class="anchor">Revisiting our first homework </h2>
 
 <p>
-Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
+We will use linear regression as a case study for the gradient descent
+methods. Linear regression is a great test case for the gradient
+descent methods discussed in the lectures since it has several
+desirable properties such as:
 
-<p>
-It is convenient to write \( \mathbf{\hat{y}} = X\beta \) where \( X \in \mathbb{R}^{100 \times 2}  \) is the design matrix given by
+<ol>
+<li> An analytical solution (recall homework set 1).</li>
+<li> The gradient can be computed analytically.</li>
+<li> The cost function is convex which guarantees that gradient descent converges for small enough learning rates</li>
+</ol>
+
+We revisit the example from homework set 1 where we had 
 $$
-X \equiv \begin{bmatrix}
-1 &amp; x_1  \\
-\vdots &amp; \vdots  \\
-1 &amp; x_{100} &amp;  \\
-\end{bmatrix}.
+y_i = 5x_i^2 + 0.1\xi_i, \ i=1,\cdots,100
 $$
 
-The loss function is given by 
+with \( x_i \in [0,1]  \) chosen randomly with a uniform distribution. Additionally \( \xi_i \) represents stochastic noise chosen according to a normal distribution \( \cal {N}(0,1) \). 
+The linear regression model is given by 
 $$
-C(\beta) = ||X\beta-\mathbf{y}||^2 = ||X\beta||^2 - 2 \mathbf{y}^T X\beta + ||\mathbf{y}||^2 = \sum_{i=1}^{100} (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2 
+h_\beta(x) = \hat{y} = \beta_0 + \beta_1 x,
 $$
 
-and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
+such that 
+$$
+\hat{y}_i = \beta_0 + \beta_1 x_i.
+$$
 
 <p>
 <p>
@@ -301,7 +330,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
   <li><a href="._Splines-bs036.html">37</a></li>
   <li><a href="._Splines-bs037.html">38</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs029.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs029.html b/doc/pub/Splines/html/._Splines-bs029.html
index 669f6e55b..b661bba59 100644
--- a/doc/pub/Splines/html/._Splines-bs029.html
+++ b/doc/pub/Splines/html/._Splines-bs029.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,19 +272,29 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0029"></a>
-<!-- !split -->
+<!-- !split  -->
 
-<h2 id="___sec28" class="anchor">The derivative of the cost/loss function </h2>
+<h2 id="___sec28" class="anchor">Gradient descent example </h2>
 
 <p>
-Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
+Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
+
+<p>
+It is convenient to write \( \mathbf{\hat{y}} = X\beta \) where \( X \in \mathbb{R}^{100 \times 2}  \) is the design matrix given by
 $$
-\nabla_{\beta} C(\beta) = (\partial C(\beta) / \partial \beta_0, \partial C(\beta) / \partial \beta_1)^T = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
-\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
-\end{bmatrix} = 2X^T(X\beta - \mathbf{y}), 
+X \equiv \begin{bmatrix}
+1 &amp; x_1  \\
+\vdots &amp; \vdots  \\
+1 &amp; x_{100} &amp;  \\
+\end{bmatrix}.
 $$
 
-where \( X \) is the design matrix defined above.
+The loss function is given by 
+$$
+C(\beta) = ||X\beta-\mathbf{y}||^2 = ||X\beta||^2 - 2 \mathbf{y}^T X\beta + ||\mathbf{y}||^2 = \sum_{i=1}^{100} (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2 
+$$
+
+and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 
 <p>
 <p>
@@ -291,7 +322,7 @@ where \( X \) is the design matrix defined above.
   <li><a href="._Splines-bs037.html">38</a></li>
   <li><a href="._Splines-bs038.html">39</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs030.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs030.html b/doc/pub/Splines/html/._Splines-bs030.html
index 9c1875db6..55dc20273 100644
--- a/doc/pub/Splines/html/._Splines-bs030.html
+++ b/doc/pub/Splines/html/._Splines-bs030.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,16 +274,17 @@ MathJax.Hub.Config({
 <a name="part0030"></a>
 <!-- !split -->
 
-<h2 id="___sec29" class="anchor">The Hessian matrix </h2>
-The Hessian matrix of \( C(\beta) \) is given by 
+<h2 id="___sec29" class="anchor">The derivative of the cost/loss function </h2>
+
+<p>
+Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
 $$
-\hat{H} \equiv \begin{bmatrix}
-\frac{\partial^2 C(\beta)}{\partial \beta_0^2} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
-\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &amp;  \\
-\end{bmatrix} = 2X^T X.
+\nabla_{\beta} C(\beta) = (\partial C(\beta) / \partial \beta_0, \partial C(\beta) / \partial \beta_1)^T = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} = 2X^T(X\beta - \mathbf{y}), 
 $$
 
-This result implies that \( C(\beta) \) is a convex function since the matrix \( X^T X \) always is positive semi-definite.
+where \( X \) is the design matrix defined above.
 
 <p>
 <p>
@@ -290,7 +312,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
   <li><a href="._Splines-bs038.html">39</a></li>
   <li><a href="._Splines-bs039.html">40</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs031.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs031.html b/doc/pub/Splines/html/._Splines-bs031.html
index 7478f48c2..fa83fe7da 100644
--- a/doc/pub/Splines/html/._Splines-bs031.html
+++ b/doc/pub/Splines/html/._Splines-bs031.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,44 +274,17 @@ MathJax.Hub.Config({
 <a name="part0031"></a>
 <!-- !split -->
 
-<h2 id="___sec30" class="anchor">Simple program </h2>
-
-<p>
-We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
+<h2 id="___sec30" class="anchor">The Hessian matrix </h2>
+The Hessian matrix of \( C(\beta) \) is given by 
 $$
-\beta_{k+1} = \beta_k - \gamma \nabla_\beta C(\beta_k), \ k=0,1,\cdots 
+\hat{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &amp;  \\
+\end{bmatrix} = 2X^T X.
 $$
 
-<p>
-We can use the expression we computed for the gradient and let use a
-\( \beta_0 \) be chosen randomly and let \( \gamma = 0.001 \). Stop iterating
-when \( ||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8} \).
+This result implies that \( C(\beta) \) is a convex function since the matrix \( X^T X \) always is positive semi-definite.
 
-<p>
-And finally we can compare our solution for \( \beta \) with the analytic result given by 
-\( \beta= (X^TX)^{-1} X^T \mathbf{y} \).
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-
-<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
-<span style="color: #BA2121; font-style: italic">The following setup is just a suggestion, feel free to write it the way you like.</span>
-<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
-
-<span style="color: #408080; font-style: italic">#Setup problem described in the exercise</span>
-N  <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#Nr of datapoints</span>
-M  <span style="color: #666666">=</span> <span style="color: #666666">2</span> <span style="color: #408080; font-style: italic">#Nr of features</span>
-x  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(N) <span style="color: #408080; font-style: italic">#Uniformly generated x-values in [0,1]</span>
-y  <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(N)
-X  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones(N),x] <span style="color: #408080; font-style: italic">#Construct design matrix</span>
-
-<span style="color: #408080; font-style: italic">#Compute beta according to normal equations to compare with GD solution</span>
-Xt_X_inv <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,X))
-Xt_y     <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>transpose(),y)
-beta_NE <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(Xt_X_inv,Xt_y)
-<span style="color: #008000; font-weight: bold">print</span>(beta_NE)
-</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -317,7 +311,7 @@ beta_NE <span style="color: #666666">=</span> np<span style="color: #666666">.</
   <li><a href="._Splines-bs039.html">40</a></li>
   <li><a href="._Splines-bs040.html">41</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs032.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs032.html b/doc/pub/Splines/html/._Splines-bs032.html
index bf241c7bb..df9278bbe 100644
--- a/doc/pub/Splines/html/._Splines-bs032.html
+++ b/doc/pub/Splines/html/._Splines-bs032.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,51 +274,43 @@ MathJax.Hub.Config({
 <a name="part0032"></a>
 <!-- !split -->
 
-<h2 id="___sec31" class="anchor">Gradient Descent Example </h2>
+<h2 id="___sec31" class="anchor">Simple program </h2>
 
 <p>
-Another simple example is here
+We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
+$$
+\beta_{k+1} = \beta_k - \gamma \nabla_\beta C(\beta_k), \ k=0,1,\cdots 
+$$
+
+<p>
+We can use the expression we computed for the gradient and let use a
+\( \beta_0 \) be chosen randomly and let \( \gamma = 0.001 \). Stop iterating
+when \( ||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8} \).
+
+<p>
+And finally we can compare our solution for \( \beta \) with the analytic result given by 
+\( \beta= (X^TX)^{-1} X^T \mathbf{y} \).
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> Axes3D
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span> <span style="color: #008000; font-weight: bold">import</span> cm
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">matplotlib.ticker</span> <span style="color: #008000; font-weight: bold">import</span> LinearLocator, FormatStrFormatter
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">sys</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 
-x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
-y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
+<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
+<span style="color: #BA2121; font-style: italic">The following setup is just a suggestion, feel free to write it the way you like.</span>
+<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
 
-xb <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)), x]
-beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb))<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>T)<span style="color: #666666">.</span>dot(y)
-<span style="color: #008000; font-weight: bold">print</span>(beta_linreg)
-beta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
+<span style="color: #408080; font-style: italic">#Setup problem described in the exercise</span>
+N  <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#Nr of datapoints</span>
+M  <span style="color: #666666">=</span> <span style="color: #666666">2</span> <span style="color: #408080; font-style: italic">#Nr of features</span>
+x  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(N) <span style="color: #408080; font-style: italic">#Uniformly generated x-values in [0,1]</span>
+y  <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(N)
+X  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones(N),x] <span style="color: #408080; font-style: italic">#Construct design matrix</span>
 
-eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
-Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
-m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
-
-<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
-    gradients <span style="color: #666666">=</span> <span style="color: #666666">2.0/</span>m<span style="color: #666666">*</span>xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>dot(beta)<span style="color: #666666">-</span>y)
-    beta <span style="color: #666666">-=</span> eta<span style="color: #666666">*</span>gradients
-
-<span style="color: #008000; font-weight: bold">print</span>(beta)
-xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0</span>],[<span style="color: #666666">2</span>]])
-xbnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)), xnew]
-ypredict <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(beta)
-ypredict2 <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(beta_linreg)
-plt<span style="color: #666666">.</span>plot(xnew, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
-plt<span style="color: #666666">.</span>plot(xnew, ypredict2, <span style="color: #BA2121">&quot;b-&quot;</span>)
-plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
-plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">2.0</span>,<span style="color: #666666">0</span>, <span style="color: #666666">15.0</span>])
-plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&#39;$x$&#39;</span>)
-plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&#39;$y$&#39;</span>)
-plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r&#39;Gradient descent example&#39;</span>)
-plt<span style="color: #666666">.</span>show()
+<span style="color: #408080; font-style: italic">#Compute beta according to normal equations to compare with GD solution</span>
+Xt_X_inv <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,X))
+Xt_y     <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>transpose(),y)
+beta_NE <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(Xt_X_inv,Xt_y)
+<span style="color: #008000; font-weight: bold">print</span>(beta_NE)
 </pre></div>
 <p>
 <p>
@@ -325,7 +338,7 @@ plt<span style="color: #666666">.</span>show()
   <li><a href="._Splines-bs040.html">41</a></li>
   <li><a href="._Splines-bs041.html">42</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs033.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs033.html b/doc/pub/Splines/html/._Splines-bs033.html
index 73cfcff08..b344e4069 100644
--- a/doc/pub/Splines/html/._Splines-bs033.html
+++ b/doc/pub/Splines/html/._Splines-bs033.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,8 +274,10 @@ MathJax.Hub.Config({
 <a name="part0033"></a>
 <!-- !split -->
 
-<h2 id="___sec32" class="anchor">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec32" class="anchor">Gradient Descent Example </h2>
 
+<p>
+Another simple example is here
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -262,7 +285,10 @@ MathJax.Hub.Config({
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> SGDRegressor
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">mpl_toolkits.mplot3d</span> <span style="color: #008000; font-weight: bold">import</span> Axes3D
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span> <span style="color: #008000; font-weight: bold">import</span> cm
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">matplotlib.ticker</span> <span style="color: #008000; font-weight: bold">import</span> LinearLocator, FormatStrFormatter
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">sys</span>
 
 x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
 y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
@@ -270,9 +296,29 @@ y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>
 xb <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)), x]
 beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb))<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>T)<span style="color: #666666">.</span>dot(y)
 <span style="color: #008000; font-weight: bold">print</span>(beta_linreg)
-sgdreg <span style="color: #666666">=</span> SGDRegressor(n_iter <span style="color: #666666">=</span> <span style="color: #666666">50</span>, penalty<span style="color: #666666">=</span><span style="color: #008000">None</span>, eta0<span style="color: #666666">=0.1</span>)
-sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.</span>ravel())
-<span style="color: #008000; font-weight: bold">print</span>(sgdreg<span style="color: #666666">.</span>intercept_, sgdreg<span style="color: #666666">.</span>coef_)
+beta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
+
+eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
+Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
+m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
+
+<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
+    gradients <span style="color: #666666">=</span> <span style="color: #666666">2.0/</span>m<span style="color: #666666">*</span>xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>dot(beta)<span style="color: #666666">-</span>y)
+    beta <span style="color: #666666">-=</span> eta<span style="color: #666666">*</span>gradients
+
+<span style="color: #008000; font-weight: bold">print</span>(beta)
+xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0</span>],[<span style="color: #666666">2</span>]])
+xbnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)), xnew]
+ypredict <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(beta)
+ypredict2 <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(beta_linreg)
+plt<span style="color: #666666">.</span>plot(xnew, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
+plt<span style="color: #666666">.</span>plot(xnew, ypredict2, <span style="color: #BA2121">&quot;b-&quot;</span>)
+plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
+plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">2.0</span>,<span style="color: #666666">0</span>, <span style="color: #666666">15.0</span>])
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&#39;$x$&#39;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&#39;$y$&#39;</span>)
+plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r&#39;Gradient descent example&#39;</span>)
+plt<span style="color: #666666">.</span>show()
 </pre></div>
 <p>
 <p>
@@ -300,7 +346,7 @@ sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.
   <li><a href="._Splines-bs041.html">42</a></li>
   <li><a href="._Splines-bs042.html">43</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs034.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs034.html b/doc/pub/Splines/html/._Splines-bs034.html
index 8181deb1a..46f8f5b7e 100644
--- a/doc/pub/Splines/html/._Splines-bs034.html
+++ b/doc/pub/Splines/html/._Splines-bs034.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,61 +272,28 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0034"></a>
-<!-- !split  -->
+<!-- !split -->
 
-<h2 id="___sec33" class="anchor">Gradient descent and Ridge </h2>
-
-<p>
-We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \), 
-$$
-C_{\text{ridge}}(\beta) = ||X\beta -\mathbf{y}||^2 + \lambda ||\beta||^2, \ \lambda \geq 0.
-$$
-
-<p>
-In order to minimize \( C_{\text{ridge}}(\beta) \) using GD we only have adjust the gradient as follows 
-$$
-\nabla_\beta C_{\text{ridge}}(\beta)  = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
-\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
-\end{bmatrix} + 2\lambda\begin{bmatrix} \beta_0 \\ \beta_1\end{bmatrix} = 2 (X^T(X\beta - \mathbf{y})+\lambda \beta).
-$$
-
-<p>
-We can now extend our program to minimize \( C_{\text{ridge}}(\beta) \) using gradient descent and compare with the analytical solution given by 
-$$
-\beta_{\text{ridge}} = \left(X^T X + \lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y},
-$$
-
-for \( \lambda = {0,1,10,50,100} \) (\( \lambda = 0 \) corresponds to ordinary least squares). 
-We can then compute \( ||\beta_{\text{ridge}}|| \) for each \( \lambda \).
+<h2 id="___sec33" class="anchor">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> SGDRegressor
 
-<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
-<span style="color: #BA2121; font-style: italic">The following setup is just a suggestion, feel free to write it the way you like.</span>
-<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
+x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
+y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
 
-<span style="color: #408080; font-style: italic">#Setup problem described in the exercise</span>
-N  <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#Nr of datapoints</span>
-M  <span style="color: #666666">=</span> <span style="color: #666666">2</span>   <span style="color: #408080; font-style: italic">#Nr of features</span>
-x  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(N)
-y  <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(N)
-
-
-<span style="color: #408080; font-style: italic">#Compute analytic beta for Ridge regression </span>
-X    <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones(N),x]
-XT_X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,X)
-
-l  <span style="color: #666666">=</span> <span style="color: #666666">0.1</span> <span style="color: #408080; font-style: italic">#Ridge parameter lambda</span>
-Id <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(XT_X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])
-
-Z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(XT_X<span style="color: #666666">+</span>l<span style="color: #666666">*</span>Id)
-beta_ridge <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(Z,np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,y))
-
-<span style="color: #008000; font-weight: bold">print</span>(beta_ridge)
-<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>norm(beta_ridge)) <span style="color: #408080; font-style: italic">#||beta||</span>
+xb <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)), x]
+beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb))<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>T)<span style="color: #666666">.</span>dot(y)
+<span style="color: #008000; font-weight: bold">print</span>(beta_linreg)
+sgdreg <span style="color: #666666">=</span> SGDRegressor(n_iter <span style="color: #666666">=</span> <span style="color: #666666">50</span>, penalty<span style="color: #666666">=</span><span style="color: #008000">None</span>, eta0<span style="color: #666666">=0.1</span>)
+sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.</span>ravel())
+<span style="color: #008000; font-weight: bold">print</span>(sgdreg<span style="color: #666666">.</span>intercept_, sgdreg<span style="color: #666666">.</span>coef_)
 </pre></div>
 <p>
 <p>
@@ -333,7 +321,7 @@ beta_ridge <span style="color: #666666">=</span> np<span style="color: #666666">
   <li><a href="._Splines-bs042.html">43</a></li>
   <li><a href="._Splines-bs043.html">44</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs035.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs035.html b/doc/pub/Splines/html/._Splines-bs035.html
index 54b3a6010..cdf78c4d5 100644
--- a/doc/pub/Splines/html/._Splines-bs035.html
+++ b/doc/pub/Splines/html/._Splines-bs035.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,59 +272,61 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0035"></a>
-<!-- !split -->
+<!-- !split  -->
 
-<h2 id="___sec34" class="anchor">Automatic differentiation </h2>
-Python has tools for so-called <b>automatic differentiation</b>.
-Consider the following example
+<h2 id="___sec34" class="anchor">Gradient descent and Ridge </h2>
+
+<p>
+We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \), 
 $$
-f(x) = \sin\left(2\pi x + x^2\right)
+C_{\text{ridge}}(\beta) = ||X\beta -\mathbf{y}||^2 + \lambda ||\beta||^2, \ \lambda \geq 0.
 $$
 
-which has the following derivative
+<p>
+In order to minimize \( C_{\text{ridge}}(\beta) \) using GD we only have adjust the gradient as follows 
 $$
-f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right) 
+\nabla_\beta C_{\text{ridge}}(\beta)  = 2\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} + 2\lambda\begin{bmatrix} \beta_0 \\ \beta_1\end{bmatrix} = 2 (X^T(X\beta - \mathbf{y})+\lambda \beta).
 $$
 
-Using <b>autograd</b> we have
+<p>
+We can now extend our program to minimize \( C_{\text{ridge}}(\beta) \) using gradient descent and compare with the analytical solution given by 
+$$
+\beta_{\text{ridge}} = \left(X^T X + \lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y},
+$$
+
+for \( \lambda = {0,1,10,50,100} \) (\( \lambda = 0 \) corresponds to ordinary least squares). 
+We can then compute \( ||\beta_{\text{ridge}}|| \) for each \( \lambda \).
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 
-<span style="color: #408080; font-style: italic"># To do elementwise differentiation:</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> elementwise_grad <span style="color: #008000; font-weight: bold">as</span> egrad 
+<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
+<span style="color: #BA2121; font-style: italic">The following setup is just a suggestion, feel free to write it the way you like.</span>
+<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
 
-<span style="color: #408080; font-style: italic"># To plot:</span>
-<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span> 
+<span style="color: #408080; font-style: italic">#Setup problem described in the exercise</span>
+N  <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#Nr of datapoints</span>
+M  <span style="color: #666666">=</span> <span style="color: #666666">2</span>   <span style="color: #408080; font-style: italic">#Nr of features</span>
+x  <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(N)
+y  <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">**2</span> <span style="color: #666666">+</span> <span style="color: #666666">0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(N)
 
 
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sin(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>)
+<span style="color: #408080; font-style: italic">#Compute analytic beta for Ridge regression </span>
+X    <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones(N),x]
+XT_X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,X)
 
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f_grad_analytic</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>cos(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>)<span style="color: #666666">*</span>(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi <span style="color: #666666">+</span> <span style="color: #666666">2*</span>x)
+l  <span style="color: #666666">=</span> <span style="color: #666666">0.1</span> <span style="color: #408080; font-style: italic">#Ridge parameter lambda</span>
+Id <span style="color: #666666">=</span> np<span style="color: #666666">.</span>eye(XT_X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>])
 
-<span style="color: #408080; font-style: italic"># Do the comparison:</span>
-x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>,<span style="color: #666666">1</span>,<span style="color: #666666">1000</span>)
+Z <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(XT_X<span style="color: #666666">+</span>l<span style="color: #666666">*</span>Id)
+beta_ridge <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(Z,np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T,y))
 
-f_grad <span style="color: #666666">=</span> egrad(f)
-
-computed <span style="color: #666666">=</span> f_grad(x)
-analytic <span style="color: #666666">=</span> f_grad_analytic(x)
-
-plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&#39;Derivative computed from Autograd compared with the analytical derivative&#39;</span>)
-plt<span style="color: #666666">.</span>plot(x,computed,label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;autograd&#39;</span>)
-plt<span style="color: #666666">.</span>plot(x,analytic,label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;analytic&#39;</span>)
-
-plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;x&#39;</span>)
-plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;y&#39;</span>)
-plt<span style="color: #666666">.</span>legend()
-
-plt<span style="color: #666666">.</span>show()
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The max absolute difference is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(np<span style="color: #666666">.</span>max(np<span style="color: #666666">.</span>abs(computed <span style="color: #666666">-</span> analytic))))
+<span style="color: #008000; font-weight: bold">print</span>(beta_ridge)
+<span style="color: #008000; font-weight: bold">print</span>(np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>norm(beta_ridge)) <span style="color: #408080; font-style: italic">#||beta||</span>
 </pre></div>
 <p>
 <p>
@@ -331,7 +354,7 @@ plt<span style="color: #666666">.</span>show()
   <li><a href="._Splines-bs043.html">44</a></li>
   <li><a href="._Splines-bs044.html">45</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs036.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs036.html b/doc/pub/Splines/html/._Splines-bs036.html
index 7bc4f9ea6..856e3eefb 100644
--- a/doc/pub/Splines/html/._Splines-bs036.html
+++ b/doc/pub/Splines/html/._Splines-bs036.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,37 +272,59 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0036"></a>
-<!-- !split  -->
+<!-- !split -->
 
-<h2 id="___sec35" class="anchor">Using autograd </h2>
+<h2 id="___sec35" class="anchor">Automatic differentiation </h2>
+Python has tools for so-called <b>automatic differentiation</b>.
+Consider the following example
+$$
+f(x) = \sin\left(2\pi x + x^2\right)
+$$
 
-<p>
-Here we
-experiment with what kind of functions Autograd is capable
-of finding the gradient of. The following Python functions are just
-meant to illustrate what Autograd can do, but please feel free to
-experiment with other, possibly more complicated, functions as well.
+which has the following derivative
+$$
+f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right) 
+$$
+
+Using <b>autograd</b> we have
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
 
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">**3</span> <span style="color: #666666">+</span> <span style="color: #666666">1</span>
+<span style="color: #408080; font-style: italic"># To do elementwise differentiation:</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> elementwise_grad <span style="color: #008000; font-weight: bold">as</span> egrad 
 
-f1_grad <span style="color: #666666">=</span> grad(f1)
+<span style="color: #408080; font-style: italic"># To plot:</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span> 
 
-<span style="color: #408080; font-style: italic"># Remember to send in float as argument to the computed gradient from Autograd!</span>
-a <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
 
-<span style="color: #408080; font-style: italic"># See the evaluated gradient at a using autograd:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f1 evaluated at a = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> using autograd is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(a,f1_grad(a)))
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sin(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>)
 
-<span style="color: #408080; font-style: italic"># Compare with the analytical derivative, that is f1&#39;(x) = 3*x**2 </span>
-grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">3*</span>a<span style="color: #666666">**2</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f1 evaluated at a = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> by finding the analytic expression is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(a,grad_analytical))
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f_grad_analytic</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>cos(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>)<span style="color: #666666">*</span>(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi <span style="color: #666666">+</span> <span style="color: #666666">2*</span>x)
+
+<span style="color: #408080; font-style: italic"># Do the comparison:</span>
+x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>,<span style="color: #666666">1</span>,<span style="color: #666666">1000</span>)
+
+f_grad <span style="color: #666666">=</span> egrad(f)
+
+computed <span style="color: #666666">=</span> f_grad(x)
+analytic <span style="color: #666666">=</span> f_grad_analytic(x)
+
+plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&#39;Derivative computed from Autograd compared with the analytical derivative&#39;</span>)
+plt<span style="color: #666666">.</span>plot(x,computed,label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;autograd&#39;</span>)
+plt<span style="color: #666666">.</span>plot(x,analytic,label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;analytic&#39;</span>)
+
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;x&#39;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;y&#39;</span>)
+plt<span style="color: #666666">.</span>legend()
+
+plt<span style="color: #666666">.</span>show()
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The max absolute difference is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(np<span style="color: #666666">.</span>max(np<span style="color: #666666">.</span>abs(computed <span style="color: #666666">-</span> analytic))))
 </pre></div>
 <p>
 <p>
@@ -309,7 +352,7 @@ grad_analytical <span style="color: #666666">=</span> <span style="color: #66666
   <li><a href="._Splines-bs044.html">45</a></li>
   <li><a href="._Splines-bs045.html">46</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs037.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs037.html b/doc/pub/Splines/html/._Splines-bs037.html
index f52b5b3ae..d50116e74 100644
--- a/doc/pub/Splines/html/._Splines-bs037.html
+++ b/doc/pub/Splines/html/._Splines-bs037.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,55 +272,38 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0037"></a>
-<!-- !split -->
+<!-- !split  -->
 
-<h2 id="___sec36" class="anchor">Autograd with more complicated functions </h2>
+<h2 id="___sec36" class="anchor">Using autograd </h2>
 
 <p>
-To differentiate with respect to two (or more) arguments of a Python
-function, Autograd need to know at which variable the function if
-being differentiated with respect to.
+Here we
+experiment with what kind of functions Autograd is capable
+of finding the gradient of. The following Python functions are just
+meant to illustrate what Autograd can do, but please feel free to
+experiment with other, possibly more complicated, functions as well.
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f2</span>(x1,x2):
-    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">3*</span>x1<span style="color: #666666">**3</span> <span style="color: #666666">+</span> x2<span style="color: #666666">*</span>(x1 <span style="color: #666666">-</span> <span style="color: #666666">5</span>) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
 
-<span style="color: #408080; font-style: italic"># By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1</span>
-f2_grad_x1 <span style="color: #666666">=</span> grad(f2,<span style="color: #666666">0</span>)
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f1</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">**3</span> <span style="color: #666666">+</span> <span style="color: #666666">1</span>
 
-<span style="color: #408080; font-style: italic"># ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad</span>
-f2_grad_x2 <span style="color: #666666">=</span> grad(f2,<span style="color: #666666">1</span>)
+f1_grad <span style="color: #666666">=</span> grad(f1)
 
-x1 <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
-x2 <span style="color: #666666">=</span> <span style="color: #666666">3.0</span> 
+<span style="color: #408080; font-style: italic"># Remember to send in float as argument to the computed gradient from Autograd!</span>
+a <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
 
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Evaluating at x1 = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">, x2 = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x1,x2))
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;-&quot;</span><span style="color: #666666">*30</span>)
+<span style="color: #408080; font-style: italic"># See the evaluated gradient at a using autograd:</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f1 evaluated at a = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> using autograd is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(a,f1_grad(a)))
 
-<span style="color: #408080; font-style: italic"># Compare with the analytical derivatives:</span>
-
-<span style="color: #408080; font-style: italic"># Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:</span>
-f2_grad_x1_analytical <span style="color: #666666">=</span> <span style="color: #666666">9*</span>x1<span style="color: #666666">**2</span> <span style="color: #666666">+</span> x2
-
-<span style="color: #408080; font-style: italic"># Derivative of f2 w.r.t x2 is: x1 - 5:</span>
-f2_grad_x2_analytical <span style="color: #666666">=</span> x1 <span style="color: #666666">-</span> <span style="color: #666666">5</span>
-
-<span style="color: #408080; font-style: italic"># See the evaluated derivations:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f2 w.r.t x1: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x1(x1,x2) ))
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f2 w.r.t x1: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x1(x1,x2) ))
-
-<span style="color: #008000; font-weight: bold">print</span>()
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f2 w.r.t x2: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x2(x1,x2) ))
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f2 w.r.t x2: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x2(x1,x2) ))
+<span style="color: #408080; font-style: italic"># Compare with the analytical derivative, that is f1&#39;(x) = 3*x**2 </span>
+grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">3*</span>a<span style="color: #666666">**2</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f1 evaluated at a = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> by finding the analytic expression is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(a,grad_analytical))
 </pre></div>
-<p>
-Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.
-
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -326,7 +330,7 @@ Note that the grad function will not produce the true gradient of the function.
   <li><a href="._Splines-bs045.html">46</a></li>
   <li><a href="._Splines-bs046.html">47</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs038.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs038.html b/doc/pub/Splines/html/._Splines-bs038.html
index f52485bfa..18a066195 100644
--- a/doc/pub/Splines/html/._Splines-bs038.html
+++ b/doc/pub/Splines/html/._Splines-bs038.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,36 +274,52 @@ MathJax.Hub.Config({
 <a name="part0038"></a>
 <!-- !split -->
 
-<h2 id="___sec37" class="anchor">More complicated functions using the elements of their arguments directly </h2>
+<h2 id="___sec37" class="anchor">Autograd with more complicated functions </h2>
+
+<p>
+To differentiate with respect to two (or more) arguments of a Python
+function, Autograd need to know at which variable the function if
+being differentiated with respect to.
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f3</span>(x): <span style="color: #408080; font-style: italic"># Assumes x is an array of length 5 or higher</span>
-    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">2*</span>x[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> <span style="color: #666666">3*</span>x[<span style="color: #666666">1</span>] <span style="color: #666666">+</span> <span style="color: #666666">5*</span>x[<span style="color: #666666">2</span>] <span style="color: #666666">+</span> <span style="color: #666666">7*</span>x[<span style="color: #666666">3</span>] <span style="color: #666666">+</span> <span style="color: #666666">11*</span>x[<span style="color: #666666">4</span>]<span style="color: #666666">**2</span>
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f2</span>(x1,x2):
+    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">3*</span>x1<span style="color: #666666">**3</span> <span style="color: #666666">+</span> x2<span style="color: #666666">*</span>(x1 <span style="color: #666666">-</span> <span style="color: #666666">5</span>) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
 
-f3_grad <span style="color: #666666">=</span> grad(f3)
+<span style="color: #408080; font-style: italic"># By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1</span>
+f2_grad_x1 <span style="color: #666666">=</span> grad(f2,<span style="color: #666666">0</span>)
 
-x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>,<span style="color: #666666">4</span>,<span style="color: #666666">5</span>)
+<span style="color: #408080; font-style: italic"># ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad</span>
+f2_grad_x2 <span style="color: #666666">=</span> grad(f2,<span style="color: #666666">1</span>)
 
-<span style="color: #408080; font-style: italic"># Print the computed gradient:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed gradient of f3 is: &quot;</span>, f3_grad(x))
+x1 <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
+x2 <span style="color: #666666">=</span> <span style="color: #666666">3.0</span> 
 
-<span style="color: #408080; font-style: italic"># The analytical gradient is: (2, 3, 5, 7, 22*x[4])</span>
-f3_grad_analytical <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">3</span>, <span style="color: #666666">5</span>, <span style="color: #666666">7</span>, <span style="color: #666666">22*</span>x[<span style="color: #666666">4</span>]])
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Evaluating at x1 = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">, x2 = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x1,x2))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;-&quot;</span><span style="color: #666666">*30</span>)
 
-<span style="color: #408080; font-style: italic"># Print the analytical gradient:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical gradient of f3 is: &quot;</span>, f3_grad_analytical)
+<span style="color: #408080; font-style: italic"># Compare with the analytical derivatives:</span>
+
+<span style="color: #408080; font-style: italic"># Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:</span>
+f2_grad_x1_analytical <span style="color: #666666">=</span> <span style="color: #666666">9*</span>x1<span style="color: #666666">**2</span> <span style="color: #666666">+</span> x2
+
+<span style="color: #408080; font-style: italic"># Derivative of f2 w.r.t x2 is: x1 - 5:</span>
+f2_grad_x2_analytical <span style="color: #666666">=</span> x1 <span style="color: #666666">-</span> <span style="color: #666666">5</span>
+
+<span style="color: #408080; font-style: italic"># See the evaluated derivations:</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f2 w.r.t x1: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x1(x1,x2) ))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f2 w.r.t x1: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x1(x1,x2) ))
+
+<span style="color: #008000; font-weight: bold">print</span>()
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f2 w.r.t x2: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x2(x1,x2) ))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f2 w.r.t x2: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>( f2_grad_x2(x1,x2) ))
 </pre></div>
 <p>
-Note that in this case, when sending an array as input argument, the
-output from Autograd is another array. This is the true gradient of
-the function, as opposed to the function in the previous example. By
-using arrays to represent the variables, the output from Autograd
-might be easier to work with, as the output is closer to what one
-could expect form a gradient-evaluting function.
+Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.
 
 <p>
 <p>
@@ -310,7 +347,7 @@ could expect form a gradient-evaluting function.
   <li><a href="._Splines-bs046.html">47</a></li>
   <li><a href="._Splines-bs047.html">48</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs039.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs039.html b/doc/pub/Splines/html/._Splines-bs039.html
index 321d77c2f..88baefbf2 100644
--- a/doc/pub/Splines/html/._Splines-bs039.html
+++ b/doc/pub/Splines/html/._Splines-bs039.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,31 +272,39 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0039"></a>
-<!-- !split  -->
+<!-- !split -->
 
-<h2 id="___sec38" class="anchor">Functions using mathematical functions from Numpy </h2>
+<h2 id="___sec38" class="anchor">More complicated functions using the elements of their arguments directly </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f4</span>(x):
-    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sqrt(<span style="color: #666666">1+</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>exp(x) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>sin(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x)
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f3</span>(x): <span style="color: #408080; font-style: italic"># Assumes x is an array of length 5 or higher</span>
+    <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">2*</span>x[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> <span style="color: #666666">3*</span>x[<span style="color: #666666">1</span>] <span style="color: #666666">+</span> <span style="color: #666666">5*</span>x[<span style="color: #666666">2</span>] <span style="color: #666666">+</span> <span style="color: #666666">7*</span>x[<span style="color: #666666">3</span>] <span style="color: #666666">+</span> <span style="color: #666666">11*</span>x[<span style="color: #666666">4</span>]<span style="color: #666666">**2</span>
 
-f4_grad <span style="color: #666666">=</span> grad(f4)
+f3_grad <span style="color: #666666">=</span> grad(f3)
 
-x <span style="color: #666666">=</span> <span style="color: #666666">2.7</span>
+x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>,<span style="color: #666666">4</span>,<span style="color: #666666">5</span>)
 
-<span style="color: #408080; font-style: italic"># Print the computed derivative:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f4 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f4_grad(x)))
+<span style="color: #408080; font-style: italic"># Print the computed gradient:</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed gradient of f3 is: &quot;</span>, f3_grad(x))
 
-<span style="color: #408080; font-style: italic"># The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi</span>
-f4_grad_analytical <span style="color: #666666">=</span> x<span style="color: #666666">/</span>np<span style="color: #666666">.</span>sqrt(<span style="color: #666666">1</span> <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>exp(x) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>cos(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x)<span style="color: #666666">*2*</span>np<span style="color: #666666">.</span>pi
+<span style="color: #408080; font-style: italic"># The analytical gradient is: (2, 3, 5, 7, 22*x[4])</span>
+f3_grad_analytical <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">3</span>, <span style="color: #666666">5</span>, <span style="color: #666666">7</span>, <span style="color: #666666">22*</span>x[<span style="color: #666666">4</span>]])
 
 <span style="color: #408080; font-style: italic"># Print the analytical gradient:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical gradient of f4 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f4_grad_analytical))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical gradient of f3 is: &quot;</span>, f3_grad_analytical)
 </pre></div>
+<p>
+Note that in this case, when sending an array as input argument, the
+output from Autograd is another array. This is the true gradient of
+the function, as opposed to the function in the previous example. By
+using arrays to represent the variables, the output from Autograd
+might be easier to work with, as the output is closer to what one
+could expect form a gradient-evaluting function.
+
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -302,7 +331,7 @@ f4_grad_analytical <span style="color: #666666">=</span> x<span style="color: #6
   <li><a href="._Splines-bs047.html">48</a></li>
   <li><a href="._Splines-bs048.html">49</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs040.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs040.html b/doc/pub/Splines/html/._Splines-bs040.html
index bcd088d66..9e5c23aae 100644
--- a/doc/pub/Splines/html/._Splines-bs040.html
+++ b/doc/pub/Splines/html/._Splines-bs040.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -251,27 +272,30 @@ MathJax.Hub.Config({
 <p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
 
 <a name="part0040"></a>
-<!-- !split -->
+<!-- !split  -->
 
-<h2 id="___sec39" class="anchor">More autograd </h2>
+<h2 id="___sec39" class="anchor">Functions using mathematical functions from Numpy </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f5</span>(x):
-    <span style="color: #008000; font-weight: bold">if</span> x <span style="color: #666666">&gt;=</span> <span style="color: #666666">0</span>:
-        <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">**2</span>
-    <span style="color: #008000; font-weight: bold">else</span>:
-        <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">-3*</span>x <span style="color: #666666">+</span> <span style="color: #666666">1</span>
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f4</span>(x):
+    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>sqrt(<span style="color: #666666">1+</span>x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>exp(x) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>sin(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x)
 
-f5_grad <span style="color: #666666">=</span> grad(f5)
+f4_grad <span style="color: #666666">=</span> grad(f4)
 
 x <span style="color: #666666">=</span> <span style="color: #666666">2.7</span>
 
 <span style="color: #408080; font-style: italic"># Print the computed derivative:</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f5 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f5_grad(x)))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f4 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f4_grad(x)))
+
+<span style="color: #408080; font-style: italic"># The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi</span>
+f4_grad_analytical <span style="color: #666666">=</span> x<span style="color: #666666">/</span>np<span style="color: #666666">.</span>sqrt(<span style="color: #666666">1</span> <span style="color: #666666">+</span> x<span style="color: #666666">**2</span>) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>exp(x) <span style="color: #666666">+</span> np<span style="color: #666666">.</span>cos(<span style="color: #666666">2*</span>np<span style="color: #666666">.</span>pi<span style="color: #666666">*</span>x)<span style="color: #666666">*2*</span>np<span style="color: #666666">.</span>pi
+
+<span style="color: #408080; font-style: italic"># Print the analytical gradient:</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical gradient of f4 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f4_grad_analytical))
 </pre></div>
 <p>
 <p>
@@ -299,7 +323,7 @@ x <span style="color: #666666">=</span> <span style="color: #666666">2.7</span>
   <li><a href="._Splines-bs048.html">49</a></li>
   <li><a href="._Splines-bs049.html">50</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs041.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs041.html b/doc/pub/Splines/html/._Splines-bs041.html
index 5d8280745..480fa658d 100644
--- a/doc/pub/Splines/html/._Splines-bs041.html
+++ b/doc/pub/Splines/html/._Splines-bs041.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,48 +274,25 @@ MathJax.Hub.Config({
 <a name="part0041"></a>
 <!-- !split -->
 
-<h2 id="___sec40" class="anchor">And  with loops </h2>
+<h2 id="___sec40" class="anchor">More autograd </h2>
 
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f6_for</span>(x):
-    val <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">10</span>):
-        val <span style="color: #666666">=</span> val <span style="color: #666666">+</span> x<span style="color: #666666">**</span>i
-    <span style="color: #008000; font-weight: bold">return</span> val
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f5</span>(x):
+    <span style="color: #008000; font-weight: bold">if</span> x <span style="color: #666666">&gt;=</span> <span style="color: #666666">0</span>:
+        <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">**2</span>
+    <span style="color: #008000; font-weight: bold">else</span>:
+        <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">-3*</span>x <span style="color: #666666">+</span> <span style="color: #666666">1</span>
 
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f6_while</span>(x):
-    val <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-    i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-    <span style="color: #008000; font-weight: bold">while</span> i <span style="color: #666666">&lt;</span> <span style="color: #666666">10</span>:
-        val <span style="color: #666666">=</span> val <span style="color: #666666">+</span> x<span style="color: #666666">**</span>i
-        i <span style="color: #666666">=</span> i <span style="color: #666666">+</span> <span style="color: #666666">1</span>
-    <span style="color: #008000; font-weight: bold">return</span> val
+f5_grad <span style="color: #666666">=</span> grad(f5)
 
-f6_for_grad <span style="color: #666666">=</span> grad(f6_for)
-f6_while_grad <span style="color: #666666">=</span> grad(f6_while)
+x <span style="color: #666666">=</span> <span style="color: #666666">2.7</span>
 
-x <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>
-
-<span style="color: #408080; font-style: italic"># Print the computed derivaties of f6_for and f6_while</span>
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f6_for at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_for_grad(x)))
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f6_while at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_while_grad(x)))
-</pre></div>
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #408080; font-style: italic"># Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9</span>
-<span style="color: #408080; font-style: italic"># The analytical derivative is: sum(i*x**(i-1)) </span>
-f6_grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">10</span>):
-    f6_grad_analytical <span style="color: #666666">+=</span> i<span style="color: #666666">*</span>x<span style="color: #666666">**</span>(i<span style="color: #666666">-1</span>)
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f6 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_grad_analytical))
+<span style="color: #408080; font-style: italic"># Print the computed derivative:</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f5 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f5_grad(x)))
 </pre></div>
 <p>
 <p>
@@ -322,7 +320,7 @@ f6_grad_analytical <span style="color: #666666">=</span> <span style="color: #66
   <li><a href="._Splines-bs049.html">50</a></li>
   <li><a href="._Splines-bs050.html">51</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs042.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs042.html b/doc/pub/Splines/html/._Splines-bs042.html
index 6cb15cdf2..c5804b20c 100644
--- a/doc/pub/Splines/html/._Splines-bs042.html
+++ b/doc/pub/Splines/html/._Splines-bs042.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,41 +274,49 @@ MathJax.Hub.Config({
 <a name="part0042"></a>
 <!-- !split -->
 
-<h2 id="___sec41" class="anchor">Using recursion </h2>
+<h2 id="___sec41" class="anchor">And  with loops </h2>
+
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f6_for</span>(x):
+    val <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">10</span>):
+        val <span style="color: #666666">=</span> val <span style="color: #666666">+</span> x<span style="color: #666666">**</span>i
+    <span style="color: #008000; font-weight: bold">return</span> val
 
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f7</span>(n): <span style="color: #408080; font-style: italic"># Assume that n is an integer</span>
-    <span style="color: #008000; font-weight: bold">if</span> n <span style="color: #666666">==</span> <span style="color: #666666">1</span> <span style="color: #AA22FF; font-weight: bold">or</span> n <span style="color: #666666">==</span> <span style="color: #666666">0</span>:
-        <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1</span>
-    <span style="color: #008000; font-weight: bold">else</span>:
-        <span style="color: #008000; font-weight: bold">return</span> n<span style="color: #666666">*</span>f7(n<span style="color: #666666">-1</span>)
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f6_while</span>(x):
+    val <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+    i <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+    <span style="color: #008000; font-weight: bold">while</span> i <span style="color: #666666">&lt;</span> <span style="color: #666666">10</span>:
+        val <span style="color: #666666">=</span> val <span style="color: #666666">+</span> x<span style="color: #666666">**</span>i
+        i <span style="color: #666666">=</span> i <span style="color: #666666">+</span> <span style="color: #666666">1</span>
+    <span style="color: #008000; font-weight: bold">return</span> val
 
-f7_grad <span style="color: #666666">=</span> grad(f7)
+f6_for_grad <span style="color: #666666">=</span> grad(f6_for)
+f6_while_grad <span style="color: #666666">=</span> grad(f6_while)
 
-n <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
+x <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>
 
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f7 at n = </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(n,f7_grad(n)))
-
-<span style="color: #408080; font-style: italic"># The function f7 is an implementation of the factorial of n.</span>
-<span style="color: #408080; font-style: italic"># By using the product rule, one can find that the derivative is:</span>
-
-f7_grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">int</span>(n)<span style="color: #666666">-1</span>):
-    tmp <span style="color: #666666">=</span> <span style="color: #666666">1</span>
-    <span style="color: #008000; font-weight: bold">for</span> k <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">int</span>(n)<span style="color: #666666">-1</span>):
-        <span style="color: #008000; font-weight: bold">if</span> k <span style="color: #666666">!=</span> i:
-            tmp <span style="color: #666666">*=</span> (n <span style="color: #666666">-</span> k)
-    f7_grad_analytical <span style="color: #666666">+=</span> tmp
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f7 at n = </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(n,f7_grad_analytical))
+<span style="color: #408080; font-style: italic"># Print the computed derivaties of f6_for and f6_while</span>
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f6_for at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_for_grad(x)))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f6_while at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_while_grad(x)))
 </pre></div>
 <p>
-Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.
 
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
+<span style="color: #408080; font-style: italic"># Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9</span>
+<span style="color: #408080; font-style: italic"># The analytical derivative is: sum(i*x**(i-1)) </span>
+f6_grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">10</span>):
+    f6_grad_analytical <span style="color: #666666">+=</span> i<span style="color: #666666">*</span>x<span style="color: #666666">**</span>(i<span style="color: #666666">-1</span>)
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f6 at x = </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(x,f6_grad_analytical))
+</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -314,7 +343,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
   <li><a href="._Splines-bs050.html">51</a></li>
   <li><a href="._Splines-bs051.html">52</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs043.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs043.html b/doc/pub/Splines/html/._Splines-bs043.html
index 3a8efd0d2..313fedcef 100644
--- a/doc/pub/Splines/html/._Splines-bs043.html
+++ b/doc/pub/Splines/html/._Splines-bs043.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,28 +274,40 @@ MathJax.Hub.Config({
 <a name="part0043"></a>
 <!-- !split -->
 
-<h2 id="___sec42" class="anchor">Unsupported functions </h2>
-Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
-
-<p>
-Assigning a value to the variable being differentiated with respect to
+<h2 id="___sec42" class="anchor">Using recursion </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f8</span>(x): <span style="color: #408080; font-style: italic"># Assume x is an array</span>
-    x[<span style="color: #666666">2</span>] <span style="color: #666666">=</span> <span style="color: #666666">3</span>
-    <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">*2</span>
 
-f8_grad <span style="color: #666666">=</span> grad(f8)
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f7</span>(n): <span style="color: #408080; font-style: italic"># Assume that n is an integer</span>
+    <span style="color: #008000; font-weight: bold">if</span> n <span style="color: #666666">==</span> <span style="color: #666666">1</span> <span style="color: #AA22FF; font-weight: bold">or</span> n <span style="color: #666666">==</span> <span style="color: #666666">0</span>:
+        <span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1</span>
+    <span style="color: #008000; font-weight: bold">else</span>:
+        <span style="color: #008000; font-weight: bold">return</span> n<span style="color: #666666">*</span>f7(n<span style="color: #666666">-1</span>)
 
-x <span style="color: #666666">=</span> <span style="color: #666666">8.4</span>
+f7_grad <span style="color: #666666">=</span> grad(f7)
 
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f8 is:&quot;</span>,f8_grad(x))
+n <span style="color: #666666">=</span> <span style="color: #666666">2.0</span>
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The computed derivative of f7 at n = </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(n,f7_grad(n)))
+
+<span style="color: #408080; font-style: italic"># The function f7 is an implementation of the factorial of n.</span>
+<span style="color: #408080; font-style: italic"># By using the product rule, one can find that the derivative is:</span>
+
+f7_grad_analytical <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">int</span>(n)<span style="color: #666666">-1</span>):
+    tmp <span style="color: #666666">=</span> <span style="color: #666666">1</span>
+    <span style="color: #008000; font-weight: bold">for</span> k <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">int</span>(n)<span style="color: #666666">-1</span>):
+        <span style="color: #008000; font-weight: bold">if</span> k <span style="color: #666666">!=</span> i:
+            tmp <span style="color: #666666">*=</span> (n <span style="color: #666666">-</span> k)
+    f7_grad_analytical <span style="color: #666666">+=</span> tmp
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The analytical derivative of f7 at n = </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> is: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">%</span>(n,f7_grad_analytical))
 </pre></div>
 <p>
-Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.
+Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.
 
 <p>
 <p>
@@ -302,7 +335,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
   <li><a href="._Splines-bs051.html">52</a></li>
   <li><a href="._Splines-bs052.html">53</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs044.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs044.html b/doc/pub/Splines/html/._Splines-bs044.html
index bcf453fb9..c46b0ffb0 100644
--- a/doc/pub/Splines/html/._Splines-bs044.html
+++ b/doc/pub/Splines/html/._Splines-bs044.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,45 +274,29 @@ MathJax.Hub.Config({
 <a name="part0044"></a>
 <!-- !split -->
 
-<h2 id="___sec43" class="anchor">The syntax a.dot(b) when finding the dot product </h2>
+<h2 id="___sec43" class="anchor">Unsupported functions </h2>
+Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
+
+<p>
+Assigning a value to the variable being differentiated with respect to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
 <div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
 <span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f9</span>(a): <span style="color: #408080; font-style: italic"># Assume a is an array with 2 elements</span>
-    b <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">2.0</span>])
-    <span style="color: #008000; font-weight: bold">return</span> a<span style="color: #666666">.</span>dot(b)
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f8</span>(x): <span style="color: #408080; font-style: italic"># Assume x is an array</span>
+    x[<span style="color: #666666">2</span>] <span style="color: #666666">=</span> <span style="color: #666666">3</span>
+    <span style="color: #008000; font-weight: bold">return</span> x<span style="color: #666666">*2</span>
 
-f9_grad <span style="color: #666666">=</span> grad(f9)
+f8_grad <span style="color: #666666">=</span> grad(f8)
 
-x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">0.0</span>])
+x <span style="color: #666666">=</span> <span style="color: #666666">8.4</span>
 
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f9 is:&quot;</span>,f9_grad(x))
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f8 is:&quot;</span>,f8_grad(x))
 </pre></div>
 <p>
-Here we are told that the 'dot' function does not belong to Autograd's
-version of a Numpy array.  To overcome this, an alternative syntax
-which also computed the dot product can be used:
+Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.
 
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
-<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f9_alternative</span>(x): <span style="color: #408080; font-style: italic"># Assume a is an array with 2 elements</span>
-    b <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">2.0</span>])
-    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>dot(x,b) <span style="color: #408080; font-style: italic"># The same as x_1*b_1 + x_2*b_2</span>
-
-f9_alternative_grad <span style="color: #666666">=</span> grad(f9_alternative)
-
-x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">3.0</span>,<span style="color: #666666">0.0</span>])
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f9 is:&quot;</span>,f9_alternative_grad(x))
-
-<span style="color: #408080; font-style: italic"># The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively</span>
-<span style="color: #408080; font-style: italic"># w.r.t x is (b_1, b_2).</span>
-</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -318,7 +323,7 @@ x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>a
   <li><a href="._Splines-bs052.html">53</a></li>
   <li><a href="._Splines-bs053.html">54</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs045.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs045.html b/doc/pub/Splines/html/._Splines-bs045.html
index ed13b7ea9..2cf7e23ba 100644
--- a/doc/pub/Splines/html/._Splines-bs045.html
+++ b/doc/pub/Splines/html/._Splines-bs045.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,15 +274,44 @@ MathJax.Hub.Config({
 <a name="part0045"></a>
 <!-- !split -->
 
-<h2 id="___sec44" class="anchor">Recommended to avoid </h2>
-The documentation recommends to avoid inplace operations such as
+<h2 id="___sec44" class="anchor">The syntax a.dot(b) when finding the dot product </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>a <span style="color: #666666">+=</span> b
-a <span style="color: #666666">-=</span> b
-a<span style="color: #666666">*=</span> b
-a <span style="color: #666666">/=</span>b
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f9</span>(a): <span style="color: #408080; font-style: italic"># Assume a is an array with 2 elements</span>
+    b <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">2.0</span>])
+    <span style="color: #008000; font-weight: bold">return</span> a<span style="color: #666666">.</span>dot(b)
+
+f9_grad <span style="color: #666666">=</span> grad(f9)
+
+x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">0.0</span>])
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The derivative of f9 is:&quot;</span>,f9_grad(x))
+</pre></div>
+<p>
+Here we are told that the 'dot' function does not belong to Autograd's
+version of a Numpy array.  To overcome this, an alternative syntax
+which also computed the dot product can be used:
+
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f9_alternative</span>(x): <span style="color: #408080; font-style: italic"># Assume a is an array with 2 elements</span>
+    b <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">1.0</span>,<span style="color: #666666">2.0</span>])
+    <span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>dot(x,b) <span style="color: #408080; font-style: italic"># The same as x_1*b_1 + x_2*b_2</span>
+
+f9_alternative_grad <span style="color: #666666">=</span> grad(f9_alternative)
+
+x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">3.0</span>,<span style="color: #666666">0.0</span>])
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;The gradient of f9 is:&quot;</span>,f9_alternative_grad(x))
+
+<span style="color: #408080; font-style: italic"># The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively</span>
+<span style="color: #408080; font-style: italic"># w.r.t x is (b_1, b_2).</span>
 </pre></div>
 <p>
 <p>
@@ -289,7 +339,7 @@ a <span style="color: #666666">/=</span>b
   <li><a href="._Splines-bs053.html">54</a></li>
   <li><a href="._Splines-bs054.html">55</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs046.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs046.html b/doc/pub/Splines/html/._Splines-bs046.html
index ff588e0ad..5f8401b94 100644
--- a/doc/pub/Splines/html/._Splines-bs046.html
+++ b/doc/pub/Splines/html/._Splines-bs046.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,21 +274,16 @@ MathJax.Hub.Config({
 <a name="part0046"></a>
 <!-- !split -->
 
-<h2 id="___sec45" class="anchor">Stochastic Gradient Descent </h2>
-
+<h2 id="___sec45" class="anchor">Recommended to avoid </h2>
+The documentation recommends to avoid inplace operations such as
 <p>
-Stochastic gradient descent (SGD) and variants thereof address some of
-the shortcomings of the Gradient descent method discussed above.
-
-<p>
-The underlying idea of SGD comes from the observation that the cost
-function, which we want to minimize, can almost always be written as a
-sum over \( n \) data points \( \{\mathbf{x}_i\}_{i=1}^n \),
-$$
-C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
-\mathbf{\beta}). 
-$$
 
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>a <span style="color: #666666">+=</span> b
+a <span style="color: #666666">-=</span> b
+a<span style="color: #666666">*=</span> b
+a <span style="color: #666666">/=</span>b
+</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -294,7 +310,7 @@ $$
   <li><a href="._Splines-bs054.html">55</a></li>
   <li><a href="._Splines-bs055.html">56</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs047.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs047.html b/doc/pub/Splines/html/._Splines-bs047.html
index 2708ba343..521d90c18 100644
--- a/doc/pub/Splines/html/._Splines-bs047.html
+++ b/doc/pub/Splines/html/._Splines-bs047.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,22 +274,20 @@ MathJax.Hub.Config({
 <a name="part0047"></a>
 <!-- !split -->
 
-<h2 id="___sec46" class="anchor">Computation of gradients </h2>
+<h2 id="___sec46" class="anchor">Stochastic Gradient Descent </h2>
 
 <p>
-This in turn means that the gradient can be
-computed as a sum over \( i \)-gradients 
-$$
-\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta}).
-$$
+Stochastic gradient descent (SGD) and variants thereof address some of
+the shortcomings of the Gradient descent method discussed above.
 
 <p>
-Stochasticity/randomness is introduced by only taking the
-gradient on a subset of the data called minibatches.  If there are \( n \)
-data points and the size of each minibatch is \( M \), there will be \( n/M \)
-minibatches. We denote these minibatches by \( B_k \) where
-\( k=1,\cdots,n/M \).
+The underlying idea of SGD comes from the observation that the cost
+function, which we want to minimize, can almost always be written as a
+sum over \( n \) data points \( \{\mathbf{x}_i\}_{i=1}^n \),
+$$
+C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
+\mathbf{\beta}). 
+$$
 
 <p>
 <p>
@@ -296,7 +315,7 @@ minibatches. We denote these minibatches by \( B_k \) where
   <li><a href="._Splines-bs055.html">56</a></li>
   <li><a href="._Splines-bs056.html">57</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs048.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs048.html b/doc/pub/Splines/html/._Splines-bs048.html
index d602f4e3f..0a3e119ca 100644
--- a/doc/pub/Splines/html/._Splines-bs048.html
+++ b/doc/pub/Splines/html/._Splines-bs048.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,27 +274,23 @@ MathJax.Hub.Config({
 <a name="part0048"></a>
 <!-- !split -->
 
-<h2 id="___sec47" class="anchor">SGD example </h2>
-As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) 
-and we choose to have \( M=5 \) minibathces,
-then each minibatch contains two data points. In particular we have
-\( B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 =
-(\mathbf{x}_9,\mathbf{x}_{10}) \). Note that if you choose \( M=1 \) you
-have only a single batch with all data points and on the other extreme,
-you may choose \( M=n \) resulting in a minibatch for each datapoint, i.e
-\( B_k = \mathbf{x}_k \).
+<h2 id="___sec47" class="anchor">Computation of gradients </h2>
 
 <p>
-The idea is now to approximate the gradient by replacing the sum over
-all data points with a sum over the data points in one the minibatches
-picked at random in each gradient descent step 
+This in turn means that the gradient can be
+computed as a sum over \( i \)-gradients 
 $$
-\nabla_{\beta}
-C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
-c_i(\mathbf{x}_i, \mathbf{\beta}).
+\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}).
 $$
 
+<p>
+Stochasticity/randomness is introduced by only taking the
+gradient on a subset of the data called minibatches.  If there are \( n \)
+data points and the size of each minibatch is \( M \), there will be \( n/M \)
+minibatches. We denote these minibatches by \( B_k \) where
+\( k=1,\cdots,n/M \).
+
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -300,7 +317,7 @@ $$
   <li><a href="._Splines-bs056.html">57</a></li>
   <li><a href="._Splines-bs057.html">58</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs049.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs049.html b/doc/pub/Splines/html/._Splines-bs049.html
index 8c110af9a..e36f6dd19 100644
--- a/doc/pub/Splines/html/._Splines-bs049.html
+++ b/doc/pub/Splines/html/._Splines-bs049.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,22 +274,27 @@ MathJax.Hub.Config({
 <a name="part0049"></a>
 <!-- !split -->
 
-<h2 id="___sec48" class="anchor">The gradient step </h2>
+<h2 id="___sec48" class="anchor">SGD example </h2>
+As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) 
+and we choose to have \( M=5 \) minibathces,
+then each minibatch contains two data points. In particular we have
+\( B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 =
+(\mathbf{x}_9,\mathbf{x}_{10}) \). Note that if you choose \( M=1 \) you
+have only a single batch with all data points and on the other extreme,
+you may choose \( M=n \) resulting in a minibatch for each datapoint, i.e
+\( B_k = \mathbf{x}_k \).
 
 <p>
-Thus a gradient descent step now looks like 
+The idea is now to approximate the gradient by replacing the sum over
+all data points with a sum over the data points in one the minibatches
+picked at random in each gradient descent step 
 $$
-\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
-\mathbf{\beta})
+\nabla_{\beta}
+C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
+c_i(\mathbf{x}_i, \mathbf{\beta}).
 $$
 
-<p>
-where \( k \) is picked at random with equal
-probability from \( [1,n/M] \). An iteration over the number of
-minibathces (n/M) is commonly referred to as an epoch. Thus it is
-typical to choose a number of epochs and for each epoch iterate over
-the number of minibatches, as exemplified in the code below.
-
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -295,7 +321,7 @@ the number of minibatches, as exemplified in the code below.
   <li><a href="._Splines-bs057.html">58</a></li>
   <li><a href="._Splines-bs058.html">59</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs050.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs050.html b/doc/pub/Splines/html/._Splines-bs050.html
index a0ba39efb..11f05ecf4 100644
--- a/doc/pub/Splines/html/._Splines-bs050.html
+++ b/doc/pub/Splines/html/._Splines-bs050.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,34 +274,21 @@ MathJax.Hub.Config({
 <a name="part0050"></a>
 <!-- !split -->
 
-<h2 id="___sec49" class="anchor">Simple example code </h2>
+<h2 id="___sec49" class="anchor">The gradient step </h2>
 
 <p>
+Thus a gradient descent step now looks like 
+$$
+\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta})
+$$
 
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span> 
-
-n <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#100 datapoints </span>
-M <span style="color: #666666">=</span> <span style="color: #666666">5</span>   <span style="color: #408080; font-style: italic">#size of each minibatch</span>
-m <span style="color: #666666">=</span> <span style="color: #008000">int</span>(n<span style="color: #666666">/</span>M) <span style="color: #408080; font-style: italic">#number of minibatches</span>
-n_epochs <span style="color: #666666">=</span> <span style="color: #666666">10</span> <span style="color: #408080; font-style: italic">#number of epochs</span>
-
-j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,n_epochs<span style="color: #666666">+1</span>):
-    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
-        k <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m) <span style="color: #408080; font-style: italic">#Pick the k-th minibatch at random</span>
-        <span style="color: #408080; font-style: italic">#Compute the gradient using the data in minibatch Bk</span>
-        <span style="color: #408080; font-style: italic">#Compute new suggestion for </span>
-        j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
-</pre></div>
 <p>
-Taking the gradient only on a subset of the data has two important
-benefits. First, it introduces randomness which decreases the chance
-that our opmization scheme gets stuck in a local minima. Second, if
-the size of the minibatches are small relative to the number of
-datapoints (\( M <  n \)), the computation of the gradient is much
-cheaper since we sum over the datapoints in the \( k-th \) minibatch and not
-all \( n \) datapoints.
+where \( k \) is picked at random with equal
+probability from \( [1,n/M] \). An iteration over the number of
+minibathces (n/M) is commonly referred to as an epoch. Thus it is
+typical to choose a number of epochs and for each epoch iterate over
+the number of minibatches, as exemplified in the code below.
 
 <p>
 <p>
@@ -308,7 +316,7 @@ all \( n \) datapoints.
   <li><a href="._Splines-bs058.html">59</a></li>
   <li><a href="._Splines-bs059.html">60</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs051.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs051.html b/doc/pub/Splines/html/._Splines-bs051.html
index c27ba6568..96d798de5 100644
--- a/doc/pub/Splines/html/._Splines-bs051.html
+++ b/doc/pub/Splines/html/._Splines-bs051.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,19 +274,34 @@ MathJax.Hub.Config({
 <a name="part0051"></a>
 <!-- !split -->
 
-<h2 id="___sec50" class="anchor">When do we stop? </h2>
+<h2 id="___sec50" class="anchor">Simple example code </h2>
 
 <p>
-A natural question is when do we stop the search for a new minimum?
-One possibility is to compute the full gradient after a given number
-of epochs and check if the norm of the gradient is smaller than some
-threshold and stop if true. However, the condition that the gradient
-is zero is valid also for local minima, so this would only tell us
-that we are close to a local/global minimum. However, we could also
-evaluate the cost function at this point, store the result and
-continue the search. If the test kicks in at a later stage we can
-compare the values of the cost function and keep the \( \beta \) that
-gave the lowest value.
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span> 
+
+n <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#100 datapoints </span>
+M <span style="color: #666666">=</span> <span style="color: #666666">5</span>   <span style="color: #408080; font-style: italic">#size of each minibatch</span>
+m <span style="color: #666666">=</span> <span style="color: #008000">int</span>(n<span style="color: #666666">/</span>M) <span style="color: #408080; font-style: italic">#number of minibatches</span>
+n_epochs <span style="color: #666666">=</span> <span style="color: #666666">10</span> <span style="color: #408080; font-style: italic">#number of epochs</span>
+
+j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,n_epochs<span style="color: #666666">+1</span>):
+    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
+        k <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m) <span style="color: #408080; font-style: italic">#Pick the k-th minibatch at random</span>
+        <span style="color: #408080; font-style: italic">#Compute the gradient using the data in minibatch Bk</span>
+        <span style="color: #408080; font-style: italic">#Compute new suggestion for </span>
+        j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
+</pre></div>
+<p>
+Taking the gradient only on a subset of the data has two important
+benefits. First, it introduces randomness which decreases the chance
+that our opmization scheme gets stuck in a local minima. Second, if
+the size of the minibatches are small relative to the number of
+datapoints (\( M <  n \)), the computation of the gradient is much
+cheaper since we sum over the datapoints in the \( k-th \) minibatch and not
+all \( n \) datapoints.
 
 <p>
 <p>
@@ -293,7 +329,7 @@ gave the lowest value.
   <li><a href="._Splines-bs059.html">60</a></li>
   <li><a href="._Splines-bs060.html">61</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs052.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs052.html b/doc/pub/Splines/html/._Splines-bs052.html
index 2b2dac843..09d531cc1 100644
--- a/doc/pub/Splines/html/._Splines-bs052.html
+++ b/doc/pub/Splines/html/._Splines-bs052.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -253,51 +274,20 @@ MathJax.Hub.Config({
 <a name="part0052"></a>
 <!-- !split -->
 
-<h2 id="___sec51" class="anchor">Slightly different approach </h2>
+<h2 id="___sec51" class="anchor">When do we stop? </h2>
 
 <p>
-Another approach is to let the step length \( \gamma_j \) depend on the
-number of epochs in such a way that it becomes very small after a
-reasonable time such that we do not move at all.
+A natural question is when do we stop the search for a new minimum?
+One possibility is to compute the full gradient after a given number
+of epochs and check if the norm of the gradient is smaller than some
+threshold and stop if true. However, the condition that the gradient
+is zero is valid also for local minima, so this would only tell us
+that we are close to a local/global minimum. However, we could also
+evaluate the cost function at this point, store the result and
+continue the search. If the test kicks in at a later stage we can
+compare the values of the cost function and keep the \( \beta \) that
+gave the lowest value.
 
-<p>
-As an example, let \( e = 0,1,2,3,\cdots \) denote the current epoch and let \( t_0, t_1 > 0 \) be two fixed numbers. Furthermore, let \( t = e \cdot m + i \) where \( m \) is the number of minibatches and \( i=0,\cdots,m-1 \). Then the function $$\gamma_j(t; t_0, t_1) = \frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length \( \gamma_j (0; t_0, t_1) = t_0/t_1 \) which decays in <em>time</em> \( t \).
-
-<p>
-In this way we can fix the number of epochs, compute \( \beta \) and
-evaluate the cost function at the end. Repeating the computation will
-give a different result since the scheme is random by design. Then we
-pick the final \( \beta \) that gives the lowest value of the cost
-function.
-
-<p>
-
-<!-- code=python (!bc pycod) typeset with pygments style "default" -->
-<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span> 
-
-<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">step_length</span>(t,t0,t1):
-    <span style="color: #008000; font-weight: bold">return</span> t0<span style="color: #666666">/</span>(t<span style="color: #666666">+</span>t1)
-
-n <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#100 datapoints </span>
-M <span style="color: #666666">=</span> <span style="color: #666666">5</span>   <span style="color: #408080; font-style: italic">#size of each minibatch</span>
-m <span style="color: #666666">=</span> <span style="color: #008000">int</span>(n<span style="color: #666666">/</span>M) <span style="color: #408080; font-style: italic">#number of minibatches</span>
-n_epochs <span style="color: #666666">=</span> <span style="color: #666666">500</span> <span style="color: #408080; font-style: italic">#number of epochs</span>
-t0 <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
-t1 <span style="color: #666666">=</span> <span style="color: #666666">10</span>
-
-gamma_j <span style="color: #666666">=</span> t0<span style="color: #666666">/</span>t1
-j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
-<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,n_epochs<span style="color: #666666">+1</span>):
-    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
-        k <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m) <span style="color: #408080; font-style: italic">#Pick the k-th minibatch at random</span>
-        <span style="color: #408080; font-style: italic">#Compute the gradient using the data in minibatch Bk</span>
-        <span style="color: #408080; font-style: italic">#Compute new suggestion for beta</span>
-        t <span style="color: #666666">=</span> epoch<span style="color: #666666">*</span>m<span style="color: #666666">+</span>i
-        gamma_j <span style="color: #666666">=</span> step_length(t,t0,t1)
-        j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
-
-<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;gamma_j after </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> epochs: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> (n_epochs,gamma_j))
-</pre></div>
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
@@ -324,7 +314,7 @@ j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
   <li><a href="._Splines-bs060.html">61</a></li>
   <li><a href="._Splines-bs061.html">62</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs053.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/._Splines-bs053.html b/doc/pub/Splines/html/._Splines-bs053.html
new file mode 100644
index 000000000..2e823b435
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs053.html
@@ -0,0 +1,373 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0053"></a>
+<!-- !split -->
+
+<h2 id="___sec52" class="anchor">Slightly different approach </h2>
+
+<p>
+Another approach is to let the step length \( \gamma_j \) depend on the
+number of epochs in such a way that it becomes very small after a
+reasonable time such that we do not move at all.
+
+<p>
+As an example, let \( e = 0,1,2,3,\cdots \) denote the current epoch and let \( t_0, t_1 > 0 \) be two fixed numbers. Furthermore, let \( t = e \cdot m + i \) where \( m \) is the number of minibatches and \( i=0,\cdots,m-1 \). Then the function $$\gamma_j(t; t_0, t_1) = \frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length \( \gamma_j (0; t_0, t_1) = t_0/t_1 \) which decays in <em>time</em> \( t \).
+
+<p>
+In this way we can fix the number of epochs, compute \( \beta \) and
+evaluate the cost function at the end. Repeating the computation will
+give a different result since the scheme is random by design. Then we
+pick the final \( \beta \) that gives the lowest value of the cost
+function.
+
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span> 
+
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">step_length</span>(t,t0,t1):
+    <span style="color: #008000; font-weight: bold">return</span> t0<span style="color: #666666">/</span>(t<span style="color: #666666">+</span>t1)
+
+n <span style="color: #666666">=</span> <span style="color: #666666">100</span> <span style="color: #408080; font-style: italic">#100 datapoints </span>
+M <span style="color: #666666">=</span> <span style="color: #666666">5</span>   <span style="color: #408080; font-style: italic">#size of each minibatch</span>
+m <span style="color: #666666">=</span> <span style="color: #008000">int</span>(n<span style="color: #666666">/</span>M) <span style="color: #408080; font-style: italic">#number of minibatches</span>
+n_epochs <span style="color: #666666">=</span> <span style="color: #666666">500</span> <span style="color: #408080; font-style: italic">#number of epochs</span>
+t0 <span style="color: #666666">=</span> <span style="color: #666666">1.0</span>
+t1 <span style="color: #666666">=</span> <span style="color: #666666">10</span>
+
+gamma_j <span style="color: #666666">=</span> t0<span style="color: #666666">/</span>t1
+j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
+<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">1</span>,n_epochs<span style="color: #666666">+1</span>):
+    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
+        k <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m) <span style="color: #408080; font-style: italic">#Pick the k-th minibatch at random</span>
+        <span style="color: #408080; font-style: italic">#Compute the gradient using the data in minibatch Bk</span>
+        <span style="color: #408080; font-style: italic">#Compute new suggestion for beta</span>
+        t <span style="color: #666666">=</span> epoch<span style="color: #666666">*</span>m<span style="color: #666666">+</span>i
+        gamma_j <span style="color: #666666">=</span> step_length(t,t0,t1)
+        j <span style="color: #666666">+=</span> <span style="color: #666666">1</span>
+
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;gamma_j after </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121"> epochs: </span><span style="color: #BB6688; font-weight: bold">%g</span><span style="color: #BA2121">&quot;</span> <span style="color: #666666">%</span> (n_epochs,gamma_j))
+</pre></div>
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs052.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs045.html">46</a></li>
+  <li><a href="._Splines-bs046.html">47</a></li>
+  <li><a href="._Splines-bs047.html">48</a></li>
+  <li><a href="._Splines-bs048.html">49</a></li>
+  <li><a href="._Splines-bs049.html">50</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li class="active"><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs054.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs054.html b/doc/pub/Splines/html/._Splines-bs054.html
new file mode 100644
index 000000000..4c457fa0c
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs054.html
@@ -0,0 +1,404 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0054"></a>
+<!-- !split -->
+
+<h2 id="___sec53" class="anchor">Program for stochastic gradient </h2>
+
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> exp, sqrt
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
+<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
+<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> SGDRegressor
+
+x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
+y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
+
+xb <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)), x]
+theta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb))<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>T)<span style="color: #666666">.</span>dot(y)
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Own inversion&quot;</span>)
+<span style="color: #008000; font-weight: bold">print</span>(theta_linreg)
+sgdreg <span style="color: #666666">=</span> SGDRegressor(n_iter <span style="color: #666666">=</span> <span style="color: #666666">50</span>, penalty<span style="color: #666666">=</span><span style="color: #008000">None</span>, eta0<span style="color: #666666">=0.1</span>)
+sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.</span>ravel())
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;sgdreg from scikit&quot;</span>)
+<span style="color: #008000; font-weight: bold">print</span>(sgdreg<span style="color: #666666">.</span>intercept_, sgdreg<span style="color: #666666">.</span>coef_)
+
+
+theta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
+
+eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
+Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
+m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
+
+<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
+    gradients <span style="color: #666666">=</span> <span style="color: #666666">2.0/</span>m<span style="color: #666666">*</span>xb<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xb<span style="color: #666666">.</span>dot(theta)<span style="color: #666666">-</span>y)
+    theta <span style="color: #666666">-=</span> eta<span style="color: #666666">*</span>gradients
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;theta frm own gd&quot;</span>)
+<span style="color: #008000; font-weight: bold">print</span>(theta)
+
+xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0</span>],[<span style="color: #666666">2</span>]])
+xbnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)), xnew]
+ypredict <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(theta)
+ypredict2 <span style="color: #666666">=</span> xbnew<span style="color: #666666">.</span>dot(theta_linreg)
+
+
+n_epochs <span style="color: #666666">=</span> <span style="color: #666666">50</span>
+t0, t1 <span style="color: #666666">=</span> <span style="color: #666666">5</span>, <span style="color: #666666">50</span>
+m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
+<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">learning_schedule</span>(t):
+    <span style="color: #008000; font-weight: bold">return</span> t0<span style="color: #666666">/</span>(t<span style="color: #666666">+</span>t1)
+
+theta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
+
+<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n_epochs):
+    <span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
+        random_index <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m)
+        xi <span style="color: #666666">=</span> xb[random_index:random_index<span style="color: #666666">+1</span>]
+        yi <span style="color: #666666">=</span> y[random_index:random_index<span style="color: #666666">+1</span>]
+        gradients <span style="color: #666666">=</span> <span style="color: #666666">2</span> <span style="color: #666666">*</span> xi<span style="color: #666666">.</span>T<span style="color: #666666">.</span>dot(xi<span style="color: #666666">.</span>dot(theta)<span style="color: #666666">-</span>yi)
+        eta <span style="color: #666666">=</span> learning_schedule(epoch<span style="color: #666666">*</span>m<span style="color: #666666">+</span>i)
+        theta <span style="color: #666666">=</span> theta <span style="color: #666666">-</span> eta<span style="color: #666666">*</span>gradients
+<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;theta from own sdg&quot;</span>)
+<span style="color: #008000; font-weight: bold">print</span>(theta)
+
+
+
+
+
+
+plt<span style="color: #666666">.</span>plot(xnew, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
+plt<span style="color: #666666">.</span>plot(xnew, ypredict2, <span style="color: #BA2121">&quot;b-&quot;</span>)
+plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
+plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">2.0</span>,<span style="color: #666666">0</span>, <span style="color: #666666">15.0</span>])
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&#39;$x$&#39;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&#39;$y$&#39;</span>)
+plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r&#39;Random numbers &#39;</span>)
+plt<span style="color: #666666">.</span>show()
+</pre></div>
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs053.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs046.html">47</a></li>
+  <li><a href="._Splines-bs047.html">48</a></li>
+  <li><a href="._Splines-bs048.html">49</a></li>
+  <li><a href="._Splines-bs049.html">50</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li class="active"><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs055.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs055.html b/doc/pub/Splines/html/._Splines-bs055.html
new file mode 100644
index 000000000..c8946b9ed
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs055.html
@@ -0,0 +1,330 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0055"></a>
+<!-- !split -->
+
+<h2 id="___sec54" class="anchor">Momentum based methods </h2>
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs054.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs047.html">48</a></li>
+  <li><a href="._Splines-bs048.html">49</a></li>
+  <li><a href="._Splines-bs049.html">50</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li class="active"><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs056.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs056.html b/doc/pub/Splines/html/._Splines-bs056.html
new file mode 100644
index 000000000..cd578c56b
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs056.html
@@ -0,0 +1,356 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0056"></a>
+<!-- !split -->
+
+<h2 id="___sec55" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+In the CG method we define so-called conjugate directions and two vectors 
+\( \hat{s} \) and \( \hat{t} \)
+are said to be
+conjugate if
+$$
+\begin{equation*}
+\hat{s}^T\hat{A}\hat{t}= 0.
+\end{equation*}
+$$
+
+The philosophy of the CG method is to perform searches in various conjugate directions
+of our vectors \( \hat{x}_i \) obeying the above criterion, namely
+$$
+\begin{equation*}
+\hat{x}_i^T\hat{A}\hat{x}_j= 0.
+\end{equation*}
+$$
+
+Two vectors are conjugate if they are orthogonal with respect to 
+this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is conjugate to \( \hat{t} \), then \( \hat{t} \) is conjugate to \( \hat{s} \).
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs055.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs048.html">49</a></li>
+  <li><a href="._Splines-bs049.html">50</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li class="active"><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs057.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs057.html b/doc/pub/Splines/html/._Splines-bs057.html
new file mode 100644
index 000000000..47f3d52bb
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs057.html
@@ -0,0 +1,344 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0057"></a>
+<!-- !split -->
+
+<h2 id="___sec56" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+An example is given by the eigenvectors of the matrix
+$$
+\begin{equation*}
+\hat{v}_i^T\hat{A}\hat{v}_j= \lambda\hat{v}_i^T\hat{v}_j,
+\end{equation*}
+$$
+
+which is zero unless \( i=j \).
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs056.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs049.html">50</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li class="active"><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs058.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs058.html b/doc/pub/Splines/html/._Splines-bs058.html
new file mode 100644
index 000000000..1a439944e
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs058.html
@@ -0,0 +1,353 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0058"></a>
+<!-- !split -->
+
+<h2 id="___sec57" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+Assume now that we have a symmetric positive-definite matrix \( \hat{A} \) of size
+\( n\times n \). At each iteration \( i+1 \) we obtain the conjugate direction of a vector
+$$
+\begin{equation*}
+\hat{x}_{i+1}=\hat{x}_{i}+\alpha_i\hat{p}_{i}. 
+\end{equation*}
+$$
+
+We assume that \( \hat{p}_{i} \) is a sequence of \( n \) mutually conjugate directions. 
+Then the \( \hat{p}_{i} \)  form a basis of \( R^n \) and we can expand the solution 
+$  \hat{A}\hat{x} = \hat{b}$ in this basis, namely
+
+$$
+\begin{equation*}
+  \hat{x}  = \sum^{n}_{i=1} \alpha_i \hat{p}_i.
+\end{equation*}
+$$
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs057.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs050.html">51</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li class="active"><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs059.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs059.html b/doc/pub/Splines/html/._Splines-bs059.html
new file mode 100644
index 000000000..c38a4263b
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs059.html
@@ -0,0 +1,358 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0059"></a>
+<!-- !split -->
+
+<h2 id="___sec58" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+The coefficients are given by
+$$
+\begin{equation*}
+    \mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
+\end{equation*}
+$$
+
+Multiplying with \( \hat{p}_k^T \)  from the left gives
+
+$$
+\begin{equation*}
+  \hat{p}_k^T \hat{A}\hat{x} = \sum^{n}_{i=1} \alpha_i\hat{p}_k^T \hat{A}\hat{p}_i= \hat{p}_k^T \hat{b},
+\end{equation*}
+$$
+
+and we can define the coefficients \( \alpha_k \) as
+
+$$
+\begin{equation*}
+    \alpha_k = \frac{\hat{p}_k^T \hat{b}}{\hat{p}_k^T \hat{A} \hat{p}_k}
+\end{equation*}
+$$
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs058.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs051.html">52</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li class="active"><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs060.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs060.html b/doc/pub/Splines/html/._Splines-bs060.html
new file mode 100644
index 000000000..496f0b81a
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs060.html
@@ -0,0 +1,362 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0060"></a>
+<!-- !split -->
+
+<h2 id="___sec59" class="anchor">Conjugate gradient method and iterations </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 choose the conjugate vectors \( \hat{p}_k \) carefully, 
+then we may not need all of them to obtain a good approximation to the solution 
+\( \hat{x} \). 
+We want to regard the conjugate gradient method as an iterative method. 
+This will us to solve systems where \( n \) is so large that the direct 
+method would take too much time.
+
+<p>
+We denote the initial guess for \( \hat{x} \) as \( \hat{x}_0 \). 
+We can assume without loss of generality that
+$$
+\begin{equation*}
+\hat{x}_0=0,
+\end{equation*}
+$$
+
+or consider the system
+$$
+\begin{equation*}
+\hat{A}\hat{z} = \hat{b}-\hat{A}\hat{x}_0,
+\end{equation*}
+$$
+
+instead.
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs059.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs052.html">53</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li class="active"><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs061.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs061.html b/doc/pub/Splines/html/._Splines-bs061.html
new file mode 100644
index 000000000..8d2b160e1
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs061.html
@@ -0,0 +1,356 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0061"></a>
+<!-- !split -->
+
+<h2 id="___sec60" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+One can show that the solution \( \hat{x} \) is also the unique minimizer of the quadratic form
+$$
+\begin{equation*}
+  f(\hat{x}) = \frac{1}{2}\hat{x}^T\hat{A}\hat{x} - \hat{x}^T \hat{x} , \quad \hat{x}\in\mathbf{R}^n. 
+\end{equation*}
+$$
+
+This suggests taking the first basis vector \( \hat{p}_1 \) 
+to be the gradient of \( f \) at \( \hat{x}=\hat{x}_0 \), 
+which equals
+$$
+\begin{equation*}
+\hat{A}\hat{x}_0-\hat{b},
+\end{equation*}
+$$
+
+and 
+\( \hat{x}_0=0 \) it is equal \( -\hat{b} \).
+The other vectors in the basis will be conjugate to the gradient, 
+hence the name conjugate gradient method.
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs060.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs053.html">54</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li class="active"><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs062.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs062.html b/doc/pub/Splines/html/._Splines-bs062.html
new file mode 100644
index 000000000..676d1c3fd
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs062.html
@@ -0,0 +1,355 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0062"></a>
+<!-- !split -->
+
+<h2 id="___sec61" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+Let  \( \hat{r}_k \) be the residual at the \( k \)-th step:
+$$
+\begin{equation*}
+\hat{r}_k=\hat{b}-\hat{A}\hat{x}_k.
+\end{equation*}
+$$
+
+Note that \( \hat{r}_k \) is the negative gradient of \( f \) at 
+\( \hat{x}=\hat{x}_k \), 
+so the gradient descent method would be to move in the direction \( \hat{r}_k \). 
+Here, we insist that the directions \( \hat{p}_k \) are conjugate to each other, 
+so we take the direction closest to the gradient \( \hat{r}_k \)  
+under the conjugacy constraint. 
+This gives the following expression
+$$
+\begin{equation*}
+\hat{p}_{k+1}=\hat{r}_k-\frac{\hat{p}_k^T \hat{A}\hat{r}_k}{\hat{p}_k^T\hat{A}\hat{p}_k} \hat{p}_k.
+\end{equation*}
+$$
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs061.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs054.html">55</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li class="active"><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs063.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs063.html b/doc/pub/Splines/html/._Splines-bs063.html
new file mode 100644
index 000000000..1f8578536
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs063.html
@@ -0,0 +1,364 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0063"></a>
+<!-- !split -->
+
+<h2 id="___sec62" class="anchor">Conjugate gradient method </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+We can also  compute the residual iteratively as
+$$
+\begin{equation*}
+\hat{r}_{k+1}=\hat{b}-\hat{A}\hat{x}_{k+1},
+ \end{equation*}
+$$
+
+which equals
+$$
+\begin{equation*}
+\hat{b}-\hat{A}(\hat{x}_k+\alpha_k\hat{p}_k),
+ \end{equation*}
+$$
+
+or
+$$
+\begin{equation*}
+(\hat{b}-\hat{A}\hat{x}_k)-\alpha_k\hat{A}\hat{p}_k,
+ \end{equation*}
+$$
+
+which gives
+
+$$
+\begin{equation*}
+\hat{r}_{k+1}=\hat{r}_k-\hat{A}\hat{p}_{k},
+ \end{equation*}
+$$
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs062.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs055.html">56</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li class="active"><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs064.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs064.html b/doc/pub/Splines/html/._Splines-bs064.html
new file mode 100644
index 000000000..f3a1f5d45
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs064.html
@@ -0,0 +1,363 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0064"></a>
+<!-- !split -->
+
+<h2 id="___sec63" class="anchor">Simple implementation of the Conjugate gradient algorithm </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+<p>
+
+<!-- code=c++ (!bc cppcod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>  Vector <span style="color: #0000FF">ConjugateGradient</span>(Matrix A, Vector b, Vector x0){
+  <span style="color: #B00040">int</span> dim <span style="color: #666666">=</span> x0.Dimension();
+  <span style="color: #008000; font-weight: bold">const</span> <span style="color: #B00040">double</span> tolerance <span style="color: #666666">=</span> <span style="color: #666666">1.0e-14</span>;
+  Vector x(dim),r(dim),v(dim),z(dim);
+  <span style="color: #B00040">double</span> c,t,d;
+
+  x <span style="color: #666666">=</span> x0;
+  r <span style="color: #666666">=</span> b <span style="color: #666666">-</span> A<span style="color: #666666">*</span>x;
+  v <span style="color: #666666">=</span> r;
+  c <span style="color: #666666">=</span> dot(r,r);
+  <span style="color: #B00040">int</span> i <span style="color: #666666">=</span> <span style="color: #666666">0</span>; IterMax <span style="color: #666666">=</span> dim;
+  <span style="color: #008000; font-weight: bold">while</span>(i <span style="color: #666666">&lt;=</span> IterMax){
+    z <span style="color: #666666">=</span> A<span style="color: #666666">*</span>v;
+    t <span style="color: #666666">=</span> c<span style="color: #666666">/</span>dot(v,z);
+    x <span style="color: #666666">=</span> x <span style="color: #666666">+</span> t<span style="color: #666666">*</span>v;
+    r <span style="color: #666666">=</span> r <span style="color: #666666">-</span> t<span style="color: #666666">*</span>z;
+    d <span style="color: #666666">=</span> dot(r,r);
+    <span style="color: #008000; font-weight: bold">if</span>(sqrt(d) <span style="color: #666666">&lt;</span> tolerance)
+      <span style="color: #008000; font-weight: bold">break</span>;
+    v <span style="color: #666666">=</span> r <span style="color: #666666">+</span> (d<span style="color: #666666">/</span>c)<span style="color: #666666">*</span>v;
+    c <span style="color: #666666">=</span> d;  i<span style="color: #666666">++</span>;
+  }
+  <span style="color: #008000; font-weight: bold">return</span> x;
+} 
+</pre></div>
+<p>
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs063.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs056.html">57</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li class="active"><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs065.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs065.html b/doc/pub/Splines/html/._Splines-bs065.html
new file mode 100644
index 000000000..1b27db650
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs065.html
@@ -0,0 +1,358 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0065"></a>
+<!-- !split -->
+
+<h2 id="___sec64" class="anchor">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
+<div class="panel panel-default">
+<div class="panel-body">
+<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+The optimization problem is to minimize \( f(\mathbf {x} ) \) where \( \mathbf {x} \)  is a vector in \( R^{n} \), and \( f \) is a differentiable scalar function. There are no constraints on the values that  \( \mathbf {x} \)  can take.
+
+<p>
+The algorithm begins at an initial estimate for the optimal value \( \mathbf {x}_{0} \) and proceeds iteratively to get a better estimate at each stage.
+
+<p>
+The search direction \( p_k \) at stage \( k \) is given by the solution of the analogue of the Newton equation
+$$
+B_{k}\mathbf {p} _{k}=-\nabla f(\mathbf {x}_{k}),
+$$
+
+<p>
+where \( B_{k} \) is an approximation to the Hessian matrix, which is
+updated iteratively at each stage, and \( \nabla f(\mathbf {x} _{k}) \)
+is the gradient of the function
+evaluated at \( x_k \). 
+A line search in the direction \( p_k \) is then used to
+find the next point \( x_{k+1} \) by minimising 
+$$
+f(\mathbf {x}_{k}+\alpha \mathbf {p}_{k}),
+$$
+
+over the scalar \( \alpha > 0 \).
+
+<p>
+</div>
+</div>
+
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs064.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs057.html">58</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li class="active"><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs066.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs066.html b/doc/pub/Splines/html/._Splines-bs066.html
new file mode 100644
index 000000000..354eeef9b
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs066.html
@@ -0,0 +1,334 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0066"></a>
+<!-- !split -->
+
+<h2 id="___sec65" class="anchor">Using gradient descent methods, limitations </h2>
+
+<ul>
+<li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
+<li> <b>GD is sensitive to initial conditions</b>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</li>
+<li> <b>Gradients are computationally expensive to calculate for large datasets</b>. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, \( E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2 \); for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over <em>all</em> \( n \) data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called &quot;mini batches&quot;. This has the added benefit of introducing stochasticity into our algorithm.</li>
+<li> <b>GD is very sensitive to choices of learning rates</b>. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would <em>adaptively</em> choose the learning rates to match the landscape.</li>
+<li> <b>GD treats all directions in parameter space uniformly.</b> Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</li> 
+<li> GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</li>
+</ul>
+
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs065.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs058.html">59</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li class="active"><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs067.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs067.html b/doc/pub/Splines/html/._Splines-bs067.html
new file mode 100644
index 000000000..2d12196b9
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs067.html
@@ -0,0 +1,343 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0067"></a>
+<!-- !split -->
+
+<h2 id="___sec66" class="anchor">Momentum based GD </h2>
+
+<p>
+The stochastic gradient descent (SGD) is almost always used with a <em>momentum</em> or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically 
+implemented as follows
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\tag{2}
+\end{align}
+$$
+
+where we have introduced a momentum parameter \( \gamma \), with \( 0\le\gamma\le 1 \), and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that \( \mathbf{v}_t \) is a running average of recently encountered gradients and \( (1-\gamma)^{-1} \) sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when \( \gamma=0 \), this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is
+$$
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+$$
+
+where we have defined \( \Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1} \).
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs066.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs059.html">60</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li class="active"><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs068.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs068.html b/doc/pub/Splines/html/._Splines-bs068.html
new file mode 100644
index 000000000..9e3d20a8f
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs068.html
@@ -0,0 +1,341 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0068"></a>
+<!-- !split -->
+
+<h2 id="___sec67" class="anchor">More on momentum based approaches </h2>
+
+<p>
+Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass \( m \) moving in a viscous medium with drag coefficient \( \mu \) and potential 
+\( E(\mathbf{w}) \). If we denote the particle's position by \( \mathbf{w} \), then its motion is described by 
+$$
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+$$
+
+We can discretize this equation in the usual way to get
+$$
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+$$
+
+Rearranging this equation, we can rewrite this as
+$$
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+$$
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs067.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs060.html">61</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li class="active"><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs069.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs069.html b/doc/pub/Splines/html/._Splines-bs069.html
new file mode 100644
index 000000000..215e75fa6
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs069.html
@@ -0,0 +1,348 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0069"></a>
+<!-- !split -->
+
+<h2 id="___sec68" class="anchor">Momentum parameter </h2>
+Notice that this equation is identical to previous one if we identify the position of the particle, \( \mathbf{w} \), with the parameters \( \boldsymbol{\theta} \). This allows
+us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:
+$$
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+$$
+
+Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as \( (1-\gamma)^{-1} \approx  m/(\mu \Delta t) \).
+
+<p>
+Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models.
+
+<p>
+These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG).
+
+<p>
+In the NAG algorithm, rather than calculating the gradient at the current parameters, \( \nabla_\theta E(\boldsymbol{\theta}_t) \), one calculates the gradient at the expected value of the parameters given our current momentum,   \( \nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \). This yields the NAG update rule
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\tag{3}
+\end{align}
+$$
+
+One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of \( \gamma \).
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs068.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs061.html">62</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li class="active"><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs070.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs070.html b/doc/pub/Splines/html/._Splines-bs070.html
new file mode 100644
index 000000000..4307ed9ba
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs070.html
@@ -0,0 +1,342 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0070"></a>
+<!-- !split -->
+
+<h2 id="___sec69" class="anchor">Second moment of the gradient </h2>
+
+<p>
+In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates \( \eta_t \)
+as a function of time.  As discussed in the context of Newton's
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.
+
+<p>
+Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs069.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs062.html">63</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li class="active"><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs071.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs071.html b/doc/pub/Splines/html/._Splines-bs071.html
new file mode 100644
index 000000000..8dcf652ed
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs071.html
@@ -0,0 +1,334 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0071"></a>
+<!-- !split -->
+
+<h2 id="___sec70" class="anchor">RMS prop </h2>
+
+<p>
+In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2] \). The update rule for RMS prop is given by
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\tag{4}\\
+\mathbf{s}_t &=\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber \\
+\boldsymbol{\theta}_{t+1}&=&\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\end{align}
+$$
+
+where \( \beta \) controls the averaging time of the second moment and is typically taken to be about \( \beta=0.9 \), \( \eta_t \) is a learning rate typically chosen to be \( 10^{-3} \), and \( \epsilon\sim 10^{-8}  \) is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs070.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs063.html">64</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li class="active"><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs072.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs072.html b/doc/pub/Splines/html/._Splines-bs072.html
new file mode 100644
index 000000000..7921ef55f
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs072.html
@@ -0,0 +1,343 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0072"></a>
+<!-- !split -->
+
+<h2 id="___sec71" class="anchor">ADAM optimizer </h2>
+
+<p>
+A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. \( \mathbf{m}_t=\mathbb{E}[\mathbf{g}_t] \) and \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t] \), respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\tag{5}\\
+\mathbf{m}_t &= \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber \\
+\mathbf{s}_t &=\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber \\
+\hat{\mathbf{m}}_t&={\mathbf{m}_t \over 1-\beta_1^t} \nonumber \\
+\hat{\mathbf{s}}_t &={\mathbf{s}_t \over1-\beta_2^t} \nonumber \\
+\boldsymbol{\theta}_{t+1}&=\boldsymbol{\theta}_t - \eta_t { \hat{\mathbf{m}}_t \over \sqrt{\hat{\mathbf{s}}_t} +\epsilon}, \nonumber \\
+\tag{6}
+\end{align}
+$$
+
+where \( \beta_1 \) and \( \beta_2 \) set the memory lifetime of the first and second moment and are typically taken to be \( 0.9 \) and \( 0.99 \) respectively, and \( \eta \) and \( \epsilon \) are identical to RMSprop.
+
+<p>
+Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance \( \boldsymbol{\sigma}_t^2 = \hat{\mathbf{s}}_t - (\hat{\mathbf{m}}_t)^2 \). Consider a single parameter \( \theta_t \). The update rule for this parameter is given by
+$$
+\Delta \theta_{t+1}= -\eta_t { \hat{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+$$
+
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs071.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li class="active"><a href="._Splines-bs072.html">73</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
+  <li><a href="._Splines-bs073.html">&raquo;</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/._Splines-bs073.html b/doc/pub/Splines/html/._Splines-bs073.html
new file mode 100644
index 000000000..bfcdafb90
--- /dev/null
+++ b/doc/pub/Splines/html/._Splines-bs073.html
@@ -0,0 +1,326 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/hplgit/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
+<meta name="description" content="Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods">
+
+<title>Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
+<!-- not necessary
+<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
+-->
+
+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Optimization, the central part of any Machine Learning '
+               'algortithm',
+               2,
+               None,
+               '___sec0'),
+              ('Revisiting our Logistic Regression case', 2, None, '___sec1'),
+              ('The equations to solve', 2, None, '___sec2'),
+              ("Solving using Newton-Raphson's method", 2, None, '___sec3'),
+              ("Brief reminder on Newton-Raphson's method", 2, None, '___sec4'),
+              ('The equations', 2, None, '___sec5'),
+              ('Simple geometric interpretation', 2, None, '___sec6'),
+              ('Extending to more than one variable', 2, None, '___sec7'),
+              ('Steepest descent', 2, None, '___sec8'),
+              ('More on Steepest descent', 2, None, '___sec9'),
+              ('The ideal', 2, None, '___sec10'),
+              ('The sensitiveness of the gradient descent',
+               2,
+               None,
+               '___sec11'),
+              ('Convex functions', 2, None, '___sec12'),
+              ('Convex function', 2, None, '___sec13'),
+              ('Conditions on convex functions', 2, None, '___sec14'),
+              ('More on convex functions', 2, None, '___sec15'),
+              ('Some simple problems', 2, None, '___sec16'),
+              ('Standard steepest descent', 2, None, '___sec17'),
+              ('Gradient method', 2, None, '___sec18'),
+              ('Steepest descent  method', 2, None, '___sec19'),
+              ('Steepest descent  method', 2, None, '___sec20'),
+              ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
+              ('Simple codes for  steepest descent and conjugate gradient '
+               'using a $2\\times 2$ matrix, in c++, Python code to come',
+               2,
+               None,
+               '___sec23'),
+              ('The routine for the steepest descent method',
+               2,
+               None,
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
+              ('And a corresponding example using _scikit-learn_',
+               2,
+               None,
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
+              ('More complicated functions using the elements of their '
+               'arguments directly',
+               2,
+               None,
+               '___sec38'),
+              ('Functions using mathematical functions from Numpy',
+               2,
+               None,
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
+              ('The syntax a.dot(b) when finding the dot product',
+               2,
+               None,
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
+              ('Conjugate gradient method', 2, None, '___sec55'),
+              ('Conjugate gradient method', 2, None, '___sec56'),
+              ('Conjugate gradient method', 2, None, '___sec57'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec60'),
+              ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
+              ('Simple implementation of the Conjugate gradient algorithm',
+               2,
+               None,
+               '___sec63'),
+              ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
+               2,
+               None,
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
+  }
+});
+</script>
+<script type="text/javascript" async
+ src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
+</script>
+
+
+
+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+      <span class="icon-bar"></span>
+    </button>
+    <a class="navbar-brand" href="Splines-bs.html">Data Analysis and Machine Learning  Lectures: Optimization and  Gradient Methods</a>
+  </div>
+
+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <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="._Splines-bs001.html#___sec0" style="font-size: 80%;">Optimization, the central part of any Machine Learning algortithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs002.html#___sec1" style="font-size: 80%;">Revisiting our Logistic Regression case</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs003.html#___sec2" style="font-size: 80%;">The equations to solve</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs004.html#___sec3" style="font-size: 80%;">Solving using Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs005.html#___sec4" style="font-size: 80%;">Brief reminder on Newton-Raphson's method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs006.html#___sec5" style="font-size: 80%;">The equations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs007.html#___sec6" style="font-size: 80%;">Simple geometric interpretation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs008.html#___sec7" style="font-size: 80%;">Extending to more than one variable</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs009.html#___sec8" style="font-size: 80%;">Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs010.html#___sec9" style="font-size: 80%;">More on Steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs011.html#___sec10" style="font-size: 80%;">The ideal</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs012.html#___sec11" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs013.html#___sec12" style="font-size: 80%;">Convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs014.html#___sec13" style="font-size: 80%;">Convex function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs015.html#___sec14" style="font-size: 80%;">Conditions on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs016.html#___sec15" style="font-size: 80%;">More on convex functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs017.html#___sec16" style="font-size: 80%;">Some simple problems</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs018.html#___sec17" style="font-size: 80%;">Standard steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs019.html#___sec18" style="font-size: 80%;">Gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="#___sec72" style="font-size: 80%;">Practical tips</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0073"></a>
+<!-- !split -->
+
+<h2 id="___sec72" class="anchor">Practical tips </h2>
+
+<ul>
+<li> <b>Randomize the data when making mini-batches</b>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</li>
+<li> <b>Transform your inputs</b>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</li>
+<li> <b>Monitor the out-of-sample performance.</b> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</li>
+<li> <b>Adaptive optimization methods don't always have good generalization.</b> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</li>
+</ul>
+
+Geron's text, see chapter 11, has several interesting discussions.
+
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._Splines-bs072.html">&laquo;</a></li>
+  <li><a href="._Splines-bs000.html">1</a></li>
+  <li><a href="">...</a></li>
+  <li><a href="._Splines-bs065.html">66</a></li>
+  <li><a href="._Splines-bs066.html">67</a></li>
+  <li><a href="._Splines-bs067.html">68</a></li>
+  <li><a href="._Splines-bs068.html">69</a></li>
+  <li><a href="._Splines-bs069.html">70</a></li>
+  <li><a href="._Splines-bs070.html">71</a></li>
+  <li><a href="._Splines-bs071.html">72</a></li>
+  <li><a href="._Splines-bs072.html">73</a></li>
+  <li class="active"><a href="._Splines-bs073.html">74</a></li>
+</ul>
+<!-- ------------------- end of main content --------------- -->
+
+</div>  <!-- end container -->
+<!-- include javascript, jQuery *first* -->
+<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>
+<a href="http://..."><img width="250" align=right src="http://..."></a>
+</footer>
+-->
+
+
+<center style="font-size:80%">
+<!-- copyright only on the titlepage -->
+</center>
+
+
+</body>
+</html>
+    
+
diff --git a/doc/pub/Splines/html/Splines-bs.html b/doc/pub/Splines/html/Splines-bs.html
index bece1e921..8625c257e 100644
--- a/doc/pub/Splines/html/Splines-bs.html
+++ b/doc/pub/Splines/html/Splines-bs.html
@@ -69,74 +69,86 @@ Automatically generated HTML file from DocOnce source
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -196,48 +208,57 @@ MathJax.Hub.Config({
      <!-- navigation toc: --> <li><a href="._Splines-bs020.html#___sec19" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs021.html#___sec20" style="font-size: 80%;">Steepest descent  method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs022.html#___sec21" style="font-size: 80%;">Final expressions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">The routine for the steepest descent method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">Steepest descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Conjugate gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Revisiting our first homework</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Gradient descent example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The Hessian matrix</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">Simple program</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Gradient Descent Example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">Gradient descent and Ridge</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Automatic differentiation</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Using autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Autograd with more complicated functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">More autograd</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">And  with loops</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">Using recursion</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Unsupported functions</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">Recommended to avoid</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Computation of gradients</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">SGD example</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">The gradient step</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">Simple example code</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">When do we stop?</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">Slightly different approach</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Program for stochastic gradient</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Momentum based methods</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs023.html#___sec22" style="font-size: 80%;">Code examples for steepest descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs024.html#___sec23" style="font-size: 80%;">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs025.html#___sec24" style="font-size: 80%;">The routine for the steepest descent method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs026.html#___sec25" style="font-size: 80%;">Steepest descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs027.html#___sec26" style="font-size: 80%;">Conjugate gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs028.html#___sec27" style="font-size: 80%;">Revisiting our first homework</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs029.html#___sec28" style="font-size: 80%;">Gradient descent example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs030.html#___sec29" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs031.html#___sec30" style="font-size: 80%;">The Hessian matrix</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs032.html#___sec31" style="font-size: 80%;">Simple program</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs033.html#___sec32" style="font-size: 80%;">Gradient Descent Example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs034.html#___sec33" style="font-size: 80%;">And a corresponding example using <b>scikit-learn</b></a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs035.html#___sec34" style="font-size: 80%;">Gradient descent and Ridge</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs036.html#___sec35" style="font-size: 80%;">Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs037.html#___sec36" style="font-size: 80%;">Using autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs038.html#___sec37" style="font-size: 80%;">Autograd with more complicated functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs039.html#___sec38" style="font-size: 80%;">More complicated functions using the elements of their arguments directly</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs040.html#___sec39" style="font-size: 80%;">Functions using mathematical functions from Numpy</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs041.html#___sec40" style="font-size: 80%;">More autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs042.html#___sec41" style="font-size: 80%;">And  with loops</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs043.html#___sec42" style="font-size: 80%;">Using recursion</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs044.html#___sec43" style="font-size: 80%;">Unsupported functions</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs045.html#___sec44" style="font-size: 80%;">The syntax a.dot(b) when finding the dot product</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs046.html#___sec45" style="font-size: 80%;">Recommended to avoid</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs047.html#___sec46" style="font-size: 80%;">Stochastic Gradient Descent</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs048.html#___sec47" style="font-size: 80%;">Computation of gradients</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs049.html#___sec48" style="font-size: 80%;">SGD example</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs050.html#___sec49" style="font-size: 80%;">The gradient step</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs051.html#___sec50" style="font-size: 80%;">Simple example code</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs052.html#___sec51" style="font-size: 80%;">When do we stop?</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs053.html#___sec52" style="font-size: 80%;">Slightly different approach</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs054.html#___sec53" style="font-size: 80%;">Program for stochastic gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs055.html#___sec54" style="font-size: 80%;">Momentum based methods</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs056.html#___sec55" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs057.html#___sec56" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs058.html#___sec57" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs059.html#___sec58" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs060.html#___sec59" style="font-size: 80%;">Conjugate gradient method and iterations</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs061.html#___sec60" style="font-size: 80%;">Conjugate gradient method</a></li>
      <!-- navigation toc: --> <li><a href="._Splines-bs062.html#___sec61" style="font-size: 80%;">Conjugate gradient method</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
-     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs063.html#___sec62" style="font-size: 80%;">Conjugate gradient method</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs064.html#___sec63" style="font-size: 80%;">Simple implementation of the Conjugate gradient algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs065.html#___sec64" style="font-size: 80%;">Broyden–Fletcher–Goldfarb–Shanno algorithm</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs066.html#___sec65" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs067.html#___sec66" style="font-size: 80%;">Momentum based GD</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs068.html#___sec67" style="font-size: 80%;">More on momentum based approaches</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs069.html#___sec68" style="font-size: 80%;">Momentum parameter</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs070.html#___sec69" style="font-size: 80%;">Second moment of the gradient</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs071.html#___sec70" style="font-size: 80%;">RMS prop</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs072.html#___sec71" style="font-size: 80%;">ADAM optimizer</a></li>
+     <!-- navigation toc: --> <li><a href="._Splines-bs073.html#___sec72" style="font-size: 80%;">Practical tips</a></li>
 
         </ul>
       </li>
@@ -272,7 +293,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 6, 2018</h4></center> <!-- date -->
+<center><h4>Oct 12, 2018</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -296,7 +317,7 @@ MathJax.Hub.Config({
   <li><a href="._Splines-bs008.html">9</a></li>
   <li><a href="._Splines-bs009.html">10</a></li>
   <li><a href="">...</a></li>
-  <li><a href="._Splines-bs064.html">65</a></li>
+  <li><a href="._Splines-bs073.html">74</a></li>
   <li><a href="._Splines-bs001.html">&raquo;</a></li>
 </ul>
 <!-- ------------------- end of main content --------------- -->
diff --git a/doc/pub/Splines/html/Splines-reveal.html b/doc/pub/Splines/html/Splines-reveal.html
index 70d6a8a17..1f3dae32c 100644
--- a/doc/pub/Splines/html/Splines-reveal.html
+++ b/doc/pub/Splines/html/Splines-reveal.html
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>&nbsp;<br>
-<center><h4>Oct 6, 2018</h4></center> <!-- date -->
+<center><h4>Oct 12, 2018</h4></center> <!-- date -->
 <br>
 <p>
 
@@ -793,7 +793,12 @@ $$
 
 
 <section>
-<h2 id="___sec22">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
+<h2 id="___sec22">Code examples for steepest descent </h2>
+</section>
+
+
+<section>
+<h2 id="___sec23">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -831,7 +836,7 @@ $$
 
 
 <section>
-<h2 id="___sec23">The routine for the steepest descent method </h2>
+<h2 id="___sec24">The routine for the steepest descent method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -865,7 +870,7 @@ $$
 
 
 <section>
-<h2 id="___sec24">Steepest descent example </h2>
+<h2 id="___sec25">Steepest descent example </h2>
 
 <p>
 
@@ -935,12 +940,12 @@ pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span styl
 
 
 <section>
-<h2 id="___sec25">Conjugate gradient </h2>
+<h2 id="___sec26">Conjugate gradient </h2>
 </section>
 
 
 <section>
-<h2 id="___sec26">Revisiting our first homework </h2>
+<h2 id="___sec27">Revisiting our first homework </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -980,7 +985,7 @@ $$
 
 
 <section>
-<h2 id="___sec27">Gradient descent example </h2>
+<h2 id="___sec28">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -1009,7 +1014,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 
 
 <section>
-<h2 id="___sec28">The derivative of the cost/loss function </h2>
+<h2 id="___sec29">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -1026,7 +1031,7 @@ where \( X \) is the design matrix defined above.
 
 
 <section>
-<h2 id="___sec29">The Hessian matrix </h2>
+<h2 id="___sec30">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 <p>&nbsp;<br>
 $$
@@ -1042,7 +1047,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 
 
 <section>
-<h2 id="___sec30">Simple program </h2>
+<h2 id="___sec31">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -1086,7 +1091,7 @@ beta_NE = np.dot(Xt_X_inv,Xt_y)
 
 
 <section>
-<h2 id="___sec31">Gradient Descent Example </h2>
+<h2 id="___sec32">Gradient Descent Example </h2>
 
 <p>
 Another simple example is here
@@ -1136,7 +1141,7 @@ plt.show()
 
 
 <section>
-<h2 id="___sec32">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec33">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
@@ -1161,7 +1166,7 @@ sgdreg.fit(x,y.ravel())
 
 
 <section>
-<h2 id="___sec33">Gradient descent and Ridge </h2>
+<h2 id="___sec34">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \), 
@@ -1225,7 +1230,7 @@ beta_ridge = np.dot(Z,np.dot(X.T,y))
 
 
 <section>
-<h2 id="___sec34">Automatic differentiation </h2>
+<h2 id="___sec35">Automatic differentiation </h2>
 Python has tools for so-called <b>automatic differentiation</b>.
 Consider the following example
 <p>&nbsp;<br>
@@ -1285,7 +1290,7 @@ plt.show()
 
 
 <section>
-<h2 id="___sec35">Using autograd </h2>
+<h2 id="___sec36">Using autograd </h2>
 
 <p>
 Here we
@@ -1319,7 +1324,7 @@ grad_analytical = <span style="color: #B452CD">3</span>*a**<span style="color: #
 
 
 <section>
-<h2 id="___sec36">Autograd with more complicated functions </h2>
+<h2 id="___sec37">Autograd with more complicated functions </h2>
 
 <p>
 To differentiate with respect to two (or more) arguments of a Python
@@ -1369,7 +1374,7 @@ Note that the grad function will not produce the true gradient of the function.
 
 
 <section>
-<h2 id="___sec37">More complicated functions using the elements of their arguments directly </h2>
+<h2 id="___sec38">More complicated functions using the elements of their arguments directly </h2>
 
 <p>
 
@@ -1403,7 +1408,7 @@ could expect form a gradient-evaluting function.
 
 
 <section>
-<h2 id="___sec38">Functions using mathematical functions from Numpy </h2>
+<h2 id="___sec39">Functions using mathematical functions from Numpy </h2>
 
 <p>
 
@@ -1430,7 +1435,7 @@ f4_grad_analytical = x/np.sqrt(<span style="color: #B452CD">1</span> + x**<span
 
 
 <section>
-<h2 id="___sec39">More autograd </h2>
+<h2 id="___sec40">More autograd </h2>
 
 <p>
 
@@ -1454,7 +1459,7 @@ x = <span style="color: #B452CD">2.7</span>
 
 
 <section>
-<h2 id="___sec40">And  with loops </h2>
+<h2 id="___sec41">And  with loops </h2>
 
 <p>
 
@@ -1501,7 +1506,7 @@ f6_grad_analytical = <span style="color: #B452CD">0</span>
 
 
 <section>
-<h2 id="___sec41">Using recursion </h2>
+<h2 id="___sec42">Using recursion </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1539,7 +1544,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
 
 
 <section>
-<h2 id="___sec42">Unsupported functions </h2>
+<h2 id="___sec43">Unsupported functions </h2>
 Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
 
 <p>
@@ -1565,7 +1570,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
 
 
 <section>
-<h2 id="___sec43">The syntax a.dot(b) when finding the dot product </h2>
+<h2 id="___sec44">The syntax a.dot(b) when finding the dot product </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1608,7 +1613,7 @@ x = np.array([<span style="color: #B452CD">3.0</span>,<span style="color: #B452C
 
 
 <section>
-<h2 id="___sec44">Recommended to avoid </h2>
+<h2 id="___sec45">Recommended to avoid </h2>
 The documentation recommends to avoid inplace operations such as
 <p>
 
@@ -1622,7 +1627,7 @@ a /=b
 
 
 <section>
-<h2 id="___sec45">Stochastic Gradient Descent </h2>
+<h2 id="___sec46">Stochastic Gradient Descent </h2>
 
 <p>
 Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1642,7 +1647,7 @@ $$
 
 
 <section>
-<h2 id="___sec46">Computation of gradients </h2>
+<h2 id="___sec47">Computation of gradients </h2>
 
 <p>
 This in turn means that the gradient can be
@@ -1664,7 +1669,7 @@ minibatches. We denote these minibatches by \( B_k \) where
 
 
 <section>
-<h2 id="___sec47">SGD example </h2>
+<h2 id="___sec48">SGD example </h2>
 As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) 
 and we choose to have \( M=5 \) minibathces,
 then each minibatch contains two data points. In particular we have
@@ -1690,7 +1695,7 @@ $$
 
 
 <section>
-<h2 id="___sec48">The gradient step </h2>
+<h2 id="___sec49">The gradient step </h2>
 
 <p>
 Thus a gradient descent step now looks like 
@@ -1711,7 +1716,7 @@ the number of minibatches, as exemplified in the code below.
 
 
 <section>
-<h2 id="___sec49">Simple example code </h2>
+<h2 id="___sec50">Simple example code </h2>
 
 <p>
 
@@ -1743,7 +1748,7 @@ all \( n \) datapoints.
 
 
 <section>
-<h2 id="___sec50">When do we stop? </h2>
+<h2 id="___sec51">When do we stop? </h2>
 
 <p>
 A natural question is when do we stop the search for a new minimum?
@@ -1760,7 +1765,7 @@ gave the lowest value.
 
 
 <section>
-<h2 id="___sec51">Slightly different approach </h2>
+<h2 id="___sec52">Slightly different approach </h2>
 
 <p>
 Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1811,7 +1816,7 @@ j = <span style="color: #B452CD">0</span>
 
 
 <section>
-<h2 id="___sec52">Program for stochastic gradient </h2>
+<h2 id="___sec53">Program for stochastic gradient </h2>
 
 <p>
 
@@ -1891,12 +1896,12 @@ plt.show()
 
 
 <section>
-<h2 id="___sec53">Momentum based methods </h2>
+<h2 id="___sec54">Momentum based methods </h2>
 </section>
 
 
 <section>
-<h2 id="___sec54">Conjugate gradient method </h2>
+<h2 id="___sec55">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1929,7 +1934,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is
 
 
 <section>
-<h2 id="___sec55">Conjugate gradient method </h2>
+<h2 id="___sec56">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1948,7 +1953,7 @@ which is zero unless \( i=j \).
 
 
 <section>
-<h2 id="___sec56">Conjugate gradient method </h2>
+<h2 id="___sec57">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1978,7 +1983,7 @@ $$
 
 
 <section>
-<h2 id="___sec57">Conjugate gradient method </h2>
+<h2 id="___sec58">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2015,7 +2020,7 @@ $$
 
 
 <section>
-<h2 id="___sec58">Conjugate gradient method and iterations </h2>
+<h2 id="___sec59">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2052,7 +2057,7 @@ instead.
 
 
 <section>
-<h2 id="___sec59">Conjugate gradient method </h2>
+<h2 id="___sec60">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2085,7 +2090,7 @@ hence the name conjugate gradient method.
 
 
 <section>
-<h2 id="___sec60">Conjugate gradient method </h2>
+<h2 id="___sec61">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2117,7 +2122,7 @@ $$
 
 
 <section>
-<h2 id="___sec61">Conjugate gradient method </h2>
+<h2 id="___sec62">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2162,7 +2167,7 @@ $$
 
 
 <section>
-<h2 id="___sec62">Simple implementation of the Conjugate gradient algorithm </h2>
+<h2 id="___sec63">Simple implementation of the Conjugate gradient algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2199,7 +2204,7 @@ $$
 
 
 <section>
-<h2 id="___sec63">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
+<h2 id="___sec64">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2236,6 +2241,201 @@ over the scalar \( \alpha > 0 \).
 </section>
 
 
+<section>
+<h2 id="___sec65">Using gradient descent methods, limitations </h2>
+
+<ul>
+<p><li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
+<p><li> <b>GD is sensitive to initial conditions</b>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</li>
+<p><li> <b>Gradients are computationally expensive to calculate for large datasets</b>. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, \( E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2 \); for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over <em>all</em> \( n \) data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called &quot;mini batches&quot;. This has the added benefit of introducing stochasticity into our algorithm.</li>
+<p><li> <b>GD is very sensitive to choices of learning rates</b>. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would <em>adaptively</em> choose the learning rates to match the landscape.</li>
+<p><li> <b>GD treats all directions in parameter space uniformly.</b> Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</li> 
+<p><li> GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</li>
+</ul>
+</section>
+
+
+<section>
+<h2 id="___sec66">Momentum based GD </h2>
+
+<p>
+The stochastic gradient descent (SGD) is almost always used with a <em>momentum</em> or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically 
+implemented as follows
+<p>&nbsp;<br>
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\tag{2}
+\end{align}
+$$
+<p>&nbsp;<br>
+
+where we have introduced a momentum parameter \( \gamma \), with \( 0\le\gamma\le 1 \), and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that \( \mathbf{v}_t \) is a running average of recently encountered gradients and \( (1-\gamma)^{-1} \) sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when \( \gamma=0 \), this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is
+<p>&nbsp;<br>
+$$
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+$$
+<p>&nbsp;<br>
+
+where we have defined \( \Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1} \).
+</section>
+
+
+<section>
+<h2 id="___sec67">More on momentum based approaches </h2>
+
+<p>
+Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass \( m \) moving in a viscous medium with drag coefficient \( \mu \) and potential 
+\( E(\mathbf{w}) \). If we denote the particle's position by \( \mathbf{w} \), then its motion is described by 
+<p>&nbsp;<br>
+$$
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+$$
+<p>&nbsp;<br>
+
+We can discretize this equation in the usual way to get
+<p>&nbsp;<br>
+$$
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+$$
+<p>&nbsp;<br>
+
+Rearranging this equation, we can rewrite this as
+<p>&nbsp;<br>
+$$
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+$$
+<p>&nbsp;<br>
+</section>
+
+
+<section>
+<h2 id="___sec68">Momentum parameter </h2>
+Notice that this equation is identical to previous one if we identify the position of the particle, \( \mathbf{w} \), with the parameters \( \boldsymbol{\theta} \). This allows
+us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:
+<p>&nbsp;<br>
+$$
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+$$
+<p>&nbsp;<br>
+
+Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as \( (1-\gamma)^{-1} \approx  m/(\mu \Delta t) \).
+
+<p>
+Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models.
+
+<p>
+These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG).
+
+<p>
+In the NAG algorithm, rather than calculating the gradient at the current parameters, \( \nabla_\theta E(\boldsymbol{\theta}_t) \), one calculates the gradient at the expected value of the parameters given our current momentum,   \( \nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \). This yields the NAG update rule
+<p>&nbsp;<br>
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\tag{3}
+\end{align}
+$$
+<p>&nbsp;<br>
+
+One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of \( \gamma \).
+</section>
+
+
+<section>
+<h2 id="___sec69">Second moment of the gradient </h2>
+
+<p>
+In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates \( \eta_t \)
+as a function of time.  As discussed in the context of Newton's
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.
+
+<p>
+Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.
+</section>
+
+
+<section>
+<h2 id="___sec70">RMS prop </h2>
+
+<p>
+In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2] \). The update rule for RMS prop is given by
+<p>&nbsp;<br>
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\tag{4}\\
+\mathbf{s}_t &=\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber \\
+\boldsymbol{\theta}_{t+1}&=&\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\end{align}
+$$
+<p>&nbsp;<br>
+
+where \( \beta \) controls the averaging time of the second moment and is typically taken to be about \( \beta=0.9 \), \( \eta_t \) is a learning rate typically chosen to be \( 10^{-3} \), and \( \epsilon\sim 10^{-8}  \) is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.
+</section>
+
+
+<section>
+<h2 id="___sec71">ADAM optimizer </h2>
+
+<p>
+A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. \( \mathbf{m}_t=\mathbb{E}[\mathbf{g}_t] \) and \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t] \), respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)
+<p>&nbsp;<br>
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\tag{5}\\
+\mathbf{m}_t &= \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber \\
+\mathbf{s}_t &=\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber \\
+\hat{\mathbf{m}}_t&={\mathbf{m}_t \over 1-\beta_1^t} \nonumber \\
+\hat{\mathbf{s}}_t &={\mathbf{s}_t \over1-\beta_2^t} \nonumber \\
+\boldsymbol{\theta}_{t+1}&=\boldsymbol{\theta}_t - \eta_t { \hat{\mathbf{m}}_t \over \sqrt{\hat{\mathbf{s}}_t} +\epsilon}, \nonumber \\
+\tag{6}
+\end{align}
+$$
+<p>&nbsp;<br>
+
+where \( \beta_1 \) and \( \beta_2 \) set the memory lifetime of the first and second moment and are typically taken to be \( 0.9 \) and \( 0.99 \) respectively, and \( \eta \) and \( \epsilon \) are identical to RMSprop.
+
+<p>
+Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance \( \boldsymbol{\sigma}_t^2 = \hat{\mathbf{s}}_t - (\hat{\mathbf{m}}_t)^2 \). Consider a single parameter \( \theta_t \). The update rule for this parameter is given by
+<p>&nbsp;<br>
+$$
+\Delta \theta_{t+1}= -\eta_t { \hat{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+$$
+<p>&nbsp;<br>
+</section>
+
+
+<section>
+<h2 id="___sec72">Practical tips </h2>
+
+<ul>
+<p><li> <b>Randomize the data when making mini-batches</b>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</li>
+<p><li> <b>Transform your inputs</b>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</li>
+<p><li> <b>Monitor the out-of-sample performance.</b> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</li>
+<p><li> <b>Adaptive optimization methods don't always have good generalization.</b> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</li>
+</ul>
+<p>
+
+Geron's text, see chapter 11, has several interesting discussions.
+</section>
+
+
 
 </div> <!-- class="slides" -->
 </div> <!-- class="reveal" -->
diff --git a/doc/pub/Splines/html/Splines-solarized.html b/doc/pub/Splines/html/Splines-solarized.html
index aaddf1a72..6a165bc46 100644
--- a/doc/pub/Splines/html/Splines-solarized.html
+++ b/doc/pub/Splines/html/Splines-solarized.html
@@ -89,74 +89,86 @@ div { text-align: justify; text-justify: inter-word; }
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -198,7 +210,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 6, 2018</h4></center> <!-- date -->
+<center><h4>Oct 12, 2018</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -782,7 +794,12 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec22">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
+<h2 id="___sec22">Code examples for steepest descent </h2>
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec23">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -822,7 +839,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec23">The routine for the steepest descent method </h2>
+<h2 id="___sec24">The routine for the steepest descent method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -858,7 +875,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec24">Steepest descent example </h2>
+<h2 id="___sec25">Steepest descent example </h2>
 
 <p>
 
@@ -927,12 +944,12 @@ pt.plot(it_array.T[<span style="color: #B452CD">0</span>], it_array.T[<span styl
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec25">Conjugate gradient </h2>
+<h2 id="___sec26">Conjugate gradient </h2>
 
 <p>
 <!-- !split  -->
 
-<h2 id="___sec26">Revisiting our first homework </h2>
+<h2 id="___sec27">Revisiting our first homework </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -965,7 +982,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="___sec27">Gradient descent example </h2>
+<h2 id="___sec28">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -990,7 +1007,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec28">The derivative of the cost/loss function </h2>
+<h2 id="___sec29">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -1005,7 +1022,7 @@ where \( X \) is the design matrix defined above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec29">The Hessian matrix </h2>
+<h2 id="___sec30">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 $$
 \hat{H} \equiv \begin{bmatrix}
@@ -1019,7 +1036,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec30">Simple program </h2>
+<h2 id="___sec31">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -1060,7 +1077,7 @@ beta_NE = np.dot(Xt_X_inv,Xt_y)
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec31">Gradient Descent Example </h2>
+<h2 id="___sec32">Gradient Descent Example </h2>
 
 <p>
 Another simple example is here
@@ -1109,7 +1126,7 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec32">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec33">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
@@ -1133,7 +1150,7 @@ sgdreg.fit(x,y.ravel())
 <p>
 <!-- !split  -->
 
-<h2 id="___sec33">Gradient descent and Ridge </h2>
+<h2 id="___sec34">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \), 
@@ -1190,7 +1207,7 @@ beta_ridge = np.dot(Z,np.dot(X.T,y))
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec34">Automatic differentiation </h2>
+<h2 id="___sec35">Automatic differentiation </h2>
 Python has tools for so-called <b>automatic differentiation</b>.
 Consider the following example
 $$
@@ -1245,7 +1262,7 @@ plt.show()
 <p>
 <!-- !split  -->
 
-<h2 id="___sec35">Using autograd </h2>
+<h2 id="___sec36">Using autograd </h2>
 
 <p>
 Here we
@@ -1278,7 +1295,7 @@ grad_analytical = <span style="color: #B452CD">3</span>*a**<span style="color: #
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec36">Autograd with more complicated functions </h2>
+<h2 id="___sec37">Autograd with more complicated functions </h2>
 
 <p>
 To differentiate with respect to two (or more) arguments of a Python
@@ -1328,7 +1345,7 @@ Note that the grad function will not produce the true gradient of the function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec37">More complicated functions using the elements of their arguments directly </h2>
+<h2 id="___sec38">More complicated functions using the elements of their arguments directly </h2>
 
 <p>
 
@@ -1362,7 +1379,7 @@ could expect form a gradient-evaluting function.
 <p>
 <!-- !split  -->
 
-<h2 id="___sec38">Functions using mathematical functions from Numpy </h2>
+<h2 id="___sec39">Functions using mathematical functions from Numpy </h2>
 
 <p>
 
@@ -1388,7 +1405,7 @@ f4_grad_analytical = x/np.sqrt(<span style="color: #B452CD">1</span> + x**<span
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec39">More autograd </h2>
+<h2 id="___sec40">More autograd </h2>
 
 <p>
 
@@ -1411,7 +1428,7 @@ x = <span style="color: #B452CD">2.7</span>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec40">And  with loops </h2>
+<h2 id="___sec41">And  with loops </h2>
 
 <p>
 
@@ -1457,7 +1474,7 @@ f6_grad_analytical = <span style="color: #B452CD">0</span>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec41">Using recursion </h2>
+<h2 id="___sec42">Using recursion </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1495,7 +1512,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec42">Unsupported functions </h2>
+<h2 id="___sec43">Unsupported functions </h2>
 Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
 
 <p>
@@ -1521,7 +1538,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec43">The syntax a.dot(b) when finding the dot product </h2>
+<h2 id="___sec44">The syntax a.dot(b) when finding the dot product </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
@@ -1563,7 +1580,7 @@ x = np.array([<span style="color: #B452CD">3.0</span>,<span style="color: #B452C
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec44">Recommended to avoid </h2>
+<h2 id="___sec45">Recommended to avoid </h2>
 The documentation recommends to avoid inplace operations such as
 <p>
 
@@ -1576,7 +1593,7 @@ a /=b
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec45">Stochastic Gradient Descent </h2>
+<h2 id="___sec46">Stochastic Gradient Descent </h2>
 
 <p>
 Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1594,7 +1611,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec46">Computation of gradients </h2>
+<h2 id="___sec47">Computation of gradients </h2>
 
 <p>
 This in turn means that the gradient can be
@@ -1614,7 +1631,7 @@ minibatches. We denote these minibatches by \( B_k \) where
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec47">SGD example </h2>
+<h2 id="___sec48">SGD example </h2>
 As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) 
 and we choose to have \( M=5 \) minibathces,
 then each minibatch contains two data points. In particular we have
@@ -1638,7 +1655,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec48">The gradient step </h2>
+<h2 id="___sec49">The gradient step </h2>
 
 <p>
 Thus a gradient descent step now looks like 
@@ -1657,7 +1674,7 @@ the number of minibatches, as exemplified in the code below.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec49">Simple example code </h2>
+<h2 id="___sec50">Simple example code </h2>
 
 <p>
 
@@ -1689,7 +1706,7 @@ all \( n \) datapoints.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec50">When do we stop? </h2>
+<h2 id="___sec51">When do we stop? </h2>
 
 <p>
 A natural question is when do we stop the search for a new minimum?
@@ -1706,7 +1723,7 @@ gave the lowest value.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec51">Slightly different approach </h2>
+<h2 id="___sec52">Slightly different approach </h2>
 
 <p>
 Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1754,7 +1771,7 @@ j = <span style="color: #B452CD">0</span>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec52">Program for stochastic gradient </h2>
+<h2 id="___sec53">Program for stochastic gradient </h2>
 
 <p>
 
@@ -1833,12 +1850,12 @@ plt.show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec53">Momentum based methods </h2>
+<h2 id="___sec54">Momentum based methods </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec54">Conjugate gradient method </h2>
+<h2 id="___sec55">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1868,7 +1885,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec55">Conjugate gradient method </h2>
+<h2 id="___sec56">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1886,7 +1903,7 @@ which is zero unless \( i=j \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec56">Conjugate gradient method </h2>
+<h2 id="___sec57">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1913,7 +1930,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec57">Conjugate gradient method </h2>
+<h2 id="___sec58">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1945,7 +1962,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec58">Conjugate gradient method and iterations </h2>
+<h2 id="___sec59">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1981,7 +1998,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec59">Conjugate gradient method </h2>
+<h2 id="___sec60">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2011,7 +2028,7 @@ hence the name conjugate gradient method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec60">Conjugate gradient method </h2>
+<h2 id="___sec61">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2040,7 +2057,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec61">Conjugate gradient method </h2>
+<h2 id="___sec62">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2078,7 +2095,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec62">Simple implementation of the Conjugate gradient algorithm </h2>
+<h2 id="___sec63">Simple implementation of the Conjugate gradient algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2117,7 +2134,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec63">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
+<h2 id="___sec64">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2150,6 +2167,177 @@ over the scalar \( \alpha > 0 \).
 
 
 <p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec65">Using gradient descent methods, limitations </h2>
+
+<ul>
+<li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
+<li> <b>GD is sensitive to initial conditions</b>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</li>
+<li> <b>Gradients are computationally expensive to calculate for large datasets</b>. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, \( E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2 \); for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over <em>all</em> \( n \) data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called &quot;mini batches&quot;. This has the added benefit of introducing stochasticity into our algorithm.</li>
+<li> <b>GD is very sensitive to choices of learning rates</b>. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would <em>adaptively</em> choose the learning rates to match the landscape.</li>
+<li> <b>GD treats all directions in parameter space uniformly.</b> Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</li> 
+<li> GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</li>
+</ul>
+
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec66">Momentum based GD </h2>
+
+<p>
+The stochastic gradient descent (SGD) is almost always used with a <em>momentum</em> or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically 
+implemented as follows
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\label{_auto1}
+\end{align}
+$$
+
+where we have introduced a momentum parameter \( \gamma \), with \( 0\le\gamma\le 1 \), and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that \( \mathbf{v}_t \) is a running average of recently encountered gradients and \( (1-\gamma)^{-1} \) sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when \( \gamma=0 \), this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is
+$$
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+$$
+
+where we have defined \( \Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1} \).
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec67">More on momentum based approaches </h2>
+
+<p>
+Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass \( m \) moving in a viscous medium with drag coefficient \( \mu \) and potential 
+\( E(\mathbf{w}) \). If we denote the particle's position by \( \mathbf{w} \), then its motion is described by 
+$$
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+$$
+
+We can discretize this equation in the usual way to get
+$$
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+$$
+
+Rearranging this equation, we can rewrite this as
+$$
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+$$
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec68">Momentum parameter </h2>
+Notice that this equation is identical to previous one if we identify the position of the particle, \( \mathbf{w} \), with the parameters \( \boldsymbol{\theta} \). This allows
+us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:
+$$
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+$$
+
+Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as \( (1-\gamma)^{-1} \approx  m/(\mu \Delta t) \).
+
+<p>
+Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models.
+
+<p>
+These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG).
+
+<p>
+In the NAG algorithm, rather than calculating the gradient at the current parameters, \( \nabla_\theta E(\boldsymbol{\theta}_t) \), one calculates the gradient at the expected value of the parameters given our current momentum,   \( \nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \). This yields the NAG update rule
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\label{_auto2}
+\end{align}
+$$
+
+One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of \( \gamma \).
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec69">Second moment of the gradient </h2>
+
+<p>
+In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates \( \eta_t \)
+as a function of time.  As discussed in the context of Newton's
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.
+
+<p>
+Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec70">RMS prop </h2>
+
+<p>
+In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2] \). The update rule for RMS prop is given by
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto3}\\
+\mathbf{s}_t &=\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber \\
+\boldsymbol{\theta}_{t+1}&=&\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\end{align}
+$$
+
+where \( \beta \) controls the averaging time of the second moment and is typically taken to be about \( \beta=0.9 \), \( \eta_t \) is a learning rate typically chosen to be \( 10^{-3} \), and \( \epsilon\sim 10^{-8}  \) is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec71">ADAM optimizer </h2>
+
+<p>
+A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. \( \mathbf{m}_t=\mathbb{E}[\mathbf{g}_t] \) and \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t] \), respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto4}\\
+\mathbf{m}_t &= \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber \\
+\mathbf{s}_t &=\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber \\
+\hat{\mathbf{m}}_t&={\mathbf{m}_t \over 1-\beta_1^t} \nonumber \\
+\hat{\mathbf{s}}_t &={\mathbf{s}_t \over1-\beta_2^t} \nonumber \\
+\boldsymbol{\theta}_{t+1}&=\boldsymbol{\theta}_t - \eta_t { \hat{\mathbf{m}}_t \over \sqrt{\hat{\mathbf{s}}_t} +\epsilon}, \nonumber \\
+\label{_auto5}
+\end{align}
+$$
+
+where \( \beta_1 \) and \( \beta_2 \) set the memory lifetime of the first and second moment and are typically taken to be \( 0.9 \) and \( 0.99 \) respectively, and \( \eta \) and \( \epsilon \) are identical to RMSprop.
+
+<p>
+Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance \( \boldsymbol{\sigma}_t^2 = \hat{\mathbf{s}}_t - (\hat{\mathbf{m}}_t)^2 \). Consider a single parameter \( \theta_t \). The update rule for this parameter is given by
+$$
+\Delta \theta_{t+1}= -\eta_t { \hat{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+$$
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec72">Practical tips </h2>
+
+<ul>
+<li> <b>Randomize the data when making mini-batches</b>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</li>
+<li> <b>Transform your inputs</b>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</li>
+<li> <b>Monitor the out-of-sample performance.</b> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</li>
+<li> <b>Adaptive optimization methods don't always have good generalization.</b> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</li>
+</ul>
+
+Geron's text, see chapter 11, has several interesting discussions.
 
 <!-- ------------------- end of main content --------------- -->
 
diff --git a/doc/pub/Splines/html/Splines.html b/doc/pub/Splines/html/Splines.html
index 31883185d..6f8548d8b 100644
--- a/doc/pub/Splines/html/Splines.html
+++ b/doc/pub/Splines/html/Splines.html
@@ -94,74 +94,86 @@ div { text-align: justify; text-justify: inter-word; }
               ('Steepest descent  method', 2, None, '___sec19'),
               ('Steepest descent  method', 2, None, '___sec20'),
               ('Final expressions', 2, None, '___sec21'),
+              ('Code examples for steepest descent', 2, None, '___sec22'),
               ('Simple codes for  steepest descent and conjugate gradient '
                'using a $2\\times 2$ matrix, in c++, Python code to come',
                2,
                None,
-               '___sec22'),
+               '___sec23'),
               ('The routine for the steepest descent method',
                2,
                None,
-               '___sec23'),
-              ('Steepest descent example', 2, None, '___sec24'),
-              ('Conjugate gradient', 2, None, '___sec25'),
-              ('Revisiting our first homework', 2, None, '___sec26'),
-              ('Gradient descent example', 2, None, '___sec27'),
-              ('The derivative of the cost/loss function', 2, None, '___sec28'),
-              ('The Hessian matrix', 2, None, '___sec29'),
-              ('Simple program', 2, None, '___sec30'),
-              ('Gradient Descent Example', 2, None, '___sec31'),
+               '___sec24'),
+              ('Steepest descent example', 2, None, '___sec25'),
+              ('Conjugate gradient', 2, None, '___sec26'),
+              ('Revisiting our first homework', 2, None, '___sec27'),
+              ('Gradient descent example', 2, None, '___sec28'),
+              ('The derivative of the cost/loss function', 2, None, '___sec29'),
+              ('The Hessian matrix', 2, None, '___sec30'),
+              ('Simple program', 2, None, '___sec31'),
+              ('Gradient Descent Example', 2, None, '___sec32'),
               ('And a corresponding example using _scikit-learn_',
                2,
                None,
-               '___sec32'),
-              ('Gradient descent and Ridge', 2, None, '___sec33'),
-              ('Automatic differentiation', 2, None, '___sec34'),
-              ('Using autograd', 2, None, '___sec35'),
-              ('Autograd with more complicated functions', 2, None, '___sec36'),
+               '___sec33'),
+              ('Gradient descent and Ridge', 2, None, '___sec34'),
+              ('Automatic differentiation', 2, None, '___sec35'),
+              ('Using autograd', 2, None, '___sec36'),
+              ('Autograd with more complicated functions', 2, None, '___sec37'),
               ('More complicated functions using the elements of their '
                'arguments directly',
                2,
                None,
-               '___sec37'),
+               '___sec38'),
               ('Functions using mathematical functions from Numpy',
                2,
                None,
-               '___sec38'),
-              ('More autograd', 2, None, '___sec39'),
-              ('And  with loops', 2, None, '___sec40'),
-              ('Using recursion', 2, None, '___sec41'),
-              ('Unsupported functions', 2, None, '___sec42'),
+               '___sec39'),
+              ('More autograd', 2, None, '___sec40'),
+              ('And  with loops', 2, None, '___sec41'),
+              ('Using recursion', 2, None, '___sec42'),
+              ('Unsupported functions', 2, None, '___sec43'),
               ('The syntax a.dot(b) when finding the dot product',
                2,
                None,
-               '___sec43'),
-              ('Recommended to avoid', 2, None, '___sec44'),
-              ('Stochastic Gradient Descent', 2, None, '___sec45'),
-              ('Computation of gradients', 2, None, '___sec46'),
-              ('SGD example', 2, None, '___sec47'),
-              ('The gradient step', 2, None, '___sec48'),
-              ('Simple example code', 2, None, '___sec49'),
-              ('When do we stop?', 2, None, '___sec50'),
-              ('Slightly different approach', 2, None, '___sec51'),
-              ('Program for stochastic gradient', 2, None, '___sec52'),
-              ('Momentum based methods', 2, None, '___sec53'),
-              ('Conjugate gradient method', 2, None, '___sec54'),
+               '___sec44'),
+              ('Recommended to avoid', 2, None, '___sec45'),
+              ('Stochastic Gradient Descent', 2, None, '___sec46'),
+              ('Computation of gradients', 2, None, '___sec47'),
+              ('SGD example', 2, None, '___sec48'),
+              ('The gradient step', 2, None, '___sec49'),
+              ('Simple example code', 2, None, '___sec50'),
+              ('When do we stop?', 2, None, '___sec51'),
+              ('Slightly different approach', 2, None, '___sec52'),
+              ('Program for stochastic gradient', 2, None, '___sec53'),
+              ('Momentum based methods', 2, None, '___sec54'),
               ('Conjugate gradient method', 2, None, '___sec55'),
               ('Conjugate gradient method', 2, None, '___sec56'),
               ('Conjugate gradient method', 2, None, '___sec57'),
-              ('Conjugate gradient method and iterations', 2, None, '___sec58'),
-              ('Conjugate gradient method', 2, None, '___sec59'),
+              ('Conjugate gradient method', 2, None, '___sec58'),
+              ('Conjugate gradient method and iterations', 2, None, '___sec59'),
               ('Conjugate gradient method', 2, None, '___sec60'),
               ('Conjugate gradient method', 2, None, '___sec61'),
+              ('Conjugate gradient method', 2, None, '___sec62'),
               ('Simple implementation of the Conjugate gradient algorithm',
                2,
                None,
-               '___sec62'),
+               '___sec63'),
               ('Broyden–Fletcher–Goldfarb–Shanno algorithm',
                2,
                None,
-               '___sec63')]}
+               '___sec64'),
+              ('Using gradient descent methods, limitations',
+               2,
+               None,
+               '___sec65'),
+              ('Momentum based GD', 2, None, '___sec66'),
+              ('More on momentum based approaches', 2, None, '___sec67'),
+              ('Momentum parameter', 2, None, '___sec68'),
+              ('Second moment of the gradient', 2, None, '___sec69'),
+              ('RMS prop', 2, None, '___sec70'),
+              ('ADAM optimizer', 2, None, '___sec71'),
+              ('Practical tips', 2, None, '___sec72')]}
 end of tocinfo -->
 
 <body>
@@ -203,7 +215,7 @@ MathJax.Hub.Config({
 <center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
 <br>
 <p>
-<center><h4>Oct 6, 2018</h4></center> <!-- date -->
+<center><h4>Oct 12, 2018</h4></center> <!-- date -->
 <br>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
@@ -787,7 +799,12 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec22">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
+<h2 id="___sec22">Code examples for steepest descent </h2>
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec23">Simple codes for  steepest descent and conjugate gradient using a \( 2\times 2 \) matrix, in c++, Python code to come </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -827,7 +844,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec23">The routine for the steepest descent method </h2>
+<h2 id="___sec24">The routine for the steepest descent method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -863,7 +880,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec24">Steepest descent example </h2>
+<h2 id="___sec25">Steepest descent example </h2>
 
 <p>
 
@@ -932,12 +949,12 @@ pt<span style="color: #666666">.</span>plot(it_array<span style="color: #666666"
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec25">Conjugate gradient </h2>
+<h2 id="___sec26">Conjugate gradient </h2>
 
 <p>
 <!-- !split  -->
 
-<h2 id="___sec26">Revisiting our first homework </h2>
+<h2 id="___sec27">Revisiting our first homework </h2>
 
 <p>
 We will use linear regression as a case study for the gradient descent
@@ -970,7 +987,7 @@ $$
 <p>
 <!-- !split  -->
 
-<h2 id="___sec27">Gradient descent example </h2>
+<h2 id="___sec28">Gradient descent example </h2>
 
 <p>
 Let \( \mathbf{y} = (y_1,\cdots,y_n)^T \), \( \mathbf{\hat{y}} = (\hat{y}_1,\cdots,\hat{y}_n)^T \) and \( \beta = (\beta_0, \beta_1)^T \)
@@ -995,7 +1012,7 @@ and we want to find \( \beta \) such that \( C(\beta) \) is minimized.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec28">The derivative of the cost/loss function </h2>
+<h2 id="___sec29">The derivative of the cost/loss function </h2>
 
 <p>
 Computing \( \partial C(\beta) / \partial \beta_0 \) and \( \partial C(\beta) / \partial \beta_1 \) we can show  that the gradient can be written as
@@ -1010,7 +1027,7 @@ where \( X \) is the design matrix defined above.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec29">The Hessian matrix </h2>
+<h2 id="___sec30">The Hessian matrix </h2>
 The Hessian matrix of \( C(\beta) \) is given by 
 $$
 \hat{H} \equiv \begin{bmatrix}
@@ -1024,7 +1041,7 @@ This result implies that \( C(\beta) \) is a convex function since the matrix \(
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec30">Simple program </h2>
+<h2 id="___sec31">Simple program </h2>
 
 <p>
 We can now write a program that minimizes \( C(\beta) \) using the gradient descent method with a constant learning rate \( \gamma \) according to 
@@ -1065,7 +1082,7 @@ beta_NE <span style="color: #666666">=</span> np<span style="color: #666666">.</
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec31">Gradient Descent Example </h2>
+<h2 id="___sec32">Gradient Descent Example </h2>
 
 <p>
 Another simple example is here
@@ -1114,7 +1131,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec32">And a corresponding example using <b>scikit-learn</b> </h2>
+<h2 id="___sec33">And a corresponding example using <b>scikit-learn</b> </h2>
 
 <p>
 
@@ -1138,7 +1155,7 @@ sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.
 <p>
 <!-- !split  -->
 
-<h2 id="___sec33">Gradient descent and Ridge </h2>
+<h2 id="___sec34">Gradient descent and Ridge </h2>
 
 <p>
 We have also discussed Ridge regression where the loss function contains a regularized given by the \( L_2 \) norm of \( \beta \), 
@@ -1195,7 +1212,7 @@ beta_ridge <span style="color: #666666">=</span> np<span style="color: #666666">
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec34">Automatic differentiation </h2>
+<h2 id="___sec35">Automatic differentiation </h2>
 Python has tools for so-called <b>automatic differentiation</b>.
 Consider the following example
 $$
@@ -1250,7 +1267,7 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split  -->
 
-<h2 id="___sec35">Using autograd </h2>
+<h2 id="___sec36">Using autograd </h2>
 
 <p>
 Here we
@@ -1283,7 +1300,7 @@ grad_analytical <span style="color: #666666">=</span> <span style="color: #66666
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec36">Autograd with more complicated functions </h2>
+<h2 id="___sec37">Autograd with more complicated functions </h2>
 
 <p>
 To differentiate with respect to two (or more) arguments of a Python
@@ -1333,7 +1350,7 @@ Note that the grad function will not produce the true gradient of the function.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec37">More complicated functions using the elements of their arguments directly </h2>
+<h2 id="___sec38">More complicated functions using the elements of their arguments directly </h2>
 
 <p>
 
@@ -1367,7 +1384,7 @@ could expect form a gradient-evaluting function.
 <p>
 <!-- !split  -->
 
-<h2 id="___sec38">Functions using mathematical functions from Numpy </h2>
+<h2 id="___sec39">Functions using mathematical functions from Numpy </h2>
 
 <p>
 
@@ -1393,7 +1410,7 @@ f4_grad_analytical <span style="color: #666666">=</span> x<span style="color: #6
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec39">More autograd </h2>
+<h2 id="___sec40">More autograd </h2>
 
 <p>
 
@@ -1416,7 +1433,7 @@ x <span style="color: #666666">=</span> <span style="color: #666666">2.7</span>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec40">And  with loops </h2>
+<h2 id="___sec41">And  with loops </h2>
 
 <p>
 
@@ -1462,7 +1479,7 @@ f6_grad_analytical <span style="color: #666666">=</span> <span style="color: #66
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec41">Using recursion </h2>
+<h2 id="___sec42">Using recursion </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -1500,7 +1517,7 @@ Note that if n is equal to zero or one, Autograd will give an error message. Thi
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec42">Unsupported functions </h2>
+<h2 id="___sec43">Unsupported functions </h2>
 Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.
 
 <p>
@@ -1526,7 +1543,7 @@ Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec43">The syntax a.dot(b) when finding the dot product </h2>
+<h2 id="___sec44">The syntax a.dot(b) when finding the dot product </h2>
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "default" -->
@@ -1568,7 +1585,7 @@ x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>a
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec44">Recommended to avoid </h2>
+<h2 id="___sec45">Recommended to avoid </h2>
 The documentation recommends to avoid inplace operations such as
 <p>
 
@@ -1581,7 +1598,7 @@ a <span style="color: #666666">/=</span>b
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec45">Stochastic Gradient Descent </h2>
+<h2 id="___sec46">Stochastic Gradient Descent </h2>
 
 <p>
 Stochastic gradient descent (SGD) and variants thereof address some of
@@ -1599,7 +1616,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec46">Computation of gradients </h2>
+<h2 id="___sec47">Computation of gradients </h2>
 
 <p>
 This in turn means that the gradient can be
@@ -1619,7 +1636,7 @@ minibatches. We denote these minibatches by \( B_k \) where
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec47">SGD example </h2>
+<h2 id="___sec48">SGD example </h2>
 As an example, suppose we have \( 10 \) data points \( (\mathbf{x}_1,\cdots, \mathbf{x}_{10}) \) 
 and we choose to have \( M=5 \) minibathces,
 then each minibatch contains two data points. In particular we have
@@ -1643,7 +1660,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec48">The gradient step </h2>
+<h2 id="___sec49">The gradient step </h2>
 
 <p>
 Thus a gradient descent step now looks like 
@@ -1662,7 +1679,7 @@ the number of minibatches, as exemplified in the code below.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec49">Simple example code </h2>
+<h2 id="___sec50">Simple example code </h2>
 
 <p>
 
@@ -1694,7 +1711,7 @@ all \( n \) datapoints.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec50">When do we stop? </h2>
+<h2 id="___sec51">When do we stop? </h2>
 
 <p>
 A natural question is when do we stop the search for a new minimum?
@@ -1711,7 +1728,7 @@ gave the lowest value.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec51">Slightly different approach </h2>
+<h2 id="___sec52">Slightly different approach </h2>
 
 <p>
 Another approach is to let the step length \( \gamma_j \) depend on the
@@ -1759,7 +1776,7 @@ j <span style="color: #666666">=</span> <span style="color: #666666">0</span>
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec52">Program for stochastic gradient </h2>
+<h2 id="___sec53">Program for stochastic gradient </h2>
 
 <p>
 
@@ -1838,12 +1855,12 @@ plt<span style="color: #666666">.</span>show()
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec53">Momentum based methods </h2>
+<h2 id="___sec54">Momentum based methods </h2>
 
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec54">Conjugate gradient method </h2>
+<h2 id="___sec55">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1873,7 +1890,7 @@ this inner product. Being conjugate is a symmetric relation: if \( \hat{s} \) is
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec55">Conjugate gradient method </h2>
+<h2 id="___sec56">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1891,7 +1908,7 @@ which is zero unless \( i=j \).
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec56">Conjugate gradient method </h2>
+<h2 id="___sec57">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1918,7 +1935,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec57">Conjugate gradient method </h2>
+<h2 id="___sec58">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1950,7 +1967,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec58">Conjugate gradient method and iterations </h2>
+<h2 id="___sec59">Conjugate gradient method and iterations </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -1986,7 +2003,7 @@ instead.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec59">Conjugate gradient method </h2>
+<h2 id="___sec60">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2016,7 +2033,7 @@ hence the name conjugate gradient method.
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec60">Conjugate gradient method </h2>
+<h2 id="___sec61">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2045,7 +2062,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec61">Conjugate gradient method </h2>
+<h2 id="___sec62">Conjugate gradient method </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2083,7 +2100,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec62">Simple implementation of the Conjugate gradient algorithm </h2>
+<h2 id="___sec63">Simple implementation of the Conjugate gradient algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2122,7 +2139,7 @@ $$
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
-<h2 id="___sec63">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
+<h2 id="___sec64">Broyden&#8211;Fletcher&#8211;Goldfarb&#8211;Shanno algorithm </h2>
 <div class="alert alert-block alert-block alert-text-normal">
 <b></b>
 <p>
@@ -2155,6 +2172,177 @@ over the scalar \( \alpha > 0 \).
 
 
 <p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec65">Using gradient descent methods, limitations </h2>
+
+<ul>
+<li> <b>Gradient descent (GD) finds local minima of our function</b>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</li>
+<li> <b>GD is sensitive to initial conditions</b>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</li>
+<li> <b>Gradients are computationally expensive to calculate for large datasets</b>. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, \( E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2 \); for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over <em>all</em> \( n \) data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called &quot;mini batches&quot;. This has the added benefit of introducing stochasticity into our algorithm.</li>
+<li> <b>GD is very sensitive to choices of learning rates</b>. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would <em>adaptively</em> choose the learning rates to match the landscape.</li>
+<li> <b>GD treats all directions in parameter space uniformly.</b> Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</li> 
+<li> GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</li>
+</ul>
+
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec66">Momentum based GD </h2>
+
+<p>
+The stochastic gradient descent (SGD) is almost always used with a <em>momentum</em> or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically 
+implemented as follows
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\label{_auto1}
+\end{align}
+$$
+
+where we have introduced a momentum parameter \( \gamma \), with \( 0\le\gamma\le 1 \), and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that \( \mathbf{v}_t \) is a running average of recently encountered gradients and \( (1-\gamma)^{-1} \) sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when \( \gamma=0 \), this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is
+$$
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+$$
+
+where we have defined \( \Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1} \).
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec67">More on momentum based approaches </h2>
+
+<p>
+Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass \( m \) moving in a viscous medium with drag coefficient \( \mu \) and potential 
+\( E(\mathbf{w}) \). If we denote the particle's position by \( \mathbf{w} \), then its motion is described by 
+$$
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+$$
+
+We can discretize this equation in the usual way to get
+$$
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+$$
+
+Rearranging this equation, we can rewrite this as
+$$
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+$$
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec68">Momentum parameter </h2>
+Notice that this equation is identical to previous one if we identify the position of the particle, \( \mathbf{w} \), with the parameters \( \boldsymbol{\theta} \). This allows
+us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:
+$$
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+$$
+
+Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as \( (1-\gamma)^{-1} \approx  m/(\mu \Delta t) \).
+
+<p>
+Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models.
+
+<p>
+These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG).
+
+<p>
+In the NAG algorithm, rather than calculating the gradient at the current parameters, \( \nabla_\theta E(\boldsymbol{\theta}_t) \), one calculates the gradient at the expected value of the parameters given our current momentum,   \( \nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \). This yields the NAG update rule
+$$
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\label{_auto2}
+\end{align}
+$$
+
+One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of \( \gamma \).
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec69">Second moment of the gradient </h2>
+
+<p>
+In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates \( \eta_t \)
+as a function of time.  As discussed in the context of Newton's
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.
+
+<p>
+Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec70">RMS prop </h2>
+
+<p>
+In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2] \). The update rule for RMS prop is given by
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto3}\\
+\mathbf{s}_t &=\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber \\
+\boldsymbol{\theta}_{t+1}&=&\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\end{align}
+$$
+
+where \( \beta \) controls the averaging time of the second moment and is typically taken to be about \( \beta=0.9 \), \( \eta_t \) is a learning rate typically chosen to be \( 10^{-3} \), and \( \epsilon\sim 10^{-8}  \) is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec71">ADAM optimizer </h2>
+
+<p>
+A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. \( \mathbf{m}_t=\mathbb{E}[\mathbf{g}_t] \) and \( \mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t] \), respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)
+$$
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto4}\\
+\mathbf{m}_t &= \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber \\
+\mathbf{s}_t &=\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber \\
+\hat{\mathbf{m}}_t&={\mathbf{m}_t \over 1-\beta_1^t} \nonumber \\
+\hat{\mathbf{s}}_t &={\mathbf{s}_t \over1-\beta_2^t} \nonumber \\
+\boldsymbol{\theta}_{t+1}&=\boldsymbol{\theta}_t - \eta_t { \hat{\mathbf{m}}_t \over \sqrt{\hat{\mathbf{s}}_t} +\epsilon}, \nonumber \\
+\label{_auto5}
+\end{align}
+$$
+
+where \( \beta_1 \) and \( \beta_2 \) set the memory lifetime of the first and second moment and are typically taken to be \( 0.9 \) and \( 0.99 \) respectively, and \( \eta \) and \( \epsilon \) are identical to RMSprop.
+
+<p>
+Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance \( \boldsymbol{\sigma}_t^2 = \hat{\mathbf{s}}_t - (\hat{\mathbf{m}}_t)^2 \). Consider a single parameter \( \theta_t \). The update rule for this parameter is given by
+$$
+\Delta \theta_{t+1}= -\eta_t { \hat{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+$$
+
+<p>
+<!-- !split --><br><br><br><br><br><br><br><br><br><br>
+
+<h2 id="___sec72">Practical tips </h2>
+
+<ul>
+<li> <b>Randomize the data when making mini-batches</b>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</li>
+<li> <b>Transform your inputs</b>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</li>
+<li> <b>Monitor the out-of-sample performance.</b> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</li>
+<li> <b>Adaptive optimization methods don't always have good generalization.</b> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</li>
+</ul>
+
+Geron's text, see chapter 11, has several interesting discussions.
 
 <!-- ------------------- end of main content --------------- -->
 
diff --git a/doc/pub/Splines/ipynb/Splines.ipynb b/doc/pub/Splines/ipynb/Splines.ipynb
index 48e3c51fa..a4aeb3112 100644
--- a/doc/pub/Splines/ipynb/Splines.ipynb
+++ b/doc/pub/Splines/ipynb/Splines.ipynb
@@ -10,7 +10,7 @@
     "<!-- Author: -->  \n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
     "\n",
-    "Date: **Oct 6, 2018**\n",
+    "Date: **Oct 12, 2018**\n",
     "\n",
     "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
@@ -766,6 +766,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Code examples for steepest descent\n",
+    "\n",
     "## Simple codes for  steepest descent and conjugate gradient using a $2\\times 2$ matrix, in c++, Python code to come"
    ]
   },
@@ -2595,7 +2597,365 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "over the scalar $\\alpha > 0$."
+    "over the scalar $\\alpha > 0$.\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "## Using gradient descent methods, limitations\n",
+    "\n",
+    "* **Gradient descent (GD) finds local minima of our function**. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.\n",
+    "\n",
+    "* **GD is sensitive to initial conditions**. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.\n",
+    "\n",
+    "* **Gradients are computationally expensive to calculate for large datasets**. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, $E \\propto \\sum_{i=1}^n (y_i - \\mathbf{w}^T\\cdot\\mathbf{x}_i)^2$; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over *all* $n$ data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called \"mini batches\". This has the added benefit of introducing stochasticity into our algorithm.\n",
+    "\n",
+    "* **GD is very sensitive to choices of learning rates**. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would *adaptively* choose the learning rates to match the landscape.\n",
+    "\n",
+    "* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n",
+    "\n",
+    "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.\n",
+    "\n",
+    "## Momentum based GD\n",
+    "\n",
+    "The stochastic gradient descent (SGD) is almost always used with a *momentum* or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically \n",
+    "implemented as follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
+    "\\label{_auto1} \\tag{2}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "where we have introduced a momentum parameter $\\gamma$, with $0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a running average of recently encountered gradients and $(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when $\\gamma=0$, this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$.\n",
+    "\n",
+    "## More on momentum based approaches\n",
+    "\n",
+    "Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass $m$ moving in a viscous medium with drag coefficient $\\mu$ and potential \n",
+    "$E(\\mathbf{w})$. If we denote the particle's position by $\\mathbf{w}$, then its motion is described by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can discretize this equation in the usual way to get"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Rearranging this equation, we can rewrite this as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Momentum parameter\n",
+    "Notice that this equation is identical to previous one if we identify the position of the particle, $\\mathbf{w}$, with the parameters $\\boldsymbol{\\theta}$. This allows\n",
+    "us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as $(1-\\gamma)^{-1} \\approx  m/(\\mu \\Delta t)$.\n",
+    "\n",
+    "Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models. \n",
+    "\n",
+    "These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG). \n",
+    "\n",
+    "In the NAG algorithm, rather than calculating the gradient at the current parameters, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t)$, one calculates the gradient at the expected value of the parameters given our current momentum,   $\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1})$. This yields the NAG update rule"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto2\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t}.\n",
+    "\\label{_auto2} \\tag{3}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$.\n",
+    "\n",
+    "\n",
+    "## Second moment of the gradient\n",
+    "\n",
+    "\n",
+    "In stochastic gradient descent, with and without momentum, we still\n",
+    "have to specify a schedule for tuning the learning rates $\\eta_t$\n",
+    "as a function of time.  As discussed in the context of Newton's\n",
+    "method, this presents a number of dilemmas. The learning rate is\n",
+    "limited by the steepest direction which can change depending on the\n",
+    "current position in the landscape. To circumvent this problem, ideally\n",
+    "our algorithm would keep track of curvature and take large steps in\n",
+    "shallow, flat directions and small steps in steep, narrow directions.\n",
+    "Second-order methods accomplish this by calculating or approximating\n",
+    "the Hessian and normalizing the learning rate by the\n",
+    "curvature. However, this is very computationally expensive for\n",
+    "extremely large models. Ideally, we would like to be able to\n",
+    "adaptively change the step size to match the landscape without paying\n",
+    "the steep computational price of calculating or approximating\n",
+    "Hessians.\n",
+    "\n",
+    "Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.\n",
+    "\n",
+    "## RMS prop\n",
+    "\n",
+    "In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by $\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}_t^2]$. The update rule for RMS prop is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto3\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto3} \\tag{4}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "where $\\beta$ controls the averaging time of the second moment and is typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate typically chosen to be $10^{-3}$, and $\\epsilon\\sim 10^{-8} $ is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.\n",
+    "\n",
+    "\n",
+    "## ADAM optimizer\n",
+    "\n",
+    "A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. $\\mathbf{m}_t=\\mathbb{E}[\\mathbf{g}_t]$ and $\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}^2_t]$, respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto4\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto4} \\tag{5}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\hat{\\mathbf{m}}_t \\over \\sqrt{\\hat{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto5\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\label{_auto5} \\tag{6}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and second moment and are typically taken to be $0.9$ and $0.99$ respectively, and $\\eta$ and $\\epsilon$ are identical to RMSprop.\n",
+    "\n",
+    "Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance $\\boldsymbol{\\sigma}_t^2 = \\hat{\\mathbf{s}}_t - (\\hat{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The update rule for this parameter is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\Delta \\theta_{t+1}= -\\eta_t { \\hat{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Practical tips\n",
+    "\n",
+    "* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
+    "\n",
+    "* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
+    "\n",
+    "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
+    "\n",
+    "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
+    "\n",
+    "Geron's text, see chapter 11, has several interesting discussions."
    ]
   }
  ],
diff --git a/doc/pub/Splines/ipynb/ipynb-Splines-src.tar.gz b/doc/pub/Splines/ipynb/ipynb-Splines-src.tar.gz
index 7b7bb3026191d00a5cfb5e773ca79c930459c5d9..dc764628049f484c14704f9c8914017088b42e34 100644
GIT binary patch
literal 209
zcmb2|=3scnb0C_5`R#efyh8>8t%=v>B>4$gs_b~}wc!O5r=xy?$YqHYvN_5VZ<{l&
zjNNJ-68d-l*~=&VuboNzxhF!myXNfV_CT+fyQUe=|MF*AR@wagQ$gO5p;d1}w~Cqa
z6q^cu-7$4vOpsY&#8TUc`D^}fGr#ifxBS1I^OffRbl<a0@8s!S=W{<ia^ALEpl{P#
zzjL=kcC7nuo!R93c(zORz8x7yf5iD*-tnf%e0iq$;b@chD`))sX3BsJKGfGR$m>Y|
JV9;P-004Z)V?h7_

literal 209
zcmb2|=3v++yfd1C`R#e%E+#{Pw#4i67WrLR^0)JKW1(R;W1zmkOAFchNoJi1_v@ls
z3zu38&isC}MspQM=;xQmpMT$SV)>nFsijlodY{Y@w%xZxD&}?frYk{w?a8(;;-b1=
zajmUdG;jN*vxcd{yF*{~em(hXck$gDRevAMf35jxdVW&mZk71WX4emP^WR+ObmP>b
zo0j>(4`*Flzl6(dZne<chc6b1K8`jFeY%PJ-kV>(JoXpg1YfNGYRZ5NKGgqV%D-{{
J1A_(w0|5D+XD$E$

diff --git a/doc/pub/Splines/pdf/Splines-minted.pdf b/doc/pub/Splines/pdf/Splines-minted.pdf
index 4e31571bda3fd14878e2be526be06132d370c4bd..3c43ab626195f0c6ec83c0531aab36c46a411784 100644
GIT binary patch
delta 176350
zcmZs?Q;;r97p&Q~ZQHhO?Y3>(Z`-zQ+qP}n+O6I0`OZHRb9L@kL?P<#S(z)Vd>XrQ
z4mW`um^oSaoGMX)9~|mnXZ}4gK_3_|@g55>_tQ1IZq``(<l~W(kV9_8#qcuT%lIK5
z{6eDd(Q?76Ok5trl182YZ_H3?&a=3vVj%~OieR<XNA##Z`ui0zX#Q^3c*_)u>IBp>
z)TF9aPDz}(#-c)p-4@+IhfDv*6V-5l-jm%W&Xh(v419@^N!ql5=p_dRUY)&Cu|XAZ
z1x-Ip3Y&>y!803zyr{xF-E7!?#NqIX12O?Or9)GDbhah<+gd2S;k?@Wz$$1z&6`EL
zRd=&Hei?_Tw>ra;0YzbpLVw83lPUAq{cuj%BWj7=fA`V0$?+nhJzs>^SNX<!F6?z$
z4%pabNK+_MYu3A0=l3f4d^|H!V|N9_?7uSf4~gJ%+U;@P4i9C$g&Mr|=_2RKdnG#z
z7y9jCHsg@GpZVUq7@%EFV3O-jN?~aVvsXS=y*H5fQK7?1=TPCxGT1s2iPacpGCSWB
zMT!1O4~-xp9R~~nkCi#~18+-Yd!iRrlJjHNnluIdifxrshNvaA$OcQhE`I<#JfpY_
zBHoxMxUmA;uaWk>+=78<KILz{@}y?4mw?6*gM=(o#iww_s7b7E{Pb4kC68PxIH=wR
z5goSAs%WfnHad1bCV3D!oHro}tB5~4=J&XndS9*J{_MhFo2i8eBmU*>KOw*i*ZUFn
z=`u!kMs#(MbdE?wvN9%3r5OX%KB|1Nk#-pBBKWk35nWsoSXduh4nMQAWXT=7Dd!g1
z{Yf*0Jl_d{zk<584SQwWdHCbn6jBQH70fS^PeI;kitXwsC6lujcLLok%~75EDIXzC
zh*^gvtRrl--hE4>ij3X_oj3Q-id~n#K01$X%bjvW4I@))+vJGgSjP+yv^gW!?gi;<
z>U7$RyMxqxqBC-jx)Y63EB9UKVE!D}G1b%yfKGE{-gTWD!x0xuUFH`Yghsc<eDvkH
z)<ms}H0JT4SOp8^OAPlh=eH4o<tgj&l9I)9s-M)a&Xiuh-1AQkFUi)Ra&v6_JkaTW
zxWWDX>d+as<qRdX`_cvob{G(uMn};gu~<HIBTc``(ShDE6(X=XDV$D$=wF^!>I(Z3
zWmr_}niZtZReZ&C1ukcloiOid_;%GkI&aI9pb`6kueytOKN~uvv?4)3EC>TPLwi>8
zp4c0?-c;#&ERE9rxpY16{K^S3Q(c`TXw$r6i)F;G&x)_T8e;%pS^=k0-CBp?>LtqZ
zy`evwbt7<zfmJf!pH{f1WDF5c=uy&L1WCwk`iS_;0P`oNQ)~zAC-a@ADTz7_<j88W
zt~p9eD?cI0@sJrT{TVxUSOX`Sl(rW!jM>Y^H?3XsA3Lsp;O?(_poY_(IoxDl-Mxso
zF5@pHFlCYPH#r0372p>yYLzV8akujMbvh?$UREU>eil&1@fp}1cpUc*Bye(>g2k4H
zYbS?Il3f6{J6b?pkA*GQQ-Qesr;PCU9HQ(FA8_DBgeN0<G;sFt3HIC$EA%kSy2}t8
z-su-m=|5E0A~JZ}|DCScRY$j#$fQ6@*7*sF_uaw+CIkTuc}JpqwqafB`*$BomVw1R
z(0}iCrk0IdkkY!%=e7dy`x)<KfUF70E`YN2aJ#0?%5Dr{1V8#Zgh4lNdB@O!TfG{*
zE?Q6)hZifjU;CYC+5+LwS{b@m?YS}pLe3-j)a55=d7DDPOLht^^ge|rY%?tu@;z@Y
zbhA%6IE(<$p<;V(p*B+!Lts+#qM(uPx#e51&rHh^))nhOMa4Yf7)^YjGt@x~2MP)d
z1M-V=n33OOXtyz$cgGf%g(27ni<5b0c=!RDR)|<=7Epx<ktYF2<g{YfI#(a=^w64|
z^w=^NlEpBlrFF$IYP{V`9alKN7$_HmAMy%oy|{qc0X4(D@CNFWcshh~xP@mjhFx4;
zTGfXeQ}gKz_q_XAej?-hQ*VP}syTf)W?rBIVAcC%j=l9zT77Y#=9Q>Z4YN=o`ZKOD
z`Q?zVtra~gZVGz~IhjapcwK@)`W38equJ&i9}ya0iuFayMU551%|V+KELuFJjrUlc
zHzz<CHT3(E(O@}tS&YrhSw_}WnPKZ<kw&vjlcfZitZ4_&`}~Zwm^4YMKphXrB??#|
zR;8{dyYHz=ZwSyp!Nn_x;D8mu7a?=pNgeY^exh7im(rlnVOPvNOBzs4492%v7(s8P
zMKUTY<s!Zz2ZhI2)LDlOzxHCxicGukZwH{~?S7OX-4TIMu8=kQU}dqY@9kZKp!RQK
z0Ek}vUU#XRDe^&DPG6LN$D2n-b#4NjMI@Z&oM~`|EH(M_8Ns<+_{L0#e;32cAGvY>
z=kjHFh5|qusOk^!+s1;Nl*;75p?d6bN}V9LH*P|rYbD9=LS)=;=7nz&Z`Nz6`4k|g
zX5<~2a}RS(&}NHpWyM1E#~Ol}zI08F=Jtp1h-RmB9~1?{B{G<m`j-(pZn(9F9>Jc0
zzlF|$<N1d0Zzg_M&1ciLTzzGfqF**5fK0bt{uXm7_cc1;sjNaNHmjo20BbTuzQ1Kc
z@kCCGhq`NJb`EGSrc%}4Dl;GHs|GOBJh{)txUUUd)|3Kk!FV-`8gkDvnXx!%P77cV
zv1>u$5eAh7INZ^OGZ`JeNwsvbZ1YlHxwVx5Tz2Gx{J*x5@00uSckPnJinY)iU<U1j
z5kkEqT0cR{UVQd?{?4z%jsl-=KUzzAFiqcQ-Da0bSoG8A>BN&eTJO&l`(Pw+1fS`m
z-n~~%p(o~EKpdO`Zo<j9(t#;JP@4&%ArwGZIsZ@N0NB-*bvWig>O0qfx)isflPDob
z%W4tY@+$xbp+hN7cSVd5+qSlwOuf+K9R2zCNUoD|x{(y>*^ViRlRWH@mxDddK@n!x
zBiOvUpD$^lagW4C1Xg%XY{JG-a2!xbh}FjlHt{z`*_JP>-xM<qbT*?wP;{P*md{{D
zig<ra3&23Q!OKQX4BME2rkZ4;B1YD0Nap?5=^2-ILxjT-gvv{hEN4CR^rH{kZZ0qf
zza0AYt8hW9`^Rw>Co?Kwx#J||r!&W}3QN%$kCGi}0k{xX3Tc`|ni7TKY~P?ac%rUq
z^aVJGV4EV1v~z5c4HIY{VHzE<!C`GmMradb4WKaGatb?5;x6-Q!jW>6rumgfPmg*$
zB;=Wusj{cYN<HB|JkQxQyujfw6xkkVi_PH<ROkfEe*t$PB$Ge;r3W`=5DpZYXvRU}
zoyf}VlUuRrj78a8ssb^0W}uveAJi#hc^of34lndXW~eUbTW|jhJ~l^P@D55e1)qh^
z19(WX+(1vhX%c-`n#L`gIyn=a=Szt->v{v&hQ)!)&e_e|^z7+{t<X+q?MJiSswXQP
zrjvo66D-O+6{5i7T%q3sE1V4n+zZ`0FxmRl6FUr$brLH))mnYsMp;V7jlU3{RtB76
z)2+mk<$C!OrIRooy<{G{xW5|E5|}Zl0BlqC@KsOADIAyaenNTx@>72uaV8*O7|zQ$
zXcaT+q)H3g)>g<EyaT%?D||=%m_D5IWXpx`6Cff9rJf?{Ih!u$_q|8ah83!Rya(^(
z)Au$}DC*`Jg8crbG{L{_686H`Miy#9?AouD3hgF2Gpm0;OI0TTwzUMU$gB7g05I%i
z5t1sNn|qS#2~SO@eq*lAI*4kLy1uH5MfHu;_Uopo3aSf*6PnH^^;&$@bq^RH{Yp6D
zivszPCr|>YRK!h{$m9}e`3Jc^xwH~0eYW&CJ(%?&<FZ|((g&_&T4Nu&1^^vB$5!m!
z`szmOP2FaeLZolP`VsM~T8(`?faCsPWX|b8V&a4?*DhKUYRlb+eZWBr9^Ok?9k%`k
z{^7R>;*Gv~(4mj~#pmFXwgV!r`<)Z>U%N}NCO${jVDzi1m*7-dODz^B=gZl=k!-<7
z!mL4R)25dI4I@=81`Q))O<m)>HS*kQu;qw<!u+{js%CI)1zD_xe4IZlK;WdN=+wVS
zZT_XaTaRc3y5{1h)Y$u=m|10k)0luFqzj*KGOD#vl|NPIV3cHDeNq?hjH__Md|JM}
zYRpkB@gy5X4!vuXwsUGsrrZgG7L4JUZP?EW2TPj?47i$<o()X6Kq5=z-1jS;)l^!>
zdRSZAUoTE=@pVK!MvdDDpm4#4YGcg4vcfCq=IbU_fkR)J_$?Y}E@_VgW|=AeVzpX#
zR~bkFTIeIF+ZeoGiv5$C^o3B5)^zd_G1jxRlvl=Rz-e_L&q8T67^D#$t>DsGrp`aL
z6x5cdLG9_(=9|^am-R#(aOlk@*^E8uq#gI9f4F2(r$~2km!U@maD|*@7+Xz0|42E?
zV9s}L1Z}w_N{c)2-e4bS9z{bmCXfASqlt}*)cDhGLa4%6>kSiECd+vr`p+)AsZD^`
zmfWD0?sQi;c`9icQ9JIN_~40c^LX!rE<Ie+rqKaswsOeOPjFK8!V<^-2L_MQfzI0-
z7{j8dX$tba&RLBNkgPvv9lX&~MQarM?4^Od@#n{Kder)hyr6Uqf$ih3m0S#|LjJh7
z6yD_9Xbti8n9LH@&s-?vCBwei+QJ4;O>_p#_$!IXI3&US(TWrm<y-x?U{)<4l?LGZ
zH}m=CvrZ$_%d4}P?MU0Ly}QU{MyrdXaGK9f`Md^=3==q<hq?0cL&bvC^bYBxN6=W;
zGYK)wmh=~1@0(Jt;?|Rw=M&KhdTkBH%-+<+)!EF*?*CK{#?~;*Ov!)!QJcSX6Tp)n
z6wsOrjOSsJ3+vIEgY9l$Kv<cYojd~|fVq<YDxfxl1J<GcTSINWj}U-BV1r?lGqbmF
zwIpKZWM%me0@O%a+xEDeNPheE2PUv=x(M9KuJI%Q?v*Zgm<>$^w+Z|?ZdSazCKehh
zNgCRwk_jpp1!a{ruuz0)EpfAEH4d74xGWmY>IIlV4J<5q^||Vc+$P~sywvE7a4GH?
z=`rfDk`ZC%vvONB9lq&CXW;b=wC17tN{|rWfqQ6)39cAKJoMp$1Zl6B=`mVF-!Ye-
z@YD>z&ag_drWckB2X($vY}+H#zKW7?8gMXw&A$vjL*0?B2Bqw#KY@)jSg1^j3Yu7H
zhIAjObsf-}M96APv&aNEjlSV?5k3$CQz|5P{AmdLVq9#-O%Yxwd{N|GV8_5t)R3XX
z49%5A9aP+*f@LS@KO4qMLDf0zG?Pn4x+s`{%o3F`^rr||ZXfXUhVbO%QT9$4*+Z<{
zA;p{qDZVJyu|c%}6TC4CR~SltJV^)z)cHVt#yrx5JN&_Yth3FLsDU~Q#+kuDy5hl_
ze?z58hsn=|eHQ}=g_K&CgM8F5_XX6&*;1Z=i=dz;u<D>_;Uu^yq9q_IAM_GJlg$zU
zB1^}M4@_{$5QyExSZrd%A_enH!O*B&6cNm(gfv0ai&!(qcsMcTCUy&z&tl-R%&cD+
z*lkF#fkj?aL_@e2gAY`OP^=UUA{iv++10)LYJ?RZqtCOdtMjWyLeD+wFF%t<QvCig
z`PCn@<;@bS^%D2lRsI~gbXk+ebx8++st-5T{Ji<GSv=y_o3}=80c`$U{R&Z1C#fQ2
zA626_xZ{E~@*C^3?DOxh>3XL1D=bqj{ovNg_sh#gjuIUb(TFT(n!qN~+W`sSm9rYX
z3!H+6$K}hL16wxxly1By>lRJ6=E$b>_I*7%eLOmeXo<z9;;Mg#bmRzo>3m`Ujl9+*
zT6H_9>DsNK9kp%QJ<V3~K)u#N{wP{L&)I5@qdnc$+>?lEcM%_U!Jr}ixp?x`dh_MK
z!p%zIn&VG?YW-FW7*|`&y(!!9b9Pt~U9qDz9)%h$l1m|Ie}YbtTtk4#HLs;v%Rfo_
zMD?Q^5EAK;TOw^?#a}bk`jbZhy+cIY`;mt2!VS1m4YZUSw?dADX|b!&pBB(-5XH?;
zh$4={uI>}pvtXc+ru_<J-9}<8n5dhfbxn0})Wcg)&TA~s_>)$sB&DJT&#lFkqFZSz
zJ*fjW#BgM@-EK>K@T9Zb#!Fob+r{;W)05Vf?lKKjUoB`Z<eJmU%`S)l<VrgcUJ|Rs
zJ>=oG2?_2Dj@P$9V<>k$xWOBeu#ZVomQlWNXE7w+Av5mA*A?=rs(b~D@mX8$Lhh>m
zdV{rjM^FHMB)Ey@9K|&d=7HB1mg+gP)mSAEB&DgrAbw82p5fd_c=BZU$K>ALBlJu1
z-y>6=O2n&t{r;5SdVd1|-CSSo^}8{fS9tl=*;|i4@3*UN{BNHpZ?1nu|2w=}k2v=?
zI~~6Hjmnd<jAL<ZP8;1dnHwi|?pvN+YF5%zv^GtAzd(&5wk%zcGtsRNO`$-ID0xcf
z3|RDa`iAQE;U-NbuiBsPDQgX-+8#gDHc(M^`;%MEw06|mP-`}TN0hS2TnrZtS1=!}
z@`l(J5BH@{tjV2ySH9>Qp`icDaVNpAS6|AHARsqhfGvJb!eZ7|KR;H1qI}l($C5Ai
z%jt(eOu$<Z7eC+7?BnK5kCVjsJr2!dBhkBY&l;f(&L*jhq{PEHW<p$ZPQQCZTobcb
zKUly~cq=m6-EJAMH|K3)XV^ogAD?dO5t)t~PN7j##qjK|_G080vE@uN)Fdgw)&>_{
z%^1vMY}?xjWz)P2d_KrnSsj#oBj3rcB<m$A>s65E+?n=>pnWy!okAQo)qtjCu}M<%
zR595xqkoQ)<_^f_FirS__(|r_7u(rq;#KeO7rtVA6E+5bunv~f#SHJ+$1g$fiq@rx
zXTQ1qxBxFM8VSRn9!QBvYhU>{deW;RhWl5RjVT~<iqsR{=X3hRpUIdjO@XdH@6X`~
zl%ZV?BdE^&)~ByQy<A(`Hu$Nij_B<lx9*yYl*9FUqcH19`<25-VY7@hTd&@(uy47J
ze}VkP0*Z|QxR@Y)N}1nmjf~rN3%f|&{^&jbN9$>0{#jR#$m|kURlGUdC{pyu;GBIW
z$vt8GPK&2m49I4YhE|0qfb5$##(hU$_9ri!ZL&nP{yT+2oFHiyZ@OR0dub4ipxX07
z=kPep)pr$AZrh-M7zV?WL;15kq@}~<F8tJz(9SEaybD!vPiAjs7|RrIiNhU#YO{M;
zYTqyTlH*hI-#AoIW;X6-;j~u>VD@BW4YX#tTvP~Pmj6oBW|v|Y@c+^Ay`lo*e{^iE
zZ~A}f=+h+u1H%0uJO9Jt+K3;_|F)UWAAtSmqyGI5qdF^8Q2#rTzLN~|-_3s&1e&eR
zk03GGiI|A~4|n<a{(pS3vNAKL1Fr*91GKeVj>nMw|J5Jp3^cKg>0%Y=N~h}CINUTP
ztBQL?Jq3^x!yrRX02x_5T`#X66bRYjr5i+WdqeQ^`}yt~c5&M-&3?|Sc=`MN+r-?z
zYM@q4%(Qj!=wGB^XG*nymgv?6x8uk}oYL&?<hA?B<P%iYYyDo|{b%57^Z4G?0iZ$?
z%Av>fqlb->FN-pC(M3x6XXH|yO1pDrkEj|i=a!mF@@MSgbk426*KLl{EO?%dIzO+=
z-RAM6R3P=dEA`N2+Vng;3KvlK(H9pT&{S<;Ux3Po*RXd8fyjqxz{F?gATRZL+POuV
zKe6d)ZlgBwD1X)iQpjX-UIhx_4;ZYiIv&5RZRMe!|EigKgSmM*e^lCq5^uJk*6bzG
zP3AteYxGoZcgF5)stiRZTk|1qkZp|ff#^6LqI><Kexa_XX=3MaE*81Ml+{<S<N8yn
z(|c6igQjk_r~g>Aj!s(FWL5QOJc*!>JC)3^v&F{kdfHc)MZa^HDY^9t4v18^3pZ~M
z6|jQWTV~Wjta8H}lT}np#7u8TP_z*vJPg}!fH!3F7<C@aI_Q}aGR|*`1!oobQ&2Wt
zi(XNum|XwBM$Ek?KU&*I(=81ws>1n&CLNHruGdP+tt%Kq9rNhb=6k$+Wu#&UST(YR
zaR$NHvYq9Wk%Q?LMQk530niHqWNK|*F~hB@FuVTp38T&>W5n4+ozzA<9~k=<0*1v0
z{ZUi@*t3k!ueV@tG{eL^sFzQfWl;+rpeLR?PC{p_N&8iOc5&A@-O+JL?g&*6eO{;C
z8}T$bkIvLi1xK^xH`oAn>w=efwr3&)3=XrkQ3bc^9ze5dNhg<S0K6Pe`KIHQAR?17
zmd<praSzYMA$_{tw0dCZa8<5KoeUXCK?pvdarJU&3l!gVd}%iJJkzRq=F!W+L02b=
zHu_CKYPhLXdWWzG8SzD`P2ipoDo~<1n2uk%4nzr+I~H>9h)WeZu!W2tQm#>aP4yqU
z#s{jogbN$4P4^C-fD0&XuQJW;V_8XCC+y(>!SFVaL2AY^((q{Zf??TPtobhiXN!zX
z+Y<!{5bEbo57$PqfuDl&IplW^XkCbZgC#(uj@ib*whIXOh=z0-cn7qK=-*&OWbiDn
z2OG8Pto7B&{p+)JQBp=DOadC%73q@WATkQDn#u>I_wDUG0I%`eM^DS{k1t2#u`2-r
zY)5eCz5Hu@eIb3a7ykKGl2H7H*(od`Y(zD}OVgiDfhed57P%BYnLV_NDdrPBX9uBp
zJl1%X(DX*tR`bfEYseE_*^E$V40^UI2>q8t%Hj-V^Eq+@jc$}4o_S?ekPkw@!8xn<
zZPd0IW$fz@K<*Ie;-8uq+Ia+t!Ng7w<)anw7NHScMA|G`k*G#4SkYz)E&?P1Edw_Q
z4(Rb|gYt_UQ!QWW?2ITQ*dPJ!$~DCY2!a8FaELNTQwa^YtUlC6U^p<=$kyVc54q=G
z2TsE3uFp15bN5v5X&{HqtO38uonOIM$gE4EC=?P30NUa+JBcn+Ra7~YIch-wG#VH}
zP}1%7BERnVKcqt9T}NEZpsB~jG`^0EeiUbDjDJ_c0ju+(p=;tMw%r_AiMjh?U{~ol
zH!O$@x~_%P^Prcgn!t7t(SIA>N^C@D-h?*rC66{6g4?<A<HLwDfl$@xB0SK`;n5co
z(nqIl0G_gQC8ifu<&FeO=7ti)$`^B{vwKTfI@gbub8&k^q8T*@$)01Bg0E1-1C-jH
ze<MPSa=<Xe+zRKbq9v)KP7pT45`*K^9<Q|55*>FgtOO(g!cZnoQ02rb5=0&-YIk$C
zLKcn4Dy}n&S7(XgQ;2fhP?MnIn-*mzzylRK0I6?64&@zS>@;_cA-+ihDQ0f6-GFCB
zryvi?vdh0*)nk?ehDFtP5YSiu79phnB&=T$avk$BNGjS<!g}0ZUTWS`l@<UiuykpM
z5W{lu4&DL`iu1tLTCQsh_oLuXTn{Gn2^Iyr;1pgT#f;Em0c?Im6wBk{r%s%Bhps#1
z0Oms;At6ZhM^|VS;$nu+s~rH%J7Ws``xr*2%y-JZ5RrVJXz(NW=dsYw1}Q23B`BK>
z@x@;zBraiIcdpdZizwhJ$Io#>`;0h#XtpsW@LMx?sFM!)oztwBExtb>u--5c5)BZ1
z%n8ZN#f%39LCqzrEVK0L?3PNKL}Vh7fS}{m8xyK};B1QZ<79{S&O@QVv3HfAwL-NC
zSZT5bXo}Dn`E`(9cm?4ln$WPT1*6pxJNrEu*gss%C5X|b`!%a<DnKoyZ{H$RJ4r*L
zI|x(Y!>Rxs;a?Fq8zQGBxiv9<*n?<if@+ON7SRViuD4=+;a%2Dtol^&mOicxK#FiJ
z?66NM@rzE)dxtYr`J-><&<ZVyiy?@A=1_?Zv@U{`c*ME4zL#E|95T`JWQ(n9`(s<d
zK%lTWkMiL4vv;3mlR-M;n#1%~*#QyJZ(mBQey12eElvm?AJ{-R(cM-L{5~){&GGOf
zyFrjqNmeXEa-)e4kt}4-ET{`Fpo2XW2r=gpKrj_2is)WlXG6K%1xL%l3X?qE*mkJ0
z@o}knN5v%MF!NhD%K(kjU3VMWbri7JswkJ?GslmoOWC5M#l(HGDd9~Mfer_%5~;i6
zPgU-#jxptbF<$4zi}=`*gw^uL9GE2WS;NO;wEx_2Y||MsgfzpTPfeK?z&98>+I4oT
zWGtk-P)xTL!5WHZdMO7@e&Y35X9jmDL5D~mrh#xB0uoRm8v&H}-RXU_1_=>}q(rO5
zV}_4hv?Xf<g2y3@cA`clu_9HNF<{2%X72ng{-}nU`&DRt<&I>!)jlpflx|d`pa>?*
z4p|i8QNAhd!(g+QD4$FXu-V~D?yYEh<zth|1<v}<N%RGyVD%L`u9{P+H`_>75Z4;1
z@#S0qwvU6$R&j)+5HFZwC5(s}Hd!6c*|VPDhdQ<z^R(HRvwo<|gnB0qYHf7>bN7!K
zGlkZcriK~{FBYpdE=+2}S@5PplQN-M5cZ@b$R^Ss?7?LQcYL%KV9O0vgZK2i&tKl$
zd1^C{98FS0Djv2c9u_V-LdoaB^}4XuEu)@9cL2?8N9l>{jc+-JZdxw-JOp()K$$%x
zOvYG70&}966BepWZ;&}l>o?+nDuC*The%`(r)*C<Utw6o>Y3CDk@YTIAPGrq2h!u!
zzhNAk(tb2DG}3ecki1KL-PaA)r2t}(iSFbtL^i?*cAt_q)g)sPQ4tt30jZ<ShWaYI
zf*9)Muy?FeJYmoclv<3JLKY?wdD+N~gXp!N-fv)gfBrFdg&94iez-ivctc@r&^Ml<
z{Pfm$V#(|CMxHe4qP>WuJu?^_K=KYJ?KXqx<iX}iK^@5eB$re`#Tk(AWs>c^g~s<U
z)r2w~vjmjF{>9v65grr32xE$lXeGvbZG2b|cwMR|yv%tsQ~qO)g|g`sQ-2IaO~I%5
zRp;mTt4u*~^t!A!z?7}7i_?0^5+xMyhj{I30H<Riu)&ZH<;)eiLXUR|iZJQEA<dmk
z%xT!tC=R{?u!}JMtu2?&3hX58<&Z9y^7#lYr(){~o)cRQ8k#+7>|R82_JguC0~TUP
z^O2{azmFxV<fLrCJNn>+44NiB@VklIeZ-lvF<?I3oU%!!dUQZwRN<R`U5d8;@Kkv-
zg{mG_%JNV3u7re>jU5A0c%y*w%FZxE4aWo&h^!a}K+Ex<ww%`pf+ov*D3aDSz?*zM
z=*%N^xvz^0EP5|Bn=j~i^g$Jh`<S1ps?gIhNw>C9z&;?IZOJe9oPPDb!vR22`GN~9
z<wWS<bn+XG?G${yiLcM#{m~(2cV79t05!n;El~*PKn#it70NTC3-(>X?<(A_!NRgK
z#|+T}bP<hmwoEL8>kP>(1n9HewlWnq7c3c``@_H;sP@f7-J2p$F!R{D?k;k;#waTo
zr;tL8#Zq4{ERX4iSC81Nj?^V<a+iZnL_3I?P$yNT)1SJqtjg5yft5{Z+a?_YtEXxb
zsA^buEUt$`L}%EKpXRZSa^!Hutqvwo_}onZiZsDTqLj@kf6XWQPcKih12eWx_A6w)
zGsY(~>wEbEn`JEi%9L5c2?azO;C&NQBWVug@51|+K5oCABeDAVVzOXBFzg<|vpVbV
zS|<HC=Wk+CPbnM&?~G!i*bM@gI77O`8;n%|Q;#DXURFq0Ry_8Cwcf7&Ly5sqIUCCW
zu)6l!@&};Sv`@EuAp#3VJ>(lo<(7rKofqB};TkOBIJQ#wQxEb%9@C|gv`TOI5g`>U
z#{IfJP3WoW`3CuzT(uRVlw+*Ni-ucrJ@v;CjfM+jyrBE<9t`@euIf(n!}bXeT7-_G
ze2{?2{jvhlz8=Iq1qm3r%o<}e^mTqh-1M^$sX6>_xP-~Z^nX!GEF8%~=hT2zZQ11Q
zG337c`UConB#f~hX6g5Xk+d6CU#S)~feis6Fn3I7;RT?I*stqletsb4gNMeXD&5Y6
z0Yd`*T>}pQzfhaEu32?EXXfwk_4llXLx$GoiglgFKg4RfR`tPV+fjA7(@GBO(p2eA
zrRq=f7Z;UuwZ_g~R1u2rt}OtD-tJMZOrC>RUdyMvG~)jL-k_iOd{`RJ`lxyDKHBic
zm#XsTKehe!(KPM-{U%ev82+oguA8pcwCoemI+gdfLVQU%8)Z@%=g;f!eIwN9TB+2>
z9QP*s>|KAVu&!N<>{&@X`lPFV-Ynbg^%nIgRC%1wt5`!;x81{1&0RnvU+M$EV5q0x
zbcSvWuTqoo^oVD+Fdg;gw!OHmjci5f3-X_SC`sG4bu<dXi)BKgy>Gtqp;|wKyUXpf
zxR$-p;LqB;>ay6kjbM~}UupNbw`Y-7x3NweJT=Gcn=_(ZS*JMx#Wv1q6~N;|-r=4u
zeUj6VGgBudY8zgkvjYH~Y*=3v@{&4{1M+~qrN0H|&gZK3r!cmmQ}P(jGS3QQhw=4!
zIuDKcxN`Q{^4Cu5xQi*}x&*RzW!p{M<3;G#j9pdlj{~xElF!6Zu-+m(dr)UFByP|y
zj$PnCrZRh_AwN;jowAOiSzbY5Vqmy;5h=4mWiNh(vV(?6{zE{@Hs58HajczUfi|`6
zqhIuQ4&o6~wkkdj>oTi}vrP}PQ&`XsfuzUae$tl6@#27g?DD{!76`5gP~%7~P@7NC
zb=|I@K<-jEODAaWHcBOvs0sJ9M@O6V)b|!HsfqNbkRFs%fnP|OX<7>uVvfUsxZp}Q
zJUmYav;Yw&^BzDx#sk$?#QsQPq&Q@WV)n!`a3K_|GofGqEj}9Ep!bjo9Tb=5&KN8m
zh^ILSxN?abJd#ictPcnoiEu~=iT0zaM0TSj+X9=znHvV?PoQs9C0nor<#{h`84CMR
z;l+b;K+xLrK_l(d);Jv6K1dgHSUmi~X}X-*{XmvOe<*-f!j1uC7|>|7wTDQ@fnW{(
z<NG}Sk4%v71sQbwEtbm5m@;Xbjgw<XCV1*U1Kq|5fk7z<*sn^iBt{2ktB6+yc%y1S
z5VlJg^HoD}R7k^bRlXDKKKgI|Pga#xcf9NEzy*YctMZy2dl0&PxntNcFJMur3&gbH
z1UZ}Rh#w%7oo=9=#&X<_U{q?!bmm!e8|9X|^zccIxg-d6veI9@9{#1q*)6~7nXN8>
ziP`rn+P$fib0OV&ki@#`42JG88Dk^O^?iVBr@_-Iak8Nt>;jadMH5KVp&xutZoYh(
z5==YG<9Ew@`o!L>$}AUVa;AzrsA`Qx_}L>xGzhTh70WVvZBR{n&va!%JvYA@F6v(D
z%(%Z&Gu04-DNE&wo`7Q(zN(mU@drjGoj#v-ORRiUHRa2ISvx`QJaKNjC*ftQJbf4T
zJY6L-BT~0tu?^-UNtH?MjX~Kd&;l=_#nAd2$BZxoPboG#X_KCIxb%TWpg$TjD@KE+
zr2~M#LJ-q2elsHhKZ7W75iqz1S{@+XSxqHqTo57<PrrXo*BntZw5vXgFf2|?JH&EE
zNl07~DvmavS41BZ6<!I!qHBs6`tx3S8UfR>aLNMrr8Nb`P}b=RO&>0V9Z924R_HaQ
zNigLK#ZrzE9q^2(KoH|CU)?o>0X${f01mh_93IpfSt*WT0p+vlO-Y<aT~vuWw#1gp
z306M0OgTSI1t|*BhMJk9h5EEMD#igBl1THh>`pw??v(S|DUtYaKKIk`tDsJurID6w
z2mpB8&NbJwP~o7X^vL(tL0)y(LC&iqf|o1ke$W#OBl!1OJtx5l8(eIC>W_z(QUJU!
zGoGb(;#s&8uuOUdbc<e8@g|X6G$9mJ*ZNIG0!(HiG1Fi@?xO=W+b9)5V{t15c3(tW
zMI{PUAD8Xwa$FZ;@B+f#vo@LA#@j$gI9ANIn&iJ`NPnBr2o}aRgG^)$H98;4aAbuA
zcuM{vK+|Jk?fHL_hJ~eQ@9mr^u>#s+DQOke3>Jg0+IySPSF`zuabf0dJe&4Z#W~|Z
zs?kJa>S7E>Mhxw!E}}JuP|h|3b7&0BqbnteVGU64+qb<xxhfSInTP{+Pdn?$Vd9}9
zeDwZav<SB%C_v>bi3UyJU08M7|I3?l3;E4N7yif3UN|qF>zgD21xi3GY6Z}x5=6}k
znfU`+XvAzuq98j}97nor71$zIsw4^02<5~Z;$p}nGJpln!6x~rOX4i)o)<FNDf=AA
z<j3wQ%M0gykpvLA(+ZZh*3hA!ep`Hiz&JLUm8E2b!{X<v>K}o+WT2vI6kQEm@5?dP
zoTlqSZ(dO0Bl*yMnk!YzHUvDHPWBZK36ldr6+x8|^AP=dDZ9079)>+x#^o&Gvy<Lm
z<(kZ3w&V!nxMM@C$eC!`Acp(KI&8*!yqbV!h}{BZAw>=TK=TmbWu5GQ?m>Dw5))zc
zb-KQ6KDiS-z^BBU_0s1+AKc;Rj#wE84Hk46-1``uTSLw4meuj7HUrisIsZN?P(ks{
z90QRUd>^V0#$;>VB~I34l|jJ37*a;;n;J5M05QC#pvX$ue53J@TF(*9(jcq59xyQn
z$%~7<jz3;iTMrx3)WC1nRD2%kbf@Kq7r|Dj)l~v9GJ1_HGO7kV8iQM&HRo0V-J+ux
ze3^DcxZv`c28uVbR0Ft8LZ|S@K{-wr?+}m2VZ<V^Yg6h#Ccme_ytUN_rcT<T%$Mju
zHGZ0?K0}g|kE@n_ue>EI%#GmlMs54});u?(434NM8aR=l?9PqH6%8_tDj}|gjWV4L
zS%2PE3x_I3)ZiZWb9fWz-4k>ILx)Wa8z~ViMoAuAKoefZy#c=!VSf`=&MDJP5^CFj
z9Nljg6D$|T^J(tCWnp~Z4lY}AFWA@=T(?reS>BB@@OMPk%dMMzHXMdt))ol&JyTS3
z--@>$PFFgRV_PQrf3J6;NmC`eDS3Wt*PkI^mT=Z|M$7!Zr2d%<7DO;~uTw05S}u=i
zsHI#8{fh7B(*jP(JwoUcN+WfQw*r({W&`F!gDaSxq}7nSMHVk#K}+7!YQRL)%;d)x
zB%^@cN66`Dho+>2N45EuVr+QA#|Mhm|I~VU$Ky@K#!MROJF@y2rQ^|f61y?QR5`LC
z_ZDE8*Tc+10gY&%9*!A9lPoZ=NJP<_s&8fn$pg_M9{@T7KNxC3Qd`%&JK?&)fXx4l
zsxi$Z8fSk!AaUDPwA~)<KED+?{Q0g#WZO#C7{emOoRH+-*+Z?2t_Zf4Aw0+<<qc#r
zFHhcBM+JXo480!ghqv7NyCW*+0MXEJfAz097!_FxB|~ui0Dr5ueCpx32u~08Qwlh7
z<84J(;t0T&GQp%-g2T<=ev~+?Qq!0H;*8t(e)n_Mo(=6ERSxk8X2FBraMIQJ{=ROj
zHYEBi2t4KKu9uAt3Qs%Jmc81Y4OsGk8_eq%`X|kV89@K^UKrD;M&(58>_UX;Mf4K{
zB*X$j6R&mpVFEbs7%0nV9p};QIW+8qDQH-LLj#mG6j!r>7EYEHC1*7nhRThxquS!I
zSt_e_A^{^pBf?_P@lP9rp`SoFz;_(Dhz0Y2uYZYo<4~~`ls6uryscr6amzoRa~+>l
zg1PND@hKRtJW=w!KGryYgn-hH*Wq04k0Y|>Noe3Vw*y++_0qh*^OCAFqQsJYa{#Br
zcmNMB41+)dcr-u`sQdFwZM*>mn8FVpJySwb(0huh1#N#NhL2mpBrysX*kk27HxCaz
zJ88sGO800m0{)`@-s&dEX~l()+hy!bG+PJR*bRBlTSyXn4GAcI_}>t%OD<;6s41W&
zi=)U@YE)-r#j~qJ5?S^K-7;`||9E@uWB@%8E}z*L9Z*9JRBhy&ITU*h1Y?LDbg%RA
zP@4c@+dGRb<4iZ)QT{1u^K#<6GYWx65~*&K;zJ-3BM1x)aGxu<KGPMGKLn!)lTeD*
z5qVT<L0OzIxHS*(qhVaqZ#=h*-jwp$lZ$HHc@su5`ozu4cYW1Gm+>bTueR=4F<`wp
zdD4vInuaf3w}j<iuJj3;DDXCCo?cUFCul6#*$?QF(leU5_7#umXhe!TV+D~nl#ib0
zO8StAzqn_LWQnhId#n%dT)~a1(BC<()`{hu>t@&O`B0x(TOp1#Id2R*1Ee_2wn-M`
z$-s1DNkd-fL&+J@aku@ooCxSE)Ia^z?>h-V&vBA3R1ZGb{E~X8&^Jn0E}lQ+OiZ(G
z=nxy^a1o3lfz1kWSP3q0IgxVfD$;JVket>Sjf#F$b<R-WJARy1lv&A;qyrhhpfP5`
z#QzgLSZrMXH_^k*{a?C*2A~sv-G=PHZ*bUdo!CmUCq^T#R3hb^1i~$z2>y|9B0PS!
zWo<g0c(d#Bam_o7ebx4OC!Gc1ha#Rhd^q!v4Vzl)UTynwMsa*@aPJ`StsRw$WMvei
zyDL}|qEb1#OT)>LI#qMmUj3gdkQFSrN0XSt7{1-wM8TbE=k;K*57_&0{cTt5$8c9G
z5od5AODqiqecY6RTS<}44XcMNcx~g>zy)-th04r*>LjML+YrU#qwrM43A`IHoOW8r
ztq}TD(>szxgGr^ZFI!qpRKCQkxf}-0E<VjbUU?2#`74|rikgN9<{lg-l~sqeW<&0r
z9`%{#b%`wWWrT<y0)Tv4`$-Sc-le!mR2(rrMpA~BX_x38RkJp$JPH!%6!U11%rtX1
z9VaBv?gm9+TUHlAv>6@AqUqR;#}?x=Qy5vv1F7MAldUdqwW~=wEzG(~YOW!`e@5;x
z55luc1g3eMdKGSn7DO8azaU=6tEg^tF-6Kljd5{rTxwGk08__lIIWD^CT=^6Iy!m$
ztx~=lFww@xO78frLchz3lqs~Ao)Z0pkD6}ThS6_LcGG$XIx}8#WKv0?>hAf86{Wb5
zU5=Hm?yVSM3JV;T;#dS#5~6xlcEHcW8S|Kyfl)QU@a5{u1w^yi^>+^botLu%6ROtD
zEOk;&TW5|>fMLZ=Ygj_%I~cTIv@im7&k7^4wknPN{jcCf(<XgISPFCFma`a_L?hOw
zpUEVwG0*{;CvY0CEHi7Y<VbKH1gy);oM07KYgq8)T;s|w>>7m=jC5q!X)0(42MXt~
z;!JZdfux)G%*nb2B2yY$fkUG{5$mD%s1y=(-GYWGz#<l;O(h#9+|pwwLuycS=H<S4
zI%sYDVyUNm`W52RsRir>`4SU7ff&6y#d>98+T7vykNVch5^<9?>^MsPUrU=*JYcPg
zRXum!{amXOTnQ$9t=IGg)-h7g+KjVGyM_IY6061C0?FZdsK`TTuwb{+%mmg8AV4k-
zZKT;4fCfl&s4B)QFm4%0^<hjXmHcO1j=EpCU5THhy6<NIbqivj5I8>5-0fMY*i`BF
zV{P(eX$a)D(CS+cPgD_NfUa`deceUSe9v@r>H-cf{S?0d<%_=V<8b*7s1HPa$sBA=
z`y6g<qpDieEzGTTHu-Ex<$Ms7lhE?0ljmUpfKUXs1JO2ZKdB9Q)`CW)#chT#&%B+7
z0;~ULI4)=6Jh{pC^1!09HCUd}_$`Alx%7Z2|1auhA}QO&CNmBaCODiTd440S1QHa5
z>HORh0c-@vj5Yrd7E@MfFcb{up<F$6lBwgHuNA<sw+YK=JE;I_`v()~uagk3a5OY4
z;F2|ZjiJ?%D;DTxp6lbyLI{aX;&e!B{2UFf;e6>mT=qMCyR}v8@jIK5@_2{I{{9*j
z6?z<2@vx4*9X&^%LfYVP#NJqPB-S_%Hxoe^C=~Cd&WiY1I3>xeiS`m}xU-OH<CDI3
z{Kszf171W;@*a;<IGWOMVpDCm^BlGx(AymnCja0#9FVm)MBrJE@AfX~`y}Z-3{Q~G
z1jbne3vHMmZ+xGS(bD%c4&M*X7Gi-JB$sZR@X>bzgpBQgG=nshBb)cCHv7~y4Grzq
zAOId6!M0mgWg{ak@(`6P%)n%1aQk{aTk6-tPC-4NzV?qgIO_=>VZ};)fJpJbAP*_G
zsd~YT2iXFA2I#-Hid1=UtVl=rFeQ906RUahQ??yIi8N46iX?L)<$#@{C{{JT;foWj
z)Z|J%3|~0bVB-L2I>f|1bxV6fPYA*zQ<+c=(`hCTC@WVNbRDWTswm4vhEN6HlV;mR
zFkWJe0&IDHuV5^7Q2(%eM2Yx20DD5I{}laS$m=20OtHNk5E#16f!;&EKt@iI^hBn6
zy5T<=XMgW9%#B3*?x!xRb|d*K@b*3jkVHGAMyLu5RG17u5ypM>9Ge1hVS8*{{vO+`
zV~&z6y#T^1+IYV-)_E>=ARi-m3vS;tf-DTh1{I;ZfWoovjEoQ|5hJlBfO9-R5jkAY
z9UY(J>YlGjq}VAqhg<oqqx`rTJ`n-sGGoFpGK=0Gt#w8#++vIYdJSfLuV3&fDaYgx
z!umIlr@h49GWLmM2fp$6n&Fl_bsh<O*DEa>YZ;jCz!Y_U6`7Q%*GN1AE2@xd9zB<9
z3^5f_4ncEe-1Px@6%EG{u!`mEnhefidd-Aet`akf8pJ^&FaxY@Ax^Ww6<BHF0?f57
zu_W{ks@&^JhZxK)@aoE5poC<j3$bj$W!<r?(?VNib+FOFItH{M56?`7u67g$tzg;x
zKA}NJt%1&g9##skYCYffi~(Y*IR2if`UT#`iEH2kcj>v2oyb@KAm9^s7~bIYWb>Y<
zy^&j-%1oKP+LlIx`I8tRzvuXX>oLGgOV^L+9v6Kln+H4Nz!32y+_eN>=z3qj(a0?l
zX2hT2Yqi}GJyD+-Jw+3-_*|p3xZ8_l1_QYO+jwkBv%W`^g=5SU<H-ak>$XT))ELAH
z9ZR%7d1K9XSAA*-XgSvp(mF%B_%9@Q)P9<TBIYB}{hpIo$b1eV!pwX4^@Ss;Qr4+F
z&xJBgy>F?XhhtIpbSG6<XdO`~*#a^j2yL?=zzQ-gaS%q#KVm=8!<^m4j&pNAL^^b7
zQl-&TJ0(s7jAyPMR2Ze;zKTRSXd@NWfIJ)T864-t^qv$5ptcgRa%#FFG&XeFm&pb?
zLPgMTWGpRI{O=LJbA8@n0had9DQ_y=#ph!(0RzT!@^ViUW`?K<(aBNc;O@k|i|;7i
z$t{R@RamD&gxRNhyDR~o2!!W6NQ{`ut`sVu%#)@#BPL$vCVa4EZ-tL9Y1``}V5$`=
zzGT>6lUBNb3n{zLDEcw0^ex8J4dP+uP~BQ$AgT}_t+D!SFes!~4xHzAXKO_4gQuOJ
zU$slGEKy???F*ADSK~ml2#NXzx-u{Kv$1KtV2t<1g(Ll7jBJc0{(4q9N3cIWtXl^T
z<M2xKd&S>0Uiz)bf3spY_NOHt({07dy+IB@k>o-E9T*Wq4U6ph1D4;orQEf47Fq_R
zA7XUri7Cpk<<3`>=H-v;jckpEstq|Zq%v+r{geEo^`Q9wmIAeEOoE3Shhk!NCCKSR
z(GJ7rnYw=X#dx?aK)hza3Y@4wSAMFkE_-)Wo<*F*I$?<yEsu~)hGkd9t%>P|2>f5&
zf|!N?WQd9W{ST$tjjBteDM{Pn;l#C|FOAcg6p??O6-PG+a>lY5`->U0bCOpVE-I?x
zsV%8c*bn2f{w#-9x6G6db)A=c6%|4smCKns@Ar*iVf#`@@wvt2uKqV6YY!vkLT8v5
zC$H^0LI+)9I$52LBVr@}Lq1NOyrxUi+~G3~AZPhtg7qw<Ov4_;8Jd+uo(|yI3$gA}
zwiDS^%=Y@hvlx909)r<STW51I2>T5GF{v=tWwpvIr8(bvQ%V`YH9d_o6neOjD)sk)
zc0;}({^pf)*fiFiIm*GsO@g&5y4R2TMEZ5+KRtExu%amc&6-n1=xX}2btqxIu{(SU
z=r|l9@I-tK%&tTrFkzxjX6&;0Wh_9qSzIUSo-Ms*G7B_8pW=Qi(ecz#nk_rXf_Fbq
z;X0}X@NkX`x;<lD8!>F|8GQ?n0C)~?)htW~F@0o6(5Va%-cI%C$inYiATXG%0bD7f
zz2ou@4-flLc8`5q!Ob^PiEk1S0ksnV#SZBrcpbVrG)-M>yRES#Qs<T2%4$ZvrR(KB
zlBc3|C3G10Dt1B-IV;>ty!MGj^k58xV%#+;mz?kalDzjr`A~<iOh2_ODTflt603S#
zc!hH}Nj`MGoVp*C+C5NWf4BRT*lV25l3Y9Ld?Bqnii4C|UkcwmM%xy6GvDR`h-MYZ
zG%B9(NDBx1L@#OH{s`xJSN;dMTh77O?_S!iMKV5fsqQ3ruoGO>U!C=~O`iuao16JO
zXL+zjjREkEXs>1_haXu%&W=T+&5!&bY6Odnif<UKY+mxSHY(|Yht?7!#+<A3Zh&Es
z>_gc=k!C^7@h01jTRimKdTJp+H(R{mNJ_SnR&5vmuiNr()^av~3uP<gjZg;M?|qJf
z>adRizC^yLR}O&lW6VPjJ*NLa2gnvL8$(R_+lS4J%5M&Ehz#?TbUw#-pWB(6BD6U|
zza?7HD3J^$kw?D&Ko7DtWb*c1ZH6zIO+h83ed3^97Bke9Biofy4&ni*x$e;9VMGC_
zJ*$ZJOsp;(*pv(}eRjTtJ1#QhM!HjrW`@zUQqA&M;>Vq~`}P@H0xkKzg~E50QBp2c
z7p;;?cm2JpUR;sJ1l^F&FSO9fo70si8GFX+d`M4vYd>(D%+ZOczMT?oB7nVV%82>C
z`Z*J%h<jrE|3d5OP!u3=AngAqONR=|!N&T(Z%4H_)6U0ScX{;-%5@4{N1`PyIxZKr
zcbU1BGOKs4_Pc(D|BZ55zci)uY(K6siHNk4%qaO=DU*qy13Zxfa>TBwBK>=%-~JII
zateNv=%qyO(BSg(iK~#oq$Np7sMs9ZVr;HJmo8rz;rhjG%Qto`^TcMiaUD#I$-n0s
z-2(Fb+xzqwQldHG%2+w-zU)`&_;Z5A1)g-<vcDTkCkKxk)1BM%a=@&`7-G{uZx1&<
z+IH@JTi-q&cpG?(HcCXyM(zt4(t*R{{wY3pKd(M&0)rG8ANk3{{y0|rgH0X%rEmXk
ziu=`KlfU$cB{C*SY$LT~IV_2yLt2X>e+Ec4(z!>J*6L$qMmYe(&hUMQq#k3`ze^cc
zSP?ryKG^|3LeW--sdEs_e{~vW{+*;_2$0K2<JGmX5pdVVpw+hI>@&NPMblB^$hI%F
z?YbtrRP~pExxL_sm-++;FANAWIC{p7mKf{ylMVi^yW&WkGVQ7Rt}>P0LAm%lu?_HB
zy`kLBHtyW7wd~n-cqcLebOq_;Yz8DI$~(Uq#q!xkh1nG(+e<8gOLgj~kE1j8OUBUt
z(iZfSZyQd87g>MP+kG7WEbsPTeFv83b%YHQD#731gNh1%7X@HbKeDM^XhbepVFdb%
zrJXJg!@!^ZpyIh2z68X~$>}L)MFOl<szYyFpL7-ga}fdapf2DIN$X$MYDLuxVFv|3
z-xx8KTnQw+*E7c-9ox)sad|U!uh+(wW!%*u5C$lAS7Ea;=;uL4hRE*CiSofRSu(_|
z>@YNEB^u)#CdcQa)atJ0CLgd1F>uSkY__B>%)y$i2~H0Bml?7f?KA^%!GQUJ6J{|Y
z6-oQ>s{>rD+7OjvShku+z9te6p5bqa5|;S85~fb#(DokL`EeZ+p>_&<lb_5vpebwx
z6?*66F-U<vkr4_Ka9F(Dci-DCL#Hu?yKZw5cgKBI(=7>YO;_HYx-8@=JrYw8e?#%3
zrgrJk!a+HPcegz~1&f<^a)8CLSe1)X+4V7)*W+Iy;-Pl9ig@(+yo*Mr8&@FcJ=ww#
z(W$NzLwMjO&MMor3R@aFG4Ke~q|wH_L~R<p9*g?SB=o7$MZ-T9yv|hQN`eveh4?RU
zjdGSqCkY$rVs2e{S;SbLM`6!ra`TaR4V3srY=!(|aIcn$+%8+or~up}X<-rf0LeMc
zfFzj>U4+WZ<+a3}`xNk3cHL!|OD>}RqtQzpvHUnO!K8J~X9J>+dF&7_y(bVs>p1*c
zh-@~#E71Rkt#=F#w28WQV{^iZJ+W;k6HIK|Ht*QBZQHhO8xv<@p65Gno%hfAx~hNg
zs_v@YU8~o+I{(*rROg2NbC<--&bX<kd#T$Vx)fyn#Lr1E(mzcZ`P@mMF%Ru96hXzw
zrxgU@7RJn}h4HA0f7J@&fkE>mZk`{fWBfP90cQvrk$jDd^_3;<nJy|ks`9{~o6|sQ
zoP0pRY_`WxS`gNt1;-(`ouNe$e-smGfEp|3Tth;mc*N`i!tfou5o8%<;Ksm*{aNSh
zi~YacO!~A7gaLCX2LbR24@|mNj@({~c{og9bP8T@*5HCYV3daqIKx$WI6v7{28lkh
zA1D@0scS%HVRdr%W&wY9mdvl6Qx>N@9AO<@+1hs$?DT^9^8Dk^oG7Bw;}!U;<Ca%=
zzbIZmx9IEhO?q;+?6=Y!dFkeCW&!=lfu0)_GhAxrUA_`+o8-jL{QfnGQKIt0jnaV8
zRY41s1b)0A#RfS&KtvUHWzuFXPdI~<Gd~Z)A1iY~Gz+N`CCf`QZa-T>5La;+9FID`
zq-x+DsRDXB)=5X^5&^<^!sU}==%*!zq+Pl3wKR8zdxn9Aw?-74VNh^`chIM>Bt9b~
zv3Ai)RP1NegL9TPX{pX_=zM!`xA0_N;weSb{ZF>onWBLr0FAqK6+4h@R-G$(aJbL-
z^y8F-L%)(bov4&|Hn;$`6DPQ~-7-L9`ZuX6R@wvp#4#AWZbhsP9`)ID&v~PWn<==O
zi6tvL2Zd$oxD4i;*)7pLgkcU7QdjwNYovxyE^v0yASB^Tk!=|v3f|*L4(1$_FN9Wp
zF1tG2C5;jZ9PM?_kGtGS)`dU>T);f4+)0*&HLxNF$Zl0Goa=2~b~rO?3kh?ZLeNQY
z1*ZfGOk-XKgt*l6tM<_MdR45TLgklP_+SN~EL@*I%VPnK=>3{mew7LOj~#1tk>dJs
zQU~uw%PFC7B+7zY&2=S@ZSh>3kTmg{IDS9nQxM$%<og;{BqNe$>t`4H5HkAy91r)c
z>bZ`Kl44c(=i;`?zD!<Hx{3n$Mz>j$L7iYe6@8TU_zU}F-mmCRxc=`wx9}V{rZWm8
zUC)$vrS9E<pNaB^@YrMZ37a9N+Q+bc+YNQ)c|t@WzEV4gAWyc~F6Ms=tlEg}CHhn}
z0<Hake<6FfWCel|uy6PceIKW`j-c74`C*7yoK_YHJo-(d2<iH4CW|?qaRvfwD>xp4
z3OMk^^fnTr!KXSDw(6I|5%KuQXdV0g(+By*veH{D9IHQjl&j$CUgnH^uHP#qO2iCM
zPPMJP0^F*c_W2N6JCIv_Olp`Ui+ZfC;z%%owS4OnT&Kg5t#@R2_x;^nB{N&V&pH1?
zcd6D)D2`odFR*HRfo~T)1n-50`bZw?Uub*n%6o@3hgJp@-I0zNivSxc?A9W5vp+=n
zA@r^7DjmM3uKhL0p^zCZvOk4=zfU*(G-vhRbg)_sI_p^G?eV}&u0zTKc^qtW_45@F
z(wD>s+GPiE5adX%ZX02O!Y?PmwG2XKRNr62l>Zmk874>_6(a0VAK%${ZXoCBHyfFR
z{wbb|+t~%4dcBWK3Y43c2MXglbGzTs^ZL!omgTkAO#gLUbIt2^dd{T`vOBF19L~b7
z!SmamRWIE}0TS^#<<bGU7+G3|a|9>QZ2N9UW4h2WTte9|SG@^x;Sv@jvc1{El999Z
zGg&-81KE{tL5XJv;jMVuBk*xRRyifI>D`>w`XT`42Yv=jG38M5NMX=RDRDQp!Nv@k
zOWl851zk%j!(13^qo5bfTooZuv!tJd?!~hed+TzSLGM;Rs*nMbkIMEy`%g~581j9>
zcHoN!Upbi~PW=2XoxeP@*DuhR@cwo_{#)8eTZqb5_6Zzr5^-t%Zzy_5O{wBP*WmLZ
znDWc6ffL-rC%WpgA}fg=5)8V2>gEsPX3O&#2H4mzg*1Qm4+GbANAOP1{wLhpTwMxh
z{T)psV;h(ww^T=_V<N1{5rt_$?LqdYz9<TX<|d<&;%j3x7v__hmv~f3Mnz``-}{I6
z{bUQc2LYdvt2Sdw2DI2B693H;sO}^3TCuc#Z4XVZunpFnkz?j*U?`%}M;3q5zOZ0y
zAU}-a08*S0T3TOzY3^It`iU(_i8jp*e?Kvbk=ge+9B6FYzKJkWP+yjbzTyU*PKOrU
z$$0bZ*&%cr0r1g>idB}?mv0j^wKbQDw&ieaFaHy1F794mk`taB^`mC8roceayEKY>
zW=R=NX=bCmq937{#`>+74S`>`ea;Em=|)RjS?I}2fPd=)8Q=b>=6|$#cIN+!HqXfZ
zKid3m;^u$ad~dICY)AO;9!Hq#{hVt;OS<vG2*+Y5XLdgM4!%`HS6tHUlisc!s62^B
zk+bWig<cF%69{IcUGFwzZ1uIO_2ViHW-idv{`SUWt48l2p0+%F6(OCjo>&vr5+3L2
z(x~;>FjKMpC@$5$gJBohQdW7J!p6n6)B)7AcwBZ&M!a0)Zyd{RF0bOo*PPet+yrnw
z#t&J2E8(T5zVg@B%+K2pM6y4vAPbd@bJK3dj3l%D7U(g|(EIlM_qn>u#j+KqAO8E;
zlGOd6POLY+lZbL_f^23Y3Btwju4g~o(V<f(DIxG&hNMatF{lStI01RpIQ#@E<q`NX
zJ!NP?l8#OH6akA0x!A8vJx_~Y^L!Ph$nJnW^cKzv&n$&#Y@8tM@MK)S&x?bJGxqR=
z2ObE*gl=fre_z)o#d%rRzbN!mz)-*lG1c5eVEuvAD_ZtD!T}?A>Z}Zrh)>(@50FfG
z7;-^Zo-<QUKP)Ik5!Ifk7&T29d<DR6PTsD6qQyYd_&|QZ@6Y<p=ArnR%^jRqh<GVT
z`&P7z|K(#^1)~)g)OH-wNQ{{uPM2lnVxKcvpj@Asg2p<SuU~eWE9NKcI8Z*I?O4)S
z9?m+^`=R|8fU2o)#_TKRC(u4TR<uwZl1^L>G2N{T3UuM1m|vk6fkIglL<9_$$+AKc
zj(W|?QM_v{bSYj^5BeR}q!ZD#ZGTkqXLQx{bhp1<MGQt+538-|4@B#nv&yESR$hJm
zP1Res3?=N<s~7EXemoO<Mv)C7mQSioRr^NJ7?ylI)OO$4(RaFSfOUKOdG>?l%#n1<
zY0w{z{B<qQ)O!nu7;$uZ!5LT=W0(4s@gn}KN@8})fQ3wkH>>$Yv5Hj_rHAr!OV#JW
z6W+{*ti_UlR>LY8hW-nf)toYx#<l6=gnMcT-<L}$acEnZnIS0BAUUr+*&8+?Y0l!h
zh&Nn>d2pbPzWn2$8pZX<)q>@Xsq<$&(i}=w(<bf%?!yODBf>2Hm>I|;Pk;!O!PSSN
zp8?Z^lQ|plBUr!qkCL!m+K9|zWta(uOT-1)&SDjy;G?d4PYher@2jRsgszi^cb85X
zs^34F-gi7^`x{Cm*!k9s+;HjRP#ct(tf2B1GJXHNJZ8>EX7oTt)JPG(;zf!pg_3h_
znqVOInTvWR{j!SCNEAq*<|25gZ@*GM^%q_tW6qZO6MXm62d`}WPHsseYgK|VRGvG%
zYnq2TUO{B{G{1iK+2tR9)8qmBO@z-!aZh$wkD+3|J~Bi7ksQ-;%k}2_M(UX>A4<e2
zJ2z*CpgatCMBT*|x-A?8RDm(@EpOe};7!=sz`<(bJH2{$LIi9f!|0tZBC`ZBtE14T
zGjeFeWpiQX<3U9of7@H2PA4jF-Vt#C!lgn`uVew^Yv>YVv^6F|4*EN%c9g-Pq(R<W
zF^Z9w1`YYrJPA=AyZF(T_v||hdoZm!cPoUyVmMSTu<kU^s&XZ7G`)E*sP<^B0{`0e
zw>V8wmhi&Lr2w#auBJbSxdu{o1fA<6TUCS3!_K(fhnGkZ4C5nn-u}fh5N5m)dklEN
z{bX*SpoKU|6?zFJ=@=9L-BJS2?m0rGZ&)mAZ}fL&f0S7uN94@9^Mkl00=YgG#xF<1
zo!3~lWwx^mww4D+5KXz0ed67vT`#=JG+eq=OBtplNe_r$dB3co?iifGoe=ABxG1m^
zIjk9Xh5R||!LKlP)e24ov3UJsBS~{tyENn)>3mcqc=sdO@Q4DTli@&H6vH;#4d0;7
z164f9A94E)r8wiGo~px}(cOaZ2WRU1+iNGZAg{I;+-cY6Ijqu^g(0TQdFL5Q+1(S4
zL;{<bxD;UbuRZAcEc6Gx$*A-K>I?*I(GCdQ_(h{wmFTogdW~%A;HUoT05RdbXVm})
zDS~uJ5q~rZ$|Ff{CCm@3f67NG!VE{{@I3Klf6^pNM-Z?IOQ-je+Pk_^cT?kX<`u`u
zd@9Itx$X)l;2y)sljM<b@U7`Zu;~lM29kf)io^hrt1r?z&H6PId2H~pEoIjeyhI&l
z;EttERDW(5d4qk=<2!~g^B0j!ZMnp8;}#?BYMILR_<gN8A#^uPbS}-2$eW@VT3yf*
z!^RLDC9NNDI+ovJV15Wy{uQ8>H)Y0RO}};d78iYskw0QF&A;&R&6mVY+xOlcV@QoQ
zEU^Z>-^2!VDI07IRo*n<_{JSPQ{ecxYBa?!3{qJ6R8im8XUSZzg{?IY??n5Uib)f5
zXj<j57|kficg{%19jN2Wa@fqId9N+vj?U0$lan75#Qs=zIU84UVuAS`OGIRn``Wh?
z?AX)Z@i!zzKaJ?{lAsi68l-CSHco8Lo+SdFL)!9TI!ol*`~o6BnbaJq%kpK0Byz6<
z65J11WhEhy{x;?b7J>6qdd>r^>n*b@RpJLvdm>ABg=b5_0}@q;*ndiFt48z@<{I_;
za^q{4ymDQMqeeX85gFAnH7TvbgVRK29!m0r&**zFRq8#mT{f+XlAk@i{BQ9OB7^~V
zr?R2f@SFI?&u-EM<(!WoF=1W)AG;<=-raVGcJFZ`tJ5X3ky#fWx@f&tg!=KLA?@*D
zuTyR>Dp<~!t+*9D&9*nck3h6H$L4h8jvT(thd-g;MsjWjCM}-Rz&fAf`>KEe1VkSa
z-#apo>*gbzCM-IX6||EiyO6hKAQlkcGH)&H;S27%=J#&d369^af)h{--wN(|+Mh#j
zo~8X=V4Km!>sus_tT-aF9^9>eWTSL5sv=ZNBQmsTT1MmZZ0kDeuJR~O9YB0g`eNR#
zBv?qB%#QAwxOkG_)VBkXWXqW|;0;!1SCgH8XnVet7gz!Um$wp1(S@-*m=AP<Xc`E0
z=PBkwBPXIaei6_92U3XJ{HpwJ**R@8h*>07>yJ;Pqs8waNgyIf5-fxu*tA(mEnAEd
zAOJ5HlI#8QIgy=M)o{OzblWCI_vT$;%95g{j_*>Zl<Z>Wz7Y0OV^t0YMd?X1xX7*G
z6oHqcG3vA$DDQ!-W%Ai4cn9_nHa@||f?dNgB(@&DndS?QaK0Kvb0HtE&nHW(?pod%
zUB`*bbkV|gMyZf%d1ll5nT~(^=9-~q2Uh0&iXd@orpRakQ*L0kwk}j8xL8q^A1@La
zZ;IyY5eyCsRWKKp^vGW=J_Qd|e$;#Zx~4>av_%^UA*&Z(hx)w~s0rlF(QSGv{2sbs
zWgelw*-me<@SI@h%d4+p&x%mmk5oE5%hefsj2WitAh;0`Ki4y4mr`oVAEnXZ-y)Ez
zP^|_JexUN`HAY_krH--p+GD?NdUYgROH0l9$DHF;r%HzpCKwr_2hJ`~FsJ#>l@Wvt
z(kS%1^4t!((S02&{~Y*(6+*dMt{RKRCX0`?y<)SvnJz~fCg}a=T`O)=<XGoOY;THG
z<vZFLsmN-eC#3g8WoN4!`N{_h*%NC+tZ3&OZ^M?^xNo-50p5IXCiq*MnEa5<SmM_6
z0sEqGnJEe1A-_qaSXel8W!ER&{}*D`%^=g*Fqd-{DUxTD8waq{oIx3{Hgp5S6OV3c
z9#x8&U1Jtpl}X7>JUFNJKAHF?8%6s3*wYgjEn@$#GcqE{Bx*~-5*I#-n(p$6c=Keu
zpaN5)I*Q#_BM2Y{*SoO-Jk77b`U_N!b^6H8*WJbDaR->yzaL_a&wR9w_*?J#hP*I~
zV{QFiS0$=Rm4JeOE%fJl6I&gGJ0fd;*f^*SRvyp7Mk6IK>r|GPDXLVR2lb3X;>|`m
z=_z?3QD=1+g!SZ!q<SNt?Ke4j6=5~S!X82oAgpeN&bn$Rb<D*c-XQ<x6qVu@WP;^W
zaE*ma6q%(nWXgP~tBIZd6b&y66ee&!V}HCVnKm3!&H>irjgF!PdZ@uJ{|l@LrpOfN
zju7Z{<-aVFeI_HUpD2K?@E|1e$F$XLoWQ{FHRtM6N*DuIKl5aso~Fcv{1z;8<6zz*
ze$X@CGk2{ngYdD3v^A{ZuTPBJaPxyM)4~sK_}of7JbAoZ2&%6?L8SdSh@}28ddK@m
z?QrDHD}Z7tUnas|>^`3M@7^~Ur!mOG|An-|%AWd19tt;+C>8;klkI=w-%M;w|AWw4
z*69B~_>}G&wOe>fM^jERP|{F#7dglPvd|WP<PaKkNHCr{45H8Xo_M;<3!U{PZpY0)
zI{IgavFv9~yaa^;czP)Zg}cmv!lYYV{N)HeN7{hrb%%O0hu@cK*_u8Rf8aMt4w(O;
zD7kQLvUCa~WX>-e_P)SB3C~mh*nR>q*$VUMnKeLbP2S<~!&J<06{19xaTObI*2d@I
z%BYwM{6Y;yW*8N~HPty(s-Rpgn{gb`*EI74Rh5QNQ(5!MNr^!s3*wkM67~bk*=~gz
z?hXda89i%GFqr?<DH&jVaw4Jf4Z`9rSuQcD;2Vk|7K&BD@{8UC^*aoVD)<3v7%5DY
zqg?3d`o9J(&_QOFE%i&omeVdGm;3Zha4410Z`;uW6G388@re7gU}qq{#1MJ*!{`ki
zNz8?AGs0Z__aoG?>N$U}K=!CAQh}o)Q1>LkK(XP5WEo!s4E-J!AaS9}gY<7iU+Nn!
zHrE3cpeW4Y%+uGgcMcDNHWUW>d%!9rt#ufSl4Q&f0;%l<2J-^&2QHGPjSvEtJN%^B
z1daD5EP}pa{wj?*5;0b5nYMAV8RelKD3i8u%UUKN{lVaes;A7$AhK4elQ>gn(LzL6
zF~)Y`lEjBOn8`12Q*sOPVD=a_WV>we;Sk!>AQBj$bZR&U*L7l^#1;Zn8xg3?*oF-#
zxs>q#{DEqHyZifZ`7xB?6w7KfE#PMR@Aj){V^5E>^ZUzU>+~!k`)Ou#<Yt6{i>FJw
z!>?bqE;u&#!JD350k>e=0_(=`ZgTp}JBN93U39%3ELA%?dOF_fc3Zz5KAx7U`D=P@
zw$}aBuy_9+?&__u7YVEa;31yv8hW<2jC7T3gsL~I9BO*C3@aR)b9L2kCZD5vrvlnO
zPPtW9!S;^DEY428(Jg6*7LlDS-zz>1d5!q1wY{IV#C?Om?cML=zK&OCb7!B7JR+Cz
zy6fj5p$>PJwgU7d2fD1@$2FvcrO<x-U?2yLxS=qJ>VBj#ZJrGS;C1v<&aAE>NHx8*
zsC!6_4$JS-(owAtbCG!&Ok^wu(n5-(EH2Hgqq<2!eTyZ?KI8`DPs;U_a`l|DUR028
zD`$d8V|Er&=<9;^=uTg9$fl&8UiK*`gMwtFe~)d+4PbYY3U!g&=<Jb=YjtcuVjAkj
z>ACoqhqcn)nb%tZ-y4eyozp5e6OzN`YO!Q0*TshGPc_!<FaOQc8oGr=9W8YCPy^{=
zy^@>(w8x}2Wxn9IWtI{CM1?7TG?Q8Xw?1VeHnODJINzosxA;w%!oah7&lr4d%e09?
z+7t;sL4rpVk14-;+<WE8-ia526fJV~zZf*VnAwYvo%Dcioz-r@=Rw<MB00S?OfaX5
zq|O=2Ml}-tn{SYh=I*~ebnpJ#_ddL?p$%xvYJNtSfMWL}ZyoiS;nf`lduo1%YjCuc
z0CeeJoW_J2dgRQksQP+IYgj)wn)is07%)7ujKf=SZ&10nV`?5PFK2%c8r-DV%ElS}
zx8l-Gi-Q1t9mKtfE!?!f&94+w<}eM$;s~bafc26&Hx>2R1f1chl{7w{#MdO}@`3;8
z0EVH_@EGEsqa?9)vq1|Qw>|RQ(0}}W#<B-dD5qk$I{Svkm1<37%&kL@dVdUw`&Y&<
zD^)&El8-8l-x-eIfhHVs85~_+F`uYQ!0}B=3@!oYvFo;cI4M^xX0{je6vfi*@r=hM
zv?nD5eX`kFA`Ms(a)DyQX63H?0j$NdjL?s+k1k{j5=SkIPEA&8URiZ!2Q564syK$v
zObo`|GU`}56K~grp6Y}~xf&3fw=pi_a8&h+%=z&pZ#eU<<gLVK3WDb8J7^ISRlAkO
zRP(^1G>TND$PH*J5vv!hV!YhUmQ_?APXQWtUA?P@>1A-!y;T<4^OT|JoN~^7`|_|P
zBQlt})Y}6=F!znZ*>y#p!!zhJCFy01#N>vxsE$4lZ4q8Bl)$A@;q19NjR)2|Ur-GC
zTn=W-yWjfpmj&ntxY+Y?=KmfPsc;lv@Tr3<pg$mqm>9YK4^fK}a8Z%AJ7P!p53Bg1
zikmjSkz%qwioS`csqbHquC*9wNn>R2iM^H~v!JJ^Sj2+H(Y=OF&i`;nnk+s_8BK7l
z`1S4G_I^*ds6h9ZnW1pdDJh~Opqh1}Kt`otiJCeYvt4=KAnYqj>rl2KRRi^X#yw$6
z_<M#zW2?0(ZKjI{;Hy2QgKu;w#Eos@o>pp@t!%4@@4Q3%#B%27C94}x36V>yw9p-`
zwQKUuIk6$@d^xHew9DP8kSD1<Q;d8hS;rD1_>LGaiO})8O`ycj-0AP$W=)uxae{$7
zIGDb~O4weTTA{UX#1EOBA8&Ku*fY6kYv$XmyV?Z>_i`o$NCU-{#`w@IC|bv*sf=gH
zK~bD#7^mgRX$N$S@d*>Cp_li>51Dv}ig^Xks?)iCRFy$-FX^*g6S2V{KgbUw3fMNr
zn@~HF3z!<AC6Ab1*HcP?2`-)o`H!W35vqyRh-%u<x3nFe-HJ#5yz?Z;f)Z^pKT40w
zu--yZS70InU}_;sf-cs7QZlF23!xMR1<YRyUhhi68{fwLM>nkB;W?h<NZ&r{kx&qS
zNBBy!h0o7jkg>DA{}>68QRMc{9mC5wKiY<uN{d&#gShDbY;;6q4Sd9Z0>{&pT>Nt=
zmm|8UH@CKT8r|Ai*Wuzx=Jhnd&9kxo;Pn@&O@hJ_P*JqR)ALqr*yOLU0$q+!R*5XA
zfc+G(22YYGAl}pH5`=ztx~M~H|HIV&ybx!4E{v=vuDKvDG|tGmT8IEisp;C9g}ZgL
z7SQ~xr{MAJ)7m1}vmd#jNvUB!u}cVyLS>wwwNzIav9t_rdo8t|7_e8}x^Ba<z<u3d
zEd;dy#uW-V22y@8^R9j)%`MEfCHuyvUM}OWC0YTMim=5$4@X05MVI#Qzhd`Xmvypk
zBymdm6<4!D@ym(Q+@{-4uOZmwp(S(RiJY(3uC$;_;7ig$hs_J2b>F_h-~>xtijvSx
zX8ibzsa*yJ@ZyV2XH76-!{$BuqTJW^olCocThTrP$vMH~tFE}69(K$<A%b8wo<%h?
zZqC7#62yDu>RI%+A}P)RL;p)=Nm(j=n8k0F5cG6PX(&8(H-3@|3|^Nt4~$tG_1MH;
z`TgNiULh(yT5|m~4oyuS=ZxpAk3l-L;WX`Rk6c+@*&3Io1>fXz)i=Ajp*Bw*bj~Bd
zao&&8*4mn>J<x_<3$ahUO7RL$XKx7**I(+c&hGyC8_+@fQ;*f=vn<nU?ho6skLe|(
zK^>3<SDzk1IKJ$yDkZ_H%ONX)8mPkjPSj1zyfcBApf7XKGBh_=9}YdFQ-UPYG)~-)
zHLx~e8;mCfKDuGt%eSFIFr*9!1JFFcV3kgr*k$EzH3LLv!8y2-WptW}cafG7qQ3?I
zlobOL7G2+II|;Mx_CglcWyka+T7S))82(jc6MFCo72QANQeUpEPk3RY;K={&GyjYJ
zV_{_Z|0&u`L`*E~|9dxOh9qKV<YY|E|AIh=;9z88{eOE>w40f-($xZc_wPiCY*}c?
zggK!I=Q!OWED=c}lpioU84n~xlwuh$U|@<#F@BVi@$_O;Bx0V>RMc0|Z@i~jr{24o
zH=PYDGdWf@>0T!}R=(E0wxmi57{8)Owb25fFoVPVk3rddeDGCZut5UJhx+s#;Cy{q
zia6lD7@#46UM{?g;Gw+Z@4$kPV3BTzH0~wb(WTKm|4e>L5E4+qqGMv_dwoVCB&f+x
z*&+R7P?s`>1=u+(a9hJUdj>dPwkQb@%=62GXr8khH9;5(1i_;tV^QBwaO!J&+8<D2
z;BWGFSZzGlqS)w=X@>feZEk%6iZE1d?p|JFfr7q(udkuJ8v_%<ipFnsh+7fQP7n%v
z2F?|%Ylsg^97ey6!S8F?r~pDnCn3+zyEH?T9bb7`ygpD$GK83?f#H|D>^*f5H(vdU
zLTGHyzIkBG6M!M<(`yA693uLbdRBX=6_tFr(WgWRad`GC0FN^_1MwH_2NjX!W3mJ6
zP(gqQ*Eg}Cf-c53_c8|b@Br=um|m+;ung)E5cJgpJw(s`I!R<Z1||lwziNqjdKUK2
zRsODugKeFI^E<ley?>P?4EGtghN1nwa%ypL4nvVXQo{ucvQc_*9PaNxwuMRgeD=8i
z0`c}J!@W#qZ5%|9DarA1XwZ8(AX|hdU~hm+kcJ=hM=RPr{D=!G-kJX$2uhpyUcV#+
z-m?Vi8RTOy_>MZEyZs)({bivbNaTn1;{=g&AUobX0x%oxw;v+J{RK+9Kv)NQhz<kV
z*X#T3**F+J1sf<1`H}hMH9;g&nEBUoWA*F$RZmw%B}xE=5-uK0bhx+=L==w%aSYhg
z4fswUgNgX4jQb8-79wTzyUg`;z<P9>?g7RH&uYn0p}x{5K?0Q+@KD}b*KGO~^|7x(
zUj?MU+{V7;&U+g^ZVbO~5?FoY%XT61d$GTfLI1{xLVk$#kFSp6w!*z(ZwcppXIg@O
zH}+LvCoKZ+&RzL!!SX^phoW?F@c=rw^jCkpZiXb#mWaB5dvY(q4%nAr*?M&W$VaJ&
zqgSH>XqI^f*rj@rWc1{Sg7xa=Adt3UoYHVGL3`{ou-D&OB_NUr(RU-kAZ-hQpb${f
zcUFc6%pha%=a)#Ikl*4&4InUX+dDuUfCu%j-_T+CgMgzZq4#Q+1|jqv7&JgnBxI_)
zh_6|Wr`y#lt9uQnM~skGbh#QOjMJdCtb3`!4y~m6c%is^*a@1*tUvY=I5}e<lBUPm
zqD}9!eQFd+e?Cg5u+j=cjnNYe2suXwY~9aa!x%1Fnl*M)1bMhvu2?f3UhucDF?vW2
z+FMz38cT|a=F~m3_Zvh2YV}?!@!yPT?y*T4s;U7AL=7tBrOk?u#S>?1R`~q2pSXcq
z$Xu+ezQ(Rk;nH-@vdQ6lq^B(FE34(a&d81{$pqCc(v5$22%yAYu{PP#<Pw4hkTppL
zgYdfFq8F&0)fy@ObbzNl{bFAJnXa~m##&PrD5AqN4wlDX@mP8UoG7`jJ?g{4FJF6a
z2flp@rnfcDG2>U>pb<|B`Fv{4njDkzen=ktrSF-5H4uho+9!CNf(u={RN6pBlLsHI
zU;PucJ+rOPSHWrWki_PHbSIqc1En<Ybix~89_f;DO*W&1;Yu}3KF?rC&#cTBno<j2
ziC`S|hbp(VT%@fD2!JRh{sm#cU4n7~_E@Z?{e@P%pvVF_n(t=fB`_N0bJL|@t*DY!
zp)sW|O-|wWtlls0IgERJvLh;)Nm016*);sers>taDE$7k8aJcNI2P~l4RJH#2<nm+
zOIJu#8gw5-sYGhRa{m=Bknf=SQAl4ma>AB$`ZTnYu$b!(aKV<ghK3f|ke=9LbozbM
z&8ZS#6LUOqFJW4<m6nn|H;86xLW87xcIXy5>7JrCaVl$^>oQjD!kbL;9E-zNDIHbJ
zRk*Ai_Ko9O8kb4KJ<2at$`@Bi5vh%$t0=VG`qUL&#cDt}Klr3S;nQaR60exnwXh=_
zLE~B7J#k(2pVr%Wz(EQTmXrQI*~75C-bTlo)G6i;2}Ee9`K)jAPg2L~(N5iJd`Zxe
zeEyDpd!#z_^gdCx$f$1QgI+TWxzYR46;NWnw~r_Zb?j!Es~6j)CZASOg>rV!ga;<g
zm>~@lY#dN~$=6VF0=&T(uvf2o)9&t0%e=keTWneawqqj={o6}LOshwN2O50mR*p{%
zW=N^<uq|i?<RNY<)C)-YO#6ZRC-zUj{v+YG6gM$V?qP)bIx%}O1k?|XcE{vom0gcR
zXTV0Y48Ap}I^k55LNi_IwSr}Y*fEw}i;v6MR9-H47G(1jZ4#m+#`Ze(>_4i!CF<f(
zc!j(IEkl-l>w?z3cnWeiePMG@DF-WezGWZQ8X&LB?0ogsEmn5oI5(!KZUAALTctOo
zRF#a&0;u@0wVi6lx_<2(U}utqiKmR)y0W>l2~TbJZfSeQVqvd^A$>D9-St)YT9`kv
zUEI7xz6|@6teSD$u|N0~eD!f&9}>*_J2(r#ioO&hvCAlVf8zQtd1b2lq>-}Fo>+g`
zkgpzIz!E}A3B9j!yATyz@#`5ORIxOpHq23H5$}1FY#KRAK<@^lX6&`NkwT!8%6thg
zZa$B1q4QN0E|@5TK>CJ^Oi#|x?auT3YwEhv-1fY&KF|T^3ws%#GWDQ4+Bg)>H!cOZ
z4mDbr1BG_VW~!R4qVgW!$aXHebqkI<^Lc&^lp-DT)pV}Y!0~P=zec0ZO$>``1TAhW
ztQzjTwyFBp<B|_=L?$8WlrpG|g<m2Z3_^z)&OJD}aUrJH>q%S+1=*-c8tdwrt<0l)
zV|34lw-7w;u($K1eBD3d?lV=`Jy8RTc;$2^G^*#zL?u3+E;}6MQNx6}<>cY%L)2Uu
z|JoVqQKWf&%?Dap$2kn6T^isEk%&!wF%8qx)Cu@GQpvp;Tns<xtb6C8I=<AIc;Bvk
z#m>znM`IgWIOLKG7Pb_Ef1wTF=#@N%ZXmiiZWbHeaWNqam{d2_5(S~+29^SwcQ6|=
z4EbX}#`F0RofeceF0&?8o#a+9Hc6faUQZY3`+tDaT@O;#)!fO+j76_WenlT;zdqDc
zvZT%jqo<Fza;?OjIbmW0Y|fnfJ=wed>=tz2lV$I%h@j#M@9i(IqlO$k`_EX>k|t5T
zG(8@Ad)1R{Dj})d`XhugQEb2;Rxd7X`dwAV6NfwK<8yIIkwj*2Y3A&a$?W>c_mc{!
zNRuLSC2p4W@#Djy#;vt~Qig`bToENxa@~HXifKr!jpwkJp2zZy0($TErTK-bkrRp4
zC^Naa^PO==A>g*Wk=Gy|YP&|eURq6!R2e*BC<_W?9o<@dW8X5(0vCYGpE>$$|Ces+
z^i`fW3OmwY!n3urg;%}_ZyNCl<_+?Ae|Fo4@wDC2lymiZw{LyEjTS_v)Od9cTX5le
z5|6WXOCRn&nx6!=bDwnQiz3;|*osou#37!FoWrEv^mwjpO<$h+p=I7I2mNVHeO~D=
zoCa9v!?b9Lh3Towm<<3<ZGmLi1mG9!d$r8tW(8)&OQ5}5+=px>PtF<LEYDAJl%4d8
zm*<lULX2y!6N)Z>*$o018k$lMG}UB{Q_Yh>0~*7l)AlE8ITR`>G7GJG?&Sy8B+aZN
z5rcC7*j5+(1ZTrMmCDysVViUBgSX1^S+fqi4ixwpW4HQRcoX0xL{xH7aY&{C?bLBg
zjgLpo?k<x6653@0ak{*berB>uF@lv(O(K6vBP9%@7x531tJFEGQ&ZXq{s!(wZ>LBn
zRckn?J44GEcW>vcw@aw-01F!j!2<lWDp8phnvVt+LL2|KIkY6qFeK^mh6UZ*wE#Z~
z9Dc!sZ@v#X!4$A64sLML#M{gjt{$V7V+&XJ)8H=CF`0qqcrSbJ0uQb@ug#rr=-*Xh
z0mi?L3C0m>GHYZlfeBsg12~lF9F6;kR07?7Hj54MMQwwU4Um#{9c``j0pW<1iZ##5
zd_<vKLRIt!CvLos7}8D5y__3ucB`}y4|W8vAI(yjA{4-^Pm0?WVZpBFj*^0dPsx~$
zihcHT`XOS`PZ3|&e3`cJak3lhJ&YkEX{!(L?GNOHs}zK&2Crx<<iQ-o4tDC-?k-z;
z=VTi3Ye&&hW099?E^v+#*Br7^so$bd!ISBKu6gYBZTe>0YM_Z>4L!1Spu`$SZ8F&(
z<mkK6yXJvXN9LRb&+;R!Q~6%gyU7WL7qgf|u)HdQoT{yVelvw{7O094ka{2ko$9>0
zMK)J5bSwz!BTi|nltx!SuE%0j|5g6RMrzBTb|e&?b2XA_M;OU<?S2wVBqeV4(Zeo!
zB#I0&ZPiQkz;Wol4@AsXLATqAJn7F`d``%c-tYp<MdX!V=egx1p0~Zb%I@zV{Joyg
zDkya*X*3M*NlMJ7cXuh<9%JtJr5QShF7L!eQi@8Q3F}db>GXK?hRUZN%-W_T*Cgqe
z?2P-@)RHS9(4Ut?u>V3(1-2WGLH4HJjuYD?M#k*@?kC;UGH?4g>-tZlP`)H6qxx$`
z8^;Pzru$}Wj&X{f36Pc;?P=`y>@W<84>AS`E!Kw5{KU%E%zRAkbL`!9eJ)8`RbOos
z$4r5GE(NJ2fhQE%E+paGa?9OarjjYEJQ+T0>+yaW5JjzwdVCq|(NdF$0%wIva4SAa
zYEca(_mpt)67^a~_l2uX%9%NtsIBg0*u4NqsBj?&epjEMVlm1(W79fzN$a-RV}5Dx
z*L*kpY9f6-$WcLhbYHvUeneUxJ~n15T!rNCLChg7i`LDjTFJ`R>_0F2^+k|ud+E}`
zSHq;saM}4N<fAtd<#^-#qp;G#C2)r1_`HDRCQ8D7vgN|=2Ndm-j$@U_uW>=C^C2tX
z@a?SBp|)l#_|5Qid!haTWFnTAT>H9D2zA^#<Y@5NNgtCdE85e2`eFU>5ed}iP<5H?
zqA(@)=ii@ftn`VPB*d$R86Kn<KfN?bH8|9B{<As{Ovga^oJ=PkB6L+?Vz05gF9Elm
zeSF4Rir1H7Q0vOcln5p}4KcCmMAHj^YD!`!t*<n)c7s7Ie%cM10~d31g`P`{nq&uy
zkcH|LP2mI6a!4@rh)LXn!v<?5BCo(bTJe8&otV<U5lR)R+U%LzI<|IhDRr~GmTWlW
zXWtRHR65FRSC2=(&0d$(E`oDCNY5k*&n@<sPGI^IYI9mraj1r&y672HBI^i&xL^$#
z=NS4*A0ukXj#nx+QaP6lLFkdd6^9Iv9hKJ?{OwP}B+j9c^#r)vUi8o|<h!y;Y)K)R
zp72T;EkfR^r{)LmH!?H>YPgCcgvclrBZNw?STdaOoNSO%{O1$A?QCJi(0>Ld15zXR
z=!>jE-EN5J=tBH<r^n`LcCsh{CATvr)2e?CHzEAgY+Mpikh`p9<q7XF!#!B>&V-yp
zXAhr>D!T^#z^Tb3o?lC8)A+)D%kL)44S6RW^8`ki*TeTHA=}Lj)=jZs+%re32uj-M
z^^qWWmS%eDv<jG&eKp%s=E~fyRL3LG^CvcoVN6;!+T18khpG}<%EMaV$I49FhU>{L
zhsJkJiw_K;(t*Xn3<$azS(Q=4y_wj%8tjC5m6399(0|Spr!UG`9J97%Cd}*JyEQR`
zZ^_qanZ4`03gK4U^vyz#;rbWZgIoLz+XD=W9R2$KD`lpJ``k5NW_~qYA2*rbSN&ZG
zM%sfME#T-4gEVwg*QkVm$dVH|TnBdb+1KQ>dnfIAMWa*^{}$U#S#ZFqSXn!YZI9JW
z7`gWhd3A!Dz@PuT4D4G!zZgIBEy7MiEt&c1k<R_I@uw~HQ4T4Zt^crigw-=thVS6E
zCa>`)ZZGKOj8|E8+&R9Hqy7tGZmf1nu-i{A&dP8V-4!PbN`C4AcrH4(*8Y+azE1tQ
zNOQ@kxfkEa_1F-$y$Fv<WH4<UTdqDCmh&aCte%0fA~i}bC4MlpIT0Ysu#GmmnV%Fk
zf*(=+J$O4sITnpNBgii&mF$#0>09Dd@vztSN3KJJfFu6#b+rVir1n`gZ)Q5Yn-SPI
z#kAr%a}iZk2&ifXEN*uq#0<-j_&0GAGIJGOt7M6VIZO^T0OOw0m}*;ZKgFLb4_m(j
z&?VUIy}2z8w>Pom-A8{u$<L0>emC^VuR1+@-Vv<+98z%vxAcvzfQx}UKl&#sP`b)<
z<vDl|Z-k<w-(j3&$Ot`?vi-}B=O3|kOfBc$i#m0h>yI%Wz$6eMLiNlo&9F4fl|~nv
zfp=nV$z#x(4~1O3t6YA-<wS5{nb)e8+%Y~adSi%T?`0jDMnzh$H<i>UhL~ZLMRiGU
zQv6%6c%%HrPFdD~zLi^{$}5T1hIffwaw!FQyGEDaQ)f7k@agTvo9fZOF}?&T?u>`&
z<F|P$(WtuvusNIbM?JvKiT2~})tU}AwN7UZ<9&<J@+^S^g&JkapqYX}HqbuzUt_TZ
zYkG*JZj`D5=ub-7FVsbrF84~u99^B%irE~)JH`>Kg2X%6>j0V}hY1_R#aLxp+UJ_N
zS39IK&fC9<CW{!_w8}r4YgsL!J7UmVd&qAqQ*&a*fO63Y<ahgdo1Oyp@)$<C2UmEw
z?OwXnr$AbJb$AVFcf@7=kX`ea_0%CHOv5wH2pxfxBm!mtXMO#EZ3V5d$_mTO7SD(I
zhb)$L5p`a?DwxHddL9z37xcm0^re=H*OJM}Um|we1>8h;3r)Jvt46fH|G0^DMHkL&
zx>*mI0cXhO7xdqj>09;i!3dyC>u&{0@w*?v0qd$pP1xxh@wh#-0a~>QdYM|ZnA8>U
zr7N9HM8E|(XsOP5#R;NhB<9vKVin0?#9!92ZmabVL}zF*p~}M}BAKP*bwii~WfPBE
z>iB-m789B#0~yK<s04lMQjm|AhahNz3ngm?K<yhY(<LisL0m<>%66gDX2Qe6p;1T@
zv7`z@SDvLPc(+MCBjm}OAPkLPV?BYOlj!w_)nfh-mL*0&lNCnAUlMiLth8l4>SQfD
z=PGgBU%QZeHQ>={3}iJ^kPtz?mmHp4;-|DGFeCRc^zM7v+ux`VEo1c479`dhqf#D}
zfJ>SsHl)8;Y6KQqISc_^y^Axy*63!P#1C6N{&8EekJ+ud_tn&<yXxiqy@W4KAEDWu
z40qI`_Hmc^?AH$3^d0TIv4eot8>JMVS0$!k3(O&O@ZxR71TKuVx|uE-%O>f`&}&-6
z9DH-`libx0ll1T@X0YwKgvJH_ypbq{0EAyouVxqzsMra$^%o_Y?&TRUu{)WYH(t(W
z6!YYeVRf^CLpVs2>L0~gYDfZ-xdlh+R=s4AaK2PHmUpxy+D{=@aJrAwro|el30oee
zz`vrc)Qjal3#94gKXrcdKRYN=+(QfsjT^rN<43s~-&jOzfc0Ub@sLPM&xeWzpyu>b
z9<_!versLmdMi6=Ah@GFC5#wO#O@s4zkOxQp7+~1+>_=wQ=_KZ1u3a<oxODW(_%iO
z+YXt5ihC(L7aMCKPo}!8`;cIvnL+o{P#R6IYDFvYmwJ77_L<olm$I@rpS#AfNEffd
z`TRJe^kQ7Ih=c>sRXIGAZGnCbXepv*{uLa^X1izg5MY`^hukrV{9t|YJ99DLoq1@R
zQr&SQ#+eJZSeHOX9-f*=^I2$flwsQKYkZ;}ozz=9RfVw{E+rLiik^h2J{vEYReAdy
z7c`C|yU}U0+9H@@dlkay-b?Hjf-gEzMJk;3tSE(?-U=u~Eu2ls+PGc@7|88BdY=B8
zVC@=Mcu<%i!>Um8-;8?o>pnL_<@bxQmb)L84*N|7Dw5Yzz7*TTm;PeLiOt}T@^{k-
ztM+l>5SU(k?^wxP-3=@;F-Y3YqC@JSju{<}MBOdE=E7c>*J`+F2##g+-g9Sobf&2K
z*YGwcI7>rry0W=Z$r{K5+$c#Vr$7s+Qj&2+YsI*@ngiSzF+vQ0dk${`s`pe`{0m-p
z;bGUG(l*JLEKgdhqP!J|`RAZRUENW4nBMS|>1r3<QUdxXwXw>d6Dfn>(GrtKH>k;t
zXi{i2Z19&+iSH7Lf#q~^=4gY~&+vB2Vt1G}?8t}d<Jvdlk}IshisyN8EtkEME3s@%
zMuv(vTp=wiyK!-hF4PL8^k1+YR%%@n)G5fC(pvJrSC~u%WRu8V2I0iND)kHlnes!8
zn-7*vrjpOcr`b!o&Ys_+*0{%Ktq1blM7BFKJP&{VE2j609RV-k=xEmWkB=I<@e3-j
zExASxf7!fRHekU5($31DfQVElb9f1A3zU8nOl&<;hIkq;I2pn6>3Lh%dBK}Kcndir
zGV<b^Qz_z>Y-AaNR@j3qN=ow=B#2>*9IoaY!kv{rf0(^*X6NnSNp0MWgwrR2kK5l{
z|BDW(BSV}~A39D$@iKb^{1(iOXeX2TH)Yn(4kj#Y_HmE^^yQmh-+>e~GDkM#)c`~a
zaoFsWL58`cC33quPDrxTGg&Kd;>x0PK92TIwH4nO3Us)9nNNys7}=|B_+(sKcM07-
zfT+IMD%|OBPdOESpRKf4cV*i*>^)?98<-zA@DZ4-Xm4G%Z{EkR9U>BSn%kj|4pF!N
zkpLW1I-X|$L#hAvnkZ(sx=_Wxb{`jmVQ;Q~;R7xyBfrVrdnwf$V{@r!E`<i+P)0B9
zFRXM58M*uz2+qJFT=5E2dL=pi4twQ>J?B}n-RXP8M8g>Gly@ATuY4v7E!mec-+WP$
zTuwqXEjWg$^8lObTlw;l%awzpGg+(ag+zSLFT`D-z%H7x2#+skCbYXfDB$AU!(2Ki
zFqo74C+3>}NW<`Y>Y!Mbvoe|`#rtwGSa|$eUURUfVqmj1-___!jrR5oT_;=8p|W*@
z7nq^!Id*k@Bb5UNJ+aFxT&Pt2m*21vlIf6OEL}c*K5YiuehYHfy(_VJHa<@I6H<?k
zZ}beXRAij-jyq<#ry!}SH;n0%5it`;69Ji03N5jnq$Ts~=wp>SH#0<fDpiV*?d(S{
zr#%G5QpXveuP8iD6jdW*uCtpR;R9a0{tulz`f4RIvF>b>^kxAJnNLPijk)5%(GQhB
zs6zZHbvNGB7^e4Y?8v>#O{PcjqB=3yll1j~sg?+cu9LpibNjQrN5RDJWy_`geJoS-
z5pO|P9XPsgQp>6)hYdrEM~(It&_gksy}q{0-{*)p89C>s&Kup8p$0touyMRyXzeK!
zZ)w6^+u~AOiV4Ic2M0qa!>$`G^CLbL6T=sx;hj`ovls+M9^yX<ILWMjH($S>>Rgd9
zVmr!AQ>WFAs!jw@6jzc$<LmVL1biTqlICgt-yZqcQZOLVe=xIg{eO-#W+G;GHb&Oe
z{cA`J2o6p*=0pSZUqDm4i*lCq3SU&>9;P;q+kayf1d;U*$Mt`MU~8LA9p)Mn3<9wq
z%%6y`{ol+MPowX*Z>8GvqStD?PU)ZJMPb>Rl5tvFP$uwk!M>WQOIm9%5ONd5FmRNq
znGssh`c@G8y1IG?Vg)5>?m)j9c9c5wISew8J(p&vvW!lkhnpLmb8YP<z6`X1h;i)I
zWe!aL1X3QV9jv(vPv{badrwag@!(*>8p_!NAIiVlx{v5h4eNJUVQOP^a`QzlcGlDs
zK=OH)q7O<5GJQovK<~;9LbL{!*H<tFChzawmB0?d4TG%@)d01j1xAztLKjCMsHLPS
zf<{!CUr`N|{GPqXQD2;%M?LreG|AYSn@rL{6c4C17eL~W&;(VrlrCl~F=0L`b|YZ(
z3Ld$?e$7_y6S|pL&^gfguvxgS2snY%fo}=T(6a*zU$N{NY9@ZY#oZm6+#+~iQXqMa
zt}ZU<`X-OJxBB&tP7WsioLcpq8{frplN%$Dd!T?r3wW1qw$M{vFWezii#uIuCEJ-E
z=oc-l;P?n0ge&N$LxTT@)!cq_QthAGt_vWj8*|`MPUam*2iF$N`<607bbg&w`z<RA
zy9d$)+8NL%Sod0)PcyeX4XOWz_522*G4~}+1VeOwa{2Kq^u9MV>pSsecY&O!mW8F^
z`3?a0{J4n#?YE`h`7WCV<TmlZT<aYiTwc{gQTi4}2p%N5Cv({vLBEHoA}hxxC9N!(
zXu8=6(lmbFYvMCTR+e7qtpEq%(p0b@FKg}~mmk_7EvppCP+F40czC)hokX8hxk=Mj
z+1kW2x>etc%dYxi&}*lFhBR(n@NsU17SP7kU>RtWwIz73_-*zsMf^Ff;jay94HAb2
za%5pU{q}2FFZ({!^joAirEhi=^#G<0Vx!aV!<ts87K@A!D~|_e@9!nl{lC}KK7f?W
zRo5>#y8Xf`vDX&8sJCD;kd7GS3z)B!`r>;4Cgq-2DT;yZd`y(OZmd2q<M5#h0L;P1
z2CCy5cv|~DN^odwRRiVrJNxR)`?i8~uB(53v+MlN)(rU>FZKLw-{KHoe+Qvaw%(SZ
z^<7!<eQ>PfUn|Ri)Y1UmT{EVa^pxvk{Jl|E8yYj6%L3mwH8cEAz^Jy{+!h+Dy$!_u
z>ln(jy8rvkhwg*08AKHW(uU3kuo(HaNbQX(>OVn&$F0Ng3(SNDadw6BB(Cp%0)gh>
z=nMU9PNoyg0oY*uk|7Zsd|W^|JKEnsX^Cef0nCI@+&=2B&^N3D$U3R7=ogSG#c!c5
zYY^4+UQ`}Gl_$F)Q2pe0TnA8fj4$z8rsVIy7hO8GFYzo8)#={(%G?zIK>4mDytR9%
z7{0U{Le^*dMm99_N;bVieyKowKz_+sxVIa-`)g(KFLqxIQT5xemZa(%yj^$F=<3)U
z5$t>LAo;yi0NHQ(iSSmXWm{mc()JzbTRlPoM4r_4zr&`!sPXQRU#Pe4?5Jv6V)|Cm
z<_V0?-#8|}fXm*eH2^qMQ-~ol!yOZtxDR!53~USd+Dyv+bQziXuhgQ`E426HTj|}!
z!`2t5Ug_x<@(VX#ERgi3(s24;Db?ElN}YRrLw<K&Eq`S_1Ndgvz)j$HC+b%)n@%>d
zE0GRv<SH`gH=_bn2lu8sPD6K&*k$d<#o_MF&bJ!a-`-eY{=eTxBn5eW(%N6#L8kCN
zwm@8SR)dYrPLCem8T9@E+lgP?(0Uw~y?42|U?33p5b31VbRtubA~q}=12mt-(x#Pr
z<*ynumiA%~=m~o(4Q5_px5aS1ihiQff!ttD=2FB`j$k*RivfMdo=f>Rm$|JxN>*mJ
zv`fQJeqR&7m#F!|ff6J)?M6S>M5Vuq5BkF>9OUpDVcUsQM?!}r=!Vj-gb%*YX9v7o
zJ;vGvs;G(%_Q*ZH3C#6Phpel5UNt5duW(f}uY4W7Ylk0({vrof2=FDt`)x{aFfoCj
z*icbFhczkaTqY$jVd@_PheVMwob}OdX7k=Q-MA`&y5{>L?eQ7XA7!-YHH8X|hKqOx
z7+g}l*gKnctf}hnq>?jO7j3U8n%VRTK~Y3QX=gudEJog6=H}tD?;q3SArJ9qEHnEm
zmb?#k+k||nDIIJj$3O%bLM!xH_H=1RIGyOScQ1PADA`hmM9RT-`@?R0K@c1nll=V>
z(dtKmuoQ(Ia6vrytu*Fw1!>suFGUiAXGsI*D5G7=$4vg3b6D~w9No=Y{~5}xiy6Ur
z^%H%6Zk?B0N8Ewl6tKlfM6A4J^8sJD%UefMhp;)A?SJzu)}fV>UF6smW|eu(7wfqe
zEvlXgc*P6^P`7)&B<lD{9kP*GWds(#rzz<HeTV3OvUB@7nd<FxS3>tWzyIEQ!<Sx4
ztMT&AWjzl`Z2S-j)mT6uE==pj0S8Pc&mN__w74tRx()r$f&>2_098P$zj*5wlks9`
z@BlO(Rhqxy=~7&nj||{GI@mj=y0^<{NeTWz&Ny#?M!a&#(XyQFH5<0r+;UePl(nKY
zI^<GB@cVzM@*evu=GM&TG}Kz+xnP8qGWfaMi{9?xk2Xv>hlR@J5k2X+kY_pct-;z~
zI~=i7yNwvMU-WfP#78a$Zso<l6(UFqdd~T2I>NyjO;g-=Is^e`_EFl)pAyz6QWp3M
zB#H}Effb7%f{Vmq^|@!4HyG>m478>rq3IkSGxmR;YKhdL;Eej5+gXCkzdEoE(dg`N
zt5FIK^o*4$7FfB3nbSC?jCqIG{^m3lZLV-1a~wyOG0?oaS_;B?+Rg4PMa)M@3^P)v
zDqx}zYda${W<v?!3q{!fD4m+Pe>>UL%6`VKL1J!*^N#N_d4ZJbcs}w*AS3FnWS;js
z+wp&EUswvA?yPjrj02uU{}RjJJxodP?UG_*h#qDidbG6h;OWRpHcpsbeQwUkb~Rzm
z2r&sQ*Q=@=*G&6VD4CC~*WZH4bXMKcxH^2uk1>8U>EmD*8ZD%>rEx8PeI{A&4J|`d
z)Z>8Zv+Zi|Y+vMT4Y6KO(ZgTDdk{}ITQh&qC0uGDNJ`A{fpsUlLPVyyL8_uWgFean
z`DvJ$tYQ}f8w21cr}LzA^F%G#{>}9%?5oh1Ckph&L@xOAlZ#{HD-V(MG6e5*!E)`b
z4ne`{NX0e;9y-}R2E1s}_njbUq#Y^I-r+U#Z@pN!Y|0pB8j{9e;C}jvKhV#<i2i?o
z&47t7*OHKQ;8?_X9LnD~1{m>Tnn3ryw4T~u;Ygt=&s?Q`A$V6(FxR{CwFXM`TCJ^Y
zrTsJ|g|bb|QpOmnS~b1DiYYoaYEh-GsMN6SED`-cyLecE_R#sdI6SG6eZ87<U$#LA
zKh*8$dK@^F_=V$pH@zf7v!?K*gQkD9CgEsbk^b}b(!&oomFWq}_y*rf8U>;(s_p!(
zHs^yGi-TXe#q{(cnZI<k>-<SZD6{$s>f??i$A{2M#Q^A+J#aXWnHLw_d<JClWfN;K
z$hUOFHS=28(MJ|?B&zP+sYLi3dr$oz{F)X+So4VF0A?qul3y{=<b<mI4~Ks+hC?se
z-1FR)31D8PxYpgbmvo8_-E&BZwt%)(mi>lSTIasUXh*|s$0LyOo>Hzd8WjuJ?!yos
z<TMSM(9PcV5aWzf%j5*<lOP#fDRCNqEmHWVhKlLJ77el7Sa)MprGYCgWq*%xC{7#+
z#7zwdRbzO+Tf##{o97Omtvr8m79$&Qg_NmMh#=gdH*KF7t{<xwSdd#GGG8TDyrL>i
zb~4RY>im(!3&1SUN#D$H_EvW8tb;M}H{7MG*`qn*%)^G*{Qbn$*p-gBuc^{#>8A`t
zOywn6tOOwi1uD8$e2vBRKo%JUDcKqa!gn(yguEFuM<%U?IyG=GeF=Y<cUPDl;9!3e
zb^h<sSWF!tAKI`>xbQJ^&9^Pqt8PlVtX}UAHUc!2t!D1!Wl!=rgrOax1l2P`YS!WT
z>`p#$&~X~Jd1CS+NH3K{0noq>MSisAySr?-@)GMNj>>!QGlj{vqXpknWQ!LgP&gD5
z*`eXXH|s{Moim5TqNIO3oY*<vCHnAJ!Tc=y6*TR>-^9W5Q-!7~G7M5r*v7;-e1h66
zFNYTY`|Y=Rt{oU(;Mfl&#8465nPJL<>T#rrm6UfPStBj?GTxcp3`8)|^HhsRPmq`e
zYIWFE$__gxrlo|j7okJu`XR($Ow++?H(hW`s5uVaO~K2*>Z*UgF~^feD!ZoOjZW^n
z1QC9cYuvS0v%i21jt|gmQh96rLAzMiz*-6z)n|X8*K^WD&EvdgvSDzTsJ?6<;&y?+
zS%b?dM{kk3iUmH`q%lf>MO(i191-q2ESE+J`M@KacLk0a$0EgaV#;gUf+q|^04qg@
z;DyN{30Q4XfSZ3hEoi+|8|P8;RE@uVzL}bK*Yp%nCkUi_VUo#2mk1_Ao|xy?U+r{`
z9Q42rT3G+tD0h+h`D>A`ou<fJQaQjN>%Kp`mS;Z9Gmj8^k_eUYf!6z#mXFb*UNS>^
zR@Y^pBDENleHr-o)#DFg1Sh1%wfX0Ng9OUDP7Um#cQ${<&epv|HE$*ZE0zrM?nt4z
zBhHqGm|rwSjQoX0N038W8{rNEJZy$&BRLh4CdgnuTfHAt7?9mlq4Ul#+KN?nM(b@K
zLr~`bE}6J*YI`Z=4kIVPMW|oYX<QsOp<0HY0&9dw#{-<3{ynUu7n_bMnLw%Q=h9c?
z;L=wytxkV?(60-9zqq=OhtPD<vd$2sjI)Ui{FJ7(!6MTL+}~R}YCVS``+?iWxf0b{
zn}t=lu5IlQ6>`5ROS&u<T^=?oA=xhjrM|AeWO~N&sm<hAJ{UJ0>1|1borA~*sIw-D
zjXaV|Q0LJb6)MGsbYPgrjK-ltzljQV@UkHa`t*O$)Eg;$lyVsSEs*J$$dL9qV|OX-
zFyh!;|2&U!Y}c_ENkUqPT;{9AaC=;v_3zK0!&jr52yF5>xI!>iwx-aj3hu#7*cc7r
z!$ZeaEl|L6cNJ~lvxp5{28ouN8~`mg^a?*FtxVkfM7%hRwUd9*qK`(5s#0)Vz)w`^
zg0_DN>~4+c>+(gvuhN^e;wYCCXhIlYTa@7IZSDQK>aa!EcdTKCh_rzlgY4*B5JjJ}
z!xWoXx1RO9mY0?pM~(i*bB@Pm`ZPYbd!w=_)E3OT84}vjfRoQ3rIl&VDInz8G&b*!
zjAp6M`;7ZsoedY|kYWu4Rg-<IuY$*rT7rL}bt~5d?Le5-s+XnQKjL6ZclQWzWi3{@
zJziRoz1+)s@dJ4-synu>hmDobq%-ta7IaM@j~|-?Qq%QtAGG6zmOE%GHpqr$9Qut)
zb?J^NlrM<ygw6~-JrMmRu#@Sz5r&f-O(uksO7e^L+FUjn?^4*0JsS-*36`4AUb=rr
zgVgKc>o_%_oJiNCcViS=NfCs+P;J8R$gMuKKDKlB>FHiE&w3H<F~5k&!4s>p%Ov^T
z$BJ!sFrh|VPU>i%T5z$LwCyI4%Rk->+({NKe8T^=L?x3|JXVBxry4(`nm%O%l+rmY
z`YHPJyAKP{&&)-Kg^ssa_=D8T<Q0EVGr=@ArS?K<IA^}hv|Xe1INlem31tmEK+>j#
z_RR{BxF{T8AhZTGkY1XMjW#uNcYP4I*Ynx4FE87E6bb&YYmJ)kR17P&rr(&6K1l8X
zYS=~!!%XNX7aCJ;{k&Sblwf`!WI=^m;)4RRQNUq=*Yu!+u&x4QeJkR8aH4;-4lctC
ze2T$l9wJ};qUghLRsvr8s)I6wnOKubPRV7!2sk`Kt+J!cXJDLqNr4kU26ZJ!I{9Ak
zYm!v_{P!gbbWK~m$myUJL(_1BJFSpVm_UT<YpNJ6t?v$F^q<rmHIy+#7Wp{_m@2Uh
z3iIeu(&w4*rX^o0qWo|Ak*9wQ9nT3OmR$<S%}J5Hw%LYvmGTwf=t%>Gaaec{Yszh#
zym%uG5^dx0cS8~s=Oub1ZE${#8uql%s(&LaHHgnlCOvryu2grB{e%h(S&n|u?<LE5
zx6kb9&UUi5l1ip^EqC-ChVj$X>@XgpEE@XzN3v<}<hYAzzW6!O);NDM>KgyO!cQF*
z1*U1v^555t0Xt|nbS@HBCyqJ@%h#O~9B;l@e0f6fI(M$)L=2;+43QXSPz>^nW&g%l
z2vjT&OTFk(S8w|LHe(MBqmh_p5pm<@NEAzUX;emU&zKM`6LG<G)5QH*Rpmzjn%7~k
zWoZX&d&_rtrBzax5jcOhPr{}8&CBr`e$O8#>@N}tf|(dxVLo}3^8X|ms)L)>PMj8j
zl6Xr}`AN^<Vk13p_feweuwK6vby(CJw2DyjM3EUM1)Xc-{Gu-0CVs=<>8E{aq!n}q
zuMQRSTv~(<cUA5L?yynh!wdKljiQ5moN+$!BXk_q9<AEun@E2rYzaS75XNb_dhojy
zH7;z=vZLss8Y+Jcf(UO&g6tO!cUy${ov+t5J9VjNIrV}8={P8oaHz4{1bZo0O8LCA
z2~kIiBpf72`A%oERA2bz)O*S+59eaJaRtv45fHW1@UT4BePE5wd66m$zRz<a8+*is
z?C%e;sm#@l?w@~&tP@Obm5jx|taAkG^Zc03b%_w9`p%VpTVU}93}bm!<004L+&AIM
z`ir#<gUt$`BX}tfYsN1OC;J5?#Jb?3nkl?<T+0WK>Ji$?UH5v3n_CK=zC)mimmW_(
z5WcQWPg<nl)@8M-F+v6$<i%am&rd#7-ax-)!N*w=Y4v|$yIqV5Q=eQYxvcQ?V!tJH
zG~sG9@WboqOQGbIhQL3)Zw@lSQ6c@!EQT~oeOc?Ac#cJqOfpZ%oHR5Z!IP!v%;xyK
z?cB#s)NQPq7AMUt6&kj3tD0~gj5X~+E{e1R&3e0OuN}d^b=v&`bnN=<I)va>6g$cP
zwRb*CC;xxI6M$PbqxKP0{d@+nm7>~|YMDDdOuE}HrTzW5qY8DhB*ruq5xbCPxPg&>
z+VK-k(ypU|&qex;*(~?B8pqwn)(e*O>>c}Uo@L*)*%w7!0!$^;^0|gusiUWsz&C2*
zu1>4`C>%v^vG$2PhFAvX8m_T38wG`kgYA%e`{IAG)5zhL)sEILdb95tbu$2s1P^(Z
zylq|LqM^2tK6A|-`9EBAOoUOH$=oNn;G^Ii=%c`K_=xXND1t8u5J|11^kqlk{d0(T
z_LrP@n(z?NufhbG+ruQv%Oy>1EKd~jiAsrVzbZ7rFj}QANJbOELZe89<p&m%lh)6F
z<J5oSPp6FVxS4~J&y?N8U>b0Hz`}?mNn1W!ui+OjH*u+3Q&aEd6v~XH4(pzSE(pnH
z+j2uMbSaPj(AKAV*Q>yv?InvDv4MBEWPh^iNkBJKyeYKP!zh>}xo6&)|N4c3@i7Kr
zx?b`mBS1=%Auk~bu@wI{e2dl+OZ$C?${~M@?1P}?+3xJ@^Cz`hPNvm2q)t5JL9S2o
zM92D<;t5(I-Z%D|KKE~y{E?3nwI7^9>aqAMupi};TJl4!V<mY7@DeX^pww8`ap?Jo
z?XwWHkiUFEAgoJ@1x?|6z44RlP{pbwdcIcm6KUQL9bcxV9L`_=IURtU<vFq&fSG>;
zP9q#=VwMH3#vEqlS(H$4LGM#9ey!dwSC*x*%5<>nBYpOQ7Y*qzU=7}_XgWLRws?m%
znTxg@#P<}o(FL;r3l`FOdNN0034!ba{Kcq0I>%9~h><AKV>Lf}3E7RH1YdtRUDKYo
zPfVuSPE*op-RVmlhx-`q)-=J?JBxoFG8$<6p250sWn1VD_KJ`1SC#*}8qqgrdNE4B
zEqYKte?aAjO}|{|gQV8Ln_ZyorDi~oSmhiyP|&AN9dNVYvMkoThDCYG_WJ1kpRQq6
zkCr|!$`PU97Mc#E!R!W~G#t*(684a?qx&&1emrDtSDrGxaK2U#<}B806{CL`T<B}j
zPcHp{!r)~yGWb=6w#v-eu9A^vpO&W}P(bw>b0wZdOxfbya8>6@WfEnh2BAhrS65sq
z2_t&2(WU0Eue$rhnI`<#+>gx`!8>8c-D8d43o*L8McF&EqzW*7_cxMuGwRq>6oMT)
zGnsU;QdX|5{78mh*3P9Jzp#G>&eTgQCB|-l6oiIP>+MyhRb6D<M!7Ia5<*ltIo(Ud
zQJG|^p8L+&Hmb508yI#aC*AI2+v1Pbk#Tt5%Z%dSNx#%0Mu3hvp*cMM__$*Ps4NJZ
zArg!<y};-~K>uczViSN^PKCe4J`l9bi7C1T^^)NwE_K1hX<dnje0F~nu=MWb`X)0@
z<-n7>OAIl2B~bQA&HvYO6zt)|NhLiMT_;a)==bTvwq!^JSPoQXW}3bbxVo4d2=9WN
zm_gOM#Hy^AUCL>Aguid>knT^k#Xg8>XCwIqA${;}Q1qN)Kpqao$hV#?&j@Kgc{?}P
z-fInY24;I^kz&13r+R<KW$ME=H@@5L=PK_UqEa05$T>9~GfPrMzpAb_!g-b3r!KJS
z8~yqf6=z&;VZl`hAL;x^5DC?yN;F)Lu)bIWYyN1dN2bYR`gqX!Ru{E=7(lYMQZUx9
zd=6qUJQF$}Ksb?;=p-dgRCACs5wL>D+;J$>W*dqsjI5YHi@ks8$dV8Wle}{&@ow?v
zhsTwtXy1Mzr@-t&ln-G@UA9wmGyn$Y2^!~md%RYj^D0{)PZf^%WY4W|dbUh_Y%Fse
ztBhJ?W(f6rZrO9MVc0pFhF49UqHDZ9q*k$Wx9;e9(Nmb290-<Ht?yVg8kggYK;xlV
z*WT$rpU`qPNUnct)on{LZOm<5xbl<zK`SP+STB0CUry%SYVPq)7&+>#Qw3E%icR~o
z{lpA0O6p_`f&f^(`1INdfL-Mb6&%Cz#sIga8_JMv5U6lcTsKmuBUad{(>W0V3>xhh
ztett$91=v~1U*S%vR0~5#6LOqH@)5M{62#!ygbeDv|WD%f4Z}B(fU%UQ-E@{Z6bA^
zm(M&iQK+=>uF-V(Yg1VF%&ro`NFu(DsclppzY|gV9X9cD3Q6=&@gy(S^QvkNy-t0v
zUg!3u3sX%CLA1UTTGk1k!!FDsIzIF<%eXy*)fX@5LMJs0xOx0Bhh21956Mv_p5LU9
zR=@hsbMt?QJAEgD7w>Oqg3zAyr|X39zTQ~c)b--B<vr5*>cO@`#Po^^P6k-bn;m1F
zx-Xs_BG(j+@CfM@7-DHS<T$*vc{IYZ6PXm;?M!O--6AQO@MUpGbbKj_8j>+|zd5LG
zZ`@PIUtt{#1<45J1r;kc!S&<O1~!Uc?b^&AD=vQ@%HsmE!d250OB-WnwqcOn>(zeT
z2+#`q%$}t(sm6rsixtt{<jl9$%=oXO{7^lHoQPvbVJ1e7awTFWk*}wcB&1KwG^RQz
z*bKYkFXOR;;dNj=IXpj}wemIg!{7(QzL$EUH*-u4MR%UrANv`)0PC2)qhBUdyGmfw
z?E`;ydq$ZgF}}ae>2-K7RItQ(nHtS=5x`=>0y#HX$ea50B8YXDYX-B&%fO&lbwV#A
zw}CBt!&u`XT2wLd<&rCgH3fxLZYQ<(7yicz*o#EUh-H;o{I_3bT4FZQ^u23J9uv9I
z9wpYLd{-(^;(hBHU@mXvI=;92hQM>2jcI>{8eQy~oVRKcQF!xtiLaWHLKzs(Of_rO
z*XNmcn#qKn8^hBzTU<mh<p_S$tUy0*y~SQmJ%^HTY<;=Yeuw_{<Cg`QFyRku+7H#t
zwQF$Oc1_4S6)+#wFrAS(-Su`a!HD^m{2V9mYNM?VRolq`)Egm9fw4Wej@CDBrlfzk
zU4?j#;esY}%hNSE*(9}kaJBu0FMN5xFO;>WGfeB}KThZ9B4210XarI7m$nwZoDhx2
zYp`VzKw$G*t@<16`a5nuRA^@!LG$TLnfPx-eP+PT>59XMLxPA~_DOnb)2~~$98&?P
zJtRB=fDX%D(6hV8>yy&=DvwD^)*pXGQGcrQF4-<8L;vbw!-5yMKOG-0fe>t{Z2#i6
zwWg1q2OH*JOZS(Y(PMt?v_%%Hs}7QD48LD(K<^&w{K(xM_vRTS3_oC-@qQ#b;yNZM
zk$ioP5LeyUGr)0X|I%rI&U;Z`u8G0~I;2;QPy?b9cw6oVuiJu;$u$)z3+8`VSGLT=
z4&7uicchOz?%TlHIUD9u-|~lNx<KDV3R8h~@5G!359A`5#9{EM*-gs2GZE7G{`QVU
zT@#N4aYwbV{|?1XSR}XlC}D1}W)X2O@_C3;M*aTxx;4uin=vNr8spfEg>H@HV-kXK
zXb@0zu}3^L$NFdWgH$d0(9eHCwF|w<W0?nqNeGqLs$MSdbPMtEn=(QHH1&sal<Vl+
z;9jV<H$Wkd2CZb5O^>L<<O{4%7;^TmMVL*CP#E7B?@3Jv-Vc}w;R2nD?gag~wCbG$
zpUy>Ow)9ltQtV!DLd0u_wk|GtXt&QeNVW%PavulN`K`{TmFw>6*b9H+B!-Gyhrir2
z)5Mv#>X*W89$Gw}#BY1rKQaP+pOwLeVjeAg7Az8vvs{}kK1O27X8qD*x1k3)+2v+&
zhkBVVa}w~{H7$Ez;irz~rzsj6P)zVimVl6l=-|CKF_z=eK<vOY7-?R34;jyM0bidZ
z?oj_l&n`WqUqBJ|deDE~R!dzGT0C5zxIj{^3eMV8)lU4qKnic#z|?PNxJ@8Z&{Ehc
zg3UVSFQRK!$T>=mpnC)T67W}Yft;(zV7TXlxH2neqb=P?xyOA;EN^;!?OA;0N<4H2
z$=-(q$Yp<;4<Sso1dVU%i|KDUMw$&d(W&^1>m11^gk>wfo;H6X*l*id=6E%0R7>S#
z!`M67a%5i|M|Ff_!gCN8Hs3YbB1CufTR2MqvRC`pzgT23FyS<c;;+KRP`#9y($0;O
zlM1jw9THxQXPDcNU<Cq)XcW^oe%Qg(JaN}1HP~~^<<-4(s!RCMRQ7+(EIavtn4aI&
z+g`by!{y@m75{%Q%{6I9%b2@>o@1kuw|1pZK+YChiCmb3K#ofH@d;C`&T<|q;B>$<
z;xtqnB3ZXx%K!V4zsOdbi&<n*p8Go*LJT64DCW$&5ts$2`3G;Ht~Jpj>Vym`j$8p%
zuQpLaA&ZN+de4E~r_VThksp2^OCxVeg66-OmS;+Tgq?rgh(OkTqb9WEGf=rRw4<9H
zOKQ+N+kQ{^39F4F78<_JB$fnL6shNf;RD>)Xu{B^J%-Z@fr*5n2l_cj2%MW(S2Z)z
zSiZR8BLciJ!c)Tzv(cRPq>g<C54;HDES<Lyy9k-&g`e=&w%AZr2)jXaBUmWa8ybr|
z&GxI!3v_>vz87uilb;r~!SHAGBknLX;GE`ta9e<n$GFH!&UeDw{bIvUKcU3<Ie2Xh
zlSeV+#0uK(8gNzXVQZ%IK7<I6ix#}u8A{5<L35061}O+xet&tut5kj2Tf4uHCOoL=
zQi4`smR<j834e#*9#IlIuQ1=(1<<cuuW^2lurGf_CMJ-FVJyqH6dukAJ1vR0!6TK2
zu5Udl_oH+!s$Pm+v|$HYHjD}iyU?VQ20-;SlH!od7b#i^xdto7PZ>B=74cRSH7Sz&
zjZRbbtS!d%p%KsVWNEDyK7oj(r=>nTs(q&>3ISf}uYkL2^9EmPLmlg$5p1$K*g5)f
zpyhuwu0Mxwoch7(d%wD|7lZdM*RcdjR@+dL7z#hXVO!1~AG7&baPww&3n@nJzUiWN
zUPZH&h%_=oT#+kN_Gg>GGwL8Yl-f{Jj8c)m=_tvQlnmg4mU|v}Bhj_jWqfr}N#d`F
zY5fZym{&tM7vkusP6;mzPGr6w@L=xcY;k{I$PrQvkQr6s11`elZWn$Nzmm0sPKHG=
z`KABE@B;G^`R>c{M%vjSmT0c26_3!zArEX7X0qlF?+-*zciTH@Z2o*^+h<F-e##k$
zUahvEyr;QaGQ-?=U>rE2(pGY{%AwXrN6bSZZ5dw4i>e;KE#~~f;AGhLRYpDPQMP~c
zPT6|^1DKs$s36Hv=LZXKQTW5PI;DjfScHI8JCSiVXFy3TXkq|`4n*HMZFSGW&7QmX
zu(1&}doD;N_#ULOf}f}G(7Y?u_;^D8I|{*gE%v+zi4k|{bV9Z$O$bL1JI5}l*)-Xl
zZAa;*t-QkA*uOedk;cazqkK;HL|}j2_g18ic)M@zN&?<AyA&LiWp{Jh9?F=YH{Gs5
z{(VGiu!F0YKrMZu98)@(v@7!ivc_nyai`1Rb;&GFNN9CZGxZCpbo9m)ktH92L!l_@
zp26tncg+@82gkpaN=`i*=um=V95$XL&ynBFm$y~=Nb}j^FKTR>X2dKsT4;Z2sCsLf
z(u(G>*U6F?P{;golq7fjY7KrQm=mD0B#a9UsnURz-!mB{>}ha$v9at;0jvP+MEwy^
zS<lGGqY)4{ZLkG(;7H&&&Zgdr{`>dfJ+I2FiOo;`@za3=W+{D{F-tMG(_aMkcndTV
z`B7Y0-E|C1xfNUr95&kJW;=f%<oEJU<dFd*tV!d-qHT~&vU>}rJ_M7GQ!kSTVxXru
zuK=@x@;19iYg?y%=;4(gCAW!o+#W7RKSN{)8#)=o+W93;v;}IxieqfP61O*xYrfZR
z5NvNs56$fvyIg#V3!Z=^Vy<_{VKp~2jM#qp==GWjk$gV}wQ#1j3qXI3&T-FcMI!te
z_F2t=`(>0=4b;NG%AeJC4P4sEE%Y=q3`66AZ!1ST88E*ObI*ExtNEC-ta#y6d`LZz
zh&TK1R#@?2NeJSgU>eY6Ax2VNpB6-3+^$BeL76~E6Bpfn6A~T&94<?VUZ(rOIwKW2
zfhbo;O~Kawo76I!h?9StcU&T2cpy|uX#|J6ibzjWt=C|M*jq85{qw?aU&09W^-;qx
z7`BGQ7#5;r^vs-MfZ^RtH%*E4?}=c2X{>iGIp4Lg&5ffn^Z$yESkzYRnvPPQc#oMN
zWW6hixyBuZdkiS(R76|JfHer_WjSbmSDee1-@X0uS=_2#J>-8F#+hA7oauc_c{g`Y
zN(@zy5li2+Y-N549clq5pyc8AL5)%6;Ue6V!n*@1maPgLAZ+_=>LW>i1vEY28h>n<
z8pW+pKYoh1ht;vMRN#fr3_%EaN#gQN^eO*2xtn<Dpx<R7)_j!1?*-~&ueeX<;g-kJ
zF$|@+Rspe<V(WjrY`=1w4)l3<P&PRCy$btWyT`VY*TlEXFhi<A2hUBss=unH3-Tp!
zW%_Ww_M|;?R{%t}+OcC$a52ZeQMz3f;oS9C>Qt$RK_k7vJ@2_tjoJLMdkYjo_@uT@
zL)Ai0XMk{e0_?^X({9q_7`dvS`5sb!^&|XiuuS-DSoeQ-E)#!ns~<eFWli6n!Ama^
zj!a%3+`Hh_#;*4+)^-T*6jOzxmia9oGuI|LI=whU8E|?(M}K07tUtXD6R#y|WFh7o
zR<tp;Ce_{nALWxyHZkcHS;bfK+y<(6uAe+!;4rMAHP0+Z&+DhOQJN|3Y+d3RbGT|)
ze?HA-2?>8zz@LwTvo*aHataYCPjwMkz5YIfOr~Cln{)ub4qMHeRYPlF&>ZW<|5iLO
zNO1mZG%)=0s=xNZkGllf3gjjr;j#?63zcxY`S!+*`?b2&Q5$=zZ!_%Z0q$jjQy#8+
zoBN5)&)yh=33Zo&L~Ctc>gq}fQAL_qJwyueWn6#K%VhkfWx6Aq5Z_!UfAUBu8b)&-
zlCnK`2J`G|^;#!4Brkyr`RT4{$B*-tEONK<n7&1^rJ=iIZ2AdO<;JWY1w9i<{odFm
zWqn*?xlqhAjPL_#MZ;92CdLzSPQs4pQgjEo$_eZ0L^Bo-wTU_qcQ&I1lJ&*|)fZ(v
zkLrJ)=5|f7F3BxRP01uXT<R6Jr{Y|gA2MtYtn>yj%i_hq^?#*7R#0nh<Ro$O)go<N
zb9wKCbRMbu9*QbO$JY07I-8nbu$&S?-8HH<6nyAIqpq`K=b8WcGk(w|@dka1+EfOt
zaKaYUeu%p;gvg$6{`f?@iS|wc=Ao3Kr$>J&Awm`#W0IyCRUh>o%}MNZ@LRWEN>q%R
zLMAlU!B{%Kd<W0-JCRCx=TwS$eV^n~_Uw<)=zY$+H9@p<BA&U*gs18iKsvhZ1(j9E
z23*@P!S*)GnDBmq7<S>NKTC@1=sQIaD_VcIVwIT%Sr`M&)T1r1G@_<O6E)jD?|gqr
zL(2<YK&1iK<ZOUXvrYA(A^2LToM<$n44bL+h?V<(N4a3OXX_RK#f;DJ3(jPZYVz4r
zsl(;kf1d+WkQxK};>|Yn4$S)ZI+0^KTv%zg{;S}6ePB9YrN~DHm{g}W#MqbBI>1HY
zVq4C-i8Zy0pxna-!u@z($F2d7cPoFsgkDo+T2*MQ%Q97<Q!~R@h7^bUq%mHwvTcs;
z+z#=X2iAiznC^Ug-~l;iD_jBxswGeNpe|wS`+G<5=?@@#HRWx!%JC0!a35(7@>|#J
z4QyLZ!j6ciq&PvO$(AjCRY<9G^wsC@h(lo6?OvL74aRGvUQ%tsWcL&Dw+MfmW-?kY
z8I%z1dPvV&JsPfu#B47bHqlvz-bNoII>p6y{I5>hO?$1g>p)T?T9)|TNbPyn;#S$X
zz{hTRK5(Z{t1Z?V_v~nf1z-#^2H)tdbxe+O_5<D0OZVm6$m%V*{5YG<a7%>Thl|Cn
z-jO_8^LDMhS%IDy;gXx%p$&g6YgXr-_CtCAK30<Y4Q#&6rP;Di>xPxSj^irb%N2|Y
z9~94-sU~(BrRDXo`i~J#YO`<rccRwN6^l|M0d1Kp_PTLUsbTd$-QXJIAQRWqwCvso
z<3GNC`X1f|xpzA+FMad)X(E8{EG(xbRR*Rn!U!#npEul*WAE+6A|QVW+r^aGsVq`A
zT-kotQ80|jwQ=5;+FD64<2sP*%jw&f3z&MeyGP)fUtA;kj^hkRcRY~XRf@aRzF0#A
zm1QxXeHrsUrPRs>xOrOH=SFV9g&4}gq`#CQ^e6{%+NW|%+ZiPn>uJY%{U!x4M(%^n
zhyNPF>FG`l*H+2Z&C`Dzdjw3c2#KVxaz0#dR@Y`%%2CheJu8fjdCbnzd3sDzEW*je
zkTUa04eCEdKa&5Ny!;^I0}A!Xi)rw3f3sRJDb!|Tq`3R#_804Vjfn{b2F|Y6WX&G*
z`3$uWX-;XRHf`2E8U}N|Cbum}o<s87)OYk~3_ss<mOzKu2<?ASm%pljN-GZPkOGFR
z)^RPL_0zWp^4yL3u$qx85hnCxuW9{s5;dNdfJ_Z1mtL1)&yGVAkc`aCXZWRqwhQi2
zLjdOULL>6svls!8_@lFz7nA+~3~T^a0DoXPFw1nHoS>r|={zKOjl9$$DEvs?Z|!!3
zGTLeITAhr-iQs=W7Q8E^{ZeBn;)YPMKu3`OnR4*f<WxvnTh$hx$D-b##A54EH($Rx
z!Mx?m+{hA~r>tdOvDxT5qSSbe0u*m@cveEX&s<zcky%-Y<8^jlh#yeb?vYJ8%t?N9
zhV5Clk~)1>Eht5hvKM9RZF)S!Iz`SF@gn--%HZc3WjKH0H(AJ%$(lbm2328&@t#t@
z_8n7=RNvDZqq3O_dgUP7cA{?kd0N>gwotV?7rtg;FPlo1X3^^>G|6T(-1lkD_m5vl
z+E??Ss>yIRKg9$4d$<Z+rv%3b-DJ#K7arlvYUC~DqP!z|ekD3hoEn}|#2OH7h?@kK
zP7xcVJAr?7ii%M>u2&h?(KrMK^`A;^QF-r?etk3{zdok!I=RMSSoch+@myx|Fh?Iq
z=0?Zgs83)Z=82cHM^PaOb^E?O#9>`#HB!_weGxa<wBx4eBw#D9C$a@q2|9>&b4wKe
z!RwQoa8A;{#C*ZaO{?lAkI;M?D2>w@Z%%n_O0a+Qsj=YH$Ff0|GyPM(WFq})62oll
zph1hdw6y!sCnwTxLoNYAcT<}^I7v14J)an;w#aI>9#%EBaa)S65GjF$WokOD?@>N}
z!}9nlu(x24jIfcQuRq;&;02}LO+lYmxoL`WAJrhy))1n7d*ay1N(hOA7iDRFh`AbF
z{&9cM)U$)H?tKSC5Kz+@B@VW&d_XKg>p&`CU9=1xo=FyMl^g-w)%5Ot5p^_=auC#w
zp+bSO*-v|i;X;e)1a_Qn`c&AR`we-rzD%3Z;__X`W~hxKX@%H=bf!akdm+CWg~;P3
z-3^@@$yZk-Pg2%uI8TE4+}6&dSOl8izeax=QJ+KVsokW;kaX(=76N<3s@Md-Ie5iN
zvAy|PPjqrpRNqjA!t6(lDEO1X>)GhJHwceO#CkC}%O!m57Vmek>VR_-?9I=d-P#mO
zM-rteu1F#%bGqM2T&9_9xt6GEaC(NN@mm5`#skjQo{L}c#9*D<2Gge*Ff?7POtgQA
z>-hbPYyDvG-JDQB%J~`2-ooG$!bny5s6oI(FYp}i)959MMqRWo_4z(&jWBmf)jd}{
z_N5g`L)J(ahX2lweq;o%3Grd(P!a|0?a$PD@?eK2;UO4iRU5)GG5i5@2TXlO`6{0<
zN_+>qpNCHht4kL?Yl3$R9iGAYD9V33@$#WhDN<IB!&|QG_u6IGE~+-{y}rp+Xg)fs
zopWT}tIR|c0~=MzSp=)7#~V^#iD{RfqaF4?e@yp>AVB<KwBMU{A_My<3b;9>q3h5y
zq4FwgMlTq{<1FhQmiXGFQW@<s4n3hzzh2caQp9P}gfG2+&eT_DlZBpR7O;Oj=Y#S2
z2|s1*y*=>DXGGB5{V+N1WyAO*hP?vz5hnB@1G@3O{&-d%<zlPQctC1(EgD%`CiK#(
zgn(j*9dvp+N?EkJqq@_G=!cVfNSi0b>`uZa?!1@gMOt`Jxu9nDge@IlD^M@z3fm53
zr5P`&&BLcY#U_%~?RUh3wx)ks&eB5Lynmxva{$*%wNPh#KO}bQ#nLQa9;)R7F~&pd
z%yeJ&k<Wv|&#<3@v$99W*>t*g<iiH|d$>qsfT)ep%j|Sxs#PwvQ>0kX^{D#|WXT?7
z4CBNe%)2zFoob?u=WtZibMzH@L9(>)PfuA&5sDR9KGQ>Vk=y@||5JbYFSELy8J>jg
z^TSwFiOFquw*#+86M3rh+^f2+;;>NnE9!(M(q$Ec;FHEBj=s4FW=C-e2+YkoAOD7^
zuGxJdnT_enr>tjr<24$FTZ40@c3DFI(5kA5dw!pHYn7LYR`n5^Knw;fM3J$Z@jIIJ
zcjL}AUKkIJwQ^6AqGW%k=KPsXgsBU~C%12+bfP#^uELX_kd?mgU@<5ZQNt)P^UA7u
zHfGtTE3cGuG`JF5HI#&#$Ka)`?u^6-y9IdCq$-@m0yl$TWv&CDw)xh5R`AHS37W(L
zqJ%X>+QX4rQg6HFQ^P^K$LPxU77ebu(ao`<Fb$)b+5BsyOv!%%1NV!VBl>xHkU`uO
z<}fMK$`r-PF+1Zt>boI%>lS4q<v>;YzN?eR;;LZJ!<502vqkSFt28xnWcf?3C!jfX
zNyutEEgUJ|;}M}9Wzct9Nx=`STVxovB$FYi+D)Tmu0K4Ev}1mwq1@OaoY;g(54)R+
zaCK&;>x+J9)^2}>S$Fk$1Bm<bS#UBn-v)II^;>SLs=&r)#Ggu<qZ72I_7-3(z{+E;
zxj1JaCj19?^-KI<Rr^_(w?EoY@IME?C31)(a%e`i5<Ao&W%iXOf=z~fbmgu>7a->}
zJ@sWW{gF^{UA0hMEQMGrne-{C2C3`7G>YvYYYw{otbTvcNQ9(2*5JWXPMqldDJAOp
zuP=FhiDb95CYwou+MekYvQBbil70>3jh6nj%Af1)u;{gdnP~4LQA!zVypE`4DFMxi
z9G_+bI-lZJ<}TS6u!d$_{kVUJZSZCaqwFa)wZt{&*DBja@e?RF{6^h#5n@V>y#zrj
zz2Pf)OX`0qPWUqtNZfsj-xpo+ZX6zeA>+lawCT=!4rgRokt;DGu?)8W)#g1hQ?I}{
zgoaFRt)@4XDFf-{uypSNvy4|-`2h>45$L(4s*6|nmtG8b+dpJoKG=Bco}3I$tH@}8
z^X*QFVi<Zd+c#9z^-JH3`2lPPfDR*z8IjlseinaUb{w_vlYoYs{es4$bb22Gq8H9M
zC5cH#Kb<VN;q#N+oiQ!7J^oA;{Mq;8^1eTdjkt}t^(pOSO>%p$myv<IOFmjoi8z5i
zwkVNRo}_OFQTRdMdn(h~#U1ay9F<J(Q28zUXM+YlwX^jr=<e!LHV#X;0|<?~ZD+KR
zIw*htP$9yo0~601P?5?_;?{C#_u@82B4LvHHck1`IvuFrR07ihJyo1MH{jpO$|rxR
zx@;HCRj#O6;(HBs&TgN{fT~y1RE_MQG4VnAMywA{pc7>y&cIBbMQWa(wAYfl?t2rJ
z#HZ6xcnj_(>Fw%&{~d=N+qoYF&LZB(kn?}IS>*mqCL~3_v0A?G>UUJDOKM8Sc|MvH
zLQ=%9@oNPDpQlH6xxK%od6#PxKyp?OOAQM@vQJs<Wi%CNqp~(_=PuT{qK|z6XIy_o
zX34n9I~865oE79q_+8~MV28YAyUS}>Nbs2sGlPhI@orynKOnUYS#j^<^quI%0G@wF
zx|OaUBK)=;G~b{LgO<#F-(vWIZxKZ*bicW>lu^plpsttQgZdbXAHki-Ilw^H)A)Ks
z^V^;Go4SJ3GQnyZFMaZ$9o`kRZkH6omkodV-)Mc=gEnH0kHjGjNhf$vJar&@!J2gP
zZIp$$K;NR3QMOU}h6Mk@ebUZc{VacKA2C><&2C3-TB>j8kKWNMHj5k~2v7SRVCJ)M
z=QeQ`vTZ%B((x6ED?+Q)HTg5*Php0Ohr8VJr%&WyfyziM{c!LF^w}Wrp0p_IBaeBs
z3N9twDknX(?lDf8<~1rUO<f*8!nr=M6UkKz)$NeuTMo^dsbq|)u1Os|JQ;tUz!n<F
z{Q)EO35`?Np9Pa>KgNFiLplzT%(o|wfzHz?*Jip45E0L?e{V`s)@9@qQ)^!)H`JQw
zQDb@KCLqZ7!?Ft%6F<C_ahc3c_tJH}<1Ay@jX}V~X*X7#mlT;~=hD)zJQWUjv9pd;
zrUWUDag{g;1L_<O1-3r$JRN^^F*@-}`M|uPc&!aN6|}X|f<I2HdTxVb;j$8%;`sX+
z6N)$BdPLr-_NDVKj3eG7nSq2PACQN;W*9++kNy|~683b-jX}Yx?WtE^lTXD6f3bK}
z^}^2^vxw7}ixncSKnp#LyvtGUIP^2{%eCdqcXgz;MUdywKHtj-(YJrrw;fXLB6_AU
zAkoh&Fb|kbW@meg8yeSvnT3LwXE=_$%IUrJ$O{%;YsWJ2i5nx7PO#?E@~|%-<b&v$
zdo<lS6}{dIpu4W)9n5E7+PPj`55Yz4Ywv#)_37$5I`<*Hq7qOS>nXa+eJ+uvPIeZ+
z8HAHgOFZ1H15Oo{r<Q+vmqAI7Qzd;2dVF+-<7Csb>{I`)2itNx`V&h(xr?|*s#$CR
zr>y$1*X3f9cM2&!{LJK8op`lo0fGv;*}C&+8u*Uw|5;sJ(E5%)wgs^LQ5sH5tk?>Y
zN&YTQCz94?uinQVJt54tHABZ8#xf<wCL5=RtKgPfJMpyAd+~o+0of%Qm*9b<j&cPW
z?j;_bs_+f7*^#+fS&?8PVf>t0TjIF3@}r8rCuXXwY=)^Tix1l5$c!)nB9|EKfZ$l6
z=e}#3Tv=7c%AokJLX6U#1B>x^)If~p^_*`;?oW}2WBoQ#x6p~j-mv4ayW>=N;@$6&
z%*`q|1A=x*!+w7QfXJS~`y%9>uwJQ2BB6*`Lz)MuqVGyqu;!&YtRdi0oJIWonl)PK
z)Z`xpx2a6mNNAfg{?g&|{ErtG9amq*e1FIYS4FiIJMK$sI)XOJKkLLqF=o%h^n|kn
zaFL%;ZUOzM(0xf_x>#Z5-gBcgh+w<u$aORn;$WuhWLST?wjwMU8|L;B1D8~30A_Wy
zOwZ8Swm2iQp^62D-w5N!FFp$r-KeB0t;)pM(CkR+)>rxNVR>%JG8cgFD#TYapdN@3
z-_%ak_Rw<<&aMx_8W`A#_W=Qs-|SN(YbDFCthjNQe!>ZcTB>DLMcD`OtonEEaLM!+
z)w0yq@LYd}sjg^7%lWcDV}3rv5a((~H=UB?FR|-4>Zh}UX#xOT{owI_!{|OF6JaoE
za{9aXUL?FBOBL`gm_JRCA-o;fdGBhJgiM~l6ZJM%HJ-coSC`wcem<)j4^VBVrlo{q
zS1d^AUOWEW7;jeqOYdvms`+8MSdd`jvW%VkT%>>YC)_9qJ#m!L7e60?n>Lby=hV)p
zelgIaeYqVBfbpp+(AdIj0%Tq(+S$T%BqA+y!JSOjA7LMWCYXD?TMD}3j+LFkD7Fcl
z$Ouj;j$XExYmFZ9cP};N@b+COd;>jRwPQZu!5{oXaGC@<k$7G`^Z*qJ$8b^@M<)bb
zUwD6qU}0_hR8zkE?asrZr8tbuj;w9!a03P|K)J0DX;rESO|4zi+*#FE67DRShPS+x
zA%;(&8p}4d?7kzDWZ>~-E<*YtK2@2}O5Z1z_57M3<ck;Wi=F-Ik=R+IyF1H~e}kCQ
zX&|se1Xhn5He#v;zqQE|?9rA#85FLlN*900<orN1cO&vLY*-S5_EX`UC7!cp_ZD<K
z)z6p%FLO9}yyo<gWJ4M2c)27e&HI7b)8`j>B{X@Mc>k#OEw;Hol_9U8y5n^W4>Vlx
zX=$*2VeXLaF<UgI*kp>noUOkkSJ3hILtKH~#;J9XK?ZiW^A`H_I{h&-7sR!G`oMq1
zf`~XdUBPYus@P8dY?4$o5k%(!U{NRJ#OT^Yk0;oDpZ2Efp=eq`!&?!XB$(_ee|sq0
zwuhB+ny4v^+|v|a*-xqrH_i0zmZ$qEO9Y=!rFR>HM&?EI`g>uthKQ;VfL5e`qsMZG
z4M%djrh}|#hR!70`S8Y2fWIdm_R@d02+NJIPk)B)lkN(Fj+&d)&yMFGBqPs~!g4_u
z8NT_o#tvoc2{l>o#PnN+7p%)hb8YOXGd6TMs5_?h?(2$78D#cQL_|wyei`jDO#u2=
zFb7K4efr$H_$B2z7e+W$3W%P7XvF3g6Iv5>M)%3y!TuxH_tV58)?5*p((-?v=V9wI
zY{KqTP2r_+Z`8a~CX+CBeP1v?KbXo-$&uWB38V4^G*0YZc~d-WRKVk{iS2qPo<v$$
z1RkC$#CN5}I&1J&-9)5VARrFAlC8DZt;tTC_^k%-v+Cn#qUzmfLw}A`Zlh)`at%AV
zi^?-2f~V)$XpqWA;d`%Tb5DOT(AqVGX9)n^t4`uof8jFERNPe6-?>CP@qx}}Ym}OZ
zmyWgCfi+3lQ8(=+PAUO%@8RQ6(z$xAeRs?MdBbU&HW=|yO^WXgw7+lRFLR$4gaV73
z9R+wi;_sN+`TOB<sn)oeKMIUQb4l~)+6k%b;Dq*7KzH>GY508WT(p0&^XJEh^=bMQ
zsIp`3)7$}*N-$gtke@^~BXplKv$udr!tBdDYM!xdga*fQcA=aPNX&wM5%>vv+DTmq
za)>sPDmj;;5tM<Z0<xbC*y<!v)^5vNFb@b=cMm`Qc<a`L3~y+a)u}^{FDbe)`mIb}
zl>I2Z{>|DEJW{grO5=Y+;&4Ypuo5qYOm7O)0vX(CI?F-8cpsBl6e@e`(J&Xg@&^jp
zTp&eu8^3imzs9OlV?&;q7!r{oV%pR(?3)ElqzfAz41zBT1WuSA(df4PO&x>k&?!9v
z_oD+gLyxtO6O0VdBf=io+>2GwvfP86NoSZZM6KRtZ|V~hd3t{nM=%d3@baRSkk0Rb
z3=bW#*vs`fO{Z4$@R&)3-%4ljz6+|%d1Q^n-aGhaz<jbUTA!=+!%OtrwuBL@nctP3
z^ArlycTq|!WjpOF^re$*Ig9TdPob-$CNA$*onntL7o~r9chP;V<W5E0i<yA|%k(q0
zFlI~2KKeFP3;=(#DdH>@c1;XrTG@Z%9c8t1BE}>|-N5<=Htt%WNO=km5XFEkta*R(
z(ya-yPnmg)G4GNiKMNgh?+-f2O}t}BYg4ke1;)^RdCQ5^?M@Ya9cC5Kv}-~F9M0nl
zTH4cQc;hgWf*X<{tN0iT2)eMGFEja=o>?3qkXyv#$`OC?79Wnoc;|^}wg5H`Z7u$n
zl?9kj>O0b7y&10C3HukmBA#E=c7C4<SJVU$)nFVY>X`g3qn3gt23(KAp}5;5&l3(H
zz7aq*cN~pnG6+$_i*9?9E-||hA5E*j?NM^*v)1YJS){IXu{kydseM2K%}Op~_{;@L
zSS#x6Y}$WE)=R)6^6Itz{Qnm^E5+39&CXavWv}x@!AR?oQccwpBZB%n-(EJ)#f6nR
zFc|{zg-=}L>lI2xZCZD*#5f`FLzXn0gPE^{{{^B-U(W^AQqUSPglNgw2ht2cV-z69
zg|~Dq(dDv-^>jOB6*?TU5>d0;g68Jis}xacEKGmKeeQX>@XtI0ZEZ2WW0P|Zk%Fh`
zgli0(jlV;%mVcB5GULjH2m1lA+;m7sks>>EkdJ*}4E<{M5nubt-0uh#<nVUzK6MqO
z>E~y8twXCF3~LgH)+G1Wj3&X?M_KQLF;SO3slDj?e}hLb;hsju8V)uNuhh~b|C$BW
zaPWV1aq+)DDb4UE?@b&J(hnDqp+q-Wb7b{7d$KzDF{}4tR`?@w>Zf`fdS);<<)2PG
zBtTlwsG4^G_cVg<#AB^`5#BmnO8pu<vB2eOS;Tl#mTd;s9AMQv6{0bg3FW-tzGPRm
zll-VcWXih5`@)%c4Z5M3EsS(WUpD$3nFW8N;c20uD;MGAqapmq2?|;oa_SN4CoEix
zga3~f?Ra3~s(_>DUF<^yd$Z(Ubsp$py4Fy7p!TK67qD@=kU^gMMG~<her*wS%zZsq
zvNMl6RJsk_Y*eFaNmoO$(PipG!9ZyhbodGeQdRaV(zdBQnC^bccDNfyLF*H<G=qQk
zIL0g*M#36-8BAJ2qvQdChKBv>N~W9}?f2>0Fe>=7=@qDgvO6$c3)MBK2f~<7La2Hu
zL#V~Lqo!4pe&67gAvE1+x2%(b#90{-BR6_5^^S7Xk}x-wK&<DZJN}MhV|Y?oWbPas
zN>)2*Q?cw1{`l5iBpyqgcyr%0;i!LT$*~qOpbr7Yn%UEY*_(73k+O=MuI(%n*d40V
z=3wxhQVKBrgm-y1SeqWWk$i{aqWzK7Sq#kBLiaw6*GlHL03zDMVt@tfU_AlqU9SV6
zsgNqi^TdT%Xi2P@FP?2T!*gcz(*TVWd(3Rz^?`^xHy{68m>muJXc_w1bhm%1cL}d6
znGFM2O8!-k3}kw2I=o4<K7C7l!*PRW#VdnvF#gJPAiNG1_;xl5<7BW@hPI*QH;NGZ
zJpO51dOTxGG~E&i4STx0#cNE$KoKEKvThkmkS>C38?pNe`-FZQ8q-=@Y4ak9*o|ux
z;RmcM(&f5toL%wiEETH&AUJ>8iX4yo{sb$PHY{6t3jOc>1h7i8Mx3w4UP|*M=ExZK
z68N-bP*|^%!meGLnw%Uau~5}Q%?D_bzKsQ>8`Q_%m;b32j2-KTZ`(GJVivPh2W%Kk
zY)2!u3%5TI#X(@+Qdt$`&~UEFr8G7}0u>ClDt$&>e6RY~nvK|sA!vUEF!D6qrRFK1
zH8Ykfpd1qd$tFfj14*DesWr@_4%AvC;kjdvIkLthgth}c$Uhdj;#;95u96ik*VGFo
z$zx?xUt(!>F5dhMMz@>G!yq=P$aqV;P~obbm*^sT3)fO>$RxPSU`oRB*cObQ;w82q
zXp!9lm)RXy*38t#;wFEwXdG3%5RASB3Tdl+5vOT>zfex(tvGch5x3x39YFiWHcRx)
zf6}-SZHU>fHxy*%+0@ogR9TTwSYis?e%NFB!vAzbw|gB#yn8_my!p@cuPQ?rHc8H<
z0HF<Bb9wm?v2?GKGbXFFc{Qw%1c#z0KVm8=KKOvqxfFVQstbQ?NYks;IzUhp$;p1a
z)f`!T8ukz&m!ZgUPKVy(@YH5cPB8S>5Z~*k2pMNx2hkzAxI-Zz1qkE5u=CZUt&qoL
z4xo|65lz};a*&*^*W=kFE9=)@N%H7624OeN|6KZdFw8E)>(|zbnvb@dNzbncr3|tZ
zkmK)-IRK1mAgzDm#~(qKk<C_zoJ-u7ES5roc93kHLv*0Qwnk&y9VZ=|9oy*Gwr&4G
z$F^<T9dvA)9ozQnyWZdp-mO8cRW+|cednCLd%W$$nx4(2?F$@kWTZrI-MvKq+pV|9
zYUOei5Bxz5EF&H%viBzH5XdoyY&xD3G?lsHz5KF3w>C@;UPkKY-98xf>|5*VeS}pM
z>!i>6#sjmF>Q6w0@2wPAAtUXsh;ft92lQ~A%?ws6_2?!0eeZkjl|Kz$NAZ#Ijb%od
z1i}&ttQN2q^pXuwr0N7-=Qy3LPG5<+r;{f0(FLv88dP~1go6TnHBs9B@?TKP=SEv=
z%;_>SS|#l$o<`hz;09irG3xtB#}1LwZk5-4(S#dPoG*)FULpV^<V!-)SQj&g`mV9a
z10S9smIyx~1ZVlixa%gd57v&OS*wyvi<`CN`F<uCDlk<Vm0Z8Jy`?w!cjWQbA7CC#
zUa;u?T;<xVgJSx67fnz`C8~b*21Q)pzn{0^wSH%Y|CjWQ>O*1vF-&#HHT#T&uP%yI
z*!SzLSr#bS7zqRd!-*4SV~WCNFI*NeL&Bw}@3hpY#yr)OkL84U+1z(~34P^<Ws9Zp
z)-reXl|z`5aR>KSket&<%-^wiMj3pCQa?Qq=3V_~>}tYhXKSM`i0~TB5z#fQ7WW)$
z(U8YpGa6;OR@3-(MG2l{!ViKmKBJXCAuvxI7hWDb6k`C6edbBZwC`C1qcVp}4Us%Z
z_^(VIcPocdw=pHQsDzg7m4mPB)@9#M$JEm#;B$BP7LQ@*R<o$2xw~>>GZ?2+3O+^a
zY|I8r)5_XR&Dr2(Ys@4x=t7Q<KYirzrnN0B<GL`=paq4r6_0cO?1%Y&LmU2Tz?tJl
zu*=51r1A&qOxxd}hR~@Dp=gU?vm!w2$q}vFyh%b@DmO!}Wo5KE?j|r1(ObtE=g+P9
zr^2u*bPN;_i(RwB#xT`+JwT`}SfKYGgJ*tiH*Wlj_bEeQ?vF3GMz2uX$fcs}_``rC
z)`(Iah5Fe8W3(BhM6ZrUVZ<NSd1_%ZwjRdiTTciG9gsCz#{1jvKux7t$=TloLKs>n
zsS&*-77;=Aj3fU1qyIu_67FHWh&ISUS2-X+s<ag+iw}+Aifnwfp#EV^gK*iE+Jf#h
zeqpgK_CbTq;+*z!fqgT|&FxW`dZIxb=Nl@gZ6ny+j<Sz?|APGQu~Ro&oK!z^uRbEa
zEz|?8e<27TBbsY7lk8u982G}i{|(U3-nO#>m_0YS+Cw2?V!PRF$6S>BM_7S^piU9N
z&9i|ywH*PEdxl@50*%af4e6d2rq4y<>4<fZEswv@ih{6_p@}T&MBGo-R;~?`WPko%
zprCLMq#M{!{~grfYgmZHt2(|X0>bgx&eI3<p(OVlOXD8Q<vjG9n~WN?F8R8UI!##A
z)yl%iTa2NQtyielg}K8X2LH)J45U2Gt(Q0-hhM_c=xj4kwK$WeufdclrL30xLj3l~
z-!UAcVjvyyw}kv|eIaCR_o!uN%9&nKj$NkC>{>dMlrRnC$Z2Iyq@T{?RAXlt#V-~>
zJnnjzk(MMvdXR`tTQ8cE+<d9<?mNI;KVG0T8P*T`m}7*XGIFe|lQ?4aHap|me{`L@
zj8q6a;jWNJ8xo#*Xg?7ySb4nDC_Z10Qi+8=Yr5y7B+|x;s41X2hZQ9+t+B_Ml3Q9E
zO`37qfl9ewahuW9wYg7H8(r2+B}@gJu-qJ>MN@mPXVh7Zpo-os23B-%Kn|uDJyAXC
z&SL1?j7SOTx^?OxA*8~=&i7uil+PPG1vZd~8`=?_1N5RZ^42eYpR1-1{Tz&HX0e2q
zX+O(Mw{E@R?vg~>m=|$azjOT6LBe{4`xiA%gM!w48`W|~grg!wc22T_Mq~)k1``oe
zUCm{nVlygaby-K)G7C~LRn-Xl@C$PAng*{nBJLvRmyhX)EeT^f>`M3iP#j^`CXZcS
zGGFkI$sM^3L_g^7+HYb9m81iia=^kbSn+rx7iu<SAOUsjdsFRVYK~V_sZZTbG_=~G
zS%aNTyl7h=JT8XbmT-Y7@G}O)qLWk@CI4DGk;U!}p=zhdcNH~WS!xfWojBh+TPW6a
za&ybo%|^ykY}RHftqbtGnGiS7v{$f-1)dxbwBfq{$;w<8rMNvjU^GGLa@!XgG!kO#
zE*?p<yRVc@g{2|D#>zN+ZBr_d(U5x%akQsS4>->}CH1~cv&ul``dI}`?dM=_yeoUT
z%f*7*6?PFdYK!BRoiQat+B9|jBOO@YO`g5f+7^51g5r2gZfAZW`*KJ{*fB=*?N0%B
z0=7nqa={QU0lF>ggpCq3_^-+gp>0s0{T1pSPa!CeMZOVQEcBos!WzqlK9+W+bRr~c
zWmp=*MVkwy$>K}`Q3Jp;CF`EFP^sQRg1Oz8*gl&*2a3K!U<AQ*=*eF@uRJe8EKC`a
z!Z;m)KSR6=FXgA}GJGRr#eZEiG?<|V43AFl58Ki%K+x|k0>P*b*1hJIL{nnwgtqfr
zogw=0fBd+bxRo{`Ul^`5u{2b@pkqkpih@7+?K}Kyzv?%)Gy)oso5=I=P<}5rq5WN)
z_B&deGwBAs59g2G;K_B{zpNyru%Q&@!aSs_;RFtAyEGPZlZ-9drYoxsKX>rWqE8Uq
z>&?;dMv_>Yn}6FL#D9tPXp{Ra!~~MU$df}vJrk5XH8<MZcn(-nKVOS*a$}7kp+HLN
zixSckBA#3DsH%ViPfiVx=F<YOv$&xd1Ucmijc=amghtoM&bauT77OHXI1+GP+1)!c
z<X}peF0}7Bo-8%9y)I1ZW6BG{Gd|W3AN3a2FmIr9;rxF|l9xW)71uwS*VL0lsiAPh
z=uMr_9N(+NIW$>$D7Pap;b<Ill+OlVe(*p=z8;#)Rj3UBCiR6p%;pFhV-eq8<~d4+
z;fhlr^<1N&6Y7U-nWZzN-?^1%Zhjx2xmFmfC3l7KFj|w2q|UN7^0oRNO4b^%i{Oew
zmNs?_k*IB9`rodmTl1;{3@<no3FP`-X;YbrC1SHKRka4?MY`Q6(ERL>{bvPm{bXCs
zW^Tc~+oP)h%dLY)6oY9_kk<>NTrk;DOy|g$eutb~dRYK?qE>u4N=uamT!i1KQ{oR_
z@O8G40Ve8T3~59uYzElqKqH#E09EJyrSdCAbI^U&HLSa~Fc!ti73j)EMK!24Sjn(k
zr6=m*Bxh(iS569*M_urVH`LB(YZ`}Qi?Qe><fT_&ex!2JoEy9(>D3*!pZJeUH<XmO
zV9OK;Ve_R|uCYCYO`l|H*}>w$nLABQi&?%#@d}S0ayMB&EFBiL^s%a|%m_%DmbwW%
zts!K?+-S<<ET7Fmu8LlW@`<`)0sWs_=&}6e<U|@jrHw?VI?ggi&5xOC!6Nz^mYzpv
z2S+UcTzoQDv+xKs<$~j|o5g6hwj+@Dxo(GT$LmB*(I8x>Z1K;x(L<^5TpQvc+38wJ
zv@uinVwH%UQ^&`@<GxU-RLwDmbPbeRBzYf<7uku@nW<RzbQu~#t)#^19}yf^YZ1KD
zYSlR>4;x^DBg%hZ>>vOLfu9~o8EpNBj!j^|Q~2b>pj8v(VW@b!82eqAV0SNiYtUht
z1Jh6AX#|U^Af8$o(gwTtZ@$vu+*+sIDm@Ff$?EOAP7br^o29<uEm>0i>Q3X6Ni^F*
zB>kqvDDpqS$9c!CVz`4}`bC0Rs>7`3Z4EU?6ZDBy>czfwj2A$5m1cabe<$^sOs5zH
zTz%<jlG&s)hmi#l0?@X6`+m5RY1ub`AL{%Or}g0vAe8UX$o$a3Ts3^9NCHwe&9$%f
z$uCUd|1z4PamxPUz8eHFGV(~?I&Wmqu13qBCEP<h2?^5L_L=nhq21nwU24|Nic(E<
zGt5*Ef1~CWMXDS~m@)=W^*3ZGmvrk701NY-kf=FMFlB8yeeGUWd=D2&zYmA>S=4N=
zD;!WLEuo7LP*sc4szzxP&}(mvNw+VtkaBktsaw0Id)|T>%)|NE!PXEG<RoYe6yLR^
zK+EWkw_rg#M&gl7@G^wUT!`|Qg#dq1akj{YHhYfF4z_}c8xFd)#&}G4BfUugmf|;D
zhirY4Y0(Z%%#0Q)*nHXOXV=wr7>|e3Goo)3+FHdam+DTQ#_W#DTm|*a6*hj-18(0t
zO3%S?VmA8o!aC34L=ZSdsTu>RjBGb68Cg^im;D>ERud6&a5VYmK->AkG@TQ5;zvi`
zglnHK2x<HsZ7D)yuiS65pes`VNLxJLc#sCY<X`iKijD%VsUTQ%QPbGyC}oj+oKC#n
zZ*Y$?ev7KO%yT;V4e=zfo;LV?s}lCBvL$)iZT)$_&R!><kmbhY`rI8<e>S8HXPZHU
z>N<t7&RL$oxT|UtW;`Y>$OKbsTFgxJE3Q3kYsA-r#D-*hJ?vk73;*B%{1RCB%a8k(
zL&oJ?+oxv1rEI`qxeVLL?s;0BFaPMZkIS<3kj-(^LFAFARnIjTNAQVmej_G(VzY2M
zmPm%ohC{nPiU;>M`E5bUTl{S2mC@cY%=nco-qPkUS826Qzb}kT-Fr?no)h4c)?e;Z
zSAEm`NI4TA(A#|-CzU4);QY8U)hqB4zAjg|^`n&L-I|HX5K2O+TK?<f6cl=Ko2_mh
zdZm$a?BYG^uBO|Dk&K`HX;zb!Tf%chfOd@w@~|H0kynmQA%usFu9l$!|Dnw+9iO3p
z!M*B4>daDnvYXY0<%IS|Peci+wcei`eeZG9;Wxu9V*Yv(d`Ex`P)H3MZ3&`vT(NGr
zawQ;5-=Aoi?9@hw1&0&bc#Y`=d;iXN>ZTAU*6Z&G(BaTEUDFI~mi#n-1pB)H$cyO1
zMza|k%=x#Wmvt9dpPguK-Z>PdQ1xN|0iflO@F=-J>^ydMTpP`@fB4wn@Uoh6v;g1L
zll>9Ou5cm}CDDxmbClJKq*4Ur)@~3#wDrG8Ns|@scBp2V0jK3TFPQMrT$Z}97UZj*
ztn7_q{<=8q*ZMR&eF)GZA<_!-K>IQ(3;j9Q%%*dV0EGi3Ymr=YBVmfQdjb|FA{(?4
zMpdC}f>Kn@-4^7X8`3wTel62)+gc+zX^Y2IITxrkA5WivFrMHs(KU*BH+N6gcFEb+
z+ZafZpAXn<n>#E=+x`@u65A!|5wvDxg!Bf)Q$3$l*<gEWQT%ghJc*5cc?mr$Fo_oS
zyXN4U+)J4(1^e!P^}#83xKAOD1a-d?D=a7zAq|3b%`mE`m)olZ<8>~*zDefc6#sK9
z_{f7;-ntgptC+xT;qa`3dip#pbiOy2p7r6{xdlfayuWMDz5%<JzmDWu=H#P9-)#ua
z{JG1pJgAIFxguWKs>rsWq+V~;ylURQtK;)3VEc|nD<I+1vWV1*1Zq1+5?1*lIuXp2
zPxzZ>Lc<7cUFSq2VZaTe99$2ul))>I21j>-n_>Y%gCoeDluMx!NZsJG(+&4G;uoG<
z{ox=P(A?D7?-2_mahvT?(~IdEBgAAsG{qTp__cy>#<IK$c;4Y2kvy~`op`aH0C{!`
zSZ{-!#$ZVE@^X>*N)e_;UpYS#uod&dKF_L<i*=h)=VGEc7c5+=JExyzD20f6an@t%
z_rieMeBUNywsU^-eyITsJ@Jml-Odly{n{cJjlJDJ*w1T3lX2*6V*6XuyTg{^mS_ZO
z-xKf%#t$W74)NS;jww`1b{2H+$+~Uj3A^iBhb;2Tue@Qg=gn2Qt@byHs^?j*x)-GB
zJ^v0jHb!0KyNrS0F_Q>&*bKI31tUoN`T@YXK$qp9UQ?p+m3y@<#Pg$MVfm4>=pCah
z%LVRK7SkG^H(TF^JbOw^Z?;aoEFj;SeEt(gy+YTFcvOL8Tj*ML2Rb8i&~$F9b+0W&
zlg|mU$855}wx!J1FGoH0R}Kn<W2&rmJK-ONcwRi71vmCQSDM;{o{pgi7>3P@@OnV(
z6EtA0l_4I*Cez5*smRy1B7@4z*3uNEp+Z`-E$okh!@$ypg!_e;6Mv!iv<A$9QSG8$
z?p{9{=&fLLW!}B&`oi<@D&8Ir8Rd|NtG-cTlSv*EB>K7}yEY$=!^#<3GX;e{uCbDe
zE0;g|wT#rGqscXs=SgnLzZvLXyWfEjPceMrIbAEV>k$(Z1f1i`c$b$t9ZVw7ipwm~
zQ3jteYezJ1A3J+m{6=xcDK<HIoQaG{B)ur+)J_eF1cy1HQ^6AS=aB5-iQ?%<7<_>}
zf%C^zP0njz50&U`&ucMB@$q4vfSrv|fq;SoZa!W27po(F)W^;(nZcTMawo8r%@>yw
zB*sMT2=2OiZQRIyIUR(IVPbqvzczYICL!DAs=ua(KR?iN7FSYn6z~pZViVv7uoCd`
zKU8~i?H{S&b=To|<G?ou=8-1JfsNaK=;~^@M6tuI&!U2vOhx=5t+#$br(znpKh3_#
zDhSJ}oX@Mpt_#(C6GLZ-9|YRP#?k7?Qw@1FhbT!*3)YKLgGldMp%%V_jM`t2XB~Yq
zF=A2V%?R%2kL{7T<}C~D{c84iqq)*>iElxoVvEmJBCDtuAjIwza!|8rgk-Mo8*kJW
z#Sb#JM4d>edB>}PyYebjmBf}8S`G(q0ymG>l{-6WrJ7}giTzda9UF)=*pFHF*6I3n
z3nDQhkepmH>&!D0T{%m3wOoUqb2b_==j{%?R5h-xf+%N;d5T=KzF~Yo6NJ9~eT<oU
z;&%owe~PUDj|di9YxHl2LRe=$*37##Vcx*<E2`svL@eHPJ#YC$Fb%EKY^lBH{G7zQ
zmJ6#M{SKdZ67`YWuRDOWmhLQvJ#+OS3*o_g?sEXoLVz^7KW_B>HEzk7Q`y;HcboXA
zwkb0BH=RNG+^f2tfI%Aj>S|^1^*k^=3=tyWJ-%0_jE;b6cA0kd-l?9b6EN*Fgk~^J
zOX_=JnX!48i?jl_{&SOGrQ{vtv5k*)tsI8Ks~9NNgp*f7&;n}FX(-!ZL9yIQLDaTZ
z2PP^_%HzA2CK=(*+5pqVL+=8Ry$r+&76vWGh(X#rc*Mqr99-Vf7~BVvdI=K@SuVnp
ziVa(eoB6uB6HkvHWAFqz=^2}H2`#w2COsn8CbI>fQh78C@b1(V%7u}etmA4i11k0*
zGHGpZw6Lw$9YFeLs#6Q#3FI_4p~tU<9#+TE4?t%RgV;<a^<O7Sn3~{E7=oO+W-aqD
zSBw47`qRd;s2sRM$|IcLZ~j_a&v?m`1J#t<NarYtHB+B*b}?lp^;Cy~j5x>YBUeN=
zc##V?RT5P+_z90#!!$7(tbx(hTds?X_|1yfBeh0y4Vb>g4;{6`C4I}5j%gEzDL&C6
zPb~H7Z;BSZIBzrYe~ok6KL{b7ej6D&KvTG-4PDHE!sQ9$HI2*3Tb(C83|Z<K@HYKL
z*c?7}dahQe9UA)W54sFNNxf_csHl|<SHQxsr>pDe{I_PNkj-5A{Mv5U+B{nR@>s1k
zNi7p;HeeFjp}D$rWAsRy=XfD5y~$oWj^+Jb>t;GsxSXa95AH)2_`M~5vwC>MgSTYV
zIGFB9vt%FFk4ZOdXK%MZB|Uv?PUF5Z$y&u$=`E|{*kF3wu~5AmciwxwX5nRsAqdWD
z^^lsf-G3f;_i)q4zzeEfHemai2llTdHMZ162Y4ne)FyQ38UZD#J1D=&5LTeF{kgU|
zRFpIwwW+!J{C-K8Jj;ZwrgrFf`{0gcmKDkqx;MN>J@JM5;+i2UsC~`Mugv;0GK?6#
z1?P(_H>8vDuP7;j4eJoTU2*m4o}bZ~fFnsd^GtQWh<(RwmjB+JKI%&imaxWN@84W>
z0|2KjFcE8ys~_sS`ss+eUy%8rYj-{Qfg_|RDD|KTMXjXny7deEi)>Q~@fIQ<D1`ZK
zE&jh@(-Hw{pEhGE>Kf;P9i?fws&WZ`f|%Odair2K(9V4&Uj4<&yDi+mm)D8XGeaC8
zO-fd2#u)DTxd%H&VQtM@U9*mbD2P8Tft6xYv))(!DviG*e<ifSg3qlyxn%F<o`ngj
zr^mtk1gc=USoKx4O`J_B-5xpT&pmQ6GE%JgikF?n*gORPRTfYjV+Kb<tZ1NFG@W7~
z4CJ8dzm35a?vE78Rw7v9S@p6IRF|HRbg~*S+ozxv+!6<sZQGn77pHr-o_>u~0c_k8
zH}`M$%p()AE2Q-J5`#pvSQFy#o9qkCvp4MS^R%$aq<t=!CdreH0!=@Rf<bX#&oJ@u
zudSU-V&r_QPN%WRyI#Q72cT$=Q)b}UwJ;7iDcIn1vq^941aYK)r1o3v|II*R%!+v$
zj6IiEv1V4Y^$`$R49qbDuY`l60=5(*>25C$hypmtWQN2ftJqk};8V-O|H0}Ff|2X@
zpj{L{q{-BgN)x38(w&MH8f`K8wXuVurF^3*g@x#&ZKFzm{GE1zKU~p|wGUzLs-LNX
ztlT{`G<6LNU2+;9Bgv-K5K@lasr&pDclGJ?|LQS70VT^NuHGWomi^+S3K}K^7YuR}
zAex%#JE~;_vc@{g)47tqgUZ)-vIE~uQ}M#p7LxlXdZDysMIimO&X>_|z#TLRg`g|O
zn8CH$ugUE+5~D=+b4=#^$tw4Qph8)!zro`h7&B%%jAWB2llC5C3j~{YVwMWr!%Adi
zp_Cxdqf)3t7>WIAPd|L6q8&jiNo9F0K`{gxm-{ZjZqgEmmZrCU8Ewe^7*lzVL#r)!
zNG9atzx(wj(ed^|=kj#J<=5OP87*Ne=W~yoIihWKVXl<j;5F1ZfF+8qc4z%Na!9zS
zuP13IugY!OXui~Nl7D!TGe|DbNBF*Z(;^h0zI#hjx(c0&KrK&3sVi$WPkR+|TbRMn
zdUA@?#QMdrEuYk3--NUDC~V+&Fw*Et`<>tBAYdjz`EjZG%iPq=GYJ0%{;b0^ecdX@
zcJr4De+GiSAd^P)cF~byGu02RgYVo^-GyL&mATCm9P#kNUZ@XDF3j8``9qIcr?TGw
zyINaaYIL14dvk>%R%tj$m$9>ihnZhhv$#oi??qiXpB*eePXErcQEpB4K-!>61jS>P
zdY<1pv}T(r(owSBS|7*W3i~^1#$h@<g1p{0y<LS|1*Eh`)3DiG5px>p9mH^TP`Zhm
zUiSE}>lrM|BtYx>P=|_%gCX#D98InPQX$`6V&S_h>Nl`|=-v8NaoVQ(k<M=vQQDsK
z*xTpX+(_qlZqZ_3KyeR?I?AVtHd%Z8&5J*P!4k05@3wIbLGM66z*u$=x?%ZShrO-z
z?HSOn{oUU+CIHW-k&+B6;r!EbWL<oCtLd2VkN?R|4Bn?*^p~R`iKH4Z-*>DIL}E#f
zF9<hD26deI1}qBe$IT+W(U%KV3VBi%yX>uOI7{zU>0O$oJu6qm!ZhDl%pMvz>?8i=
z?kJh7aYyPG7MS<buoZHXoTZ^nqLKX|%hlD#4b6ktKg!uXi=0(LX;@*J0Wg_W3{>tD
z_qjHkk>?R<B&gDE%peJJXOgA?s9D_G3<5772%||q)UXm>=Hx_Cv7CtOQ)l}HCs3aI
zp*?nP1ln%;nqKkU{dl#g^_**u8$|43;dtq;%CPFBVGq>ZYxovW&_SoyM6I938crmR
z-XQ5<sr~1mkmstqikSneLjL3W(>r<?f1aTGsF&5=7Y)8lVZGht+6dbKGoG09qr_Ll
zLGUw$VDn++=Up)!xyxfA<P7rS#P>63O39~K3rLu){sW)uqf6Ki2#kuMW-aBwS>;uO
zLH--)Y$6oiDdzny8@h}&qABD4rj)BX!^_4aReOvF!+9)b@9Hz#)IkE22NwJaIQ9Pe
z`J^kxA{CsHom-^3v{nT`HzlV))|3)eR?dp&r(kw@BQ*;CsI}c6X_Ddzj?^j~C${PX
zH-VJ<3xS$AZz#d9rN`^LMh;#F{cU`-4b8YBNBgA*0|D+<k;%{Zm=X6(^mzt{xp0r-
zGfE`IIlJwJ0U8`pG{Hf4_26W?*M^Y_ripJdV(?{_(ZvV{=M|KIc)M@3S_^?z49+~J
zmHRZ>@UrWd%bC$;naPNUrO(n!qPM*|Q(?i(8Ot29UG<+cW1qgdRKOJ~Rh8+{e!_SI
zF^uo>hWfN%pvsR%wp&K=mHjTVAZh>=9)e~yQ)%m+0DU&CbiRll5$bN`(X#c6!=d$e
z_0x^lY)y~lkXA1s9EYJVLz`W_+0baoirmxk@QW@q*(1Kuo2%{~d~RPt`aMGxBK9R+
z(Ge8?TlEbCw{`K(rHe%`wpTsFlfA|mfGySR7`>p<60>>qk`pEEKI}X#$~QY6DuUXT
z>QL;(60G)ZQfiaVIUerj(jj`u>=@o#KEc2`af`Jz3eOdQIf36if_7vlYElC=!f5hF
z$_x8oK#j8-Zq$4u0><KE4iaKIg&}>rr*3&o-*$$RkMPqrG;mJaGDO7Q;zlSNo9#i!
z(UYIdg*WINaMulZxFKa^27Rk8sXx?oEqcPcI8bdp24}2O-l0!G#Fz`uppdFcX}lxV
zW)iwOBzyp^yV{HgdiUiiII0zb$>`DM#-HehujA-R)dLk%aRkHQwR$2l_#j4;C09DL
zwNd**pD^xX%D&=GJ`BmygB34iy9HvoM?C&m#zKw%)Yc(R>VxY3&-kJQ?f)2#V?^Uu
zkiJ)Y*`Xo5NRl`?rf`svcr<ft-}a>PZ#N>>S>A!9Hpt|Zj;g$a-@f;WSsgXMCnNXg
zCi8?hg{1a$l2Z9L)a&_Uc140G^Sx<e6y{jJb47#u2UiU><gC~l;F$|y_lhpJLv*rU
z$3kS`=FtRvMaHw05l(B7X4BTBvhkoOGC+{YMRr(X(HdO4C%GUr+P4P6WmnBoAKRxa
zoCN|(DRtw))x%=K<yvV=|Cz)#--GZC%Rc^9!kHmqb+cOd!zyC}*$S`UREIkA_5kgW
zWsW&T%5f$n1S4!I9T3pOT}~S_tCTg_9Fa+cNv@Iihz-5f;J4n<A~O}aHNdYslYEeH
z_HI#<+<5uxGlQQVD)Zv?@4t+3Sm30x@c}Gc5J~VlXf>#@2{Td^ZPbc40ed_fN1Z%!
zQFVs?ea(-J3;C@?WKKB`PX3~>Z9*s!lk%|gqv+n0!MzA&9`K{<dUHxP7_&iAzrqh^
zi_snyZ)`>S<5HHgzAS#7#fsOUDwWhs;+bOUzTG7d#Ub`_!~GNE#cx-9&!SVU{{;v*
zn}CSQcixnEf2aP&W=V(cAp3hvfU{SM^<7+jpP4pM0i=l&b%0;OfyVNlRU=o6s_d1P
zGIU5A18A*iR(T%W{gwi1{jSn_Ov6Z&u6vKgVtxMF5v_}Luzi5%Q}MFF$|iXXD5!O*
zf}zong??8!E<*;}NZMikBdMS*Ck6!8VZHl2>bUD-Q(P8DYs_s0NU3D1l&YqmMd0Dm
z`3st68|Nr|ppX~@6nul~mKDF}pkcp0aL3(uxZF&G4kS=;U1YChJ)-4v78MrbeQG$#
z66`o?j~>P&H1$5>kx2dL%}d2_!koPddBjDxFU|CHC2M;sSQ~sBfZKp+RsdjxjgYpq
z4o?2QmhgP<A8x2RPBLSflKLph&Mm0=uEtocfgWG|4wOJ*?9A*QLPm3RwY?`bC=SRJ
zahk}Z*L7Mqr5J5YfI!=#oOLF?iK%MpCSH-e^d!}2&RnDvh2$TkAW3<{{h^$P!*j>T
zV))51!avyV73+9bSQvBIK@1o>ejuk!#aly3f#ODjvqUVh|Isia)D2c3Y#Xu3!0VFk
z4(9*)tGmw;CRF-nUn%Rhy&5z>=;5>L#{_+fOu9|ZC^6sdMT+XP(F3>01o{jHSEW?M
z47_EEVu$<WQaM=ysA~R@Bm5CbxPM3<39rN1VoDj=aS286M~4DW0tOIHugbf1taJDc
zC3_G~x-j7R)OnV^{LtzgX)5nFa}-11(Lx0Gewev?oZ2<MH3NfAh^4TVlE*bU=t2Mi
zT<CKX!vihyGsQRpUdVEx5k^Ku#>Pep(ElR(3(daO$yNH!?`&!U+wz`|0*~8<k#~xO
zp{5zv7Eo~R+;%6F@d8{4w=ojVEYcZT)%@+vEzwubGtIRbse3L0v1*l%oH;k)72Vc?
zk;%ILLq73o5dkQ`DLgi+>qciRoc7IUJwWWt5k0ExLDc;q|1jZfQLn_F?;$ioUS1I5
zGZRF>yuhyY6(ng)EniW{YzHyLg_nXY=louvLtxXI+&F#Q$PRR7fuM@@{_Aj^?H8*h
z@eSp&j5bBMDvWMfK<Uw)g&Zk6qUONh;nVxOF<XfK>wOI-Hmb)xn9q1#AFrou9@aG`
zipuRo=D2qi^>95O7eV2)&f|B59ScQe%$YOz(SuCBp@{Nri*D`BJPHrAzjXQ!&zH=Y
zoF#}SbJ_V_%F%yTH#|fljFtP1Wg-ne-nCatvlQYTQBLa37WSL(M+U9f9YOWTZeziz
zLb(vNm}l1$-y^F{4Ydg0+3lr(VgYFfr@rpLGj?{Gw}VxC1;+j#DrChUzq^qf<J#Rf
z)gINk?QOb!EPrl57*zKl3CmTKUvPI#dp7;B?&6k&gd7C0)ba&m9>0?{6B1ZQLtSCR
z)_bD|?~qD)G><&n*i_+w2t$~C$4!d)lJo!h36i}&W#HyUD49b{ZX^n&@}diFBKjdg
zea8Y{t{NJM$BXiU3Nmw`Zxs0xCd0hnJu70rER#0ER%;4-*SH)ekMNgD>9F)7S?+^O
z{Zh<NX@p^5_a#In(dj#{3n#f%5D?y864X6ll*MVbQM1w=8~zi)&=H3dDS?ZVdJXyv
z8nuA6W{z)J>T-?a_d9RzM3yebHD0?c1`b0>gk~4Ru+};xvjM!U9f$2>#MIc9KctMu
zR1!TN|M+5BBF=vD07PnkER_wPh-4<#UOEU(h$SyKl3|k$*0{ourYhH*=~AZy+wdNn
zt5ax3`qIhvyo#o^0cJPD@PG5Was0>c)=Fs#n&Ak}%Ea}b6Dl(&%m3NlSUK33Qu99{
zFd*2tIDVvpE`!nmNpDZ~s0rjQ@x_D<jK*eB^@&|3+oq#`zp+N8GqW}zG`Q=ct~SV+
zNVSSOMZ$=+P?eX3(Ne2OwuM}=c07sqY(G71U$NJwo9Eo|AN`(oo_g~kq;|CCA@?Op
zz_t)3ol8PtYNIf)GYrVzi4w6Oj*p;3MRg$8p5X}d&j*14aL|yB;u2Vj{Bdw0z8PBN
zQTPkaJNOewmIQ$65kvaxuyGcFD96Dl5pO_W!$Hys;tugAA&`P-P8>$Fhf6Ep_9>9y
zkiG7P=iy@*Ns@*tU3YWhvW7+^ps}K}u7N<M8UFr|`lABy`jfnZm@&cQ7)Zf|M0p6N
zh(i1p#1HWYASE?=30<J@&!cQFK$Nv<p{;qiaFSLS!el8FKWheOrndg5pfb(1HgP}+
zN{IC?{F%ymu|`JAfAz%#mGOo#zZHy`aDX@V_VvcLHvYwO_YDNX0k?>W=T5*XF@y%(
zF9|Bxh`PxCCzv3XL}5I8a&k~mkYTrw3T~9>O>jIckomB>cdbI4CVB&%M+-^jpBW8H
z`YL!)w9|V9n+6UxakDj}B4`!|d%}YQ(u@Wdc-{oS2jL1CACmdFLzfY^MMH(=+YM!C
zYiELk;_#wou!kHYa?LR{5!3u_w+!mei=B7^6Y6CO6E<|xcn4SfEPg3<0Y|$xv4ik}
zpm;t4!VSZO7V7A`RzFv^$Rw>)a38$IQF?b_i5tCWoXtFTOD2W4Z`;D_v%3<wiuei=
zAYo6DP{rZ%ZM|6UPVmyL!7LCl{QbLSvvJXV5u`vt6&6*H%-*7|6>=@eq|0uB<u-wM
z4B4VDA|wsoS?KYsV0jeH)qpT$1h81V4+1D4ozri{M+g@Lx>pbc;bw@M6@Fy_c|OV@
zBY#MAW|WM@e-Ne20D=%+7#oQj(-{}SB8iwOup4v5Z#X~!+~<0WP4ac-)xpM0KyDxb
zB>Kv%ECI;t5hIEGC8SLbU0s75E(rtq51<g*KpqYyCHnYfe&@H#0!xZQ#|)Zx4qN~i
z)1YY}yd?Jk^2_KVtce<<wNwFw0gQm5M+GcD#C`qH{BOr??T<~rtdM|5k=$b$kbGv_
z4E!`&3I8U<Y<Z7ESZFE|h2vZ%$(F58(Ku;Hh3$U9GG+l)q@O{W9C<c&)+R<K#n;;h
zO(*uU_Y^OG!@EJ0FcA%?Fl4Eq@#g>-B~{G4?|G2dpdvrSAgKDo$Z#>h;({ztK~h9_
z43M-`Ar&4A1X)2XAy8!Q`rcky2!1fTE?(eVKo_(i22g#9wHy`x>oQSM{36ZtT9pg_
zgx%;X?j~51epDW#x1mB5OpgkX`!|6A^-Lsdv3SvoEGlLSzuQbMidj#v64(oTiT^lh
zoy`M;Tdwn3gxAC31V{vk$;fa_;h?k>5Dcwh&_GcYgTTOkY*+Am(4_mreqf6ctF+`P
zoOQRlcJ5ZCm);)UfPInt>Csoud~#!h8zpk-dlO_lqi2YtqkcwF=XCi&Ow4ota+Le_
z1FW2AcrC>O99#)T7d9L$DGnE~kgTVYB(ky^3A4@L+SbR<97b!R`PyKWw*`R^5wwp<
z6(O^)=Il9t{WT`JH~yjOUBqU<x(L=WWoAjo==_E!_A4r4m|U=H?l`23_e3e-h56^x
z$b`i%rg?drKFpc@=SbV5$L#RoF$BdNsnV}?jh@aC)I*d+^BdBN)0|(xMw6yuxD3~+
z)K+#APbf&}C2|OE^d#-*NH^lv3mt501y3!*1uO%e=mx(a$#wAW6~+y++kzfTN?YTD
z-WTUIwU5+Wc|I95h>l5((WlI(&YFmvvay0Aak{I5i~{VCN9AwSB5;Mv0V5x6b@C^n
z(KTFEP0=tJWx6erdH55690Q8xi9&b-)eQ$xjzqoyBf#0W#TUTGrFEd><ifG^c3=}S
z%oVQ1=r`@%DX#ZqQQb((K(NDw-Raf04qJ+XRqr6(8=L=REyTNK=*xYH73amVD&XX4
zl3$`<u(c}FtoFk^7Atc``>TBf+^@t<1RbFd_A6D@`nFMSc&h{u;A&OLcl_(`_ek>b
zXmPcFc*rq#`f&NSEdNmE=K~_Ua_ivW&O&ppGiA}A#D^yijrzSNP*dgA#iI0iqq>N2
zRl1nuQoi*2wy|7i<9w%h5qwz_^|=8p3;FeR{Cc<UWl6#tJC@6~GvBE?Mx$iquG=V>
zQqNGm_DHlhx85G0#<}6APqTY>iPyB>elw1rm_bDL?IJ_wc7@0Ov7Eb_&W*YE9TQXe
z1uq<p&gfFd`ZcG+zCP;odSJ)o>f7w+jic@!bar3NRw6QMvWfkWz7<bR%K4OA<;#n6
zkh<~eX~#GOUDwv3QB$Mk=7uiv?53SEmb>dc;e#`uZ^8zER?Et(wSF`87so)$^)az<
zsBV4H+j-N1KYAiWG%?_4IhOB=465XMjXw2q5uP1s>&Ag)qQ_7^ykq-X#;#cY<T0D%
z@^}9dmiVR?PCk-MJkuX^at)b;g$a8^VKC1=C7o5J?wzCokh?!JHBSO+6smBD|Cn6e
zub<t^GMEDZl#cAR>h9q8x2a&b`lCeX-rAki*|*>y48Jw+OcpVRWVVrZV7&03-Arm2
z%f&B~icB@Yd8U<XymiOzGuCEZml;!t6G^|A{)odrmZ2Aq)bDKA?<c1ok{*INx*i*0
zj=pQ0)UrDNl3mgA|JPgnaJw+Rh!w$gm+^7baFMePP-mmG(~Z<S?LRao4JB<8!Z)?F
z(~|xQ-NOb01(&u8Ck2e=&vU3s`xadbd0aG@Ew-Cya<!joqBrMxVCxJGQu(ueJmiyQ
zNN+|A?ez9E1vUr=b2u}nJvZ-aCn)6f;F_f7VXY%0|4EugNSUK{@MX;mN6yRmzI+^I
z?<_fiu7=x`b^T$Ma}jNpLM&m53`0BI$829!gZVDu9O-(`v|P-VqTb_{-N<?U++-%2
znho)XHu4j>!OkqH*Y}dp=w<uq>U^PZZH|BPOoK|L@`vqiFxuPDV}k1_YJ1~pO&_2I
zh^{o-iEMku9Y}kF**QS4nXH}L-Hi*3Z676pG1%}joU8R9zn@AD_EQ_sG1n`cvARHv
zTm~oqxaNS=F@+ODqvwwfxu2M?`5`<CYEsPvJDlm*YsLlPkU3Xbl&(ClcjXb#V;|gg
zJ5Ci^p`q1>G}D9=hn)b63x&-;gnK6AF-L$S4^f>SaLjgHm!f7DFWcDx!>E#m_1**&
zV!byzWYmvoFFoD_O*wf4B#dC+M>?0VcT6MZl!Q6D^<4in%|v#ScJ&?X2}*h*Y;Uk1
zvj0f=hE-a<_*lB{T^h>=rd%;FPYKQUzQO=i(jpIEc0}R#7^gqs9Mk1?R9UlPN{DPp
zJfcWgTm%{FN!QcdzrCxlqgu+RTuTfzeuIz{SV}%ZS>=dVt()6WPx~`GC)=nypNxji
zkhj2fhd=&#I-h~9w7I&fc*?k57Pr1WVD$qR-IM}CV2#Uc`O)<9QA>r=4e~^dKPRgm
zm@tmjo9se=v<fAPkJaGRdD0!F^ZeLp?&l9t`rTp>pR{|&6rocq!I-MCG#m=>dA9h%
z_vxA?v<+od=1}PWKJW5TO?fM=894MyJK=QnVq&ByrItSQQ@CbZL$_n~lsb&?HyCK0
z_i8lDw^i2`Ezu`%vg%3G=uy%x#<^kZZWX?5BhLQmwAu(hPK7Px*fKsHa^>hze8I$w
z;%eIZ=Zf)rPz)b!U#=g5^EE2qzs^(E(lJ>Sys%={qh{dK<*m5-elaqHB27GgeoZbm
zX-rE`v=a1cb!#XAJ+#;~bO-)V?2$WC&BD8DIdv8(vW~oUEFEF3iAGiX{<;MqNR4qi
zH$2AO6ZAI{#l<_aTU<Ox>tESIcsgF*vSfX~=R0V3FRL>eo{`AezWD@bDUsdge{mUU
z6hJ}FD|dc2_`XQ&Kq+=tLqDkBnFsd;Vi<UFFDgHCX1g3@e(X|C-+b(19f%2~-bb(?
zmygOcoSpOGA=AyuEVh5cjbF1>wh@^gx;nHBD0W5VeuB)RT$&OXQ7so3Iqc0SQ%k<}
z>6Ud1)zyFRX55_)Il2aBjZd<ceBt0dxeXDwh;<q`%1?L|%Nc~YIQD6_5JUKSjC*7@
zEXmHuWDisJ26D3_M6p^s?co~^>`w~6(H>*YY5i)t>1c;zKYXgme}G3-RPPxWEzy~a
zbvVl+_5K06NJ?2$*I@WwWen{fP3e5TxgiRTK6E3s%(*7^yuSx@zGM%(=-U)UBRmg9
zMb(%3Uy4)>Ht65p<4!Hj-pt=ZWpfeyKK><qQs56$9#XowK@lQiXU--3+Agyl?m5EZ
zB43)0wB2OUW&fox)t#GsOt*^3`04+UIu_E!;phu~Xvn_g{9ccE*z<SFP_X9SbC!@&
zG;r}}*2_VefVLCx8@YbSB=gppe|j=(QR|Rf=dmxjq>7RvwSsCrkR_+-ce!TrnB>vM
z5&bR;g%`WSvDRZ%z5GqPz}DR)1?-B2--l$;Ld3byi#p>gVR(|x=HQ?=&E2v^k(3w)
zRn|>=39~f$=6Q=7!);{a#vT|YdG>~qbpzA7qI3AE(!c;9tY(O;7FBZy&3Hf~@~TyN
zy~GrCRZTh~wSC%_RDxWF-8pFKS4n}pLfijgq$oq5KT?d`Y<ccE&>C3t?LF!!R*wD(
z207gMXdKq09Gjz-q0{UF@Lj8skq@BvaM$jZ{pLgJL<5(T%|d$k_qzJ()n3LoSFyD}
z6aVQopC$x2RehpJ`rCj+{o9Nv>${<tF<NCKQ9^f7*W+!&%>}FJrnea*w7{vCux)f+
zd`fH4fj6qU;?oYiJ-0908Ut4gLZ!6R)8+Hb%5t1DlikP@HncT|qjUWo4{9f3<LSmH
z{uZ^xs`mcy_`}6w*|*f^Dc0z<TGNz?>?=u0VhBW_!^w-B2!mgthfjU-CNy+-SHb>l
zzSmSEMCn4f%ua^#<gNfB({!UMOeo6O;^)fyRZ$Ke@&HCoozYZ;xxira%I!J-wgZz-
zt)U%_^poQNqSIR;iwvxG9X~C}4%m%~=dOyyalAW0Bt__p)^HM!nHMSU2hrnCugB$i
zT6YRSCU@4TOW(0fBa}bit$#7{O2N&tUon08rJAO0uJ=Z_H^B;CZU42<OSJRr_;rgt
zDi&eXEc+mkOD5(j;ILfA{T^kJo6tD1OnZFQ+?f1lOic}~0Jpn6d3DX!#8ID|=)XF8
zjGCvQx*4OnNoc*KzG;=MfTf;=$AinQ)bb5b;5Oux6S)^P%&Ctb&MIJ9G|jjydM8=$
z`7g^>ya25{HmBVwysMJBgv=e})vTd@s`>L{42D3afn(Nmf00UIf^InFN^Y$kN25df
zPr2&%A9ksuQ*n0gsfVWP`t7&{{DeB#OQ-^gUUgxEX15`C(XGR6ZB4Lqc<k1eYIMT@
zo7uopU<^O(54?KAk>u$gkB9<C`ual0-=aetrX}V%>#Yjsc+DP`2c;#NDUGm7#=c>a
zNQK_bB@HzEdKM-(;-;w~)#hX?L_DE=h9`f5m-kcQR2f)wQePj`I$X+OR4ZUd3_pJi
z;jkYl`fjjT`GQ^q$xZEdl)7Po!t9_3C?6yQ^c7|}6D3ksL36Bu_y0DXLi*cPw*Bkx
zqRZ^za#V9vP<<PkZZgus*pL!N?Uy+2nMNThRt&K&XSu#pTlE}G7f#mX6ec<cr^CPY
z#NTTlxAx8wE)j$WQ@k7_b?mr1_(CC7aN`<W@zpe*Fwk1K!_kGxol^YurUym^K>tfD
z&(fiU9Ua1NR_9`TB#tbAc0m5hFwI6X=IT>CJ*QkXi{E3jjQL)rbi)6ww*C|wr9Z;-
zFjxDY+v}qvNbhui3Slaj%!0$AUSL94scn9F`_3iV?eMO(G+~-jnyh)1v>VFioxi^k
z-MLA;nhLtpaXtGWNf~;@DwOOVh-t|wwcgHpKd2kRH~;(`sz4sI2{)XRFa5l|ci&J)
z71+@dU>xpvgK`)B(PQIo**EW#;(D_sFMKM0y2o2EM~`Sj?)+JS^^KHgQ6{9SQ!_td
z;k$<2_Uw2!XVg*SuytfZ#BT|i@D<!kw)>BXc+BO>Wbas12kT_z2Eoiy;F?DAPCOT2
zRJb{Y{pO>bP*rebLO)}b?CI8JQSCZ7oN>LPeikF%q0w<VN0>AWBBQ*W?3N`qV=TC3
zXAF0tt^Tg~xVG?*<%#Ym@I|<(TGS{e*>}+T<n^hPzpUz`WUGax^Edae@@7B%3ZtTH
z)7$Ckgo?&Z>C@#1IFIZgaJLs@uFQH7n96!4pvNuQ-Q%6_RP~(Mt{O30Wql>{LAJ#@
z8H;_^B&)xQd03mxT`7V!Q4Q{<)})>iliWJ2da+D{gW5dH(C#VtlS;y1VHdWt1gG?)
z^cP&}O%xQOGAP5>jBIwuCeVZ>v7O>varXMkV3*-@D+S&%I}2z6*{o-`q2;HdOhRnU
zzXxik#%wQy+XaWx)yLFb%^xuvTUURH0v!ywRE65tKd>pb@T8uiE?_RKfaUk`lY$7O
z>5jp^>+Me)&L>zrqIfR_550l*EDpwN*|6zA^^1)wcj>W?5Q@unK12`f1VVd{u(fwg
zV~Sr#-?g8*@tFfC94q1mmbMqtCichQp&3i4=>AKx$ISenEDw#1i~0YuJZ5GtuKx}5
zAemX&*f~;X+aRa_cUKLJt&V15V(Nqh78mz_YZyeNA4Nn;MuuZfcW!f&U@oso2~1kr
zH>k%uCg*PB?da*cw{A<v`@;PSF{y~=G^*gxKsgR$1+;HuY@iQXK|uvVxXOe?kjI);
z4NIIouDFt5=3DRBz))YHtQ7Sn0+?{sA0#wEm@wqtF-V{utSkthgxFg-juiyAFH#mZ
z4vNb^E8oxAznoGK6#~@CgF8?Il&yDL5b_+%kPWg!aFZBX#u^%ho=pt@{P@Ji))LaQ
z;?LB`v&spzb`&fzG+QHNXXlC*xIfY%2p5GIg+JN~fmIXKj6VTL2{CP6HYA7*=nTjS
z2-_n0;sO9VXEl~VbJ`?3(|1}E6Jv1nwL@A{lTSSf5{IHX7YE_rgaa~{af&N1z%GcS
z@R@=DLXKGWRgTPdO|7e_B%&gsE|!q|Vu=W%=8reBI`~?C0XP;0vVgzmL;Y-afLi~u
z1Ieoo6vTf?OW)kwOsCV;C6+ZXm!Xj8+<s@PsseODE)C4JLGI_jnLxkNM^y%KsmO(4
z9_NC|cY-U_{Q&1`^Up~r>iy!p$X60h%yS#*2^R|X=Ur@iqs0FU2KFI=N1Hc(r2~nH
z3F*%_vjz(01j3yr1WqCtRtev`--`H($Wr<lN(@7Md3yf7AabM6a0IlzV7oFixtKz^
z=>hzLPhVTic|n!q>pe{`)25jL1Ugl^#0+055TJBb7lQKVx;c*%Ydft!6;-6vq?L4o
z6hXPYk)k3D%D9naQIJQjj!V4?(BOPP81#@pXz$-F<;V#p2LC)hDl9RK$lpq7h`0v&
zXY-|h#e%lFf^_nDeCX@JTSGfXmg+LOy8<RlE_H5BkfYM?@<<E6-iOU#|H+|1h$%rv
z`X?e@${(&qJy{z0)AJLaJ-7l1K(PdQu;XHzAz@wv&JVy`z(I+pYKVzydkDV5<22hr
z50}hPj%P%Wk#4U}8<4OJK&}MLs1kwpPjh^Wm9)I0a4av2$v;SLIUvq)kSvX8H~<&{
zQpT5n`DKrnRQuX0HRy#9+gE4Z7Xe~ZYs=lc{_Yp89Nzsvra0`m4RX^PV{UU~QZw|3
z&LFOl*+cBe*UHyF-k^acG#FEZ6H|SibN$EOtPi)X+f03k-p?iZ)b+&NvmT$BaP~%5
zkoGnZP7S|KK?T##NIn;yoHp<@Re*e9L6rUYE7tIpfbPTq>PM?v9Ymd@6R7{xl%Tu`
z*72`@2e987`9bzbx6gdSAZ8TMOb{7h4lcpZAauP`Bl7DLgRllzzAPU>Z6Fgy01Ah{
z<~#B(D3i>)&~Fg4QQ*5B7D(d)(EyY|%1h7+=tKj6(iGH31aXn~Y(D@FR2SSr3sshV
z2+c@d2*8Yq9c_nUpMrnl)z=GV3-U-*3Q*{k4c^y+P`N7~!`}`gv!{LFIXVcU-cNkp
zG&TsPr+-0ef==WKJZR+03dQ`R%^N^3^;FHU033#<0U?_2kog@NpO{FthOqCQv@TU?
z^tm}w$LueZ@LG$fj4+!3|5*>Qif-n=4QIVaOVG3qd@VEMYY}{H@zN6KYhUo69EkP^
zw&T-L;GfG2UYLvfGdx6&r}6vDHzUL**4CEi#+7ZixJLHp*f1L#`EtM!m^-TtZV*;K
zyj5pgI5V<+N#(_#8Ejtx)%{co!d!#8#df!VJ#PMbBIK3&`v^cc2&wPgsG}cud%cUD
zz<Pf|=0|ORhJ1PIspjM~Znv_I=YqcrT)o>@Avr>=2R2nt<^u=sm|%PhQ%i)ebTgI7
zm{y^FA7>o>UlxKdN2<@X+Oi1eJA)%rPzEM@CZ4zmgdiN0k<)-l#>d^?&+di%r-`2H
zd248p0A4|}5nvqNfc29&GifMJNq_YHgvCQzucXjPhlHS=v+Z93>?X_`o<+|R=O855
z2ym-{Y6yi)&u~!p=1YdMzzkpRILjCfF0{8-jQp5UpH00kE;`m|!Ad;rbQvW7YLH`D
z^KC!p-870>y<ciu;sBYf2Y1|htjVNm8I_148a0731*)yvuP=jhH8Sh6FPQjJ^iW+;
z7=F6<3KH7a8IuNd6^y$$Q+SfJ89Twm@abysFvSP=xudf2oX~9>e6L0@BJ_sTn^Wgv
zE*S+x9RGf6r;5`x&x*qo9P)y4me!eUS}aF<X*}Zj$IR;Par@<QOJ8{;kHZmVzCWOH
zTxh1B3@lNEqPla(;jybE{tp07K(W7mGKUd;c;IpW!apLVy|UE-aC^JI;-f?Ng%T{M
zHsF^@79m75u$FNDIogxBX73l?MoX<2kCi7K{RoQ3@{Kt>#gNYQ!>tov8kz+s>SAQf
zh-8sq<cr})LyOJDWwRzNKWg-5x7o)xZfAD{OR!QqSaaNe#dy})Uyl&sWbP*9^_C>r
zLYHiZsCz_;YI`mzczJD(hg0UI2CpeF$lj5JJ*4My(8I~?=L_s4f1F>uvL$MtW6g=Q
z|HNG!jU&moUGvexe5xb9C6&nzU9W=515QluNR1Cq<^vxitnQw2oFb>t49$Ty<NzG{
z`F^H7Ur$tjsBqCpY`eiiJspBwh4e#!xbi-Zow{-CyO*)4&QwbT&3ifk{+z@<yK&)6
zm>;r`-6xhZ&~{-uFZj8EZ&0YQo)Nc<>w_`9tkzqH$Y281rB-E|pJA<!*HN%F7C-$^
zH$Qy>5NtWXIR<SV3vrn?J`3O0tbC|TmX;Z~=IZBv?iOp5->&lf>{_nmtU1~J<E4G#
zv)T0F<#y(?ji_i?boPz|#QgV0u@kdAA$AsBCxraKA6g0%ODNMaIu?)?vA9)dt0`S8
zhh<&r+v^E73T=8TUl>mkk$D1glx)nCB^$rkoRr8PfM2X~^{gom4&KUS{ap%*SLH(|
zUk7V{)KcX)9@k%Ee{7iyl-F(6y^d#veZ#TUc{voNm9k~fu*gVf?4N)WhIeE_F1V9O
z7Cj?4{Lvz~keyt#9rh!@yzJTSmhC+?l>nR+7WHizV_4&iv<J>PUbz3!IqF=+8`>}V
z($*hG5<b7LdjFDI#<%d@ys=Nq`;E&9Ux@mDV`8O=Vl!DFxC~|<wJklRFMWdrO=&KP
zA~5uG-LHydf$*0A$@DlA%*oL%StO=~gj&KnWeZb@igITB7uBUD7)7%SA>`6B6>(##
zkLH^*3Vbw%#$#=8i$48HMnSkSX@dt$l*0q=8wUqEf$(VP4eujT#Jw{<tivMiBYj<e
zF84tTPF?hRp3u&h%a&Rv?OG_zWYJsPw6>!tpO&e{{bEQCZlVtNao0w3Ga4m|zdj{$
z<4h>yY!M!JG?d0UtkYpGk0;51bwh9kQkcdR`LdpuR%0ISLPhsi>ZHf7?YH{meBM|u
z?whQ<_b3{FQpz|5<OgLPnoi0Fu>8D#S+zB}z))0&5gAb~Ps}9tJE&A^CqC}guoJPl
zU|b)HZEgOL(GL@f`Eyp=DT5}3s{Z&Dy?1$<<69O%5KCQ)v{XS5U9MjXUcA#r-i>`t
zE%7_-4>orWN`;j3)O#NndW;_OJa*G}=fycSUS+tKE)vn+1hY9Eo{PEe^{9J)&Pa#7
z*AR%o$(V=x8KF$w%8?wA6p`=PEF(%|MPV<e=gqHh9!=ap=35F=&nPl%QyEn@SNGwL
zKe*rU;wN1(l}r%QcZZet;qhA7HY6Y5n>Nx<zOk@QifKKBT!OTD>dx>=TPkBt<p%t(
zIy@fr4oKm{YN`3+CM(yNHk`PB!){>-VVTt_z`dxA4Dd}>S6-s4<NG@?NTqDv{6xt?
zOTl^$U8{mPDb&$q0z97fDC{E(sums!s3skk{XF@r^^+rYGB#eiXbJavMEn(bIqbVQ
zMQLsDugnvr@hTozuAZN5@9Ufu10BS1TWf_Ml!c=~xpwb|BWW4t(WoAOo4Fv8jj<F)
z0hP!+*22&6iU`nIY$v4xH>~BOWB~*<hvgl0)fTaB;rda0S?!o_7><L57^LXi50Prx
z8oMGR?#oItNDTN~Oyvl!>!j2SNf*YEKrXWFaoIZ2-_v{b5Or$My2Zy+H6<uhTGd`!
z*;Pgl0DlV2rRlp1dWQdh2%JsI|4GvHt{Q80R)rs_7Xa_aMFPJCX36~S&WQT$E0uqT
za*cuUVzBeZK!BxM)Anln4P*Y&?mZZ=ZtkgbL7#O9;6vgq*CIBWrp)W?>HDlkD^+CQ
z3%UFug291Ca0LGBo~hrA6SUT8d(<o%l3M)oJ92^3*3K7UVsB)B?I^56@dL6KWmw;V
zPPVx7sNXnqIcKD(abAhz;aKIOsDrHpiRCuZzT?_h?!P^Ug#~AQew5?kmqxM_GKA-(
zub6x0C{17S#(9G%*?_aojUE&ES|IbLY;kNN5qrlde#oj%VXBH6a}?xWsPTUD!0B>h
z%m*P>4D`a_JHbVNm|6q++-r_u$0P9`Z~Dqjx3lkp%1f^m_ig936GETi_R1^nU!_hM
z%AWST_kC}3hOqc9)K1@qnC53GjJyA{)G32XR&_3IoeOx5z04stCaNNW4Fm!B_qSzV
zwiQUV&f(bzC+Tah8{QRANp3kuelrEWu%VP{McuNk{sw=4=Wg3`xAf*FFTK{n=iS7L
ztj^6yI0M1gGw0OOzJoW5b8=Yj#ZFrh+=y5`@@(^4K(N)IQwYz(^RE}QEcC`N5y#8K
zyPyYZuXb_3N{$Ks(0SmdUbg+^ujhtDpT7Bu6M%L+E(qo_ZVjI;)IE3N$U4T_w2r)R
z!$1?hC3`o2{^>qoFzQ93GR%V~ka0)h^w(RFIr~fw;dJJdI38pvkQ&cPOcA!a?=^Xn
z^=MSvm^}8eD7DSw%Y@ZMSje}FYvy3nON^qfoEXf)1y+lSRf8Ipgg$-7pj4IEQC!8-
zvfVEqd`zvGe<8;?-E&w&9&|bN<bfJPB+6RRc%{C7tL+~@Dun!;=19`@M(AuV2)`eF
zt+y!rp|Gv~jCnb2!G=gTd62AHd16(BNJ*iew7~+7$L@Fx4(zUoc_=c-$F{li{qS;6
zePXT*HqU;Z1?{K3I$nGmUpYPsfl|aLH^}WxT#x^W&sr~IiK8q{T|OeOPg8l=?ev{n
zEp4-Z(m)A*;Y+S8-IlCgT&b9Pb0NCi?VPQ;14swrmROD<j9yx;RQk($w#tviH75qW
z<!}as+hoF_FPD0<V;XYs_@`sz%1LMNo{2<II%XG-(*g6fp3&eKeFsk^{TO@6k}@_t
zxkz&*U*aMZYub#SA$BAGX^(R&%DFE-<FF=wBM29LBILudWv8!=8r<sV(#1EO;!R8e
zn?%J)Y;V-n!j#z9ab8jxcl?}Uvtx3#d)K`ZLB1<Yo4vb&Vi{P&tcIy>!^TMi`<X_w
zuG?ESQL54T`77>)Oj+WxS%Yr{XY19ljlen756o)_UrfuVMS46YCvTp=U!jVzPYbhu
z5S#CB%u?UT)h&_$6BtFl$}bYS@07#2M?=MzY1M)}3y0T5hu>KdW?^(>7vi_Lsi?~H
zqF8dpu_#*Gx?-1$jh#HIyG>5n2he<mjjBvEmnCZ)>n*Dfm$@Kipdgc1&kdpHz~~e7
ztMbtb1e$V~>w_|mRFvg+GMGYI83PP|i>xvblCkj;hvl1bOW7E6p4H31Nl?OZD6NYv
z7S#3~=MJ1%OcD`bHb%j10aj%zw}RTZZ7-0<JlRC?nU{N5`dWl8gGlL&2GBq0E;~6D
zh~|e`ThI7vA9!Heha2P{j_%&w5WT;G=zD#@Wt-S!v0;m1sjO9g?)+uvG`7}%)=Ybu
z>)l(7PVUjRo@uR!_~+<)`1?hWqwd9(q#&IWikgBbY~5_6m$Jl_%c6(&_3U3cWvU7)
zWk|b9b<>(x3c$X74u}I1e7RL7o0H`CuM6cAW?QAsG8n#XKlqniOQ*9&bfL|u#|j72
zM_PE341ycRKsG0!)xNn_y;y>Ox<2>RiqLa?`+XVw)Kyhje*FYtaBP{!+cXfL^5P+>
z=o=<(>)mqgFATA_Zkh80qt(m?Q-^UQu*Y9~vi-6sS6>l!$+P0ezgCS=tIF3s^%#4P
z63=k|3Wu-vWrvXI246l5<<HiEJ<hCUiA1S6fq5=j(*8`n&w9crA){q~#c#8<eTVTJ
z;iX;?Q@@~y+ZN%}ahYUjl{(*xCgc&AY6j<;Eg}y8I%=PWt1HWirZSIW1fFLq9cdM9
z&gALKFv&~QGB)fMUrD}g7pcV)nC;&<$#O%YNJ0R0ZDGn7-%gs*YfK`+6;soU7DY5g
zoPUq~-VzyKxRNC?0#3(&I3w+r3X+eaU@FBb{Hb^Q28Zuml`myRv&DpE74RV&X<k+6
z`fJrtGSQ+(<^*7D`0~iWy@PkWE`BZCqv*u{%wWi`7B@ewEl57-lUmg?Ov!>*yK5=k
zlOcI`p7)_qDRR?t?ns*vO{PrIzSvEH>KGF~_zwJg{O!352VenzyWM4FyA4BoiXjAz
zYOe}*JmLX|XhGRf7FLyKU8|)7A!UihtoQ@?U&1Ox<k?;I1h_qqTcUp{3ca76kBR1}
zYD8H68s3GqPfRYq&fhb*EzOU6o!*&??3q+UmhwH#C7Pn&G<x*d^qK1`2LE{1S@mBB
z5>DQ3VUD!*=3sn(_W6g4+?ML$X~YcvV3HUd)DyM-Na<*z`hHGqhXaMyx9ajErdDQ^
z5t3ZS(r&S~gjO|KR|u~aEa$(H%0XZa(zxd`!Z#Oczd9_H7VGfnD`f@jyT>_Qh`7M>
z*$HQh5Pi35bum5{Iw7<fyIg;+*D$EwA9=%1!!<ul#3kl`?JF1quu{44Vf*E$!{nPu
zZg-x%5+>Q39bc%5!usP1ohh|{=a{q?EL8BrS3$-=Oel=wkZz}#5AJp2`~mqOEb@65
zwSH7W_))0{`2})@Xgc5}JN%I7wXG%0ua?=WZ;Qu;4n^y>8`M2-@rr~wn%I_fo(Dz3
z#GO844^9ey=SappZnK6V;!D8HKv8{7X4T8D*asTx$K3aN=O4NLhFUUHT}5I~Hdd>$
zGY`TCmtb#Uq47}IS#G0cf=CvK$pwcUDt4g1*>0Mwp2>e@%u6ll>ACk6)MwA!+A+?$
z%;jvuciQDxIln_$HRy{zPN?*w)9ZDwJR~;~{ta4xUz~9!MWR+pT-_MsnK@}vQFVi4
z!VOB{{!s7gfd9=ec`1#a(+`j0@kX3qsAJ81#a#oEX72Pi&OT$zOW=*IsP3kIBVnin
zbJqL_Atqqx)t{foTWr|qFL)u{INwRO6#^a`%J1V<aNr<l(48|_39(i-Ru&f{Q%Y?e
zwv<PI5z+4(!;(jE--?m_M5#O)hmZpn(^7v>XxCJkA8a6rokI(m?bB)yuP&5XVV7bn
z7ttKs*JX4{ZW-wirwZgTKoopYg~gA>c}>v&dLVOsw0HvSZR4#rX<<ku^~y+RVyv=r
zP&h5644sq2fkUq&Y{fxGgM~PYtn!(V05PF|I6kMUjBPgq5`TN?SR*To!ipW-PNg#`
zLz8>%=gRVWy2M3avx$rY693k?<T<lG^)k$sbMfwOd!>MNPTFV<>XNV>{<m`up>1Bu
zIdl{?27$S&hj3?cp;>7>qmMxz`=2afX)H{d?)XQAVFr64VMbgji(yWgW|1OQmkShs
zm?N?Zgl~V4$a*pOD$y>)SOPCAfZinw7WHo#jo)=p$dSHWD_cZo&A7%^M7~85zqxGD
zTtU!O#I8NT=|QKU-T-_eN})*H3+ZtWE`4oSXJ)a@3<pPgcr#?zu%j7vWFn)x_Tgb^
zsG2mgZFh#$AbKsGaV$ct;3|g~^kY<iV+EPykY|5hk~n9ehXGW*EJ5bUOQFmk25-bN
zt_DlxZtJRlr+5?cDt+b?HEi;AKQ^rs?p6H0x*#`(zc@B?B;hx&IQSY3rE4vqgqrxw
z+q_E+mlyBuRZA=<gh@r@$VU=Yca{4N(5oc%l?X5<Y(AxugopWN3`CO@tuTv!#(On2
zyB#84QXPh3I&Tfm@NXIwe9Fd~euE}}6Up%k$)vFMF;TScC-2NTHn%};fI!z0qI!-^
zR6dXQ3r2!+wy-@@JGK)QO(aBXL-Ub=3?(@X+B@6{Z<uz6d&dpZGnT4vVejc>L`_PR
zxE$@(?ZdW3OtpEaE4+3%>QW4U*7ojB;j26OZ-b+nS6S>PZ`*doJ^Q;`{WON)YEAVJ
z(5&Vt`;92KaL&TL5Hw6<jds2<wYz0>UzV``oX#6<>c~=0yRKfnwA7QgrHe_GaAi5T
zJ^#f}-XYk^=suajz7$+A=X0{6K2fQiX=TXp!dmAp)#zF{M)IXb2YQu%3i;ykg+spK
z!?J}2R}`T_t<Cr+$mfR)Nc^ZnDOK|{@>OM^J>3*i&xGhoYI&2fJ+k1m8QVi*Ye=#G
zq_wAWM_Ox!mnih0U##5_Q%t_5io@U=bqqJ768^mP@p%jD=B7>*X+*GAJnMCg9YTeI
zYS0oqqi)YGU_eHXT}n)U$f_UHMuqv>*w}#8FCblX<lG%(Ql0yy2GX`Xb<PNz$<>WB
zkMW_7&_FIfpjn6b=k=6nxCcR~r^~&IhJ)<6x~iKaa`jD2lblZNcrd5-Eb6O!fa8>4
zN2peO?6PIE#!GQPX>Q+hUiEH&FQK59SBOUry>u@M(cXmq&`WK9n}2UWYiOJ&t-hEZ
z=sxUDLK6}ewZ@$VlTjn>56Hldof#)SMO@3LTh0_3B>3S%tK|RqF(xziw(NMsX1%}*
zS>icGAj$LhF7Y*?UD3aE$8&K5n-y@ZB7q<u>~&1F4nSrrdA-s7&3V61z^^!#oV<{M
z(F`_o0Rw4^k9#(M_bE|bUnw)#R2shm=pNH*Ct_nj`&K>)x7D64T)8xfhQgXz!U=E>
z{rFSwT?9%`<?<>YtBWzVcBWJxTG+jq3u1~ohn%mkVG3nRS?rCcZs*EEk*mIb_^|*e
zU}};nq--Siev?sG09O;NlzUw6`JL$3Q0Q{MFjau-b)+PJFjygSN|}=ZSLauj@Vzj#
zEJJBc-Y&)lgPv+9x8n>OZdwCZ%sF<zg1zat?82~+lD^iq0KSMe+@x?$?_cvIscq#Q
zdA!(X3g_pTE<bUW7FaQofB4eeAmTj>?>59@3AVMfH|40@>t(s%Sb-@3eg66y#rEDr
za<>d)!coG1__(|Q_-)n%S)rE+`Ku`dxVD!p=(%Ebt$Lx(SX)!5CYBjeMbdSOMO>EL
zj#$VAnM?cWcxc*^H|pB8t~y#8HBezE5+r?;*==I)(x|;=j&PBx?u1XoKahnseqe-_
zO*rNs{Ux-3`Z>k`xWP~`Okh|%QYrbhy$&27;SQ32G$i$cFECw$FcSMa^?rX=1_WV%
zV#D1PmIYhPG{-dhl1d!m1qsl2*&k3}m<&XWls?g4pOIB(SkjWwUDy@uz@|g|u$<vd
zBL4k)!5YBc!xJF^-->#g)K%sw9dt5T4MX|>Pz@0sMiE2dWm7#B81)D}GPzCP(}OF&
zCZKVDe9NPvc|gR^vvYs(K_TOw4&<C5&CdI1?h3kO%9EIP(&_Z)E@|RMm$29iLCYUw
z9YM0nj4H42@Ixg>QN&_{eK1YQ$W$i?z^g&mm-8dUdH>$=-YJpyotWOk8T>J7xreOh
ztS(}(g8KVt>rHNKxDAF)wy4f{k-!Jj;ah2c%8*iz(_wgzwG+LsQXkf1ewtB$6NN1(
zI9iWBUUiP|7;p56FB|t{y*PZ>M5EdM&SgIu$sppO-K(Wgp-UQVVfJj@b=P(<ELnPu
z-jKambOlbs{dFie4b6TngPcy|bDUAm{>R4Hi=5rhofnTUB?^hO)gl&cV&OluWLWrr
zX_@k~hdJ{pgIB^T(_buF)!!Mv``|QFAu^Fza--lgJVOGbxk@iuQY8XzzIOAF`xYou
z%tSo2<b3u~hw23T;Hy+038fUdH!%j9+^gbp5Km3vIDf-Ti%{W85%poW7@R7)m|mRo
z!iuO&6>m4kP_A+5>B$&iYHe-p8@uO!M~$YSuGr8bN8IS5>ob(5rRvLDB$JQ6`FmX-
ziA?Ta4enaO+<`lnaLAJ)#&U=VLSh>a@V^LadU}f@i_xdDo{M{1Wq!AieOn#ZF>;^o
zVKx|Pf~Wr(UGZ_N$(`{<)E<QJ^_cTJ!x%B$IU)}2;)_!{N@e3w7@GjSv5Jm=3{+Um
zY<ELZ7~IhOvW=`?s{8nO39pS@TfF_tEm2C1XM#I3o2?j?BYrI`pZh~lT4XXu-p>nF
z`ogf`UcaqJZL|Zwl8E;75IXy!@lA&C!ab^mij}=ClF)vGc#`y&5?!@i4L*<1Xd6%i
zM=R^}{U-sCW!}b>--%_wGEQE9N@t*CAfK30&w;FyyW5*&yzQJF>dFo4kxO2gjvY!{
zbm2rqFgsR%rAxp0m)eIF%YpQ2t16LSOTUm;vt48}N}~&8Ka$q$5gg&LaJy259?HJm
zBvfT<C{3VxR}jsx`R=GE-hN(Tf$gVdTs(eBHa`+P%dB6yI(C&iYa8)@nr=%@w@N|5
zG_XizfAsVnVno+P$adE)r^ETAsp)(N{-XpxFGQ!hRqOdjGh-Q=v%@&-(PP&3I;5bT
z7l9?X&GPA?0}Dzo8TU?^1b(QIvHIoDOB!>+=6+K5li!x$O}c70mp;+8@qApR$}+3x
z7w%dfB9S$*Y}6yb#cYv(`2I?zxZej;&GICa>><j33PlJBMnkC%8JG-)s3<NIe2mnX
zPnQ1LO}2v1h+ATU0`Tt~JGHRh2ZJhZDXR~4BpJG_o2)LZ_#j9Gvmv`;I@unXp(Lzl
zjP4=<w*y#rhJq3Lm*qeo3(;O`&zbp}`K|a`5iazOEstB7lhzb}BM+>Xf#9{|b%~QL
zImOS1iTC+z(N(H~(mm9@A(DETC`4wL?H}~>P5eDoD%Cifl0Q>*bQ;OS-`U=U7<D*d
zG6XDOb>kaFEXQ;h`$opt_aZyD<1FjhMPC6iD_%r4<dmPq=k%8fdD1<@(743!+1fQ6
zS)Xb!wFQ@mj#pZL^t97{_klNRx`^|+qHZF};rkE>kKS5K1fa41n0TfkdhmcQ%9q%^
z-cv3|2AV0YK`QU(4Q1eu71Qi}n4@JMBQE!lc>5!O9NxQzra^*x0cVQNalP<zili;^
z_ySjQZG8T{t|a3(imgq#pD+PO3v*S%oav-XlY}~jGGFa~w`uF@<cX<bc(vp{>V%tL
za`k5mQ5@-&uF=a|NCzx?QMOL!g<?w$2{T3;pi-u`<h1p%rBc?MmopAW;n;tokj_8~
zjGV`>x#5A32K9E|x^feI|Ln>8p{Da2G3i!G7&czKPr;Il4?kkA-eWY&J&U8RBTU9V
zTIh?ZmYX7fRZ?W(pE7LJ5c0@sxgt5-23%ZuZ2~bhp%WpL)Oy(oVrSiPN`WOu$AQaj
z;(~7vjr_RsTcjaLHz%7B#ENrdXC6r`h3<5-NVth*hiQqHmI<YyFgjBL9^Z7fFE-AK
z!v(?no!?T29M<BxIVpf6w!{*N!$Kv!?fLGnSU&21?i*kP%WaEDWV>pcx##~-UYPRM
zgJ})^(xuV<<#K8v%J+=2`aK_Zp_lU2is7X`M%u+G`@&AShC@k0vAMQi4-sQKr!9)g
z=?*E*l@a~QQHAtS6n4ohVy@UtgRlj*Ctar&#-%8GZU&xC#mjwl8My615&chTM&rZ)
zzPQhSxus172+Q`)EZv~T$XE+Tge4g~h+96M`Kh$Y9Bg<pcetGGG;y)b#o)UgXP93-
z4L6w-%Q$k=#m*14DzWxoG63X~yk%*ifhi);ijp0ps?vput&A1J3*MX&dqZHOMlc1z
z5<+6b;A@GJ(R5N4FdVrib$nf<tWdsiIN>&bO45`X5-Dck<K$6dmtPi#unl_HytwS3
zk6TH@bh+ESfnod*Z--JxR_WuU^5H=pioKigXUg^avcL(nDy>HZF2hrkf^b)7moykl
zgZn&6W!as(764mf_L)ldcjs!9FwNR6KJ#i;4Epas3v=Qc>n*D%$wAGKHLU{RY_xHI
z63Y4rKfHh7p?{bu8h2J!c(QIueo}b#ChhPKAY#zsA@1ZCrS$@L3*>%cg*I)va5%<0
z^X$bm$=JI`ZKa||>{JH*gL>ai_oQ|p((97sUyrVePK8`+eq!Io&0KVKxfQ<^<)~QY
zD4=bc*kbl$pzOmI7e23W!kMabZN#B}SGydpOX+!az8G=pwsi7teZz99{)O0nGmHTi
z+g$dB1d?R`lwDx->Vn?lu75yXy0<irxIgvPxK+ca(`}-kw7Vu*fhoN!Lg;7d9Ta|B
zo9~&?9V5!6r8VXWm0}DzVh@vz&lB&IKM}2UQ%*<d-XnI|rkv&>Q}ba%IIj_Z!liw8
zj>1>!$@Q%COqt&eP+6*&M|(ttP&O2ekbbbZ*`@Y7R&U)KZbJEBDga|AgOf5~wG|JW
zG|Vb9eVX*L$}wZCUx5#SRK8%)>!T^EeQBs<Ou6vau!*4q&5Uf(cW#|)ht=qHNezlc
zlM&k#+AqsU>E}Z#JoNA}?+9Ig4t>T8jgmM^x8NfI=M(2xNhuYAobw`Em}oy}L#NFK
z=n^vB$G@0QY>HhZv8h$MD@=01O$DtGq5i56o{-#~KL62th450PjgdY=C4gE9>$v4e
zm6%MIio&fd-aylX)kmB6`eFOLRlx=jpgpxD=Hc>Vk{HVzZo(wNu@E<ZAeS6fWs%@x
z6jt+v=eyGmr<B63V@kC4y1-E(I)m3+qfI~zN9CjVl{Cdw%+7!n;u|iH#<J$_`idDv
zEs=3%lXx~=l8aYjGu?bWj0P~@)kCi{<I;Eh?c^Y@wks)5!!OwF>8Qw>KRENNTHzdE
zWwf0;H&mAQf+P0>rqu0!RGXi@wz5*c_re(`XS?f1#LQoFZMwTJ{n9(5>_l3*Fk^Uo
zR2F>Q={7_+Y77<$Xqw|D7Sd2dqv$^U6p|$`*HZTt!{M3b7g{>>sx(DSUa^Il9?m92
z64#U1o1**-U$PQ1ZTi=?*{&`{z>;-bNH4hNZs8#Q1D-`KENwS`y~5xEpNx|0EK1y0
zKDvA3C~w-?o~%+KRC-j;=%pC9tMM~Q6|3S02QNGl(Z&YErk+mE%%NZjTE=!wAuEeX
zA63x2Xi$!d9KWUn&tT09PT}PmOW>=U;WUK3PjF!(@zM=m*dBq&Z7(|Q$3iRpbWHQf
zV)dzoxrV+X@M5ojH|iI{DB2@3edabZIoc3jx~F<m!V!o!MZp9#cpuK-Pnti5INX8U
zSl}3RyiK_*O%3n#V7Un&yiPxt^K3IQ3_k^Z2!CMRFqab4^+8($!>Z1|E{Nwcn0!C;
zhCL5^Jcawsi@li7;bLWk>4t0xI4}#BpU&^NE0ZMY(v6LOnjVQeH@-;QvVSLn%lt0A
z?CGPTE*h~a_%o?Naz1SEo4?<F`TWqUx{EKp2PThscZF_k+EmWmIIq$3>-lrfcS}RI
zP21Gdqd{Lr3=|8dtjdmVQ81{*Ub51?JU{VWiRUY?Z?!)wYW~`^<bs7%UmQsF?C6sX
z7XOtGNuP*+ggZheT=^~jT5$=SgEpCqxaSU4I^nceIKv^`?Rp30QR7XyJ6+n0uv)A<
z>vr%8KtHTnUW!YeTCf7fH@JN+#U=OHW&u{2wK$Jv#t)$K?UAUX1B-C;#T>N>La%eu
za}ze7>!UG26-yZoEv;JmCiJo9uG+FR8e;zR_6+TRNR|8Q?@M0Ou*LTmXMvc0$oA8h
zMM<r~_h_iERU4^3H`jyK!&kfl5H^Qc5z!cgZ;2D^`~-XSkClGqAw=HdHfMI};=D!0
z@iKKbPg{-|zzmrdC*nM9zD?b54Q|A|N8nj|9p)PLMZ_*_NxpR&Pj2L+z~<(owBTZb
zWKzd}2W=0J8jWguenL9;iJUR{g~9F<S8Sr*?)~T8Hcd2<HjmsRy<f-aGoI~@ruu>o
z&~n>P+1TrNFh^b{_=r3{D5nd2?Y{452(M!rC~}hF*uur*_W~|hy}h~(Voqq9L%^IJ
zY~&%Nb-8%E6zUO+WofA!Kd@JcmZU<ZuqP;g$^MbMY9wn^?V->JxrG>(F}`b>hi{{p
z)NDun9f8>0r;mY{0zb(oTu}@GLuM&*mL}9ratb?O_8-?>mVF{*;#cA&-l*)qB&3Ss
z<#>>3oEBx!+JLtNfRy?iTk0zFxCYeQl-I&8A?{fOAKbjAZz~v3^7Woc%e-svc$R>F
z{_v&#jHCzo$4y?JNsaCWpZCw<haos7sfGdPHwU4iZ;8|u$%kXA2fltKqG#{oK05UJ
zwaY?)7ij42(!c*4Ceb3)lVs-YB3fj`_)3Z$w%+ksg?37mR&BqGW*eV0zDI1s=W*W3
zBEqQpqtWEP1Nl_3&t8f8pP#AnUqxnrj<L0X<w;{Uy0CJ&UGi)M?KEXBMpJlCh^5{8
zY|9a|TlnKUW{T!%CpUZ%z61h8OLq!2ZE)n*ZpvSgq?#cI<`U%^?<%aK=#;6rI9)Fm
z@9cFKrM09JD3DP~?@LNth<0|=>P`i&8EV&L9s1vYbH+bG25ACsiq=cKb@Ata;@7n`
zgar4o6R?3QX@P^8={3)Yk4f6KU&mj9QK!{BID=w3z_ZI`(uAu8TTw^K9_)z<XJSW=
zTQ|OL)i6|~yb+D{x<gyN7238yA6aMNH#>4)pL6p+X1&MI_u{~(JGZ2{9RHYLo9LWB
zW{nmDDe?%I*Pjp3(kjoP-n<)sa2w`rc0{#CRn6|zdFN{J;OA4g&!wC53gxj=9bWgA
zP1h5hmDTUHRmM{57>%F`*K?gy#hZAR8!W&(v~|&hh%~fdg46uRNWIIYz$+I#WySTA
zC_Zxb_lR9;yGYbi()au)5AI6#n->Yx@lN>Ejp+UfN1L+^v&INQ75K1!xs=wHl5;ZJ
zC$CM45ewF6qA2hSxMxrdQj+2-BG?#^;=flL4knMS$rUV!m@?im_OBcAptd!<Tm7)s
z`l0X5cp?&D%}F@=d4`XKe2<6BQ8?IgLB#xdg;&K+elz*xka^p-wCzd1%*4)k&oT<H
zqyQDw2q2q^pLSf2Fw%E_Eg9}b>@A&Z3PyHfMDp7}vhcv+Ld(=n!wHWDQyfel@t<}c
zw6Cs_ghQPSH??Xyo?X(%6KK?AY<#>4vpVID_TzzYov7#sQ;%`S4wrrrMF|QewxFPD
z&?bRFOE0xlfK+7$e8*XL$xeR8aeKGxwK=5KJWfqy`GY3jiY_64rLH1Re>>u`fB;vr
zqP-g@m|<2U)sXm@cC!hcy%7tEC^iaXM%RZim94MoS4e;z##{PPuU8g(p0BjXM1I;`
zxy;t^8kX?<tj{UoJiiIzMW|V<AKz6K4Y%dA%;J2lSz2UNA0m(3AFc4Cu&*U)2ZF-(
z6GC-rsJ;nd3Qhulm0*X}V)dk#W-R0+r|kIfjO3?&guG0!Myfii$&88b;Qb;<k`0D8
zoh@xTcINat4E>xECxPmmbIX+7?L>`D@=jIAo7!0r;=WvmJnWt($dwgmEAi?o&tZbB
z8den$-9KlfyF-H3;#jcYjpsIqBa`j+b!$K~+sMnol%RHhsx94-G1^Jz^#eIfu`y|{
zGG7Ky`d*FEIO7@yFNglBR6RzMPXMT&{H;BDe3fYSt?Pp!zYVX(O){conK^mV;=6vf
z+zIpp;>p){F4pJ680(a8-T{_l9S6D9qZ}wb2#IJ3QF_K@s^W6k59OP)4=j)C2JeUs
zwi)VuoHQJNMRnICY7GY_AwRS)NHJX7>@FaPIv=|Izn<|mya8db!zVDT`kmd1uwgnD
zZ03=mVme)@m0s9Wz{E2LH~JZaP+|`$Dq7(KEPr{hARFm&)Dq?%YYT*yu!?i(IqSgp
zBd3l~>PXFZ+i;YXkyV_bCJndHoz^6w1<TuX(#95lz7gBnKDqPZ>7*H#FoRF+B%TEy
z=Hs(snbVuSV+pQ8r3~~#-wO9aJ-~doRk*X+;zb*DX<iU^^$5sIRmqB?{?X<MiE9qK
zIA_Dpx(KiZrpzD6^P^y7Sta^1X+@vzmF7K9eh_PR>OcNLT3@<UdP4ylz37=}5G%Ib
zJI>aB0jci`G^hS57=E=ky!fI}LL9Z|O*U=JgbFdW_YK)k&o&~pXBID>ldqO!CP*O~
z83KQ?!JI4^5siV~oZgEQ)ebLx{@Gg=wq;}eI<|(^?|fLk-6O1>h$!;ti?Tw?@`%;(
zG6ja?5DjCy{|o1{g9SHDO`7QN+mn&!ztGu#zGb7bb_;6gTqR_7^qEk+B6_7x|LNT6
zO*KxmK|1gY%HiFsdA{7mB2sC=^zE41a;x(i*wu<OTZUo5$MPzXL!J_jbp<kZLy^9R
zl}|kz)8!(y@Oxok@4*-+C)Yqq$~@h>Wdk@SZ0=2Xs-bO+#44#Z;aHwD0?m~#G~Vfd
z8bmN%@z-Ykw8vq1;CVYt(L`1|TjisbXF=!PB+cVRRsw{9sWeS3^7R$S=!@Z-^Pj0K
zaIJ6XCt<uInOZeE?A&>>$pn=S-h?wMLOL*C<Q+i&gXRc~-B*%BRgBC?x0E|?9x8^d
zF-qqr-|?KK`aEo{_WXMgCD%8Q{n`V6Z0l`vN7Dz@7-ffNpA0v)VCy0qDKna*mu{b1
zBBmLsn4g&1mLG+g@O#%1*AIU~YRs6<#9o_kBktpOpAVV+_NjXrCwZ9PZ;u`Bt4Y=-
za6wfBGJ@2V)_x_7fnkac-VvJb)U_##=<)0os_SyII@||$y+^PZl$RAb6X7a<eYunC
zmOiPj<{CbS;6<2_c+B*!Q8i2X?9Ip`&1Q`6##BqxIn8mHp^E#n#Uu`AZgBe2kLBi)
z7)rvK=Y~Nx(TS<1$EzzT6JC;jXhml3;xG_#vE{k`Lz_HGE(8^#4f+ER!|hsXmM{kH
z=%#T3@w_yf&_PJPZWOJ}<UYcGCseB!`{au)Ov9Y}iyhn6+~L=1H&ea42GhnHwt{Pi
zar*U~hF7{p-Skc{rd(g?;qOL0hfLwVsG4S4QN`c4qD7k^u#5-hnE0|Q-TZJGu=^DU
zFY@|R^260;Yb2SQZ`-Fy<y#%NlpxlQOh_^QkBVnb;WTa`)g$?XeZH7~H;9T+d@|RV
z^>UP!qZ|U|i;13Np8WTTmT}G`BCAE|1Lqzc`_z||bObcUF4i;dhXJ|DyQz|o4WE>r
zZ^a_^B3gVwg=?R2I<43vHWM(J^rNPJ8EAfa@upbmmELesD!!AFA8yNfC$`YM4e~e7
zK58y%>(kZ&4{p*Xs|VkIoG$ic<yw$^osCPPHR7}#wZ5yS=Sx22S2!mleZp7XlPlKr
zhG4!P{x_~R;NuSGHUE#1aK^k4^&e+?kZ*7-cER?m79j_LL2cN|Wpe5Ud14;BX|=s#
z4NByQ^sU)ZOwS@%rPY8yq|)q*3f)r-Ou08(Ex_C_H=0?Sg~h6W>5cv5SreVzbyWcx
z^e!pbU=h2F?L?I0L221-x7x$Vnv7Xh7R-EiAL?6Vqt(`?U!17H3AgVYqH_h9_i5br
zu&epD9k43~u!U#)icZB5Wp|t=&<eLA7*HT<)xxu8`gd%s_`QmY6uWy_VsF9yHe9RO
z&9o#rR7y6v#qmCWsk-n#BBE7la<N1=X;o3<C)M%1iKdxpW`s5fWn@sfZmnD;e&EtE
zcLj?$3KVW3ilD<-`&K+u9KC&XdQ;@*5VrR|?D#t3^+dstR%kopf}3nlkXj{T9>FQc
zQF-UgDyPhRxmyff1n(#8w$VT^+DCnQ_<^fB<K<3Jfj$X;!+E=n*$$XSz9+Gm`o{hG
zA|J%Ge!r~NP%Y(kdyysdCUXF+;Vtl!B$}<@JI>jTei}b&j$?1%oPfuMV<$)%kV|0B
z95h>>L|2sm>r^qKlVArX%#L-;zWt?@^$itCy1t0>0b&TZ-U%>newhO7^#1@Sn0`tM
zWo~41baG`4VQmU!Ze(v_Y6>$kGq*w;0?`TsGch%nZ;S&K5HK(bFHB`_XLM*XAT&8J
zH<zLQ1QY}|FgZAv0oMU6f0XOnr(}-^N$4SDX^gQ;$i9!gY{i&)FpQZoGxjWH$sXAX
zW#5TI)<|`1NmQ1QUC2_YY@_fF{m!X#-rxJ@`<c(oGuQRKmhXKn_aiJ|Y5`G4;haDn
z9F_!uNlKjujEs#DBv*YB0)s{>K+HiGFARbJz$B%mq!@*TH3=Yse}u+iwGbrmJOGm?
zxdIj-o&<V0fdqhJqQoc+=z>^~K*3RflOJFVk`R`Dcn}7NA`S#o9FYWZLJ%o1h;>0@
zK{1MpCJygMK)bk-_G8FEAp4Q_y)`5O0|e3?=R<Ty0|+b%FpxBs1mHLyiV_Wo;;?`d
z=!(EN12|{E60`=ae=M}kEdX6}6Dv~-F-b~b3okq#NB9pHO$$pa-E)AJI^0ql056>b
zbge8b_kS%xEQP<zIRI`+!T0k}4ENoQwJp^xZA`Uc(ET$2Fu)rm5YhW-|HVy&!VLID
zjpFJ|z<C@b07P9$B>Z_O)W^q1(#4BNlEe{QB=ML7ewMCie<I+6Be(;UCjrEO2Ziy%
zqA2Agxq?3f>^BE6LL)&e5!`pu!Tkh1D5a!0QS_w0iBSqc+K-9(X$}xU@E>Vh5yS&u
zBU4i&zypECl0Ym1i=-Hm5F{@m;CP^;d_mONp9Dcb(~CgZ&td!*MEE<+U(_{ll#|(G
z0s;{}|Lzz9f9pl`|E)IvJT?-CC8CKW;?Ia6;EcwA`|OGPJwsy;bjIp%eI0EJONbF=
z_OK9R9Hlx~Ns=$=z<NKPx|Y#-Kvq#6fXT=M`*W&|MQP$ZJSeP*jQi!&LR0EQ!V&zS
z|9!sQu{a-W!2ba{qp>LG{T`sa@K7r(+S3cv*ZPkOe?`UkOXmWT04V_U1VCS;D|A2c
z!QAYtVf$)IK>`EtI6UBtz!1Sev@=L~Fa{72-XK6Cc!7ZdzXSi27-0$k3XLRDMxL@Z
zj0e&6vCcR^>8F~)<S*zy!yqaxN!cbb%F3c}Sd1Tl0-YJ5a2$y;8lwL{8~3kVI$jtI
z9N__qfBx6H{@WPgfyVg#Z}WedT?Y4Ai^6dP4+Q347@DYq_61R<XcE%(XNiC6e@0Tr
zx?n&60+W@Ll98AGiCFD#8iq2`lxqpSf3Z<;sefaXX+^qYK_U^5kv)JwN?ra%p3;nc
z>HyTjTF*+`MB=|s(t)iu7KuZlu`YnLoIHRae-IFUj8c^Gkd~7J0$`MxM}fWv^8-L7
zu{aXN1;Bfe0s&_nfpNdb^6~&wV_)@CQUIWue@lw80MzntNt)79s1xPR{aYhT!I6}`
z_@&uDE!6opQ4WBje-kOm+<p@&+1!7LFew0v{gqCZVvI)+NN5BGg?9ceD2xJ-e%Zk&
ze>o_7{TnYBjKb9CmncmM?0X>ov&^RZH_*XKN&Tw(f3D^O*@8sCxr3L{D9VfJHxo)P
z2xwnBDat;;D0<50uYXtmkwEy@D*xuKp@H)afWQEVv>c^TFa;Q(ASV_04@czBEAn6w
zDbw+nynjCdAm|Gs8Apb2NaZlMw7Q6re<1C=SEWaUl_Xcnxm2wU5@|-#Up1fN*2<m{
z1l97dH-uz}<l~I=&R+>ixsENg77pXY>`pW$SM;r+%r4F%f{cSsv1qHm$hstHbtA)g
zIHdHkpxB~8R<2Ev?3;|H#3p{g>cx_#QgbUgPP%uG?Q5!_eQDEJ&Jmx20a!f;e*wep
zJA90%<<#)27HZNSnd4S0;+gu0c)w$A1lJ1#TKv=2<Ma2MKB&&%f_hCqg)B|+J9?AA
z4=<zhkE?SxGef&R9E}joqD_7FmfPSq^zE&u*O$}1%B|lulgrbpdl7#w6fvTVw{9R^
z6~rT?=n|r^Cr)|KObX2RdFW^dfA*ChV!w1tr)`TMK#Zk6<NC)p8ZHtoz>dyFyuMpn
z97>mbC+x7V<GCT_Q6uhmj<0=BKNznW=*#Mtt>niA9-EfXGQ!vY*mU=W-V)auQah@n
zs~(H5l_lUH^Y5B(>3E4w;nHe_oE#loG}h6=N2Q9nH&t|IwUk`~$0B_Zf1U3(Gxg;%
z2ghHt>r!to<}2URYv<{EB_4lYNvnfAYH(jt<Ye*39xXRyFlfHerNk7Hewur<O7o8L
zE5)_^hg+H<&%}y*Sngt%2L6zsYgANm3}`zRlGx2q`S9Cw{te|bpK*?QJZiOHZ!Pg$
z;o}M>3|&irdv<C$v{XFXf06m3`_j<R6&XZB*ot*l<%iau>0MS89bK+EtehS`#)aLD
z{>Bh8zO|d`6j(UIxsph8X7=L`7Q?*8k{CYIf(Lb{3_;Q4J2q|gaQHC&Y5q!wQ!K;U
zJ7mogNoJ8d*7MK#ie%eyQ^+@Oo*MXz>?Gql{V|ViI{bLwewW=HfBC+UdAZ%+qso_O
z_;t1Xt~z09IpB;&6wOIxwbtYsjn6>2zZdIEreZ5PKQ-Q&5$eSEU-hg)xvGFii=G8s
zGA%DR(wwF*b0?Nm%rJ40;X-W@70{bBiStEv=_w+?ecMyrwAuy}7nrQT1(_PP3OIaJ
zcO<D3EjQQww!Al0f6#5%`YlnU$-^kN(|~I{dG13p=TWv*b9M2(P#W)chA^_OObRDe
zAM&9yR48h24xKjLHH3uUavVL|Jy2>;p)#_;#gBY+WIdgMv8r0l{gm~_S^aD~P1lI0
zk4KYpwj~J@!68tM+9^g_%^n|<#g>b?)wY6?OMFcHFkg-vfAi*nEWV7_GRbG0Q71Ko
z6$V0Gf*AOE&3U^XmMlE-aaTBY&8pWyr(g`T@aLDF6I#;RM8{Js@+SkfHB$uVF`KBc
z=c{&QsbmHotFJVdlGM6UJ*Q|{MCfij-XNS#iL0+HPU-2ma@m>T%nw3uxkHha-<x~f
zZ<|+W@&b9Ef3-55-B=I^yw}*)m21AxjrN}#wWhsCE{*x9#FRCetL9ICNJa!(EB=Q?
zes`TsMI9A(?MQS&Z-@ZL=|Uz8vf!yCHrI(OD`c)~O6IpS*$$r-ZM_NMep~nCC1j;m
zv4E=8s+-f^xRFVu|K>RDi<T0;ixB6qu<uE`=z9>}e;ffeDe6!82KMH8TV;ly&*S=A
zVGZJky(Jbd<mS{z7ks`Pdw2VX@g0lnuyHR{rztp@T&O!EU^>EEdpCsvp;5HdD#tk^
z7iz{=(Mo5PKxITb&53D~wy8yNVRRK}oW%2+Qe^|s0VjL)CIsFFdP(MQsO&ks%Y(J$
zl-w}ue>mmWu=yo+ukot5?U!D!bdyAyS@psZ#>ZfR+r$-9J0mu)houO@$`|?Q6Hjh9
zZK;n*DrMGihRey>8gtXTx9?WLso~iP0rjjeFIF_6!YgsJmCN^Q1PeY$Ynk*caHc2_
z2kT;S^H<9))Ok7<X0ZB?9p+C%w5y*{T^Sdge?F44_P|(J?0I9(3o|Ar<3RXE%pR%a
z)isgzeq%!PidWv^yi5yE`TVMzQot22(fj>$ol-@s=UC#tGZVcE?>|6h+CiKoYsUK^
z$oxFs=dm1g2#!T&vkT|6r&i`tpY)HX31r1-<_;Mirq@|xJ5d#1{zt0Rxx@4P>^!`M
zfAOEs-%$?hta5tM*|n{|t`Ni(f*tLtV?7!YzMZy<i$_{uTvl0~AkyRMw3j{+h$~8b
zYGo<RseAVKH*0CE7(Z#uQ!fm?I$Zf^QTeoYlg0`cwfB?N$)clq@2=+WlKtH1iRMN%
zpGy8bhj^-Zp_e|cQD(NY?VR15k15lLe@uZ<&HZI0!6&}Y4#NzkHqi|=##}YXyWU{U
z_iZbs?xJh-nNTm$&=vz(2(>C>u+@vzayMi^TXhf97axl~=G^(^VaB?Uo0~r8dnOa#
zdvuB@PDRHF`91d54Khng*0k{Rh$y`(!6tbsx9mCcP?b9Jhd?kSjrmad8v%(QfBdR$
z?%q-tqvZX3MqTO>y#9Q?;BCT|a-*F_F;_|ny(Spj++1AFROx3Sqkw(*G-8}5oJNL5
zziNDV9UE+P-FVaHxf4@0(=3X72OYU)XKk;G@49nW0rS{MC1s$pR#4Z!OV#0nCBMh)
zj_gS?ne~o@E%nE9)4at-lPz2;f2DP!Gs6kqo<ia1BPKdBLDiv^tPk@dcwO>4jFgwU
zd9^BDXKaO67iOM*alv~vS3$zl?)FoOo;J5OE@o#@BP`K35JgUExKYQ&R(dnuCGpMB
z;gYXGR`E*M25VQozAF()->JSDK@*LFpz9vXQB7El_TiU_9e{j4{;Cgue-il&bXl&r
z9MjQ<8cH|uGN!(8>}o*8$F=bnCwgQ)9{1fU@e-<eUe)|WIcIw*y)laObL1n3v{ikf
z553~D7wwAMIC-m@N(H-iX=#I^eBW>u{$ap+)&9Ze_#5U3uCXBQ*vDm#_s7^;Aoc1{
z7p|24LU}R&yZ4J5s~Aq&f8HF;9~2c|$eu7X-OAw3oDzy|*UxT?vi9KhcJVKdeSLW3
z-eR!#lf!2@EY@FN@?y~Z(Aqe+8&7XF*r-rd@ZgQYp2W%H${r(qtg9>xX{-@Wdk<#X
zZUsBUs}4ubPT<NqKf!EJM-JiR6f2UoHB?c<6}Ius`OA#qw{qYtf6Lr6Dyg(xMNoLx
z>u<Gbu4OS-HZNjVH{l<OvP~w1P5bN05PBANDAd4q;O^QKDKXwP?%o+UmP<#5L}V)#
z_=MvO&V1_Tc-HjhA#KI%)1I7dNP2PO(PR8LbHmBlym96r`dKjm@Zac^$_OtEYpg7i
zUZ0{@TCHo63F~@bf2#h+KrP4AqnI9g{qzML#!d#6<{Eg`HBZ?aYfHDr;9nnpy-a@a
zVN<4JFm6hnm_kgD$RU0^HCu$Jr&7syZUbpoDJfB3K5k#^R&{Tw?R~T4Sr&H`O7v35
z<xsVBD%%^$-GR|>P5kMKrmAnWwdQTU)x;mB8jQ_dJ915%e{TKOa2SoJRQBbLqp_p&
z2!+_A*{^#O2G@6|%hoN4%);N4&32MwhDA}++&lWVW21yR0e$JvrS_*68e3%8OOI*%
zc&^wyp}#RkNQTGZ|D@XxcnMY*J;=*QDcf_Oe;n!OEKw|3A^Y?bgz?eU_BH+Sqm`TR
zz6<xtOyyR%f7CkI4QgK7e|~*uZ&N0u_x;YO9=RYj#GX#Kzi_Y2UdXk^%noj!dQGA7
zqkZ$rU9KLV)c%OhK8eaX(pbu;ksBMg8W_dTd&)YPo*1a)h-2z3KC+sjYe2u~N$-55
z{(XNQKQGMoT}*T8s!@sytC0Kkj^j^imvM%nbAD<}e?BIj3ZacOHrCD;bLX-y*Bec8
zWC-x@_^*ZvM*=M$+op?@K0@^Gc_n8aH8*$`YBhM=9$EWPI~#vh`!!Fpc2xKK#7ar$
z@1wkzt(`il>-0Pa*y_m5vMPmGcQeJB+lc_atUapRc!XeIfp*mTw#k$;lmFf4e%B?M
z#aB+@e?oQHRYFKQnXJcyG)VsT<;GB{Zw=)>aM$`FS2n%WqYi~RX7Y_iVxGa39nb#s
z9TSXW6tP)pO0PSnIk~KlQPsR_f~XPAc!nNYGJP8D_@jbuh`vS6?`0$V8}8C!Q^(a{
z<&A#!kN#9I<onyBL)pav!B@jwBlaEq<m#%Xe~YCk-ADWp*WK)yb8{a4*oj@>4wHN_
z16S8{(;nWt`#w}OW@&AgK7HCdh1UOK<$F&x+y~<+zrIjbo)Nc(Q-Mo)=ML?<zsiAU
zw@uRJy3vQBlWO3Q{(4qSKBDmue`j^zOdCVB=lx5VNyy`5zU@`zYfk5gLiv3gOUxeg
zf8+0~yVb5I>=NWRCwf_JHwQP|){$ZFzl*iIwV@4X@-D}pQwWyg^eL}0+*u#YloNZx
z;C1OCqwLw2O0rB0N-J!k_VHWS!+3X%ew=Bzs+>(58<w2Y-D7X$S`aUM_}R;{JMC{i
zwA>geoK*co_VTh=pfH{Cy13u&bRvUPe`chz@q{Jp&iX`#LW1ohNA9~(+DF2fEwX#N
z7yx8Io4>;yiR*xxnC`SHSCTzP8nQarQ@UtYf6~a2O!Jz}SE9+-j*V%1BW_^8kDh0k
zTz^3~l^zrJz+a>RvJ{`D=wW!~dko&4E~4~%%`29OC3~9^Pr3@WJKC+DWM$OlLKnh(
zjDNTJq`tw4m!9`n`aRE1gl;OGFzcN(`vjSZb@xfftLyz~iHaJuTn<e49qhjA3M>Eg
zMa+(*w`8p{5PfVTmpVn{(j%h`2<HPB@Aq-I{qED{Pz4(m-i=_M9VNQ8=6f$O3ibkL
zlHP0B(yhxu^+iTG8d%rwt|JsdF$P?;f`2`!{n-|?4Z_nTVaT@K#(S6l+U>PxC#HPs
ztDKyAG9{G6-5KY?+5b3d^oYixY4*+TokiKC4_!s=)UUUd+-R(ywqSF+79mY1*VnQ#
zNwSe+?;FZKZf-szZU#vj2-Q8ms5v;El%*0!8=&$4oqk-`JaTH*@QVn#gz2WOynn?H
z&)rq#ASQe-k|v`-gevA@4%7m9x88=`m#F(}<xcl=2O6iF%h%25g7NI{1^3SDB#A_-
zd{=FxTHy}|=OVst;8(>rX|=b4(h>q<xcl=T1vTibkIHO5M$MZvDw>q9-JhoQJ?>xZ
zOm{?P^*V{$39OAyrpm)^@Xz1WXn!2Ge^zo8*?pnkZ7Ym67#25ozEo4GcgN~}QuxCA
z!K|B`rrO0j6PY3QeNIx0k!L|LLR=9&84S8wx&UbRfh!TTygbU#)I+WgCCGKvA1Bz0
zR%>ruXff$J&h>n-wbF6eFKC(UXwW)hbWM2YUDB)1?AI8tq#m(!Z)&h@oPUP+$XOT6
zna^fZwYAR}<ve8OIgi}zFZo6_(9z*JR<2yBzv*}3GJa(%=1-NV6<ul3SBlcq_HJ<K
zz1r_5tk7F%T&Im-b2Kx-v<jB@gf|ysUoyq?5uY+vzag?@k^$<pUcH!VMrJfC*H^T-
zfqqR-_Srfr>}q1WEg{_aL4ScEVM!}aAa_zEuq%zp9FZ%=sV#Aw`bxpcsfPxY+aghN
zQwp2MHLjT7w#z28=3Yv_)`^>HZm6&=^t7zC+FWYXboR_+gxAycUz6-}{F>&{-lsV(
z)vl#CSX87$R@bl|KAP3_6<z+Ybxtz-)uJnl7=tB7&gX;wMAAED3xA<(v0FnySa||V
zH?Abg<i}eFsD-((=FQ+e3D{XvOFXpCm->3dx!Ho9qQuFuGZOl=37Mz#X?lm)m`hq6
zj?8iKCzNK}wTg3ONbY2MemO0JHV_$46=HTh<ooET@SU?_i|dj65Ho|lZ^h{m?Ax3R
z#m9YJYHwlUxUUBDFMmgV>de0m31)?`r!}TFqzPu75_;hH`F4|1wGxM45cTA7>}Y(h
zj$Y1kHD~SU39k-;IvHt8QNNSV`acWW++7GUrM~@G2zxgu>w2I~y!)}_mi3|dTXHhy
zqMj$CYZm90Gna2VesdC;P59=Mz$_XUv=wIKJbbb0!g3jY^?yh9H&bittyn*Z+!3Cx
zMKR~4TdB&fDvZ>U(ytAv*&-X;_RjrS+aVwRSlm5+`L2D9#Cxo~dcarHj8CmxsNJ}#
zF9xlP+ubL&s3f`)19x{KS3g&~?Y$qxGcA4mdb0#&Knv;_@`v*!KAnzA4=ruZ89R*8
zrkOT&OTPibD}QLLv)A}Z*?8;4A6{Qhh(TXmX926c-yV)zYBpkW)*L)ECzuaTJt{FR
z`q-UUfi@Rxa&oOBEXH}9AE?hh>+HSb!D>(MvalO<j$_G7%>yH<>Je7VJb99CYuE;{
z`(l8Nud84yI)1Q-P$S72nQB6v@<?H^ZK5V^DW;%vGJj~eRD^q8c4lPf{zy<a3$MEX
zn8?hr8N$=R{1~IjwmGudky;gF^zc*oMB9b4v?YdI0UCNv7eYD*E;*@Mk<B6kguUrX
zAN$bMfAeAor#*Vx2$vS1`7do-XqLJ71_}ZqLY<8p4YMjWHtx|=>kJ)ohj)ixI$5SP
z!lbp`kbiHJ-Vi3XGr%LNwUa3%X!!1BRHPU_1iOyxb||;(dm1%FFI%Y>qg}>#{FB;x
z7L9LuISlzd!B)%zem1;rb+7%}8mE&DTBkYgN5ZQXK28VUcEefglovK%akr=aIdLsj
zRK3%llfFcGkSws)BH_REiI154KQFxtlnP~TWD#?8a%Ev{3T19&Z(?c+Gch-o6$KO$
zI5#i~FHB`_XLM*XATu*KGB=l@{sa{SH8eFjlVKDmf3&w{RGeG0HHrk+;7;T27A&~C
zyVE!{?oNU`3GVKJ0KtO0LvVK|cyPI$z0Y~G_j|s-cQBxtRjX>ws#WV*Pg9X8t1*d~
zgG_;vAO}|_HfB~nfV_e#$lk<(jg?6iXz6BW;tXJCW@Y6>q@ogY2Aa59gB-+7T!DN5
z9#<=Xf0CIiI2OEum6aEf3Lph^06K%6<^WSKfCA9fMBU2~$OfP_`3oq6TwIw<O<cfk
zpo68g1CS0JA_j8wa<;a#a{ZlygNf;Prr*(`%m7&vGh2{{i>)=l#K9aO%dEf*Py~5^
zjn)8KkOROJXk}t&0RUM5)PdRn4K)c>HGq_=f0Bl>8XYq@v6`EsBgpxGw1}yxYe+Ey
z#6=X<B>+H8Mu3!tn)>g*>OcpueoIDxqB_|Bn+Lq`cesLtx`?`tvIHB;?-~GX0C%9X
zi}i2X|I$VcRtESZ4IFCW46^@=06=Ty>gveH!s6lK!EEW~;>rwiwq$m+`%9m?m9-1N
ze*@%f3jlvQ1MPr+HO9@s9NbP<E8yP=e(wrE-r5Z4-~#*|BnkT4X%B8CI0$Ta{f{tk
zBV2#ywEKHGzy%2W7mbyP%U`kb%F6NpdlPF1SD=H5gBf_CtBI?d3&8j<8~7J!PV=`w
zAVAE`+4(nz!vDIQ|3mY?(nUew%Jl7gfBZ~5{(Hwv9Nb*I|IwR&mu&`eaItoAb@@9Z
z5MW_#2mGzx<@cUhJN#u+5K)wolu%P=k_Qi-1Cs&>+#LsIS5Mc!R{zc?A}-Gdc*n{O
zVB_Tku!4tF!oge&WN!~v?SlBbed5;OKDmONy;%P5VB0!?JRE%f9}Wv^2Xl+xf4w(%
zb7awQuy%3-%838Za<B>UkIfS33Sb2Qod7^jGb@(ggn!M;Z!_C(Gq@3cK8_$qfQ5;j
z3((Kn0to&<^l>q92LfE3-GF{R|8)EtA+qrR%&pB_!J`g7E{K0+mvOKF0eJs5gO&WR
z>wkuT_OGK#2R^6fAO|}yfH}|tf00EI<O&`M+W&t}+JA9Ly4l$&n%Dzr|4&c<d!dQF
zwVl_$m;TohE#Pmpw2B~SdlS3=@>#n`T6+S`m91UPtp0B8-*y>S6Y%_tI9S>N!Q1ke
zN#pmCvIEa9`1xb~`|$-}V&mlgFCTa;&1@ZjE-nDhzr%pwM*NpzaQA=fe+96pE9pqf
z$T0lhvH5GAgo7E#+}gnsz|O@DFmZM^@j_$;&jLFa7r=)NJlN(y&%cHRz{2bRas`I~
z9Nk>~02Ux;#NQjr%>`f)`EB|eaRXRH{~#U!i`XCZ4!|P*2k`<}B>sbVSOF}Oe-Imh
zMd}Y?2e3&0K^y=UnLmgVf50O92Z7n;{~$2C!XE@?SNwy(>`MPZ@4)QJe-M~Y^$!B`
zsr^A<KJ`BcT)V~}1ZLO#gTU-s|3SQ9Wby}rwV3`v;A%~s!P5(LwF6qX{;_lX$Nu*@
z_>TiD-t0e!3!KahWCxy;|Fv*({<hfL{~=^!1y^YP4+y3N{>cCqe-8W?1NU#glbea%
ze=HneG2kh%GqL|i7I331{y=uHEDP&DSvh_~_dhgj9AFU^e^PS&4hOk8|05wd#PS~y
zT!+=4s=&>*@^Z8SI{ae=*k=6?2rk6t9}wJh+kZfCqwM|x!E*mm3>#S7pUhm~PzUfi
z`-dOg63`zp;9$_df85|=9RIk%$sA3<SJA&Vl#}g$tpDCl@Zn~01Ug%T{%jB@xDk$a
z;7jgLez3*q&;I;IZa|m69uNOn!^!j83Ig9prgr}#X5)PK$MbLU-;b8RUH@fg12_L4
zTf+wK^dC7~;PPF7_SXNNJFeerfbRd;ATDqc7i-Tyb%7PSf7qG0Sp6e0nEwwg7q~^P
zR?fhG3@5mit{$L&1b}n6{R4tabN>efEA#lrOoF35{{g}2z5W5go96vT95|CV(D`qw
ze?Lo=f4@)sby2eZdAR=1i`HLQ&D9xX3)HeU2ft+gV~K(Z_~?4-v4U?oHn1K1^S}QY
z{EL9<&jtODe`rxrkf#q5C-~SfvGanT$(-QQ!Gp%*_pey9zu$TOx?#b$!2jakFB||M
z&=Y8exHtzg<Nsij@-4K?U!q{L9EOUQ`J@u(y|!$^o5l3W?}T{bxm)Bwp~9f1zzpg_
zki0aXf&b?qhhlB257>4uYt5gkCa%p@gttxn75oWNe<eglax|GWf-@8r0?XUU=?-Oc
z@^wl$e`K^Iw2%NaMvlaIzjxfnu#dmKy-X(8FK=1NgYhVuVQa*4w!`pTKqqJ;T$pTw
zbbY<Yii<Ys7Fnd9HqH;l8Igr`?CQYWfs8H^dWxdm$>6)gl%TzLT3gaMgwu;~X+t7{
zAP%4;e=4_>0?;JsBjR|Z_bA|gh7O-Vg-j@PX?F|Cmzfl!$qqTfZ+JVk@W9J)<*OsC
zz8st)akAWfkYY>8mu4^Jt(p;P*(%iNDTw63|CwF_5TB8EEc^9A;oVpU<1e?njpwfi
zy7oFFh%a04cMXfi@R6TL95RkOn4v}rLZ44re`FCQ_>xfqhag4klr{)&SuD{Fq2DUt
z5!>*_L+f&1RGvv5d?>|Z1&Bt-iNa>hhU=x&NKGqsI7_VE!Z++f?2}d&|I&HaHMGGE
zd4b;C?9fbtN~AsesfONz^h2N|XvOuNm?RS4E1o5{pSd#bR>_bpT5B0zR+>Qt3|ZAV
zf91n>4l9P`P#A1O13b(ve%aLc1=VHx0VX%GpD~<+Tj}9$vF8ok^4K<lWc*|C#u1D>
z>KlW*Cktb`+Nimj1j8ipl?EPk>m{`lqeC%GbX{MMsL&J}<kxGXG#4YErW3E1WL|PI
zpFUyway@)>5si<XP=LS(!kQ~lzkOA-f2>KQ#C4+H+0dEqE)&TmTyT4-q74<6CSKDl
zc6#hlA@JHg6T*H^ZL}aPC1=sZI;@Kzp`Z7qy_WKo16UO-zr2ZvTNBGCMa#H{g@j-+
za~wRP2d&V*Vqn+qK$M1qRC`_OCb2U&ed5pBp?Y_l9_EU3lhJBe2&aakeDspse__*k
z=}}ss<&MX_lXgi~yn0xP2wgRKmcaJaL5!W9RB1L-r2$(F>4>1t)$58d+u_r$6e7~q
z8|dc-;`V4i7(qg#+t|`!$g6P&l2|Pv!-MW%c0!p(!L0Y0y*&^H$MOaF!BI?6W0f-3
z)elaPFouA!)Ovt~0wSZY952WBf1paVb0T7uAEt9ny7SGBZpf2!m&&Ni6;wTv_cq3~
zdFb{`#qW#Yx~HnmgxO^n94S62Ox-^tZ{1#77Lv>tq8){{&LWxXmHG>2q!u7Rak#v?
z$>55ai(_{G%z~FLeBfZxW{P^fnw)ySv6BFGvNcDUTXcF00iz>thz6(df6EYBqnx9^
z^K$kVS9OvV^G7|xRl7qCQ|Axg(-YDz!k-x%+EaN~dF^*arh*{t=gu|xs6P_SZf_vX
znK<MY;>0uYHJqgQJ*FFuo@^UGP1ois;RJ&SsXv|tZzM*&GwtLGst(Y9bfDdw8nn-}
z_zBsh!AZZfj26iFmd*yLf31g;yFll21G4DRbUa;<eAGDp8nMHd4Jr5Ht#_t}WQ?Q`
z!Z~k0RCC3E^wrsy%NDowkz>#oGsO9cn(34l<f-+NWZ|`{cH*&ob(@ZdT*hK}C3jKO
zw03<LZn+{hAkVg%)LeawC*o1qDd_@CkPEK9nr3e~uYYDOFzUxre`W9SnpOKOM8+yu
zFy>UI>{#|9RyF*?MjqA)!4vUAxbkBLKh(#8hh^FVCn8uHey_)Av8YVEz3T&&?n`LC
z7yClYyf6V+cBr*$l#Sp9@%k@LG)MM&aldk1R8sxbsE%UjK7R4Z!8&5}RY9-_YII^u
zq#+H8dVY$$L&*HTe>(QMX}Fow>V+PuV;!NX-ic_$T671wERn*&gU7?iAD0}3CETA-
z`{3lhF`h_+5=O5F+$s_lV@Mebu)eh{_P%P_U`#5U%khTCVP1H&(@`X}LvO!aQ4jV_
z=MI7OL}K$2?9q<IMb!m-Me_Ccah>(1V7FV?;vjdwA`h8Be{-@vRc&+k<ZKlDm^eh<
zL@RG+uBs<rcU<K)p+7^At-38VCF$4?f<uYE-8c4;yrFjL)bDY^&OtG0+~mH`QVQKD
z9(g&8x|}2myreqCx_XZDn5;r+nIIk_jPD|_2V!*lkgPpdy?<}X$?%4KDEVp6g`bD;
z%9xW&Z)<=5e<g#AbNj5l%eJTn!OuC~!$o~cm<O{ji?4kv>Vae<$ho%r(44x=%R_2r
zYj>ZECldWp;Kf?sH{Bzqc9lWh=(;&6hWQXGV-83?l8*#UL2XzoG?-lGBG8r-mj5_F
zX-e9aDP$@l8uYzEpwK4BWR|;o5|V&%Np60gKm}(Le@Sn`jgdQZgTKzz#QO&ngjvk(
zwoZ;|4XsVcOQ_!g$I?4cQWXm&p?+zD-epW1jx$niFJpR2yS6%`#JQGqZC)P7iQnre
zl_AWr$sPpPCp!mLD09#lq)TLFbCv4%$+_{Y{h`T{ekMDTSK*Qsnw?H^;rDn|nYj$w
z9t}KFf75K#GdncT-YqY>P9(SVy);IvN8EC#G2_L%i+afX*=$(l!%WC+qQ^eyNNF5`
z5F#28k%}|D#+#QR!s|TcZp$XeGISNDVN750=e<&KoPW*Je88W4pV&ZRIxgI8;E86u
z9DG8lHejE-eMU~QDS$pMi5^x1qh&W2M&qRTe|@QT!}?K!fl`KSCBGsc!-!jyM-z2e
zhl)RMF^7Y~(<(=))^)p|Q~k?VtkO?%<Z1Ip8XJ;|qO}XT_Ro%E%SoWp#tS_wE9!<*
z1wG@pGcOT@2{E0Ve30-k(t+ffj~H555oj)Yxsnm;s$cf!1ygjr_*F$bA`_&CZKMZM
zf3D;cM`jM7+5Ea$riT_tNuNhoaS`pT5#92Dk6FlxYo@OI&76dM>ZK+c*!I|@<x+FH
zvs_T_V{bf1alK!(ru2v?{R8^>$6mu^-JF!BDW4ZCL=<PwR~cU=?aLEFvY=z<N7}8E
zT3t0pc;qEnA4Pa(jojhG@dN2QPu3*ke?NZjDgLC8zGu7I&vAy>0VJH(MR2hl9?qrN
zIH&8I=V88-d4RI)62{DCFBoJY2qx5SSF`-+O2ws7-k+&tv_v+w)gmO|C*v$or<_9<
zpAL~>K{ck9{b@=M^SkR<yTg-3V(keQbEw_E5oz0}NdhKv5<&Ax>2Xd?qz=elf0M1k
zRzBZ!Im%9%oLUo1fDD23+7D=_2V1Bjh=i9fYVt+2y9=?;A1xw;G`|uV!Cs+moqw#c
zec{`n%2j7U39uqOf8d3^e2e9iCpjN&`i-T%AXg&fs#hX<X(Ax6|26W49mNfbtwHrM
z{(`)w`yDRwse4q>x3;+{71T%De=|z_Awr6q_)i9v!-=QyCJ#NOn@t{e)-P!Q|7IIz
zJMxs{P|e-!;Dx4z#h!!isSkTVyBB+U0;_>&Z?Al)R^2z)&dKwv_b)8`NjOg;9tPK!
z;RA#!K4ZbO9ob*B;7PTX@8=bLS#izr%#sBPDhx13U?9+KvuCFqkR+Z*e=OYwL)FTI
z)+30o<D09#RVzC&!3%Q&C1di;o0tTII_!yjk{hYnv)^zpp;0<VT^M-|9#jk;*BFIy
zi7E}it?Z$wd@p3A;b#_GfO?B*7CuhDOz0Bd1ktx9QJ|9J#9bQf#E~}0_D(5}Ivvvp
z$VdHwF_qne5&Jm!z>@Pdf0H`F=VI#NCh>lvFuI5oxBi41%8jseHDZf6_8C{Ve<>DP
z=xQBpB|yp2@F(imMqtcM*iebv;*o%}rK~1C?=#Dk*^?hTf}M@OB0RCls<+T0k5GDm
z+|tvmUR(PKg$AtAmzM*(s1oLx!*L4<Y{jlRB(?}k573VygpiR9e;Y)y<us<YAOZvl
zpH38CYO75P4(xi?sX-Jb-n-ba84cmj`Bagkd~T?pCT6>TRLpTL1-#(4Ije?@LkeUg
zWb(}#w+@xiE7#?4JBqbL>m`4HEEo$)u_qI*?0*n4HryVRMK5bq5iPuPpxN!vg1nzu
z*uh1-eeMuIz+sM5f9fBT>QXKp;Av08?tm}ie!hWiB4M@3y^YHr3XzS;%;2%lP|NuF
zxYLn#<txisoTW*F);h)khvig>nHfJG5Cg{-Ej8o$f*bzDJ?`*@&y{mmh_+M2AL&Pj
zPOr023rkntmooNRX<h6v?k7V&hr*w-3OssDqRUf_DBgz9fAvqP$7)wDXOyMPD?i7T
zvl4A*w|j5)x=(*GNGk2Ass3{CoQ=BJNMvc7p8swIMSU?HN<!?FOdDhqW(R61zoS8g
z#`?JVzL!vhNR3awf2%>Wj$2xj55)w7VkoRTi!dX+U#DYnl>feuP}oxx0hKfDQ>@tL
zU}po5oe?*De*}f&8XO;Px3vt^)N6eYLsFf6kJ4*j<f{E6C(M;OLcNDT+7V?wfk^&F
zmQaY%gRObVS(Ys9<Wj9+rR#xD<4&}4%JYf8`zK7w{R1JO=)g=iEE-`_&rr{bydDgT
zkSM-3lf<WtXg)8v5~{k!ATxtG<?A;sSUrc+vq|o$e_H$x{c@eioxc?BpyX+92<Xpx
zpL<+n-|eJY<Mz1K-W5N7*$~W&$4HKWr<j$lNs;oq>+hK#0;uJe&K1SsW_`Nhi~m_1
z*!6@HLw9ajtgB*{qdU&sws!sl0s#Lu5gyU;AZ3N3MDvm}B}$fG<!wv{?dSIuO>8Av
zYnOvUe{DA0*A}vZhhisMIC6>Gv&I-U=j%A%p;vKrExOu7S~9NU>BUfB*Y@|iSP(QP
z%D<wG;e_I3O)f#vL6-IpHa%RSQ#}*{sJ?n0HO?%ks|yB8j{73tt6@qJ?`qm7eYMaT
z^k64;d>r_pZsqg|l)o1cZ+?=9Q^H4#<GcPXf1NbaaueF3Lt?8=L_$!I?+4{s$;M`|
z-bqW`X}GONunro9Ojl}aw>ZmGQKnrst$67kp06-+aG3X|Z4ZiOt|DE7CJ<N`6LLL~
zfj4a)y={);buDcWK=EML%Ql%HuyOB;9CAM!KsMXyt?;_8`z7HQO1f?79>E$SJVX}b
ze{oxENegpMRNM{($7}tAw)7aofC?^>I4GwRB<GMPF}uzM@tKQE_2wD))C}Rt#dbB@
za7Xl>LI%fR?&G}8h}IVOGqO@Z_x7A<m|3_6Mh0i*r66^^Pi8~Cxo;J`tjf>Jl7=}(
z^%GO&7${p0=SucDdjN?{!<()OrWrT~f1x6>hEIgDu9Mj$y_W!@vgb0Gj8TcFS4Pv%
z5+*df4;`U07zh1yh+z*oox$%wRYpH6(&u{OHMVY-e{I4sDaZ{m2|SfxpvCdUief4e
z+9FfNXkJQ{+rn2o%V`Z?$Z<Xu+O(xKROiz3Z^FtPW6cuKXPGx3Nk>SW`tfr5f0x@*
z%!nE<sO2mdwQf7k99BYkD~m49(vu;8_EqbR4*kO*$#V<sCa4)YZWz*T;!0i@s-dF~
z7PVt4I!z4mgY*<zhpQ0D)jBj`>73W}G~UnQ%d_81G#^!a1+9D_+K@YT)zTNIK1*vE
zYl8ZGkl<{K5dOG5z^|{u>V=S*f7wFSI-J*gkvWdH0Gg$6(l7r$Ih|fM;8x^hd^m5L
zHt%-HLSgmINukf4!Dq{;(c5@ZVNDGx>gWj}3|VH<(#{$Rxk#NJKKBy&d<N?)Ng^>P
zZQ_tp>o*mR8&A+<b7}*wmib;J_%eEY;g41rymp(ooh1!^x!^Vm5E-*Gf6yL=X%9NO
zu|b4JwG`<z&P_BG)lV0uhf>-E7TLv#VZl3nR}B@pzA(l7$Xk~5j0ycg^rIWY9L~Gy
zasTQ%8#p956e)50(aU*qtawjRwj;aCh~PpgL??CP9ex$D`uR>OjLUA=BzsL<hxbgB
zYvs~Zw>=FBkFN3An;^9ce>8E~6N>kfOPX2z{xL7_&&nJkTlJr5hw;YZG21;0zjoJ_
zeJLAS6Q^~bLf(2kR`m}Exb7;|e=%1<s4X}8d6?1q4r0cs6{7bAUZo}1C9jk;YCNx2
z^{Fc0%ZF5fqZf44eJKG4s2I~Jml<7q-1@w!MI6kLIOw%2oJ}gOe?Zj(*ZZiplAVRC
zm?(>5&pBC{qS|`CND@hQuCMOfqL<=49g9O97|#w>!lYuxgrfnx2RZYzho`@W6M4PR
zY>@=#9wuOzn2Av9B%RCsD#U@CGdg2qhurF|VRRLdKY$to*f;p^w@<?9;gq3qw_{E3
znwuS%C<(5s;La`*f3h>mAU|!%TASyfJVQv%IufRl;<qX)GP08{=tSd>VtIy>TC53i
zm?~Q$i?lZiu6;wu#0CMSVyL?(kT{`vz5~p%<K#V%1P&rPO`V*lP$u(7lgX2F)Wh8g
zFUhk~)om4w+0k-un{10#veFA|I0H2R;=gEG5%^n?ntiS(fAuh=iB_jxyj@ll@Q8G9
z!tH3!-q{c#5!z8kl2dmnUldR31-1!K{CHcrO0@hq7pi2Wx$<2T2H6$w5Jq*~VM}8r
z)211xV3SpJ*z<CAk|~tEo*HUgB=p*%yNdqCKjDNyj__dM4ZebNNftY&?yY|&udQ*V
zidYhpX`8G1e|&FVQoKY&;_m(tNkP7M<9&OXfD6K#z{B#@ZTl9l_XGZh^~6k<Z+pq`
zkQJOZ$Zw{`P{^2*pyb`L)bE3SVB}s@rSe<IGpIfYSbe%EY4qKw5J6Trc%lz<Ikl8P
zKVvt-S=Pt5MN9eWB2gY<)$g$lZSi0Puk~uukN$<Hf32M;u3l5Lu1f$qYm#AR=hz_1
z#qmeLkhE}ay$?6HkP%)x*5MEyF0Uw)H}gEbi(7J|uBE*Nh3g4N*7_Ob)de+Kgxp6b
zc~&4(9;C*7ujUq{z)$9c>ewBj7`V8;;__ZfiXjbK{aCtNqU>MNO~>CJQ+3BiV@goe
zcxBRXe*w%l&euuK8HX-U3Zr#8s@$aVekailZ%X%Z<`dEiq2dTUTO39Df>$Y4D)|Q8
zYbKqKS{jc$%w9)b62xXLv3`UqUl25@#;o`>dcg}}{Pb)TQFE<=)6%1d*_qyi)tvL0
z3`&YCOE<A?Lx&%o3|Z{OLxP{>CK*HfT2nffe_O9AoEhzIs3hNcsjlGfT4wUgb2*5t
zTjpW?(fX3kKF3*1W?8PMt$YX4NNrW;lZrf?Ld=KacVm^ngvhtIk;&Th`CkcZ<6~G1
zT_g@7NRY|}cux8#)ME*M()!0q?Z41eb}=o!|IC)$l-G>$oK|NYz<PJ82C>sFUxNQ_
ze-NE|=uuSmI{te+&K{GWZg*9NHVQ^r1tE>C7vF@9{dvUC4v9q1r1hDmSuT5OSn6Pf
z>`LUiSpGX%=6cJBj#>9$Tdb{FgGdn>t@F6!!+}`bX+x@Z{Pgt32xcop3S%L1OI*H)
zvploD2_oQ<q8-yA2z^{vZ{B#inwM$Me}1vzL6K9goNHu5)vWiO&9pp}rJ%GkVWb<N
zyE85tJ+;FL-_}E4wl3S$((>z~giI;wwB|djf;9(fHH153JmF&#-K9C_{&sS~)xy}%
z`DBAf#bRvkvdA{XT+g>(3u=9LxO-5LLUW<rszYnwnFP|NVI_H<`;olp=@4h=e>X|l
zD0;;v^5ZA3Ur)qI7<FG<vr|}OB3WGsm~h%}(BJD{y8Gc%9#+}rxGPe}pg|3Optxgl
ziW-_veM2w%v2*=vJwM9+b+Q9QG_38-apr7<kkMcvD!ba{OppvfU}SN$1nMaH)4G&^
z_`p<RexT{BgsV9aF@Plew#4U!fB$sE0i}XA#pH67jcnl@wRcHQ?iB@X!qzz-<g53H
z<)HV@oHeM7IB(Hv&Q85_MKQ?Mv-#9T1aByTmH|U}ddGb8GhC^&CH0#N-rlrP3bMG?
zd|V}v=%l)ZE47g6^xhBC`@k`F;o*ro+wA`I*Szc-Psw;nAt|6zRXS3ff3!Nu%S;PC
zo*X`Vfo?eqvx^x=K-MM+c{{$i^Ggg)k9Jg>!{dHPar%j;8uo7EV8nSFM!GxRK!DxP
z9K;YCJk)EQDOH=|$3dl1dEkY0%Vy~-;|vV)TibAxv-K-zFNsL~@TDNBKsn{H&wjhz
z)mgad{?>IV_>xD(OW1@ne`C_ShNe2ObkV4H;+l=5(6wdBv1$+s1~4WnD5iHowbVpg
zrssf4u}aA0s5vL7O?H;a7#q?x_Ch<RdE;H(cLid>!apu%T*hjqObR65PbwQ(zkZZR
z2gY8Pb7|eNuMGxyUija4=6OaTMxVaIqZ+)WgT}Jh7r`Eg$BZl~e`}A;F0m*6iDxkj
z2^ai^a@Up+rtp1U;4t4E8?zXr0q;3pS{!+GP;<;`WN5<G3$agfAI_5Bi*$#*e&?wI
zRfnL+A|=(K{G>rRvSMF`PL82y>GzcW5IJsr-s@jISzY#5u`^q4gt?!Kco-HmJU8cr
zVkbCFN6NW+ZkD7ve=(jp_hm#u`3NJVwUmqMww@R*u*(YX$1)T%0$hYztNon?sI3~e
zKcEy<db016`*-%<>6eIlj+44ytLwi#Hxa9PcT)ONjwJd1`7&w5>CJZitq@in`;GTx
zM26`}P6&i4ApH~b5{n*}q9Oe7(P}%LD+c6M9d$2E9Ob)3fBAHj;_zA;!1?yMTr%2x
z*J8cZx%(6y_vxWLd;nc|P1xJ1ZW~ZQ_m<L}l8<Zq7Nq6dlT2A;+U@rXwHo8|Vvem^
zj;iT1=yaM^i;rYR<*#E1YeS8~TcySt(x%C9jNELgb$G@whqI3Rd0WSt>|gkA-xlRQ
z*tP=B*Qq$ae`sb5c1OvX^9N>Qk@5PxH_PjZ(rA>=Kuout$)qt%=}B)m%9YNvM>x{R
z$VPb@Cg8Q?a5{JsFZtEojpH>S^`|wb#vKbnoXo4VJEJu{<j>Vu*KWOS0y^8pn{@0a
zwzUz?&bfl3&apy2ee4uDe~RwPWjZ21(5XmCCe8IUf9W%uTrg48(GPy<c2Rj9PV0_d
z5>A#|$*NDEt<0O{56h&sd>c`oaIm}E<FVSeL%x6g@Yd*SUPi6SnO{>(VGZ}akNcT{
z`dwh0qG)eCT1E|AAo2A*lUf#g((=8pVnAQeFDacq<sqI8VHzE^E%L64fQ2t#`{~9Q
zU@$g4f8!$SXM!d9&IhCerb7n_@>!?QgfHE#ywm+qgeHjRY(k#%5JV*~lOzYTHylwS
zrkD39_nG+?u6>C=Sj|wlioOu4*o9=3LK0ik=H(2&%?~+l7+)(?c|r;Z9HRUctu~CC
zB#O=&(+d>IMgqZXnwGa1gg+$`nCL5EXg2x+e;A$e`#KS==N<cpQDqXoXT(H0ra=Z8
zyW-5KiF~D1(|mdP1?`ippfDOb-OqBkap<Rx?6Ge0#noK(-A|(s<>R=8mxO0FN||Y)
z2z(2PWIEBcwgq}*+0b)VIRchUs1%B<x~{1&HTH8~?#fEBw6iauX#@0d;h$kY_PL2?
zf6+A%vSKS@BhDys=H@jsG{>=5RSOED7^mgj5lmh}V3W;GT7ghIciFQ{2}a4vwN14~
z<ogz`?Gm$Tantu*-+172s^S_h!{3nU=9X>M@>*FZ@yAfK)At!Y2bUPpF`NxM;JOmu
z1Wby^LTajx$0zJUG-%Cctv4LPFD7vce|($1l-LgC+<K0zvC8x@h{ZWp(sOnW?;LIM
zc`gW})cz)91)5BUwbNQ{Kpl_=?4+zm8^o_Oe><<lrX(EWr)xUXi*_KbchDEE{qaLE
z?O_{Y#jW>jk2EJXJcNb^&zR?aw*rSSl0q=FH2o(we!u5UK4%jDqQOfv-ny)ie?~v9
z+0Q_i^U7c^D>ThL$besqrZ+ybF8V>-i<x>0eclfwZRvZ5GRv^px*<u0lV6lXFot3A
zo5oHDTWd3}7DQpuP*%AT4-hs6C<2>V<UZN>eBlhy|DydsS5hYuvD;TMaWbWd8e`gu
zR3YCfam&SW7myP<ieRq{xyhBee+8r2>-|9)*yl&5EZC_3zy@VzAuy9T`n@o0UBJ(r
zAr}{4DEPC~<FYe5BDo-3;?RB^DU!7kN%OKdrd?G*laAB++-$-WG1t{+yOkf{ZzlZy
zQX;;r_^;C$xS|PB?A3`G$%}3A#$KKheH9cUEA*VhnUBk56WI7>eBuWYe<My?iXZXm
zT_}av6%%Si6?a)5YKZE6#>T(pd`x;03R|nWF{6p1V%iVSZMOK<bPhusaLC)1Ba4Ag
zh^-#E<#x2gzei8YUC=9o${^kbe|IJ}XcXD;ZM0|zGVV3pOW^6LY-wl9H{C`t-=B-D
zH+9l*o_AHnmCc%Y^WiP~e@}?8g)>9e=Z^`_+6nXPvzT)!f_}YLdOg^uswNoU=0fu$
zhy+wAQ+z&|YwWpF6Ckjk)G#6U2pyF4Q+5O+5i3hj2bxqY4ZbG$8Grk<NY#=gVr!{g
z5^x7elf#zaydB6%R6dX@cP(CNSn<$c*+6>P%dB#i?5X$zU>}Ije@GJsw2H!w$sfQZ
zaJkCYdyUKecv{GSQNFZJ(!KMD6IKLo`G(7)((BzI#$3F+0ieF@0nt>{#m1#8dBMbY
z!5JS?1-*f$aIB*2Yw|^co#I0!5C<gXCdWqT3)khr69&I<8+&nPs0XqUc3GwQf`6(3
z@Dc1v*A*C}LQ{pgf8S9MTkc<M0^GuOG>SrNG+o^e2G$;Fa4PSH#W$sEdH0IklFapz
z4d|RCIYPT3)7J0GqhAxgUQ)igQHvAMfle2xL(E|h?PLmLs)>s+SJmjD&)+?*(R(?h
z;u@dMONGbAJ#2HM@4gE}l=?2;UuU>?S}PhueOjepbBVCAe~lN%p3S&qGOwM@C{g@X
zm<g>@v>5MThs=*bQajyvV`akLiJdPc2>2p~@Zj*%PfyK0Rq`u?TRS^0uSq}{BF`^a
z2mnZ*_;o)nr@k>A)(R!4UtaS@m<KcE2(Pt_oYpRNyfh<KXJI!!pJ~&oo{HjZ7mG=Q
zvWYzB=UamTf5Z&qW15S1aXvZKOgIBE&7Q+)jbolyYi>jj9~x^@Lz?e{o@c9RsG)a$
zp!%?!XkkfDN2I-=xuhqRIYxasYY6{-P$I?5_3feFYq8d1M)aFG@&==6@3?b;-kpN3
z<m8=#HmZ54^)38q;7$u8(z1Ji%uiLwdnhp-N$wQ|e;}=<X2aXH#$fAYd{_Z56zkAi
zGRu;Nr$(-JZLLeDWqi?9J@3Kx(PT0hEdvv)cc!yD-4oGvk!hZ@U3~NJA{(h-NZG?q
z^%ar<5eoFUpcQ;jS%|R2;B=H2EVh^ZPdle#(~e`pH8CukoeiZDg4Q`nOy#Isd#P;&
zowPdbf8L+dnrEJaSoPf!)e2#$cC2qISL(D_o8#ZR3$XVS*KAk9kXWc6VxOB1Hx0?W
z&WGlH*)uVbkc33}iLD?Yc_f1BowR@Gc-KWy%(07|g+-#+xr_8pys6X|fw%Wv;OEvO
z-YonsZY152Afdx7a{8Nv_F~h6d#<HH%1dmCe}<U1qHBeXZB-a_(A&VrAi$4q@8AsB
zSbg494yAY^uO*(ft@vwREa|Gcj+Nc@KHx;Sc9jVN&$*_~_irSX3j8=u@WW+DKOoc>
zS>xXs`LgjVncIZn&9m8-Yaf}*WS*qfQ>8=IaBCba@{_M=z9Y<cd(jD-2Eu(0gx3L7
ze`K<X{Ak-+azMsf?7d4AXlAkqp@R>!tvm?T5`frdO%mlqe4bfPcHCuh5v>|e>q~*_
z&7#+0I*Q)u;C)-JRkql^N@S5RC&d(QB=9hkVb*M4gsy*rd%XrJp6l-PGPR4qT{G^$
zEoUl1Vt?x=t1zSLsS1U3-W`BzaQI~ifA?}eBsV1Ho0hS99*mKS_BEL`<M$vfH7p~c
z90E7jt?wX9vfQNXba6#V|M6Zf$W|Da8UZiKRYXW`(ONqvsjtqPK|Z2AE~2)3`inYN
zER&M0s+R_N!XJ+aLaBIaZqBMYaw6!c*LS|6h^$=s;_#S?oS2e%81eY3l)m!Pe+QF`
z|I$EN-Fkrj6h8T(V_cAUL2!JwW~y4ujf}k&|H?#+r>qdIIhvG;s6M-zuAmwga@p)0
z@u)+Dk7yD$oNF#aQe_LaE@f-(Y7<koa$)16;ZC2ufYzqWX9VlOq4xP^eQJ&OEgvf1
z43Vb=&QvW7X5N0w5U6bIkVUvYe~?Dgi=?k@^1>!*w|`2kz}Spa^m3fO@gc0qr-1sD
zEV{+u_5!I)5bG7_-pB2K9VGr)wj&||muIwdSRBQp3^)71R3946{e$=3=ksWcA_vbT
zv5^4EXXh65{kR9+gu_xd@(dH9GKLv}*PF>|v3?$Nv{kH>pmi(<-{G@bf0+?W5oA_2
zTM4y3*8>j$5_ah=3p-5K=aMJ}XLO-YICC$yd0yL?UFqvZ$^s4mA|erW3ThoWq*1w*
z3QBg>!(Ml8D=k6Rnygns3g6P>*7LI`6uRBZmeWf9PthUSjAgLaep9DiyN~bN;YLWP
zTXHWxRu#QtcE?VQy(xOsf4V=+U2eB!gbFu*QQ@AQp?OqaKduZ_d5;95j~8bFvSVH|
zNZGP8h|NJREfMea=#A`3B+ZZQ5zqIkYmRV}zE^lkyxXF6o(MPGIxQZ_{#YC@`=w6x
zPWVoOAIWIv#*#+J)|V;cf_JFeZHT=h<+u}ZGoKncOJUA!Ic8}WfA;e;e2z^7Rz_z<
z_zXnBbFvkj1iW~;LH@TED$TQK^WfBHZfw<C{AUcM`LQIC3XK6ek<axJ=3Cd*TH>Sw
zl+L@fFz-7>wv#yo;-!&;FIzUtH77CcaJtbm!%V%2Uh<0_{cI7cF?O*H+wLpqVT8o!
z*<>19aH0#tOGYPde{o%+YrIQ5(@cmyQ^FkN=y}0^ZYbomIe@zllaImi{#i7AZ}Sc9
zO{&>7&)ZBE?t8{s>zZF>Wnw*<FL+<??x}@hSEAY|>NFekq{Ea87h~p=EqUG&*!taK
zG1u{J+>OM1XTk_w$CQZ3>WHvopmjTW{cvPd`@>R9#MU0re-h+fpV1sc^Wj3d84q=I
z)I-~WSKGdEL`{L<VO8U3116<M1v4J-!`npR(wEP<*7{4$AP_f0s3HWFq`W(+n&%WD
zX*%{u{kg%uRXUM6t~OoyT{Ep@!Q0tGaRFHP1knA?*KPEf5766?*4fIf>NFxe2>LM}
z{1D|SNH-8*f8w;I2i&&B`tf+0SWfGg>x_rp@Emhozc;_^!1;FeW+W11Av?2{I?frk
zT|qY7JUB14fsi)mi3==2EXoL9;}#}l@41CIUl0{XQ~Xh%V<hq0VJ4yyXbqeLY=nIM
z+ZA7_@m0sO!Wd`l)fCGg7{5!>u-a);d5Z?FYlvp^f7)dt-c42_Z?ItR7-6dILC}cN
zOJBW+$wPP$UAqy-er!!CxzNz36e{d9I$?mNOwd6)Cpo`zNQg<DaQ{w}o&LVjkWGwK
z6R_xT9Ib)Rw@~X*m@fzrWQ#vdEbtRpQNNif*zr~a$kVup=^@$2b~L%PL;_q!O4hjW
z+^%g)f2*)&86#IOgEI$0jq$TB^j0qRj%VB&>WQVvR-wss#fjhC_Fpq2Ez@4s8S%8U
zzi0ZPX{>Y7v8SPu=;0hFm}1IK&54wgMSkHRj3>*T(qpx=k&a6F>xlPQz&E?PZpKBr
z*Do<@Fr;bU*pBn$4Zly<V(|WONfPbaoAcWOe?j?Kq;VMOjHZGl#-N{^^?Z@(;*T_z
z0ni-hSx^_z+H$`xIS`)?UK6+0Gq|p;%LzpIJL@L(CNf!Ki)DNIZpWD><MMau>5^bp
zAy|~JY$DEuksf-AIChjo1~*Z?&x~1~_QD_RsYq(v`AMJM5KSc52RltJ?_0i@fpCw*
zf0I#5&`8ms{T88Gb5372MZ|z|YEGP}=$84#c)U-8eBGX?Da5?0=26>~^$aKWdIq_}
z7g>TQonG*`DP^5bzPBA2ccL9P*X3m5l;(&^^<<M?SFVI~HrnU2^*eqizk=pe$oy^D
z8zF%_qBqvRB(>alMBgxHguv=>gdgnUf0+A}u4($=Dh?q?2+QlR`Mt=R-BI$bBg6G~
z*-UQ>;96uwJYQ!R+WA-7rU!BM9$Y79CR*L*_rQ{<i&1u#UoqsOjI*&hAl2M3E0ox~
zh*8m>hp=bfN`J;^l~4QlSuA#}_zeMFWkJP?JTV!=p*yS+u1#iv`^R{kNKNi{f62IP
z)8shV5SzM7Jc7zxs-2CXo<6veh><On6XGJ{r>(Fi2VQ|-8RMlLVt3(<rGukAC_FBu
zj`|20v2sSfJx4Z)i7r7-`=5&XA}zE(k(iYHG#HS=)O6<qV;_<UCh!cpw#iR9VS5a3
z>Ewpr5&c*bY<#1=sO9_y(SWMce;i)i!701t5?(Otwezv69&wYk>=J@uEb{F&i%Ig2
zofg7s=5n=HF}`wp3@Q*n{&euf@z#x6m;8f_FulF<?s1q5!PCc9c=z4<Cc=fx;01yc
ztecN-Po`vhXuho3?2U#V)F*NK5?1hc_6Tc<4A0u)K5deVZaR>decR-ae^~PDD5_?C
zz*~0t^|_oea6|srww3A#qim-6S-|(<WrAi=LPm{30l|O;HdisYSiXQ|+t2E9jFl%g
zwBskUDznxDQChDJ=^z5QIl(>#0<OW?+R?Yq35Ez6a6LFi!`2Q+eILy2JbANW1rWc8
zdl=edJDx|ehHW@kuD{_Ef6M=LU2^`=mu5-d_iR)*aA#|JhC6;0Xv2$zJPXI?@W#IQ
z^Uh8B)*IUqyXrgS?xReeFS^~R$u+2?pPNLI2i|hmc6|wh&dc4!Z5JIggMG46>R2Bt
zN=bnISk}HXQff7=TGfT9Dc6snd4o(>5hdc!WSn@{>X^T3@N=dEf4`I*T`vE``MjGE
zio0iJbaD_P&3B@%X{v}ydMiueBByx;X~O&)(x`JlJO=rw8^>8wB0iy6D|%Qdsmo+L
z>`pgVNKml}<ErD?s0U?Cr6LN}$gj7FB(XO?1L!|cH4R(t5EsV2PyZTto&6F8(Ufx#
z%%<~c-%*JQ$hJGke^@>IvC9431w_7BNwO#Pv+!pGHC#{Gub1`TL(G~2NI5vmi;y%Y
z4d|Mqv#^=$P=+GU#hy~VHGXO@xLFLYTyT)X#q3Owq)^;!m^&+>G}F(CQzY%o`ABI~
z#&hjT{?ZEUOY&?vh;w-V<$XMV#XB$5Fvh5MIZC0P+~EVMf4VB|k^QE=LDP_9Ma%ZS
z)O6lO62`=U&ik3Sy*gQ0pe~#gkR^{}u*PN*xn4hn%BYE1A;Ki7seN8slrGFOs#reU
zuh&8;WUHdgO;^71H(nysiM$hepU2f(Uve;aF7WY%ET7@Gb$G%<ID#(G{Nsa*$AdZ9
zcKB13qUL0*f7?YM*H??kpXkXw_*A6VJsZkO0=7t{f~6<OQtf*~PLwWP;IwsxPw_C2
z1fYk-T@hv((juQu7;Z^4t$0ti@i#(3zU5ml(yo3Qca7{iKg@2j324EZJTMiha1&rB
zQ?iNTPm}{8i3>5?KtFlq!t)HQ_m5Ob!Bdq-cy;qCf6^0=v5hu%4%{|8cI<<$BUZ?>
zvw-PjX`Fr&=bS!;G_2}PuuOtCuLv^Y71Y7VSjE_|foC6d0!Y+DpS^C3dsm4{jm5M0
zwHgp!_;$5{@r<tgJn9AcHwg4Cj(hygv?=~aGyCH<zsyCIhnqvn-}M^NQ3T~gpkx@;
zHr_oRfB3Rec*$Gn$q8tTB=^lHZmm8i%+9eKSs8{K{df=c<0D(-T<^D@F)H4qmE{(3
z1RN@S{*3OKs%To9gG)Jif&s_rKAQ=3Wg%%=jV-Q`TNW{>ZT;%y6|-IX5X_YvbR@V~
z{n(*Y%lA<P0R;mTO9MXU1(Q>sAhrb-CzH_ke*<KLD$ZiV?5oF0C(IXSw$=yq(Xfo#
zTcss!mVFO6xp^s+6A$;fd~}?-%b<U9RWDNc?|EEY`tXj<i2H1G&#mdywwdNgrBS-M
zNqf$B64G$oA?78;L93w)HVI55h+X9sZRz{4EByl6Q*JC#kGtmx{Q?faX3m4kzG(nG
zf1_L+Rb9>dv`kMVS*;)%)vPKEJdD&EqrK#~3Q32XKP4@n+?c{+C>pfJ@c8rCAE(Q+
z_AE5eQ5~<EF4Y<Qzn-ZI1rP0RbU03L8@3USs~X1-zYmkyk*v&0&+SIvp)(-V3`<4Y
z*j7eQF=-Dg{{p#uf{*D#BqHsSMT=F2f1YvVgCk95horZu(N-1Bg%Je!+k$M{sDd-!
zL15GmryFl^jLfi_gnss3%>T(oPJ(_y_9-BF)l%==i0UU0X@kWA<DLA6clcv%GoY%9
zd|P#nX?gl%IAgXCB)RlB=X)MaPJT6~J}lb}YOE$EAOyEsJ9_N8+;E5f=7ZQXf0j=$
zdrLvQR`zKRQG*<veRL_-9gzZ3M}Y-ujU>TSMQjZF^)7;3QUqeXl`j0v4CV;LY+-}<
zk@bk*`_reD)dd2yRQYCX>ABZfq8`OAMio77T35K3Rvq}>Z-u?mG`hg!IV$o%^k$<Y
zkXAb>ndQrtMQR0IE{Ub8-)qDze=N>6N=2sQgKDXD5+>LiIl4P*<|7x%hwCMq?Rx@A
zOP!2{NFPY>uHRa?UP77_VN~rxC|2T!^yK@@=THaWL0#q*?##a6?90b|*b_Vm?V5WK
z#v!nWFCd0X8JJurwhyoBeYN)0@6U8I`d}k28mQLa4@+i7-Y^1j{5FMaf4Q%2J{(eR
z;<_ZM7|Q?Cx>tJ*Otd@q=h*fcW595C>e4>s_=Vi-8}v>O6?J&0(Q{Ra-fHKow8#|U
z{_#kI<=V;OIU#AJA`MuP&{<Kk`*;<K!+}T|T}b;n%Sb(2Ny{O`%ae&}SI807hWaMm
z&1=EEr^X>#38d#4`}J@Le_8m9>S5_6jEDT>*IdfUSY<9Lf#)K=)FBnJRfNya%<rG%
z`bfPpO-q|>{Jur`uQcq+y?B6m2N2%DIM8h1gpxu#b<4YhHfj!cq!1nNWbj<t#mq97
zS*~hV4E>gxhGiY^lL?^eluJO?{<L}zbmGa$o_z9{C&dIY)P#Jlf2`h>?;4O%HK>i<
zWN<ApZn%f^aw4nmeq^S|>*6g%EthNwSI-rRq;rpLJ50Icja5l$ec<FpXg;15DbMLx
zJtOtd+vt7k83iL-hAO}X(XSco!!J{GeajV)8D6i<**3bMd}+}mBmHGPVZ7*Bj9(H>
zs{@3nAE}}t^q_4~e~zI?VIj?HwzGDD4td&ne-cQjqkDmS-yo~@ILi|&z5duA^F&13
zZgFjTjr)Xs>a`ffg8f=TLwrRC@s!U5>8;ED^a#`+Oe(GT_51r<#*ueGRL<z=at^y=
z%GthPOSW>LW8aCOo1HA{N5S}Zb$~Ce=o>@%TF}ttYcXzhe?;@nm=OLL&H@q<ySq1s
zih$^K)mncUpB<_!{eCm+w|JO>{4R2%^J^wby1|6YC*<|om`DY3<CUcO%C~ThQe>9-
zT)UAOj6?uHK)=7!Esq!$a33N;0q6GCeOVaAZ@X(?j;!ABeTxEqWTQy?sBR$pYIT_M
z?Y8~AkEvNQ^9eOO-GAQ8s2(`P{^KL7#B6@ZeEz_2F)|-c_B{liwDabxv;UGpLw^`8
zJ^D0pIH{e~*Ho2+Yl&67UNU8fxYw1eQbWlC{PB)y2>?7bd7I*U<=O~x!Fe4)ZrAE>
zFIEV#5sv#Xl=rvQ@FeC{q)v0ApmVhv<n_rk1Bj1(Sil%>^nVX)MLkc8`rpE9(*<*O
z6{85Mt|&Z}UAN9DCaBe2G++n6>-N@u*c9Sxk;RktK@W?~3Pjy*yC;(hA92~K6RYaL
zfagK@*=-{E>xtE&VBQpf$E5X$w^mIda~Uwt=s(mOE;?`HmJUDHP1A$N%s0(Yi-Ez}
zg!B4@V=BWd+J8;zImlM^MN!xU8|LBX)M~C%6-?lFtYOFMvViNxH@D`5-NwEH^`#eu
zy^9L<Qb&n?&R4SL?n3KLuMdl&S9I^a#vl`_W7rU63riFns`>E=d)Vi?_#%B0Rpjgz
zpy3IANVTOr9x-yK*&oAuI>A8%iy&|`edEY5fi)K;8Gj*s9mu1!P}}gP#@ZzoTnzn+
z*%5%O6f(JJ@@2qsA4+x`PUT9*MbGZM{l`6OO{Gu7#kS2H>)H<!Z_BQm<wEErbi!pt
zW((zIyV5gx#^c9bNyTeSiZ$Sf+J0?>?KyNg_O!?CH3v(JJ~G5aU|va#&NHTW`R6C1
zjE%CAdw+dm<6BoTf^w9Jt~$N=0DUUk^nF7sd^#y+;-{`KoLRmJn<!TTM(1d8Hc_Y>
z9SPGw2V0>T&gV_`jI-U`K}B8<_5`8)cbA1fyU&Bs5q??iVUK^pj>$&Ep*oI;&Fcwm
zWws8xgNK=3!f;Sr4S#b^0<gYwO{J!lGicg^jej3*jvJw5Y~(Zb&StBcC>hghLQh8R
zGrLB-#_9Abn@^XAd^S1=x=#~NZ62n2n^;C{xQV*)-V*KQBh%&~+Dj7E@%x;Qst9;&
z>l0ziDfIXWE5NJ}Y9anhN$eT#2>(-E>=`m8&2<)FLQ4WJ?DUt4j?hN>4-Xm5R>FN4
z9e?SMP?7URsgH@T%yBZ&hFE_4d+pW;Ex34D_i?m>#b-4u6@B@@tf~y=;F8y>$lzWR
znSvl0`Ju8Wg$193e3xALxJ2~B-jfZag_+>BtF{F5<~dORPDYDmRyGPO|F7D-iej@N
zll;*7nfASuE}*w?CEUbDWqU5hY769#7Jnll%T%!wni7_(1%<j#qqO9x7xsi{o6I^o
zc!`eN-D0h0Wb$=W6|u-fJiX`r`Lm&fNnIk9*4<iDI1OT2=k-b6+JZ1`>6gPW8e-3A
z`}b36KOf)*37TJm+N`LAzvNF*e1DKG`)Xs+g}Y{%J=JK$P7<MX3(X8UK!Sr7V1E!E
zN!ponrYzo=GUn5sdzz^A@Kcva4?->fkuXQfn5Od{YY%w1pd5QLuQv6-wpt$Dwqb%v
zWbCx`g{LMu!`y+FXo=3F4URs?vGh$*RGw7dygovNpnY(ONy*3|@1_ZBuKWAZ!hjbe
zn{TR~-*y)gDQ`xMp=>r{5MWmWsDIE18jH2yJ18+NbBwDlDy9HF!&=+5`l6n;L)B+B
z0lO|UIW5iQwoi5ZK{}{{ie=%XVI4EU)Wcu()=|1R$FbpCETF~)wxI$Rgx-F4KyUjP
z5xJAF%l_l4d$kKR#WrvSm4E*TJQ=N$#7Uwu59DAhz#SO4I8?X(Bp6pDp?`guy1$HM
zfX&b7n2LWABy9Wbf$ifD#>*2XG$mD038dq`q$cr3UrxH#du96DOC2#btTgx;^r6q&
zM%qaL+g3}ykSLPfC*K=eBjS=b1$C#89u=rWZB$5OZ?7f-b`bhg)*hJ-56uT_MN43$
z*63g;5&0XeEg7=;BKJW3eSc64n5TCBSc3Z;$y-9}u9+6W`tNC5OeIZoJtbOVRQ=f8
zKaC*)-+m;HcqR3f5uV|u{=tEzQL@f{wnc_YW|=e+rcFp7Dzqe{9He-=!a%H=<*G6I
zN<5HR7H9$?h3k{xK#w*@_Nn}}<@vMJdhJGp6n%Cxh2<J$>lah(2!FrXzS<_%m0>CR
ziROjH^*c{awip_|yE{4tM@jTJ!`2ST+OPh#6(i3uzXHj<xi|0_aAoZua4IqP<oa^!
zia#O1;FaqY0vCwqt%Dg`ZlnNi2GJJrLzdn2MomH&3o`neWNn`_xQzQsE!r7<HP8DM
z<;(;OWnaC#6)5|UgMX4zJ3CPxIX;*66C;`)iw6HN=MchaoWnIKIt?JeQqDt(yU)9J
zT|~S-z~o^;J_t$0q8*cB+Xz#5_IMbTLEX3irKNgNfa>7Bxz~FD+X;h>lEIf1-0sue
z#YMW<ke=}?L$*qP#^dGy<!Iwl)u-AkKZ#|VFSlf;@J9BO4u9&~0bG!quw|;#P&(uU
z#acPeTFuljd+L3^S0t(Rl516O^?o6|(yh3gYEzS7goJYx=QZ*9YYQzI_rSI@jmR1?
zd&isJ+_kA%DVNGy&gww&hR;J9F>EYIxX*=T;$957KaCP?N7G{%r^lZ|#Hr;RF`SRc
z1MuD?m%LR&6o1QCbfnIzD~X>aD{+82Vh~j)=fg%&3?rj?nff&y0#R-SJB%U$pVJe~
z%CWMf64|s<M&|W(8>b82Q@Jv6o4X1RE<Kuv^T|7T7YSRTfYhi$)kS>i0u;s_-My*e
zTf6H^y%ni#%aI#N(7>f?J;jIV8qq~*e=44}=ew9wUVpb5ES2l$$rFmOu~aJ2k`W30
zp{A!ADy&(}hz0}e)Y%};B~8{NIu!SdDh<}Wn{V>!3}2Iwy@Bf>+Yh>q>lqt3+bp3o
zb|x)vlefIAsC%o*`4*E&x<VU!zWz-F?b^3*nnpKGQPwQkuf$-*|33gFK-#}9kMwC2
zu2df!f`2OnD3(J1!6O%sNl$a>M-4=hy@hGY;{i=KDz<}Gx_YnCJ>qJ26V_7jjv)<`
z%Q{2foh|<Er=}Wp`kN_JGESj-Lpc*Y$iXv+<rM+(@zbYt+)?IlrMqE%oQ9q@p+iFu
z0BcDrF-t7PI-!_Bz)Fh;@h~5+=A4dJITQ995PvUO|6&hT#HN~m{W~W4N0d&Ht-T)q
zRa>xE)E#pLpyEHGUC<;Uy8j1#F41XxS0$z&Oq-J~VrrTs#F`g?5fD`n|MrHAoR&&r
z$EN%KZDr&z0R{z5oI?!m$m=+m3Uhq)n&}J0k*OJ^*bl`KNVE%cZ&7m1(5XKo{g{qT
zDt~d*Liw;p14sG_HpNZi(Zjod-3;}g@&?uDSrisLA37fox9M8U)4R~GjFACnA4WH>
zVI*z!;3Pn70W#8-G1m{S@mXpk8Am#mt0-_o#iJ`8%o#2`b)vz79UN&JpK5~abj@ID
zPXxwAN>$hli;59ON&;!?ul1Lis`D(WVt+WCMqg%!R*!EbdQ|r+x3C!^2>w{mfdF9>
zQN4rTxlvyp5@FFXFm7ludhYzVH3%18s?@UAX*}f#O?Z->x59{6D^J;gyz)-4{a8P|
z4pkS`wBBLgd-Wdqz%UdZBd0)ghY1n~2KL}A!oB2rR}HqDo~&!;Taezggs8a?3V$)v
zJgqhD1HH8?t(<F${;FhU-42i=dD0>Dj0P>eKEZeN@MMb&@Akj+xi!-t6N%?%r8E=V
z-4#F&fLcuDopxaX-V09wW{~k)o<Kb65SI{|ogTX#dGKZ8ZH&L^%B6sL#|u|Ea}cI6
zf5QE{<HleS7ayNN*cOC_-9n0psee2-k#zOpS^y-{dZ|rD-der;)%-IC=Uq1cZGp@A
zM{`Y+jUVhKOQ~Jv0)>~HMQE{rF==c1*9@^#c9p&^i=nx5U7?nQlSIIpjey@cAEoV2
zQYM$X-w0X`qh_(u-q*jq3ka|j)hgUQsvWt4I3dub6_);yLC;(|Otz`?MSn;R4J=>Z
z+vy)nbl_2*HE*$N!c=UlL6Md!rSEOyE&(fD^pVQW%`P$8B+-Zn7uwc30!7u_<YnW}
zJ^Bp~d{tK=(pcM!O~*3qyUTYUzOsQR)>m0>IxS+9VU<56ZH51$U%KSKaP&z49cMi#
zu=Gv4lKpwUBfshv0AM>>*?(r?L@qPddZ(V%V7!b2*ITZ!p-gvJN<D%uGJ6Cdm8zuz
zXksCQOpUrN3OD~hKzh5WkuX9;7UxpFzV&#~3Hnt$HMpxOG*&q_&&!L(W-XurKzUtA
zSwm-DF*(+HjKcuVq(a{?OO`@+iHuGEUw!v3xtvmUs}ljUb$pU`(tleYXQy-}^tH@U
zKKs_W-?Eq4suI8nDu=m1)zFsW{GYEZEN?TY_4syQf)B4I=bm$(?C!qy!jkp<lQ-CH
zK_`^|m-+DuAbNM-`yJOTc~s%dh?c#un$xhZ>o9XOqKCUcUcmTYfIW--gZIF|PPw%!
zZk4S_^o2(MW%-kMEPqSf?yWAS`?<>lowHD6f5KL5z7omh3|+vAab*W-2q<3UuYi#8
z?oVIdn?xhH;)NMy<y171Go(8B`R56F#A$0=1wg$WL4$9uWx%YIPS$RWAs{kGKZ9w9
zFuu1eVyAcLoEdd2DwC-g#n0i8ldO<3jnzu2Vd1uh_Ag-eWPeJIo%Ce)oeVR@W2ok>
zQpljaoBP%mKUau?tH5Q3<q*~*6mVD&{6_<H(=`FwV2nRLd#8D~KzBNo8@iLwj>0r4
z5GU)d^__v;*g%!ld9mAI^unr=ww5SLTi^2Qy&m6)H5YF&ROoej93h2uR_;M70Q2?o
zxT_0A1JUWKj(<0H5N2*>zZf|eoU6hhl?il7cC4&MWJXse2m5>@*}OybpWEhe@cYQd
z!X)@8sj6zEiK(}feNWO4<40D35{?D77=x`p9uZ=J5FwW2<%(nO^__Pe5I7^Tz#~TS
zGK;DO-Q8ioiNKFw$u=~VmZAc^Vj9^o#~Z1%^10pqKY#z%!mg0_(XhC}+TmZb?q%xQ
zFRhq*dSWNn(75&XJL_P4%hTE9cG@yt@D-M<RayYE4rzmRa(6?fnP`C;#n+HewTr8|
zJ|bGcG}WZWxX_)MR-4E>!#t$`NBz}OB3m>RiG)6ZqkZ-X{7%;<#2_OX@O?DZ7gurv
zlKCd3D1TzdJe&-p&v!hZ;@xRMp`}TYo|43XGi+0Km}q+kf#n-R8#~eZg%nJES7Iy+
z?H}{Wg;2cQR44G$%-O0DiT0wXfCoP5em!e44(Lfxrlm=kWEq+_1@U2Ws(v2bKCjol
zO4Z-2IK^;8lAkHF@Xbo@)q^H2=$9<tHfU00l7DNX#chqikR`t=l(4o>4#ra5h`>oJ
z;>z@)Pe{$QvUW$3K_RQi3MHNkx*X{HR$=(~IOpcIX69%iI(*W@-$OK2GJCi9im&nQ
zc2)hn*c@1+`UQlPu)OYFLz_$f*a&xhAV6Yz{DO&lRZZm((yYQn8s)B~btIl`Nn^;0
z?th=>Q+z*;A!@m?8p@G#RLy%>5m10r$+eMB!)T@OOT9KFHc}YQO;?&NK?^a4ySBCK
z8aLdhJD#AT94t81dXv2f8zy92jWd16(M)u`^d$IRSBG?UUE#QDxRgNCsz<?DCrl=k
zr)9As`fg*jdg>qR_cdKyO#k|+^`=O(p?_fo7U+MCmv*+hpPaymU5|CwCVxsn@qzCR
zK5K(-qZ9XTTA8|5?pTVb>T)75QCM}IJ#Z?8F&uE3=x=(83R|tTI5$o>aQv(Lib=R1
zkNNnZztG%}dny?f0X4Vc3^fUo7-P-$s-00ySJGZ_*MXpdOd=$#UP|!WwE$-LZh!QJ
z^6=YNj~5PupOf;7#;xYrmu=(8eD49DD4As(?aS1#-OgUo$>dA==I;b^Q)(&Ig-U4H
z0|r6GpnFn)93`i_A+%qML2)}C&WU~md;yP0&s@k9oAzLmz%3y3bEdl{u6zuP$7Xk^
z*R6l98NU5J&?9UVaa_Z@<zWi15`UmI1GJB1QN6q6uO#x^gfsNPtByl?2V%^9FDnSz
z@*1a81yfQwi!OK)<0WANj;9E}+?CFP?~$d^%qBLn!{Z<OjHqk4_PU2eDKSPf@vr*1
z;;+*wZ!PQt3+T@{5K-J^9Tup?UZWe5fFc#nU`Fl#lf5GZ?h^>3JOPSb-G7Y;NyHAd
zrW&Dk^*YgbMZ+ndvwx=th9!sprdS&&hR*d^sI-~KwiSvHyN?D8K(Jy?Qt}uH@CPq(
zEmG1%1d9U#CGL&U9m9gLu+MW-CCgm}>4N}u^?IZgE6{@%p|7C_b36&G8ng{^>k1eM
zkSZbUM0-GmB(6@0`rc~3K!1cDp0!lz?i|vL69^c=A&gabJfp_cg^Ro2Gm*8XJ(jWb
zewJQ*2XjaLpcRn>6Yjs(TX3-AV2RQHgS#Z-{pwaI>8XrB)x{AT1{#DQp+H%f9|A|r
z`3jDSNRo#P&wwjc&Ig_G-OVdWypsN~^`wW`kB)N%ccAU4BS|ee*MCV*jLQfdo_(<d
zN)_LRl>-wDBK%AECcd(vZGs8f`Db&|_-(HbJdjNcZarU@CA5yrIk+$9E%diskHtBN
z>$!Z^{`TbtaWSg{gR({cC}^P)pW3=*vyEOcq|Ixk<*Y!bec+a-Q+WrcnK4<$TAKsv
zS;Kd`ZD$Ir(?VX<bASHr?zsGKpOX#30JQA@(H*-nKrYDMhs$&g3*Y2|&Tj=ZM6<D-
zHvcILOVPLobeq3mcfVDHf4&Sn|D0T{9JRU{@wTYZKWYs-izStWzd45-Lt3w;3*dM=
zJv-L)w46+7t!Fyv+-SZVozf_%V(NT}KU5&UNaq=W>ZZt!Vt*9yj?EF322{>{utKaY
zQNHpu4Ir+h^E^7k{xnb(mH3k08LeNvW)#@*n}NUAJ8=5GH?)JVNqCWxk4AXI!=M!(
z=FRXy43mG7+haS*e^S?!)U}F)?$yq!l%cGvKT(@COeYet#-2i^on*Ez4t<Y)TkG!J
z3Flk#w7FkQ$bUVPuiiOIf0g<s4xv3s=3a#>^>Hy}1ql;jPmT!W`I!c`5Qd_hq~}A2
zf!`Xf1cI8~?p$R1D|XSWPoK1YP``AYKNj=#5N}9+U^P~VX+vWJ<=CT4$rAg!7RoUz
zifFX06hcUItVEHUR5^uTyu#-zc6r>~7Q+V1tULx|p?@Xsp5<O+Vk8m_#pE&~Z#}BB
zSl+uh+8Yn_vL+fnuk~JeBdPans1w@kD5)pat3$d3_41BIT7!ZAM6@w$+0`}x`kd0N
zU5(q+WfRHCAf}6;Tsrv<5sYF&cUl<=)r-%uB8Db9o3g#>+sM_`tA6a+9T9rv;(eON
zGyoT+seeoet}Oa7m_V-kbM^*9upKuLY!6<;4P)-@T|HE2<FiV(D?_M<!UJiD9ccPH
zelO3^sMXzk6v&s?&L4Kk{l38&Jj(9<xdww%C%r^GG1s_$Y2S`Hk}@X@DD-Llu%Z&T
z@#FiYJ{z}o0g+}<|3n#BoP>{RjJE{VXZJ4ukbfVZvdoX?ONe`8E%{b*>kP>jGAj&Y
z^i`IlyD=>+QlN+ZW!K}LF-AkdC7yQt!MsQiHoe=|ldcVWyHc;)-SCB-L>u%>r9G~z
zA^+VRJni<J>c6J57(;bw;m({8dDlll`Gkuq73oRradN731FX^p0W{17#%tje2b|It
zrhmnb&<>9I6mTPV)@8Ywlc*0hI;AT|Mv0He$eiR_;*pf5O*_wC75CU$YDMIs8_fCE
zzpk`uIj2|{XC+|m%E`MV(<G)-HbPI(tH;WY1I|hZp=Z!QGUe9hhq)5q<Wk0a?MIN~
zSB}{<!$>y;yN6zy{F@(Sdz@pyY<&6k9)EXJ&;hVCo&-?s+O|SO30Wt_a{7?QOp9=w
zTYf`^pnl6gv8?(yU7V~}R$*iO&cYRX{EywZ$M9>csPsx}w4+ZPwfqY3v18)*TijP~
z2w^lj-Vsye6q{H-fdJTP=Vn?2u}&P0MF~uW!!z(Z-aH(e<<fJf{|;uvQIke^Rev4#
z<v8k9w9_mgJZ#h@m7u8<;4<MdN;SB)@FI}5xeIb}n>9<@xe5(mnYKuxkrckR`96wP
zy15ZsHFoe>I=U>o&vt5^7RVLMXA*b;aEk78A*>raMEDeKQ<kR`ZRqIBBB;oe0w*p<
zl~R&CkL~5Z%olCuslLtZIUKYj3x5;_x=J5A(YQ$qx=-B;@p-3WT4nWL+f)bC$GY@5
zhFTzRL)JgD(lssRS(7}APNGwGM*-ABXKvc!(~15bjaie%d}yKrPUFusfcL~e|G||I
zUys+!aZ-*xx`A|zgYz|?Sl>T76q7)5nJCIY1jaMXcA2a-cV(QZ>Q4`n=YN}?<9gT7
z=d!c-ddPA<w7n?8Hz|BE67fxWxLOfBtE4gz-Q;C9>h3wS9Fy**j7GSoGw3d>mlpiq
zwwN+7%30-TWW*K{oi#hlF+GpVFs1R<9<yYihyy+NgD!X3E}k~B3)#a3Ea9Dv>%79K
zaEm~otU2HYemAFj-an=VtbfLJZX3d6>yNiqu#Y;P?kiajLC%oZyJj=XNFBit{1mFV
z=_XHE=Q*oU!EGKad8bH=oK(Kd^>DirA;_#pUss<c_V&oI+4~zcp13|zBSLjCm#%Qg
zITvo9dpgWy+phEd%{qX<tCzq4#P}2g)7KziZ_A2=f>+6N$M7nkU4KTGZgXIf(?4Eq
zMF=O4=*u;0TXk;FT7)mZC38qB{o0=$C7EYhe`*<!Xw0+^=1-9maXjX!LoC1bKL_!f
z$%@dBVkn~?<@-?MFg>?R%Oz)_sKq7C#Tlc@w~a`*DWX0@Y{zbj-1W4&!4HKB#c-8l
zM*UXZhtT*J#e{moz<>2S??SL)C$Xed(?v&tX;ni`u9a!4pS5M0_Z8C!s4bby{pS;G
zm!bD^!e`*rc>Su}IQ`{}f>FiL`u4Uy6*EM*%<Gu<N2-!0lGI_Yu#{3k2niGOYFf}D
z<vq)Ff!YNlD!94YLNeeT*1&M}lC;*D5lWQ}Q=Bvh4dybSe}9Or6DMR>7=cgrwHD}2
zy#S=W!h-FOqmG8$==pYgSm8m|_Nq#UB{K7~Bp4c|&^wEoM?5jRDT9oqRmBfzCUp)g
z?<^3V!D%;LN;#ytqCTaswH)(BE&6c&=UUFD4IpBv+Eu{IUi~|)R*8kl)LVEcqDlMR
zO2vFnlrk&_>3@4AH1cTEr$!M;3}ZGU%b?_>UF^-8F1#k0@euuA+Bhch>qP_7f%QZ`
zcU$gol9J|5$$aq>*WPN64Z%@dj*<nAOwSbLa;HV8@zB}0z)vB(ay1~_vw9a9R3NM=
z<m{Mx<Yh3dbJz;3gHrQ4_E<+j@BVRhbsrAet2d@$JAbUx<Ymy5woIB}){s<nmLJ`u
znAa>%mhN?Zd*i9Jr2C=4%hSKAg-D0CB!Vl>$zsaFl~by8YMM--EQ-RSk=%2bu4fuN
z%Mo`(m<9<JQv@<E`h~JPoA((f7R_$Yz2)-%yfrhAN!>E&TP2XLB^&?r*_}&I5L}Oy
zR(o(DBY%vz&SE87uK`7AF5|T(L!jP1Vm!VNXyy=aHd7(aXbI*wD8XJ>mfo^E;-%b;
zASkXDKckOOA?qOqYm%WYEt=uS9B$;(?;+N%b;Nufh27nk_v40?IPOB(N<C>c^*RM1
z#H3!@?!>Cv9os0MOC**NzOLbbF9MfCI!*XKlz*liimn$t(LKSy`P*KM$d5h1x&R7I
zlz1|`)!fJD4wXCc@ua+AB!<=WWa*2x_VyUpe?)1fc93hQQ2L**(ZBE1_&n<xL;4K)
z=mUY_k_~UI>E)PNVtExQk^au<f{8LwDtr3dz@t{+5R2za_V0!+zFvS3a3kR6+HXst
z=6`Q30C~DQF{!3p)|yXsM(|25%8SQXUd_XTUVtwK)_?>RE>NqrbHU+dzS}z7vG}hu
zOL;bT+?@?;Eb{Fw(l7|m`&9KH)o~f1(;tym`ZwXDg!=)Qw-wmTCzaWH_)wZ^Dgc16
z4!Z+yq=QSDnlAymMH~;YHbi)z8@x*>^nXI(Lk-#PAF3<cjjL2PuhzGb=t?~LR*lkQ
zW9t1rm~C*z&@Q?k)W0sq+{=4kdc3+DNs#!B+mvUOi3I)(+Z*;ZVnMf-MUpXfi0P55
z)mS~1wA0z886OkHBnOhWN4dZ#=lpeh-n8VjU0}}*c{lWw{v1c0!fLt5%=ln~z<;#!
z1T!^p(=Bdx<Kflgh#uitnsAEHll|8JZ%m5*pF;FZP%@!|Y5P8yHJ1TS+E3!UX9VP&
zl{fneSs>(wzve&_%(k>4x;Rp&0aq~w2?V^hP`Oam#I-<Hy)>A9Q4cz}xg!4G*e8fL
zd1OjFlq(H=jVX?-*>44;8g@>T?|)4zh{s=6lSZs7hlhgEFOZSnLDj-fn<xD0u^fa$
zm*82!1y3WMt1cPH)sGnu)$+@wW{VLn{xwp7Sq>XpD^D(X(7xEfrAs^QWa)zFli+gV
z9@ocYjD9T-hb=d^E^NN59qK3|tWApldGT~>6s+5C$UQ~5*FTn&{QA%7(0@CaQT&hY
zzbJ8WW($^<4JjjCs!Xl|A>zS}n$EytB{R)kP2=TVws@^p6)6jTKLk^f4KdFy%545A
zBr^rP7uA-lMqRvd8ZW^CW&p2ry4qDexKJvOvt%#Ab2Ud0bQV-_N<cNQE*pcPq~7RS
zTF@sZ9<Ne!rWOQ~OR`6&=zooTxa17h#QJH^IwI0iuDWJsOw`cGNrKB!Wm9_XVxagS
z-r@wvG|KvX1(EbH!5!VGO|o%=xF|xv<v8INtM?ncVZbHi!9nEp;OCw;ek+Wd<S(E$
z3YbMXA@S{Ul&{ruzrc+}3s~bP6)^jW03nz!Yzvao$9mt_3BWcOihuZN=+}|{J<r48
zpnguN|92@TaY4b}GXY^H!pf<w{B5>$DiiONyiAM?<7$MX8GV=gFA&U~dKRP&l>2Ao
z5S?BMZOz=W;u1|$qSX*>*_khZugzfcl~MDW{y+NBVm5>*UD|?)0QI0V(;(l7yutaQ
z3*UvkM9LdHgg~_@Cx4f|!I5N9EP&C*=z=ScRK?_mgE&x&If_3Nn=ZY}f0cd^wd8UD
zV9NITJ=#r6(8U{6wa1gUC79bO;xBUX#2A#o;>wA;SReI$+y8iF20AMISHfVBu>3`e
z>=@QZrrMo61nBz}*Fpq*1Jpo!Cn6dvOP1TqY9u*&k`K7*)_);YU+9shqYYijz~$jQ
zvNE~V;PnSP4X30t21fn`n+K3iD{;(@clV!G!yfXu;8x8p^z@oS%>Y)$4*ya{0<4br
zATi?;80qbx{I?y)aH%F~iXLuoZ;3UqC_W!ArAF1Q92-CNZy+D?nKnWsJ66{!x}jw^
z(%67^F9zBJS%2z9l^4wgfM-MGTxV9@T_w<HO#x&Uwo#kH>VBO*WqVlpgd+2!l&6_d
zzx1p?zRMm4fjNhko2e81q0^RiQ<jM)gRr{teUQztLLwhjlq5Acirq`xqW{K(k$7>4
zB&&`=e7p8TJGt_|FijYHy6%}xzJQZ;f@?!=kS-_C#eeNy%Vp~a#hRDkk~tq!<f#cu
zvqlfJDe!(TgaJbDB!lQ|=D#N5AcTXzN}~4U8FVb0dpLQN-IVLYS)Or~_4*K`|A3Vc
zbd*5ts6k!MwDM-UXH3WYs!awI1SiaE-WF=k?2Mmdza#4`L4xYp<D8vbVxpM1zDTO~
zo_r$W(SJ+cF9VH<J4d|9#eu~U;6LWo`wqLfM3q7VHd1Wxls4rjj<MD20z68Pb72>0
z=1o1`6{ic{cAkgHc7(aDohj9;eZoBZXA9bDUT!)qVw7Q(Kab6<n(qUW5#=^Ou$+=*
z&)nPPP=PWoADaLF3m}ARBi{<!HTsW-t+@?mJAW@ec!6iLj+gMPJL99ct<Fi68O8LI
z-9JbB=xHl=>8AE-N0s14FYa^;&yQxO_2hi)+0DcD=N2ueJOckybJ6;D!WRYwVPLL|
zei7XzBk8wo_*4QT<&L*aOc*ycy1t(*Ma}b2+6?RWl6_y$k6u)o^TZUGPQ%1+2oVN3
z%6}RK79x?rT&U?S%`?Z{bNjEYDn7%lL{XEy8v+d>4k(rmODacD`JYCuGaA5N_z(Qo
zOR>ckZbBq!G~EC&QAN+m-Nhmyo*}*!MfZW014%p$-seL>v#!zLHyAVNL3od5yXvg|
zo7)0?vzR9$u26Zge5Ux1#Gu@5D)@u)S$}+*1DElJ`2U<$j%2D`kcQBX+{rG}`tP*4
z=OvV`>F%eV)#f%WVbq_S5??!2=9ayDxe_wuMot2sqA7Z_05_Z_B^bUy3H4TzN+^IJ
zOiQ1DjA;MvI+L1*pm6X{i&WqjBQ#rJNKB$?y>@<3UJ$vD9-H{z>^9uqp4mDQ!hac+
zYx{GFMY<1WPZ`BNiTa@9!!#kd0Bk(jHW%iwvEbkBakN?TV~pAVRg%>|jpNiQ_0VrU
z)=;S!xRSe0L0;h3cWZ_(?B2$a&M@{}4h(rd0JFVw_P!$h_mrruJC|ZKj%8!wP+(`o
z*MyXm<JeGzEqDKaW<81+Se540QGcLZBxtiyTTWaqeEqCtO6V+qt%0Xv<L166N3|+@
zVBl|+=yKg#P@F6<uX>y5y{E&-qxfA69<WwtDiG}%uzR!-8}lp{zp>DH!D{nAw3YKt
z$H`1ePErxS-%wArb^Di`wMk6Tm7&`MMb&~Vxl2M(iia^buW`ujgQFE*u7AgxfcHW#
z$sZ<SEzu@S7brT<ps=+YCMxMg3{-sx)>c}0*2^w}1C>Cz-yxDQs!9AH?o&;007O3O
zgfwpU(jfoPue5&|T!OqE7Hk($BZJJ{-D=?x|D=dTz^DH%49O|Y`9yt#ryrPrMKa-0
zB*k#}DsmL4gc+P>vdQc-b$@YZ9(G<jcAn;XB3PEndsxj@e?0>`?+e;o&>5#Yc|^&=
z1ydwW?<=*ue_r`JVnhFG(#d6?U?OQpUFoncYG=mxo9RZRgq@JV@f$(3ODrioE@$I7
z9jmt|oJJXds59#~wii+RgZ`=gP@@ZqZ22md(hjXDpujck-Ijr+Eq{pwXL;Gq40nZ@
zfIj4&ysvC-5gy!=hp^2O#cX(1)UfQ-<Q2@4kjJ0mPaI%)1;^dQh@rcO7MhzjTud%9
zgdIefOs^SIK5H0G5|j1fMdFm;So5*_TZdYAtKdoT@?YN77Yp_kYk5XST^&)%TzOOp
zHFS#*rbqG4sINrB_kV(J$4&u!=2=x2P@Y*WwQNHkEcV&C{(Z~5KvKsK4Tb7^DDiUa
zTOJM*mHUBr%uDOVPiiUL@p+A>2!ReVFA+&E;?!w8-KCOmO=d%oe0kl3-&HmFEsdg=
zf}w|8Y>srW$ZQQf-hG|iTx?oO$>JQ~tnt7qn{xBQWa6(+*MA+IXF8>hb8)64y<~JR
zL`tmfpSEKQqp{u-FB|dMh-tsu$>H7S7R0A?l^GyqBJRQ{9!;h9S8=D!>u!ZPmJaJw
z*XQiNs<+A2O`U7kimIE!JcSSxp~%`0VzO2aie$6J8wa{@uq)S#wflWF(;luIj*#hj
zg)Xka)*-{VC4cOdk3l%tB|yxRcQv9PnlSK{oBg4v<6q&2L0n=&az)G|Y{Q#r=h@u>
zJNPizQ({io9O3POcq9@&w2)VU3TL|xVc0=iXW4nfKQ^V~zA1kF^8(oD)y~vN9ptuV
zec!`rm8+yU112Pi9W;Q^-O+FrsG-{~OiJW6Z0HF&uYdNd=P&tj!(y+UcB;E)jS>yy
zsIEN8mPbp01(C=>J!uEB9=2;B!z2X<Nl$+ev;oPYXB^)D^lz;*gUG9t?AoL}Mj!`M
zc;}5J!6;s{6#zV*b`fI-O;|cr!^mz@<Ojw_)>TKK>~Yi<p3GXB@mw|^OrXn*7^k*|
zs?ncLIe(`;!r%iC+l8-<kbvsC&>u$!kL$u>#pH`FXJ#@jyaGh9cuPgK)Pbs`;6_hU
z^KHO-y3_Y1r*MpW9X?1|f@2UzXMuNfg3wwBpDgYH%9ibb0X-uO-jyoP3wKn^O;vE-
zz({y<KSZGd)T|WbUF3@B(i^5bZ_6wm7;w_urhh4R5{*dbEE5FqCcp?SpOBb|yI(T%
z^Nj%7PYX$<-{jX&G~f52$lXmba!k`ohe`CNQs1u08e8q}Pd=q=RoUmNJQ+(mY4e))
zdCt`?LTL|}2tV&j`rkt!YCrk;4(_35eWZckBsw9Ad>VAHc2VS@34^)xw*lnZfpmY;
zW`D`MScF*r9co5sEr1%XcAMw)o7PfmnDQi%!(7Ras28=dkK$2yIn@v_ww0@ve&FIk
zdFL6{XHC1c61tb<2wWp`50XWH7rS2t=a`(k#svS$81aOKu-&miS#doM9LM47a|a&y
zpw<ZR`Ywl0bBorIB*Od>v~-9`2cZEGkbj+2nXZ2oS~^KIj}umFSrIBK2~%*f3qexw
zU?A|zrB?HRO3JB)apO(itUaI&cwiRP?bQ40P(V-(W4Xu9zaN)euPP(!Bj7m`*2Wf!
zLCRcVMWe7XqkFxXf=JwFPj$L&Kl`qFpe6}9JCzEm^496SN%X-|NdR+<eT`7TBY%iL
z6`kON{LYO4HN=rL8eK#WY70*X*Lm6IPaZLuD<EVMU(75E1dd|03-(Hyh73ECTLb<a
z6qkh@dl4`UJ!weR|4TLIg3L?!z`>Bd*3B;p>$rdDG+;?#upidf%H1|xAyqQ`;!S&F
zlp<^@_Hjv?UC>H^7YdJxEPq+^pMNj#U!IARw;5SGJpu-UX=`|CCc#7A+rU(|yZX@n
zcV_LqeBf$i#G-*pJXYqM|H0pQjtXCMB;D&*H>}&{81Wu1+&TYEyaRvU>>1Cu!Uz>n
zXKykaTFA+?EFtS1o1}8!sp9Rze99b}>KH>NjNcF0?oVxM3MB$%OGY@Nrhg7W=YrG!
z1w@N=WMmc$#|<ivP|qKjPM0oXj2MK}#>*Ia&x3{@CZ+uKXuoEpA3Hj@*W)}-?cJ9G
zF`?N1@WnLq93!w!=?}{ywswq1NhDP=iq55b5N9oDpQ8{m%0pq9NU%zr$IFLJU%+|L
zA!Nu#2avSfhg;?U-7QdYMt@H*SNni3_KN&U?pE_sGfK@0^pM|TkCt#vH1~m=sRVAg
z;`TEh3krH%tp|JH5IVDOxwemvgJ+o<uLj8fvv*OeU!7lmXk0|~udE!v4{W`I#AoV`
z8o#e(hN;{3W`$6`cv$s$4X&w2S4t7YFvcp~Y{vV22`+c}gpZ5abAP}ndem7+vLasr
zgS|)^Qg2p(_M_GlnxbS*z=zfw*Yyb_NobK=YM-k)=v^%KedBA;6QEtR8v#@aV-=o0
z`?xg)k01J9zw##2bDEJ*t1+sD>`YFrbvURa1-A#en-4QX0Brl=4LLG|X7WzT47kA5
zwn}H2$V8r(;XI(KtA818kGE}qB4G#XdolPN^`MOzxi0WzZ7v479Z*2%;G}qi9%^7A
z1VJx_3P>KeUg0lsb;dAT%>5E-9%VUgh=D_lq9Zo^3^{}gRBCO3voclp)9$%}<zfBk
zjle%_Jm{m@;Xl)lt{+&4%}eg`Im<Yt>!h40E6-r!A11I(TYpolJ_5RMmbfKaq#wk+
z(7uzM!?O3{J@aEF!;H#lo6hZxfT0&S(y-X01FaZpUE2kf6O0Z$b$*Sz5_eFvsv)dG
zu{t|AW=i~1^;d4%>sQ$^O%j?2TN4-60x8vxs`{*6in8qbxj`4pE;_&hog8AAdS9M+
zV>YpR^1kH^LVs_^d#?1?r#EaKX23w2U^!ydKFE+UdRKBZSmk0bv9jT}`F?h(N2Q_V
z@(kW;_Ww8?U>U2!m64MvRfB#<{;@4gI6)R%=i;^b%>`6IF!ja2+iE6vGw$JB+Fga0
zNj-vF6vF;^xK0vgVIlC37RZgo)K^!?Cp)t8^ZE|17k|poGAGA0By%=lPCj3~#)m*T
z2V`52n>H_rU-7$}S*sJs&^nPAHxI$;JVn6Fa@?T`am?^iMZ~Uh^O=g5K*r9BUE8tK
zJv{;VgLZz3U7oWsmW6r4-n%|HE5zUwF49VQh;~PTd44X+kv8?6OF;!@T4(j7$slvt
zsb$_Mq<?PM>m-f{hGE8EF&|TUu?hCv00|QFw7)$5l>-V3mNKnp>tT6hub6x;52Ua%
zzHUR4c*R&4<Tj~3l~CaH=x=}87^f`|6M>;mS_zQ}a3q{0D_3RSbpVEu4Ho?>&*xe=
zIlQ$$$`XEfC`5r#iiEP*@8@d=*NIUtHUt5j9)E7Us)#2?nXBQir&8k=OoT4suxoa8
zo_*1_(>urXn0D`2UKk!MH6*!zW%Zd?)0P);6|2l;tuPad>a)yFNV`0b1?p6vDS70I
zt!<~Vayt}+Fj|?nG5u*~0}y~PQnX%!v7X+5^4g4GQr+KC|0!N98X0C;6M>-ANs4f>
zpMM}YFll=Zft8JYgG0zb&2QMvocONmmlbF~mOM{?M#WAzVN`e5JF?{g{0eMG*X5sx
zt~s4Vu6aiWVlABm1O@ytO1c1Y{C`F)2*`m{Xw{qAj|v(Ca>n>NA0ndaOV!t$_<Q!X
z+GNpDWd7w^mhbb>WY&Mp#lQT;&YXC^qJOwBGLM>VLkS@=3q|Uv=hFqO&UxUd2PxWi
zlfOC8a%t&_k|0fmj*pfsnAV=%XQr8;qSJ?Vljh!21lgY*(=(YH7~t*N7bSo@WYXC4
zrxawQ{iykDE)xM)_0}aKibv$wGw%>{ypSjttm}<(I~Zui?OQznjtfzrds8ENYk%;N
zYHj~G=Y7h}I>U>ER@jPULs2{OF6i3CYeWojkOe{#L5G3Rv=BbKlB4(m7kl2D-C^R0
z>BZD}rMQ9|6M<uub#t_x)wI1BEj2a90D@Yc2;@jlMwJiP0&FN83V-M_u_91`cOm@*
zG-Rh;o(pV}r4K+AK?PVavV_5g#((J+0?G;>RRei7;@shAv3q!=XjRcYNTP_C?k$`v
zf3P^cFza?f3#ww%iayj1u<L1a=(^ifR%<AbZ~<~kotf=4<H1au4M6NrI)N!Y^br#v
z>1|l2=ue?mYnI|6hDt@EO4{sW_8gzlirW5kNt-0zP*U_7j>P~y{=jo80e?Q-33wHw
z(1$#>yc0o3&ATW>cr3O-Cl;WJUrh&$XJC-|J!*WDnCx(gif`Xv`Q+1QZNyGuMTxT*
z_Ha6}HFR#5!m^usO$yw2z9Uaim>#((xC$N2eBK{3f)YL{{h{@*8W`zv)A`+(0>vQO
zKyB<iUz$)J%b~{U0t!sZ>3^n=WYW)@PU%*1!9PuKoG6}Kgil{4k0IEj4uV>=Z=`b}
zJx5G^aiA5GJ7D4RSI2sC&5T_PiW=tyrYabz#VwVG;wf9ybck`)qe(XkqxM#`TUVwb
z?0hAyXW1#vi{}yTNDRA+o>}3vyS8imAA8AB+XMwvi733-9-;M*7JoCF0=wK;n)6Dc
zVO60QF+TMw(P-E6kKiddh|z@dnyg$WMiHV9iB`DdH0GRV-O=c#Qu~df22UL`Q{&|`
zZ7$oJZAh=uugETyIRpHm2JH*Z8F`cvk#Z_P+&(b8mMdH3$LBhw*7>|Xyye*F>ky2g
zh|Un+ey6cCiM7oC;eR88ZK%6k;~T1uNwhUA*dYL;DCca>@>j`8$|eXtj`9{@;Hg@K
z9j^GTZcp2^hApy{XDq(>z<3JL&e1h4x#B3}YsI>xOSJSWQ+?zYPu7j7*0_Dik#l4+
z|7}wTYs!LWi=;L+u7G`T;*pj0DsD5L$pa*&Z@xK9ZKhPJL4PFGch_{H7u1P*CJ+}L
z#P@b!+SK*4qk(i%Y^ARdBN3x@=&;Wbuyd5#1lVBtX+{jpfU+sA%vz!z8P1P1un34X
zwo0|VCy0ZlNdtjgTU3|*2>?`Na}IY|$qj7GJkPSbB$R6*LK-=(vX{MGHPFiY3Ay_F
z>&1q=xN_z!oPTD7>HSplKUz<K$lAwdBeBVQVg24jHdsMhA)I1$hWAXULVm57BrsH;
z;j86~#wmLR{Zi?ibQ(SYNO&5Iczn}iqnHJX)a@aGO;Ix7eVV1g9i)wHsm2XDcS^^!
z2>eN+KdEXhg1M|ar=R=8zTd$kDDMrXRCkd`-C+F!8GlHupSVE^J>o730pn-IBycK)
z5wv^tPuU1%4^-{X@P8lNM>@Wb6j{a7z@D5JZu~6D>n-5%@T>9u^}_nV5=^>JSw;1)
zSE>45s!trou_B$XN2-*X4_Y6XtYd#L75Nqwq#CH}ZHdmsfT?D$T}pY?lL1>yW8;C$
zI)u;A9e=q&0{e*eF`<TC{1f;TZCw{*H2yMet5)rpM<}9I>E)JOId>-z(LcdNR;Ts5
zY%qu;j8BDc*%bk1as-f}B&V8_#~fam@~lgPCpcSHhmK3H?vZy<)OAERwpcZQBO7cA
zva;Iq>}L84a(~9I6HEbto9GfaF$*5~6^R8SkAG9OR##zWif*G!tFNOvbMZi7@<#PA
zb1L!6AQy#P0%~*RBT>%WViB>&wU*nsuVm~MrBlMY%f?>$n)BNZAzDdzFBDDL^%fEO
z-^;{~@vM>wALV`d4ym1JxU)zOi?Pc!a>{%vBmVOnnwI_Wd5S}q{A(!p-?uMVm8P<#
zX@81h=Z(#y)CS=TVVW=TWgwOY?XjWy^l830KS#TcB$EK7;-+9$yBPS-9Nr}hn_4MH
zUTutdL7;iD{fW8_@b9sWdq~IC_)II!2Dw#0<NH3NAl(V+jzL<u);i+!=GHo~DxnlN
z1?(~=iyA7M>>hr({^=)V^}C-t)V)D;=zo*!0t_38vNaCwc*0BNgfQqi&~+N5s}fGd
z?3WpAC3Af}#@%Jf3W^*q(Hc{QCxScFIGhDaR@i3$(NrRNnC8|{#8yp3E@x_oKZp3Q
zU#&a5^*(<9KE>&oXtosZ^{iI(uv?YM3EOO2`Hq9ylh9q7@Sxk(6kiXdP2jR2gnu`u
z{#D<Y+`hS)9ThESoRxc3O9D@B79|(f%9$HD5MaBFbznTeFS0yMd4w&-CmIw9XrSwC
z2Zk*$kgSS<*a4gQXzno~113N-34B?TD;A;=SSK+`EbBDYlzg9yb~sYP`%70qZfPcj
z%@F$E1hn7Fst7S;_}rtl_H@+cX@7#{pc&XoB64uiH4><oi=iClNNM0U*8L-2vZqEr
zm*a1KI;$YwvGVZUIF1bMrPEN5+~BUctuWWsK>K>P6>ly&N{vNL4_S{3_8Y1@5$uo}
ze4El^PTBVI_xMNCkW&*@PCFIKRFm|j2@kP+9~XHPQvvG8g76@Wc?jNz#DBbeS)pAs
zjjXaQ^d(I-e>No+9bi_T%r5V@wy-8Ui(KaJW6s(0saXv}HcTst;|i;Mt`hDCu+|3m
zjCP>Byv;mhz>YGPPUiN{sywpWC7TW|rnYA$(65P`EdaiuGdazNm=1=GG*)VScX9nX
z+I{W{cd(6lV{mP_tF>BcY=3!6W3Hd*#%=w*)r;=B^;TZ#3Qg1>$U2%Js0&2rxN2X9
zOfk-~tJYxBygV(4A%yzDX9ZEqUJYq0Je%H6g(N13(Iaawh(>9y3=Ob(D2OVbiAF5<
zWUpUftsx4YUYY3|YH899oljoo&h*EPX41t;56{9Jw*pQrk4Oj5Cx6LpY49h+_#7D1
zkD<KlJDN}i&u3N&Sn4EZ*4+@^`RF9Fciy>3o=rwJbLK_<<4+<m5LqBt4q@}06WV@P
z<EhXG^x!M<hMJm}IgSh<_3#(UowvHPy14GR#cf_)({M@G?ew$c`Sz>}*%b73abIki
z@#kAOHgr)Dne(Ob)qkF0JDCYAi~_aPH#TL5G-O#$zgVDHZKRFxa%u!00qia~c_|x&
zKo4goyzv#<6+S9&uc8m=ZSg*QgF_lj?nEWT4%IiHgI{LF`TcL`M0qm4u^^NBYNI%G
zQ9<HqmhIc&l$?}ZICa<A$Xk_?D6AcR{t6gGBcZ&(?{~TV!GAN)(~QU!j7R63bAc>r
z)4k4ri!Mg|$>7@#stbJ%pm%=vMxQT42HR~8YemiuGZ-ZtJT9~m@!wX&Gw<?d-1<e8
zv*AukJYDuB-{Uh-+#chNM2bzv5v<9>P@u-KI#isHmu-&+ubGWt1cKRjHOQN!sV{0U
z_-c{<z<l*0Qh!-Sq#S%*>S21X(Jymk!nrJoH@zJL_-WNgue>i<`ohV=Yz0a+d|SZ>
zfdO6>Q1*H(f3FDQOkD~f2f60P8fPrbyy!6t83yRCf$Kb~5Z#eV{tZKK>M9%=XcQ^s
zlJAhV^gw4WZwXsXDG^WIGV*mDdA#ut&-zsWCR!9+3V)6ygo;8(JQRYnwfT2Z@OoN!
zx%l33jN;qSXv&w1WZScqnU!U>@L>=|YxzCYqGni$YE$N+e+f&6fzwu~ok+#H$6$y|
zhtxn>B@X7qp=`c@?puDsJ##ZmA*1@V2n>_>a{{Ca%{#qvN~@r5XIEeLWh1*TUDy#<
z3<qlDI)4=1EbIBjK2+bwWJ+G|J{1X-eC)K4ROV5Nq}eWWcn{dX@oTao=3Ya%t_`I5
zjE!$dG*=pQb1q=X)_jFErC|3WFNgJ{+1@Mhgd-kks?9+Ks9;;CIMWc?p~nyx*PmG7
z@e+D%pfq-*Li<~4+i6W5KAW)9*7SZTrx}pR*?-xtHn>|l&Ru(yfF1x#;}5F_bclsE
z*nnyKX`Wv9j?2m{Cle4^+^Ngt-`iiqdCk?07&KjQk8$OYm1e<py!fecnJ@6H?<$GS
z#G`Ae@Fz7K5fEwh295@l-k(!Q=@h0(Y}vl4H)!klH(fbfQ5Q62bj3`}TXv1`lt?Lw
z#eYH|q^DECM$+_|#-61Z$GV<ir(z2`g=&V^ifa=G`P=v3B9}qZOZJEfA-)4QQq1pQ
zcXVc<pL>{bNCEXIfsXBUFwRQ28p3Zw6nfYgJ&HtVS)Rrw+n}pIbtQM6(Q9GsIsiJ^
zes-A^%)?X(>~Tnk&q<7TgmWYZdU9#RFMl9%{DBRIU`&XeH8W41P6RhqwjU7>SK?BO
zbip{oyoga(UGI$WqUptYexe=LevG`eZAFs-W|e<QsRj;5StHakd3alB<NIj8vwX^!
zvXe9&yXufjpapmeOK+p$cyhf1^~^SNa+x#v&JPv$+TVFMV96rM@<j!E%YRqpPk+u8
zM<Iulag@uUFM**)*dp(aVtGSx^lqBknbeWc^A|NK;}TflTQB$P*)tx_Ogrz`1wNLu
zj?}U9v6S;PB2qj}AFacR)|PKzK)M$hT!k>h-z7#ehe#mxGKWNB8P=9>{bU{Oqh(hn
z=z3u$mA%9ON<MK<jg6#brPZ2z{D0!+m$&p|qwTaAk|u7jHOx84C@9*nn)s6<?~vEb
z36UraJZGk`L;3Mx2`_CW98c!b=mn8=6VPXiQ*rT(;6ff!N|yH-#t-du4|w&KIEYF}
znOXj@<Qesza;RdnESEp39NA&=@H7=)w&ljEp1?5nwsP7-36tYQe3EV;(|=d|)yTrC
zXoBX^gk~bN-y-7CaK>vm*;$7*8E}$$m0B?EoZDqVREoLGd|b|mp_Miw6TJ_U09m69
zWYtfLc0cgOn8K+03f@v8)B@CZJ{ZN9Z~#q2RrTZz28K%GWtkc+X5LgE)zDR{&&W~4
z*VBLFwFILL_&7Ednn|L@lYbBinl2Krg-GQ9N<g*04?C3HNWC{$`PB;^UVFt4l%p=x
zS*3Kas~<#P;6YBwMLzu-5HvAO{t5m;%HcN-CAEXY5;I!11y41Oer)U<ltYLQ(7j#)
zxW@Sb{=0kfTDeXiPMJwJu&Cm2JGCy#&(8LfA^}j`t3xfL$333PJjk-*1f+jZU9R&I
zEb+aqnpSD%`?72_H@eL+ZR4Zu(0^~^X?knhX$;?GT3v*W<(55H-ULvbWPOVXv`v)+
zU9Rh3l8$tAajMda3spdhe$Erl2hjRmy%i;!QClE-C4{DCK4HF$&n7VQekUud`gZ~V
z#~vps4=FUbNOCSjINjsDf$e{D2j1>c3n0*}b0OOfy=(Yr+<OxQd~e2;$)33gOS}xR
z<=!~dz2yC`QN+`jjLSs{GM&#=(dL+lld(wS^+6NV$hyCI8=K@ypD%g)U7aDjJc#6J
zKD-*m`bRinDjNoW$#bMgki}Wsj(oBd=Bs;>DXLofakp!+*`F@MU#EW+9RBxAb<?is
zL(qy_6J_J)49Pu$>J6XV6_g578$_I{@^&DJj$fqg;Y@f2<kS-u<ntw96eUY$e`?8E
z#B+#t_5|C$gU*W?_di|E!)kGsb;SKqjH<qoIu>Vj_j7o!2H9OkSQO|00Pv7>!}nr~
z3{H}QTMNqOXjFoDp<jO%Fw#>6O8a(Zl?G)jsl8>>FcQiqP{(P7f|B(ZB~z(FbW<a1
zRMUWmj%E!--7^`w6D?K*hlewX#9!Yb--m_J!Hxf`+ls$syCM1!?Pl?EfQAla2w6il
zrG?-E_HhWeB8Wyp=%Vyv0i=}(?Dp|Q?U-;VpdV|U-r_M(Eg*k~+{3boZ^#M-;>y<4
zok2kz5*)-U!$dA@D#!~FE|Ar?lAawstyNnDxZ`ib$h>{;IT2Ssm050xo)dKHara#u
zh`rhfBbHDr5U2l+dL7fqWC)yZtmf!lD${v>q&jE3iT`x)iD`&Iz|wso_>#G<B)>F1
z_U%Tv_=WZpLJ@yS_c_z}Uu$qL4hmw}VK`e=`gKy$I>A8lU_5-eslVcUAp_xu+3|)~
z;5#bLcl-HTkM!1#!QLHP51xCK*Kb|cP_4{&R>u(wrS}I1Z=QrUfX(xC8DrHw<KElV
zAvtZi^W%bLe+{cDD*SpkR_aIrW4vp?jE&v3K^PtRw!wetLnLHB(+wjskLuTOKA~YY
z+CS-WeuS{mpeg-jqsi4q?ApjGj{D%*+)oU29r>;?H~Yw&q$X}phcrkj8F(XR*}(Y+
zc$_kJ*CHZdu*F1ziv~E+EWH_pHCtN8$qk0lu)(7`eG+nCY+HZ|_G{>a8WX91HE`$J
zrM89^M45ltBHUYTCMoTTTLkKwDAbfay5H5XHUuSSR+XTRq+#kytQ@<iz0+S~(JZPO
zh={gL!H5W4VEc7h&~O<>Kr%w&TEv#up1(S(4`FE_z>e^~ofK4gEgLe+C&RS}uHz0B
z_Jp~CU7#`5<8;;D;q7qHwEgYM$%vS|(kx0Uov(kSmJ$N)(z2M&yUzkSjNz_0qMPS)
z@N+~jZBGOiV~2>=<rZzqfY2LkuGQUDMNdZy7Jw9LtOd#<3u1PhY?_xOOjBlDh97J%
zO7!Z}!iS~k+QI3ZhVWwa_#<i!b-(_)sLqe4{LbDRbMkmnu91K|2MYR)Wy8!ui$<tq
z*uj4a1Bps~`=PJmuZCc`uun}%0@F3N7FPO6gZ7YUQ+YCIUaC|gA_?=mY;!Id6uRGt
z@bmSRgVls;B_eJvoPtA!#q1N{%SwLuj+uflq-zJAt>{(Ei&N^_v<Mps_vrxlT2grg
zK4|~BodUU^e^Y~UU7o3`7Se_@VZmGMwjh5jT<~Izjs>g$CK?TCp>O%k@cQN}C`&{*
zL~tS!kab^Pc3~*G0YOZOqOsXUmSqMxqc7Dil%he`E6qRMGV!&lOiM+Bd-fh>Scb?b
zWgLJcFlR_X=ptc+0sUW)EyH2H=5Q2EOKDsU(+67Rs8o1@sA_S@6=>qyS??fltl)p5
zpcXm}Du=%Hsga<P3%its8$e}zLiSpebvm~Ny*w$W$<qpWCt|49Z)?RR)phqW%^KsO
zRY`#1J2(D#ixWAQz)~rPM`x@5_NTIn-7HeKJ)DG&_z|?KT@^Y$9L!d>oEa^ds6^U#
zZ=WP#Gv%MXo`O#BSk(V4lT2a)YtDZi7Tt-DmKQ0Y{nyw(sK*z!;c^fd?cXCZDR6q$
zvaWu0f;3t!cLlu$(6VtuAQX~8s?_V2q?RDT_MOYSSssLD#Ys9-Jwp7Y_oZ2f-T19{
zI=otM&JY9$-~jfw9fure_q0CB1J9bsfXKv6-Qdq8Uz~LMjErn5Fo5xaBTj#lVjq)f
zKL7G{_AYV+oe;^bZdMYH%$qsRxcHV?075Lj!ZdG2v6W*{3{qVM;W<{2ouO7FZ*!tr
zT>NLt?%Zt-BIi8+zCr=5n-L5iPu)?b7=1d8@gfg3Ob6IfDZ8?}FRHvgon0vx7BXs(
zj0+6CA85S<03R5a3>jQM>z98hM~*~7x%Eu8AtY>f)ky2yQgrMD2qH>xdy8!X;HVlz
z{vTgzHQr@d9T9G<pgMoT!y!neVS2J)gv<L|+PcK|%1oj|r^ANtyWNG&HduvnITYLq
z2V}}A!V1o_5L$*+40GC=UN?w?GlB9CesvHfv7U?UCq&GX=-N4W2n&DMLZ@1DFXii%
zUriJDQgTf1QWpKB>Y)UXJmKCCu>X^HRT5_CVm^^@c@=<pF`J*x2k!~RO0`+*69n00
zlTdq5TsIEV@??RMgBSA##?o>>gPV;jlUE~<zSYbSImgd>=r3v`UGJ$hl3F;Xr8Ce1
zg~a`SNi}s~b#QmB|80MyhF0|!<)&K*4RQ;|LFgSeVR?A}EriHPp$%8G<{3Z=YPKqk
zUU)9u#k_EQvs9}MpI(d-c)$7Mhn1>%YrKq)-&USZ)C+~2elnhS{TSRn{i8S*fvi+)
zx>@HX{8ckx>0DZUKGD+oLspE^KQCKWa4ep#*3RN;(`<cH%~pTTnOK64;p{MqzaB=(
z^`fMmShQ{B^@hhEX2&Z5VhEl0aCM%*U)hHYoqH5U#HyisXD^(Wuoy5LIIPE2QH`3t
z`mS^c1uGP8$|!%8J3L>Fkk}U9U=0vCVOdpLq6+*LfJo>Vg%iMg1AW?L;s{QUjxDP!
zC35`+^;p&Er;C3ah}s`7mpZ+IBcYu>l+mMDBfE)qAXr3Rc|wMse5+G76MXVCk587S
z!rEGY69DzS)j$hf!6}*jjy-5%jbH~X^V%{O^h{ypgs?mxz-)&gL`W*Jn?KivG{ooJ
zT2YSYoI9}Cl;jU$Ypu!@P&^4Lq}=MQgOgqTGh5i?>p_3LFZr?U6=k;_pYANn`sF*8
z+`LCbf=)pRX;j~D!kp;s(?Y0&zTf`re@wo$dE-Fextb2*bkWo0<u)l6$OCdtH>_TR
zAl&@xrpb8uROtX0bfUn}ZKKUj`^Gg`|5e-JH$V#oscnnZ(%kJ-l`>D90*`e*5)Vog
zjImfmyyJiQL>q`;IL%+bsqQ<XE=~HL+%^I|!AOqj24hqb@r8r-&>VJsA-_LK;fzcZ
zaBBUb(}NjP8pnWzr!_yJrKE1W5X@E?oFWtO4etOP4)i&fFY+UA>{g&V=W~FH9n98f
z1wrRWs+K96j-hxgZiK|lNot)_$K8&^Z6(|uMjwCXP4HT3ar`_HDkf*E?g9~!ZD^iV
z-+it`EDkKO^~1o2;;Fq9u>n};;2J6^a2JOqtk|umvjS2BVpxU3WgQMPDBPhrwlg2H
z@Ot%9owe+`g}TumRt7VLp57&6%pF$-XKIbpMrr8z@?#)DDL@zo>^`}kx|q&-JAiEx
z7&3p){*sQ86Cr*DBq(Kx(c;6ELth}wGVbn?kl+~M<pe4SDmlve0+XzJNU?0NF7Q^o
zm&duqLGml4koXtM)M+`8?$3o!BZdOt<TO|}XDbYwY89HI)679{2UU8{(CMpCri6$u
zTKccNs2+heP@+D4fa05}E6}Aeb%oK<@Xvn(V$ho%eUY2zZrDn1wO9vNDOpm8Tz1Z-
z0qY=I9Gm<}8S+Rzm}n?Yo=u``H9LzsTy&r{52HZbdG&Lq&a7y1CSklh74|LdwiUp0
z6*^pVLtURRIO&EJD{ZQ4yNVCmE)_8h2f7FyWb)&(hS1o{;@l|QHvWDpp=(gyrFDPD
z1PIOt5$xZDI)Pf!n$y}IW{5(@s5hYYnGS%SF3%WDmN!U8fkC(`AFE(3PTe6D&1)Hr
z03Rt<!DecgJB`f66z9w&L5W!}Ecu4cxk+?gIT`+nz>lp)KihhBu*$%Oi71?8f^1*i
z7?}Q&WTrg;B^B4wBb-oEZ~Z*rYs7zXd!Z&y6vUUarom<QGpQLPySfLx{l%3%oovk9
zp=~%X09*!}Jrxo-uXzt*L<iharI_#GJ<sAR2303B4)5V}v%tmt!b~<*r$}A7_(Y6T
zERy<$_GgJYUI&8L;))qcWH;k!*Ij%v?j9u&mz$-NxXV~inp)4D6brPBq;P-XI=>L{
zcfdy4-`}1>NGBCv%BVJNuqP$S*OH3uYaf=0kSPX%^co+GrMLng^XO$)u-A<LG=KdU
z++4bEk&0yC3fgbB=*v&3a}z^ymkOY6ta|&(Du!!lw89G@!HD<tn2RFD`sEECjy<^%
zD+&+d`APWIj&2Vi2!@>2@o;}a!RzAK@l6I$7M@5(f;4Tyo3~NcOz-TFd;%3#1v@G=
z^jAK#QW@gaVbK?_{}e>A2~+8iSr{&X$npDv@$5vNY?4Ya;1BA{f?4=v=1QAXU%L|u
z<4yx9Gqt<yAyD;p-TpGfBjK9_NjP1$FJ!CUD{ClUVOYc`fPa8_S37^R!+U<&gH56v
zdKJS^{cM-cYsmA8H30hkx&xhQT~N-evKDeQ`rW{OX9q3jLfL0*WH0wcu7$8r-VCzI
z1dfminR{Q<g&Vm1;$Wj6@;|3c*N(TW8U6c8Qbfx){)BTs_Wi*D2!o0dQh=g2zOhIy
zt1YHUMB@)($6lx$^{0QVZz#P@1yj}ee;&4)_u#3HX|b3kqx#iXG*k9qM}u&E0<&Z@
z!Ca7`fH%_C3(33bHi_R?o4T6NNkvay?RYa_pi`&Je*sw%fDZnJE#c`8{*$@VRqJ-m
zk@e~b?MmTTpsTvJxv8SbMBAZ6Ki;ab3n&h5Zoc@XTPxHd&9#4)@Ay5PSu5GH_d0-Y
zs|avpO>2OWFV{Y%P|%kT@W}xf^QX9Qx_mVlIHWepU`}YxO43VS*j{yPL37lv(_1`|
zy<;4!0V+GiX-s1ITrVtXA|S*WCMF>Yu!<iEKHsTA3zVy*>rn*rDN8}sZGvnAH{h>5
zZW|V&ll!teUxa^N_MIe$=?2JXmFF#N#Bhxq-I#`t=^(~{ZOhYHDu&gPHKSB=d7EL-
z)rkbwvKUI2vX<rN3v!^(<?@E$O1?d>$WsQ|%v$qe39_tl8Z0Gye}s}_L=Aw1PbzPP
za%Km$fIPPay!xK}1J*Xl{uTIlbmGCDop_|i*#IPLzsrB18b8((Lp{AB{iU?O>>jZA
z#yyf{)0m&9PuqTDy51U+61}me$%Xj2BHcCgTIuEpTVp`A53*j%6YvIc5RjIbS$PdL
z--AK}G!D>w8x$#d*bT4#D$=LJH3>>el&JD&0G>S@<o%2(>8!BcRvm$2R4i`7m7G1(
z1U|8N`P_enB8>wRzI{DQJ*-G9$bg{UCktn3F|n#q4pSt)JP$9G3alV(iUM-sy?BtE
zecvldDi!q&?KRJsZx+f~5Ck59@Q2~Q6p||_jjGaBXfy&>Hs#f9J^gPPRFyAh;}LAQ
zX&Xok-uivyw^dWKMMy50p>_53`mVyWf%0s*tQ##YA)!^V)%0?LQuBNj36JoE$%63x
ztyOFaWo~41baG{3Z3<;>WN%_>3NtY|x8=eDfJ6f`GBLMk2Lqf+12Zx+w+B)KWjX^h
zGBuZPi~|)BH8lz^Ol59obZ9alGBP<aG?(G-1r-D|F)}%mVH78Sw0dP&n_adxuEpJh
zLveR^cemmmEI1U`;_gzc6nA%bEpCP4F2&`e@64HZX3qKhUAgik>t1&6wbx!rt|yeF
z%4!TEW)3Fik`6!+0}CTFFF;;F)xq8v$i<*)Zs}@g><nOKWM*bZprjOYHa7-YI{?Lv
zLFT*wE|3*K$rSW|?)q-Q%*=y836L@enmfNM%>X8z00nc9vAU<DISYWs_%A`(!3D%%
zV(jv+HV0Z-1I=mQUBnz5J)NyBtw4WburV<FiS)-?lo23nY-;P^?qX{VFb0|dWEmA0
z0g4Xp@1Qk+#sLU0F}E_dvj8|)0MyO30UBx&s%ii!RV597Wi?vH_rPkdj*bq_|KuX3
zrmi7H4-gkoRF?plYtjRxG}P4pT-D8i@BA(40gCGH`agNz4ga_+NT`db>nKaGF#TBr
zfCb=Y?(AayC+&Z6qk3ls_?z0htA(?J{a*<HG*%#xBQFz^ySqE1rK<~w(ZSi0(b4WN
ze(F}%E&z9b2WMNr`>V6Lo%vsdaRr*amlI@V{*M5EHU%JWZE6m5G5_Nv>F^Jw{d+0j
zo!)WKzlgmT0`w=Q-9O9$F6QR{k;cl{<u6}(Wo3DQy|FbAWDYb2n!X!?j6tq0fKPv6
z?@x0x>VFV42Z*^kJO9a{@INZ&f2H{!>Y@(sE7P}s^Y%4%|L+|$2D-X<{abDRbJ?a2
zKo@Hlkjp<JngcAX?acqMclont*1*3o1rbFVNeMM|2Ko2K12QN$yjKUv2=V~^W&J0f
zh`2m2fSZ{Uz{0~0V192>380yngT4JbYZrt+<rBAluM^0@*^}vi^|dX~!5!%Rzi|s|
zpqa&gpURuLIx=Yht({!WWyJq!{SG1gjaiz50L%b$CxE$!sTI?obbocrADHD2{9XoM
zZ$}45fQ7N0i@C40h57png13vYn>hgF>}u}o{qKtZln_|B0A|*vp!Y_9KP(7;MVA3u
zH~@J50lzc(AJsowfab4*O8b6F%^ZMso&Ym{a|;9}MF-G(L(u&HIcNWsOVZWOPSM!j
zoaVnv`rmfO_SSZu|6%!G7Fy<ixY8&(INKZB{g=+#Mbg^C+)UXTWNP(~!u|u70U5vd
zz6j9L&is8-{(?0A94EW?zI~rP)_+D9fPsaX^}lrQEoo{CG<R_Uu(AK8GJh|_e-VCv
zul*mo047~cQ3)v#y8qQPf0;=DO&!dvftCPP4o-lvv$L@$0`q$#uySw!yjk9R+RWVJ
zuTB9lF#;Vx?=ApGSCB8j!oeBg&u+3XGXt2+{$T$USpZDt{}SIrGW}JRe<7TI^iHnE
zc7NNj0hlbT-OT?j#yev9Zz2bP$@<@aL~a1n-`*@N@A-j$2jhB|-s|&k`uBtm{}S1G
z-lcz2v%h;g8o$pAJ9CS_NwTy26LtO%?(FZp9PQr6&fme=0Zh(+Cx3SXSvi~k+xp+b
zgWMhd&EY-2``-cIm*Qpa{15$q?w<0W>GjvaWd3_Q|2fwGlGQ-Y4z}i6)@JX2A8G$)
zqF@Yiw)W6tem_+#@A&)Uf8H7VM*_;f2g1L3i;6mUcr&nbvjG@bc~}7~9GveL7FKrO
z|L`^a$AtasM8Egl|HyyF8^GM$!`u{MdBMSyFW4rvF|_ovM8WiTXi6T&lX7f9ZP|FJ
z<&5ce0$lODZ8CGA!hmM~OsYbE2YG2;gU`tUz+!F6U@W`Wjh3W}sT(sD;T_}83ZDs(
zB}B$@H5oMmGZmKnzju<+9?Ir^)hS`0&1{WtB?f4W9f|R@cRfV2PQIaCrI6`=Z(YlW
zb}yP|X~J~2L-$xh#qS_kn(hDxy**&YMj7{tEPtH)^feTFOcutmrwe0$FQ@fDaNFVY
zr1D`idp5qC_|>7%gNX_@vjJ~p)A?cJ#EIW!RXHtYu!K`j-w!o(3d3YV5JTza4<e`l
z3!klvu8M;XyUEHDqYX_gzAi_PpdFr*etw>>@Oe<X9j=_VU^emdKw_V;y?c@dS+;fY
zDm{UFd^UcFV1_KP3FIGt0|(wh8QrE0i|{yG%Mik4;z6U8kRS)$?|e*`5RM1>Cq{a9
zMEa(s0%t|1@F(diR`Rd;fFUTX&WITBh2&&572HfXBe$HCia8`|wf()1gB@&C(#Acs
zdP9?e4_G-I<gJ?Lw%6hiEHzW&%N0sHRY>cT_({%(B1e#u(wk0yU1iJLb+nCopEEWW
zUS<`25()`b)&1Kz)&g;&H?ifjXQh4vIsr=Tbi~MVa3K02X#*ju)eU}|_RL}>-OPKp
zg3E+g7?>D!ie^zB_l;dOX!N9bX9GH#3+#M4{xUIklw5#j0ew7XI;yxIhAMs$W|y%1
zCWb$opXmAPhXO5s&S#n(>Qn%laXM<YOO1-w{%xK($Qlpk?g)f852c>ryyK+MNEK=E
zNfNG$e!yHShuwLumom+(eO>JMDBAkq1jVs(1Y~q+xVgj|co<($-aJ<!XiSspm7Ma$
z!i$vr<vVEk2KO!Tweb!%SClAggZb6Q$Fp^l6_@|AC2~Q3bZpbA!_@LEl#K$0O<C2J
zjEJoiA}z#i1*2tLL>>77J~@F+ZU`*bA&m4_($7<Rl5G6@DMa7f3%Wc$K3i%vnz5t?
zo|WnLC$QNbz4jtB26BdGTvAJ1J*fzGjZChT-DoBzAmnNum9bSN@b)G_1`M(9(q`tZ
zR=YH@1nQ@MizJ-F#*N+G)4-$lrwQtn06)_&D9H6YY$Ce%rNw1tLzsAMwZIyK8L&ur
z)Ne$`A9?EV?J+0`J{u~KmvO)=+96g~Uny0lNHo@NiRE{$^{VAY8!FeMu%LQcg6#FW
zzIPmEbS^KnbhKrmE&a;S5fbZq<5%2#^yda^nEUO24}UR&->({Z+pq(h7cy(xp@Ylj
zN^_x%<WD75H8Pqf>j~6-N`l1%D8SS&fO7k*8%Dqi8PMfyU1q^QGQjHE26jfspzAdb
zI!}?Am~GkfkQ{9-?Xdj}x!D#(uvnkb+n9Om^KT)ERrB;#+fxwMFdPB8eF&7uugF!7
zAs^3wm?;HcaMVYPnY&=&Ou1|#w*I=QZP9sV+o4N-#o?Py;q^_g{Y2$Htyv3z=!xF*
znn1f4`2nYM;67jxLPC4z*!hA$SX@ZUn?Akh#sE<xaARetDm8_%b8?+@<K`p6n2R<N
zTt!ZP$z()(E67eEHNreNeB0l7^p)M3jyTPKeGy9<k-i-*V6RjU`tT!*JprkM)}D+%
zCRz(8MkVUr&<RThozoDDz?ZBBge~5)WQH#M=j_dH#9v{pmCI5SM!rjdW{OuEI_cuV
za-YAum{Vmk=6(Lb$_>ZX7A=9<L3JUTCihT=*ew=ilu>Q(P#oSL<vUvUI|5ut6be#*
zIOj3ow&4IAliR>nb$d*S^7j`z9<IBBC2Ye@dC*v+360>_(Qot)C*``|pYN1|ZnZ>e
zz(1#q6WZq!FOSvcs7UI}>tSRx^Mz3mIBdzqWuSed=xz01rxCSlGHJzf+3Wjxi3&C$
zY%CtU$W-7%)sH5QE&zS$uE0s#_JKQp;rcBL=he=r%!(t1a9(Eg_=M8fuG?+R*|S+F
zpK@VcltZ}vrU{pQwhQ>!H{OpVcwM^<hk_X_>QMBdZeku9Y@HeNhajs{VnCu@HE5A5
zY#_ex>U(P<Qi`YrPk36DSOaG4%~-f$5<-pV2#5ZzP^X?$XabxB>%47wq1xPk7b!b$
z&+oj*U6YYIyqB5_%*Q{Zh_*pZ(uQ5r@b}01Bgh=YsY9p)Wy2_g&Za4~NRPs&HiJE!
z1&Cwvh!Mz&k?tvKJ%>P?ioihw&yUfw@awDaW<?m`jn)IHnD{H>Zb^91OML`cEFKtK
zf#q|O`ubnz^{v9yS(eHSTp3t@V)CWG-{ts_ZO_PUe8iMgqWJym=eKnArq6HUKZgdI
zH0h88xnd)9th-%&MA?j2i)aQ5E_=<ef9L(+cA_x1VhLrsARG(zgZP|$(c^&{sbd|X
zsosrX#9VX_zABN*#zlP2311`Eg}P^A_CgG-#L)>GN805XzsMNEy@ox1K%@=VTWWC{
zwnT2!^tJiwY?7UMHWS0RJ>oJkKr8LKE&(yUH*tcarOx9q-VPcnCl@8qUM%9+rO>C*
z!y)=^yAS=Qr7S(}_NDn!s6t3ZgpIsCP&tmsoY!&Q&B-z<))1>P|1l;ydwzK9H9&wf
z!uWD4*e7Aa;^OrQA96W=Cj(wx!b9IwhzxW3ayfUDztLJ>?&sF+J=03Lkr5dx=03G{
zfmb>2F5&t7D3#FEay`D><szyeqI{)=ls0|n!NIGKBEgiNm33Tax7Kwy$)|L?a^C1)
zkucGOiMJxH9thN(sp4^0z4@n?P7OtOrxbMp^nyF9c6g=sMABz}vI@%zW@3^)#uKlT
z?ci|$LT=hsvaR=z&D9+Gv%Jg4#zRu!HLw>W2OP>u?0LD^19?Go23h+^R^0Rej5L3k
zQKRK(`0@x}yiI4-wLxwsR1xezwGL)6xu?7nwRrwR#a^v?`MF{FkK(u)ALB&rU~e7y
z6e@~7y~MGz7L*o$$vPn=F-6*m(A=uc&?ArM#oE$_*}<lZ6&o{SLSv)ky6fWlaB<De
z(40k!d3}6B6A4<8s5{2_?3t#)rcloH>4-o(Q^VwXK2)pAkA#i=dl91Mv;l2PR5lia
z9nwfRYMW5G$t*PCcy~d>BJ<HgweD=Rl>G&E6U5TF$;@bf0jCS&?r#rf0M#3NxPF6W
zgf8l7Loo`SsctNIc(J0q4_!Cz>0#(Jl8{yR*Z?#syG__vlJm_QJ#rZG^>h)m{Db<g
zhogqQ17+4`|5hiLfru4j&6ZH)apJ?->_>}!*iib|TDZ+B&Mo+u&f8wEVF`BpL)sN~
zu@joPbO7RiGuR6R=hZQI86-5MzYq_*L%e37rE-bqMmLlj#QqGRCIGB+Pn0GdS?4q9
zvuWFbl@SZ!K@QTjzOC5MFhM*=)UAq7mPmA7s?%!?oOj75Q>t)6-MxB7xZvG~nJ3KH
zM%?pfuBhOsj2Xhs0HI89howl!V$U7E;?*(|d(%39+Fx&+GwPk6=bK;3^O-!u#6Mv;
zx8Zxp=+p~pCs)aGt(`Q)`X|rv1rbj3ANsP_2-=qiFnWU+d)nY8_XiamV{3U0DdW@z
zqN2CUCd2yA&EuzY4ZP?=&q(x)uA7>cg=-65Y^_!$M%^IEh@KO6$pnj*n~1b9lyMzW
zD|e%Rv!C5D!jK4db1PIXB-viSN(NnVA>wy6i_|M>gOz+gI11zV5-PJ|{#$zR6rbSX
z3ZZRjq5AqEdXJ%!u}Vef39og3*j`emMVyM3<=f@4bh&@#mU8P{8phgH*nTrv=lVVE
z+sf~KF_C7zEy^>@>z7#f=@Ro9C>&w0!Myc<{C!`p@}P@!e8n23-(`t6g|3t>mcQFM
z-PKGZlP}F#VKVxsGRL!iv$9IaVfN@7GH+_5yCFQRG1x+Mr|7RC#c$$Ed$qM~Z%3HQ
zXQ$t@Eq>ez|E<v7F)wmt*pUAe{bS)kv?NvCFXaJX%^?-7!q&2HEUI^I6P$1X*aN|T
zPO%b$pT*Lkm3EgH$PV!|%uKV=!40B1hT`0DatdHosO_>4@JAC1TN+ai^qc-hLzgco
zvqKi@uBpO}2fv_5qebB&DXuOm$OIdEt^qGZ8nXJKW_YY_8RJ;>gF(*<KeD%VU3*2Q
z6CNb>%TRCILoxAl1C+5?iy~W?KSv&aYOYJm!LiB!vu5x5kKm5q0uTe6RhY$x77v%V
zmQ61sNnlA%VC2|Ih!1|}hbx$EI!TD-!h2L2nDI2?Hy7EzDTlQDsNK6?L(%$zeyr*b
zbw^J6tZ=(8uAIL(n(?q#p-usp-<<rn-G`johGm&ylZp@LPE9z4EV|d1p&oC4%fP>V
zG$e<IuCobB7q<1XPf<Z~XRPg9r2275CmvQMiB$as;=%AdmWW(Sm;WA|b141$567gE
z6%B(AP&T4oo9NLt+NLp_OLSUqa0?6;?Rv=AEW|P?ihXK1@$EejCX?S28{lH$HxV*3
zjxb@fSQhk`QA&L4U-4Sh@p&qLYEwH5IF=D11$YrD2PQSj6z-$#>&2MY?qhY**YWPV
z?jJfWbMdg8j%t+yB6s`talmLQnhOj4BJ-T1iNA#UfARe#&UzdPsXe#6icpAGdtYwN
zCf1}{h4$6673Q8))nNL@JqXP$c<Sf0XO3#9qrN1MFkmOcEjxi@%0>5oLU)#KS5G>H
zK3Kl2sdGLeKW^qgEls&2R~n-_kLdp1?Q~p;TUg_TYrxgnq;}uze55AI5#r8Rxe3{m
z+b@bOvSjLUq>NkL@6EBOakI<!_Dk0prG#z8z@ty$<>>@`x&WYC5-ua{NY8Q0?$Bzz
z=yp$8HA6GjqQvFYS|faaF<utFn=lMLn5Br+*PYg2_sESYIGm84a_Z_X&P=u<+&Z&k
zWbPII^jC(QR7mmVQ)PO?Kn4jXwxwtzT@YJ-eXvC&MwW}#Y`h55^n+9o8L45e&R$|l
zpKd?Ak34#a7pI`l^QR|)<5@AM+~I}L<Z>Ek0}D^!?#}XZ2UbmgQO|Oh&Y(&CaTI24
z;hCMI3>mA_hq{rt@K!;?^lw7g4GDq#BibME9}QNuQ7;iPys2JcT4$yQMzWxF{T<#c
zPKcYGWKr<28i0w?d>k}^q}s_PVn>Fs6-yzq7+|WLakjQHrQ7r2oPgYU#S%Llp6r{E
zQ{q<(?upZ%46b8;B#HODeuR!|5ana(qqgv^V(L}*)AifnOuPP;9C_om(l*7)ZpU|R
zFi{y(zdk1D&eH^?(SohM>NLsY-NHw<uflBqaF|DmIxnn{8Zb@YOt{eh+H&3bo$5fU
z5G*(pFSd-JvPBh|UpVV=o;S?PM-&WZQZNT<V{zafPN{%@DeFPLWwLhMO3P(BGF+dd
zosK{&L|*HG<N!>v=WP@QpVXWb>Lxx^6>2OdF=<TV_BS&@10+(mj9uU!T*_;{I+{rL
z+a9=e?AjsuVM2OtRvs-g@H4T*Y0i@bykiv2wNj(howD*5Ft<&d+}}!TNey9eRm6tV
z1PWJC4D4EeFHp|judrOL?J*cMWoY%R6B`8A7puQUZiy*Vo*s$yEv(Fl<*`Ib>;uR&
zmZKSCQ&Q<-6<(Akz7tfZ0=n1Nug}Y%@d{3abyoxlE|~XxyuVEN^U3GTjw+8libDP(
zCz|;w`*TN$z5VTzM!Oi&lz;0|LfR7SY<ZDa1DV=?IxC+m4oZVJ5p~SM+Xf-GyJQYA
z&1TZ+z}$B^?ilr|mx&@*4`3Pz-C67)MBBpYnZpboMUl`K2LxBUuc@R99<rg=d!ddL
zAIe8N!-f)9KAQ%G8|SpP4AM7{l#mZx(ZOspfv4$B2_z*}jMq64`I^M7OMTh^l2=#N
z-enbkWE*oJQHdG0fSqjH>E18=2&5FAv#lNCBvXOV5+Hp+giOi&dXs~&%r3Ic#9T&&
z4%4OEF=DGU8oXHTF~~i1$hI+%XDv>8cR)2itF^XKqL0iP7aVhsR{z}qD}!DyY$`8n
zYs}9{&U&MWn`=t+A!c0Koi6>UHQVaiLIp>EOoprV^CVx2Lt%m58G!RGOJ9_i3h~3Z
zEI^f%;=XC4ymar0l`hj_LyK0|!>E`oeCv#Bm<qT3suS(T8m*2sLn!4}K@^tT$XVQL
z4nnSBe?lZnGnO&dSbdU&SL5p`f#G+=6;-M>?@}3)ljB+&Y`r_x_;VmABBQQ!iDFWJ
z3lU;~2T^fXKUM!unRei;0DdSbJwk>k@K_5C`ralh1)_*KI>HN@KL0j9+Q)nboQfPA
zE2cj3?jmRiI^9o;r}@(ru63#sA;hZG@83gJS*N06)I{axt`Sej-#`h7Rn2J;usF1^
z_O8mL8i}P}6v^`);ev&w8_6wMz${RIxCNn}jE?&Xy1#<MrI^luxArWfVU9bQz5-4K
zzJ+oP<JL@Be}O)_AW#!+cBO01)e{CWWa>kxLrWEOIt!75)&l7=l8k~iS9+u8--_|}
z(QQLz#Lit$jwisl?5Hrn{hPD<ZyX*-9SFs4MC5$X8!_i-zqLvyxX71o5n8o>3X&?g
zsR%O|>Y!AQ5q}^o<IkdnA+xx~=I;%<T5<wg#Qw3FU?;Be>Nob2Voa(x8oZRi`UCwH
za!-VX76)Wh?>7T8LGbdMw9Z7U+|1M0eg7?CQGqo>K54h-$Q;<lECQ(RNHIh+KH!}F
zXkMns>q`qV>Tvnq^%xKL{4F|vBt|D}L}5zFDU1DbJRVtSqiXdBU9hq+XiBfp-E=iG
z20I37BxUJH+#PPM2<ovR2N>(j>fj5R9i}odi7Vc#@u)8*#5t@^Ca@eMLp_9~c9#&c
zG42vgU+helQ#5W1Gbwoc{1w=Xyx6C|^72=j(`Y}3O>3qHh%Tb*=nY_haw%DiC<dS0
zTpQb#7|oEDbxPzN*O3;uN9k3#cz<L-CrF@i*wu~THOlnna$PS2Pr&sqbqNcSBVA>e
z4|WqbzS#=gJ`VT)ebO&iS^F%(2c}-ig~2}2P5k5-`lGHinS?#!lQa?OZCEeX(PR9k
zU4SF}f^ootp&Zx?K%feLp;k&efLqklNRl_{BPr3QpNePxm1&BsKevW}V>QFqn>6b2
zi|fp-5&5bdm?ga{P8YJ!9%tPAzTYzxPVDu*J%ADGS7PtW+U-q@{zm!C7ZnJw-Yua#
zO<DJh%B?Q=0=&oLjcs4+l@=O^?)d$O{h?v&looxRR?NBG)a4F;sol9c91tccvXc2H
zEBJ#CzRtD<LjL5qc@RmFH~D7?*~pIMpCsj?*wJc8-Imx7?#*@?^u2O^)h{+onA`&R
zS(Zm@u`CX{hHN+CT>L~TqJJWZHhqhSfpJ8_Z{BTQ&owXp4eWN6D1)xUQD-~ZbckKU
zQ8^|n889NYrtV;WTdT>nXD`YMz0f2v))cXUk;av={@F~dIc?TLU<|NhDg~<u%)b51
z^;L9W>*cm;vJHmxTgAQx|A^H@@HOj`vO!&e!J+Bo{ZxU1#p%ae`Ax;eX$jltx?`dr
z(TJp(j;2Z9%@If|?qM_Ctu(pT(*jfmG2v&#1F_&LPT{qGYV-NWza+kS4?O#LaaBT-
zpB2v*cd?8w4V20}HLPkQub7E56qp#NG#A1IoW_9d2}F#tR>Fj>k&}AleZB~rcVugW
z5z|Dsh!EycR$F~0WK)x)>+21jaf$iV4I1nT4^<BoRC6Duhnrkh&iI`;Hs*~;g-02@
zj{a%T*DLdXIfU({*Hg7RQg;PvWPR;3{^PkP)hDd5)YhpEpM|G-lDjt3yZRO*`C);?
zstq1lzvM?M<a_~{ZKy!;7fXiU()~Q&g5Vr5Z}0+9SeRHhaV}JBWzt1=fltOfD$#)q
z-KOvc?XpvyBVtlkDghIt*8&l@sy_xr<?Z2(ZxH%_eki^z*!<QdB5NT}K0t6kH31ze
z*@`q))(fvl8DdaCNz7YP70;{0vVU*u;^$*Y`rdV9%ucA&h>nY_Na*U`x0h-Sxhn<c
z+$>9JqQuOut1VXq{$2hBBM00NiHIY<Q-`@vbFaCl@Zww2xcH*Ajv^#RT)SmQ+Q(eJ
zF0e0u$qqclkvA#29M(C(E3<7>WK?Da7Clix9SJGyVkyD_?FZX_N;MndsuaH@5+3_F
z-HH1&Rd@^`(S)AqPvJHsBhHV?9yjZD&Q0#_c04{@P(~))uq_qrPt+|iAjBry0e9vg
z=*r{waywL?dA0X6lVB<@b!^D-q<E9dXdK0V1`6ni$MI;Hs~+2~_(<-69Sp5JZpVV*
zQw-FK#^INt^e)MvZgm(}ecPV5w(AX!j-QA+AlNh%8llBVOQRQGDc6q?Eydy(FFEXz
zLdwsGxTEzYdNDkl3|uYz{ePj~^I91P#+s;H!L(oyCKD0QbIN8-ss(38GZv4k5Baoz
zc1Z3kt_U<-1Z#snl;c}8A$bIDq2r@RU0*lsiN=rsyB@{?n7Yc5EW9npKp8Zj>TXW;
z?anQ2WE0bal645}^QRR0aLj%zWGBXXd(swq1H?=5bl4l4TV_q0ZC>8?Xy8vS=NRI_
z?Af3A=U60Gr5@&{sTWU3x%SwC!ti&0O||7H@wyRZl!A}ug0vHz-p5A6juJNaveqb?
zc^SdSHIqM7^f|A5mv0}JH&g_X>@f?{z%U<Cvl2K;erRE-ex4fe6s+mj7>THWP~2!@
zLXOkk5BTK|9n6+YXB|Rm3<#u+MFw)FL`CzMk6uIVY2NA#CPm@G@m$~K`CmnURlLTU
z?c$^2tj1>@HH5Ulwn^<Zf!(!P;E5#9YK@?2M2mAh`{DBopiZW1Y4nZcnp{1JJ4<E`
zOIk2@H}~}#{QL>@EGc-j-g*hllhT>T#v<*q<iWr%PYeQmti{cnO`C{2o=@J^hZR7=
zK3uqqQK6e0w*i5k*L{YCrb6t0yW(J>j*W3MJy(52q<fYTxz1xeP4@l9IH%w)hR!CV
zK1uPDXSX_{&W$wQWugy)>7}v2_BWISxLkY|TFeLaqmWyCOLw=RA8l!kv{WeXNa6H7
z6Nn4vZ@FA);Nv-jzZyvRkXoZH_ZdtD_4B?*4RY@QnGN-al9hlvao8k(V_YcC_5=sG
zh1{6lA76dIfRD1)zAs>~FpEk!kUpD56)ljYk)Ll5E-1c|ddj&DSKG?UO|$RZ``9}u
z>IBVWot<$ZQ6SQ8D~q<=QheIexMCA{zFzi9doGo!S#c_(4p#|U>MG7q*Xka3Y=~6G
zy#i-efa03!{|?LiQ#V6@nM8j%d*81C?36LqX#dr~YYsrje9LeR;qw_z@Yiqr8bvr0
zoHaR#XqgA2FEpLl)Hq`%Ses-Y0k7b7uqnt@0zV=*2#V3am^p*OdrT;_xlvGp0uwv*
zN7$#T_O3`brk9JwD1PRaO_VcmSFg!DM=~N#)fSP-0tR}NwlpJuhoWi-ZPX&`qkQf`
zcg7MXtc<I+VFhkZ{xo!&hQS2FX=JgD3-u(iyQtWO#6|WQ@uKGP_WTH`;N8*Z<NQcy
zRo7*r4^np&2Do(k=H*a7_L!<pUVTVrIx{u9z{hc-D+D+!Q7EGfcu2YTgFl}zXWVOH
z1}Y{dSdwK_ZDd7%ar<FinBCQaaXqb9i>R*?Qe%sT=a&`ReA==PFg*AGHvN+TH^=Z9
z%o~Ni>U^yO?D|dSDX;BIot(-@eWe#CtBszVL9P9dx+1KtyFKg=y)_uWM{eYwxKr(Y
z!9Hbi9J<cLk8+XC?j*wo9xItnC_Bwb_AIVwSD&d$+S_k`u-VHQ<pw27rty&3<JPLR
z9J;MC;(gm=)NK^5cK)_4BM^m8AfV-hOm_JYPEmEuXQiICBfEZOv^I|i<;>x~=%4f;
zxJfgIvwiR_jMIq_N^D;v@;hm_<mzyxyvDl9aV%Y$ewY%gZB6bO#Qbj<ta7F62bja9
zxNiV3n)7mh3&?sX&~0H0XJ~XExC~Y)s>|}M6ZmcU4w%Zq{sKalC~gFd4Otn)a>wwf
zQLCb2`nLecMBVsO)W&ivgqYS>bOQzqyecQaiJH2_-6`2!N7VN&{tpt<bw&Bud&`V_
zZ1aZYri%bZrcDENk^Tx;w8O=){rL{s4ix@QRJ!kfuT>%P1V3E2XnZAah?rWXE0DDX
z5gG^?vJQVj_upee&Mg8yIgCXH2WpMD3|)LIjGN@*+c+|`HPTKM*OS6X-gMxZl{gxh
ze?IX;|7dE&?I@Gir$ZX6YBlmT{3x!S<E4uEh&qjza#{2Gx5STUkIG>ALT{r2eM9Dw
zT*e!Jn}^sNJ|gl{>Pd*%-DBF$wM0x8V4P&-T<#+ljP3G={m*NN4C&O6R%wzB*%9#N
z0iA6>UYb{toIFyTO{-<(S|Mv<_Z!}pwD!juqqx#>hau(Qv?F(+TZ*dVi2GnqyKagn
zqIw@KM*HNj9YiuRUd&X@!3CYX1@jy1$Mb}LNA9^3GMo$N>+G=v^>BisWqhN`L`4{)
zEodUsC!wPX)0J%IUJ}0^&vExgt+nNE_MNf|nGKE(8U*6*8%~taeneqvla3Uw7fmFJ
z_`0B&b^dg*<N1*^TPiwUFDz0%dGT1tZ`DwwjSxZd^%B^IkjlYJU|`+zqxbtJatgG6
z>g+4^zADB}Z4jBD<TU@ytYhyWq)(sueUtGwRkz<KP~2ZrZp_dxJZ7WJ+ljt8MK&qA
zy*3^A^6_-ZoxdgON$Vh2!%}ryBD=w>md6|e5ZeYul_M2E68=M;M&1H20)r{uA~P#W
zlHd`eW-APleFifKVIkZzDjtCnHH}q&OZHIx_ew2enN@)}V0*%v`l_WWZHg16Y5SnZ
zDs$01?*e$}qJbKZ8q&F_{T$v!+8r>OU#uy4>d}E*0%O}a7vCwvr$bd~V)x5kb(SXk
zO>FA*zDwJLtoGh$SdiK0<b9FmM4&k&ch0N;Sr3^cgRZzUBC~Orj%gWw9z|$>iy^n+
zzxYW_7}M6i<X$72jrpviKxYb>`krj*vbR5_k~H#99zbT+Mr3>Jg9#)QlBssL=~!Yq
z-4!z&7TdAm(W=yacMK8fx5VMj-x|jr7seLWLpDxxKJu(|>;~UtJ=wfqdcq`3b#GlB
z5E-E|jNDxPB40A0XuXe64J%-OmvHSB`G5Qrr!8cGcRuTGEjb>}Qx^LfW2)lU2xQ}1
zSbjq%a6BiEf(Vu!Vo#!mR1|*Z5Hc<MKkfx+`r^Vqy9<?aeU)Bl!FQ-O7>6kKdYfe$
z`bHLvIQ%FGvD^T-JMb`gy`o&L6^XJNzrLbDV$uGpc12-Pa;N=VcEtC8P|eamz7fOx
zrVGQ7?i~J|LXL;B+-vIMr4^_Ir&G14=#1?pz_;YUO*}jJ=^7gIJ|=cP7SYm()+VSN
zkNbIhGd+Vob)D2jsc{O~?G+)B%gtku#3gb6*e5=kYS`(~o9&{}y6V8N4oN0ZOt)RK
z*oumZe4!XcT>t~upksu8yP?4EYgo5WTo$Usv-)|rgWCXlAml?1ddEZ~CPu>RZQt4X
zB~l5vxASk`{#1NvqsMci!qG;?61(=L)fK`%**;51E84W$ySvZW+c!*W2vE_XJ|?^D
zGe+vc%!a+6@$M9KY;M>i?dyJ`oWJNZd-()TTyG>_{)T<+L5~xEqTuP-ijJUYJ#S=e
zgW!b=8Pr+hi&s7`F0Svto3^xXgJCAnJ9IADos?6&t9m}hn2yPfWY>SFJw!(%Wj0S7
zt0-=G(W4&U_dV)7ZvUk;T?mc~_eNYJ>`A2ITYxY5V#LUMc;ipIYFmD7Hnr7?=+33q
zrsa3yJAfuKBwsmy+7*gjk^GV~S3?;8r7jxtnQe9p-(I_a-pnn)C~dd~=7s7(N2U&T
zI(Q#E5US8(bK*y>m0zgd$NMZ~DclcLxow%ZPxG0Lpa0blUSSV}h37$xzV_FLTYTe3
zvk>1~on(F%#05U~3Dlcu?eW(-1J+PR0@lVX+1v_pY2s3U#n(R~hbTDrYJ1yN(4Of1
zxHCvtTuu$9zaF)J{KYj5f`J|%!F6rw{~G3>62!7`f-e#j2%U|*2obVspWfw}HQR$~
zo0*+(bKYt6Yx|@*{)FiYXYdw#-*`l_So+@5Wj7&*pk}@Y0PVpxmp?0u`C;(VjcW7-
zGA5h}di)%Jq9(SOVropJzZ?)K*^`Q<v}t4&kuN0_{5a%<FwGgQ&KPNu+0GAS2ss@j
zX7y1LZmGM<2~@jPZ8gQFOTZVO{H)Quy&elkPYAQp#@hb!xuWk;S4NMQ&wn8BoY!;Y
z!m_64$H*a;4wGNmT}pn*5nt-dYBhDbzXmI*ZT*LT){x<snv6l{T;8wrFKe{I85?X1
zW{4r7)S?$H@JxO89yM^dlALIii8Iv&hSAq1cge${owc*RF^f+uO#N7St;SM&=1@$d
zbOen(B;zfPA?EA5P=5E)nHy>w4RmSj>^z#;{84Z_-)&<KNije5?sGP)3cE0Ex02Yb
zeoX#<VOEpD%(3lfaUUhJU%|U(=fVa&kt7UgMvpSdxi|pkhs^ZEqYql&-y5x+e~c&x
z+Qc};Y6K+ku@&lZPuP(0k!GiR%(Xmn9YDv>G#3cp)T_r$lAXtW@?4*e{Y|QDJL&!<
zbCDjnZ+>;~H3x&8zNCgn7p5O^^NMz65LkbIS|FinH2>VDsNaOP5wLQ)CCLsPMl^Op
zOLU*to=L2^CoX7n|H$|i@B4H2BZa;t%h!Wl<3T>}K1@$RiNvzX2KCrkS~8R`GUNU+
zIw&A5j8<qcs<OB<t#%wdVvuIaXhUy%!tRNzLGBi!Act&h{HFNDqqwS?b>amNlXTL5
z2-XO(sTUb9iY*454O?2I{o{SwQ_px;pBI(xZ<r?i=9{#5MV#TtL@ZxY?EbD@)Jy+C
z{%M}M^qS><z?Y3&GWZ=PmVgI;9y3j`p9Ylie%zZcUuMnvyYz=~uOHP<H*mfP=hrN3
zKY(%SOOB|EEUN+@fnAK32yRcpAb+!e<h(-Z!`~u&XwMn2DkGr^&W;$3Ri4rO3*~gI
zt0r)8SRoS`EOhXme1s%<np~n<6>!}Cb}6bfPP!aRL*YJdT=ImXa)?0^;3#8P*Ocd;
z>O}{?Bwo@0#1jl0>!=ktCdn(xl(o{z)1OQlYFB&12N${E@VJ~iw?pK#NHWrYG+@tV
z+wuJ_TX?MXRAud8ElBo~`RcpR?xFAUD70fsiS~C$(p7JiHI-mSYoIF}<U!fb8R=<r
z?jSSzHt_rjQNbFi2R+@Xb4>A)UNUY|XPA;C!i$L{$d2%zD?^5wJHwI@*o^fhBEM`F
z2?d!F&eQlmyya32sWep)P<+{c)P9+M{YZ&rXqfS+Au-uoy#U`gfAB4*ynJX1NnQv#
z6AX7<Vk8m6dy-K>4K6D|vSJF_)dNqlTRZ@ouY;b}m$JT-Epk^k^r2&wQhJcX#lS2g
z9|9c7ujX5m-Qj3HWo)Npd2xB9<-SrA34n4nsMbHK{npXy#`P2Kr>c8@)@FA9rFLf>
zRvHLPX>YJ+X3_#V)DshfFVACNX(JlWSsg=R?elf7Lr&d16`{43!9td*x=$R$>M&lu
z2szH}SV(izPrRLO3(p6Me(;YtAbR3EG%6q1QiqWf#No%J<@Gev_Y>sE-rXs3qFKGP
z%pMCffiNL6eU64~ITRItDd0ru=Z83M8px2^Hp8CorW<$U69D2w<AUT&yn1_xZ&x%&
zOms%NFLR#2I9R_t6VewlH<Q>3<#mu{DTD|r?&!Dw1clp8fc&n(u@DB3#tUjJW4K98
z4Z>sf@jmT7p}oxFD3T;tZ$<{^@7E#PF4Bkf34qb1S&#L&clf4%Z<XaA-zfMk`@JyK
zgKfeLL8dAT-1?x_ySSI;v_C2Zkf6CeB=re=Vvv=y%7oaShX?_O!mxYWp4s5dQZP!h
z)kBm2rH*R>Jp)IzFZp4Q<1*wtV%Z(<cU#{OzkB+H5VpTBjF@EDE5;E&#KW5XGk|2<
zy7$~NQb2qi4?uB$$8P0(Ae9WAjevf!%R>>9`0bjV2~w*01j7IOO+v(mlC&xAZx$P7
z7jl#q)vOue?qa=Imq3*C{xgJ0!m5>}rv?}r$UgDuan{rf;<LUNSZ9B<!mX=mFYvsf
zTA$FOqDX9=Q*a<ryRKu~wr$(Cor&#a!j31lCbrFq?M!TIVkZ;h%zt+MRi}2HyI%L*
zYpt&DeV+$IR$@(q4ntGWvpCl@N!{?yuK+2U2v<gJ#9o{qz=}Z`Z#^l@w~UKhwbmOd
zIkY(#{yLD#lNt|4L4A&C&SQbs_8d$I3kh!=8v}p+F`a`O;=47suWq=ZcM#9=gZ@2_
zx0JHStVEq)Sj0(Ybj_&U(D>+i%RY1)ht!-qx;R4U-ES|uA3v^o83Z!1|J!Z^6185b
zp!VL1^6&4KfJrC2Hy*mn6GZOn5iYx-SzT19b%UmItI*b**Uhz6oMhq-J7#{9rv>mG
zM<&POmGJ9twDD$E(Qg-8$HF-6a&W~`y91IJpC_&WrI|eyn-h!!+}#*cIBAM({B{_Q
zy)f4?|18up7MD`*!&^A3pFU+6kC9Y$MFpU`n7042u~~(;aJyi(-A6DK&KgBO1Er_^
zc%m9MkG=VKEHHUrozI6)3DxO%Y>@o1_Npnr4mP2?(ORn4zsU%TIJa3tiKG5b_szhg
zJAV{67@STxY81P(g%mJEf4~28ftU=Qxbwu=Pxcv3T+C&1|1M2WK0=I(QqYVJC7y<*
zAky$S2vj*41va{m(yCTkdMl#auGOqo4o^AVPIJC=%^&)r8KCm<hmGG>PkspD6{Cmd
z8i8($)km9k*W=~v7zorIU1PM85R({fl-yuLX}@6eb?SLMdmXx<$rQ~<FoF}dlGE%8
zTRcPw3QEqT+N=6?!KG#nUXM3md3{E4`X+bz0h(_P%qFGC8)+#Ii^0dFu_OTwkiTy+
ziBpGgyo`F=7H8d4fGe2>9=h_PG8p7Cm*9^{KNpLupZ}%=TS@%{+-v3Vny~Te(KoTd
z>wbms9$Rn-x5bsy>Gr7(%HBhfOrF!7%|!NWy+L^j877uO>11=MO`d-;Zau9zXI=!A
z07XvGvZpl@-b&*jxvIYf2rc7j4>?a;L@?~h>;&dzvDK)&?2~Cma&x2@SE%Eu83fZh
z^Y{~S`4DP6WMV7l3<a?^K29yghH=)gJK`Y+NrF_ZlrfpSd@GHz_#3vCUdAU&ZPwDA
z`-a<m9PN+BbmhGXZa%joApv)#qO|StK(-me(pU$bqSK2`D%s=;2p!SbwL-7q^>NDA
zNfm|Q>bjxy(%g%~xM)UHj-QKT0k#zdH18AmgF*Ez9(BxL!>0K)l_v(2KMnfq8Z5!r
zLIH<NMWEkspKwxfRoCEWbP4FMGVUhAmv027OjFsnAv$YO&iHfMgdRr8X;S_U14Mh~
z>lrQ5hBqd&f_iqe7^&Kc7}#k70ggcy`x2P{&SF>(w>Mj5?`jH#y6f``tDvay_r9N?
z={?Td(8fwLuNk)4%+-saGN*q<M{xYkhO_KU7x&ExYPWK}7tST0g*z&%lb5l7hq|>=
z+X6?c;!ySUdw>4hI&=Qw^5e(*9Pku+E*cK{mU%W0-Co0OGnAa~VCuWwmET2V9UK>z
zM3JdtP#Ez>e(fiaoWmNw%GKOnr<-4>aaWRF?Tw|KLhfGcT=A_JeHZ&hZ9eyUX3T%%
zZqxA5@<;b8SfHSZy@W_A|Aj8`U{kMiGd;!PUQy7S8e+C(@5Tc88G?%rD=<e7Z;q*U
zx>cC-H?i)LwPlzv@KsHjN+97<9;FxyRuOZ{r9l2C1W4Q8-9u@IASC*?xVGR>maiWl
znmH0=(*Ajh>Z;tS5-UM&hbuV+YIH;^X&k(ab8t2N?t1p+h0fah>AA=+mfTcD=I1Yc
zzr!@!Lcxk}pv?|5ni49}V1YlWu(kP~acL>uxyIGfVykoDmL*RSs<muQ3R7Y8>BjPO
zxQrG02ZpxiG_UfE?;Pl73A;1+!n>aE_!Sm#Tv2#^6jnTiH5$``uU@8scEzk379@-|
zzJTN>O9wAmj>pC@Ului`fW;gYGStvepf$e#*XuFSFi}B-@V%N^2Y_Nc#7&*zGGV&e
z`)B9LBk8;ItF^5%bTYpf4t5$=0A89$;?N?Q7Mb(#BY)yo36)_$>v!5k87h$1TXwh%
zM8BRJCr<Dz{sa74MipK>rl*zsnO_W}@&3eVV7}?7gWf2a*+P$zxwhfa@wZG2I)?H;
z1xfIvGH<2*Yr2cic>vv*&j9s_Sr>(R{-^Wme=Q^qTQ){y`-nCCcBP<Q1D|JITH$XM
zi^XcvV5?2{jIP28`HC5Mpv?D2Wx93=d-L4L*g0z3aZE<)Wf%D~u^d!a-vr-&dCmwC
z&i~@~(({c(TGIR&B2^Jy-1gzH|5c0MBmFh<NN~{2Q8!)?rwf2>eX()=q{oMkO-X;X
z#Hu*OEC_OSyS;3zWcqU4XSo-7hdxriOK*MIB+PP}L+-q-AB?;zQ0|wbx-a-OLP3$r
zwA}>zdUknlQKZSYk%r0{b1qWTK*?p3N%N$G@sl_`Z#wNm+x7sUs^Nkbh<52tQP~~A
zjo$X_Yteymodsq)V2wQY_zUfGPEU=9emB<qz+;R)U}{Xe((q60r_{gp230QDM28b;
zHHG4r5%si1iwP-)N)n8En{zbOe75htiea)%NiL&V`qN$dn2^3#CmL~AVuuXNvcZ%_
zHdI=PAdHOcyUtg#FjAaaa1Ml(Pj}|<4aDF)GbF0Tx&xuPi%K%tU923Wf37n;edF(J
z#46(b7+h%`C7p+Nqkk4qf@P%yx%MZkNFmvLn+q8>gsht)cY|+*S)TB?3-{TNT@nel
z(j())!SjoX?pl0A^x&YE@O7>@prh`OKhv5bQvc-eXOf(}DKgLtKMWXn4Jg>I&+*sC
zG$WxQECjR+eo(Ma%5zhBs1>QFXJnz%eGepP;Z3mb>9z3$YfL1R+_@O}6P`4oXe;Hw
zT`6c~!Ay_!4bJb52y5FxRnS~9cW7`BYEEdCi@$Dzd3+`H+q74LHcq1XziI<05<}MK
zFY?mjRMsc?3ucy9YUBPIoZCeVc_9x8)Odv;k10URUfAH}4^trikRq;lVn^Q#9yL>j
z0Hr3nnh-ZZrQC95zlAZ2m5Rgz7Q@_&@+8V07fg!WKv8Hwd%!hp^rvneINSo{o{7qt
zwD1<rzUsm;!r)p0iB;L?hKm_k)8VT+VRQ4?EhN%$pcWl#gp8%+;o!C?WMiDql<Cr5
zLjZ8NQ*q_>1bM3wpbUd3T$8s%^q`WbWrWsbrrjCOZ^%}d#QoC?TAZ<SCEDOTwGe59
zVPk72e|+*S;Po$G<CR5*oit;<sbCq8!X;YO*yRkRJ*7#zFfE+o4qBY!od2H}SJno5
zlVj@RrkR`)+CZsH)GKJB0pDCCP$8+QxmEyZ>;Zc?XTMDTRY&hcR^<=`kJsTFejM@P
za^A=V#@_t*Bu>k7U(|D7(NH-nf$p`ud1kZ`p{lHJ3FBE^*NH<k{rp0EXtt?<XAOrz
z(MJG2e?$4Fv*sc*{}=V7D_D?t)10Qysty}YVG=Zith!jU$G~x&Y1FW8UVYv;gBu{+
zaLAl8%QGh1$*_6(Vv+Si>ZWv3qLztI%j3Lu4x=c3YZZmUHd<f{q%=q-lB4x#=|8lK
z(|5gTMg-hQRHAtBYcbJiK=q)y%US%09ikuQ{nFZ-*bqHwVGXuP6R}RSq92}^%Ahd1
z8a9hSagW-)f+v-++~-hedBe(F{{$e{Md>uNRwA5DG<WC3v>U+`!GFO`?hy@YtGm5c
zsa)c5BYb8-VN@IBpP<ycPAjt6Oe!mx+AxrWM*hBcg=wsU=-p$S?IN_&d2u+N?l)`8
zW>kvyxn%VQdgoLZ7(TKvGUGSp#7?*nF3$9?v`Xg6EeeOp=Bq*mrDv4Ib$|#Rk9Ta8
z+}Gt5?0Ox+^>}9(RrGXcZXS~sp;!39HVt!&Zp<7`snsqTUIJeG6=Lu?pDvH<7MAD}
z2AE3+uHvkTcLIf1%BmrKjVaS0&zM8mc$5JBGf;?N$X=@#G>~Dw-ePA*6$T4>tfXuz
z2h%-vrq(MO6c~o@@CwZYWB_kj0E?>(=t^GsNluhHvMs`|#1AD~0`F}!@GbffGg_Jf
z7~3GJ)6$hD_7iLTLZ!v`mD}>aG*)elBWMa4Z+g8#dfiOt)OY<+L-CyxTmorD0=4;Y
zx|eWcmV;VtbFeA$4dIxdDMvE3A9px6!@s%Nj9pOp6a}Y>r3FxsrGX~K_qb1_Kuj%r
zIIGPryTs9`+Ly}}8e~+u1C(};D?in$rbjC++r-5-8UfQ^me$w2RavWWzHW-_75Qxr
zL@jCAwMp|r4d2e4mhGRGd|<Pe?%s(F{NcKCH#~(|k-|*lf>sz}ZHwEqDaJXi|0Y^D
zq<#>8VW=n$ysm@A4go{-DmjvhC)4utl`IQ|ADMi-#p4g>eD=;X==Q#qKgKX`<&{QG
z=i)aM3y-3PyZx|J@dqL`PkFHZg$rdRcm76=@Fi(ZJ<tdcJJYF4LaEM<OwA)GZ(Hud
zhOH;~Z!3MPz=Kx`WWA*3C|LfzG#VnyY&`)A-FX>vbw#q4?FjTENReg}WeBFPEA<k1
zcw3RApLm%w&m@{db+WB#Hhw2kSQFfo)@ceBL8Wd+*-{h1a3mP0$68IpA<qz8bws!|
z^RKKkt(z1pN+vnHkM{0gGlP9!!+T99R22$Q5-m8fRF>k<l@Qtr(yokWv;5iqH286=
zefwwPIk*68UJ=mSlpKuo1ZST0)9mt!OKf{5=8rF9LH7L~Ol0C6?3SeuK0rx-Dg<4R
zpm!0QYD~yYc&Rqz$Rpo%SXM98pxL_dVJkOE^YQ`immai758pq#uJF)ProadRm1ce_
zt&eZlv(xoV+*sOM;cO&TBcQKa6IH!ABD(e3NPs)GwGL#Y^C}#FF{n*0+|u~@+%Ji0
zGq1nAo}y4Pd^CTh4#@Us8lITN2K?JHM@24~T@qT<s|ua%VuXUb<unLa`w@5aktYhm
zmS<unP%DXV&&K%>$zfI%+(fi>HnzEn&25;??5)4&-THa^%#_@eu5@T_jf=L=;9QJa
zG={GmECHSfW7@WHh{%^#^WiM$e;1P(z!TR;y=_<5;5%H|{@E^af9Vqhsnz_<-uRO)
zEL=l@;B>-fnfq<Z+2P6nB^z~rnOGaQ*;zZTP_>Ul(rhSLShm4?h?q$IUM|7r@bZNK
zRsDQ+!Reu4{$wMDG(Ua-5)5nfG=(g*CMcEWX#+rTAVP3j9J@g}4}vY)<Rifl=n7p{
z^v@T+Ui=ZV9oQt#T1}fW_j8ESn(KM(Czl;Q2p&gWiu$b|2yLrMxt3I*GIO)D$#-AD
z+`hdCJUZO`52gk=xZZh@8N`Ars8`mMru18`vYFnirG%h{YYu_6QtSv{ZPBhig8q%B
z$Z0?sTr=bMIh-t`XB6iOuEMlh%aXZcZE|8%1<MbaM|z!|MPXkm5cAb0Qb|-Rvb4-E
zhf66$(r?L(lxVsm)Y$Mdq>_r+V<d*jUZlwMhLaahE;9PsOB4k!gFPbUZkdZV%ZScS
zipsIZh<9{Y+p?sfNjg5O>AYY|AwQtQ8?S&pMLNhW&4hS)khKIVSL@Bd6->@lmm9S=
z^`$AfnY(}Rvj&d!MMD#rXqnQF1FhXe>qMs0)Jn&c8)eu{d@Df~e-FkoYJar0s3ivO
zR_aY_)ifiIgT#q}8D5%Ker_&eT9j-XoF4<omw_VH395R3rTl1@_{|Zj2G8f_|LOx}
z2&ljOuroV{r=$lxwxAEb?P5O##qA|Rtn+N4SfYdDwpCv^Db)x0e`e`LDbqc+F5Uz~
z7#4{k{=#eJ#oLQ%jt%!I8zJCz`DLVaCa(3H9Vv^3|BgCR?o=?!MRouY&FF1@8id|P
zIGc<7<fFN|RkXZKb#rnz;p{J8t-u`++?F?x_F#!tD<au2H@1)ZsO}w=fJ{tYSbJJY
z<J@*f9CWsU#@oi>_gKcSOFW6N?tnR#(!o!14wwcN?Hk`I<>kdHW8*iwi0aI1wThH$
zCU=9`1TeK32%b_^vruS7AH-0@5F=5+@Z+!6e|=w*HhPdc3|CN$(z~VMn`;Kx1cP=k
zgg3IkJsY8h!nJ;U!$lGX4}D4*l@DC)l^vgGvzK084VgaVl~QV}H=RZ@NzHuK!W-h3
zDL-^8BRv??PsduDUM~2@vGu{Q{C!_T@T!V!QKbKP$pDTY{ZIX=OpBog`(d8-W__U2
zd3P$wNB#1!kRpk&q%5CRo_GzoPDi+CS?VfWQiM@ULU$3Nk=4l{XNdeF(f{0F+tGzd
z5S$KKN{SWkUo=hSdjCNb1eUQ#eR8{dPKo^yoy{a0U(xt;zrC!Mq~?XwI?zsOL76@~
zvJdCYXJ}T8`OLA^;rbdqn^EX8`u;bmMF12#OYV%M*D<n0sYN{Ura}qOibON>4GLkP
z7e^85uJ<93iNte2Z=xgow5Es26uX*HhpT9@Z|%5CY~h*k&i!zr@Br1MLfWyD=wpAw
ztQ@kqp)2aC-lg@grd=si(}3xtaH;k-wt&p`;=$#^t5FAfraj|7q{@#q5z6Gm#q+}}
zt%9p^7!$O{YX1JVbb?yoaJS@$b-V5{u?+UI&;R5q)cm(Yg|szWfNdwm>AeV-WIm4*
z2*wT>T~%Ndbh&UKm)(O-M|{z~DdSs`awg$QT9P-7()$UVC$>WBq$=N4wb!57D6VS*
zba$jxSE@2TlDFe}O((ujV~|+_<^zvtXqiU)L>jpi^;437y~hyXN`Wc)7O^v`10lu8
zRhQWH8C~ip1i1l0G>e(`HQ2jSn`zyM>fRvQGES_H@vFsc`$dohJ(=ZBjB+17`U9eH
ztZ7c0en%J$fhe0~$7Icnd<lw&i5uq`%Q*YN)%v1sjklU}V32o>!+VTr_Q@yF6@T77
ziQvenKE-1Xs*4U#{8kMk4O6<*u|Ri>9h2!;>ScE$3GRHP()a*i;~`Ohnrde==rVK(
za~p^vyhV+S=Y(7Q4j_0Ad`Y6MioDaRtE8pKs$F`W#{Ioi^4aN*`l9x<e=yd<p$)qm
zDu}%>?CR5^II4XP=Shlr5a4c%@qI_eB9|mFPc?V6t!Et|?a;d1OS2c<kIiNO9J&0P
zr!5q4WJ@Y2_e?vO(`5H*g(jlDlGBhE8u?>D3%o$gI{+C$q+b`d1MCFNm(bkms!dD&
zj|MnBXnn`X<E9%@$4_r&Y)jqo701r^J9k9OOu>zJ$Zgaj_|kMI^hrhSrCO9A78%$b
zHK9-QMUW0ak<5$Bs(w)dy$Sp1DH0;Ok6ZYER2V`FctgNIp$~*aw4V}`=GZGGW<3vT
zsKga%GX6bFkOapwo=}71>kuK?T(3MH%TWECQrH^fryG}chaV{fh``?Wsim)f^apvk
zM`6EO4dNVCBF5?9p%GE>Uz9|_{!lQb?MN__z=Ir%W#+>^!qO0ktJvei`<maqhZDLF
zxtIF(j9oSk^(#Z^W)2OC7~q_hPHbLj8h9AP{XWTm2Eh|D`00_;e<Xsmy|<DOB*nxH
zwNuVU9(_2!@vin}%{^P^^iJK(m;C}K*o`Q7kzIuuu}Ag8mBqi`dY8ysroJq!s*3*^
z_~l(pIla)`P=3)yoD1ifPGY{3cZi{cdHZ}J^6L2`MU0n}>gBW%7xIVw)KZ3`E}uj|
z^;c+1i4aDDWWGUVzVX=#I^}ZKy%d}@Wk+F+vY4Z;LX#0IHOgYtf;}&nz<2C#h82|Z
zf&DHV^DKTlf$608d{15>Vs6%SW}zVm!14N>uIP)I&?AG@Lwu(-8#<)Abnt}o1@jlx
zJAh|OUL4yNoVhVL5b;43S!@BHCdN~KqS2~jIw4#z6GM!kG_E!-w}3l}c{|Zj*qP@-
zplQWhCB*_7eI(r{vqmEQoy@`6UQ>PZ?+Zg4@Ljxbv8&&G@oky#c<a|F4xB(bAi1W_
z-#0aOKFxJl>v3(&7{x#RM8~cxHuN;g?@ApPTd28fb{%(dJ_>;^Dq(DfuwHY6y_7n>
zr79LmqDWSE<Z&5*Rx=`EwOo{rTgBG)$F;n<>6|>^m%a(|V#qq(59}hOc0ltLZghrQ
z%=@B88RNuKx*PVuDW`eHocW({9g^|}%gifWR-fzz?2_JKvZpt`@BSTuGSLb`=zA56
zT+B^68phj5uNtAKVk&k)buFKSKy~U~KjZyVgF(|IL4@t3APU)&^S;(^4>i0PFc<+6
zOQpZSP-QEZ*&2MYl*6LDBDlX2om+cPZ%)>d;mT>n%McXNGoqRSxAQ|2pqfwAw;~dz
z45#jdc!w**2^G_VzX)3ezK$+pyuf?>Xx^Ph!Zf=;ZTNDJCK4KNux}+7;*n;-4;>p_
zW&4U!nmM!h9C7Fqqpjiyns1Wo;7x;sCXetgUUQnU?DGR!{ddlYyc%ioB$PhG-o-D`
zN-?vG+>vd3ti`|1yX4{z0E5rI_0Ath6di78Z@lbg0rk;u&nsbFeUy8{)kz>Cf2&K+
zeF(|yF&*?v1et4U3V$#T?vHv@>^eZlNr(v2us6v)K%!bGr*-W@$(Y<{|Iq4GtdU2)
z_sZd2$U%e5GCvuC_0^6-p8FzIB9lOon0y-!>8UC$@v^}G{6Q1*3}{B82FkKQb|+xH
zJu!$)USt=ELzz!U^^-N&y`a;uj6Iy?TxJ(W<mlRVEjUZ+Wfbx*MSqW#zGj;`<D&-I
zKR;ayE&1--ih?XU7SBrq8+aZ3!0%j+#at_PFJK=v<KCRj%B3D^CKYNYmIsS{ZWWb>
z9-L>uo?4fa742yc040@T`t_IIHFKq=%n`Ez-ks|XWi1aY`Kj0WOVX|1$cdCA1rh^C
z<h!=FwW6ox)B6>h^*gHyx!{*L$%elHMoFP{;06Xc&Cll<60bcO#!1Y^FLRS|H584{
z+sqo^kz8+#X}XK(hchJ3L}PK^)UH5Kx)7n?YQq?iM2hv40aY+Z@C;1bgEzJmaTnD&
z1{6#-@CSKRZmDl($gsVA`~rpQmQ+YaYJBg%qsy-)LUwKBV`WM3SheXmP}h`0@&`B(
zpWaQ^{9_wPcbsR~I^#@9-6c2+b~;TZgJ>DM)IHhdBabUw9D2nON@K73R?Jx&wcVdM
z3=cAeak;(-fol!0HE$-{Wk$%l&CSCDmPB+$X`;<q9uq%$PycT1V%e1rn)c|2C)#c<
z^neg0h)e@f9zbPy_it|CwY(SIhwd!8(S8yEdE0>L)EPaPi8XhNuQE?Bo2sBuk&uYr
z8;>MDy&eG)Y1ChZ#Jb*4b~QG)ATJU><l=s>ev$b-V6%3vvGzx<@7Yn4$aLa;g69=f
z??RvQ3;VQ8t?8w4=p~N`mA^lpGfj*@2lM+5p18G%pnXrZA2@Y97_YJv>U05~Zd-K1
zklD<lrau<fe+2`)aXXcmzdcGQ7_rvsm<p10a<a;EpK0kMtHij$HZ>);g2czv#-we4
zxkGFx^J@V{D#!VD*u98cOjb*iGCguww#TswciL)cs6=kBbry0+sgWH9)^MziW^-@L
zjDM`~p&UV3^PM!Tf^x{6H&`w&Iz!E{+F@&=&8K(Xgv+%$ONNh%YMdfo34cc7oru?T
z&T)x8`NS;W)>6d9t+za6(%OqRk$5tITBo|eADS$xCmrRx$|U9hc{%toY^r+t#-9Vo
zy^i!unx8kGFr*P`48JT{7(dl^i)`P8G4*hl`O>Gy*B?t%nYnQab>Zh`wSG;6bX(+A
z0ndAPy``1>{6Y<?GcBDV9+lBg{B*}!zv$fqw<dj~%no{;X%cs<CmJbN*!Rc*76ybY
zNTqZh>+o~Irk8teHAYp#%2D;etBbkEgu1_t)r8FdAN6JBRYq;;=zzlBNM9_pKL_Fh
zelU_h?U?Ikq3nBiZn-dj*o;e=Jp%YZ<x#(Yb9HXYjEj6i^K(EoVF50Ur?FTqst~uF
z=Vg5%P_jGI_&7XWf&SEcAR}fC$tl!m;lH~J2Ns?2lF&Shi77C}grhFa-_uMNXR0wu
zLN{Hzz*`%L>u8+7cMit5gIa)j@rKz9lC+8F@@s(fulYf{!0tRBKkAZy=3k_)Crl=8
zOjYDwlYjG<%19%s_+(oY%sL7~T*aHHaz{-$fFYEuH{$H3N{-d?N#rp2Ce1hro=V&I
zJ9W;Pf48vC*rB2M7hF@~RA)>SwTFydwE2U@VvYd6u0*|x8rKZ{n^H|`eSY+G0EH0U
zzdubx$4$IVl%4u@XGFw};H0$8`rDLS5>7Y8?dJY@T*#6}4ep5w+S18l`!lE0yKg7N
zK*^a`Wr*o+2yVqs7zE)@h16B8XGLzqMr9(6d3%^*{OBXBPZNB@n@J>a=6rANNEvqb
zEls8@EH57s4}~XE0Yb8>7-Ndf?Rfpwn1MS&CX{~d`v_u_pZ3*!v4>Gmu>{GFq8&cx
znOem@gvybF*0u$b$mAvGFACBcXV@;hK*njr!|w60ee&5`wwL5pUYQX?2h#Bc^;t;3
z`pZUdKn*{QPS<BJyd>D;8*k1xqJ-o8TUgO;WV(ShP-r>t?@6QvUO1y{b$?s+Hy!*0
zQ$8~ze|Y{yzKNt@%a%qg%8I*?B2|&Wurp>oZOL`HsoeTkzLPYl%^}pw9*o3G1{9;~
zbs}BneC;uo8uLjp6{+Pt_$qA72Pv?M()=qj>T1H2HU4}kuESlrI*4g9V{Pa`$7C`s
z<h;y93$5w5iTj0Cu2w5RBg6Dyw7L7lFpI8~OYeoD`iLAkT!9Z+rXbC6-5AUt<evv2
zWDlB3pU-r-M8b1*vm)Z*D8R^~1F5lO+D2jTG_q*s*DxuIMrWFIsZmCt%6!%i@*aoq
zd$YElK@mnllk7*f)r|=QW-uIepDoTN*KqyDH72t+2|}JXuY3$M`SV1Db=)?GTM>60
zRgWJQIHJGc76fZfNt;?KuxeyL1LrInU(cKpJ5>CX>nPaCh0@zpev4rD0~#zRe{iu<
z3i5u(X+p8_7E+V1!)+!mbi{0Kb7KwHm-~)hhS_=@)SmxDYn9XZ{{36a8nVo~{zfcl
zH{!j6I!;n2U&U=_jIWE<{GU|@_v<kv)~4*;vm-W=6Nsi!gLbZ1=c*RFuQc1%G17(>
z^}c}_DZQ>oFVYD9#y~Fiet@bh0RdMk*D!3}Ba(DM25}Qv-mAp~Enc}5hl-GjHoun>
z@5j7mx=Q0ar5J~E`$GLVSlOD|>Jfq>dHZ(b2ifl@=T5Kb0*+KRr#fmCae?3uGCOpe
zbmMQHO>*w)YizX;9r0CK#_BYX-;L<qm|47kB@Ab8i*d5+`FMi=6$ju%?hT3&xE7EL
z`A)`P)J(ZK>6iYfDwIaI`Z^%i#0>l_pCqe(L~udovSnOgK$aVsma9AB;VQULKNRmP
zt)6GUufF7QCsi`>DAj42vO+Ye-;Nedn0m{K(I9Ks4E}ojE(JIghkBlCja6Vg@F4de
zkA|t7O#JX7hvmz*9|pLtw=lS$2zZDTsqT~!Zx+QM_SNLE@qb~vkjpM^WE)=d5JG58
zkqB_at_TqFzlLrROn&<uu632rKK&L0?StTo)24@hg?2|*eYe2Zvi9ja5)$oz<^Lg|
z>dnke9w9w1?4>rWfbS5=H6eMYm;IJ1G)-<^W(=-4mt^Co^a04{%nZZn{#j9bcBN8M
zBQ((Hzr{%i-lx_^(vTmOW68)Jj9=zvUdCuD^~F%tB~o)w^bXxo^XO{ar1>sF?(k4;
zB8m%^r!k?XXLH%SS?8p7o*)1IjYo<sgDIl7Z$y0Ln*adb)wT4^BO9%`_uM;L^801<
z@Zk97r(u)3pc`<X=@pjWc#nQ2HxkNisQSHoiuY_2<bke6mq8&Y>2sAhJWN(lT<W}6
zUMB%nIb4x~Nq}WbUJ%r^0AxqD>hQ@${Cs(|5)@oba6XiPLPbhPjht-jGDf~RNH8Te
z=_>*umwo`N^0N51UY=WSx+#tDv~`m$*F{lbV~s|1fF00J%mJ~}j{B|YyjqP|c#?SR
zLtJl3OdRc_8gvAGEiss&7u|W8d&OQz=rN6{omRP&_gPFf^n2{Io@kKc@168bhS(W{
z=&332Gi2spr6fun=QW(w-Z&K__in86n_A?zCl*!mi75uEG|n58$(mBl@yjUCd*8qv
zEoVXHD9M48ENgVYM852{9Dmy(zAY!yh=;cNo>_3Sd8glZy$>kk%)tvt{e9_Js(<P=
zL9p(77hmkANMX-7i3eKZiwkFZm*CJF(c;4{CyHqc4TF0c>lV6s2geeUK2xT=-w{n;
z<Hu|TzXk(%u*yQf&eH#h3uk%;CK9kZqAk{FB>-04I1@eM^J-)$m0I5q0Xw&j8PB~x
z^EfVCdnfTZ)H-vLsHs$qgYzk`R9}R=7R_}QmiHqIH3q(?nw-ty&ts5<SA;xwXFB?u
zTz*_oWopk3deO|EJturqU2a1`^Ya{9>?^feL}f8C2G3mr=TfW+4r-RyGy6qqS#Bz<
zmjJx*U%}(@SILXj?4bubVh9q&NEM7ND?2#sv#E<ht;Z97UwN-V5B#GC&F1K4wbiqR
zX|pyi5<+&r`t0@ZjAiRsna-TzFDKU8vSN<egwDEZ1~yyA^q$_EoAyTnL6nAL+TwW{
zgU)xf<jG&%xn9!nB0j&Vl2jcgwi48gRRHl?Q8@WJB8fgU>@6LGyc%D7pHm3L=bcfQ
zKNw*DTf_ZmHs<B<3*_HB`JQ?auw|lR0d=`sQB{s6to&qxG#ooxE!TK(!KB@Zon8M2
z4i3{ZQ%xsaS`|)a$`R=`L2p@x_&R`uP;O;@;?_$gozq9m1K8vhr{ERx%Za5c+);l#
zQ6B{dI?XoROI9-6n~<ZZw)q8l^2qQYOP6~jFnQu(UFQTKIgYINh^<kupHeOlOIH)j
zL-EJk+P?YavM@Xr4Mqu38VDpogr#jKxP%$<tPj7+iAf*Y6ljsUWjPYI|3!<)@YM|r
zk5D2BS>_T+1H3cDf~Q0ok<kf$uf4k9tWAuI>xwyn*OJ?1fwf&(mdL;r&$*jwqY0lM
ztq@r74dBjD>P}c;{uU<D31m;0h;?e8NaZu*%7|QlF1kZLimvW!U~vAr#DPMU>{w&9
zz>_C>4bc0p^~w-~^4K~P7#UwBU-Nl-2@YxrNuU2P4a_}DS7F`+91@`uxFOm_P)^@n
zA1^O=TAFP3Z(?)5ukTV;VrYrcwX1TWUc$Jy=rQvOs|vs_`D1%jPEP&mQB2=%4lQp-
zfnznoR%}$a%xX#&R(JXW2hr=RVmjBl^gBo1A1FE>&q`JodTwE1_nEeuJW7fOn=e*Y
zUrQNc1DKQzCru8}(|q8yX{oGqV&P2kC2O@kuFDpQTOK~76B?BbBuKCgjx1)GjOw%6
z{#{~J#-L$(v{lpG%H&7xRC3`bvTfP<zLBZ^@vS>vW}2hYY5T&mSMimte0-I28I=mT
z>v@UN!I+#aJwu1;z?vCe^mEuZuTM6%^bvw42S~bHfAK=8g;wogB8ZU`Fpl4kGUwmo
zohMW+yeS`bbd77z%o0g^*UI)5(;KzUZ=&=!i?lRhy~bNuv`sOX`V`0u*mtXBL~_+k
zwOmcyf$Tl!l{@gmU`UKUpHhL$cIZotFH0(RvAt1&Lp;n-oNzO65OEn^zJ7Lj+SB~w
zPZcPiSGv9<pg#m}qv7cwjwOk4p*zQ?xrCo<bI2XA7%_9(FpqeVSSV~;m)$G`@YPW)
z9v+P6BLCS=U|(jo4Wd>+^)MAY%1s~wU360AuahwN+r2C;{%Gwk+P97!{sY8GWQZBw
zPpORW{F<!Lhdx#Fh=6g21GAO-0E9xr9%y6}KT;=+Eyn&;B)K?<?ZGuB1D;#a5#~pw
z9diWsi0EQnK`ge*Qlr6dmoUd;;R|lp*@2;5)?Ss!d?igQw*Ny$NZ~mE8}}QL+gy@D
z30&8$EuF~sseI05=E8)LXuKm*b!fK*GpQ1vj09y!I+g3txgq;c*il!FS(C!;QUGks
z+TE=Wka8ihN?AUebB?+aztQUuqF*uXE8)E8c`~>Rr>ZLiliK)9+4cVSS-C00LhPso
zsuLvNymWs$asCTSwqHE?lsXEXC;H6hkMiK?ktHY~{JMp*E}xppX`HdYI&NIvm)jB!
zBaVsv5aAHD2Ve6xx)Z}+`U7w`0DS<FfE#_SL2#z|ZRCb<qwKkt-ZgeCZ~TExR-a9I
zPkgW|^>vfC%>buUa)e!bMfMKXrY#7RqO;fC_CxCZ`qF?MtTv{d%{fko;(V$#vm;6t
z_(aWZKWw`k-5hDo_a5a7PWPo+_K2<1TGF~dSXfrEDUOHs{eS!y8_TOmfkqN#U9q1?
z*PRP^gdsuaLB1B!@%?sE+|=c@C}V{cH0rfJYY)1^BEefMbePq*&K#rSZvpC`Vb8<1
z7$~`8L<yW^5Pl4cmc#5>>>VRc@FDnDz2k0{O~93^ysA<tDKqf~mHuIdE5(jQty>MF
z{+Y`lr8~*`km}{ou`YueQ0WCO%b+Og6XkeN;JeddsCcvm&ZGkm`^Tm~m62o5Qb@N0
zsXQvbCT3YG0BZjL-u4iUXT|b9yM;RjZ?w6Fu8f?@D`=Cgv0#ki##x-ydEeUc-4(iJ
zk#n}7!$`eGAL>YS;A+ARsjy$8yTMyZG$$PxJb$#{sN@3h(1LgY3DpB$2v$q8GaYSC
z-`L&f;Ip9chPpFPIV&4>0WGaNu_DoEY;xL{vN(S>09gSQc+z<P^*xPJ+W&rVbDAT;
zX*x~WR{}myUhoAjLC8<BK~9+1fMZc83vxI0X3U)M7pNZG936ak*`>c$&R#h7-6}ql
z>vOq*`7NtK2)7L&lE+hEveJ`Vd(}lGZ^8~*Mm3j?mgGo|IGbF5fYhkc&9n`6mK+?1
zA|<Tg12&ltssICPEt?0HLsv*#EplzIHV8F6_y?=>Ztn>^M1q0IiNC>db5i-U7?#aD
ztdyY!u{VRYjrK__y)(ffpggp{z@?04(c^<?!Z`73iF6O>XsW(Dy5Wqf5%l-Z&#%TE
z+Rx&}s0CggryOSM%%D@NFGCA{gq~_x-!)HINaJUst$Wn>3ysdIEOuml(kt!ys$5v=
z9*`vw8a?Wbe?Rzb<{7t;;)QV2_G9!;W8_O1mnyDBA2%c~t!Dc-_nw~oSNr5T(MF(J
zkcK;PiT){|sg`MSM6H$tdRvC%puRG_cvzwq!u(831`e%Ak<6=(W31*+AYnH1*6i3c
z{3ej{&&<$9Dag>^=UtyUbm!n^MH>{R-hp$>zY{G6mXJ$3e8TRN&D(w#uDkJO6G{l1
zE0P}#jU?>iY-RUmx*dUDntE2}cqv$Kpx6{&c~t`tqwH)PAJ_|W*J=b|!9pNX!CuUj
zC~Zxv^`^fK?A_DH$d0wa&DHS^W)*Tk$|8vjz+q9H{2Xc9<UF%b@QPlO=w)OG2b=Pw
z^tdW~RiD|wU4RM~wi*!Zua!`}JPPDNh?6?Ifg_!Q90%tkO8xs>FebWU@(?h6v6Tr@
zn(+Y?FK}q+Aj0<dv_@rpyT}Ux`9@-CQj2~cd{WTH?E$0P%?1xDxp5SRyXLk*P$JyY
z-<47t&(oYv_@u}xZ~HIq_(X;nxTJSRb4`~aW9ewq_S*|x_9ZRDRL`0Nr%ToF6JGdq
zql;DU<S|47YV#M$hncc(f9?r$y4ewaSMEHZ*}cHfHHQ$zPCst>kW!~Dvx~yO(71E_
z7$@=9lEx1Ve{3<J2RlSjh3AdAa;O&!bMRr*8k;I82jadoE}J5({3KCPrOY)80~25L
zx*y!P^tMSeMcddE4zYDm2IlVd%_x!;r_|kL%sm6LgK@CsHyt~O0E&ll4*9j|O~M{9
zYA#68hqm+HWmQHLeiPj6;di%G;hS-U6&x1|CM)pRxr+D%&8G6XeN!nRc`|`>8+;wE
ze|SYM-Rr8A@z<0no>7#uJKg!Xc^xXzI&OA5Pt}C^_WLABaPQH;=_`JL8aadU$z+gp
z07HwZw3MDqA>-6<e`<)eMA^PI|JFX>{K-KyE%0_-urdh2$Yf0-)ci%V?~Wn$izwQ7
zH7W8m58CFGyrX%&h*$&+xn@8kT?XB+E-l2<R@$WIc6-3s+B<db1~-7yg271VW%}O@
zASRo#2(%!ulk3MOC!EsCsyyrjvdj3mC|IS_X!tp1$<6l2(_;TnPQ!{pI9miz@&(d0
zK&SrKM5d2cBwM(QLn50$4Wt(RnjX>7>|>Tvh?0#bGWN&DL@(#PzhL5kYvF__>VN||
zNWnoRk}9D3N^_vW??$rCEW7$3Pw-}{q}#Bh%Nxi{>F34HNQ`?C#nY*E29Hhsh;A12
z6&fpCpnSVvnXGw*r?pmV^fMYrDy*1vJ`<_Opd)$4d#}F!W#iSUClM<nmPy+^$F|bY
z&)(oefjL^6n4H;oZcJ!&9p*-dFB0>g8H}TlQ{a8sf>*wE>?g^#gz=WwLSDv*qlSw>
z3tEnOQlNu+Rmc_ts+^SvQ$Xgj@~8S;S06LTpaf6x3@o*~zogGUls?-3rs}hCr(r^3
zw4I!SD_Z}f==1(tVYVr%L5Nw>va_?2u#o(Ry)Pi}U#LDS2`dj5&wp2JB&_UgTpZ~I
zpAZ<3tQ;I%?CEpAAZP#|4;B3N9?q*P4EU?7=Ko;zgOhi!l!CB+>|b478C6S0@eh~$
zx}S5~_J7)Z`~0Lr*A?EetLtX}3Cr2uh}RUsyNW>r3)Rlj)Km`(a)_zX|42pR$z_R)
zjm~e!4gw92kB^PU*^+@iJ2Z@kfX3|t3J3Dtuo^_plF6w;2?Rjm;tHU!4a7i!aQAV`
z1XmCQg%iO>_fUo=;SZcXWX?zM^fcw-bO~?+7fo9xA^Fgc!ddNK7+;^C_@j)dWO*c<
z`e`2B2x6`{W#4}_-MS2dp1>=TCK&{o590~2>w%y2kp$AtP7F<hfwY2@ga5yPeG5*X
zG@xz3wiXG=r0nabq=KTMcoZxNQ(-w1D2Oc^=>G-mcU6LmI^FBDfnqG}yaTUYke{;J
z2`bpCE2?QGRv%4JApCuZCx`YQWtYHjse3Nm-JPQD5<Q-v%P(7y{3cfy7Zei<4=*pP
z26qonQ&4{0MxNCV&b*G)7WO{E3v+njyRR46I_MYK2&Va`R9Q6U%{AEn0QR9Ec)`CY
zWP`sv*Lzi8{^c;dUUvGoBb;B<7p|_I1KClYi5;pHvcD!$wYAcqSF?0N3<62e6V~+e
zqa&lM*!!NDH#X3%mEN8LMFKObk{9xb;J#dWKb*3FSSGjt{hvKKZFP}v0C1fFJGQiT
zPQ3Yk-1xhX#LCVJ`?!}L3>0hGvrl+||7(riZq}IVzkGem7w)~F49q^Ki$EO%0fWz|
zPjzJp10#^W(GhTy<72S;?nn(Vb0(<PHXv&q_Y~QGf7wZ(JupW=_ba~ELDa-6;pwYI
zUngXW@sq{r>Z}i_1a0(mhn$G`QhvySJ>B7w&xa301aXG|5uB>l`D%WXX9T7$fGH=A
z=YJj|LJ%w}&uI~3JNVrV{G_&~NPLvt{X@8izn^6X!l-Ec%zc~dQ-2gsoPI!_)}67D
zz_SE?Io)qie7SzaL!5l_l|ML@EfOF!-a}-7GbZR@_A>!a!TE1rZquJt>BUt!Ifape
z30J+eAJ;tSzIOaGUor1>D2%&#rl%PFN{>{YUw@iB|JCV1GU@d@Gju<GU+g^g`bGva
zTn2(zdNN^gDG|l>3gQ8AsashAJ69y<!rH6E!ZX0jcCn2mJQyE8_^;JZSJ0i4=equ#
z$K9D#5G_Dc5z+-ya^$Nhr+0ut#L~pgE`c&IBn#SP|ImCta_Er?=AVQmkozsG^>+{v
zKnvA30S4CDRRTg_VCV;mWkOvn+&M7=Z^HRv_6pz7^iTiv`wMgpw7L%vQ39#@BTT{_
zxb#Y#fZS*Mggl09((=V^4pbq$Li<%Ad_o_B)B}9);I5!LIiH|Ac)VZWcOW{3{~ptJ
zUy+}=!Z&(JNA<~PdUt{Os`ul}mve}QkF4vjcHnEkmPyG(KR>PIWy5PmSPVnKAiG-d
zVRid(=F<}JeLqj`2RQOSpT<9=Tgz!y2eW=gXCe1Z^?$W0XZr~NSTmPz#O;=VaTov)
zc5|D)!+*8^01?TDo<*>6A+moI8lozptzJ|n13D1WGV}iY0=q71wI`VRw(bs%8uWb{
z3sR+=q@I!_rxb*NnbBl79Rr4Lz7(my#aGu(u{yhhO&fKa>sI}STr3&oC9P(>5H+Q?
z9z|tYQWPM`$|+Ny`b*x;SR0Fxe|rh2#Pk-u35A>8VcwJd6zi>a_~(=Fc24WY9UVuS
zGy^>_q@Ejar!Jm67o1MFP8Ld(497j_V(D^fbVlmlTIEle3lmdTb>}~|e?vjw8S}6|
zkDUGfLCNaCjLn8j73<@g8B)>2K~lYu>Bd7q8cQGDmo0ch6%@!1Qnx-8o)`<*C8Jh-
zoPdX2oBKLfB8Gm`rf?&`{(7M*)-71h2-5<8VnRIXsfQ8VdGpfJ8+B#lh!^+vRTF*M
ze2G7qtlxpjEh_Els$%jw+rtoAH1N_}ZYLQ)(ZPK{vbsIHRnX!&{plEDwkJ*S>5T&>
z{0l~fSHZJN3^@h@7Vd|VY$Oiw2vwOny557dnkRr-SFdoW?8{TS$$`;Kfuk|5rYLKH
zONrq}EPBdSQC=(4{z_G$a5zE5Bu9sXDrQMWV>@t007LsT=+-T+&C-)fsJ+<$CaayJ
zSG4R%$(#NrN71?P$p8k9AkK7)yh=+13(NJ)7gcq7F$bge(1|^D_#b2;f^BYZb{skW
z>6(j9zZ#K*hp{%*tIjyccL4|Yz>Kj-G)5umLv+YldSzy|Tf%qH-%gVKV%2$vd1bBh
zk6f>OgtYR>by6q)IB-K2oGqK`=$oynWU4qc7WjnK`Z1+@toBoI&4Xwxfu5cH0C@=;
z1hgJw3l&3=S2=MW<tqbN%)FR<RsH(29B+M{dcW3N0tpRsz9CJ_tM2l*_KNqoq{hC6
zc@&qaCrzrQP7puEUg2Sy++Tc%=3#?+_s1VsI=YxJIRS1L+&sy{Q*%poa=f~l&I~(9
zI(T1>sZDqDE(S7tp7@tW^MX{lmVer7+Koi9Dyb|3=27O=K?)=wolotFBd-p-(OPWo
zj}$+SZRa40RTM_V@Veb#-go@v*hE&FT6UYhcfItjE`#}<KNahVM%cJpR2?#`XL<RC
zn#u+y52ypO1U^t17Od7JGMx$hs_bDt2{CDW)2Hwcv}+A7cO82je+>{=KN67|%PXJE
zXJ=lCd0~>dNA~9dGwlujU2=6-JUaM7)k(V~2e+dM=n~JgY&k>p*!ADwA1J*@dM;)S
zf@S}b>=d%zg{`LC?k(Yu!tr%S%9Gm1nmo%AzeAG>-oX-;kHvRkUZjk$N7r}W35+vZ
z5<0J%{hu*z+y(&j&OwTBRR{KJwKn25@EUDnCY_V}9(PKhJNN5#7e`<^uKG5ku_GRh
zaaJr<yI80CVOX2NRAvcX&GC0lJb|Oalx3z^(JCFIjFS2^pSm7pb_KYrtH-B~+7f4N
zr=|f1^ysI&SWkbM09!tijXR`e<Ulk^;hOIQB@e4B;cxKp{mYj_E#uA%uYk2Xk7QI)
zRNXoE_#kwEQbD!1B{|wIgpzvf9ZYG}64-SP(WOkQ(&OA?dE_5JXPok&LKVtg)zs+{
z%0Hmy?QKF5Kln<R6T<zWi#E!K&@O#@zh?%4fhl}=jVP2=yM4%B_AugT+8*&S^W7$F
zTEVUGMjj7x+Ye9Fa$Fmyk&PDv6cyIt-1LVC{N6HfoRPN!G|ia&RcwED6%MZ*pR6dX
zInWaRQ?3h9{vIq?U-++qCHpx7+nJwNKJ2o%4!)G_Py+tfjG3_TuZrRNccFcg{Q;IG
zMqk=PQjZFiV}<0Ag0pX%vRBq>!xi6ZuknN#<^onYR+{C$FfCg86!TvPGP6tfOt(x@
zvK5tq!qz_?v7jy!2zPYu#ol2qas*OI9jq7rid^i`Q>>jTn31USiXEMq{6Di@eClg$
zf}zdMI=W%8K=hiCem>Ca>m7r5GtLxZ+9=y|$8`~mlM+6Igi)@RV)u}X1*)$tJ(qkr
zH-+%k4q;og*+x3Z!rniigygJHB%r51t1}q`X3H*3%4XW`ned>-;g@H~+kG$9;=J%D
zu`s<h+v{9HX!Z{pL(m^61(TK9z&`WwXjvK;Q&rI08|jWOi!-FrhS7>2b>wj!ccVmM
zHI%g-U3Vo^Te2nvtFf?cbYn+vHN6lRKVz+Ii=scG4NU+`M~?_y@7o3LF3(7%O~Owg
zDA`$64-X!_XJktI%8=blg^sMbHK%3KsraW8ld>HxMOVMT_=vvQ*Fx$JwZuF*Cpngh
zHvx_CPeF>e?m5mR&%(&TnHqCb39)VF8g>x8#E5Cn{9}u^qn^^QXx+4QT9u`5n^!Nz
z%pN%wtDq^DLP_LhnXJ!!3em?#<R_Ov#IqZHuu+)y_0?{MC&ja`a4sY7OC;o%Kb`94
z1X}6fBtJs%>gj3P;YqLuwNpVc?mcP`6r60Z3eCHAel&g0cQ*e*t(8@X_<FG@>R2<!
zwBU&n20ueCbNdeNX8bisfeEVW_wy>zAoay13Rwz~r68G(Fon0$VE|I$KC1_~690@D
z!qORIEqALh33oxhaj)@>I9ib8wIIGOQpeeqPhOpErVJ@*7swLRo{p*l9W3NqF$`c4
zNMql72%%ai$$#HCd$c_>%>g@xFf>HPj{b^|mtf}EgXc)hIAzRKYMLS@zz1Yw>WA{|
z2yw$o^VFD9Z4c@RDrUWdDS81?L(aR>*ZQf7<+pH*Jyn6hTY`DP8e!3T=U4K+G~z0{
zgxWm9x(&327wk|dC0b5(N7Vq^MQL|qZ2rC<RZ|Z3M2=J!l5>>v=o)qVhM$RZNsNLc
zSv2-5C;w1y4UVAe8tl}WRz}k*{be`kz4+<k=1S@ws>@bd-NiWRvjf0I|E&#_ylSiX
z+?eT2#v)^N202h5Ct%q&w}K}BOEbPqD!HyaGurA<<s@Aadr>!nmMto3me6j9-v%`#
z)hz|{S5Z>?rnN#<5D0P~8$8vq@?AE!IDziKg~V_B!;4&=6L?Xj>b&AtiBt}D{n)jM
ze1FNnE9(?1tp&-(#BD%ksEGdkyS~2BMa1Yf57@Z${U^Ka)dGk`Oi`3m?ayMR27x}$
zg%EJeMpMGkz5o<23ZIy^?=>u*PcZ)B(dTT9Z5emtp-yME5Un|Wr=KU>%am}6W)num
z8$$kcppwg)@t%fAfx8eL5(U3Ysl>JeSt8Ac%LONXm{k2zU10^rKm(NKbXbD3cR@Gd
z4T<QT(XxE$2RHC4Fl0C$-1u&H>uK)Fh3SpI?O%xx$3sGcnN{<}QFO*v)f+M$==IW}
zN69TNEF&fMF0t?shF5mZ3XH^rDKS0xTruw*Nqo!YWyLiyLw{V7Ae2S9={h1+txkbM
zYhY1<_bYQOaH#;4Fwcq@IL^348H*v6l)k2v{wjXX63-NA_xeo64(af<f0D4(7@?;=
zei%L(n2=~J>zsAmX+*ceA!~r8u13esckrCfyEO%rjhOqXrEYi+q?hlBwM!l<$v$_{
zxc_XhAg@^KNr%u9ux%tBE4y~i2{?kvsmtM_GCq||M|KB>;Gm5?ihj5uRh0%L72_Bx
zpDb1(c8ZbyZc?50Y=#otz`(t%Q_`i>r=cgf4egO`cxAPJ*OjLIn3A5+Ue$y_#qJjI
zw6^{$&75<Si>8t^22-~F1g*dk@e{@-LhO_FfwbwzjmeUn8v05Vtp#+N>*bop+hlr)
zOj-mV9sd-7{(Fz`MK7la%q2{7=+%71L;#1<TVX&=!%QBkmI13`=yw`gIf)8qthzTX
zro!V2)}H)!EzMN_LONB;{{eSEh`*?A78{ZP_>yxK*MZ?sGntY)5lHS?(wPiWpWjU?
z+~<DP>WkuK&E6(8#YYOP1EP9JGE$QtWIrB+nV8GGAj%qLFn<)~Q}#TjW~v>@>h|d(
zXxF0lhz+1te*I+?)2o;_Eho08C@Zh^TkQ9C<WPrx_72=Y0l@wi$V^d(Jc{<3a9<ZF
z^f8cao8RO`C)kL51*?rb{PPyRH?&Z?uyJmbJ!oh5dp>}sah~+s2pw&BRMoyft?q4*
zzz)xf>?A9}dw=Xv|D7TA(M<|Cy#mve+wY>&`wLzg6R)*G2rJk?11AweS!%v7Cnb@f
z)sTs&pIi2O=GIbQ&Dsm1Jm5XQWy^paQ<&Fn!V=})pXyk%ulgG9CdTt5pp)MAsv{n)
z1Ut77S%`_ElP;LVlgD~L4SkKqigohJqBkBw=sCzeO@H=II_o5uPU(=n<}oE-kGRY=
zNGAM=e>5R3CDiNKZugDxa_!6b@fSoRJW+&w+R}m2Cf|W%=~*zXNPQ_uEXRf7!fois
z7+^*^Rx#>m=&M^hhtI{u%lnRez&q`e(!#hvP;9~e*Nx^%jx7c;mMyG1&rv-Df1}N!
zrwN9#0)O^;um+-^RMtMxS4`xl&^{cPRC;qLchq4TCdbq6tP}9(mvjy%w1k&^^fB#%
zV%5_6rvCSV!eMs;ta*-IB@mHt2|9da1x+JFg0Hi)$x(TH?Bvpn?zAVYr<a7m8=ka}
zEH}9xcw01}ip9pbRuWcv>+@C@k{$|##o_i+G=IRD%rie+^9+-R?}jx(-6t)|x#{lx
zj-!w8^QR9F>AZ?OU+n}hK?d0EXGs{rTq%D3`=WWc*^C*XDjI95$R+b`!RpMtK3k`3
za2uL|-8mg6FdY5k%b-VoTGBiLTGoS_8lB8I7a+OW!LmkgYJ$>rp?#S2L+CH<S*)<N
zgnvru1w4`f!Yj-xoBJ<U?@1_6XeW%EY3Pm3ok>yQ+$Zp+7axCyX+GbGvBFce<EjF;
z4qc$S@sEFE5$1w)i7<)w<o2HjRP6k=PnAC78<S|=s`@<QUTT>QVYhjA$1)IN<ye$g
zl@%xjT6sx>v6AY~EUPL*#-sXDAhH^Nkbjo_EEkWs?frS_(Zt;Fp`b$`%=+el>L=kv
zb5BDewnOWrU&QK?aAgMCjO~uPM%5ut{sL{BM{D*>xZdOp8NiRE!8-sgA$}GSQJtUR
z=HLoCdh-Mv)GiWAcjWw}$ASo5ZEuD;bfL!bSVV%dM?pJ>>Ddc$n{^63C74|baev2i
z;%Z2ZeXlATdiKI6msnDKi8Il&<30#cyjGbkMDv_LPB9Mi(yt3ac}E`4ClO!i@LIn|
z>B<|OXvE%Uky3nuo30w~_Ek0BaP*7fjiEs-wAxvJ@mw2e?e)9$&^*c98hVmLr=m!I
z&E#I%nO>rEtQ&gTe6W!-azPr0aeo^cqCy<r-Qtj>3%UfZ^GX31b@PZH301#hmRO}`
zo2_1)er_2*c_$ULPjM;egT<pw!UPOS8rPGra?*w;OlY#R5+cmHYJeJX!ufsYi^UCb
zj~Y^Nuw?V7j|qrhu$o(~kRy;Gc^Fpi_0D_Xy_?%!e9Y^z;Sh$MES__@T7OY5)Ne-)
zgweF7@tXFJ%Eibwe09q=`A51!7W%rW*B&|i(m|xc-;KYt8_rc>1hPpZuB(20F`tEK
zQ=o9?F+RxLMyENcinYR3#m6z@TN9KA<_2TS{jgd(Rm9Thrsqw`?IbH}t!6BjhNIi;
zP|s!%LvrAz-(8ker{=n#zJC)Q87|cV%74gOmc)`-rJd8|(s>Q@#l=I>$LbIIxcL3)
z)mG)KXwGFfv$G<AcnU9C1|zeNO9je-XYGF90~)sCu)KJ2R-Bk#YvwgiBiDYMquskv
zerrW%I?dgLtsml=R@^qMC6<st{Yn4V)HGs7on9c%r_Tt!K&}tPv43snUw#Yd+S*(G
z_;!nMvP@)fs9s6~eI^wV9ZGs~$aVhHRi)+ZC!@4c5^|J0x*_$FAcdX&gK8JS`6R}B
z1`S}Ld?=5XE8(`-D3*NyM>!8OaM&M5R>EG_y=H)q{9Nj2=yOsAzDN@QYThS>@1TmW
zyqzcNM#pnoUKuOqMStd2m+a8LhOd+D$V~(l&LW*WHc~@jZPVx5Mt*Z{PEV?;cySj`
zaaQ5>Pa%(kij!pCLH??*F#(%TUwX2w8$L{tSYI1xcJZNbM|sM#{K5_FCUS%=yA&oW
zYb))vWl+U@6?u4BlIzA$GAnter+3zGW5zBE?^-SDKDv!1i+`f3h%t;!BcG$-noq~i
z^US*Uj-jc?rh_=0a{k3)D|u_51j*6TO5DdIgAO5l_5B&2{-z>~T|$^%Q8_ruP-pc^
ztfsNVCkr2_>va%}33aq7k`d8&xt8h0CJJbC4ZpzE`a)~%rsK(OmNhQ32e(%gXacAw
zMf4-ptKSeC-G35zx`8OHRm(L=^{N=q>0V{f*d^yn(cf$_%jti7C6Jo^b<t~YFc)T>
z5r6^XRw8~WGnz%F=_Q5o+Y#qye7eV4D%Tv*6sL8moEvvO^SEvys`g<z(Xp9e)Y-ag
zNWv`M#c;qDO9rx=LioDJ=Qh!R{SXn2E>UAIYFL2*(tj0P<gu6Hkpa%s<9?Q7V+odz
z-9kCxc9vUAr>NPqq~N4q{LcAMfES!w>|3Iu`M#ONgJI31dsbcB%EyQ91Y#yO^h)Z%
z&oz5DU(+tgElA~I!<9SyKtEixbJa|@>B2v$reepGR(xCM6U368&VS`>dMr)%d%<;V
zSM%>7QGXl|_}+3WB#`Zn8ezt(lkiR4U1wa`j&+N57nn6#{p<?u0aM|l^E)2MiQh)^
zT9Z8!4IER}YST~8iS%<MdHsEA)5R&3J-U%p&9w;Kk{GVG?;ON>u{rWaN~qFB9Awv`
zU9n(G$IPBh7!zmCi(LMYRQHx}+s`dUMuG=aU4QSg7G{o=(a9CSy#=G$K<ycyxAp;D
zwLfZ|Rsm99COv$Ua71OzT@@L_We1O#%I0$|L#xigsHA>4#@X{&pDQS-H>;pXL0s>6
zSU|XKl$qYHUjk=Q-%(1R>~pJ*rj2W;#dWS=@a!7wH+{RkKJq;15R*vo`B5L;X%i}0
z(tlY-1zQla?9D+VJk^k^Rzvox9+m%5-WPl0%IS>(p$;di&^BdwT9{3x{1}l~$SUsk
zyB+=7#bd-Ri(+meGHGvYG-`#*bcNlv2fgH=X;s+MKFOD}P1*w+?53+JM)~QKnogp%
zntD+L&vXqn$QAQQ-TbIdK3I_)OKZ^W4}UKI96GU^5b}V=w8r?G0$Ll0X9EObs*dVo
zbBH#8GR|t@w-%}5jfw2#<i+8A4`=Da38+O5EQYxC4KF=0H8m9|Q6`H)tc$o3XH`DD
za)q0*$gc(r_?MlhWR6-_SUZ(<kNZTd#)j{6d{>4O9>06)OZd!25X$PhL*45#eShld
zu4K=pY?71Iq_K}5Qk$hcvd~PP3OTo1H7p5Qr0nNy_g6tT)w#6teYJb|hFh#wBh6my
z<iwc^|8b%a?eVuZmU^-7LOXv4;uP6<mS1qL00v&wSbv=ON&-hY3dO8xm~JrcXh<HF
zeTO~7fIRqo#-&TF>YTQd>tuDqV1MBBwarITn2U~0qrhU>MOL)tIUYrcL4AWGU<aDg
z(2Dzng0wpD3>Y|6qASa9#8-GJ!mIJ6U2(>|c^W&D_cXtd$y9IWok+v}N5o1;+HOnc
z;=#+PdWP?)elevRXKcIAb`G<?>}K9Q6AG5EvtzMjS{r&L4GZ+^k|Ez*JbyHJt8n8#
z-|;ifD}uDXm(PIgRzo{xRH5|JcLe*s<2;B>BEuE7JYpm9^9(49nokaELyKTtp%D#9
zJt2)8yil7v_OMJIx48Of?`{-sa=|(92NS*&9K1r-F(H@H{>E#vjPMUr+LZem){6XV
zfDYPy5dHgXqA0BRl>6R$Z-1zQPY9;`NL-lV+!-}T2EitE`))>t+sw_}yJ0O_=zUn)
z=uBqhGV54fv+p}07<PUa^}*-29zQ;@i-~cbdp8VQRD{O1+o~%eD?kOWW#XL(Y)l`e
zvNYutj44V=UVRmbSjJ0X-zLq#oQsmc7)MJ*YSWLJLs@r6Z*4O^T7Sspb84+D`CT26
zW%OgdRn^d}Z(A<8#V3&Bm2cs9Hd2qc8e=k?(#IUvm!WF(VF@!wlAvzaF5cjJUB8fW
z{P5iPB=VV?SXVhlel8(*vK^ZDm)Awfr(ppX<k5T8Vo7Gkiv|W2v4{`9zmJ{VE{7U@
zvLTziA^uT_=rg5kXMbu-usIG=BCB$Vd}0V;z)qcjAPD9ZBZS&#v?$QT7o>9gn0(P6
z+Iruw2px3J(lXNhbvw-;Zj!Yz$Ug+utpiEJ(Fc|l&N6ELqx-K5@`p`K;?F1tTsi6n
zr0i-6*d`V%lSqa!CrKzS_^qLVl*U&0@%3vTNUwz#x{ae*2!BoJEv$ro0kzd`;ukLL
zK-Ge)%Sp6tr5ZY<&{jdm@10t(I?cLAu&Nlzl1?5vJXluaHIA+(a&I6VRrern2Ar*G
z?p_GsT4;C0Trr&NxD8Em!?@>a9)`JLqELf1gAL%A%pyG(1ZP<|IqN?{S6?NBPl=Az
z^Ft2pgaqlXq<>t6p(Y<Luw~fyNDAjU70>*9lAia7>i4}<Ac0%aW;lA99>qgmi`HSm
zjj5PjgwRXnH6G4D=%vwS|7G#&l!%;v{6Newy@M}<UuUIwN82yVjFDZFUcR|zlTD7S
z18a7ec+UnPj*uD;;VoE*cu*>Er;{ioz=+n6F4-f8z<<9rPPmelamHHRfU8Zi9uXqB
z7nEZo-f%`Em#*Xy6n=6&5=wl&EN1h!yR#&&d2f~x4xv5rRW|KvG1Z~V5qB2NMO@oA
zJwd^GCvP6#*E@woaA~)qG4aNu@NSA6h*vN}V`xCh0vCy0gAOcc{t_D+2SAq^ajJw-
z89hayq<<PX>)SMreK^)Idc=@PW2%J=CsQxvuBJ{;XN91{<@MQ$xfPrSTeK!of&)Y;
z9SYR@f34%R$l>`GTR5`N;7o6#*N#y3cP}U@t?Lx(EiTKzl&i7Dfxf6N#v_JG7vg2~
zMsSc9Gb&N_*Yxfq6!}MEIW+_n;bvA#9CKFx8h;!6CNczoF+d%kn)38MH!=d+xE(xn
z*Vl?jWpSaK3KLP<XDA_l=2P%mL~$xl)%`VxpIumQ#n=nh(F%H9&O{E*&oY9EUpdlE
z%#nGfI^{D;QIUsKHcRes3OOf3J2Nb;=GEhbR$rq%wPuCy8EySU^`Q<}Hi8cOd>mfC
zCV!F2K5BtBQoe6Au)pyWL0G(&HekITA#sUMos3h+f=1c<<Uup_3t3B}UN!I+OJwA%
zmT=~Z{d+wqD#Yg6>MMefFr2~KkOr1Q9Mx;#G1tu~E`mn(TB_vytlaG;=M~1=1oi`u
zT0J$w^;}ch+2m^KG-Q{0%-_*zN>Jm&yMJBp3V3}D*)D#7P-RCs8&aYbHDESR;nDRE
zsOpj;YbzhA;p6iU%dKokdV{ghgS-!F29cl!=hxuUomi$gqy1_53$Av%tGHVurds)m
zvay5<hz2@3aEsQjmB*#A@8~oruNx%P;!LfZZ;(o8iEJ1mK4j*9k{&V2TN}4}K7UV*
z`~H5H1H3a;PYLA2ZdN-~<`=8~3e#ODm;I2zf?1#K4apyr%Euh}3^xNkd4`%5`O5;;
zI0HX_3(*MoG|@0e59?0!_k8O!4X+>X%Qy{(Tt#OORzvpuEB!D^WEKvBkCfWtttf7-
z!H(?&l_-fbE7@q;!rIh*%7u24F@MVdR;eoANUh5EV$6`lT9y3IjZ`T~FE?f4_gIH0
zaIY4&!Rf0?&xRsSB}i={k+AYsObNX9jZS@ALDJbg%7Dz>CNrX=yhwa97qKFH?{hQm
z3N2g`eoxsASboh*+g(x!s3mZ#yg-paE}i?9^}wPbS^N?KZnS?C^7&;QbAOSa-=JgV
za359;4yLd-kK$l5@mQR2d+y|CnU~?iSPR;~Ks`x=V5SSXT8qYZHRGds8o}S0<EjfW
z%lE~qhY=bm?^W+eBM1$GU6sG0O?1}ZZbIU^EFN{qR*!MHS*kQ7NtpRj4X-i{(S|?u
z%Qd70j7ce5OWWLR8bWp~+keY1e7_@zYRfHtm;5`Q%H2gJPy0jf&1~<F-9vU8L}H0g
zGs&hARILhBxK~;G!;z&O{?Fn(rA49@?4U5kv*K@%<bbJd^nG~58zT_0u1ZSl$U$oX
z5#DUr1S2$GxwISsWr?Ce_s{7Bug)8M+*`B_s&XBY&z*4lahbR2y?=JgPPi-Ko$X2c
z_X#&K&B^Mhneo_6GWJ3j9zSJ)jVfJay}T2~rdN`1pEH}=KfoA)LVaGQmFQX-(VKF)
zJJJXipogp12svWv{S&3<$>ob831t$CVqejOj}gzrrgnPt1BL}>PJm(CRD4K#6eoq@
ztBrzJTe_#hkU=sT27hw}zFo+0ZO9EI=pjDo3JGI|ijqV3$%dOVbiILgVq-M1jzd%z
zG~f(@_?M#!Vid^^0#f^RA!oHO0%^UUywksKz`Vo0)An1MqZ`A9F^6SE|J=MY8ex~P
z>~7SJ`EJPItap`r;TDtQy-6(L0=sQa&XL%RM5dG}AAe8K8Gp#!uDS}-R+g(8KbnOl
zIY@f0IW=+-`#osB6Q`oaNmHMDw#3NMjV;y%{gUA~;*1yW9afL+AkHdfZP9l4%_jG%
z^vKJ{04HP2Z7%Yw!Czl)m#!eZ4lNeAyIM&djkF?@ZmU4+m3Q{LX5x3|-NsWNchxIE
zl0H<L(2!d=YJaRm#quA13o`7M;|Hy|_4vDiF^kB8<)e-ou%9*3w$uC|gikT{U-qER
zHJ0;j{LYf$c@`EDF)ZUr-B;Ux@RN30P*<JQQHhQpg+Q&|ab@m_UT{QfuL!Wv_8CKj
zX98-=yyZoY>ALA!10eLm;Bt_?NY~Q{d2#RY`U~N?hkv@t2#{I<gU!z#I?rF`Oeg|+
z=mfF%>dyuSU>sLM6}W`==09*Lv+;w2Mfj^eNnQ`8k2GwbJ5{{<OotceELR?sS~R_{
z3>m<Na^^}O9*1QL(bIU5&&rpKF6@t4#h!8biKq+3zbi+R10-Sw!e8Xm)CGTsm_)67
zah5v<Hh*F8%6_$XZKJ2lxpXf={+4cwge`X&mt_}=aZN;BbR#4pLPQ(2pdXE9M$WWk
zB(;eefxQmRY_KmQ7(FL4a#@&tC;0XI95P3blFB#T<+)`nISXw&yHJY8N7q7>lAo&V
z)KSeCE1~R4mP;9rx;1T%CqaQQ&Kebv2eY_Evwt7`jqs;>7{AdK^9n@($nR<VM>M*J
z&ii?b<;4%l3}%>q5eO*Zc=nm6l?#hDdl70<C4b3H#9b&8bt`0AnVWt5&4ChPB*Ysl
zSU32Um3jnaCu)jOahU0yX%H#PhTnQ4^Xv%0QCfrF9TFT5+WA625|n`#uA+aL)zMD+
zVt);~t+hoyAG&2vh=)BPU0m;%zHHRau!LaGu~vaDSQnQ#Ewtr;SjNCF{2==CpjwQW
zCyo#%_o}>kgZmp9DsF#1UM?07sKRdfc<!w)1_{qDSgc+6{Y`U5hYH6#hY`>DmPo~<
zKYd?k+Uj`V9$U$mC1IGHpr!8wCSQvq>3^@L8ox2Jq*RdFM=&l$(^%itIA)Mn&apK0
zY@iFn;){?j1ekF0Bnk$xvS159FC*avmjicS>Ufpz$|kb2MDZlMaJD)UM-F3%U;?@p
zQ=`-Je}9X_$=%Xph+;<TZEKfczBnFrk<U<u)jZ2;a+6aEKTy;~(cXf9_HxnYzkl%(
zMLbH*mvp#4NO_1C4IX@qb4RXjnCe|V_e`DaDRyOobR&kQT2^l_=Km#fW00r+u1?A$
z<}-bQz^_}mBin@3Nmg=VzUTHB4ED@CgA@9##e$gzX3G=CMVsond7V7ZNijl{<x6JP
zFnZ<_13kMWQgMlEf_vY{wRi!OCx2PNzz<W{a|@o)EgqG-T|cZpbJevHe66IwVE7dl
zT0Mk<AO&_KT8;4}z7X8`lp*ZM7wi+M7JBAUJAKQv{Q{CQG=Rf|P2iDyn$LLE9%HhE
z9GKbu>IubqcAm5(&7hdEoSn|XOW1{)%r^h~F0)T~ca>D~r`(BhC=|JVRDZ#G?jB?J
zgCQA)Lj~*1NX3j4t61l1P!&yYq3u;PW!EBtIrSjdSMs>RJQMXv_3Fjt51+G66jq^+
zeUg;mc@?>e6kaS6J>jyjcjxQ`FFYuzdNJ`vpgy}#zv!->A+nF2wK2Lie*%V(hnLp%
zND|DVp*(-D6DZN;;4twY8GrpT)Ge-bppiyAYvZ^X;z+o`HeXgNWnX%2uhm~ZX**8`
zGsZJ(k{J<j!vXW@q!aGhv+b}(e@ZWKF=IvnhxM{DIW8U->vk=H)1Tb|Q|px-LUR_t
zzVJ$tcz)~LJSTChO3Z`|EqujT;m$Yc7SQL6F#%_QIiM_g%vs}NeShb8DW-)g#v{)d
zxs6orQ-yU3Uo#JP8||aleGOtHwRenBo+Q9{2b-KxJyY>b-S`g4!Agwz7(#7wxch|P
zU#F`9=~B)y%eL`f|5{)juFF;VCc{9N%>*qABYJ>w%Iu1{OyZzrXDy1tX_?N*=&bZ<
zf9K>8(gQ+c{Nr3+hkw9spHAEOs>fLuP7!OiHf3|YM=M{RitD;AJ$T4hDG==_TmND#
zqCd$^e-At9I$qp59lJcj5g0&BJ+B>${0jjpl)APlbj0KyRX{~;V>17pEejXPw1pSF
z%UPU&RGZL86G5XCr-^v_NJR_Q4SE{E;dJoVu!pZ~KFY%j+kbtMzfy;EgfLMViFw3e
zm760i)Ez3jPom?qrlWi6soOZFhJy3867>!UEW)&fN}4&fGWW~&5k?ZvA@K#U&&QBO
zw6O59my?#nj}8>S%MAMuS!oTc*neFmsddOjvwS!*nu74ad9c5=p->t2Ts}9?#{B`F
zHmtRAhoADhYJd17kji$vU>INWv<K$+MJCwBg-ZxDTmbqUpPheNt<92=cRG<GIamC#
z6siSV{VlBk8jV5tSGfxmQ`oNJ2XCZ%Zd=@5n6Q`@20CrtU-V&jSUQhx)oQtF4P|~p
z=(!lkP;r(6g4_`<C(p|$h1>Pyq<~v~kJzw7xgCusqkq?;K{@nrqAQ520n*z|i~PVn
z-7IH9K)%HoJB#Ph$>-F9k)jB=Xh>?l2NQ~T)@{v1{Sd3<;ULa;dxjp#VUin&ZY`$%
z*;0VDxTJlJw6O&)u=nEHbgQ<4b1rJVBJX>^T^tXeHf?h%3hPEi?a=JVK^!9&41|eO
z+Q3g)FMj|~`C)a~6NPUFE6<8(gFHlf{p7dZ#S)QAU|FAR{rf~ZspoBt<q!Nx;Osbs
zE=;E2#L+Xk4kvFk4#PV2DXQk8Jd=CRuN5+9=ggK+YOZ2K+gU+0FAPA2;jxVp&&N&D
zDfGw^y?*a#j8`Eaq>#rLbXhO=c51qflzEm8OMmgaxiS4CO5t-F$+M=XsAZM#B}8E4
z3$e{_n3bf}PO`#bK85=TLy<5=cG8?nROY9c)8LyT^Y-ny{5y`&4-LTfD2qWv=>Qn*
zI7Z<)C2*@_(-gdss5>!B+_wVNlJ$rWv8A8kqP{$$i$RMX<Ym7G?q*yf<g|r;h21pX
zC4Z?MYeq+7Gw@sUyAcY~jZOl8aXu0I@!K;__H3+6$l_^SW<@Cs!u-^IB9Z~pRVz+d
zhXPsK#3^M!@BzOuEL@#KOFm7{VyO}-5#_$r4A@r0LS2ODm|?s>{5+T^l#JD~E#OD!
zuU1GHi$#&SnDCucB|Gs})DILzd%;7P(SL}RBSC81BXorMX&0lgAozoo2lj`Y&^afI
z_KC1}g?9+ZY9O^TY=v}x-h3M|+Z<Z-rapN=n+=B%N7!si!Vqxv{@{Z*vCm$$f@f$1
zNFf>HWNLlbC#LI^Zu8x827%L}knQVMSii;QWq8%Qb$7XbX+`ywbUSai6hU4{B!BtH
z*!mwvKH)!Tqn)AhWtEga!|snF4A>@!q^Ewl)>&)rm-FdLL(aBEDsj()0*(I8s1^GW
zr^u%x+8tE=QE)WHRH4T%0Ld1LMhI=OC_kz`BZq+-=B4%c%ERY!v|T6`9<N|GRO|EL
zoLkz1gg$;pKGV#&;g0Y9<6+7Y%zvXhZAv`Z@DARObRw-HS`WrNAMxj}_$Ff*kB|FM
zFK`SCLpA|s9l#(#mAQoDhpu0{c1Z}R3}xyB(qo<*)ctc(V)->wxsue67cQ6nmLvw3
zA^k6OJ@|)5`X$HGDY0a2x0B+yLg>0PP7_M>Xdxz8_{YV_jJAQHRkjD`$$y99pHKTO
zRXzMek6<*ocVvxMo)ZAM!q|htE67alQ0H;%1=i5t3i?PYP`4E{Ze1^qSyNt0jO5hX
ze!;|2pM(3o!Tqa0-^Z&dNcbe|AT7sd!8x6_rwn%$C)Ls>OSNDvlnchU>B9WN8!5=T
zx`jtI-adm4abjcCK55aghkr!!&s<#vR)m2R^SbwK-?8IXRI67X5&CjL3@ZdKw4;Xa
z$|C(37$Kr)Zzb3G!scvweP4lCu{<SPam_h`#BZ!02TCXE2gCT^bQJ%nM>ezKm6|$P
zKcd7MRS>a_BiReo{7BOi%D2I{`uU!Ut+h&9`#4^I%fPH0;!_30dw)yAAaR+i084Cr
z>5tZwKv2BwJAwV$kqb3Nt&>BqFyv<Kr<F<=Oh8#r7^8`BXcaMj!})RjsuXEtRJ?Hc
z`;p&D?OL?yD94Tg&KYET4q9M|gxpoHDcsymi%6EcG}z=Oq=jJH)VnE`-&wOM6OjE?
zN0<&JN++CM^%D)aSAR02wO6=!d}2Sm(tt7yGlGTZ8@san99nDzd__kM<_RPczM?mf
z>>ZKT#k-78DgC|UIw!)V4twHLY_dW6g80D&;N2d{ZFJZD1f%crVisk_Mn))`%_JWV
zW+hMYqsGghh%M`i8@YNYqi^&CXHrd5*Oc+rEb141IQcdqkAKJGOy^<oKJ~C?#B=*T
z7%ca%&FMuCz0gDm3nQ-$N7o~<CS=9Ai)~xwvR4mVIy3fjRI4L601*U$RKE=Dt`5-l
zIoCJk+SF7(sKiQJ{-ivr3Jyb*dv@2#d|%SJ5h!R*G#z+2QlX33Z7$IrW8x}bX0}U{
ziUh_=>eY8yd4J^ztLgc4mun=eaEZO3FC`T)B)`p?_N2?}e?#>#oi9)+<Hem!*67m`
zhuA<Sf!#bZ-l+Ut1&0;>c&t@uIc#F2Dlfv8(R^>u2n_y)Ay=!%((p>QF8~)+1&Qv;
z5g!5u3Z}q^pF3?>8U?3iVDd2HTITB2ccO3=tlL?QwSQ5I9sxNrk!^2#TKdX2Xf*M3
z-yN<2pJVUn?8mf5b5kltJ~CN^Q<w)wucA7M1hXj1ZK|0sjCBBi?WGs%eG41NIOJ_6
z?Mx^OiBdku$-h7G+o{Ego!CR*3*+I|18dW`p<iH`+{0D^W-Ki#PpG1d6t-z*p6MVi
zQQ~LSY=0Cla#+@Pbdy}1dXhq1*!XUvO`p}FpH1KlXwD9~xOSZgbT44kibC`0!+ZmQ
zlR?cWw&L&G7WegkNTQG2wK2VkV0!epapFN6s}pGjb?Q3w4oAJhSN%G}AW=K2&c&Ei
zKDxz|1ydIJz3$)(4TFq%diLGOKuUgVy|TBS!G8kRkfSl3|B9ILXF|g)zw?WasXFxt
z^ggghy57H%IW%IJn>Muv1Bqg3ALYc;_-iYA^a?E0(fKyvb37u?3*MJ<kLRP!>dvCT
zD9`Jp-9irMLBdv5Ln|nM_h+ETZsK=Bzp~UwaVLh1(qUy^tWCL_tPBl8*H&AP6Za(+
z_J2_g4jkB~NK89`<`vJ*&{zpG^THAM0Bth;p6auoD`bZ`z3+#p>i45Pv&XGT1bj<e
zw9!9K5B92)bV^XAhTXmy*fTdx;_VA}!n#jr=RN89;v<z&W>n@Ogwjz4JrbyIv3s?f
zEM5e`TatJn%m=jiEM-vyCrVTK3fBqnu78*Ni!9FJ9A~7+oY9#tRrfVS*nzS#$rW$q
zlA71O`bg3vB%JY2(CzMDb?M>1`qeWp&p;(f&vxvLmrtYHu(t-GcvbuOWVWhXsEQeG
zz+C%^xX@i357VF3S5V6h8QyU-yk|n;kO@a43o>W4@`Ln*E*gm7(}9={iCeD;{ePAF
z@z*FLd<y(WXBv1Tje~<ZER>Ov`@l_!%7-|VY&h}(MHmj8cN8Ve2J9KnYFev>czz#{
z!Gxtn1SA`lh`4>$4SPNfC#hd_1T{C72;ad2_SIhDpu^oM!im>%m+1gCyr<FRuF7$J
z+}x>+i9dsZJZ-KClWIFDq0ZXZpMQj5W!efI?)6ftkO#f%#LKq!I7ohDtrmOK?jrX$
zi&t%3_oCp&Rh{pzP_$2dRT9&nO!$~W!if)~TmT{_{T)wGH&3^39qg0g=tmv_LBnXi
zv9q0J5@tD=Rq(YL;T?i_(+Y-$0Y%zND|I|OxQ<ui6todSXt!MT1uxOYIDgfJqVdBd
zWTTBY`iRa=E*I`A^`b9q(9%f@<T;LxIvP>iE+lSTxVpP*?D_Mx@W}OAZd5;vB15Du
zF`I(Xw6;EcSxaH&QbcG&))5!nd<HJ2*l=Qbb<J=9PSVMF&&>eZ#1|N|V&n~rRTMNC
zbpbTj;P+UO<YZ<+e8H0$6@RJdVQcy|;|Ig>OYNoN47p!T$V1XSW2FKEs>Q{&g=={y
z#S63tug~y;riti~bvv(5OH(Eiu@Y=}wgqs@s+MbV=TS3%fXEwT9qffg>99h2Qc83&
z7@QXG*)vx_Ls%GLXbB3XnU_c792YtrOOYw?rx2}mW)Cz0g}Hk#%zw0`F=MlEyX(y%
z`&%Jt8Y@4ksLtD!lf!FJ0{{`wTo34o-6ad-`-u9m|N4=M;Y9&=bbM#_0d*I)j0wIR
zdf&QT>qFW(STe&yJ9}9U!!|0Vp?k=3j*N3u-2UKkbVk|`0%d(J@Zj<$W{AAH70b>N
zv)P{Pdy9)p`$sNGEPs(zQw}qF$SN~XB9z)Cy?pQ|CxLv{6E!rwEJR&iXYTHyIejz)
ztLpjDIPjHCB=mujFH(2@?S&|vrT(W+*Eq5cq7B$b!=+xIJ@~vx&a(xUl)hc9@rHPD
zAgBt?k|RFbttHLMa=eZwt;6HvGnsiAI~Q{)4rCb+=}B7bq<`$lxH2koD#@&^sMB7P
z#aAmin${-4Gd=+uP%7`Gd)udrW_~{@G}f#wI5|+LIeU_Xq}|0sd*BLiX|?qa;j|E@
zstyG{E}AXo1k@Mz!3_!4tn=>|y&sXy%eg#~Lj6XWb^jxccZ}u|`W#{#_WH|$NW%Jw
za3LdPPTYIVxPRUX+APeETQ;f7+s;2UiD-H`d_LM-`nB7j3RoEDurnbgz^H|lz?F^W
znHjKR@*|~f_Ve~3j;)Vh^u8$T^K?GtI~d}8CYp<=A%xiwy>Q|-<(xPq%00^sn!G$2
z>_dlWfrln(pWN-FiDgb%^vJnFtHp@WRW=BJ=&GFVzJDjzIX>|*DvEN8f*UKL{0K+V
zjb43x+^&Vw;=3YHb8%ypIq_^kzU0G>&r(iUbZ?G%G$E^eYk%_T0ua+WJgJVe`vMDx
zqB$b9*-bJb-PGaQu(js(*m?`4SJ`a(v|VwrM7&B<*(`#xw%=X)ta@VlyPfrQ%MA^F
z*@(uNF@Ji`6#x6rR}^butVF(W{Jqh`gswT!Ur4_w6dV*RqR~Y2X5u^nZpKbKA%3?E
zzT9C>jJ9qkbwjGx>*?|QdogLuuS_OLby&p9f-M9Ih4jp264So+nw>$_<KFNt6QKMH
zZ*hdswEqWqdL_OJWo~41baG{3Z3<;>WN%_>3Ij7UGnN$v6cI5uHwrIIWo~D5Xfhx)
zH#stwq5cFE1U4};FqZ+>0V#iVcRbbY|G$xuke%Hd$vimrs6_Tk_RitFadMn<oMDg1
z3K^AM6f#RfCD|gSBAckJP@-WI-}ljd-;Kxb^XKp3ah!8KU+a0j)+H)rZVA&uV%<PJ
zEQSb!%gCt%CZ?tcqL*c$j~f<EfXl%wKu;1Hfd}9+@^W$vqN1npAcB90!eVp~L{J@o
zD-*o{OAto{ecV7i0I8@khywZ`2E;>hB;XbZn1V!vRUi(81LBCigE^K!gt;LIkQl^x
zqA;KYWO53N3&f*5y@+HV3NRSi6WLl@1~5Xndt?0x-Y5WpK>|iHrZRvT)*k{<fH)Qd
zxPe{>v<HCo0IWbez}kOO*TNFew>WKWZYd!HIkqI>a9I35Tuxb9S?fy!I$CB{x&UY+
z4d`22T9N--ff$Itr!-(@1<A>AAVspdsjiilmA$zxT$X$X01o(pcmj$X_AhQnA!fiY
zYLKZ19_zCg01)>g5^?IXvi|=5GM*#?Q3i|ml)<6*_*r?O2!MY-7Vix}-*^xW?j?qV
zK|<*ydVxP3kjn#@pxi+W0VEsgVSfsJpj1Le5KjD$7?cPi*(ds^IzRxyKf-t+2z$0B
z=H@1V4+4cDf*1tG9a1DBh$I5wx`#m@5GnSPAPAfy;ql}crvHlY|AqONx;7TNnG-rV
z6yg7O#Sj=0A?Sa%-28cMcPxg0A`l5bJ%WG-3JsFk6Ua3~VfHXnEi*$sT}vyN3DkQS
zm?;*@4n~F;K-|+N`_s}fQ3sUO6ahH&A@`{+26+nW;{&lKFp$%ygM#uz#Nq>G|5t~5
zW3c|1;QuN1Kw*#`<T@ZpI9Y29%9jKh>ilB_K@7hzPmq5I$N``)00y{w$&!Qb^$r<^
zlVK<+p}{yT4)8#r31BG71BAX9f(Zye5Fp}7U}*5~f<I3Ta1{WFawkG<4~-7Po_9lx
z2NqEK2}4Z&75&o?;_@=kL`gtni^O8kfdCTpV30M#5~21G|Nk>}f5p-xq0wdtA5i>%
zWcF`$gb#lT9r*t;_)F0iBr_K`!{U7q=)Ytrf*vXWM4F?B?p{CB{1Z1MBA~g@!g!)V
z00vi-kyB8X|0%I1PaGO*ZD>8A$P11vSN=-|b*;NM1|$#wMY%l@2<7H4`cOg0<N;X|
z6MZcsTdDumPkY+B7<ViZh4BRBm6QPl9*+oQkb{4kL|#b=2!=!5j|2nux(JY!!C;Ay
z34kLJLjeygo`GCxWfeg76dBq(si*?7X8)bws&arV0*Aw613+IA0{u&%Mi$`lSpT1;
z{|}c}1Z3SHX1@Rh2*4xUp{?ZcyPncN@L%?dY7h<;8~laI%RvkwbMhSiQdEW%Ax<bi
z1R8%NZ=U}IDv)PS@&g0n|Kuz$rwquVFwhL5h=IT9LyVzqLHO%}DiCiU6ts1I*~1~v
zJ|r{|g+u?cmsf-XvKWLL8u6PV83H}`-Z%mpLGb!5p^#e~bZIP-yl^3k$lv%u{&9Ge
z&u^Deg_9vHWI-Ug5&lSu;!g?mE<sU#zovfzlo>n%n&dyO1Azn-G!_5U=Ff&RC-3CF
z1ta&X1OIuf_Rf|>Jk}euMIoW5`ZpD*EAglRM>%Laz#$y^`}ddg9|1&vEw<mRwY9MU
z!7zC>0H&r4bu1jN45+9mh5ljb{`1w?+e^@({Cg&^YyboUKzD|bL9Dw*)VYiYF{OWD
zx&=LDG@@!U3%9vW*cqkn8_Dje=i}D7F)0jc7Dm*b&pBF%H8D_k4oi!`6xoSJaiVwL
zKDv6Rdl`A=<P;*zG>nf~SF0<}M#efa$8`97S);JTyis1heX(M1PF-r9AYk3~@swJ9
z)5azFSG%m=(uJMM>c(!;_}}V>KjeSFquBz6S$G@xhI<+)iMtyd$%%+otr5vS*Zdf+
zE+bl8OB0LZCckl6y7z2y?<#j|g3@GZ`Q7f8{fwHGDHaw_cq{tOTfO$DyeztM&iufP
zYg}#?8|C}cIj&Aj!hX49Rx_zn7?qhHvvdvG&CN%2P4idP)+DoSq?`ogJC=XLo4r{>
zQ)0L*c`pQxP2diPa~s$rV0lp+%u~EefthTjsrn@^<p$Q*zbFj)ciR*Egah8rCX$4E
zMX4M5qcooOO5rt=w{k0ZmCp_og66zi%h#zNJ5}6oZDzVWbd|9^%lT?kDQ)aCe1Th8
zy^vtotGTcapYXDFj+eHq;vIj+1$@VS1ShlY_M5kO4z6Be6F4%j-6lGIVd~kTbEA$m
z5(>@<$i+)V<6>x;gS;yelc87K7O{<3#i=F2f%ng%eMDeXy9tfK*VL#LyeK`457Qc?
zkChdc$>imn8)sCMc`xd3Pt3oGy2QnELP*^tyY1V+vgHZl=hwDZ*S~-1VtdC1=+Xx^
zihsn&j@;KWMl)yn#($KiCFG6psP&2+0m3+peS)T_*;##qDj5cjAIk}HX2wno9nu!k
zANPg1VckwA+^W{sbF`EXx_o525eDXQ$BNv{WqtCV=`!v<({U@ElScH~{QLtn0gS^I
z`F1B?y?HkAVr9J8&_91SNI>m!$fJ*k!~}V_q<K^>3ML!Dc+3Z3QU<3_(!|-irQ7DA
zl+whG=)xlSh}j?b-9TT#FH|Pys$6yi<F?o1Z{X7sNvm8VzSDE8nF`B|rNjJBtFW*&
z?!E`b)C~dOx^T3vw7G9H64u581UoeM%hVi)ZFffn4ju^&+V_7swj|BsNT%8)l#p&H
zZEteo__|Pjn(Wex5tfn&X$KkpQ94+5Xvg=q^i0^yO%biMyI^?WljBy$+xX_CCUN=g
zLhuWIkIoYb`>~#>oz|Rov9ua|VsGdC1>SFcDK))Ecyg}&_?a(>0UDAsG_^%nlqSz+
z+G=ce7*SclG%kNQ)O#(SX5dgBH<))<Ovc)ndtkkH@qN*^wmfwr*(>F<_zZFFftQ_@
zN?~sY8Wk4j#9S6HL|&1Y5H!0tIpKk-;y<qZb-UEkLZR|;rY!09cliGGilDcKRz3G7
z&I9z-xhX%+^})9K=Q^|VZuv_MJ$Y5!ZWsC7GQXQ=oGyPak$N(7CYJSyJYUn%Wh>W|
z{S^5!@Y@4&n$$rLXmYjVsxsmQnz}y7H->h)Ow-C&=}!fVT^}$%cxOdw{6*DC8<qiT
z8O>bMnZlfLW4Wcanqvl}9-9Tg*(}OTKn;FHt7rKD=Tb*43%|bG$h_kzM&*X-ak_5%
zDRJgS5j}re5fia^d`v?>Z@XK?sAEe_afZW@NrZmlXv7ym#>ZieO__e(?J_gUvK9QP
zL-VZ>JVsHa3rio(Md0CaTgVH{uC6UP`kxNbb>>W{hdUn5KPjob<uLm`xHoJEwZ<2x
zRxq?G@p&jwjxch42X-N>?NBUzJ)hc4E9F`^c!qzUhYohFcyokQG{kRpY76KVPhipN
zh?ke}UA<A;x)~Sz<E)0X$o5CyX&O@nnU~rCYeD*@yyvZPq-vvDoii3L(y1jD=7Enw
z^NMyHLksiWBh+>S8ct{W9|6@db%%+DCb|=!eXA+EhhPQVo&9jPb1j41YfE^asoRh1
zRmOi!850dT6e+*^`8|FY`jxH+cbLVPXi@dFpT3rYsZhA@S@lM=R{IB>NlNeA2fX&R
zlC3OwC%FUpTRcV73pE0rnE02lLNj<b#f{yC&f=bdNc$OeV}LEg|LO6}j>&dIhBdwi
zdI!p}7B9!jlDs5hECm7fJZi*;hrppMDaC)&m8CKJehj^cRFXXFtiO4j$wG&E!P;Z6
zziRrM`tzl_ePI{PjOz=77GQ6^>e)*{r&mE<xy}1PohC7nUE@;<c8&e=muiCCOsLYQ
z&~;BJSLv^cj(lL(G7UV9;6olMXR%~)2o0VUr(E|1rMcp-u?JqDW8K%-Qgv-h_QQYH
zB#3qS;u<(Kp%T4VAwsvHMt9@-X?=FZ%g#&hQ+*Fbdri80e&(0Fb!JTvsCSM06bZi?
zk>oRJ2oO%S1<yY^x;S>3u3YjN!y3Gs`u(;YNlNp5Q<@H^!G`?@f#&3`lGLm-{V|Qr
z_r6gVUmTA1P!xME&qdO0zPb3Sw@H6rmp;R<?F2#ed_HlA;^Z>Ry$w387U|DLbX9zx
zsG2_JHpZ>=>R3d*KE~QNSXyl(=+7X0#6O59=>`|8%e}^<+QJ#!OvM*#=md_h?Kl>)
z&h+u?<lP&Jb(=mhB8Oyjun1^it%+aY&HsFBAgVV1tgl&g<1@9}=LWh|`saTK=?}PU
zDNH+lTKC7?Jo+#=BIwQ68IxN7T&;&`{NMZ74|9EFGH$4e?Hjw%mZSRV{LDe#=im9?
z%XuLMO48uNQP{5H>#eHXERRHXZ^N25XxJYOJiPTLpy7a2u&Tg<c2L`>bom5!ZmQ51
zpBu1y)OmNw{)P3rQjwvscd&o#)h>PdOeqX?Z;NlwwuRr5<P<6EtL-mfOH?x+$8)cs
zc4d~%+#KC5?T*LeI;_7nyj)(2iF_MQ@0M?ZjObZd$Z}(!^wH*teKo2YnIs(CUcVu+
zIY@ExxD$U?#>^>E)@~|cBL5Mm?skgph*w_*bDH13<B<4K8u2b{gVule#@!8Pjkq!f
z`g8Sd+*!-6htdO?v~`aO=}jWr!W|E>N@*YEjps}~C)yPvAFh4KZmzs;;abvl`@ofh
zpM*WL!<wFGEKEJ$SmuwXec3s7PSS_!N9Wm&Bim~N`JC!0>C46SwVy6-kIQmBb5V+v
zE6+2%*P|RY`(#dvHtT<S-s<i~II`*c!5)QShR7ENf&uuY#f!0<KRE6$Z{lCTw>`O}
zZPIj!9AeQ@G0$nN#Nix$lEe4U1YSXPGd-nW(lxI$Hpw(qU{Q#oW<kZq_}dpYr8_a+
zHw+d8m)@((#B~y4nfZo2gg)D}uf98!JA3FM_rX!oHp%UhzO{dhxKUE98RJYKM@Wuh
z#hcwXgs50VH*IoWtvr|LvFYa_r9Xr`vpLsa!DXit!^-aVKW96UXej=E|I9*@-_d70
zw-h_v6zSJ8`JBqnn$KQKx;xq!?ilcj*nd{>Yv=i<nis2vjhdG4Ht~qrE{`mf!m6=L
z)eS|3;o?STV9<YtS$^M)Mn&H@np!@eFiRi2lZ^ak)Bc51O?UK#Gn|a3KA_kyh*(qR
zZ;K%X<vbXj^`vzN*_d^D&{ycG%|?UtHM*uRFx*eIP(46DWWe}<sUllJV&?_yj=46U
zbj}sb6RiYg9#1o+nu8y7odmGma7j*+?m6rsTc5iWYEpl;pD5Z}S3g?ATExpdS?XdU
zSU+A+U2N`mqrFmEUVCR@VO`+1;^ONfv2*j?ryFXOcy73}Ygd=?Y(3B@s;3q~1ntPN
zT#jBA<<4u1dY1Fmk}m0liMo8EuZpM<PQrSfgk4F9xFi3F`H{9wyB2$L^s)7;!iKL0
z@BF||9ch2Zl@h;JSA>hMIo3J$Ugl^X*R}2|z4X;`&1;jRhq5P^Rv_y#-pBXoMLm|(
z21^@`0?D4t=FFv{kSYPYln!Zjp1e$o(FY@`Zu~sbmGvLLcCX7#M64%J8*Fp#gcfO~
zg_I;*t!x>RPQP!bSmDZO`k804;mrjq(k*uWykdXRk~Ejw?d&YaXpgvHmA+OyIp{dA
zx)No~LXT_RX0rxJ#otJ*Ecf3E!V_*@;?FvNGM=T9I*F=?Q?*+<VVlXB>YT3h8L**E
zuISyMnX)jfyX@Te75?aZAf-fi$UXDdRVgG}gQF!it>g0r_evahE$$B4x-)mO9$FK@
z?2CW5_L68x9Gk8wQ0KR;Hg;8)sWJ<j`-<DJ>p!FIje&PpF8OrY_}6hQt*kyvvykgp
zH&{KDL|Yo@R&YxujA0`g!BUXe!}g*z!wNoAcnJNm@fGz|BR>6-ee|=9KdvcGSUR$V
zHH5WhGKdrL&l3@<WA{b;@UMd(;c>i_=lOp$$Jh++RF6F6)=1hPcfG0c@vxUp&pn~=
zfI>toMIXyOPVe#?o9M3x*q2V<(SP;Od(5TSIpcVJX!V!H)b%+b{(yIq`f9ID_)s_1
ztcxnw&ux%O1eEHG3|%M|I*(D}HmaGw7KLeYvg;nOVS3>5dD4Mlv)(lOd_dNxs~CSO
zlC#~YsQU+H;*H+G0k6B3x=D4D?hjnWtK$kB;byx*li53WrYm8D?KcMm_0~Q->o8m7
z8VJ7^CPWevSGn#a_-$)nO7>&5nC28m%_mkD3PW77iW`bI-1fIddveW#NysQZo-dj%
z_~_f5H;C#?Y^O;R(tX2&h~Ob#<B5Nq2<$+iRj9T27n8$;2E|~*`7z)#s~l}c)6f+0
zejG(m5QSjkL|_a&L|KvBKEF(N+{oOjdyHyiJ_lJvqEf4yS+CiBHF;jY2;Mrv0GmwQ
zY=8B@n|{2Hwjo_y=!W`*am(e`XN4}$WM2DfnU=(4#a%`(JRQd7>HMuck|Td%t$UiL
zay6-8H0;p#m^`6_dKS<7b|3FAn_c+Q?+h1BR(C94N!u)6H2PFF)4SSm!g>8YHs@rb
zVP?bY4o^Gt=MibD3YsSS6of-oGnOU<LUl%Y3cq|{ZXKX_DlVJRSs~c0%WgPRF`m8g
z>1KW;<J<4Cy*9q0u4ab!vp;{(OuP)VQ2Mxi`B)22%UbW4b~(^7fB&^qwfJRLAUdCm
z8lh)9;f0D<qev)7(QhgzaxXvnZtuA`=~JGav!X!fbUCGknIbJDfP=SdU-W)U^|i)p
zFAXX$V;ck7`6g3HkKfEsDd%vvs5+jON$f&*wJ@!YB-?cHryqZC^m>1*gJUDj(Y}<T
z;)C9lZzGuNGZ+J}#(iH-uCG^Ginw)R;>iIH&Eoj$9CjyGTm_7csiZVaeVbS-Hxd$e
z+g=+kGUpOUL%hDVWMA*U`0%!*oWZq~x*s%APrvJNvIwLp%_iPH(0QJ=*dYCf$x$P0
zt>e36b_u;!u1<)EIX{1@<I|CjNaBWes6+BmH6_}>!z$BH1-Qk9HPb6o6WNoyQ!<3&
zB_&%22fFXX2&C)z)$Q|tU8p1z=rC$Gb29$Reu?rM7dcc;W#IK5F^s*G2x=VY*4UWK
z(hxnF(#>7TN~0dgP5Ex=aigq{w!pG9TjI&$Hms{001P_phMIrs%But#U3~Pd)|xuz
zWpzDv^}An4NnFr{5_^S;ah`s)`(ki0yR}Opi8|dVg`H`f{`Me^Kik<+$&h$9wX`t6
z4;_5gA-8_WnG=aqC|a#2b>;Xz6$Gvk3?f-$=O1@eDJSpDeWv_KsQzJ@S4edjy`$fu
zL1@zwX?^|iVjX|7{_%8zWb>Tij=!z#hFA0zeM_%n6m1Mf*R8hikZ#%(#p;=xUZFO9
z-%m}2FHmymDUYx2?$JG6NWAU^NC!B2vvbDrp1qT4yp{0jY0<P~iM%1MpHji({7&`4
zm)i<C;S=v}t9Q;U4QR5qlkyMhKB4mO$C7>&1P{~2s&RkfjNEQSS1DbMcZk*ql4p&4
z_9>(H5@S3pI%4i2+SkOcUDCYT#A9>2u_*=F8qn26?J2U}{lWAijD9Z0FHz>*SpTWn
zm5h=L`XO>PCJ7YPURipvsH42pvj?-2GY36p4@yYuPvtih-FF-w{${J^Mg6Yym6U3y
z=)y~VxKw}EC`Iy!!IO_(-<*g{Mvm8+Dc&+Ycyz7c_WUB7Fx}%g4d(hY!Cig4Z!Ddh
znWoEiM{|fxS2UTXNA+)cP?j;Cx47ys`_@v{u1THBh}mA5XMgI1(!sUp%8-2;iko>!
zUa!Yt=r*|FyJ_XB+@vNMp{*T_S0u#BN-Ed(!NY&Z_zcM?njPZgn1!8XP#;0J=5Yw_
z?(Xo%-QAtw65KU7gKKaI!Ciy9OMu{R!QI^*miN}~-Vb}L_QO=o>FS!U`7qr*{ha4_
zNTn&oj@2|~k@eobXv~(tf&3~<sAE?zUp4EilM1RGxoDaqd28yrOSzS1*qy%IHzK2a
zo2b-L+H-98Pr4QLr;_picYjL1vsvV{v37x%C{<I)!3*2w0in-sG-)xWrHuSn?k4QV
zy3jW^>XBKf<<uh8@CBft9^+|!cA^ylrSrttf9R+?g>%a*yld*vEGg4^{GdLIdGvS$
zi4g}woLFjfS=QGSQF38JT3AWO#DeMj6wZ>$rA;2vHzO+a(VQ|h{b80Vgbl{&oqvA5
z&RZQG9}z|<@`aJRHnDrUmGugCeYNC$%Dr68gZ2eA!sr)eZTs|aqkG6aS3ZT>cKTzk
z&;Ra$ODqEW|5s38XXkA8eTRZV`cxLUn}ZRceZD}j^EP2Yqnkr;fc_&jG}C%RC%8dy
z{Fm;~Jb4Z+s!hYe`9I+s+1XhCTay5Baq*^ZokL?ma)Nl1L=R|z7<B|54KD(grhlT1
zi4v&*d8&C;*bfr}>5vpX8JDrlEmn5RG3X??X^Vb(dr6xYJ8jB*a>=Dc)4c^rs$r_a
zY6)~EADH>3jR%2^hq0T?r|ydvpNnp7kH+?rS|kLdFg#jiGlf4G);;sH3n>y%66Daz
zl!?x5ZH5sMkiZPE<K|}^h$`yU&`ov<#Y*|d?LJ-xM#8H{XAGPYo-}Pn#)5+!Ek07>
zMp;Bd1oB>m@()Cn=jM-VV=|>h<UM&P8JW@u7$M<6p;@r_vGMUA#cP2`IM}2L5wQAX
zs<dMRY;0u6mlA1kjETNjVmZY0=vUTIVj3El#M|&!rKJ79NDrI@S-#39ID&~N<rqZW
z&p?9yP)ohO9k)PjTJlVgXTF^(CS?G4@g}LlFPeV+egSMou&>`Yk9Hyacl$c<YDN)z
z;Kq<)<1Y&*w=6o%15wu-*!#`$^@aMANIOt_q<B~#6SjhIB%^<T^?w@<K$VU#eOI9j
zamqDDWHsOepm4bez(d@5R&wI$L>|e>3?rP(1kue*YC!y#U%%6)BHT!bWmX9JNPw}|
zw#viRk0Kr9sdoHQMkm;+{a45J)l{fABU~cFgyuyDvG|YQbZ8H`2$h=5{>cznESM7q
zdoro~Ce>EotW=^x%pEF0pY&5eOe6RpxgG9H-vC@5AcGqLWy-^~e-TzqMHmV76;2&0
zXbUwY`~{szz3&tcZ>1Y75+)-O_e~~%_QlWNz8Ckem>1zN&f{&=m#*xl2?ykj$)?vO
zE8A$PVBBx?ShyMSplme-+8#omet)7tA~B1T$Bb%>xEP4~G?!XlKYCu5pODY>u%=*L
zv3p^rz*uPDJ5D|<YMBJ}J=xoaTh8|<N5)jiryPk7OG!jfIJ^B~4)|+0(Kb2ZFybH4
zu|Vh#D7zp_<OM7XGShS6N+oi*c5nhixPzNVR5HlOFrD*=2s}RVBx}JRwI8-du*4YV
z!xJG2oY3(iV6sjUKM>69OhA;U*<YP*Igr4?fk|=6UkIDglC=Rb@J@9pztSOtf)zNK
zOe&~6737VmOroG6PPK|3A~Y{$vxO9JW5d!~nqFvU$>~mgXHsg(2`XuKvSI2X<;L}n
zBDRYi!p##{xTu$>g%Q>L<^8N&D;v4*`q<}FcW2d8|M<;EZUqvp)T>z^+ZSo?*9N!$
z0GhbVbz{3R+aiWL3Chb~gJ}h{BA!p!;+9L%POyWEq|n3#A6%Y^j%-KaH*%2tDsw%Y
zQL7mj<A0Xt);bVL>M$RbD^ARdt(a!~T#%z7+R{4-(@tZ+eIu!JSV$<Fv?bod8<*s(
zZ-9Z(cqEW=fvG^g)6B4OfU|*OYFnE}2JkWPo+Bx=6VY#jL+`SG#(u=omL0!zD*8Hh
zP?6;`w46N_N^M7a_)pMVu4%RDl<TRI>;Ab@Af^|%Uqkzu_K>Sn+0{VSBk?qbF_;UP
zfHLF3*d(5GxrK5nlNwZyj6;Yl*x4Kc;_P0t+TMSN(s|S<&-Vdki+YqU7V<QQ0<!!B
zj&Zfxrym2a<Azd3FBoL)-`GUe*D;rxM)x@Hu8t~Wu3L^T@9eLN5|fX&ep~XfY}m9r
z^SheY5*KuxdnOJU8(qXXpOCo!aDY$5$s4VTfzA{fv0e+(g7u+kNsr59wZ|QcDWw|N
z6Uvk`v+^VyawG|idPrWhAs%hx0VJ|$4_VYZ0^)9r?i{oy+s{fm&i@T8Hjn`IiOcT8
zTw&a-#FBl=kGh1{m$oWxLTDRi^?yhNz1#zl8_i?Mv-~$-|2+%xCJg4IXcelHi%nz9
z{mz4>Zf?jC_7=^w62a5o%%*Sz8J>5^tQ?sQ#MI>C^IEI>#LJ!Pp@>V308%CPC6ax*
zqOj*?Ip4Zes82^OvOdrLeB(}{e<xi`Wh5DCe#d$$6_8D$Ax!17DeNo|z9;xv`e)?p
z$EefR&H7#{gCLmB;BS=+OHOtK-(uex`8YkA7e0g*iPqPNXWHS;gP2gc#RapHiX8qq
zJIU|AO5WDL)y~YWj^ypN=mDqg8*P@)>>lP;Y)JB2h5C3=>9)t(E%R$U=e_sZ=oBj_
zXIp7&<{5heN{s7{=<lo{GSzRzALWWc61AG-oyO>+7pic9)db&bwP7Ba_>+~FOxM0n
zGRYI1Hu13hh&=g30cdi~-&6a5{7tLB-z!!>JBiu(*S~olpdSp!Jpd$Li}BohylNAc
z`iv?on{RceL=Ejrataky|9q9|C|6IIt5j?a&L>(lt<k;^7%F_<X=Pxk)yK|K8|zwB
z0xUe+&*S=ZE%oQLsZjcLi}b36JdMx5fR{DRtqo^sjf}$g?_MN0r-ivy3q@E+?pm?O
z6h7HrAG=4r9Y$yyc)*74rJk+tPNt^K668k|u0m}GN-hCknAw~PmEFqJG-v1X6Ly?C
z-fHDu%y^WrESBaXX32$`K<Cn5EK%Xx%-<P=?wGW%*l83G7LH+ck?3<J?kBs0ja8TH
z%ORO>w(Uvpo)=v^5<8qHzXY@<eo_?B0P_#EGi~u)n>wqD=m4JQ(`$#J<x4W|(ec($
zKRd_5^V68!dm?df@>PscIQ>3B^;>+3!^Ouq@;z0C*Qx6;xcqNIfXD8^xmo8-$?LHq
zy~|ulp|yO3WpbH~$RR=cxi!=qmh%cv&^3tO{a1u9&$4d6IbnAvoT1_Snty1EzwnW=
zrNAj-`6zFg8Zc__T`~9V3Ski2uVaGsIDv26V1(c#j1fk%sQJ-DC)%S9*<~jhB6{-q
z*^2)~7^7mUWXW0=n|@)cf?p0>H@quK+h0#BQ<c5xLs|Ge)4Bbc_T{s5h6lgXvHU^(
zx!%h!de9>$QFa&qJz9jEIiz2>e~Nmnf!Sd($Lqq74`2|U@5g8^v=&y3P1qcNj-lpV
z`hC#&mA344sk!y(ap8c(_Izr6ARc%?kP*0kHoV$9qoe!Met>oHYC<+&9&Q}XktUh(
zRbk(TbPgqUHRj^3!GJ#7M>V=4hj_SEw#0^G+&~Sh)R+EJYWF%J;6YMdrmjq-d7#<7
z(JG797XXBodjt0g?W@gmqVSc>yfOL!A%6$i_*Dq_9p{0pC^N0d<Lkf%)fKljZU)}!
z@ZBgW<U8j1k*GCP(bzeoMhTP2p`i6ZbQ_b?o%g<_9y@`Lqa5XjQ1`5edQDfk?(c<l
zGvyDacE9x;!QZ^B)r$&`u{`Fg$>J-L;!8l`R>&8K!w&0@#nWq6cQ$2zYWG_CuxN^|
zq%Uyh6znP)5^SSz&7qVGj!c(@buzlbQhE0nx^ma>n`p_a-V-jGrNSGx-HJeg$0568
zpGOvq|8Nr87^_{Y7Z7^RV{V2$@w8yyA(FqIn5TkMLtv&d9)lyM>Zrh=CXvP=pz^YD
z{-3QODHj_L$A4`I&-ATbSDF^y&y9NH#?SgGzZ)03T5j`9%=F9JbD!)6+s($Vk0de-
z+q(d7f(SA}g|vFL#mzTLmZorEwS)o(n~Y%M*5X=bGm(tH6m)aGV6i30R<nI6o808?
z$x%;JQ@KzmhInrq8v^SVVjnq^!C_;lHA;Xc97e#Ey%G5Xd>OME6Txw0+d{ydT~UCy
zw!*iDhh+z+BMuLxOQw5`MMP)&gN8=`HJ9#CLGKiK7S}r0rzY(R*{5~PCOF2=LOd`g
zu!7XCIEvgAW}zHD!K<t<HfV5t%LP6Qx`@+^F~Hbl|4$z|scQa^L|`y28QDQRBlrpG
zA4mh%DpY(aKnubN1A9sx-CKrkE;eyW+@?oC_K>VH6p!*YVE#`bdcx0t+M+1>47<7E
zF6*Mm-iHusMY-V%*wf*}%e`Oa#8Hrv&uNha5fu{2-u|c<Aqg^?oa9c}KrKQl+lxdH
z3b;o-Zjo9F{6Q&bQ4v9wLO1NOYtc8BsD)$-UHpnN4s?Q-LZcsKfxFdmZik43K(s@@
zCc(jOB2u9efT6lbi2+}$;1(z-<F7_e0|X*a0}M#f(ilSm>%tJX;lM`3d_v&ZutUF)
zc;OE8q(>P?D?rvu21YZf{1o|a!WbZI1qRC|)fZ61x)m@A@i&k&x2AU!x&loG+@g0R
z5HdbV1}N|2OGb`_l8NC(m<<SlnB?5k2k-0SnZfTTb_zv8RWT#O0rQC034qO0gTl<O
z%&pYWH9@vg4?8wC6!{_rs)5^+y);2K=pht-Ye>rRZD+239Y3sF9VVG99(8Hc2O~iE
z*C@^Zq}uvxZESJ``plr*TQfUO+NZvHiN@}m36R1(G|A7}Pxw5eTeH^vq1bm}nL}9?
zP{0U$Y*E1PRR!nin|wDBR&b<Fnyj^lxly*b**Tfk`C=2;)`7>Ay5|eu78Ir2#hgRT
zB0Y+(0jG7k3oGJsKdY?c9{{o2vIKq^Y8EPAs=W;c+h9wJlC<x*UthoDlI9nbc8^l`
z3KYJ!eZm$L6V0FQ_6F`=uQ^^c)RQk#fgh721tmT?&ZWvVwH|)OCQi0%RpS*5-<{JO
zxXu3R4D}JOYNp+}XhYilTlTIe5E3_{{W8aQyO=EU?X;~hc2tqcs>A?NY~RU^!Nc4x
z^#=`fQ)n9GIbfGpzMc!p<v#WEEDl6R0Fryc*03&Z!P&(df*DO%2;yyKxNNisb@edg
zT@+P_r3(Dr_56{K&9!&vsp#f__xHALK;;8==|ei=6G<Vj6U{f4_|p}+k)&j#Ae;R#
zS~YD2I>viKcFw<6=q&P%wV0-I5Bjis>^B5Q%L9azYwkCu2DSJwh(^PJD^4p_V9E_#
z8aY(N4@YG-D#*Vkl4jsofNQq{7AuAxJyL?D&j-og%k=WGG`%c$4hwye62gtmOtHKp
zvh^!WNf@koC&|rB-T<o%!Tsj)zc?Ev&whR6Fh-1r-z(d$XHIL&D&<7Sug`b|A-s>`
zRi5;KcDZ$>HM|2+ty~6QjAo!W5Fj7pl}||69R*s)FIR#0Zz+Od=6pqa%#@A$<@(#^
zGQYGQyViNr^@`Ei(4kUIjrI<T3M1}TEBcrv-qvZ8Ho_e_lRG*7+3QrYF_yNv=gSbn
zaYT%&e=sEhiIZ0{?1qo|J98N-BjTL>?1TqC-#enP?16)@wY&Wy?{zH?U@$8yyY9LQ
z`*^C_j+*+7en@_ME^q&^<Szp`>TH8y!YSSiL71C@LZoFT-wa76K6=qF>Tkt#E_`no
zp;CFV!m(x<vkls-zdPq}Wb}lw65(QmvnAMybFnU2Y}OmgEET_pb2P<$TXe0#-tqb(
z9}#Zt!Fmd1SAkw}z3>zM80gUo2;Wo<SBnU*wU)>eTuaZX$=42C4hcV5Y%rrs38YkX
z9_S)1&KF^az{5kd_SEpp<d!47xJbC>$@I3K#-=KxW3}1p2<EaPq8b572=K|lFRM=-
zi%OoS{ZsR*;7%vUwpO9g^Tj80ka56}E=DsYwqw18hdu{Sr<#zb19VrkLg(`gCE7?~
za#k90^8+am5<3#D(q_5P?5dgvs(y=Hw_rLXH63v2S|#h%ApR=1!A5M5Q83%?;Bb&n
zYL}NIH{ae^YhN=_k<(h#y5Z!M-6_s=*h^8o>WI@rrbQL_7Ezw8<{&C>9?tB1qB~)b
z>oljbiIfjzdN_oY57_VZjJxi3^$K(d(lrXiLUY6FEB<pqC;yr}8nlbs*oaifGR)?w
zxS#GugABGS>!KY(c@R)Su4p&Robb4sFOD(9Vg2B*n>YE+TvCTkqz)O^S~{v}E=e2y
z4zb8;wmW$JYG$IQ;`3x>f?iy>oOGc6LzbMbF(hBFFCOPC4X7c^_n{c_P`ZaJso~$@
z_{U=qqyQ1%fQy<#wOdJUcc^?{>V(DA_#Asl>UJ7%SvPbN=TOxf%6t7-n^otlGFyQm
zL4%NQ0lrvEGgMGtkJ^WZw<i1@#!S%fOpYsnQ(g&2bhMyX?WO-I#7ARgyUgzIWm$=O
z^FDS|2byFe7J!#15R(|<#b*y+sCCrpRLY~XjG*!F^!?cQsDXa!C@HGMCWT{JtgeJa
zPrM_9qL;<NyCV2!I;JZtBG)-*Y;a*=0+S$?*_i+c_ON-kCMo8OmQ~I>!oS40k_}u6
z%giL<cQynVJPuX%2=C>Nh^%!(9qxa)tUCqZva2Z(KpV}sA#zMof2ePo@q+uD)&ebi
zBEieGUe}lmUOF%Nfjof`VC5iF@rv2Xzt+L<FXJ%JV9Gu7VfOh}5;Fzqj|#N{LnYC^
z8mAc3t+Y+`o})qR{6<+6Gy9-W^6`lEK$v$?!9y)0ds^v^PtOUWY$WLs*$y)M&Jp!_
z)G^CE@U2mjA^))n3aDJR#Vsc_yZ=yUn&&<MT$$z>NxyRpY$(bPBwI*rtQ3&^<~WC%
zV3&E2^&(U<$i>K|oX3P4#1Ee+`lblRA<_x^qB!}u-ivd3ZOp$1btWm=scI{;yjX`H
z{!+w_e|?{4M3}Xr3crOJS|yuO)T@qbnw=&K*z1z^_M{84kL0=hwVm9z4#7F$Fidq?
zS~TNidg3+A&#MKSMIB0>Q}zVUEWsRC+%YwgO+v(hmi5lX?fEM}FG`ZdpR19$P3az-
zoliA5oH%n;D`+^APCA^GwCg37mDte7SSL@r3>6SfDmQ$a*Nj&OW;*Go8nZKjHvX9+
zF+w7AzQrNP(yE*u%j*_z2Azh1vAtAWILp#@P+T*a<e7+etv{JDIg=L>k^;j=ph>B+
zT1aZSIunT~!=;3K=$V`>Pc|gDSU59u&#QRVFv}riYAZXx^R44gYT;!@Lrmtr=r34k
z*>I7a5Ky4FEclUo;jq5j#?`HobX;64Ab>{2aM+-_DW)&_4p*k$*A}7_GaYMd%CRge
z>Jc0U-5OgV3nz;EggqXt**}Dn!q_lnW)Tvp+}27Pl}?(AS=kw7?QJy3?J7<;+1Kn}
zTbvy^I?VzL=ZswuSD<c_TzvuF>Q|5NfL6&><Q!&!Sbb!yRGD{qZY_sX(g2SRC@6gq
z)&+${HR=9l+V+BZ{u&G6%hy)&Q+Mb&WSn1-a52Rs+D>di)gxU*OFPfm)1lx=WfW79
zTh2b7h(ldK_v@lZ#aMOa#$u2zbzJ)OIJ+(ky<#2PQJSd$MM<&)E$hThewRTH--H)m
z+(8Cxm-;5AUg0F>*6OO)>K#ibK(KW+GZ#NeX#2kJAvBJJ(we~t4dn2XWD_`wStmej
zG>ZK?bf<QS!-Uo;yxYQiip9)!9$EVrIg_k>!h7)r%H^0BQ9+kuQX^}J=0SERB3TMl
z2A!n*SXv?OHhY<yx%>%AYOud*M3L?IyMTEJ#{pleWVOR1)YUNe1Ah|)V6IEX|1IpG
zi4M%=^|tKSQ#^w(L0X5l<ZWD^*T{fD!X_k2x3r_CB<Y@FAyNTV<APTx@>&Iv=h?N0
zy&X5b>JzL_MZMxIdjExU7Ap4qxz+)MR9~H@M%O<*dh=%7*b0UhFnC@+k4L`^PWt=4
z9?#zhs`exeAG#!1JJd-77i5B%)IPMJ{`jDv@Jarsf&sj)7%1drrFT!aw+ccdf1P}k
zrlcK#$J4x?@X6GI;m6bITNgDkBn?8A(cjHhJKwJ#Y6(2wSVvN)2{*8w$&7xmR7*Ww
z%eN8=8uKClozlai_q#c23MJ}#yxU!*5$^JJ=V-@Ql)Q3s<l;2~I)%=d7+JwqoEO2Z
z>2=7Mk0uxx)9;RY?*vCk4ql!_-#LJv-9tuu(ofF*iE-DnuZ+S3lamfr%+z~}uL3ML
z(XSBiF*l>H^6z^qcd0JvaW@~Mz$nd=rqH<Mle>S+MX2IPG}XaA&o_UAiNX4t*N2Ry
zy4`fIuA$T?#dm4o-SVCD<L5^SQsolda&Sqt5%I#*i2D>@2=;~%M{KS;T?5h9v`26g
zoNewJg;S1%rx8R)_|wU&BGl93r>F1Mjx9sX8#+HsCUy2^dVAClygPf9@p=RN!KIe4
z?~w?Gk(y@^pQ}aj-{rN{hw%qz&DOlt)86o+Ij=!aCg~9%y|*`R#$hy$R;IeZWSE49
z=x*MJYEbw}i|!EM!PbM6!6qJ=j8}3qz2vxup2tUIWY{z^+5q(@JNf6LW@LbTyUReG
zrX8QUa~i9aqwf+uWznp2yHgr#{kc}k%=S@>dfV7R!Ohi@Rgf|^H>vW_)6LbkH{0`q
z23Xc8S9Kpi-SKYzad<c_yUWSG%_SvHIHcP?^^RRxd0yIR4;ngkI}jYrnVsk}cwqj7
z2{>@Hz6ZUWW4iI#cX_WEu>7q-lZ-`SHeNA^y`0|bAng4csEF&aad>>|o2)!C0CB%H
zk7Osged8jKo*8E{s`cVH_VR;Krg3E`u_yK=9UuZ8nle!{YPJsEN(LuCbxh+0m%Ipp
zp41=BeUR0#UYB}4<^*Y@I}eloe%Eb{Y|VyU68iXE&Yf9Byu2+Om{m!%LX-kHs%*tf
zpweGRBaJZwQuk-Ocj1<kIW$#$x`Yj4)UX<*kFgE$Oc*%JDk1!7Eu3<V%a$*DPzyRs
ztp~uS%&q;}iq#qV-ttU}Jy2kYRwn!OGH#WaYBXt#Aaw$_f3<BIq;+lj3j0X=Y2z3R
zSJ-zGVCr?4Abmq#@$%=(+t&>AaT~Ys;<Px%*&|_nGkxV;dcCO|O9dv>3Nk)QGAEZI
z>Js(@d3pG}o<Yt53kVSsil?dwP-|H6Qvi0nlQcLe7y?4xzS@q0|K{X(0Z!aWO6B5b
z{yp>o@|p{{0~GVvy52RJ1%dt&uM8#vdR_gXSZf0HhtuQz+RMYd*clT-5ggn{M)Z8c
zz<4Ll@%$#=4*W{=icA{d+y1b7RAA%WeCT|J#f<#HkVwUR?87pFbi%Trm&Hn>32+vw
zGmC~Q@Qr*cIu^+SDRVvLFzlMLuYGLou=sRqOg-u4vU7=*^!?oZv&32c;rs&^MRY*h
zL_yCWiQ3_4s|(x0eH5IG;jfSdL0KOP?Bsd}Z#gSMvvDzlbKfH*>&?SoMoe4Kin78E
z=+^+V3yxXaU)hL7sL_q(8oNUIIAFbN`D2gOnc~+Ynd<d)w95Lrd@_3Y2qFRo%iFcm
zs1||sLMls+koOg{cjDkim6B!BK&7bl5V4v9{bk57l`ZV#^-HF#AR}g+D6Z7v;?0t_
z7H`3m?>!Ae^6Ye`eqr7BpZPh?-jK0yho!P!(CP(M_#dG3<k|W<crDM0E8x~tfQY4A
zwc?Ma_70s@+3$>D7hl1rpUToDNvc9jEOg9f!l4h8%<zA~wXKA@f@1h`MBlde-M}%v
znQ#pfvzq?k>78!Hhb*?Yus5TNMcyFFBy3J|&)7g|V#Q4ejF1!HTZ5?%I~%YH%wFH-
zj>zwxJM=)MYFQ?=E4(4`;{m+xugnQT^f-i{Uwb!2YX=#oYmiXGxEaz%WxcrC-?<z~
z$V+2xZ%-bC0Riv8lT1ZRmei9;2~l3*{twx+%MS#c&smcQhKhl4CW)MGb)Oi;c2@(Z
z8F_VtH+BuAZ+7i?opHo_noz&g0kyJ$bUts<b+HxR8Jt5Q(5wUc2Y{hmeZ;T}{8`5$
zrVB^x?iz@2u6XFcIp`eUI3T(DL3N&tdwIwCFP*jq>p5$Zy5_tWF5XlK`7!-ly3!^N
zip@FhThVG|fk^B_7x$cezp3I}2{)Tv9C92AvZ3@-%XlViB8qQhB?Cz@(RG^E&|*^D
z?d{pUI(RZla_l~0F2IB{-L@u+IKt%Q@9pXi?~7}s#LW+ZYx<7;wJX8P7wCA{z8sFL
zj(sphGKdXC3xMm+RfaSZr9LoTJ{E1ZKji7$Yy6sW{V3}{XE+Q`@L=Z6#ZRKlVv>I~
z0R4!r{@T<-W3rf8Y^K(~5~tAS`4(u&=Q{=|*N_;H&h$mQ0H}({;87>rTl)NY*_Iiz
zFo|ZvEDA`A&iozhx6eLIEK4>FCJT8&i{2#1qJbYIkzn3}zIglzmn!zqz7+t#r?m?V
z*;({xtS`tWz$7zHa~Mk(ut$Pq3t15yLQQNpsNUAQQ{_`U_I}J9=3Mk2n+_03yK5!{
z65g^%FMAL(eAd$NPUY?-z$*>dw3;`N_X|x-GaaW=R=3+gc4zioPL;fRrn!-PNvFE$
z@<0nl({xdF<z@^mWoEuqNOPcOGdbpuR^VxC%B8SemAv}7eN3H%e}P{$*ivxFM$X=a
z?uhM$uJrSkHZyI$vi?*;h@D1Nq`-4KNQaNT`X*_NANV-|?%ao<j>!|WiSJmfb2#N;
z-+x{;Gf?G0V^}75HK!LY)3nz@?nWqy=A;OgGE5%%bH)nZ`3Fde!C0PxLPJFnEY*4u
zIfW;=yr2$O)J&?GqGqh^6(qs_MAqflG!yuzUUoIHj20~&b81aB|MB$`ZXmY@XOT5$
zTKoq82BhLiE~ET;=Com{4@x0E;&EaStxTwZs#Wr!l6KL#Od-rW$T8ZMAAZ8!ptRS(
z=`u=XQNw#)<t{g#cTh^z=$CWSxtEGg?4p|mt_saVj_Q?e1v7)Md}}2>omJgQ-Gl={
zA*?%VkG@alq9o0_*0YO>!nfWssqiaB5HwX~0P10tB-`bz#$403pkJ@G>mL}yszdaB
zpO8q=Kf7FTdaeu$d5X7I7~cc9ULO~+tq6oJ&*Q0mUNLcVI2-cX4MtNo;2nZ#Mhup{
zYqmz2zF0>Ng;&<NJ#IFMr_(Pah1F>%?Kg=oUv62aax76XwUEtZF2Ps_57H8ixS?=x
z0)_mS-<=SWk+O~5=uS+EHKN&)jIo<UmyAzWixf7*bm|1(v~JIc*7J|cn~9B9@G0jV
z1e=~~cq5xTUuTP|2Mx$z<{bg)f8$>|_8NaN`}vI;HgHKLEProCf^hU|FOoOjkQu@b
zkc2S)2jkbgp5~U4ZO9Td%)B*u+bA*R2ZZx=?Pcf6=NL%m$X?#~6YQ>i589xrzQ}E8
z_#wB6v65Tu6FWEWE!c8dQC&P(5+?Q$+Qr;uQMa7<oV|W|&GMZN)}wG8-ny^)(QU0M
zo0m2CPt||km!HpI#5+vn<!8DKo=x*-gC3{Bj5oYOIQUf128{VbB&zPOP|7NR{#*>t
z|HVC!1nBG?&3hKFdZg1me!F?}P4LUtVfViv-?8odk(D=g39HFuoj<w3-m-)C^|kJC
zORM*V$Y|ui2s`y6UF0$Y?eXo~yEzJmzu*VHVN}Z?c}UD{n@n|_>m!dx1TLFimn|}0
zZ9HR+XDJEbg*-gYK769X9Zm>j27`vSJ$x2p^32wTSz#qZmLzDmRjyvzuXcLw;yok5
zvw(j&S%LzFvHPR2c>L8%D3hss^HrYlwaw_G=p)Q@474wW6?ue-bzT7<>QN<QMzPg@
zM<?tw>xm^bK7IUrIek$)WZ5QLSE~+zW+N>)Gd8(e_|w0&zOIo#S)~G69@dqIR?Vjg
z83LR<$bBDuoU90C2-dYC@qW4#PCAv$B5e`m*tP*Sc@n7|_Z{xD#D1To?%c_4nga4*
zH(TQVRZMH7AO}0$oxH#04b;Xl7i!v*y3M+ZxNP)P^5hcC&=TYlLR1>$5~78iaH=wa
zDMPbjRh05VR`^INp_zbPtt14GTCs`@m~^>TjI@c}G*%6@0SRjPADeO;W@L~m7H!wj
z5BP!Z0p!qtwqzJEu@XOH{G|LZ2s>!rm|MP@8J|W)C}tuAuuD3dnpf1(=xfBHJEQjg
z2?wGvjovv8G5K#=YA`oV%Xg)=#1O<-W{Ol!y)6z@VCLQ&V7e+=9t>!8>%T<Qi%bb@
z^xPWotI6<G8U#bY<W`E1y_nkE!HP~yV||8j*5nS)&sYcEMcYBDuSO~P92@^bA`Lfh
zDzY+67~H1=mxGgojVCoz8HV7$qi$uGACT;vys1hmFa&u2$&`_@c5!th1#z?eUuA@w
zizCV8f)0rJsc1_8LJhlkVQ{NJh|$KkmI^|p9j_#zd*ewVRH%azM-N{Xyxs6Hlny&B
z)pbdHJ@?$7r#Q2sGw0^pp7x^Sd)~?9X~9g2-KC6(olZfUOuG3N$!Bs9ycx+u!kNj#
zKM6wWA9zwomyp7dQs%p2eoS;n*C(y^3e}IGNCpnY@Hz7+aUOY0vM?7Sc`5^bRV1l}
z-Q1YGncuLUtyOcs9PQVv33dr0G`Q%vA#JQ8fXaVW{?cI7+D)k%i^|V$Hq}ZXGekL2
zUI{<Ty8<C}5i>LM{fxG#`+0X^<~LOuxBz-eIS1F_6p7KIDlKwstJt6Rn=O>-bR?uM
z#RjlIbAMaZ?(&A?^QeDgm-;O`u}7a1EXvfu>_pstM<5?ktDzrC+#?d@S{{%Pi7K=8
z+1Cxm(TB9N@%_9AA?$3lAZv!ZpwNty*6^965UOTvuva{?dQ#5l6gEc`6`io;Sp$F9
zX!dHJ!eijdo<E0W=-dW52c-NZ@3HXV0x){^Kkv9=WM;X-L%_>Iy6g?d3tpP=%%b<k
z<+wPAg1*>b5acaWxdhpy4k2o`{oS&_?ljhqA0bwnP&s3+NkmdSn1-6}B4#76Qx%-^
zX9-NzaocDLsA$e$Bt1DZg)+;arX^kB5CvbF!i6oIIzZyCKZM>PCBTm+C8&@DkYbt!
z%;N3OOAzZ6UB?3?-foas>JPil5bMmmEaUB&g6tY-c!TY1etb$~((I%~LKgz<+cz^<
zIigM0_4HEhu+V0$0N>4N6f;X(@8DUbl-jt=RV)7dfLf<ODRUC~5`JoXhQ|g<#s+NV
zWkYMmM5%1H>6>dg#iHu**XSF-DoL1z&}RdOQ&>AmUy*ITc41F9)#!!pvhF0)Mx)yI
zT32+w9oDF%+7{^}kY&DEV?)hPUN`7%<45YOA>`51Ie(<^yO5&8n~Cec)r<46JMGYN
z&{a$RY%N8Z@YU_j`FGuqRb_1e`C(<yTDYP*yLj+n(3?41?E^9<jqn}ofB3q1SW`nx
zV8{R-kO4f4y0y1CDLW4co<*Bf4@AmN`kzKMM@KhOc5a@}%rrH47Fh=i$IpoOe@7Ce
zdID0C5^Ul;65JqB4qkB(Coj9CI4dWsIGY3yFOR4s7q1ZM|Gx{;=RgYP4wi0Kq`d5)
zRFEkQJuokCr{Rt{c;#y0U4p60Hw9ZHGMX$#qLSO-7L^>XBBz%tCyFPh_bl`3$U*%#
z6oiY7P7<l=f*l4;KK-j@rtuf9;=fko9VrM<BCdyA5CRVV>BGT(lIubC$J<8hL8{OA
zSoZ!{v{z{mqvg-E73oT;Jr$>VZ=!vXaSA8YV!(uO;*TniL{1eqj5?u(28I)qQZKL4
zoLHltV*CA9XwI7SpBSuPCT~{ozoNK1#9-*wVjt(hoft!Mv^1`1$W!3(h|fcf*I+H@
z4phEC-r0v}{e#NT`JQfr;3nR#_e90%(ZfY6N@EvJGzHyRgW|m!`%!GpZ-R5%>+lcK
zClAPBnp7tW0dFoF)a8PEF@YOlMTFhN<3Xlyz=_h$qa%b7ygDf5$X4Zn(Y<0M4E}=a
zp7ExQ!vp@!3H|RDqe2_gn${@Y6voW#d|_iku{(J2nxU88IDYf{3c@A%nApHsjIB*8
z9J^EG3qPWbVE}LQ@3iOrt!wzaKFQ{XcK}e3uQ^?Rpa>Vu?pqTQDiDVt^eTmz!DP64
zH`B2E9rz0U6g@9emA`OylRB>k3&o6|cX+>tkwxk*%32WUv)>Jk7e(D%-L3Yy_66ZF
zi7e!&SY$iI=lwhVe&EiD(L$OvjU2)`r0LeO)>(p`kCUYz@C9Z%n)uMAy*U>fod5`-
z_FnVnE7=$_iti=`MBjt{Gon9fEeNcTc}NAZRj{QB0kxCVTl6;Q5ZWXLji(<8^f<M_
zw|(!UGa4Ioo?HPv9j!`gAvzYsG0?J-gH=fy3;I&XtknMIDo!(`t5BQ3MdKv8DfXh&
zzUZ4L1c3wf`CKbnR~2W+cO51GiWyE{A7UGKl=Z^UTb?Nj?<rdHtLX;(ZqF*L&ySH#
zr-!_9h|_Qz+CKVH@Xo~r5hlU_zOM*(Dj_CcVa02RF_}BZ({u5-L=fztByBJb?;4?(
zSHrt!D;wK$y31^Szo2xN(|b9PYPfrz?`D)Yd7Y1NYG!5oH0Rs29|*kx3iHU559@04
zdr#W(<!yo=;}7ND0w3DV<%ZSi{)ILr+J5}SHmR0HE1#8)GFtO&nk}o}DsAE{wR6gs
zPnKS^HST=w2i-MaI%@Q_I5$K2Ny_m<qFEum9moC<j`f*;4Un9I(hfTv?zluS;!{RO
z<hb&a_w7K>spx0K_@<yh%?j%6hr+;6P+$dh^k1U)$s@9Wn)`>;f^mq~jg}6l`R_?)
d9tV=HVlh(V&0!D_IX_ouE_f;`No6Vc{{@5*tK$Fw

delta 143149
zcmV)UK(N25&Ksx88IUCbFq2^vDUnY+1$cmSKlqW5UIA>8?-+mf{<_WAWwE9Gd$*mC
zoF!@4F7?~JFZxXbdJ(TXBKk~K=qaO&WeIeHnoFsfPIR=?8B@Z9O`5hZh`m+uKR;ry
zS$<n=J4|6mYyhjUELGOoNl2!(j1)_T<sy(}BQk|I0RbGrtC@WyQ%N!qNKasr$bcaA
zk_rt`HJMMaRO){TFT*1Xof79d&4dxrQZdW3;J4y7Z~Gbw$PC6?Dy`z?+CTrbp-K31
z)xGdDKW@uAnk(9_?A^!diVt1Y%nFzYCTtQd5ji@UYVy0t=O=tXXc@om`nK6N^+H-N
zq8z@d_&XOtdF7{n*xfFcPNP+`UGG*sMWp-k=3!Mew2gmX_Ab8yp^ck1@0<2vVNLwP
z6TUB3#Aj39<lC@mpZCSA#YmjF*!w&dMLLQ_q#ok}v8Z60RC&{USdl%HiW3q<=~!}M
zL;N6N1<Q<)AwCk8A`g~H!o-jd<9xyf#-?$<fz(EucomYVB{LbVV{(H3M8>BlbXAg!
zOM^*r6a9ZXJVl%@MEscJ9D*R&bx7~Lx<USw{igOZPZZ`1Re<9MMWD0FB4uF$N{AY3
zUsrY0k@g&x4fcKT!`rsGs*0KhHZHe*vd)8xT=Bt&YA8PLvyTl-uYDE6RJTGwSruW>
zL;cQ^+(Y89%0FmLS1dy5f$i-`4>3|AO>Cr6#khY}UW=b*6c>!kVU3o^13g{iTx}e0
zc)mtKlWDvzs#Cme%98A0pPR5i9pRnL@cxAxeu__qC_~;KtP%P&E6F9xV1q+e;<R-n
zPnb=zS?k<yLQ49)aAy&$6^wSh+pfYPqCzpj)5ShfBh>S{=*gpPcS2odQJA$ortUGh
zRVII!&CGO}55PweS3bHS4GBxJMe;r&yr|B~)NlG`#_q_gEZfJIU<nt~Mdy61aptFT
zy5=VYp~BIHGM~-{)`V-Kn9iQbHNiQa$ip?Wku~838ykE*<Ry-T*JQ2L%%tgbZNJGw
z&CM&EbO^Eg5L>(O>>L05xLd<*H-#T<Jgt8p+%J%_MMVb?DrktikjwT=E(7f_p$;r@
z&g9AhUFqkUTtR&Rm}i?@W#E<0nEZ^n0n?bK;xS%Ve7ddja@$QZ6e)WJ({@F>^jL3H
zwU7n|$Uy<J2}G&e<ZfYf>`uAvWQbX&(&@@`^*M#eJejUxi=|G}_|nO$`Pi#&>}r3J
z7BGp@?#ytbD+-ARPeEU{>i|PU&>Hhzk7`GSDQtq;b;5%#X~a~#C)B4D$P;yGvMj_s
z=~HeAH53QJxq>z04Of&D^$x+ML-8d$Wjy|7T_BU3<|ZV@=)KuN*J|x&Jp2lu^Q#J<
z!ocMmo?TPjjkdUM+EeDy1gWONJ;8rEMx(Jvr^|Bcc=~eXG_lg1LWb{?o+R>ewL#vE
zj{-x{;E)k4o*r6F8YYuq|83*S4$zIqpj}r2<oGFvaqzq;wuQrMGzbSuM(n-O@b2L7
zt_xf3x-i`}b$H8ffu4xyQ&}Tp?%dj!Teqw(+LBJ9JOpy>+bN1|@AyOcf%ShBAL?c^
zoNM*%t`7$-aFll;-d$LEK5P!ca@WgQ8?fW|#a#(J?UMuzV6$sOQ`y{<9bDl@-xoLN
zAG>|SxFVo74>k{jRw8>i`ZOp0H_pU1uz{i0Ww+W58`FpI9I*%0guSvOUsyoO9a`44
zAB4)5c>(>7*M7!zS#DtyNGN|L@~$gfPevXlKzbe;NObEw)n1{8nLbp*yao^*r*r5a
z%QL{7G6?<cWak3X6z%*Wv0s=<X3TUQKf?=0m;oN0tZB~i0f?3MKtOSZ5zZlz95A9{
zg=~FGP2a911?#3IM+yDtRDr70byTrx=T{n6UE|+E0X?AK<mBDE(F}h=1@3(ai$eX#
z;;_pAO;6&|y~DM_37(y-Y#Gxo^1ZtUMC_wn@6Ra8vlm0o4ghEX)%&82_jTb8uOfh1
zYQ^%avO=O3a}vX+X`;~7rtUt;32{5)QYzGHkn#v_p}trTG|vj}39AH{Tt_3Kuc*PY
zL)0iSHaMWLiyKGyaYlbA3H{Q6;M0sy#x-VhLQQp3@Y;yz)vS>$ni0to8E#JgGqV$M
zk|?E*R7W6Pf+P?llM8Q#uUx5@PyiSd-CmFfIL(9qBhHcBHHQ2%mdVr>DmW<ImhoA^
z5`dEt(O+ix(VKcUJ2A5pT>)lec4xe3j)&Hx7tP45bQ$!I%Zq>iUhHuR=ZL`+HnT`h
z9j)q%pMT}i8XpNL(Cz5GBdsHg1h*9QRrJHfzr$7Sgk{)EWWaJJ8`NA%DPcGFIOjU#
zW+wF0ZK<E)I{mx3PCvzU`b!c}ol3yRhGxQ&jtp#W)i_V-_LHNx0UJq|D)J9q==h(7
z&KJ6)WnXHh%*cOBoF56}{lWU@nf3>D^%;}Dnn6rUsWp>IyT6CH3U}%EfP}?d;owZl
z|4W18a4m0(gPThaEz6q?J^M#|W`{28zU(&BYpUW?-{!;r2-j^>dqTR?ei3lq6cwsb
z6E%$sBbl=4mmcyHJyVuW4qfVIX8>=;R4Tvpn4d8G?3jONlYePmzO@2EWhocVU(}l?
zNZ)0WF{6XeR(@Zk+K3W1K?6(wZthPGVFKZJOSHN&+XpAk>ugE?=D3>#{rImV-Y5S$
zy4xm+Mzbp56@uLc9SZdjYxf6C>({(_<Dah=iUZEK<<*YvV3yxC+c!;(&VE(8wjLx1
zYTwSIdyo}2gXLTk?&Ye=6|tSz2H@p?!CoX8lR?xIvmgluP608O(K7-mf8AMIZ=*&O
ze$TH!=?iJhWQO6|q?J-_chyRfR*BV@bRP&zY+4)K0q=TK?SJpwuo;ZwfN3s$!Eiit
z_|A3CIY47#K;y#^RKGuukIvrP$Uq2$u4^0Pdjnw%d@nFO*9SIsjd5b!nm6fuF(W6I
z<9TMBpI8`~3426lA!+wHf0Z{yNytL{Pl}S0e73NNNp^y5QxT#psW@eSE+<i`7*A-F
zq<ke}D?g2YV+bvTLFo7r#Ii`U3FGa%X2kzLdyi~bhwga5MlRbXmfLa-)}#x73&U!~
z9}wEDjO1;DQA14-VC+{*=21!0)kuO%Gx-~zo+`@6ujMqas2lb1f5$Sf$aBKqa|D6!
z7!WuCyFh4AW+<I<{ejsGIhe^3dY;3<Sj<+)$A*PnfNf7=`Yz4l*)maFE5ieu$;Ff)
zFM_*9Vcd;d%L_yEB4$!ee`;*s500BnKpO}~ninM{(Y!wre;_3HhXNT+CG#jt7cZ`n
z<If~6b1J<*o<&6gf2PL`W)N0eD^MCmd9zdVW?fk_>bvq}0A1TPvuI9=MHK52@)z2*
z7Y1yXy$<)HOwLs#?pMTCBr0BY3C_+~rgT}1Uqw7Ma9sDxEH2YrJ>8K>nicYXN@&v@
zURVjp7z-2{Ww!>EmD8+j(;vGaU4IqjdRs*(0D&ED(j60|f6h`QQx__=bq8!?;BK;M
z6L1rZzB;0lc+~&R0k9cC@rtJrZRpD3d#j6JsZp+X!1F4W-!~K`tjsWfzWu~hhW_b|
z+(M9HXD4;t*Y>GSw_}pd)$8|5sgVEJSv_i_-E<fcWK0T)s4m3sBCE)FSaH8%IJvGy
zt0JjCs_4;Hf56()c~wQ!g5gT!D!KDgtsT|Z_X>MnsrVqocoXsb1vjLWH~CVDlV)j|
zMl<;^S(2i7)LeQhl)`nem<d~=6dh)AMeL3R4UeV6M%e0peU077?wYO3DUmnwSbU0o
zm2X}iY~IleJI50@A||Jaw=H7X2*U1aKyO(MEqPH^e+$p-4e0-(2K1KI;I*HUddj(b
z1;@Z)C;#T)emf_K)nlU>JjI@IzAU?nadFXX{xDmD)I~Obb;@Sv@whsmv|6Y-ydrgs
zeNl@ds%}Ih_Jh1X?yJNGY(*tmGHWZ=F2P62Dq8L*TlL&<y4wSS6`g}rOgDTqMvC&C
zn1>0We=bLNvSLNA$t|MAg66AqE(UX)P~@}ardw5GxVlL4NeQM3-Qt;C#amnH5ohuL
zJ7=*%;2^!>|JF7zv``2FR!3U44}u_&D}~Pa_>VGVX{H{;G*t`-tG}zUsx8N=oTQCa
zIblx9X)e|zYN)Aqe(Lr05us|dq(=4+1==0Ce{B$;Wfs+^)w{a87Mcu%{{8T_9lABc
zzm|kvMJt6YJwKo^ueG%Pi}dB|CJnqx=Oimw@M>|<YcAK;s>gX&l%3~Q3SN>g?`DsW
z<~#&YxE{@w`HavgtHycHaOgAFCl+#c%q|qVx}kT@F7E3O56vmXA!9yeiYI6j+bkWS
zfAz3y6wMaXXp|^v)W3C}Dkh#y-55SvFI6Y<K*7;=j?h7PUv?>Ln-juL@-@m*-W{}w
zmA?F-rT2#bW%V!9bdP)Mvs@lxoyERrHKz)L_4y=IA=Whf@CqD<ww95D084UFS<w;Q
zRa}W=GRV8SAU4mMN?0R(*i~2$ls~$1f3aG>1a#EeKBN0Xr7<y%c=<dwz!${y{?V)<
z>&9BrDE_9xgLIegGizvV9o9umjbnEa5%z$~yEruxq9poj|3|a+SE=gbi^rsA|MxvA
z%+u2yr4iSvqq*d_fy_xsxujW#I%lOIIX1wI$yTRUXX7(>2tD2(F)lpG2R<wF5g-UW
z^=T*6cKk9v`WJ*azGIVdZ4&}8HnLr!1pzaYAqf<-w_?r;0Wy;z2^6!MZR-jGGC8w{
zcz^~0H<KX=6SEtC*9ieKv-5~h1`ag}FHB`_XLM*FF*h?glTnX10&+N$ijN|Hxzsv#
z3fNd`b;zBWb7po(u`((sXH`~~tg=Sg;FL{@Oi;K%oK;kmNl{eZ84Oh*QW%BcD@=?g
zE9X`8PEk-XN97{cu~s>(X^m5iMJ)%#Sl?!&nD8ve$^~3wQp^fprwS131HMl%Lgrz9
z;HVe|g>03_yllMkz-K(idsvBo#XT%FiIs<;mXh)r*GQFz`DB9%;sy-%u-;?wfO!$V
z!BI-tslf0G#ssXB6C8sJhHyXOiVpz}T5Btq<}4l>;l9Joh|dgs6jvfXd$^9+L<BTq
zv50jNA_^B>g7JX3l!L+)m)TTNLX@1sAKT;={+KW+AykfxO5!?<OA;b~lT^yMVjT$~
zXRi<v_6Tw!T$8Kd3diUazTyNY@hHximoYy}@C<+%cZC!$kprz>B4;J41b?j&mV;ms
zM>e6dpx3h(>JUL*&PJ&Hl1xkwuoCPd_(|?yokSjkfI$@Ev0%pc)(SCRBmo5(!xch`
z0bdF)5Ta)#=n`2=3|1_Ec*j}+&S3z4ypcN~NLUo6L&5{CXfca&p~jFsR(6CzmUSXn
z5`BT*D6zFJsR))Z0AUO>t%#SQ5et`M6mdduF^P&XGbZs1v5J{OwYR70169A6zL~1}
zxjGC;pVzA1KUo~9$B*%KRloUk)~Nc`=zUYw&!&?_Gg-`45?ob(zi#H!^VztWBd3-(
zer%3UMo*^~>d;6cS`i5yRhT}*JjitkyIT3?c|ZU1E9@p6L0L3jBUdNqr>95TkZy?#
zA!-XT6hPTo?I7g>DCMkO=o+Bl`RR0aa5fq@%3aQRHCim1*+kLh$L}r{FAf%?MWgKU
zMpf@4SV{uCFNMf|UPYFqSggjv)@lrP`D*N?aID5s!LG*8o{cL!6q8qDB)+*CJ1G)Z
zV=zst^^p~HxjtN~U(KfDgJz));m7lRRljL27V0`My_C}i=M;vKPO+HvF7%4_XthO+
zDZz3GI>LYwEP1P$(|r-&A+JSPhsc%)+C;X6A}^ZNeJ7QFdxb%Dz7xT2gJ3t1U{_AC
z+kxOdEF01ZFVGS!1*5a`4?=K3c6P|?tpo#!WWP=%yJ18!7ZcfquBxs~DZ^3(IcpXA
zj^wlnk=~&%``X#mA#F=(-b&!L5C)Rw-8yOB4kOJ|F=<`s?b+9d<wRP#rV=bVKP}x{
z36?l&cJ3j6GPO-;M<gxMJ7U<D*=PsT#yftX7y_+}A(&mnP(PVWrda1t_6TA}xNIlZ
zp1MR;_0#F>xS1^%G)MLK^~?GhJ|JF4V!;@ev&lLj1bCh{(sjqA8QTKvoKSrQcX0l8
zfi>$NP9`7fCwqI#C)7{Ii<9Z3KB#|s{ZjtF`hBr~IQzD)=Zn$g9iFP2<MaCM^wV)Y
z{`=zXbo!zG<~Q{5gm(ICSUSwurRLEQqbb)$wp+wndiY?CPJGX{N>6Fan_63*e|=b=
zGF&WzVn?8TPbbueb?AgLmzhAgeu<ZAJ3U)1b*F1;cUkQYs#Ujd(sp2~#*Mli%j$Nr
zYpEK4&7E@8qGm>H6`Vnxg(xUlO-{D@USpfPo9^cj{>P6W^?0twf1WR;|Ic6NqYura
zv(Z^Io7ZQflgVi_pFbK;Cx4v32a%87&ql{5@Jyc_zw2g1EPo@#9o|U2SWlV*m0?ZN
zwg~B+Y$I|Jmb2F`aS_%<uh*at+>mziqTSnnv|nevxi&Cg60he=qFwUkCZNd`tEvmV
zT~&QpAEG8sMOgMIh=$6rxcV}vvy4}7F2YiFI$%HeC3RJ>lf7xT25Kp9XekfWQZCn0
z-a$*fSk#if9cv%fq0dT`%CH_i8Q<Hvm7G)NzNT4D7jwS;AcwE!`jZ^IZpvmL-PVME
zb-v~7b`armLR`xD8uoU|d%<WD@eYn<V4IAVgXjAq@?I&j8|{#_b|6Kzylq&+-hMvZ
z5B3JvLadx7r^1DiliE061}4wi`+Q%gAX_`=f{viAq4q|(-6?cB>+6%1p<1GiU9crH
zP)k(4DO<z-N4occJ)`ALu?&nJT_>A={x_$R?E|s4M6QpQw{ND}vRE%OotMN-%^9qX
zys3?{-=OTJ8y#BG4&q2Xuii}9Y88TsoaWEV_gWF}M7~@4+bnDoMvGkemD}E&ac+^!
zo%=ZJ;s%?}4`tJp|ERczU7bWbO@SVw2A9RR(@VG0v$vP-ret9nZu^aLD51O~S-RN_
zC6srl-Q0Ja6<IsuK5xd|(nPg`++T`s59_}(<`2b_acvU<G&i$Qmi7jd5myznTb&aI
z0Wp$Y6tjb)as>f4v-YUE1_3j(v9HAn0Wy;z2@|u5x<(2DI60HCuN1T9#C!??HnU^T
z@&uF7#1yk>)F}u7Gn28e6tkz?k_waYPCv7F=i&#G@lF#1H!v`lQQrnBf2CE+Zrd;r
zyyq);q>y;S_X7nAG(gj$XWyD0R9kk0+Oi?Zsr&a`ijr*xbb_KM>M^^T-I-l6vL=jt
zxnbk^Fu%Ef<d%5wMi??*5e`h?D@His%7NvA7;QmFP3Bwjo&J8V+N$_5|91Z<+-2Mp
zWIcjS8uTy*cw)d?=|X@7f2}Q<aZp~7`4UmTBI+s~Z$Jp1X0E$prj({-6HY_R{l485
z!qH>BE&F;mKJIrB)<0MA;%n7)^%R82wm#nBjn!CSy$A`O<GbkthkY><mM+V_S_Ynh
z*{NnJ!5T-5(tu5g#QLg50xuy|wfR%bq~x^h<5`u{C&FFVm+R_oe?&CP*agWm%@sz0
zmOlAVn-Rl-WD+BWwys8iOxt?OX;Eb_lAKRWvl!(~j)oIpnNC8E8Ho)rm6iA^7caqR
z`I-yQ8)J%+jDhnhogiE2=ODP0jIP^qSyxSg8uszYZk0edT^*W5f%k)J2AN(8jn>*6
zPNFmL&c9Y2Pbo$}f1<)~%mxy4%BK;z#%VCvvG-;pA)^hTP1DqX*42!D3e{M;shcWZ
zbyeA(4QOfI#B=Nfy1Z_y#n6ZA#RxAzJClBKpDl)Q`A@}2hJ8YhB&nmK1Idx@p+i;T
zvt2x&m{iU3RWVI<929pnjIg6SELV8?mQV^;jQ0FLgu;Ahf0P1s9>?39n~|Ob9KsoA
zpbU@5pFyHwb11q+(wx@Yx~rRYj=7S!976&QUhC_VukrOn<;s{#a8^y2cjj7OpKA-8
z8*%}<&F~(s&V0Dc@Ihzu39`@9kw(8uM}fy*$pz@VSQ18|`csEK<h0`6f)&Bi7QB=Z
zIsA0uwr`_kKcfL9?H1*x%&lo-z%i3lj|S!RV{S`&wA#r;EW-;6bf;EA0GxjFL?{6Q
zchyWYfwI^L5;j47p5Ochpr7C%lW}bm0yQz0;KT+d4>&k93NK7$ZfA68ATu#Am(eo<
zDSz!-O^+P65xvi^;4kPUi{F6YgQLi&0EX;C5<v$=*%$^4Ns!lp^Y8Os6}yL{nUz|z
zk|G2?Y&DxK7RjpOt0H?gq~g2_skxr<=q^P3WmL6<_v}RY9$jn=&+Jl*covtX;#pm;
zf@gCj)I-SPO2K>au1UaCTn`1$=sM~`hJP&YF;Kx@C>WtYim<vseDsiAI0wu}n`4iM
zpd&zZsO*r?qf$i202RV(Bw=l14SF_V4PKg(-~?l!5V0DurHPbu2o39t9s{<5LWcO}
zQRu8`P6}t&QB%1nj3>=Qa)+FjRXhrvHQB{LMfK{U2qgD}0@nmtF?n&~0}5ytynkRQ
z2*YY)=Exq*C9(!`N@Y!Pu?lM-utHnn8%z-VK``CeU<e7`#qP13j;2mi1#u}rKN6Bl
zk}zn1!GuG=3Mq1kP*LCzp}CYeMCd4#a-eEb4y*|%a0rPmRTx=>hKC8DHWaXAf%#MC
zDg<&mhrs%?=Md4Oz#;IGg9Jzx6n_e9qRWx$kJ;r^I|^vZ7zeBsDiS`hcsw|hNC!(~
zgYX6-3Bp^d2f^66b2zNCL}*S@g!g6EWLG_x2IoeBy($V2CUC48;co&Lua)!1s$f-^
z6i(i9mxI6$TH#!vg6<(h;P1WA+R#PtL0ARb`U)xPy+PoTLKla(qOJs%B7YW2&ymQ!
z7$Zna`S9q`;pWHxyt#EZ-@o|j_Hgs3*RSqwU)}xcXglwo9&VoA{`&g2w=Zvh)h(!1
zf4TkV&o91x{kwbSQBh#(+U5BHBHp4ew~X?A^Noss?4AYP*-zcgU;p-ZG|N)qj@9P{
z>V5UwFTXs$pEoLRsbS%s*?+|hH7@kOnb~1wzr23?!<!c`Z(&jG^ZkpvyW6*~U}t^(
z^Y3@x{c!i<?iTiE#o^`&l;IvdayL&1AXa<xByfAL<&=mb+ndlN+Z&Lk>kH;^^Znb`
zFMqhbbI&mF<0tOs$J^iU+_sj>HpuDB23fAPL5}-vaLQ|H&C-@CX@4JcOkwGDCo@2D
z3Gzt|HYxwyE+;mdta-HZwFWEU++h7$gB8EuV5hvp22iWKV}l2)b(g>2w_&bUYdKSE
zN&D1V{h3<xN2oPlz@iuy#HfAD$@_&7{ZrcDqQ`!AEUNL$1~pu3gDU%NaLT*dAT7D1
zeat!Kr6L#G#hfHA4S%ZI#f%WTg#P(}>;AAa8&{axjWUyvG0GF9Mrm^tBnD|MBTI~H
z8Og@#GLd=WT1H~H@*sx_^<mD_<ji@Rzt(wL*zY{2ydOv=E-~Y5u|zNXn30Mv%u&BU
z<}n+6mvJY@*kR~X@A=Ho()zh~)T_OteS~+kkMWKR%s6N)(tq3k)Zq6Rd3FRQlEkSm
zV$FUYtozl$y6+3t4+h;m3F4Is5%13x(ymrW-|yb1ydQAyi_F<C4SLzf9Q~3)-^ZLv
zUwo9E%&9F%u6FUp+Lpd|7BROa$GVSM5D9W<JDGi5LM&ed7$yL?4<zmbhB*=(0smS@
z4`(T&gncQZNPl?8(RqO1>*(+Bj=)_q+_COtMvCZT-p8E0EbYP;y2#8!SiX=yTx6Eq
zG3UL^kz44Kde|OMnmpzt#N2Z#xtx$*>tS+sAtEBzdYJ6L5P669{ZM+D`5q{}$eev#
zcx$<fIl;q9Py3i9=0)~OmXL53N?!|zodDP5R_}}64}W*Lc<yrXYL|=gi=;C<(#DgB
zFe(4!(6}l5L&`f6=WgEo^shH>fBJ`ew$1tG@$J8VetG-!yKkRU)U#B)i@q$?v6KV$
z(Re@BO3q7mE!2frE{hC4qvS{u$m<dCafSiM^TV@>h#v6dCyb03-1&WjeUWb@Uflq_
zB1%?UynhF^njVo0D94f4+EXe^g3K)0{qgrj|NhYWADaC?(s*ipDMTqTv}%epEdaAz
z!||!O)&elA0{e=qz@@^ke!w7pTureM|9V>ZEie$HIuS5<eUPP<$nK4dR&Ib!!Wu!c
zk)tK>+Q1<+t+rVxt;}s*3>}?v^;0>I(s<8(2!Ay^9%USnfUuc!V-Kqx{j|35BeK4C
zAaz{(ZM<wxmFrGfX{yBOt<AK=68?zuP2aDgn#Z5e;DzC);54w(QPs6akBMcSIdY8E
zFbziyRv>MPgEPTONBab}+ti27jcXOoFXy9Js2hIEwNb{n#vSLWC~c}rn>^>cF6w-N
zR)0gmMGbZ=rC8}9Tl?sxwN+=nDyP#H+L6rk-!2+^JC~>B-15cp9vXr<gLeDa&bvg9
z$Neqy*rzQgT~F((r=^U(r&AQ$bJhoTZbSsN@}NO;AET8S&pFL4>I6yW`l!B_6*qF#
zoXM!#%xG2oFq+ks2AyQil$M_Vf=_hn@qei5+eYVJW3Qgk<~g@>8bl{L9!*_xP@n?;
zN})#HPn#jx4m$XU>}?D~F&kHP8G`K&Q@bj5R0V^)_r7`U&=axRM3~h3C{8V4g+l~S
zz(zrORxBmRSUJZ)EkA&o9HUJNQGcQtF{O=i1rOtp&|^x~D5bE0$OZiDap)-zPJdo=
z6um})J|z?T3R`=n>l@FItP(~U(GI=3r?=@SV_c<-YbO;Y^=%RJg3LO`bD}C0JS;es
zqc8@}JVV)5Up(kgQsYvLXXZDag!3^x1Q<*j*HIYY)tSwut(?6-EA62OGhVxVT(=!U
zm0Ye}$2-<c%*Xe6(_CcbFOiJ%o`0>%Q|ACJrN*I4Ws0=YX_6y)bv>-*q99i2hE<ae
z1+<EUs%oNyadZo2rN!hFBos)*_-j9$@939a{g}8|x+0Tea7!8(6{RQu(-Tb$f@m1F
zp%n9qMgVo651`egvZOeAPFL+mRgqEITqkdeXKA2jT=7~<aKO25p6o$tv47%J;+{X5
zWX!HT$Dv^=MhuIJW<X6vNA8uWy{c&_`C_qCy(X?^V&uzREueC&&e9W;ZV_zc$TD&g
zi%_x+zvVZwPI6lEya-*M3QOiIQ#qRPH;$n|tCgdSHizGh+c=_z$f#-iFv!$u3(&G&
zTXaPrZ4Z?gV~*j8ZI+XzPJe$-ny$wjHGM8yYEZmb`Z>6f#8VP~!?;)-IFn*n&!%j;
zr6uPgD!FKD(7@2tIGBIYEK<YKJ9}NpnMSX4tV?K_qt{?Wt2WI_^$a7t-l<3~u%8nH
z63;yhsKn_6O%he8^`>#dT&Uwv16=nSx@=8}_jZ>3DxV>F(*(ZBmVY31wFET+t&U>^
zbv<u2qerb+GRI%e!6y7xjCrX<g`A{z)<Yruvkp5(OBzBLeDFG;9Y(Hgy^zw)!%N~|
zms9+$Eb9S7ZQW2+ZE4#qWc8Au-lK64BlDVUByJM|&q>MAHW5d%Hq{QmnL*_<1I~F6
z`^o|5xPZ|y`>zdf27g^sPyTuZJrbST%BG};P?KY{cD-SkXwrk$sHse;s%>h_0rd^h
zSKEr-L^N-Ko_w(e-Bv++697cFsH}3V-#lX092fnDbmLQsbX|`|Q&mynvl>R(jHx^)
zN~-*!y5=KVBF@H;rq-ce)?or^yti#yM^0<!FZGH0K>4mwVSj6}1z1@rBgZkZ;9F83
z=8q2{w`=BGMwxilMoNR3iejK52lFE)_el?tic`v8_(=+9*sA|g!F-Ef`$czHp}9iT
zO#r<FovB7K=2+czxV`lyB6H`2<0<&!!>$vI&gb!m&{^hv7ZoLFWXOHoor&JAB)#<E
zVW+8kYCLIHZ-1Mw=%H7z(yn)JQ60)yyr!T<PyGBL83ycn{ifjJgC?a(Ax*<rO?oR-
zlgg)Vi=sB0;Sog?yN~o#bIF954ZM0sV4PtlT<IzB-l|AeN7BmMp)`^=y;7r=O3>S^
zz=c$=sfEI6HZ0LwNrvR4hGt0PDX!FPj=Y^G)d_jWVSgb?seM~%wXWY`TGFeLxV1fm
z4w)0>NLfv1l<zHR@aj!7ecgn`k8>^)imC@cy*yRU6lA;OXf>%$(hB{?Lb29e2axpx
z(hzSv$*vW$KXy}Ex@`01EYpcT=G7d(Oxd@sPyUq)z@_P<mXB?^48n@y@O-N?ZYh=O
z9WgHuTR7P6cUfnprZ=K?_iMMhM#(X^Mb-21)_L#Wd^>IOW|}oY95rA0t^4tgT@y0%
zg0Jb;{lCX~f?AV7)Dr?WHkZLT0TUB4FgP~~FHB`_XLM*XATl&KF*uh|^aB+HHZU_V
zlTqg<f3&)FR9s8eK8(A&r*U_e;O_1uSmQMA?(Xgm!5xBIfDqi>T@u^_eB{n==H8k0
z{`;+7-KU?ePwm=OXH}o3Bvn>p6fw0k21?q2oEce}Soi?)3aWOtMj%!eMo~K(Qve$i
z3kwGVC8d}n(8$@+4kT{m4CDiFJ6iyhOq|~xe;omAEG)bTlmICp2<Z5(GzA!Y02F}E
zM(Q5+Kvn>a(O*E>&dHh4*vRQ!4Fs86f`GK|E@F1}9*&mg7S4ZSuro6LiS)-?lnEef
zWMXaS=45RNFantZWSJD00E%{Q??OuejU5PJ474z^F$36{0n~xo01Y(>RW*Q=s*;AX
ze;O^*dtfyedwV;_|Hnm4O<hBZ0U$1-s4f8jYBB(%G}P4pe5wOM@BGaf0E+7G`agNz
z4ga_+NT`db>nKaGGXEI^fEC~hbab-(llFhOQN1$*{7voM)y&b(_OAp08VhG<dp>4n
zH#avXa~CIPCOb!SCVQK|_^Df1Isx45e;lm=?^j2l4e+nRxPVOG%js+Z{8xZKQv#5;
zGy#H~fPb7M?f#{-eJ|y^)4SaHKg8Y(;ru72&A-e6PC(#)rLiz_`pZ{dSy>)nYh(#>
z27-)0ChvyMM$Rry0K>mz?{A<f^}h%L0b(wWj(>6}{9EPtpEUobE^7BaGJP8_e;*^a
z|D7=-kc*S&KWg*e!#1%4IaxY6JN+vn5MX9$1N_6@>Cc>5g8q^zh$zZPN~ozb%D*=r
zh*81ry*eN!XLskntpCIl5tru!@UU<JSa~@BEbmP!0WuY{v$cI^?S$~BeBzexb#k_I
z^kDv<uC@l*xq-a?S88SnGBx{Ce|1wAdu9!grGpDlM*RQTzKan4mYD;c0W1KZ0|4l5
zV!`|;)nA?RN6h+1{9XbdFMB(CfSHkv6VS)f4ETOQ@NzP81p=HMU4TAb|5W@pLSW?v
zm|B`Rzc=~&LP7W|x(vw74#4{_@jH`$tN!2g)BLqaY2R0<sU67117Hd?e?wqav~zxM
z2AcnW*4Y2#l60}LQ8cmz()@Qp|JTaM*3!n~zwQ3VL<{(bD$W1lZ0RIv=?*kiwsbbJ
z_*Yf`C6{qFdT)9Wkhu-;eMbHgY5ZA7Ht!AlzUf&0*|PwQtQ=hbqkHc~6KfFA$qB&q
zFE`+O4gQDkd*T1E1u!e?f9j};$<Y5#yZmJ&0Wz^OwFH?1*f_ZWMvjg~9tbS&J;27v
z3GiZlZ)H=U`(I50U}gf@IlsFA>|LCF0A_ZM2!AG$ixa>s@<;S9#0_8;`w!w~0WeGc
zjo1Lp(tjfk0JH4h=-p4@KZxhuQuS}d4q#UM58{2dH2NFy0GN&ce@46jW|RLQR+jhl
zrvHGf0A}Dn;Cm9Yf57)F=Kp~2^ep}ZIo=0p;bCt91pUL}U1s?Y$OT}w`UiX`X7dmD
z&dm02$okIgAE8*^nc4jVzB9A`JNJ8Fd!VDG-9LuH`p(YrAMl-u(?8(5hx0$+d&OM-
z0pFRq{temQskr|Gf4)=k_zV7bD=GikL;u<$SpM#<|95lw3#&Oh+F1j&EKT2Utp6}k
zFmiUZbk}2fU*D|n^7q%jzZv{j0?NO)rhj;girTq*F>>&50T|hMIRUI(EZpw{U}yLF
zFJF^??el-_E$@rq-}uia3jhM$fhGvc3w9>_!B%N4q2<03e??Oj(3HGPXH__Y+Oi2y
z%b8Q1gm~ilJ7hqi;()LISyaV#^3r?;z9|8qQf<m$Y@64Ow&d!`8&ehGT_axwUqTcK
zk<mO&CXK)>g(d%rZZg_q*}OuXGLD(7_Jnp4fX3*F7;k6KV+`BG8~Rl$nSMq4S^>0M
z$sB7dmZJ@ZfBO;|K^NiDR2R7O+ap$7v{ApvGTp3UVJOb1ER20$51KB0TA}*qrkaH#
zQ<&)5J|aR}H5w3-hI>Hm9d_0dWVH+lN2235QDi1E=fQ|6;c>Q*FIn;rbOtu7jYSr|
zFk&->nl9eO=BIPSLEm7aK5G%KtHpYG(NGJV@^l-2e+a}qoYMFVsaQ3}yLyB8l2_zd
z7ncSAUkFyjq{F$Ei*n?c|MjQ^pI7`z3>T>abPpl2T?Xi5qbmU#{TPWphBb@u>@~tN
z#fd5r8#EIY?I|Yw=o<d<1KP27rOHh=$M}dmN)@-&j=v)k`--EHP&8v8UyT;@t@P^0
zhk5_he^R|!aAm5HTfR+hP6ReVDuG8HTDpx;MNxSC{#uqV)YhGQlZ_VgFJgnVg#!RC
zoH6{RKJmMh@R7=IP04A6c}&hR-f^1T%Oi^yTAc`<lL_ta@K6fgG=&4bjX5toBu!B?
z=tT_?TymL9QP5{r^d1i)9TFLZu3u&e-`I%OfA7%gFZ%oTf!`yFb64G+3iERj0h~ws
zyT=rd)@e;if#;<3GrA~5i<fLo3z;5MA#;sQ_mu$|i|T{@P6hbSFXfMzJLv0^6Di2m
zMALyVizU$0cNbk914EV!S%>)wrD2_^ICihnsOx>z51VY!qucdp)LS}QCnDc2dhcXJ
ze-83t#Q5E(ebnrsp!CPd9@}gK0F!%2t)(w<%VbHjJb9vpc}hlK=E?#KL?CrIrxsS}
zYqWLM$HT#C?0={2zEl&cfI;bZJGL?fmhRXx_fu)^Z77oq^mY!H$mN;4gqTp-Ck=as
zRzI^F3N?Ol9k&0DD5<M<bu}M=@v@!Se^v~eixeNCuR@W>KqlOBM)-*Z$&V)(W^YI$
zIezc%M|(5t8LKL>i5?a<&t>8)3B~bD_zhoL1iV;|C$`o1Yi~$0&5n#z_q2VkIo~3)
z=T3$M=vFadVOTfgvQBjkTxgmPMXM)_&R#cXAGXyXjR`PlA{h+PbmT)h_y(e4f9_Wz
za@XQrG)GZbHOS#mtmxXJ+k)Y=!spYpRRv$;rD3R;p>i$7K%71n^(?}J{>LiHn0qyu
zw38-%{K6BYz+V^14qp$7_9H?E<-7$7<s4Yb<<FDIHjyUcwuB8-`Io>NH!zTT7}oYt
zYTKGpyn^Yw?Bi66@{i+&iK-*oe^2~p!ZkH0>&4}+YOV;xR{Nb+3Ag)hw@bu~Bzl4q
zT&-pwz%`BmTc50^_>iJoXosq#Wcx4i;0UgIz=T*bU?pxMq#Zm8k4Y30J~(q(1|98~
zBEib55?y<!+T}mHj1k8t!;WyF@wUvQEprTC5XlBvi|h&6Fr#-C2BF;+e~d)E5jjz&
zTJF|R@pdCj*echaxTyxnbiVldB9IU3P&YjtAB5edX|aEv;oiG5DPJ<24HnC%lJBS3
zjE~$s?%1nBSpL+$FG%yV!8}@!qY3jXDAWf6woCfe-yA1e9OJkDc)RgKeOg~eWg$W3
zk8c>MNHISw{2JJZ7_Ji$e?b@a>2t?^r(cGY15n5pIEj4CHY|W%yDlB>eIjZG_3lcf
zRK4K+oT8E?1)Xxg1~^NGW8=3;yI-RPacS?2P*DluQGv0*!nhwm7$*B0d;X_Odrc&S
z#;h0eNI0E#EvSqi6(V^WcC|%f#TVOPtY4-x_GL16V3~p)&ZQrKf4`rPLEoIbAF}2G
zfO`f*4$YLGNymviJOjLhU>8UGVKutHIC)&npkGy)N^7yHfT7U1E6nXiA0F@33Hw>u
zZ={LSkAy}{L3B5l^6K7Tj)btq%p*$t4)vy@RooRe-fc{r8D~{B`&3$`i363o4e{+M
z>{p;i_8rQ#M5Albe+(k}G2HSHzCny&*2c5hM@aov9*ZxQwu?@VEMj170%twtgzM;D
ze7RNloDZqeZYN~R`*W0btQ@V^MFC^j?fD|-{)1h8OntZR)=dPuq)1q+`h>$tejz-N
zQPGMX7E`nOAtqZl-)VTgEFPb|><1}ZdSU~fb((dgdq4^Pe`F-<2xBGgiQ(9@__Yq4
zslo$Fv8McL+)PSg84P?Q<V>fY`YP_v{RI5K70Dr8=KLfRwvKnzS<l!S*N81O>K@js
zqA+Cn6wPcx?Z35*g~xsGm5HC_b`CAwnNi*TQTa$VyZQ`bkQ#fjtYpJi_98jJh87pu
zs0E$V4sLOQe>6Qi3pCYxARFUM@ny2C;5B>?%|d8aNsUsl1f#Es4A2A$4nY6Myd9_5
zXV6vLXqzo9aB~$L%GkKpcqrfAE?GKek~zqJM)7G9*u}uk->B+{|D`&e`s?j#`QYnB
z^y4*+S@n;Qr_uQJ2cj%c^WsXtBZe9VG$xo)sW$O~e|rg3=~vaLJo*@a0g(VET{R@c
zu|tN%>%m^ZZ7iz~B94w<n1-RX_4E1@TxbgR9#OhwwKu@W1M9v{_gkj7q>%!oe_o1v
zOu<#|?{P%<GEk0ynDaEky^m<~)U8+iJbyaeHIGx*(>*{aN{|j~%*x3C<;$wT&!Cmz
zl%(L#e+_SpqSxHyt4sx;D3H<Ux)DvpRJA<wdb7T)ZOQCQdyToV<fD_#iEJT85S%E5
z{;WT>lN`ySL)>&4Ijt-{PAgt^woW*#jcSG>Gi^B=JmHhLA!d5*`@VASaeH~RE*Vo0
z0WVwfN!8c1?J2Bfw5>XI68X%q5k-U$NjGOjf3M0Nya!%pudsdg(@b111xcU}3|wg&
z3f$<8EQ?v@%?{H1aJgSgvUmcaoPrGlazt2Iu>hfHRID*A`36T>ukPzuSZIut{%3#e
zI{mL>bQJ3!s@9*DR5x&%3a((ujq*!WS-(X!MH66r{#;`4TJtDN6^+Ug>Q>Tq`}}D^
zf2*-VKbdK&*J#WaQbnNlnewOUyp?K)F)}SSAA#x*APZj;IW*zxkeL9r4o45WIpMs1
zP@HTRr(#2TYb0mCNi%1oQ2}6FzVd!AO5r+-E*r)uvvjQU;}QnKft8h2xbZ034=UEM
zo(0u4E=^+Ua(2DWf*_fi%k-`n%Bb&2f30leTU`U9<<xHv+>DAO2ETvtjMz8OgH%qr
zHQ9!+f}v&-p**mLQ|g9`5OeXCKqMJwUCREqMCdYl@Zu}YYL1=&d0;^#!V?30`)8g?
zYO2V#)M&TK3gr*vwWFjvZiF$zvM@hH9~zl(%?>dtz*&9>3Ti=9i1RA8g!|yTfAw7y
zKWZ_~6i_NRERY=2i{>JcvJZ-NwsJr#t3ND87;qL)qnX0Ws`l|bFW7?kh#_o-WMonq
z?h_e72&*4FLLresHns(de1sB5HKTzk5)k2DQf&RrTvraX`^SQ7FvJ{jI1G^8Yn#yI
z^kt!_q^z-)?qqL|B%jPiFj}?)e_-7^=PxDa{Gn0XoD>s(F$OHc)py~{MQcA}t%Pkj
zRP)vJWaOqVV^(rO_w^sS(K$ts!|z;@1sDJ56C2hZ%EiSEh<-sQVZ&m6#zAforPB_^
zCXlC9P1%I8X}KX{V(?`drGyPi6bK7cesH8xR3+9|@4Li{58R>FLQ$9df9{@a5_Yg@
z?w#h@M0IL&7YgUIP0vB9^;;0GP_#iso?_g2rW6{K6%h_JD`>({rYp1Rdp=Ta%@9m~
zWnD`GjyCz8cEOtE253@t&hEy-PfwP7XKtNXVLUV}54Wgl(jSZN=SJNz4}zALxM;pj
zixe8vv(Fg0`?(E=9IwkUe`VeUw(OKjNqq{1E`drUm0H;Y-@_mTPm))#EAyHb;+<u?
z#~5DM1I{g~?$xk{rYKPdfCzVTEQ1IVonOILLYARr$Wy&bAKDyrE9-XkH_uXaH-w2e
zHhp>t+@owU5Q@=1>@UBNmqbXg0i%aluA@vN0Do$HYf!Y>wHEUrf5GfM3|;ep#Hj~7
zwQ?V1>fNc;0b?&eB{36b@6ld|pe%D0ci%_OlYh_vX0bd_7m|C`g$pnziJLAl(5<ur
zdqQjm4d@-K%*{NI0?u|xq1a#E4{(_Q?a!zv!{prGGc4+N>u1~$RN7N2&K<%w`t-l2
z4VtXUtqDmpL~{$le-#LjyDfUGd_X?<4WEF3*}!ACsK4th0%!wZ3F}Us)B7ql>_BRw
z;ayBPlh^Ch;M+*_KqfII+80F{e7<7nOrk{crPT(kyI0`9kv|~f#bsDdC}3V}H{mOb
ztbr#)KtTGVmQT)tn!NW4jvcV^0a&VPU4fpfV$)g$UB4U2fBBQrj>O1+#O$#T#7m)w
zX8N<FG#pYJo?nqRmE=AYCcmttFxnE2LIr$VJt`feh56p&lcqC8%4f%A=sirj@YSza
zZR&{ZL=O@ZHVq(vMNYnn8fvzXU#}F+ZcJ^m+R_v-rEduriGp7sTahY0P8<S9YKp6%
z&=a3Uqg_qTe}!a$l6+JjUq6uVBkqj7=Ql(Qe<RBZJE>u#1nZowcfblWwxaj*jm93U
z_eBW>^;iD1ez6$=(ESN18eGDh2OU5mH6YgBJc(CTl)@p|Yh)J*&2jtdY9h$u=CC)H
z^n(uEM;V!wC_@ldSZRGz7(o!}Ye4oI6)E!JFk<*%e+t{IH9K_^2YHOfoW3*~vXl{&
zNq&X~Y36L+XYY8!K${d9UH(~fSAK5AIs#9B@L)$i;7>`AqcZayd3a#9@58yjL)&F{
zT=6CAi+yk6gqu0mD9nPrV&n7TmWsF(cMkX3Fy>r>GmPQeJ=t&El6EHKPrLg4xSi}~
znIdoae*kFb(-yA%PHQeH74;wEl=<GyuNAa3{#58q)ml-~>oQutS6kRe%e{BPl*1rs
z<!(NtG6P}sc+8uRnP-`2x++@;gWj>}vJa<#d#SSwF=Bl@`3?sf#es=1ktu7faQrEC
z4ueZ^C*m1)dQ`tp!QZUz{9N%<fx{xcv`qIIe=AY?B<{v3F5>5yOPI^*lp8sP5gmq@
z`u1==KiJ$MIp^(cPWmFU8u7DOuaWf&)_HQ$!lQeMP5EX(O1{YP4eG|cR~g;bl_j92
z)CAb_YwzG`v5mE7>S|X3XAmCN%7rU`r2$L!eTphV0NL$%H?p60Z(}2NGV_zxkOTrK
ze_zOO?U<VuJ_<WP!8%L=ZiD$3qxUfKi?)1mmr~Ge-7X$4rQOs5_8E-+Tq(*tlO&Q6
zRZ^#-M!e-bB7Oh?6gwrNSD^#B+)xgV-9cCNC+8CKiEC?a=nH)pCWiUsDLri5kGdgc
zgRu}#%KWwB`nO#RQet-&&LX`lxS?TSe`dtqI~KeC6GkYuIrxsXUx6vqg7^X<XUu3>
zkF+)xgpCTngFTY#Omad|v&3IvnYruXs4Dzouy4zh)U1_EerbA8y}9uTQ&dP46Y0fS
z9}hGlp=gG~!?wdR!a?VTdC4jpy3>+=V>sqWz-FvuFPqaI21i4ye<99*nzYCle<fKy
zp7K2zwUIvO3Rl=qIkPUj;D19Cqb}CkKTxTJ;U0nO=`45}BdRO1eYF`1&i`2^CsINf
z#mn;ia0cderdO5~oGeoktd^t<_4YeXkC<#q1NK0a&C9t3=gWnZAxiu~m800L*|Ii7
zq%oddMGpyOQqZHc%Tqjc(rR@9f9E~0x}t=9n9e+LqIH!gkN;xGG#<l;4qhpmb5+MN
z95ab;S<d8Zuc&&BYr41s3m3&}BN~hqI_l~wi><f2*Jgiux4P-}%Mm_mDihST;E8nA
zxb{*@vc-XCquWpy&NQ(rjO^kPS2YAFw!1mG>rUhE1Hn?fC`=wO6?Sq?f2m&^I44zT
z6q|+HM$aZdyetN&X?b~IF-yw*MNce~R*HoX^`Z@tF3z<kt?XN)cmlESIC_QBt-`r)
zc%H~_j@M^Zfkkgz;vpw&xokBw$h-ACxIkx8oA$cYBY*M48E&U#dXeEzANwoPs%Z&W
z*lzHnFs2qu31Jr4BZ}4-e>`+72Ovl_gSQI56ihxf$negMV9w;^*l{Q)Nb|m?ZaA-J
zdDwk5f+*@+X*+4avE=nM$gwoSDQ~~(l$GjT!NSQQJG^8#o5&~Biz70lw9$|^=^Czs
z7qJ+uHG89up|#`jXi?IA^W}pL^t4g_tV++9N5VnHJR*F=(qg;;f9-EDdh&Z&Q|Lr;
z5zx9`?_s>IC=3xyGoy`zD@rE)DUH7dEhb8|9a^*~u>jIO(g`?_hWk)!m`EX{E3GqA
z>?qw{L1!z*0x#ElEuH^e#}615h;04aYop_XibArbGMUI60C9$1nCu3LY5s9W>SA{z
zkX_7*XMTIU3Gy*9e+M1kms#|dOVIX;zA!h`k6l+btw8Zsf0LoA;aAB@*Qm#vPnM-Y
z4WoNFG!;R)4R}(0%0>~F&a|VDv*I31n-`mzeJkc=j-2ia9{Zf#!ekqL$oWqhFVbqP
zfk;>etAWO8>t8guK1$CJ#FVMePbB(g7N#Wf*rFe71IRR%e`A=U5wC_vtPxVPL8ICa
zW91<fHF#mxm5AI`t(GHiA43+Z^+vE_-~KwYLsxmK&yIOVOOG!_3`ER+Qjojod<?aA
z&BBz;qGqDyuujt+EZQpOk&-D}ihwK&M>q_IC9xJH1;1!9*}z&Q=!x>)e^8HMDL1*l
z8<yvwa8S7)e{YL9u~Bj6wGKMctTFcf41;4Xqdc!zU%P?Gu+tGvIKTqp5)>D}vcsI4
zu2hf*uVpv!!B_W=N!*b~k1s)qnV1`#&LSMssa#{3Orsn&Pa{pULxz+>3*s>${x|?Z
z1_MI^p<I^<J&7Olz^KH)1X}?zyu|%D56}Ip5Wh8?f2`z_poNIul1%#RRjkZmM-jsl
zMl!<*=(%&722b@^Duzv^Y7C`}?03#2w}+xbsIbhMgGerztx7oq!v&PpXLZI-DtRN4
z2n)ycy!`OllV?A9R>_Tmb3P{ooCoJ1Ys?tL1FrFna6zJ`>PI<+w{3`3xU<-RBKlwU
zFgQZge|>6TC~2QuFsHCB*dN&Q&r|zsC7P%u4Mwrd7MR7k&aC9<=J!?POQTx6Y>}&@
z`!l|bl2zRyWQQcKbj{Yx*Z#grJm>Mt6sAb@olThMWWwn9bt!~WC@zOBMt*eP#Ft*f
z+H3bj6G_mnbkf#C+^&_f`!G%CIJQ9DU=p94f3c^r<czT~X66^u>`EDzvl}5Dy)x-n
zF!UCA$A;_z!P>0)9DhkUPDbp`3s<fAYf>J*30G5^*z+3AtgyP<kti-b0dnu|p-`9g
z$P`Gl_Ig;0&o&(XgfaW$0#hj$e=|<ED|8e!dSk~kT<k-^ak9mJkLb?`R{fQSme5cF
zf8@B=bO!J6coUnAm!AUph@pc%=NivOC6V_^cEvARN?a98rbFA+1j3|;(^HUJ^j@8K
zE*`O2?p;3L4tn#GET=}#tLTHyX((vtSSC0tu#qhp1dE~FGL6T(N5rHoR076-Tz`zX
zQ=K0YmA8dA><uslu~bflPG-ZG*1aBzf0#*P5seP(FKwu}f%B->!=oF14x`ZgdJCoQ
z@sS5BeCB)#Y8#K7PXFT|=MFVmc!n-#3Hp*zKCG#vyInuNaoqqkK+C^d!`D#wqd+1S
zud=h(Z4oh`oSMV8mkls{QNdjb=tg@Z#V3L+Lplq<19wJ_(6bm6gsC_)Yj`~8NS88x
z&VONi5y2Jz16Lxs<mb&NdK-W1v2=v$T0)A~d@?ecFgWzwa*cf3?QGlz4mrQGeZ#^y
zJba)IwU;xi)$HUK-l8i<t2aI-cq;9^pH3Ph0sSB8b7CN&R&gb|(X@RkFH1va43k-V
zRq;fTXAwOJiJf#N*32Inr`>UO#%u$%mVW~z!D~-_t95j(7UPPLUo`L&t35<&aL!@(
z$<Z;|xkHfY_E6W*_0vZ+GH73rKSg4yqLy_v45RPX`9CVKTZJd396C(&r$WfsGRqHu
zX#+7MTl5JxzdB8StpEgf=L93?FQx!EHDun>=|#HMHFDyS^a_@epgR0G1_Wck!GEDF
zLsQBkcO9s+hy4U1s^W0SD4YH6w^J&7kimyFjm5;H$QZT0qMw`{HXUp|#<;|O(1t@y
zm`-vh;#~xu+;j{`eAyaH*j~UI`CWiuh8)iM?H1LxQ9T10lC@!@r-)D)O~{0e7Dbf-
zyI*fHs;?zXI1ZM%D8ZBiT1*$dkAKqpxfs#eud#A<8L9<zW;ihu>MVNuDz4c|_7tXJ
z&-kdsF$YTmtk1y0XV<@-cQ#Os=Dveqv<#y@EMokD6v~}OjyIi09-M_@8K^?HBnoqO
z=5uRn%dRT`%!Dmakvd{;0c^?Y^6Jj18Z%Q?mr#>Tnj0_Xu@5#)&euwRNq->w&H<?-
zm&U^Eh}&(gL}4BG>DXzV0HdaAWg}L#^2~Zzf-|k)3VD4%a{Jq%tA<xi4Un+unC_wt
zPlyu1uq*|Umv`L_-feyLSqIF&?EyHQ!&~=J%R6MCv_ZccLdp2_vtc#c1Q_$-rG9%{
zj44TQwBE%;=S3jggNIgW!GCAB?H!KrEYw3ifem$VXD1KH4f8`6Gyagq?oEVQf+YkT
z3)Z<4O_=~$T(vV$cQXF88AjvDIN10pe()~JFy9tR+OH-#p;0yeSQOFY43E`FbEDHt
zg7i+-LG>|fW}nI#DF+e;t^)T=Wy5p|?bwastN7<1>Z-zySL;JEv456#s^+KVY?8=h
zpS?A8E08shE7)wbI&l%=1#>plgj(klcOu1Ew+9eZKaR@Oj0f#}z<d%T^g{P__k78+
zONzk_Le~^!)8vkm&Ce4?xk<zB8n2u?&+h^b&I}M2btS&ooB*aw;~m85X>m>`J}d50
z+}w3J4mD!Oex*Bb;(r<297D8G`+Uo^;}sqX1NmW{1#4cA%^@iu$)?VEr5%#6$9Z5D
zUXQUEE$S>=ax~@jW>fN<+vHdRx$6MuqnN&27%!ppY+OP3cCMh=>g<QNeMuv)72&ks
zUw^l7emla7AvD$3e?`k2F4C|}!XK6w3dzcm-Y$v{d>Z)JWPhr4Akg3lSVJ8NSQ|A%
zW*I3k$@!5ShsS{lqd;U6e06F&ZC|q8vIGV?4Zz?b=a($iU-;B@jmw2l@$8Ksy|lW;
zCvfN(6OP{|UMG*Y8OfbZhR^EA8XEdDSKKca?^8|APV?0#H#72k?)<6PZL$@FphlY%
z)=r6oS!43bG=J&@xDWeDY3DhXBKlUsp<dF%^AGa$<1lR+!n@CcMSykq-I;X!JLP-x
z628F4C2pwKvGfrL<-}-UjJOzNP&mn_sr$>|)rw4B1r#{Um?DA!wuL^vNUuZ{Ih!R&
zID#3euC(6?Yqf8^rCC@VQ}Fq{7vysb_BLbCVzuq9bbnedUJN}$x69c5h9TKv(-tz<
zvL++EQZeLvk<M4c%)S<aDxC_@nsrsb!3HeF(ToL-vcb`%SAJDW6ywi~mR00Fl7lgv
z7mVg^2v>p$1X2LXi-%2Kg%rf$Btlaoq@uY}={teE#(Ex9`ILlWTNV)rjW^z#vgj>|
zBowL<Qh(c(nXc~Orh^3+EZo^6hbEIM(T_XpBG3ejTBD#<@fx`YA9`Lth8p(x1kt{E
zqW|MyetLZOjdM|z)TAMdc-2+L#eM|N==$uT53COlnFCf8tE$Mw*yQyBotP&ldC~DV
zlMed&W+O3fDLBQin9|XeWPDp6fM12`U<C@Pnt#^)nqv%=KqjaAIkXP)K<Zn=UY^0v
zF2^*%pR>yow@oHi2&<ghYwXwp!m-OQtp)9G%s3Fc>GLt@$}G(z0$57ZzLof+ur^%0
zw(>48eR8E-+Yl~-ecCOb0}9sWfYf$P&j$0ye#C<9BSUl{bx-_0fQ7cK%Q)(_@?RkL
zh<`^nmGhV{k-5MbNdx!SXZr)T9u5WFV40PM24M!ikx?Kt#K)+l$sM+X!K>LtCeEha
znu0Z$!&}7-Xp|#cT@2wJk}r>xf;O#UT$*2f2@!DH;X6omSgSFq%PO=|!1I3S<ulI~
z&}fb-u#202G-jE<a<l5z9?imB4e>^>pnqtc)OGW8N4DCLYPzfanr%aX2Rb1tXqQbX
zeKd_-S1;(!jx2~M+w1aRyKfa8C`1jPM{4f=jPbmBAWdv8CXF_uU~Ho>*ZEK>UoUCo
zl5MU{@hCs7GLBCh%{UCG`|;S1l<JFeO61KVE(0fv{(1&`d6vAPB%a;0hm^?`iGL2;
zNl@l2VbJ<HY9~_Uh=L2gJT%<f=j+PFjl}kh^;=Tg>l8O*%pFGn<>xx@1a<V<Qskv7
zQA%N}Mf)V!gjhCaDWYjJY6{2jSDhK@q2<6fxR*DO5oZzd2c#c<@QDvW^3((z-;X5y
zrt8@$LQU0ljT#sc0<rApTl3>>mVc?VUte_**5EW4O1YDvsPRQEDrTuU*)I+#XMCb~
zp`KGmc8o&HW8w*$eD-I1M~!)(8TDj$$>fAmng<tF6R&!;m6#S(_a+5=xf@n}n|Pxo
z)r^0{CNvJ~By*?r%YSEeouFX|^j^N-a-UvFZe7Y+a+>T+G7o!@C7gHO6@SIzCXx_o
zG5v%eBj%7`{aw<%#4quH4yFBw=4sunr~hn?M3b>r)3_?t03ng8a&5&T55Q~~^ubFi
zXtiLdO}%H%HbtvVz|nphbG^(*vL#z)KowbhfyY>Q*+3QNpcdG|6o_0{tFiPl`%4$}
z)#Ik@=0OCLGDI%p+mYs1Tz`kIfu@>b<!?w4D#~5@+>+PoQ4_z!kHj^|N{$HK`_}P)
ze=V#31@)<0mUF9n{pWsjWk|URRC=?Px<;255T4cpi|wq>;ATYxP-ERHD(l)5AG}h$
zpW$4i@L=k-qvEvO3s5}h5RL&;qWlp%#jm|-KZJbK^2IAG*KGdChkrsZYcxFJGp_f?
z_OG(3{mY%|0u*9dUmsNo$1%rm2S1f%!Dt_DW)t$u(x~gnz!T&6=kL+%S?;{S9>ghs
zr|D#FKTM&%7=}u{qzLaFv>s`tj1PsgwQZf-8}*CgIC$eB53B5a3^wqfK5?b|jL|XR
zk)x2oP(rxn=y-bDOMjbz$&=f1XW#yL^`*d<7o<rmFT45eMpKlCbV6&OWqJqmi@uBS
z_T@)^A`MP$E!tiywJ!$&ITG{Rk$4JWd*ElIcbl^t7Y1smlu%p@C{AAHqkVc-A+FRN
zb6LAe`d&<>y;Zy+c<e-Bqd}z_4wceOj5}J37JI45hF1L<#D7e+aUZA#VK#m+H25aI
zF6-&hU*S6YgqL~iE5onQe4zd5-YiwT#IZDq#l29^wYf)+rAakD6BeJR7*CHrcCts_
z1TK7EY1bK?PM1JGdg&Vmzf2Nv$|t_mS9{W8ra?D>3*j(#Q~MwW8zlA}I<DP6<gJwa
zV76)UW?X1g8h`8_uL``etGBV#M4RB7g0HJ8JBV?n96t~B;#PbjS|85(42Tp~WeGPm
zApRs#{C}Jsef7K2W$ULW5bHg%?nOLbgk4O(qtx$!YcP<n`FLgi7VNB@^f6J8*NBXL
z%F_s_K72^q3>a&v@xri?`1%|QPuZ<+r2giKSU;F$5`Sy%snl<mlZks3z}5rxlnlLQ
z8lhVh)x{J0tr&`Tv^qH?pkz)hotSAQg+_hu1e2@)fI8qzsU|Cgn^QN!dn!T6FHBa+
zt}}DmD%M>@Y^5~C6lCd4d8oett`9q1g}_a-%+I|eYw=V?T6C?Mw&;uSq)3ji2R?fG
zNx#R_On<id*Ke;tXqQ<{il-8&2)d3pbR{cew<2a+1GI;^(*P;fPkQsuM{xw9V5>c+
zn%8ZECG>_xpbd|nWR=nS#iB*LVj+b6ZrQbodS1-x4ua&EOt7>1S;lTP=`W@MDhCDS
z$MkSS`n~N^V0;n-iJ#YG?)6b7O6Faz<@~&P{C{)$T$d{}TPmV`)&@kj)?u!b2Xx;u
z+(Aut-Iv6DSNQwa#9u@R7r+l;L*MoxA=1(&%GGItW#{&kMLiQ&pAC&38rv}7=5Drk
z#!R=5VmI>0Jy%#}dv}y5CpvPT+IgKKFBwe4rL?`XvNX3@{rI{p@PCq(AMtyK5L5{@
z=YPukjgQOiJQt@?;9wBlT%44y9`lTc7YnFg!yDMdY8j`Km8w`M(SCy#-9=V)O2wof
zDUu8vhGr;kS=OXikl9$d<o{4p?%|s|1><tLfI3;<GGkRJ=H`leV)rZgcOO{v&q8vK
z2_7rV*EY>Kvr7Ydx*V4SPM3tbymOLp@PCG^L5`Gur5Z@uNNx~xXnrzTfdfTd`f1(3
zl}>VziiL43Mx{slzMSIc;OPJ<9TaFe``v4#cFp7IB4o~?q_%1*B7r-|-(Ou-00uVq
zvnmxj9y0*ImCCAjN^fq&$p^EOHLgmbpgC)_lQyED{N5y-X9T;4fOCPXeA}d2Gk?g#
z?v$CfqqbX=SBP?v^s+QzVovya4i&<sdZ8!(9tU^!3ri-(2FB=$1zqh9ft%z`-0~su
z-y_3304dLWytgSbTXksaOZNbS0{HL9HY4jR#}j>QJuT{A&s4!LJ-yk}hI)|YV7=v|
z?G$EmvatF;f9XHE8{cgR1Ds<{6Mqw{Fp%zdP1_5{pttFLUGGXQ`{LYMu?{;Y@o<-2
z+=k4N9!*4W$gm%9#AGo*vney5Z^yAg&S`9zdO|htm0V79Sec{FJJzSSHWrW1mcx>#
zS@ZRr6Ek~o{hrG{(EqR#GXLqxv~2Ko3BS9(GEzIPGaEEQ5~M9SUspTWuz$|e#uW{z
zU!lQZ{0pk(CBhZU#!I95g6%=?I*=G$2vv91aa@TOCD;f9_pA(&-Z~(pgci~Q^CZup
z=Xud|`#|!!=;K4x!1|3<#eD``;H8WP-RLD65z>H!aP78m-W8se25Oai&Nu6tf+?B^
z!U<UVZ{V8het_(xoDdv5hJTWaRGZO9hu00tZJgGJ(U8-S`d4CajTjvpAF#A1R^IGc
zr4I?E^1f>!NCdWLAEj1%VXh9cD@vsV-MnBnq2j8<e$x<aNIZ4Vk9ZV^KIJdkRi%N~
z;=|J2>UVyN{t`-vShMy0g5zU#<{qS><=0Ln-RLb7@U2`7WtByVFMmV0+pkD#WUPvL
zG?Uy^D$+)w$%*zKWnvpqyXBUbGC~+DUb77JkSsKSn7^@KuF1<HG6_qQivVs)!}i?k
zMH;ku22kF$>u`bDhc11$GljS^d-Z*Nw~KweHDr%GCDMM05dorKH1~+Fsosv<8)tlk
zjUSwcu6~)+=%ju<nSU&VVY#_8(+TXgJpYAqBBJ{(JMin>G<3Ca!o-*QecE*mmwqm$
z^2bkY+aMYkb_MLMgm{J^i_OW*{7aJ3-Q8ccTuXK-avVe1@OKR*FWQhk<j`6WOVmkT
z1~3<JXO0mRwqgA9VipRC-Z~z5ua$v38XxWJ7z=OGsmCs^vwyZm<ZE*wB}il7KA2+|
za4YZDfjbP4p)seg(^In{S7Pjn6(2_nqsizF_+GrJ{<^)Ni~9tLri8@UB1~a(3<(uE
zjueyX^hypRNb#YEVo`ML0{CQG<9xW9R#K)p*l7(WmQJ-iwrFzO-ng3SZUU7YK9G&0
zyrcD^U_eS%i+}$NyxdC^`GL%zhrI{3R)n5kRn7yC-{JfFL7e?;Eu9n_MMlq9nyrhy
z!JJx?_Q&)(KUPa3*QQHZad*8px+EX3;MHTVygh0M?Iv>*-G-VaYOSA$p1}BF#p<M^
zrPo*vmeD+72iZEIMSh|C7FBQ??8LRjdXVjwvco+_jeo#s$&q=NTCsT@s{YX?>71}3
z=iW=|9*j@}KN2PfIZ@T_SJ#t?8fX!9Kg(F;UZi2N7X2=2Z-eWmdTLE+^8PZE>#xzv
zayVVLOW_NFxpnYT6SwVZZO5*wO!!|8m~>l&>m0xA$b5`!B1q4C1-rlsHC<?u{Id7>
zHQL$lXn#({;zB&|8&RubhySsp8jK=NlK7>q2~IeN>B%&b9rC6Mp9u;$`|Ec&6BI@9
zkwl?pv2TF;s;=EFA$yYuTYjx53M3e?3tcU$eVm<6*l_ZMsWcaa@8z$`u$j(<n3M2`
z-#s3=72Xutd<q}1z;*IXX;<TI#CT_@X$~Q=QGd#qHE4%|f`6^IQ_6$@#G1?bqkT%J
z?Mw$IgBOh-y5#89a#5;K$%;1XI=g-(E{0AySa-r}lY8qScoaJPgo29uc_!PH<pC;d
zS;5sC`o*p7qO|b+MHnwUCpI(@Wa=l3B5~w&$m>s8@1cSxtODUMP`2oS>f2w0liBA1
zUw_h3W%S9EGaGEc@#`o~%M4fzo4x+?eF4)q?CTdo+sT7`Cc1&##g$jj!itAR4D`nb
zId3Akr(G!bi)$HdcjaEs_QqhzfsD#>ld3e5NR8!0FifUp@sv)y#14ySrK_m(V<<$f
zN&{a+P8RDKJf!J#%*aUDAnFZzt#v2^Lx0r>c^zy+U;f3l5``E(f4n<fkR!7>7ER{)
zOF+qB4r(IB3RXEP`WFq|Q<5jL4)buIFA^`c&0N*1lrc%Wc!~6zOwKBKPy*gdPfRw>
zIpOZv%4iO4Ut>75EthSye*AvIirN<L96u;Pjx%HF-Krj)oxX0dG%g#`%Gm-cJb&oe
zfMLx0En1AovK*E#>M_xnh|tbd;GcMmn6LQ_Kzy4?Ie^*iZeB-(iLq>aG`W?mFt=Gz
zrGO6xMXPc~U!QkrPoXLWDkjKab6a8fbhCsM4T5gSIX&tQc3|ruA7U&p^W;>abz-_I
zUfy&aP9+stOh=@pwV5#0QT)q)ihpFD)KgG|9p#=2|0K|*@GC`#C_J}n)35nZPqYsu
zbH)AP(BCg8usVmtR~+Q@tYgQR;l)3{#4Tbg7&4AbP;#vd*1?d{4&LLwx-GrpM3Gqz
zhPmoiWhX;6M%tAIWBqb#9`wyj=gE!r5zeqM=A&}Ef`4UulU!85GP8*^(SOAA4VB_j
zJTmUGv1`?iq(RJ+<jFzhk;!6hR~vkOTe*Y@A~w?5*4!twE+=affyf>nT%2&49*F#p
z1mK1Nj^STE4vd*>2=}p?rC;*Tk)o5wkz<!1E5@(}kqqrya>nIMP<w0PZTgJ_K!A$9
zf5kncJW1w~LnA+-jIFzc1b>gZScH2jf3fPCOsneqn!Y@fw{pe}SM$b)0@C^&enWB>
z;J7t~PRN?aR_kcAor~z+cp4I!L{BxL$vojfQHWphyZ4Dg-<-AZXy0gv-)jKNmnXG(
zXr)Xtpqu5}fx~!enotaPUoINA7iVQWyY=tA&*(#Vc|?8sZz0t71%G@x$>FDh@R717
z*ApN5bjbDw0v!@#%8{^9$QAhX*-Fm<=!tJj-NV5*m^AyL7?B9rLqLJAdN-<-J)dH8
zq9>Wp#rQj=+9sh_d7=@_!&)O{%uCpSZuQfd5Tdx=B|lE$r`yJC9p0FJ;ytI!Sva`L
zO}7u=?Kt@U{bSg#UVi~jsIH#ECROAGG$nU-T%H)#hLx$Pk^GhF-i6KfC!NuQUF}Jf
z$1Hs|AB2zSda_r`o08l6jUY0fkPcsxD4MSCk$giJkgUsv3TUri=RGlA$4`;-p!@56
zt-atm=J+!yZp*t)KH8?n*Eu{MT4fUh+@iB`Ve`w|YBx(ku795oS|1L9WS^P2S}%Rd
z2^2SD;46@X?#{cnoe6AV`uxVwELHtN{S^vbmWCcePAJ9$=qU}(da}zIbsut327a!O
z!6#!PDnD(Fb|#rAFNcGog*@85+@FJslsQsNk0uJvW2p9iH|tx9#CR%9++sPE?xV?W
zB_*m`r5Wy@oqyypPatNHgm4l+aYb2V-lfGPrlOtl>j{P8W;f$3(#J*@RICT0W(c-c
z7Q~IhbHjh$lXlenf;^Ahn>2EeMD-~!QXEs_L|^f2Fh;kscTu&k?!kJ)aIsgxn>2u}
zY1RTPzIhb*9nFhlL?;K@z}>cAgS=K?ZM94OvsNDE-GANpy5(m=&fKqps^p?B?C!fa
z0uAJA6+&L%AiTQaCap4PJ%KU#ae{>MvmGl><&C|n0+w~xQV+mt9sAyi4P2q;Hv!%L
zlFyq8cGuA#Kx50<OE*>lj{GgH*75>OOnM=~)!=H*9krGQTY07FO(6!O*B=*=Gi%^=
zx}mZ}SAXigTE2A?@wTq)q>bm!mE;{39HC2KeJAkK^m4~)@`dlOr{UQQ^qsJ!R+spp
z=$^QoD&9cZYl%A^ZNezdLs2B0`eU=ji~I#?5WtEkcp)O+O5Uh!^Xbl&Q$3K~t+fOU
zjjP-a?(X)MA)>YdruT03!;%oRx$~GGSx|#aoqvl|D%ceqr_;iRFTm5rov<Vasgdps
zs+Edej2Hs2wnoVo(u{(NV&o{!DrS|uvWgKB&#Byz$G!k{2(ew;<wa_SV5fQl5;f;j
zaYnu<<l2^>Kj`@5jh~V|ig_1KoLMx}hPmimF&sN=b}dD8Eikq;!6;u*YJ(vl_XvX>
zzkgZd?MTzu6S;}Ez2*8{qtIG|3mb)M{mg*SU@xxy{H;h8_>64?W-i%u>RG!A^a-_s
zmtbSvc8a@_lQW}Ws7|_|Z7wiGPJOkR5r{IG-0(afHJW%D$#H8Tq&v$;?KF`|DZ{8_
zLT3`Rs{BoCM=N-=k%{S=O48pg4vFzwqJOos0zv~#-KF9t{0qXsD1N2F+jZvNOhOzp
zVd>a`>>FVKdIq#CA^lI@T=!6X`X%-&`E~zY@qz=t?&!J@YmQ%Uuw$$D><tQV?U7u$
z(7@3*99i5qsq9;LgVMd#S%Jl|M0e7wPr&oAWj=Gks(iF5HyC3!&yq6{9eP3Z=6~N;
zWb6HdlM`{rkye!zBiJzCp|4>cE%zGbkGP0q&_we;rZPZBEXk>fI}%aEeBb5qQfp@L
zPhe#;77Bm*?v)bh6PG!mFE!Oizv<@(_Hsps?>xaB-LQi_3?Ayu#8uL&*-Z7KEU^+i
z{$!%>*+p&|6Z!jf7c!g&o_hZZ6@Peu#<tHtg>?PX$hE=#2C-+Xsp^&)<e@k!HJTM2
zQ7bX9&y#sJamZe{xz8ccGJ7Sl8_LeR%0a63^Y;KfDdVzcj7E7-hveq6E*_D<@b-~L
zlp=f257~e&MHA8XCIJ0b|GZq4e(Wb!a~`)mO&-_Mk3#U+vDoAW)<$0)eSd83&j{U>
z<*tH1MfcX6Nc!m=wSfi$LQQY=p1w}6s3asqWvy0Tcz0b2rsff=cRl)|FY-^uK33Ju
zuymJBTI=p8dO^(BKv9_}Zc>9P-!78YpK-jq;SBASw{$Jp>JD-S<J43@<CqI9w9#8e
zzw9Jw#pcH=dkV5-kLf&AY=0P4prn7`xJ(vp3^N4*QHxI{DIdfVk!N>O;2c@b&TO*_
zq39W=(h0l{Aw9RrivU?!18ZKXaq<e-O(MJCV^pUu%5xteEav2`KjemQ6*={ai4(x{
z76onqj&C8t^kjWZ?<Mn+OGrHcCdcOEWD%QBL4o!1d3>)(eM)xVJ%2x0CFl~iZ=<v5
zKg6eQ97#yU{T#~RUGeO&Ci1M%a+e-lk;`$1cdywNR8HKn{8SP%@A>bCq;Hu4I|MSj
zdRh64$KYuN)rl9?)o8LljkOBW0cHrn#BvdO*eN>_P=oFF3MV-Q1J=aTzkbLbK!fKQ
z%q4*9ujGCoqUluNVt-M=G-W%Nk6=o}=$RPhzju^se#pE~zLhw#+C@D;3Hm7nvwV3S
zyg1c_gB+niqJd8xqYPv4@$iKreMzoL!88%RHFysmh?2eeVzQjN^GP2C^%bIHOVTiP
zgX&p*_GJ$-W`X=;Nv1GBdA%RNk@G}VIJUDINone@8WR8>U4Ks|-X}ATGc7HM^Hio1
zdbpRQ_whzdHRfgsRz$~8J)quUi<}XX70!oDV>l}^?!If!N-){Sf7fikIuOBzKZ<U@
zZlbd%;)AEAO(!eXQ(MK$(|N#R?kB=jtUKLqe-911=8@B>w2STn;z}k8j%yONc>*5#
z(DvHfq}hvuUw^E4re3a}pNhAw6=k-=a|tUmVgz@3+si7G^Zo6q2D&cM7q#ntsY=?~
zZm`?Rea;I?kxb_$vkC)W6y)S*JkFSwId#EltIt4GrnSTKaU8X!^X*fS!29R~*ROk4
zqNw8AE%*~ae2LgavH+kZjrc|@l_F6j7DCzKOMBrh)PGiaa-~_T?x>{U1?GhW&GpSo
zWNmrs4O;2UhOpueFN2L?uc%1gdW6!>)t56?MHF#!ZHuEPv7gr;)m@>=F?@wAC5sV-
z^<KQ34PAqIlC9p4U||+>_ml<7yV!tAB1h(#7pXf&{teNb;YnH31xlifI;bFYCE|ja
zA^M@y(SIw$M1YmPriC|t-~&nPihtJe9mbhf$N9&aemOa`Pu0W`zXI+_tt#rw$v+EJ
z>MMDP$nw_xDu#K&cYmrFQRh;rj{n7I*EV$GH(|x&iS5|vu~YYWpOmNG6kR>7z*>5U
z*cQ0K0HLDdi+DXR+VX=YQ@tjB@x>4C8<{n6xqo5D@(Lx}iOcb@<eBWtnMtr;4auzI
z51ce3NA#7PlYw7deC<)+^-gcbgEk~J^-5kAR4O>#H8mqycVw)Q;*IApCkB~u-H7ZH
z(P`uhSb8C3g8I!Naqk{w9NY3UMSgsU{?((lEObp0A(Q+TyI>AVt=+2W^}abO1he+O
zc7Hm>Y>7%}gZA`pXCJ1pP-d4pA&}sZ728^KM?-#1BW2g74CsWnjnNz-K*zPUZt|a@
z<)?bo&bF9uPpw65DheesFWzWAOejGHNj!b-w{Yk*D;=siI5_YrPPmxIE2B9cq-OQI
z4+xH&E{Qyv)$N?gWX5-?A=POU<c*<M@qhL#_JT9i+aLKD3OYA{2R{~5;%1_Id{8h@
zql?C9u(&%>ke+CxpQ+&kTpk*Fw8fBl$~4cReBR?#N>ntvUz*@^vEJivR?a8dU~=+f
z&Q)jA)ze8k^r|rq4GLUw&`FdQbvQ7*H$u8e^@Q~h;NO&tmhc#l*yL6I`9F_)Wq*Ey
zCCZBx_ME8!6HmgjH>^DzZ~C<F^Gx&a9v7)b8I}lT%5S_e-dt%E_#tccC_HLGf}`q^
z>fZ#)x=R|N>pKgt4(`D0JL5nB5Ow`h1rnFIY22ARf;DBTaFujKHp4R~Mc{a@*dN7z
zT8QYu5%xNq3Egh<l<s85ldX3!1%K{&NpZgH9oh>WNKhuCbV@K;s@`vJH(^?=QI~W6
zOd6k1UQf#-6i&-c<zQLQZthgJ79g%h<itg$YN*~u_x97n>2$<fBg|qU?LEa<s&!=V
z`poJ_GDt;4a^rW1YKX$YtiCNEBpo(>YfB*&D=yl0E8h}B^W;s>e}OLgcz?{yg9B$d
zg~lxVBf>AryCg_G6#Rfzjlls`p+;{9uOk6mDxlRksm5l}akQhIX5dxws)dIV{PHJb
zW;Im0EH!~Dmm~&DHke|P>|$IQ8qmg<XE_}jRd8%*bDL6`iBW92shyg^^1etsX(|Qq
ze>_2V!g5n(F(R-^C$1Y>P=C(uQefSac!-$vQ#&%ld1WCVf4JHO=%Oot{g%HcbU@FJ
zr2Q$?lV8udm7Xnq71!TJ<X%aR!{TlJgH9*!gIqpuM}v{aRT*VQ1WhdkfZ@n?l|v^g
zx@Nv*C7|>>&ajlKoQJ%4;Wdlf0c*Z)yq9#`DcP<lQ|G+6)MT%^3V#n-NoW!yAqIZ8
zs;<%7@tL(yVu_kCOLslj&c+m>_E!tp{NW$X9X{VurRVIZMH<VA<Jqnhm+nIZBbes)
z?u;wwO+DYB9ht%p*bqb+>?x=G)%p-hOs-Pp`7vAf<vK3n$RDnrD~Hj5pO%2$XXh7@
z>-D)Z@{T{Hh%aOoD1Sb(ZhV3?Zw0e+ae@2Yyr8x+EgK?{s26AOg*_uLCmgs`_WF}!
zuCYS`MT@8Quw33-O9&SIJWP&0nAN9fjOIBF)XL{7kZdDDmYPPwa$qd*TAbh}ra0&Y
zr^EU>uf&*MXY+I5N0mTxX<`Dma9n;IzA{g|Uv6_e;Q$Xi-G8MlQt#59vC*8H&N5>n
zYng+G>vNr=6{lMvw!plw{da^1#_wapHeg=yl1Ap!mG=6)u)0L|%2nfz(uuIk--(xu
zU1KXh7lj)dELnWNGYO+7M@hs=uBUxK$(J|nvaHIL*~wOUm?>$1?y_>?S$78p81dtj
z2*Cc_JJCC%`+qW1=YiN1YtDGKoT#ctFu_{+EDQJjjB6D2b)3y}{IO-~gGf=lc5m<A
z#ni+(3>)spwo+4Vp8VFafIM@|UYBKrG4B0n{GNaRInKs$D7iGyIrW3J4=aC2@V6|~
z)|_=l5@0|PAMlbLNBWyr=|r#=*Xfz{bn}tC30>_K3V(tQ$cZN^lk+X%LCDIdq0Rbw
zHWOoH|2!%zp_4h%d{S!wa$cG!hW-^RTX4&kuq8-vPsM8y_$#Z>joG=U<}2y%8{g?=
zh)pmJ`zI+_)Zv`KMw`6XoP@+WKCQS;I;0H9=A(wB{w9;}T*J;L+sm`gxLN;S8|Tno
z34kck_<zQ>)3L1^+qP}nNrxTVwr$%T+vwP~=Do%2<|ov$>N}@coHz3%dF1(n$4_V6
z{Ct!uHl0zDCS#(~QaZ=jegqRoV?S()=}ij^a{&*Y1+@TrLi2O$NQk#aW2J(3<=d!Q
z0@IF9meP>g2nW6~(+QS^P$seE!r;}yvB^?+Ab)1=8wkoL0e~`~B9fx5nC>;E`dFH8
zJlNx?%3A!!C@_`7l8w2)Dv`-d<|4Y`=5|F<A;!`&f*8qzix&0&`r3V(PaIJrJSa@Z
z=6?2B%$8@aDI{_)w_ack90KH1RaXLJ;h&G_7^Xi+(!WHRjd11<d(2{U#W;WyJ7&)4
z?0<bBk_@;A#f(D{Wt){jY}=QTo`!tDKgY@knYMrr%e<x(fx8BOec=8y|1lvUWNbJ$
z9pFxBvhz4v3ycT*feE?!>?GYVvuOq(!l`j5Nb$vCMdmxD>A91)x(hJaP#A+paSG!c
zQN50P%P|%v<LY10>!vm{#xy0;aUy_fRey@od0K`*2(~g?>kf#BMM#F?PelI+?yFd{
zO{fO1qb0u}-H*h|t<FR~U?dDOuvM&$Ecq<<M5h^362;%Be{=ZwNj9okHx<-JWaS~|
z{wfQi`U&{)u!u0IXAI(@ec`i7;!!nq>;6d?L48DtL2nqMOJhE{L1ZOn(sW&_oqw=^
z=+WFuznK6+P%;FWf|NGj*cF@9uoI^9C$Z1_mpx&H>}!}Hc3^DNQ+2z9@3YQedaBje
zg`khv61i#8Hf8s}!&o^J8mkAVc#2>}MST-K+e{*#KKzuve$Yddp74;|I2^<A0pZ9;
zX4I<WUSsT<MVPi;<Fs-J-nw?L)PLWB2hsTYU$5yTwg)=CFM24wuH<bcnH;nz112T%
zvIQW@fwyXuJq0@#r*qb7I;QlNw)MB$yu~=(^lS$QJbFzB%@)Km9<Ykxo0x071x&y<
zg(N{vPh8)3@9bt)Jxg!RXKauU@!hb0?8ryha9TCGc&G&@@h`t~8@9t8rGKtit9AhZ
zvEp~~X-lDKea|m|;~rQ0Xh!r8%rbMj831ARbd=}sKf6(cpt;UAZQR%ZYj24Xy;3En
zNO#WM->>mlbGT&Ek>o#+5?S>|E_5RF9F<{$MUywkRqu%Pe#mV~&2!<~c?pDDZhb%*
zw|>Mcz*ob^vmLw~=rwm&M}MB+r`e{_+UAqiYSJJ0A-7UFGRiq3ZPRn-n7x`PaHhFR
zUZd&|aY9<a0W>3uXlFnx+AaLU23Svc>z32FLNASF)&S)6R_7b!K$gcs@ozV%aE^XZ
zsSM~t_v*-}#fqJ9PE#q0oLOT@p7WDjXC7~SGv~g**R!I$h5cp!L4VB7Kb^6dK@)G^
z<Xcnr+`XFq?r9>4p^Jgf;Ej9-k9^N`6M1K8Gm>BZ-hM&d(*8?Ju|1fIVf|uLir+>k
zQ_VN5=xzH|$nYcV*AVrUUdZyu!teqXhY9D@k(MxSrZtlF`9dKXpusV)s7nD+v$`Yh
z(XdT?eSz-NBz~R}^nYS&aj4VKxU*!YR0^89JRd0K41&1AyJ#jNB8R2sV}<_Ky<1rr
zc3KMOXbuc><0?0Sd9Z1zyF*vv!63CwiG(Og#Xje^>opc0;02e*XPitS-U>-!;euEp
zg6((HmylF>wzV&s%CR)pzN(xazw5txG3DEc;V+D}Y114D)PHW}Xlne>ScahoqD=$3
zr5gsq{-@#GH{*L+H5y1*HSIJJe1%_gZ`rO*9EbBSV^HXrS~IYu&>TUJobS0ZBX(6y
zXddEoluhqJx>95CS%K!<X4H~JZ;rL~Nv8Q@`ug8Cl<a}1VbskSV^KFug8@mZ3@c5<
z$c9s0pP0V3<$u@Gu50;iDY8HvJMf0TiD;9JVu6pqWx-?2^pI^cp6ET1S>r=YA2nvY
zD_vKBA8cT!@ttGogd>}?-5pJ6!5v8SVtNIkcb2GFq=voQkzIBuV-LR37un_VE3(;V
z9K>|`y6ah!EUC@@YE-)OrXiTg0}`UQ2)vzMkru^2w|~vByLyQ2DULF-*s(;^tOEW|
zXaJ29P0WM;JG3WS;|9x#Di>ekgsDxrq;f7_QiO4N%VM4U8Ux;~I_eZ=lI&>e1ohS%
zXi8})xO5gU*8kjc^eTSu*D(v`F{7j~+JRZyV12(hBoP;*{fi^zmwyks9`w!B@+EBo
zjtCegQGWr{1cVW9=r{M_=PecUwv_sUfEDvUmso-;(z+bslQRbPhv_Cw4jlf<rRm3N
zbPutU?SC8!CW(d~s6;i~MG$}eEmh=0m4L~;5yDtIlZ@DX4i$7CF-mWqIyH{UwzrO+
zJi}EO2rHe+603#kz+*~f25kB&DywNaS|n~z`+qi1C?pmP-dYt=WsmWU@3148s7>_v
zYWJUzlQLb}6#rMdGXrMP+y^goK9Z=;3<i9aZb;PQ-!o&pGx2kW=)6v7^~OlEo?z*l
z4Hrb~$FRlh*6kxmw@qsfo8(6`yz~1@k!t?y+>$uz&%!AygLWka!Fyhlr<P>*0(S9O
z<bR&tt<^tP7OJrzRZnb7T!=E=P<J{#mLCYi4uPODF0+cs0ZhbIsyvKFi)fKzpdFZm
z47wfI;=VBj<+CJ*g(skMDJ6J!qc0&1(v0*Z_NrhW3$|mFg?AGwM{TXFA@r~1K)zaP
zdK35BShTeQ>raib<$BV7iJ~4k`6oSwy?>M|#eYga&;og)Hd?SwM=+p=!6<pRX9|ZK
z7l$<ws^o_stQfte|4KxG&^+=(<hLYZ7`Vw}H)o$&cgEUu$&}nX?PC`a@b3=}UGVRo
z1vmk-$aFp9KAj@0oN{cXIqH;1UDK=pbf;>x?D(0080c$F7q<~~L@uQTy-FmiL4Uhj
zKYT#05~`5?6pG+dAPLXi*}(&Lb85ARp$O)R4XStO;-VY-1;p3*)B58GMWD_?w;;IM
z)WO~PS8rYs)}Y|;p9e0EXV`CkZ^=906!DD)fU?flu=W8@`tH{OxoW#J73h~*NEX4X
zR8~^CAVarWvy&OtDzqI-O{bMQbboM5QJc3mMKcvVA}F=BERUEs4Wc6C@;7kluDMKx
zM5AU$n7}}34Xwqa-4)L=0tZ<fl7kx=-RBzS34>%@Q#Dx2V6*;PWW+Z~jeJM(C_ydE
zhYU{?_2OOWImv>39i%_CI1vr;@9fLNQOrU2jAw6B>Cm#a8|a!oj$+#g3xDadYs@DJ
zmnxmV>m&jUxKT}%j*A1%Q~!%CgBpZWKaz12#PXnGQY}_YtdNOlj$&Q<0R3{@UL)9!
zm1i1T$~grk+J^sVg-<`#_1Z~Xor_30;e%r+Qtsb42G8g`lDP?-tE)^JY#~ATAh{3%
z{`G?53f>x7-*5-Cu|vP-Kz}Dm{`WWhnLkTTdFr+;t1^MZki__7m{wgC2~Nm~G=)+j
zlnx5%>wh1?@+_%KTl6O7TENZSK!H{akV#}P!^?8!E!)Sf(v(_=wu5ZL&o*xnEUV-0
ztly@I#|9oJz7pkxW&xa-oH>I<9@^AG?nGHP!@~~`867*B{hxHIg@4ZA-VreBi2AI5
zLZHu!u$E|_OZ<#c$0#ldX{HgI4&i#g)E^5k%<_<MrnG{Y9|$$;fa>t#w{Q9RXYVA4
z|Fpp}$e2{~_N$JfMyY)uzm(6iU2*vl@AvmV*YNgv`)v*oL}naIE|LWXoc0Ei246Uq
zx_R!q)a$U`wQw-dcYnyk{6Nu@K)gpSY~!5Z#J!tbsnBn~x^6_%tz@A?K8_Rc2v^ag
za(c@d`UkJg9)zgK_qAIO#?(O;7;NFMnlgMy2I%(?&PQq?l-ap7=zD-SxOSe8rHo%U
zff$hzJrM`N&NK8u)NpGl3+pFWcHs;BZcKw+I*c_VP0~A1qJRDO-1D3qIdjP#@VIy(
z9%S-iDXkl~UOnn84!_ayDnu#@O(TLKiW9_;=EZ2|-<x!p!EB^NSQE#S;MUFYNCz(w
z;re^U>BI(RAo>HOW>3lw;b(2XQ>7g*-1j8AU0GkLb^?)?VJJ@5bVqnS!FD#Ce9WbC
zGdg^ggckO6%71OORCL)o<L|4+?S#}@U})Q4&?=`|bW1&-66*WV&$NcKp;`8u5*ZTG
zQmho`Dhddq6pofwopX9eBo~Hh@_s3WR4$#unTaC#OFe7O5pP2J;0|38M!Ic%TGc<{
z3Q4$u>m?Q<EM;gL)7DkY-L#3>ghwgjSy;s%m^o6w?0?o^|DlV78>{U=h)lQ6&X6)=
zps@RPk*qo1k|4l$NXF|b%!Gdxt(}!x;GCcAI?1H3DRPd^<%doh_H23)<;!Fx0iD0;
zq2+OrN|LuajBNw^wbrpr9rzC6!sk%ReC;g{a~!|OziNa2ocQtUE^#GcE}VJqXjR^h
zhaA@|nSXXamM{~th@V(q{ntYL$Kt$>@e(d{*tMzZ7r4tw?Dlm$eMj!K2Dg9Kp@dF3
zgYkIb*xx4OD>J8)US{#og4W5A@uLU|W)JfQkU_$(DO>Bz%4PEJ-^3pekTl8FT1=`s
zCY8B2NZc1?A-bb_6{WM2CZ9{$$C9&zBMKO5m49kGDUV7&UuFHiQblTkuYhb<^w~cS
z%)zW&3?-f+r*wvl`p4V@OG%e}jgoaR?qCQZlQv&PZS@Uo{G-)SfcrIS^y4??)LB{w
zD1NuubRb*?oln&5#KZT?;<f8=MPiYnEH8*!XLIz~bF#-c;fC+W>c1V*9lo~p>bgL_
zm49*ZRqyLPY)?~`pQWjV1*yx&#tl#<fZN>YqMvwbefE6H+?H>AINKr%DI#Rll^0ox
zhNLIeQQVS1az_J7Kf{EjQa#0ja_JyHnim&t>x~%<*XsN_Y|!;bHA(#0$?=9t5UcRR
zu<GE|g3E-LEbEwTYvN9GNO=b`EOQOP%YTgT)uUdFTl0iFNyEw6dTnO0Su$NT&N{~I
zgb*^CgY%CPU#rj~ji;a5g|2GgC8QEabQ$}BjSkqtCzwlQ>ASD&sBQRDA9+Kt9GnZW
zCrM~lL&7p^dZC>Wf=aD5k?LK)M<2bh9SO*?r(E=YLb?at>R9E@Ej}Hnot<qJY=3-d
zM1jEHhxF?K3Q7i6Zl9_Fn;Yt9$B3ah#M12VU6WFCL#P5f>W~sR3epR0oQS@*0-V_d
zAc%~&NJO71QxxCCJb-H*r^^L3L>#X{^7%GDD9KGT7qBaH!%)q6_Tb_#89lUxv>*<3
z9G7QIcNzb<mq)(l*0v*+<oncKwttF`hin`8_<KP}nMTaLhV^Ti`8JBg2T2o*i%)r<
z)Bk6%ZYU<CqQsJYmV0z)FT^Yi;Lo+ci}yG_NLnZQ9h#TxquaQRby>7euMxP>#nZBW
zo97A+1f1pDS+XO~6ii2y`b-)?jmP6ekM@$Vg2=Q@H5TdVX351e$6%7SVSj_4TvDC~
z`)|B$_W9TFP-%952f>Mfy_x@h1d*lOB>sNWfjhKlX?x^oR*@=F{tio<P0Y5Ds0s&n
zSS5JXsuQ~5G{N!edHmHK+}uKd3wtnw3MqKjs-CSGisX=_paLdr_|k((7_Vhb;WqGQ
zLU@zR&Y15}9pX}m6DcCuZGY{_Oxzy3_$X;N_2Z=ZQPU#}i}qi=F|?X&Fkgu^3@bRy
zzY^M_MzO7WdL#0aj2vbxW~r=oO(5fZRU{QP3Lf1o`dD~lGxSe{uC5>*EzHt#;#H-I
zkG#CEoZ~7Zh}MDL_fz?!=r92jqAG%lGv5iql1|JQGB~`>SKdViNq_1ya7f5kb*nM?
zdF+;XkER&(05(1q`gC~2w(x?ZlKeh$r3gX$1XLhncgb|7qAw0Z8dbU3zzFz`OFkDj
zFEHxfASFhV-&?z%M~)GcBaS~-4T7Pc#8~vyBxrI33qp~f-8b7j%ZFCBz=DlBj;G!6
z(?)HjpMrnq8wNec-hV+dI;l8(r8pboHe3DRHPCWCKp%p1KmkA6=ZpAN=bU7?Dz*l9
zn}*emzFrnC@7m#rSYy0wJ(tay*vci)G@B6>;$^*bXKD;FTfW0BQ@(;1^X5ioazKqi
zZI8bDJAF;S%#EYa$A7@UUZ*tdA}FOW$WiA`NV?n~Rf=;2!hgXUWOV+qBKb>lv~F5u
z${F7<Z!lfCAF5<%O`TJuch{p`u(218`ODZiQWfPF9{#~vurEt=Lq7}MUk}AefReDB
zLow`SZY1BTr-jIY*U~Q;cDX=uBO8jw_ObS^k}8n1;^9?cxh5CujNaeUQ&4uo4Ef_k
z!~1VO3T7MG8h>&0qbfSIy%riBjhXuMH^w3-sjA<x)3SNHD%L$e#nkP@<uuosE~{HF
z&U8Lk$dScSrhgN%D5sqOOTXyrnE_Hx2{K>H*LF9@koLv-2btV$pSX7UM&57)AwT^1
z7>x7VxL1;0_pJtckUWEO<X4n)#{Z-~8PO77T&g621AizRD(&Z<rq~Bd*<$4;9{+IV
z((nP>`1m!m{!TPex#+0SB8!$pIe)#%C4?Pk#NYhp;qRZi2BU_|O02m=Guw2=3W<Ih
z1P_}#h+egXK3%f0V`dO~vVG;>)d_V^Yr&QC<@!c!;gA><g=6I$E|A?N1a*1?|FZlv
zySKL}7=MsuE<LjSc_!dQeV-Yz&@BR5FWbYMIZeU3he-%o0}F#pP+U1c{@k$+4SLZC
zv&O*ao_3roscaELq#xIoun^S!%~%we+_T5UW*w6z0$FXz?uB0j&j1@<GA@T-i;?~A
zld0%Z-fi-=gN*rnxbBiMgq4R`U_mxlFf;%m)_*0|Vc$9Z-Fp#wSVV{=SHTLAaLrHy
zd)%FS76m6R$SZ<+PMWV^M~=_OararFqRjby^uIDzT(bbeMmWa)wkCwZQD7od&qLl(
zQPe`g4=Q(P><(1;DboS!-<&s7bJ|?>hV^L_{+Y#uvtvZk?j7WktAG#&a}qGvu%E7!
zr+=j~^v-OP>^#!I{&mrWE4O6ABr^;NR2h@HK{&n){u6yRl$z}vpXl<`b1aDbC~`Wx
zL~3cy6|Ti|25~AEIhG%(X%lFj*X#L{+DFK{Oqok|g)hF0#UicmaEGS1Q|1c{G!Y@|
zq;olto40ANm5TP$WTsVBy8JA=h>q7Xw}19iB=qYZbD6GmAo%paer0%X3O~~m44Zfm
zQYs3V8A+7Y!U(yGurWxztyAbG?JOxkyJYedN#A|eE2WD+$W1`7J(0y~*7h92Dp3F_
ziJNnoWuF*dio11Zk}?(Ko?rZ1KW1vT$d}7*`6z?DDH`@C1ftiC>5A9=TKmf?b$_pU
zhq>{s72R|anF2?<?Gcci3)&B<zwGCk${wv(@DDvm`PrM<u!;cku%liiWw}%sH+>#w
z!OkFokn5inZhRDi*6|d%Z;LSw>y{SvGwBqG<NU6l>h|yn$5bH=^avYA-Q&LutT;|!
z5lr95?NnKxOilYzt&lW2a=86ZjDK=SIq6F1KKQ*pk?_w3=2B6!ss5CKG$OpE-XfDg
zrc7z&2HbQP6^RkGX%k{sMk8Asn|_I19@(2j#|Mp+#nMF=QnaJRpjJ75{yP0j`nQr<
zEQRFS%!l2U(|+lyAq5nS41B^?!LQpcK82!6L_EGwV#sDA($#2c2UrYys(%pH3cM#{
zH|eu4akvye860Jtr~n5vn1&4`M<)_0pyCjvW~ecU(FOgZ1j(=DKnspc{nd48YYp_i
zzlu>a0ZB(5X>Xk)+sMgYl#6ow>GU1I2;9m}SykZCGTX6U(2W6j7R;)TmqBHAx-Sq<
zW^grOP5BEeh;Ym1;46LP27kI{`#C-SgP8llfPQHko^Jn_g}egsUq!ZK!*=wuSB(LU
zSdf4_<7fF5E#nb7?_Yi158YA-6z<wsCv0%?xF~QhSF~LnHCd4zFd{JC@~KrdbWc)0
zM^Rrt25Tv@aMD4nLp;{pzg1>9iRn|rzV2>OX~OM*D*{h$4Sl<Muz!*}m8E<GfN^#P
znFS6)^Rb8Zm&`$8s9yy<<t*4H8nGB-Ex9%u+gH#ZNdHCK{zV)%R3;ZBA>5Qn0Vqjc
zXoUDG?r=!zW>ZO$Z92t(<-i6r@6O#F|9|P^&WF=?qeq>(U6n7ayUBQW^KZhIhpEiA
zL{l26abEEHUXpEe(tj6)d?$}Ao$W+%e}(hI9GZ<25VoLa&Mlsq#R8_eK)8ZRtz}<V
z8~**~ogJ8X?+8VA*3wHlgodHjBOkFW&CB~<`C!E)>WbEWH<uK`)4L!=xPINs>5V6P
zvV`d(*?7CSLw$g!Xh}PXa6hF^$0k*XwVeV1^rUpX275iC^?w?UPLkI~ljj+2N^drp
z(Xa<s9Yi1LYRXYyg9J!;U)lbB<Ui}DYrR*~bOHGi;pLIbyUznej@R@|{ey-scU?tw
zK`cbR#q)O%oJQM*OC!hE9NYyS?$-)E%i$@3UQt-jH^;*`fh@yuk*^sm>y{j+3gv8w
zYh98VJ+|RFQhy2Q&Me9`>fryW>dHwS54U$YY)j+5|H#n(2$Z1d%A95KbPNs`lfu|i
zU{I&s7%jJ5b5rO8oqoxQN?)#^CZp=$2nxBHK50#KD7Tlig`VYk1?uTi#cuCVz;xY-
zeHZNCpSP_E`F6OP|8-5UDDU}_%}KuOP^CJD>6ybnIe!F}{n(BHB7m}sGSUQ*7%kn)
z1usYeOp8w5q@a_CcPj5W(qm=HbK2uso<>Y7GxbUe)U{UbAR%dJ7w~stzWa`vWf^fr
z(lybZ8yvrI(S7_qZuly#`WM^Wj}EQ!_bqo@Yag&1p75&hD$}ordZ5Lew%_~!UO=J0
zvC0T~#X+Un>4kqr?=Kh##eO5d9dOmDV%k%BBB<7&7`HS8NO23eck2F2A0W>vf7LQ-
zF<g@e;~r_ESW_(7S--^ECz{<-m7xmFP$meE5EyqooM2m`Nr-T95vkr|S$69j(Nf=I
zK1wNQr?k+r5`k&ZoLX3oo800d)_SxyvA;eprL{*zpV5EfjkOk?6Sy&2h>)$6UhS&C
z|09lQcp4S)v!ee?&4^Z=(jheE)1H2UKvc!QLzQTS3{@HJDCUqjzKbAN>)J(w)da-s
zqwcDYrcrhgqnn)&GN=mE`WCI^<XIB{w!?I&)KJMiYd$y|<#{=(M9>bxk76o;f1~iA
zPCoK{O(TDeYMy)?%f?MeE*vi{8OyM7tr(tGf$r*jtu$KkCp3s;#i^?jTt1owX(O6-
zj#+SA8NoB*U2T!sP1F5Z>aee5H?8d$DJ&L_5c?etIX_h7i9u22ti$LFe*Kw!SfWl}
zgMUA7O5BB)($@^CU(9eEd06DJg^w2fOR*U{p}Bu8|1CCsG9pwL?``yTsip%wU?)vK
z7G+w6&uYJAL$!(+R9TPsAx-)bQc2_)fl7SD@c+m6vtiv`fA`kgr266|QkL9EXb$*x
zB*ai7<P8FBG(((7A$P*T%rG8A{CB3#hczwDT*w=rH8=<IpnM`L?J(>LQzd|?(mt-p
zWdnZ!fNn%iBB7$rVyQ<9V}TpxDaBQy#;ygFs5A8*FKckb&@R;!!~gK;s}f=H-jNnz
zNv-yks)%0{*kc}>#eN-JJ6&uO2x3No6_K0lS^A3W2IlZ4($uLgMN*Nm_=VE(2)7Q#
zU@3m$jOYn*0*lvFOC*&fj66!K!=G7t537I72f<Twhvw+2`a&MldcSKG3H1RjQB$&C
z%q|bP-xkjRfZInB-~xSs9%n;9l)hAb#o&hHo;8#&=^g81`|y|tn9(|rt3uoPA*c`G
zJyV1j*glFvggiG1^Vb5}#(y{X152ByTP^Eo0u13kI5s+SY#JLYA=jLhwoKsv3h#f`
zlIj2&paXQ))FMDg1857v8S3YU)HiG`Gt!vLLww07olSZ16PzQAS4bQ+ij^-}&3)?D
zsL7=7yOUmnQhTEIVa@!mY-P{w=(;;?W9Sd(XM=KP60+-Vi%&n(ri}LMxM)4}M-Lo3
z6mUu|gCec$Sop@Vk9)jLc~tY5x;uYS)8F2uMRXv8d=D6!M=L0PyP~sZN@@$JY)F|<
zV@`8;D;yb3Sp^%4rTlDH5n$ZdCT6M*;1b=N&rVHAPp39l_Pu#s5q~$wQyq+dcrcV`
zC@uf2i$#0*4ZC+8^gt0@*f*Z5j&(vr#DzWLgj4P}b`-KbBwy@$=(LJ+NK}7jQ;I<m
z#3TmBSlg=nZjAQIc=qQk6du|8(qKU{-yq*5O-=)m4!3M-u}L#@`BYvPGCSFkl-jhf
z%IvQ~<W`q=s0|tF`1%e7B}?^IIbj_~HTe8J|D~0xVIJOQZNTDZA<`KL5geOdtSKZz
zxfB3ME~wX_$6rCWo|k2VErfscO#*V+U(fnOJ!;h#fJ%{1S6(H_Zj~ltdm*674V&V2
z{zMx~X?I|4^A_D3<}&RPlm67}sEpjmM}xgzD>HsxKKum~Dg_<9y%`IF;!Zs?j1($&
zZ#7Mv@X1e^zQl)p`@_t(#{654Ityp)Z^9C#WiQQF3BejHlrZ3gS^9tQNb-vQp}E;Z
z4pnCV+ll}H_3vnE%;aiNvyR6if80kqHx!!jH95{S?cpxa*@$f(aqAa+KCjV5?yd3H
z4C7&9;rhUkn@-}DqA|U!R?IM^T+k-VOE}xGSW$m?Rk#~R#9paaU><xkzy~eb$ANix
zMpgC1LhPl<YRQ)!65M}`aEA4#<rI!;&pTaC#q_f<n;3SCATCTm7|SzD$^sM`9oQaQ
zBOV=W*EtrM{sIvAbV&LsZ3fZ!zbZ>)qrt<p39dy?q=@I5i1->d7KGY6e{mxHed5J_
z*$4;Y^#nN<1Esm%hJ2z?uFld{--nhv+4WK<Yq?d3?ir_1s%3vEF2is|h%=;`$k)2n
z5_^N3Q7B2SiC4rSa!z$Q2&jT3jtLRN3$)7?Lz7wm%%L@GWS6KE1Ko%97Y%f-lsZ)x
zHn!Gj)Ez4=sP~_{g5S@UnX+?!6fojEoP+C^G7^els`XLMl}gvh*`Dv&sTcHewk;O$
z`pD0=Q?RaaZ9;!s0cYq{N<ML~Whb_Zx7qM>gw`;-u&?ni!vwn;k<toO7?B@oq87$$
zuS0Y(vjmnBp$$u0a5$H1%)>b!^6?#Wq9#)j`Kq18639etwCIK@Etq=!8Cc2ew-6)H
z(M*Nb=rX~CBK_}I^D=@&pM1bk{dgT~tsg!z1O;2mgs*>Y-Pjen$h^-Qa;_Pz3206=
z0*A+w#ldDcH;Ajz)m@!K8vZ?(kkf-CCvrV!y_=1B&?#CXdWR`MNK}}p9UudNx2?D3
zf&6I%7MhEQYy`G8!>6o^6db5V@<JXAjU<1sO)uF}LShq8hdM8uO-LEbD*KU|m5YYy
zbh?u+mEV8B=@_Q~P-k2*^$-W-Yo|`uPURMdUQyaRtenJ_vT7jKg5a-rI+l;6s6`}?
z?&sOfcjtFK(GTnP27P4X1;x?GM1G#1oBI*fg0w7$GyV$D=bulRK#`%GHM#nLckHx1
zz;dVQnCPBUgg037U?;E8Ddqf5@zvy2gOA`0`UQVS=_ciJ8KstJ4E_~!RzjmZP2lVb
zBs3ys4G5a^z`e(kF>}!k$p%6S_r3KWL&xm}v-E?;6e^lxo=o&)XptL_)ecoL)#D=G
zx)Y)CP(b=@R*s!Ns}ch9K<R<bS;4cPlATjEwm}y#&Jb??WjJBQC*Fa+Ubr75MyC`F
z4eo!9bjY@_jY?W*4)|C~E<$nQy_#1z(~VB^ikw1@$2s;9?~YJItA}v|3)h$^*tHLJ
z`W&>=5&T*0XGV*HDpqET<gnec`SrHk8z-fI$SD#dBa{d@8e7}ewxDxqY39*>+Pvan
zG=gkA!XETU4vH#f9Hce@gQ1rm$p18pep-JtzN4#YQ~OcL@PWgKCj;(1A80K2DdW>z
znlhYQ!-HYBmwT-X%-4Z*VK2em8|T-`w8j|*8tWa<JKIBvVthJo(BD{j>E>*R=iS0M
zjs%h2GulDH8jJfE%l(}*={WYk4;76<yiNcbryx0Vlh(*QJlT^M@pZKvLdG{whNyov
z1dhm9DT$|lT6Zk22`fd=ji5R)hlvZbd20pTNpP5~5U;RnHD*dj+gb1fB#J}pjd9F1
zMnUsTXa`<(5*s7Ts`lhJ9S>I+`qu*j>3>wxVWoC&FU!RhEU2its(7BRTmcS2bU0Bx
zF;CC^0h}L<d*h`!jLXOfO-NC2G!B0#+S_d7{~Yn(&1`AE6uz!^CKcW$b`p|@;+Uw2
zyM3i$+tki)1r=-Nb+Bn<b=}tjhDlVR%2?D8qTxY(7l~)7ub>30;)RiIp|Kk)*{Jf=
zo1J<<N5764uV`+vG2n!*$}-n+`2+P!RYr|_qPFOXH~s@<ytZiyWo~41baInO)C>YP
zIG4dV0TZ|P!2z3bmnk#>6caHZGBGtc3NK7$ZfA68G9WWHGnY{G0~G``I5atvaqlUA
zRe3yA`}=Qmld=@q<z$O6i=9H4A#0eiWXmvT%#1O^%-EO6QnHkU%2GocrP3nFo~<Y<
zJ0a3&K^KK?_@2?dH~Rg)zyE%(dCi<T&-+>4=Xu_r=g9B2#i$zLX<ncyjmlI-!Vr3Z
zm9;gFNkoS*K`MhpqaqQi_MlH71xE*ekT5j_f=6E7gbw1E5QM@pK|KJe#Uuh4(4PtV
zd4Y5Qa?$0H2h2b!NQZDd;1vp3gG?MY)E`6winx^<TN;C@>V;!KFi7<wQ9&gr#DwM_
zN+<acnVcNzs;Zn!oM>YhV1e`Yr3Ev5NdS(D2P|OLFu;Zu3>is)B8>`ofkYgCg#ge9
z02Xux9585m3}9w|$iWt)1cMS|0{#7I^uM{7V6YBmDgesJ28#wjM-{-#0fXiIVnHgz
z-$w<o!9qBv4&=xQw?<=)u!n8YNI2&i03;9u(m9>^AKVlmX236MP$+>;^IItZC=!`W
ze?2%nI5-&Q6Ubn~XmlT#KV^k~AC^dB0Kqi6F92QXAO&1$Odu5xwUbE%e<t7z2(Th~
zLsJ1cL8i2ypdZvqC<wAM|0M=Bg2~BA`RNWYKyXbNB95^VYh`O|1^D4eRA|;XsyF1w
z#4!UIfai)0`hxg9KM8_>Ng$ohsbT#OME|$UKh%wB(381Q!Xt6PzfTN*M-60zt?JF%
z$M&W{Qe!X~KQn>=fkXj0>=~Syk*F&+Ya<(TQ#1yvY6WSJs%lMxx<iFALzpYxoP0(o
zD?LC<R|7yoUye@ERJ;kz&kthF;Ni3nMS}Xoq|rm+|6Sw0R9Y}K{Qqzukf?Y9XBPNC
zf4Bpc6c7lSqy7$qOgz7TY(5|pKmcF>0ET!I;T!@h`r(+795d9I$Z&s}KS01y7+@rc
z074g@a0V_21eo+dFfx2Ku=b7zsSV&s-b_gP(DC6}$!<<1&;Z?^W{Al@(BGm^RD(gM
zN(nl;cp8-w3gAHk58Q^vge0Q)|8w$wt7RHUq1fR3K*j&s+us9!aDF68=>Hz_o2wJZ
zVXtUIqx<0~zhNYXDJcZR+me{x#GkGHX*Xx$pz~ow^`U^!m{v><oFhkpv<>Yi5@*8!
zsz?p3-!MqF-o8|j!2mRVhJjFHeq#<zgTotuTiV+nv^cE%-{rL8kEVLl@Fc1apr)w>
z;OKN*C=UYCh?=H<CJ>H<4gekuSrHKchf!%vC<O2iWJUr68l8tTXiaqh?nQ@Y0x~He
zf$2r^@!>eEU^<#>G3GBsdkq4W_!n85kLmv}qN(vOvZ9x@rL=wnSJl#43#~5pTgp|{
zG;{&DKMvYD92Ul;UzM~p*8;x~b@f$<*QyXr<XT`Ag7_PMSt-A!jMi_+syZ60p*4ln
zenWmiYDg#{Bhb%p<?V?lG5jgG(0@@RQhgN)wdiO2)+)=Evwc_A2;!I2{(dd3++&z@
znlI=?!b30RRW6YH=%f%=1hfN?kRAH`^Ur-v0r_9+YgM$dF)buqRZRm>Rnygil&Jyf
zKwDcaa!sgz_s<u^%KCwh#6S0(?F@im2<Xkz+eP!<7e~%2O(={)7qk~~$?L*C-xM}*
zwn*F5d!fBTLKJmrL<Tgx98(sZt#FxUbx_YeDkFw^)mc7nCuM2y(b?j*S-jnWQCyUD
zlms8zsO6#~%;8wJbx(9rm5kB{i;MY(uW7u>E>A0e-vv0dd^FLms9s1>d$GKII#b52
zsC<CM6?~-w`A~>X*%8tsAYLia(_Xorxx65BDj8R2)Vue!XMTcki^U)QwbcTy-z6=J
zGQ%%K&Tn9tY0Y#AFcwq0l!tBuQ3AxUsdQ;nvBScXei2jc0_z02SXN4|#6pvLv~|9(
zRo}FKhSrz)kFwk?qXd_sqQm(IHWIvhC(e2#%iQx4^sL&@|E6`{61U1XS^nhM@0Q+9
zMCGu^nIppFMZ*)h@mdZ`AL1SWryr;IM$Pxnl(fr~I(uo}Q#{YLZ?ouI-^nN;vKgjp
zbdh4|+gtQw?}XFAx9P8vzg^cA5;Dr#WmF%3<DF7nJ*c2l>MpQ!q*e1%12AgO&%@We
zcpY>2=zbX7vuvmX+3zZn$q4@t+Pr)6K~k$?p=uZ3R8Z77F36ob{8_(3E`!M?bkwP(
z21v_3^m*oPCMTdfV=&J9v|UBYI<1KBa3*m2YaF+=(uk*HF`u$@eXV@tmyLIrDU&0A
z1w3PVALSP7^}g*Tln-vzbXu5wwg~1dsGIG*lPI%E%ANOzk*C31!s5+{#J&{o&ywvU
zBL?V(W^qUFvBnHl#k=vWC+6BI?wcP}cXt~P3}@*W%u@*ArFQ3HoXze}KK78@=*G5w
ztZ(?Vo%i*tl$v<`zM*?f?~M-vW<|$;ryO<r+-_7&wrK6p%_vJWec65cV0SY$Aay%t
z{_+;XP;~IR#<4KpGOm0ba$hf>>Qp+mImCT?pRF~jWgkwo$wnef#4?{?LzDk}vP@Js
zTU?$uOWr4fp6F-Q!E&wrRG3sK`m%T#ePg`Vt5+SljF1u;NIWOIH91t2JIDWjCHOU>
zKubV$`OM%C&p!;rNeT}`cmmr3-u6$vNGee}B4-m;#?Aklx9ZvaU}e45{oCjA)smtf
znG#||T6L)M{;?5!gL~oMCL<>Ui1)QFsmtZWDt!GsNy&iy@Y^F8a{Jopf}7SV=co1B
zld~}07*$J&0ui1C**Bf36{#nG+l1?$xT_$=`{HK;0Au>;d=<gO$_cJ$r@Ze=sPb^w
zB@p{;rv1YG_fNPzy^{dDMZ&i!m&PhhUYSH$X};~~2{MsOr8Um(OLoijfW@c_E5I&I
zKkP|dZ1%Qun`HWM+d5J<E$&%&?^O5fu-@y4@WR3eZhsv-iw&*Gh@J_58Lfu7>0+B-
z6oHjhdHjV^(=hTOLVhmlp-NBC*UtRK>sKFYw7Ml3u;ULOP5Ls}x_LX9>p@q?9t1kK
z!=}vBG|yw>?o_2XOUFD|rB^`z)hnf9U(8z<YGbe)Oh)|<|8c>O=r>_k@O*i+>Bod@
zs-;ZyG4F>R<Vtyj_qGdv4UUM|IFAkQhQ>@CJI~J&WegIx&2RRsaAmXe$Qpf38i$hZ
zHAN8j^z0v&Ow9Fs?>uJE)Skmo5xPchB19-@?vw62G+B6DENe%tOX%mY$=SPue`<;?
zwjVP+|3P+uSKngG%c_je4X0uRiqU&Y<NzJ7#82I=rO2H(wRK8=cMPgT=f86}74ls=
z*E=`Nvwf%i;D-t~!gW8ELezSK!GhN-3)wxkv-&3MycT-T8k1c10vmFwu0`6-U!=Kz
zA}5t8Oow-(?33~9P;;AcotK*Tv#U`i)wmAvFD4Ti%9(~KxMotG(1!y#umxV$DJQc%
znisu}{gwGt_KBE(^YeKf<pgOBan>TSJtnmcpUdLA(-K|E8ap&s5}+D~3}a=!N(^P4
zPhK#c=AIIms28i&8-JUL!M~qtyxcMNHD^dlckVKNa8xL{Tp{Pjm7TCXFYxk_x6|`O
zTt5!&%t0$Orruf@m78d)RkDm_FUTF*r+CWGWYbf_Hw^QCu|?EO@8@IXw}#yhT{D?S
zjmgLSQMAG33s+c0L$Q+r8NO**^{K|-ZjmHqtfa_Y^D%RU%MP*j;j|kAI{led9Y4Nr
zu@S9*Zk`QbtlQk*-q$`?;&60VMe|+m&|a`%=Y^xYJTT^ko!d{Q`jl5Ljq^PF6cRNo
zlJMSqDN&+-Zo3D6w17baHv51DJxzcv>y=KDNJY2ej$SH59>1IsM(S)jpVf$t7UPlG
zB&QZv60xlrWp%3gR{A5c$8OmfyXSe#o)d3w=JAx3_skfYk#r5d<#8?jglxkd6e%Pe
zIM6M6y6%(R&D&B#@KWFXp$XOZdW0+PGt?J`@PX@p39k_``-b^N7bME}ULuVQ)&WE7
zj<7Qs(e22`h(BLPrARig(~D+FZ<T`3v~VKou<|p}2ow=nq;|kik=v!>QLWTbRra?f
z)1AYZZTXmEg4^G#!%$Zd6BX<P%KN_JXSE#(>*}HzLe1BAEZe&y8N7?5oh9)iLqQ3w
z4F-OHud5ULmD4;+{6cq)Zte5zcR#>%Nz*c7F%jJCG*Qw4cITMz$PCZjt+U0&2~)0<
zQ8Dp|+fH_8w9nYxrrwP&NlH{WaUYbr^c-hr#ch#YP$W5re$z$s)A9<~y#H3ymMx0N
zN3VBu`zM@XZ29yc798Gn_?qmNn<tPb1K-(y+!u*tWVSw#7F3QG7q=allHZpeTa(l7
z>M+wcdSjy}JI6_%^-c<E`3VaLk&*Is;&w3`<TFWP!+u>3TYM80<}0F2-^q|;49+)`
zEl=0&N2GqS$-cf`iloT8*nGc6Q6U_z5VVW&>3PlgRP2n|NAjD$o_l=ClsRP-(pCU}
ze~=o&FDAFZ@Va}Xcu@$}?&10EEy_7IgP~USzWhj~>?ol#eNgw{^mCZ&1&O$))n*q5
z;y<hJK2^OZw4QZGDEL;dKW@j;F}vF_RwL!?v1E3kIY>gzHn^5}n!T;-n-2NvS8TcQ
z{RPuA!sah;CdiLu<G)^LtZ&RGm!oojORq;)?-g`B5g7N#^2a9j#LlV^gS)C4y`7&)
zr)@3n%B4M$@u{AfT`$a7Mh{H5rs^kr7@cFWTIv=QYa%O_&u@Mwt-8c?v+=p=W(}L2
zQf^FRZxr&DFi&kWwCdAX8r?Aa{Jc#~@)-{&v8Rg>yWexw>8dJ(^V#Zs>%#PZ=8nbe
z96+G*oqCiSWhy7tQqJA}m=l)X*Ldm6E5kGR8lsdUB7<yGdhylh9CaNs*_~3ehv;I`
z@8Ps4@Nldw_T8MbUi|B4TaVS3@Ud$gJx341-<UsU?@ba|oVzv^NKHH;{f8P+!nEmR
zDc2{S<;x--3k!0K!tZV4PNq<QRF-!OcKxXHQUy|(J)*8SnAbLYZ58%{Irzj3;|iaf
zM{xgzWr-FGvMcTjPpc0HMy6!QwC_BgE+sqK?!a5juhsSF0>ZkY<nd&X{E)+f2F8+?
z`vW6vT%>WxfShQR6{BvXhyA9IyzleCY1(17ii_a7{o>}bV2i%x*7d!AZAYrFcyy19
zF51lmp38I0e%oeC>{cjOm`WS(6`o*uoH!=jU$b@52{6%(Ba6&`2(m4mO&YkDe5KJP
zZBTXJGkC_!cZMAga>tbl%ThaIdwD+ezl;j&_n0OM@eRi`KL(XI#F~ExN@Y)Stz*gv
z)_KBrByMNTbqP~)P+Dz&`ceY8Pb0l9*p77nc-(lkcAV+vl3bm=PP<D!Y8>r4@|RFe
zLH)<6X!)(J4$*ok%WcKl3FVv1mzn-n=kI<)NoEE_>R*ryi=M8LzGxtL!;cl0xsZQm
zh&4i<Ov;MX4$o}Mn9q45n77xL`<A_%y1eX7wS8d+wlC6j>%T^SOWiHpL;xSuci!jr
zaOHD<6CWUpEetv5$k)SvD$=wb?P$h5CUCU2Jz6b4tHxmiT7O*3IA$~<`0He1Z@oyV
zlD<jqFkDn=3CBHrlZ>plvoVrfA85=!2R1bPcwAHjtn0b5p6}_`GcHn=FGFuR#x1Zc
zDw6`X%6ghj3y3U#b@wE#x7bX+b|+JCht7$)H&#2iHb#3b=H!fpf815uIoag62Q2ZG
zGEI$xwOr>PxLjM7wf;Rkg({ao!aT=UDwnzmM&wI0@3)ga^4iu0`$39V%Jw)+=4tAP
zvAD-}>9a;b9h>!GGodH>d>%{i1>Mm-ny_=2JEm(Q{ZK)FILaAhb15Jy{?zOaMRys0
zx_n+@*HI_^<SqEIydjGtny0W|uP%pF)<qRt7Z#C*T2GS1ENR_;Rhk>7k~a#{KVDXF
zy%U>K%&sVPhS4;9OV!a@k{&Tu@_ncCMOvQRH<wuIJb?-mh?2gckh1QcOLHdb^cJ(4
z!i1Lj+2?<M{%KlyV8njT@|NW!Ghn7~#I8K=oz(izmx3D;yT849;x;;znKraD%|5R?
zDxx8PZLHP~yZ(Unf=jY8Z0l8H^^;HBjk+1y)A)81TF<s8nYY4s9FfXuejVg*@aC*_
ziI831W8O+p3|yk&26oD{(5P<&Hi^F$*<<lX*{kw@JE=vcFA(xCPRg3~3*;3{4vJRW
zsl53PEbzQmk8mR8u;!iD;}m?pb*N^3?>w(ldSpOA>tLQ$(R6bQS!CH>K$z^Nb4{;H
z<olP9K9`$G@fbz_%y!rPXK4Q7d?h+Coi-et(o$Au!AmeNZv1)_j`sK=d%5Z?B~$fy
z=3-EPnxY(;&|7NXXz&dC@r6JCB}wNZzGjgro&9MqlyeJerjvHG^J&yJM`a}Dg8b<<
z5A9>8{gTe;IgY;?{4A)o%i>8x8cOHNqY~gGmBhZK<2`izZKIf?X6Kw4VSa3U!tna|
zkl{p~wV}b=r5kzn9mgNfRDq*py^b%kaFLf3yS8<VZ%f>}D;JTyTqyJ(GTieulR?xI
zm)^t%4VTO~0SFT^GdVE|FHB`_XLM*XATcp8GBKA?^aB(HF)}nXG?P*1Cx5kfby(Eh
z*0z8kA&8Vn4&B||oze{h3^_2w&>>RNCEeX6Eh$JzDJ9(@jda5|_`K)nIoJFC`CW6(
z{N`SHueI0SdxnZkRh>!99AXNRhS)=y*qB-Q0g6gWK&X`*6bQC9V`F7f16jI&fldH6
zW_DIqR4OV7ClC;74Y8L5LVrR005)!@6+j*200r5Zf}8*_6FyWbfDFhU<OI{3157;t
zN+2ju!@~i@2A~E02C5KeD3dAB8Kwr=TUy(L=wL1q5C;z@YfCHWV+;-^rpHK+-r~#v
zd7zms#Ld~(8UVC62goxkF$0t#ZZM%WfEHp8Fa=ow!4?3B1waF&1Aov|mr_#)$f&7k
zs;bj5!vd?jI5<F@{)dZ%x`w6<BS2D2Swji{(qaV2XsT;Gerka1Vf-x_0m>RM{bL@O
z;iJ2fl!lmwuBsFp%VP}yHh?S0$=Uib?SFBjhA{*Dp$2ocaDv$VP5_{_f<hhmSy<fM
z+?Xw0oT1DRCrf4r@PBW98dlcM05^z}Edcg(0)aul8{=Yc4r?dW3iMBa$JGHSTAP9F
zok5RI(vW|YcCc2$oM3Y3zlp&b0ey@K{>L2P3<CW}8Y`glZ(l`KRYiau(ApjfvIp9m
z!3?25sEaee<hKm=2AR|RLl6XzaB*^a%%SuzmD9h|{ENCc1b<eU0ocn2==R?$2DEo^
z_WY|i|5>&f#NOH38S4B`L=eEj8Vq`5@BFxC*7m<;N@B`#(o*UgOp37Cvu9F*z`A44
z40VV8wtkE!CaK5|;O655u)*Gsb1G$TE&;K#gRyo-eQckkHLOoih?57)|1sdU_7FFF
zum4MHVQp`2@qf4q<}MB_n)cR?E+9F{|M7u|Q2)p*K~MlI0OSY&xtm$BJf{9VIgett
zM=`7=K3)zG2Y>|-><sd;wgAB%s9w%MR}cW|<O1^X`djgz2$hWoU~X*&g$+Gy<DmYI
zE@y860r34JhB5h<>VL+8mYo^4pXgwl)*NCF_5hfJEPqg0lp#>qaM1q$*>nGuOWFkt
zRtDOEX#e-d{<k&I&Km6Tzu5nmoi^x^H?1<n$qoqqFP*isw6#0PT-6$CX7x{#|B?R_
zO3dC83<5B*aWb=VaI^oT(R|!(VAxp0jwb8J!|hSe{a-rR#G2XKgPffKoUFf9AXsPq
zi#=>P9)Gz5Sj5zoRP^*1{*Ph$Z7gMP1~Ip`w*;_raRY!(PCyS-R@j8Fb8!K@*kFTi
z4s!oJLI4(Kdk7Tf0&sAF`T#5-PN<K|%*_SM@+kTTaRXSy{~#U!i^Lzq3t*A_H{xLh
zut@(w>;M+oKZpasBKHTuVk-VYu$W5!M!c{ns(*hFEQ;D61hdrsgJ9Wp{*CxxI^e$%
zJ1a~H1Up#$5%Iw!rhggm!659;_@jpj%>IoyIbjI4%m3)vSlIw9pg#fFVAMbk&emXv
zJ=<SKFsa2~5LUP4Up}znEP;PVg$)Xe<>SQ%JNW*1!IE431z`(f{TGCF&*m=(E8O<4
z6o0TX!9Y7x^S^SyvVtGS>yHntR=Yp&k(T{m5XQ;jPej<fvN!;ppw>XJxwXZg;(p6P
zPSz0fKep_Tu77c5gH`fZVQjEU{?OorF?R+7o&PG84Hgsn7lak#`UkSZc)I_U47MQd
ze<gdw9)Cd?7ti1DKlhUA<5lzf<YfJ`xqtrW4*reRp-vE6khZls>=(#iCa?|XWbLlc
z3On}LU~<^&U*8P>BLUT)6Z<c3adC*d7ZV3NfQg-p^>K-L0X$r+KL6oq_RnSb`@n^r
z0sq2}HxU2?atE2A&isIw2?W|CH3XOVO67eoMWo_m-Ydrw){&2WI+Oanl@MPtdw-Q2
zB$EHG$uEsMAEGGBZ|Ixw&c0BGDi9ZZzxXM>;@heD8__kOuaYkzhLqS~mKL+7f11*?
zUuioz-L`yIu5J<MSXy&zGYLR*a7Ti#wc{$1edOWgaU!`vY4dyzqFccPTO*DW7|VSc
zlc0@o`g<E3^x+C8Is(`wHbXydl7AbFHz<$f(Aj~#4i`}%avM&&p2oTbA7Nz>{m><d
z!BFMMl&Y|WX3zWeEMIPcX;@AW75fR?FXC$E)ppg0lg<O=WQ*5++Tjw3H*6j!aIP<(
zP!LnU7%=;(JU`NpyxxY|pz$W*ge8P1<(}7VN#Lur_UvjKz}0hm)<=haiGK<ruh#Q6
zgFIZAsAvAe-C~pn@yE?;{N+zI;=EQK^bB9o+-I)L5h?q0zTe+C@~5I(a6O-ji2f>7
zC=~Im|H05=WopK(QR^+uize5x2NKt#TY_nL>2>UJo+5nfte<<xPi1e174)X1*xygv
z_R(~T7S?p0Q}XfI?Dr>4N`LoWQobbjCk?qz%i&~rD!-j4xSm)xIdx%6)H=?V9bq@Y
zQxt_O#lQBk%)<OzTimB)X7CHW3TpSK;(B{({P?md{7mq=n<}wNT*9NYJKE44$os{+
z(bhaYG2wzKBk{F*3-vT8P8G_rAaUhgEC)@);DML1sm`}g;k04&fPdHHlG_}{1*0Kv
zQH8-1tfio}f;2t|f`M<~dt*H#9$A-rV+J`bPy2`<f;ZF6DmEt}%@3E6@E<Ks-acQM
zm;ey0+COy&T-_JuHf?wkx~5rqUz;c++jGg?&GT8jL1C@RW6`Bt*-3Nc^D%~9{FAY?
z{+U*mqvgmb_!k^)JAcS|VMZ~-W4ys&i;hD=0pPKg;_x)ucUc_^=qK^mIVY=cx>oix
zx->VJ!|asW3|78y9;Bj^1QcjlSclU#Z)38PB8~yqZ1Qz%N%!{ND&*ZAib@ydeTP4L
zKdL1wEI%x~!YTVS5}=^lq<b0122aAd+J4>_sg<;9P(Q^)Z-4Cf0XGDH&xAr~J)S&j
zRH(nqBB+3aLaY_O3}9aR<Yv|Oj)q$BsWdjtO(|1I!>Eiq?kRq#-`?r-@d^^Ur92ty
zvacT&!>YnCXk>j0{3nflK7}ox5BoyZAL1)bl$yu`Af<4V&s)-xzN9U)qAQOlPzJnT
zti7&C6b!`xNPnfpnqZ9#bjYDF|M*ZtSgT@TDp^s^^7>hIN%70Vu^+({GO`u1gKr+p
zS4I{2X$_4BTb@q&bSD@E;zg(S?l4pJ_qZ+Z?C1m_qQ9sQ3r~{pPET2YN8U#HIaBU~
z9+W)gh47)3KZiZJR>q}3gxR92sBwN>Ng*{ujptdP{D0HoTD*r18_ks{v`B%vq=@As
z;q;>^M7)9bv`!)I_T#y{2?lJ-LbK3<ROSebIzBp$$){(ky4T4g?$>Lc`V{=$*w5}7
zt-LoW8&0TX9pB{zX6~Af$h~7dxtg;zIeV$34k!9mr93`^`0Y-mS}XB>mj+nW=8S2f
zFQ&OEC4ape?mgDYn6_g&Z4!0eJ|=^Ad8&gas}P8__LGcsejt6$+fVp$j?1}Mb{}hq
z{c%!kZtax|s3vJP%YJkk-RHV*q-{(}aA{zsyOm54(Om_xJMNx}yKHu<dyLA2glPyy
z<EBqOJqcH#Y357}PYBO*Xp$A9wW73>*Yg%oJb#TMt|#{`fvaN@?YF6nEFG^+xfKZN
zHat6_FQS$WL^-gZ4GWFa!m%MuL2O)3JKSPr8xhyK4?YKJ^VS~Wmwc*>{w3ezchTnl
zptnPY7*a#SA3IVx&%Er&6LJGj2+yKU3F&&?z=+srb>Ss8H?+MTjZ(tyEkKkQI31*C
z-+wVDgquVYMJ~weVTZ=?^~W0vcg5!>ZRg#*d2@9mUu$J;ymZk&-02YsRODuJY~U8A
zwjg4f$IIYX+_PRF9Ib8Z92EiWCGeVSMDA5YqCh#|u>J@-#z}PQhbC^QR6`7<(Ys1i
zUTYBq{6c~kthOW40n643k#YcnkGth<wSUzXF)g9`k^GshSR{=5LBfpE46VB;A6pta
zBEs)Vi_=LB_?=DV2`+1;)eOmg455IW<yvF2bfON@y7Z8BKB9k?7)sWZq)KX5!>|HZ
zM)d$sgvV3$-Gn?sj|0XM@=iz_{j0IZ##9ARx&Vl8xk(XMA*>k(ZcNX&ep36jsegPl
zFrEr>TJCvgsn)nQ*Lua2H@$HO0W6q%=$tWR?gIEx_{z12jlNUmws(G6RHKtFwCjSN
zAB(=^L?_sTEV^arH{k}(x7+SDi3KMYVH}|5JFc!Ti4c3EYDZ%4O6-t7E5$wlI@;n*
zKHuWX;Tn~u!Nruo$F<5qQ-@dy5r4}sryk(hSZ;fs!ox!{7a!z#1!Pbxg$)t87%Ik}
zILI(mkT@+9B^q$mx-wv)UJ7Phl}-%~$K$LU#r0WzQT$d#gEathE6@mA*>OBy9`r$q
z5eGdpI3PF+QLBG3{))5TVNasdo1t>W_2@uIW%`xUw(X?$hxbqLx)hYQFMpDU4ds4y
zhWUos93f5lzX$8v5YwKNz`6N7N&aR~$)?V&t#gLRxtY<&&P-iMu#6;#7<N;-w5CX=
zb&AMNIKuGpvfe+RT58oPV#^fx%!W$3`T44C^%ml-n{DUqG|5$NT8)K||M0Aw&ehjY
zMuMM5PRS)-c1Whi<+0t09Di5Cd62O?71$?Nfe@=+$6($c2tUv0SQ(5lkcUboI$#@W
zvu3KtN}d^U*Qw{KPOcT>8o`igV#`;80JQFYMlha!WBBApErKIw=05g{b;OzLOLUPN
za{r-;yLY{j&*D|!?md7^>x#dwJw?auGB`!jSdwCSQKdm@yob?+IDhKCmlO%s1CcF*
z3OM^>G&T<yALgdup<8E{EJ3E{FAF=eqp=Epuvt{h8GKaz@I{{~Fj+Nb08i;x>Bdru
zkEu1wHEOKm9j7()UYAQx0jSYOs-hKzU*bF0T2`hQeDa+$LDw6py(vHRZs3*Plt@ZJ
zOWhI6OzICCBHhGZ@_%ZT;W<$vWyNl?dW)yL;Qhg;5H}^PUC~~C_LcR6-SbWL;qg-V
zT)RnD^b<RE{J0kW^4Dkt%Hb2P(3`8+PQOE+`7Wkn2RYi>JY+tf#`2Jx@3*csbWO@V
z#jgu6xHEM>Wp?37N7tDP)90*Zuh#Ck_!e2(QQTt0{NmJFp?@H{5$s+!KpYwGwP4ZP
z(-*!j4$+~CbtdwAWBO6zn(kG&XL%(tPo(cz1ESP^5JzXjXyR$aGsn8fKth4&9wZul
zK{N9RGL%=MNd3oHh7BOw6Qb=mEbl9q#fUbRL}tTxaaS^nb6zi~#Op%|EKtI&jQ6Ya
z#D5sboRGrj$A8tRC0J%`38)PkOl1VfjtG*5Z^>zPR<p@;gphJiWQKoTcfBX%e*?Df
zc0meXQpL`1*e=#op(v!dO-q#tA=@vxTk+!_&oGv|m*5ycZWAy(Md`4VVD8riw@xCP
zw|DJye(B9H%4h4i^4q5gg>cb@p6Ia@F?opOah<=jNq=aGFh^d7Dy-?JWlwFxCFRt9
zCM;fg9$us-prZpci3yiSlo@}WAh~4Y;-@Yh8~Ylcuacp<{TZxo&k@|7v`YF$@-8rj
z49h31<3gjmJKg?ov`4yZ^2^1}E{spH#U%4x`>MW1ea}6`Ka?pSrBdDUJ^Fcq{5`Ev
z=xg4k8h;zB+$E>5><(_>M1^iUzpe+3wu!HF_hK5+0O!?|7Isy!CDDY(DAlWDuEV_e
zGKSohNqhyK3F^t*XHPbPIB1a+pE>g=jb>GeW_5L+%>roY+1xww6yIXVxW))+u<=4d
zu1Tu6>7H${=%Yy|+ZtomZIX0;SHgQS{`vVvtA8n097&g4yae|<1UwqolgdPMhh?vt
z_jF^C_AkQ`@fJ;4Mu-Bf@UQokBxp>z4{jA6?$?eOWDq5<gc+0%EUO*7Gt-L8^$t05
zOxxO&Vi?iS8{1xWWSNp?2o0-iP~%9$5orjnbG=s2Lej<icxTqoxYWII9zodWOa0)f
zk$+PC4pBA2rmZ^Q$t{O=4sx3AmYj$IjZZGd?f2(v`UVoAO&<_iRvR-v*H8}yzRmrd
z;q)`<{5Ur&i#!GsqpwnV;&rC|lJ=&DfFA+;_ZH-(h{Nf_ow9X*UnH@wCkMu1_Vlzr
zD*9D`j;d2U<zdOBFGB%)-`(g$c7z2Z41fDlj_`X>z+7gp!h3|iw=k3^eqCrx4wdX5
ztYEa!Y~91QKsqyJYek}e)>Y#zjNW?1Og}^trtp@r2_ybfS-bg@sQJ0(Uo0P`ol@(E
zd@1FuI!EbQQ1{Fre!cV;LS1nf)P;!Hw%hVUW6$Oeb!x4M)Kag<Y=@13QLh_J+<zyh
z@Y}mZ8YwG}BFS!}PXT^sfHy*H8q03HoZp=I@$D~PbtS2e4=jCSN%8skgPT@AlYg)~
z3}x`i<U@N3R*`PM93vW-h6Gq)No?e_1w^RPbGgXb^n&-tq+)YnbM&mmNOX%@h%;)R
z>o%(l7fGD*U)84S#@8VN)W!uFV}CW|e55kiI?7i3K%6`=&y_WuILd_rc_?l(Bvd<F
zt|yP5=*Zo;Nzaqg%C5$?_I%=dGM)HtKtfEezs|=aF-M4e3JtH7ekz&Cq<f(Ucp1hT
zbo+hSR^~{y_TZShDEl}Q;S-m7cGeZnFj)Uy3ibKu;=Q|F+6cM(VYIOjHGjua8Xl@4
zUUN*%iJLfXs?bM;2W7s{cy@5pP!z6YpzIwhIAY}q^PrAxtXmm#U!VJmkE5-__hEAQ
z>l-wL6xuj^TerlH6s^zI;w<h@FLhE}{P{qoO6!yUi7&Y%#Wm}v`UG&j(#bq`bWhi_
zY&*giYhB$SmcT432yUh0zJE}fO_Fe=V4|a>%+KHoBZCG4L4%O~Q#JPR@tR6Ts?|(q
z0>=cDq%VjVoC8f20&ai=0$Ij@p!9L<ZM3qzo{yHotON9YXQo*(>S2De`z+I5pmxt;
zrV<T1g~dpB(R(CT<rx$)*%pqu==$z283p8uwkQ=OCocvPoKZrpvwvzdbuT`>54|~X
zu&eA!T!ZJyDeNi#Y>|Hw+Z3{i_=N~Rsr7h5CCA8ew0NLYt=_ko^O*5l1fj*S69-G>
zVsnr_+r>um8Yz}@wZI~A!BrBG#cpQA*N(S%aZ0(oE&9fl53*p@!d-vpNiTtSt&yWI
zx8rNLm#lje3q?xiu77&0y{^9&-@gI!l5XIV^DeG@94FF>Jt`-d6BW<i#Ah5gb?2|C
zRi|exO3+yb$ZAlj5uD{XR?z>HOBF}AZio#T@+Mvo_{s5>RGm%2?tnqP$n`2h*?q4$
zi3V9gg(6AyDS9_jXHeP_ZoP*R-Etr^d0iOEVgl!>-$zCKEPpDfcGvr^yj*ATjb8Ky
zz2KW&)mg8@>sK3g_sU$LUmIC9=h&@3(6UR=cd+#A);R6OYvdl{vrstGcVd*Fsus8J
zBe=OVV;Wi&FBRaPT%azb{4z_i@2d`0^6{1U;6UleJ}MA5q4`BPX0HNj`r3Y{6}Rt&
zrE~TqakXGC?|-`ii&r!mLjC#G=$FQk3bA`5DJRJYj8yQe)BHA?N)wE-z3;Q{X~Tsw
zo~!{1>*M`(@QJ*lP4P`->jDuA!?n|9yn8|?O-+!<Y?gq*R(n-8@n`5V$Y<yFhZxp(
zGiBmIncSNpnSSjus4TzEy|k=&mhVWJeN<>X@)Kspd4IHksb{H!8Fv>x?NgMqw;!nD
zcpciH2vbCtwcJQzI0gEoQOhhHDX?FXog@3hIbIastzU~r0Fs}}<fS*AxSX%Rd-mRq
z5~ZqeT|80Gx1e$^-3M8h?3vlKn~3C4zPVsoDUeHud1}46`|~uLU0SpTt)<c6n*6YW
z3xu;jgMTpRHru<q5H(u|;0qM&vG_s4^=_=!zP<hQ3XmRT6BLpaxT+C0>{Pmet~WeL
zW~Mki=pj>>S)|#?az9DA#>7WrkcPxN{OiULE+D>Iy&cQB(mPxH)tc?Wfo!(vX)3^7
zGs_{it;%7kW{`hI{OuGoe5t@HJ&r}uY|Osv-hWUi1lkqO^J69NsOl0c(FK)%ZQ|&5
z5`$A(VFS(<`qGqRw41SPT!Bu&u_79Sw}~_UL8sMD;1|M%3_+DqKbxH2#=Cw4?d<~d
zPM=lz>zj@qw%)01Twm<OV-;uJ3}ZFbH{5h$FIBzd=*;V4Ho~`NKe1$qzH2QEc-Ry8
z@_$yny{a>w9!nHA2%i)j+!6cg8~2<>j&jm$z>2DvMGRc(@vC><Iw<)DokRMSnS*>E
zKU5Wx2#zI6ZY*0ZR}*7V|48<V*Ud1$8;Y-O^Q`Lh4`NX9n{&{ABT{M+g64Fe?hEWb
zJJF7flzELVd#R_snsClM!lBpmFy6ZoSbu8|7%YlGt_<F?>@y&ZZ=NH_3npMK-2c^g
zo6z-UAXgwnsQdDPwFaRuTC~|Qq?6DA*oMuyZ&^Z5H@6hADc5#RN$z72Ulg5wwx#Kw
z$y+8|)&V>;X1PUKyRX;Xrm6E%!8ek%GD73xEoN|PD*m#s4I%Bt9;U;){nkck)qk8~
z6JfABDb&eBGrmB>#5wPfQ*2NhJXBD%!xIfA<J?BdiAk}Whh|R#qR(P$>O5rBrVcLs
zm}(5Gr%TUz25+yZYY%^3u6iy!I0Vuh7{1PxXOpU&OUjhUH-aOzF00&qUw?>1ZJ=W!
za(O96pvaYILMje|)STeHP%7u?;eTW9X{&q_v_J4(DN?g|LJ(teUbs@dKg&L+(C3MC
zbNFPhR9C7H7YdfE9*$QG+c)N9g-;>hdrM9pjxWR2T%-KOJu8`AH186WOX0OvtOzc_
z;#%Kzw7Y*C@P4VV7`H!a6Qa59x6-(RM@mkc`4yTO(Dt#dXq=Px<5W7v1%LBo+(zbf
z-Aq7;e=(d0d3q^n_mxl@kpcpyw2&G79GzM2*^Z^4{zsigKmUw<4(!j-ofWiG`en-y
zI&$~RtQEm#U>7)u@&nfNtMKBJU32F5RPtX6H9|)?w0$qbq%~wE6zJd*0tcEA&*w;v
z%*ngt8SPSYDlfgoXq?DYHh+;duR52FKHC(Ap*qC#?Z425v@q6Dqpm6G%peI}Mw#rb
zRgIZ&yac%jh@AH+tp&MXb@#R;GmSm<?+b3Rdbd#L6yx-Pw06Oq-XDX?3MIsgcRIm@
zsu63nVTpr^q*cF8=Q*cc0=Mk?nl2x%c55n|N&rUMYGT!|iHu{alYbLV_K9u`7QH#4
z3lYO#P_FDkYr?vrlw27LRIV@2Wi}<<wkSsi(!2pV-tmr&B{3-^el75VO<<JDrJ(MT
z8zZhCp@8%#-q@k?pxBn$BMt3HCY0pvT21X*<0KzPx$V*?3qi9?18pT=-n?fP@?Nw$
zK`gz(c-N~RwfBPgsejQ`O5MKlRO30_B{jm-k0jQ7=2ZZ-RumL!h|#xO&ExnX_vwRR
zcGxG8!Q>L0F=nbdQeB6%J&h8*n`f_ear9qgd_JIu4iq19#qO8PX4qEat7>aV>||f;
zcsnOl<%!qO4$``&obFJGC`6V}^<tpMV)t2xlf5S&CK7JY$A1;XKcL~T$^JPR$p(C*
zj2=>|Z}BrI3KC3ui-kmmDK@_^yif70VQs~2LMo-2c*489@!GU-oxP_FeJj37F&szz
z1-Y^D{xBB)25A43fYimxK^P4^0JHt|!tjd=Q^fg&)^&YXP5(3`ky8G;y8{Psty<E`
zMsc0xc{a0)s(+O(w@w(~U5dW(&XygUUm%2EZ~|3L@yKN2djT9t>H3%0_m`I=K+8{x
zvN>1bQ!1@!uH5>CM6^l;yyjHQ7JZm#b!l<W9k9bA9qG{Y`F%Bk)~dl(-c94v;=1;A
zyt-UDs+bDDu<WSmof`P|&EtuF3Q9&mhR-$Pf@+8T&41%ImU4Mos%b^j2%_57tXssf
z8ugCRX>mpH+<-&@r-^eZfETapIDPp=SqgE(>yQuLw~Ht#jBMg!S&+EQ+o6!nu=3gt
z8d!&#v*u|ddRpHh?$W)Us<G?@*Cj0{c8eJ1RPB)Z4QXjZw2B9m^BKf?RNcsiIkQM7
zD;01RTYpH0I)pxt2907Yts>?Fx13O;iw7(cspXT9J>Dn#WQ?y4c)TgGGIEruvisuJ
zES;PC&RL<Vi|6e5GA%*a;A<_Z^YWL|pzAq++qm|UNV}k~RyDqbz)0?v6*x1W`P@yl
zIj&uhtYPAsrQ2o{@7wC~r@0puKi$;A1XK*;Uw^YNmTXkm`ZpG02Ljmu#?NNy;=Y>a
zm5oyqr@qQUVY*MOn_zZ31J*Ynk|V9h2T$E3)V<+jwaN16prUvY8cMUNU*-^<JnAv%
z7?B{NHi^VTcz7XUxx!z_=6!96cyWfUe&p6khWoNKp|$<CJ&9&4y~rLdqyu*c7%k1T
z4S#MM|A`q+TTP+=Di3Xt)vcWK-KR-Ou&*8)W@gsrqB&cjD6nF(+?IY##pCq58^`m(
zn`L)S1v>#k&-h3V|8E&^%e2{km87d*oN+$xw>Si+e@1cO{90nBts3@|fxx&mT3W_;
zsrsBqALY2oN6X+T;rk0QS7$YKIF6WjK!39c(rJzK%tsCRz^Eb{ld0iDI?C|KT`e2B
z@%OZW3GYc)KTFTM79A?qwCe@jtZ`3!VhcKDtk%E95`Mk(vFlQ<>)KoQ?Rp&BE!=W*
zoxyF;_ab3!2E*%2D`D%F%$la$GgfX{o2paFxN%c)CP^k5yhYTO11S`V!gls$+<zC}
zai$iI72vbsNDAG1(n-}d+@*M-(J#mfrZtOFwIxz&Z+oh=J5P)h>vG{Ek<FsFk!yvD
z4$%mq6BRxyHJA!%N;x}f0}0*dhRm8mZ|a-fLU%Xim>X%D7ETH!G?t@O+D2JE$tusc
zGk(($DKuYQdYz^{(L;SWz&03|tAASjy<;myZIV;PpKY$NQ7ZO~Q5Yg7wcKq&tCbL(
z-1)0c`0nEfhO0#h5h^y?f%7c#mnmaT=#1pDX<uKs+0GNQ%{Y@%;`guNUu!1$D<R0b
zmo3L2t(?i5gV1EvOwGnaPHPkAF-xNCg`8H*8m{!xrBEpe>Es2bIwbRB^ndCpSqjcS
zO?%@==0#lXPcVqZ(%bDfy}8_-qxF4N=G|8_s1FG^RV^F!$O@`<IjJxcsYK05jhY`x
z$kx={B^8Z8y)zM?_ssPTOr>4E*l&9`#>LY*`TnaUwsss{wfQRPIN@45l9TwnZQ5en
zaP9db%f}OXH>YtKBB7z#@P9(VK$1e*?%p>s-TCy4Ilq!gu9bs-dZd&;)9t2)U?ru&
zv(f@9V;k<O4A}QQTo`Hz=i25RH57=78CpM&i~YEd9HHs7kyEYll!FU#pM5!q_Y9gF
zrGL@J)rrl_umHzG^3Vc62*%p%OMvqxENMHvA63CnO(9n#DPg3*MSs$ZBEAqucNb`A
zJIJKl8>BciL3M%8Jnp~7`!+z&FfZTz_W5~^|7b~;Kp0JbeObWjE{%4<l8|W}sd3VF
zBfh_7J^C3~+QGN`$_wcU3sM-{bI<#J$y?+PMy<{F3u*`P@OxaO;d}=BqVYaAQFj4%
zY0b0!`K0_eku{0=RDYN)TuwrmOqTn~HY(SXg*<E<-;KT>(UTZXiVTya>ZEO-BKK_^
zfdf$^Pnl)UQj+GfCpf%?+7)?_Yq59hl4%ZAykufgw~yWRKQ5(I2QJ}yiEsd?Kv=&n
zB{GH>s-+lKb)iO-o{hYa$_)Wa-mZ<f>&;6Mf7`Sg%jD#Nb4SO0xX6Fo=jA$yE!O2{
z1O>O$4C0ZwU3Lnjr4`N4lSfNlzonYaLM~%FAu}NqMSA)$N-JVR3TFZbdbc<s#XG6*
z8;Mtm^iKJvCB!CZH;hLTG{l7N5olVEVlTBYkH?p0xwOomMCXhQP{BE^mL(6xCl37v
z6)P{5*}KDirAWY(I3#~I)k2}roi|qW9y=OmkmTzVh0+PLJ@>|tK)#-h#kp2NhR@Il
z6I#4zE2`wgGR?D%a|t*3nVI*C`RY~;j%9D4BydT`(ku!DY%1;M(`WgW92KF9!rNtl
z{RK0=+SP0{ii@Svvp9{sW>uzo?8tNpI<DF!jcDT%>%$P<!h(OzWa1bb{2#L6T-JQ~
z_IpN7HPziwJLX!u)`HW^C|y?J;093BPVCo)a<wGnmS~jPpfK$yqPzndFQxK=8sACw
zsTXiL%pK;Wv)X=?qA~R3{VE^eUkWM&?zGFr(`nfO{HdFAD3&Gph!tP$n5utKxJD0N
z9=sVOU92@b7*l@)uFC}PPc%5Y?_Hb{2naA(#}jGRNA%d}+CmJ<lyQoYXUNoJqsG+V
z%`(CZObWFz#Ic+{f4;&hBa8Ybwo;^|KM}KvcdVF2Yj){JN^j?WKv04JqBE*-bd<x9
zGJh5?0R}S5o7k>CvVr)QH?828*7uZ1dE_-uWiGB``?`NPmx;R=;j`KXOWwT566OaZ
zB<`Ulvhms9=1<B~SJ-HNr1XE!((@HM<L{iK%+54(T!tksglR56qnL@BTJl-o=aNf1
zMtbgk!O>c6#0$I25*PP(llG|g(w5Qn3`x|0a;VMpGOhCI12OrO+9?pc{B2pmc1r|f
z^xGDxjG%vmUX2zfKkbcAoP1K<<s~RQUARSUCr1FgJ9#X_CG7{nH|03rS6#{&SvA`{
z)ymmNv>DxgV?kT`u@U6t+o6-SmpW2Qx=9;C`T@BKJoh5%b&^3IM{0iT)%4osIUC(<
zuXXH{R7TbhV@-F|eWv*fmGSzY(J*&BYmU6lY`cHSK=EJ9`P8z>{n@!Z<86SUXLl|m
z$DElinv1`nqA-mR*~4J^$x~L6*wrkJjJfWemqS~*CL8bIvQ;#$?LZ1gW2U%pti3f^
znRiV{eKyG4jFDZU%>vU;qdgVmw+_1`XN;#9$reV4Gq4#zb7mYiyt4kUO2HcxodQX?
zc1V96nJpjC1_sN&YLbaaGtzZF%`gf#ZP@rGurERb+}Wq{@Fb~3S3OSSO{Yx-WU=Hs
z6ptmA?2LbTPcOT&VCc{$h=pKJMobbTBUa{FtEKLGe~u!wkrAB>l3F3ScZ>GT8v*lb
za~mbPW26Ky2|_FEMA^dB#i^9N%<EfNz3+efiWhkiiaAATBqN`Jj?MubD-2DM!dOpE
zmVOolkT0?l-dw1)Kt90!MG}a_kpU04SN+p}K5y$Yj<7Wzr#H>xIdE|M)!-;u*;ih-
zR~HykA>3k~Eov&p2fGMa;WL8O<;ylkcA2o#nT#ZnJ^Uxlv{I>m72r2!J+(!(<|BW4
zhjuYn`NL7BF)lBfWQC!aDz=yvIrx(5{0o9bQcr-6GN!+LRFgDvfqeLo0o9BwdK)L`
z!rAT(!_Z(m%E_^Qd<IfMapR%zTe4qlpP%$qUQJZ)otlwdHily26dqcZ*O4ueWPf#t
zgKm8ule}2QW|c&5hp+tHl_@vz!C8MZ)MFh-j`H|vqm*!Hj5=Bi)iA0=|CSA!;D|F}
z$pKNK9&Mvf`dk;+efF0m;rJ}v_>w#7DI!o+#-t?1;9fu`JbjY^I%gpvXJ&bEY<B<1
zcTPlN($TNR`)~6pG(*NHHZp0qczqp|EDA};!+M9Da<-3+-=@%YsEt%KUMqhb2is*t
zgc>lOa2tw=P+IzG9dIUAmg~s5Y6PrWwB_OTy<uoMC;8^ay!t@GHiP?uWSOG>M^_Ji
zu>NZ!WrPOHIc2?{JVzib4sAX59~imw)~YXy(~GhupTQ*=2nS$(ZCke4;j}FiMRjk3
zyFLgLY@L6y@Z_L+6%X}i2c~~;nE(L)c@S4k-l#&s3rgY~fij-_RafU=oVkKi-KtYe
zt1Q&|xDLG6Ckx=?T3ap$Iy&yMGThBvUmpWKh~p62q;i1MbfbtJCeG<Mq}Z}H30##g
zrTe0m%9b?_!~AaOdMlgAOzX!__?2frbv(Gr<wXZ#(Q~@=^pK<VG=G2L81E}|u^B=V
zF&QKC;>7?IO2$mcRD-SWKdN>)+@`)JzO%UW<K)%rF)X5dhem3VDoR(B?o9adn*fSp
zP>+fyKc^$d=OVl-l{+hbDu&wrV}ZWUS;?;heQVPt<H$1Wu1_&&(!qOoFSR2i1~;vK
z@&^vAU7cel<DFAUlhl6+j91|H#E;Ije;1=wk3^{3Nf@j~q6In0ni_78nPw+888W3A
zVAk(TT2EdRnWMUO78k84n7XCQsz)um638hh&Clsr7Y*{pfAeujr%DkO?6{fBP?+cG
zEU%oz33r;hcg{Fx*sXT_B^k_`sJR|!ZL8(V@F6-}YW{tNLIi(lSt@>-FP=k5#VM{V
zfi%>fqIw70UPhHCqI5vP+4!Mv<kFH0XXb!lnE=A4Xz}b~FvkqV*3b5?UY?N2(xXe`
zyS@S~xmgjW*(ejC_%X;g0ke3S{OBj-9wBr?6jW{E^_<Y?smcK1A{&`V3)N>sH6C=Q
zF~OV~P<c94n$~|}%nBmC;xwmvWnu*8o^HG#k1>{mk0on3mf^3qz~=XHd1-h6s@K3`
z`n=RH`nFH3H!S%23_eb!b}M#BywX;leir2f@#epO(E{@OFusA<C8O>>@=DV|46NK7
z+g<8oa}<cs!WZBTMz5D_80p<5(j_I2IK}MWb5f1jDYkzyCrMUn_|oz~XGet9?IeQU
z_RYT)Pk^uI;CPf;<W6{FKjnE0)SWZ8-7zb93tiK*IO_1|c|MNMmo1fJo;%zGPNs~*
zLlZ=6!On$D+K9~a6mO+F(G@BEae<`@b6i~cXnwnoY5cQWl8kagazKJC@iGKU+&%m|
zNcm!c9k+iV%L~lXI#tDjbLAFxU7}>Q>_ocN%hLVTJrsw@SHFh3mwxO<%r~B<j6aw=
z6X`TWE=1NRY}@%o{Om4jDKkT_je#&zkS#DOwK6N&o)jTG*G#Lyc9&gAX&5o0CeMry
z*a-vMKBTtCeAuSA2Z*(2h;^n5t&_ydt-$y75kh~tAWNU>eV36rpA7_xxxRYY-8wq<
zEZ;}y86o8%dI>UKzJlf4_l@Fbbz+29BbyNmHp(pR-ShNQn>G+9mYEbptCAk!`v)$>
z8-=XruOtjUh4lxY!KE9vw1>=wU&O8}+pK=A<_EPZW=IGgrUFV*scJb36TZUlgXynM
za!h}M+ffnX@@<kywq8tC05AwSc3eDhUxmJ^!{|%7BX5{Ew?`THo=p@BVKLRp_tA{7
zdi9hl6uUdvtG`uy)c5in-0D?gU#l^Rw-KQf_(3(1D$A~Cnzomq9*0%M&%rtr#66Fp
zTWH>EBU2uR8O?fD`>?Np(xKm-ljh8_4PSp1d6kRoA{IH7u;!5FDFWme!Z$CHla33I
zw@yt3BlCf|-JY<~3k}xgY}y>T!<U%M-5b_Ig`7`PC+sXiq>Li7T+<=zK6akof^b9M
zGl>)!YS8E1__JloZ-<29vpRQ+*3SBOx`vEa5QFnX_nx=ZPLb7)&{#Rokj!5B%eH@%
zk(sOE@7HF<w&FDhAW&y(%>LT!$fp%AX#Qb?vy)|QBK>nE=Q<#cYMxujr$%ZJ4fFVb
zXMcW!<=%vSOsw4GYJKbaLY1_<mHrniNkbN2lC-0tDXmLRbqvXuXZszeh?8Tr5sR!A
zdbq{;E>hdEd^M=Xu1Y%=_>Dea8xw!XmTX#1Wvg+dH7&EfG>xV|e_4192c_(Vw5Z+<
zVT^;*`M!>OlnAHcJ!9s$XP56>CLnw=Yd)$VSl^oSqTxkF@8RHL_dF$UpB#gTn*&O)
za?)`<I|=0{sZisAw-glHubI={We9Tig*dXy>mNT*2*_MHq6(a#V)1IuDolSAn76Zi
zxPQhhHbS<`w=Q<}X6OyxTfxIzh;pEVt-=r74h5$@w$KffcIM-uvwiYcsixVnAR)vS
z)5vqyQHSlTU_H3cL>#<?vgFb<jjrVNiA6y9mrHXt<onc~Uz7QP3-qjA1`!O*si0rD
z&qA$Sy~{De2cCpfMUOXAxp994&lRWE?W>^=9>!G#W3DdsiE^}8^mmPGe0D1JTcMDw
z&>G;fk0X2Kc;bzJ`efxxht)6SHxBN^lvL(*1aL!KrMh!xIrgirV`7ncQz8hrQ%wO)
z$RzjM+P<D+VSzO=sl^XV(;=lI0<AyIDbzwScqvDYUdan;*FTYK_yvF8%0t)m<splV
zDNvWWzbQN+zf!RHA!Hr9PK;x5TRdX79Jf}{tCs&0s&7Fvxr#x2C8V~(rbp9dbC%T?
ziUx6^EHyA{?-E4N?z)y*;~V1p<;;F!^<A_SH6MBDsWI;ticUQ<0YUmHct?skA*M0B
zCzL-jo)<1_E~4Rat$Tk|jnUuSk9@d6&^GjCcJOL7B1ym7<J-_O%A&5dMgCFF;q{Bd
z?H9>gb6!jm;tUM&H+tIoKk}vQz7ytm1EE&YKNCw9vfi_a-sufiQZ9JgP3X*7ea;3P
z0SCK6^NBeXhCVp$niEa#(^_2YY-F<PboWB(8lxI54}|b!jOl;x4=4F%!InQKlL%zl
zUdRZ|!_j^tpS^+hcJx3%JH-<>SR|#5Jm$nqO7KC3U;1V^f8gZL-@-SJWTZe|J<Z|l
z*70fHXRH;jlE5jlQZplLxb-&4t*(dz_Lz1t$Kr+M>XVJbFH>0UuGbr_<-~}-7y%zS
z|35}*c(4j(Ze){1)DHqTG?$?&0~NQNd;+`*12Q)@m%%sz6cIQzF$ynCWo~D5Xfhx)
zGc+=nQS<{81T{1{H<NMiDSuUWJk)>u&&VE8WczSd#htTP_K5725YGAFICtEgJ)<Z@
zvPxx3L}c&1XQhPHSA>iZkx~4PzN2ry@9)pw;~saPd+q1@`Fg$HA3;82Gch$MtRtw6
z#Sp~cP;mu7-@pJtaMdLs&?uy=m?`MujYi-AI8;JhoJLSk0|z1qD1R(Q6F~qK0Jsdn
z6)*!m3804~hy#c&@-%{g4u}D9M7tB<=noix1cbT2CkO{b5J!SB7Ecg!MBs^L5aWWv
zfM<vy8dy(%9LmL&aF|0<OzbezVYE6F&_f{IvA%eB6o9}u0eVmaC}4>7B`Q&X2o?i4
zg02X(Gk|pl%t0%_!hcN5)C|xuHL@@^I|C&qHuLuM#Nz(MqG4ukp(6@tsu`MV0idNQ
zpkrZXe)ww+Vu<)%L;*u{qW!QA(eW_cK+9as{IanY9CmmH01o(oI6UgG>~GkFh{%9{
zpb<lzaafO|0)U7sf#9hCgZcXULS4M^1Sl5g0`){6;WKwd;eP>NEY2MuK5-x#JR-&$
z<3yyB;0pdsaM&C`AB6-lc<?Yt8~fAfL8OuxMAQ@h21X=;aF`SQ(;dKr;J?baBJfAC
z`o_lkfCmDFA%GYJ21#@zAPC-gz~M+o{DMxxKLLV(hBpp(Si|5i6YlRae?eEr5>IA}
z4h%;4{@yVJ#(x_h@C!HpJ~k4I!K3g5{LhRa;EY0phv@N#JwsuRbOvgMy4qT1=3@H9
z*~5q#V2SKtpaeg{k@sOfHBEg5KuS&qfJ@2%hjXfhanitgco0$JX%6YrL=kx+U~&Gi
z|DJDm4AvJD_<tCkQ5YxZ!yY(!d%`R*C@*hNSM$#hqJN6!ADs(G0K@^%3jqC)uCT+x
zM{{$ih99blgaikAVm$$81R4(pqnttFgC-D<@Bsk=&KnF4{MGPpi3TnUIH8aP;>Z)%
zhUO@{F2)%P$p2Imk^E))a~MP<pu}xDLtI%WEC%flIDyVIFheYXI2t1VKO6U3Ep2Z!
z+7RIZihukkufIDZJWy!=|Ly*p+a>T2wTK}W=Yc@~W<%k%QGTG4F^Yh6{Ymjp{m)El
z7#B1Mh{2_x;*v5FKP?uAn}#NiH1S$O9bRliyZG-m;<O^&F(4ifNJ<@<Kq4={fhRWO
z5IO);*E76qVR7!iC+Wyn3xmWup)f9hgtQERz<=Qo{xssm@sN;~1_I&4nRf#Hj^+n|
zK`~eYF$D1RCIkb{SRBn^k7Z<tMGjRzC0PKb@wX%=1;EVzmL!NRg*g)M+`lzaL_3nW
z7yoDuPYZMYMU)0$s9!{4F}GhtVm0@FM7THr!~9cDis<Z#z!6Xgv=hqtm!uLzKffdK
z-+!zbA6_U&8zTM>jep*>N3t0Khjj-pp`3{CnO|Ip)Z$QnHsZwbh7<L~&tLzp{HuWA
zKb!eWw7NRhFHj5)h)GBjd56ow0a<DB;C}@of8KaUdqr&aU-IE~1Aw3(h@=@G#Ud52
zxusS`7KCW!JTE*hC=XpOVpX=%OCTRldw<@*$)=e(%@3;NUabkcFO-Ybzo2j>B>5`l
zk(J;z7WDr6+N9#)uTCbaGl&p_5Kaaywf+oCs73gFgR!u}CjK)EdKuZ5^QB(iuS=-o
z0WA6#HRKzbcWy}x9Wbq@@Y@#FO=cbU&3gr}K7~Uw`;DF8XyhDw-bg|?*f|v+i+^ZS
z8$UbZkR8d|uSen8+I(^@z3!9pG&W?&cqMFcipRl+0Dc;b&ONEd)<6gA`9vQnl0lKu
z_J&RG4(v^Q>(!++?;@+W4Le1tWkZPe`Ft8DgY9sntL)iGamw2_F{e3wrvKoZ8}`uF
z3LY*ZWwwmh?%2lh;bTc4uFp2eS$_!>05d8R@#0?L;|R*6yVuD497IPIC-m9gI=t}X
zefqBa)o{j$R0$6@_{4{En);sA-@m#0!Q#(qj;hdW>!`(gR!ZTpVsmdB;<dd+rm(4%
z0*(&$F6x^oL3;7WY~Rjn&uA*T1W(@ZLv+9W_CQzq!RvP~m~}{Y7jhLJUVrH17=C^>
zE?r);YiB|)9V*2B`163K8!{9$o$ryS4NK!?n<&+|tN2{*Yi`B1Mp)aK#{&%aFpICA
zoujOkJMR$KaUv|CkGiB{qnBq(5wePPxWJ)OxgNjBafO>T6gL`l+t909)4s8|?T6$S
zoxzJ2U6CQ=xb0YHWgb{1WPfN$S!80VluR-0`Xno6KYD{Y?A`W$ievDjahBx-a>&f*
z?+h1nY71hxjq{#Xab5&PlI~vas5UelqvGW$vFBtM)B3TaQ2?bAx@$Gp%bhRPiJd~e
zeA%iOAoL>%+Z}*zy4>Z@^=40Me|&HL!KKask5WI5u@_}B`)atwrGG$(`b~0nMV02H
za`jc9D8QR>koK_!rN0W-^f*bv$Mp*q5v-*^{eo8>t7PNgR;uHNOKb@R#nZH`JB9)s
zk;Skm@`Sm3o3v!1(Ba*wJ_;?p_e!)D;JjqHO0l8ggwA+kH%fZ8?@iHA3cuT!)f>D}
zorivGw;t=eq}fkNEPwP&Yo=;v4<g8YI;pSi=tw5B92-VfIKu>PzMe&;e&`uR8pb<J
z2=~1z)GIzezQxLetUtb)Mom*%rsB?NwI!^ZX`|s9+1fObl(h@Ry$=n8saH<XP-qPJ
z8Z9)cW|vv>Ll?PedEkDh!skqb8T@F19_&Dzo!Hd{WnV?Ognv+T51DfHR20nD`?|}X
z2(lQm*Up<n&$oXWIISt6g?Hd&kYNwp)kx-_Lw|F+*1Kl&BxQ%1!(yG>GEt?^X@HZ0
zL5MQEX$!}je5<<Taq>Xdl}palkngymBKv#`|CbNh-ZU(e=LB=LHPZ@j&GQ96tnKK@
zHl6Q71<X!ZQGYz#DUA6nPn+>awn_jMsiY95^6WFS+`g*I#Z|{JUyn!M9tz_-#rufX
zY=@sSk;(P_mE|4QAbHa}517b=MVh0;*xppN42msR%H<tvw&-KAHK?T(8i{&G(cf6W
ztt#ex?b=@AKI)+uR~8?WILS(`o~>!l_LGaN3fPfmcz?}VGM{tvO4(V}(Rr(vV(;yK
zH@Itd75>g!*>TEnXXla5G@tP}SLMBAYJ__JVzV^Mv~+|CcX2bN#qDGI6dzd79TJx-
zomkO2vgD3ubL&#10#SkNLl@rjy$SY)=5C!ouz#Ba@5m|$H|gT^ule>R_Mq18to4^6
z?=+(X@_!k%N8>b2V4mCiE5<hZOx_iR2;A})nds9k;f~vClTi5w<t*2wrL7IvsN6gE
zOASd3Gj9i0GY+a2*EwA;!OoN{rI+*PeUi{L8klEEmc_rWip9>^6`84Vbj?p=bertw
zc*V5J+Kyd$$N%AY*4L*7f@gYbv-(YFX$^u6w|`;|2nElBgf>SEaM8=&ISX@=jT}XD
zYi{y^SG+~iM<~0+^VdWfZtc<Gy&t7NMLw_*bA*<^8x}+6=5Y1Ko}xsYTA(vg64jbo
zo=s^Pd6&wUaZ4k6^dcFR_E)CUrEx{iQp82c=6IMnxE{r=D%@4P)?Mn@-`%sTyD1yO
z8h?hF7^q^T54*mbx{r-RnxS3R7#+nV-lb7kuHf*?^4uy<lIc<oY}3D0l3UQMsLzqi
zk3J_Wsb5g!^{G=|W+m}yS^FcOKIg4n?*5Ly8x`JEzkH>jT@=wOr!+)$t5$NRyF=7w
z*4LPJTry9;Jbej?^Nky}LDRuVjC3LlJb&0)pL)L8B)^^eoueb$SS~9xN8k*$p>lue
z$sk(G`s71P``FoQq29fB{qAi~`v+EvW?Htgdoelpbfxb+f$6Sa95rAR7hF=Y&`~<S
zDjC;r3)}9VEpL{A1g-Oh%w$<zoab8~Pd&vvozWyten)5d&Y+!iQkoXEK%%H==zsF<
zOdrGB!lPWXi80K)uLgte&sBG#@3I!NU*Gc)*!&o~)o$J^N%8e@TF=5|FsJ)L_{|8G
zp^sQIe4aU(&WVbG3H?A7mi_(~8Ke<1dK@a=u@bFEVl`3BnNk67ke3;nb$KNMYvpZg
zlG#(#6>rqHJ%jP^2|M#$%$!fi_kU4R8ok|}afjMb)+~_J)`Fw*Ui+e+jmGN8jh7QO
z_Zwam8Kta4e1O%04$;8g8(AX^F&YB?w<nqx%ci5cq8&(;0>04>F)6tD%${jIIqv!(
zsSk0kr2T7H(#El~x17By!s|=sRhbJ70!;3{uHoXPwQJ`Vx0)k2EE%aO4}X(h2{_4R
zFDZ9b6P^z!rH_14v|P~7y#Fl(8u{dI@d=jTZ@O=v3QJ1L-@c-IlLUEX!mMqzNwX#<
z(<@<K8J~S0mn*Y)5jLI5*=9s{t*BF7w)hyV#sajpG1lrn5qZNAdF!|ew0t*aU5oM?
zx1yWynk<9+=EoN#@(oZ-&VTOIGhLPSU9rY(T}r0R9Oo{^1nW<#-Xf3ch94>|VTw5F
zkt&t-kY>5i>MawiAiB`@9TJ7w#kL6TSw#^If&3npKS<sD;v-l3+mj<rC6eSW^LXS^
zlpiZrab@t!=b&rU_Lx<fhTxXy&WxX1H9|u##aD#{e=({Mp4Tq39Dh{PSm@khFro>b
z$weAfzv4cny52QXa^)G-!p$7EXQV42h7~g5+b0NfyfvJnkIhct@Os8A_kq20W|3R)
zqUAW*I9D(vX;+iE@(;o2X6&cJKNvW(W}h=FOU0C`zh6>*%)hd1fT_@K;4DSU$aU{e
zlGfSmE!WgHv8p=61b=oil)sQ@xk`5@@!VFKqI#RP=Ido_&&t?q0|7fP50i@%r&<CZ
z-K(O1HBKf824Po5OI~CMZz$hjs%F_9g2TS%i1?)p-O!+$Pggg;_qLwPi}~5E-Do~3
zKW6eg*+6h?e?N6+QAwe3#%mYqyxfWCRe_BW>0Z5lJE-f-(0|12kVN;$akgVLAJ`uj
zWw8jAEZP519#rb&Uy#WjYc$n)g89f9;+fv{DReQ)ayP$7Z+-W3(`GNU;dFu|*$!m4
z%?Fi}7n@2OC$V7LW)d~xCZ7vEu^HY_({_61P3TI`%lAT8&$UlU>g*SOTy@d37I^yc
z?Z<;h&&_Ym0DnnI@9Hpog7MsDcx%-=$5fg6Pg6LSu0HA5oy(*fN{;HO>ZXWfUdjv@
z{zG*K0@N|?QC_Gk=lZrQHK6@4sPelu<zm{G(>r<N^e(BZ{jFSu2IsXRrsRK&eyiF+
zEp+Uj4WoDBY6*JQ9L2CA5>^V<?oo90XOB$q?nP{Fu7CHc&|6IfDCqZ~i-IB=3rX;I
zeaUGzbRE+4cdEQ~Oou<W-awohfvZ7{+pMPvH*M@0idIbMP3AJTMOnAX+=AA^P5W<-
zuLP3XjbwH$IJ~}{Be<WALnMwR)rV8Zx#cJ?h+vq>v*eQ66AX39AT2)(0l<tZ_|@Y+
ze1hRn%YUeTM8^Hklma!%6)efgP-{;f#&8>HlKl~RyA|Ehayp$&1;tY<4<O=7%jX%2
zTZgb8BsF-yuJ!trQ*uyqorXTiU{d-J;g!;En|>oN*R?Pu4_}}b167rol7L@$d?DdP
z8Q#u5k;hkk`innJ|J3>_tDWq^r8<_l3y>ab6@RDc)dmPQH}6&!MAuwRKr2DvTFc_y
zAJvP>f(d!q2=gKH5+@iUl*auIRvcP6v!inNtTke~{z^ahWKI7G_mCxmit1HfpC75n
z-IVK#YVp?do)8E{_U_0{AvHMnvOhb0cW+8LYm1{EuuiDTWq1)q%X}U4HPLy{bhZ?t
z9e;oI9d^RRZ0C;qWeE<#@J3ZL1Kwo%X*83m7o{AyM&)y7$o>;m?-qy4MSG=_TI%RR
z{bwI#>31znYMcm2n~5T+Fb*m^lb}H^J5W7jC3#(35E8+7a2c;uHhwShBNuWA=QudP
zsuXRvV%cS6hGy#VtXFxQ{V|5Fi~AFmXMZka+uBTZh+fiu-wr2#fJ-=TB&z$R0!)c^
zy~MXaCaf4U08g+!*<0Nb@xAJC@tkuoEPx*(LoyI2@$G%8II3PKv?y1UQ7O%IyNTDC
zPsp&EVN&;zv0x3<L_3G8BQm_?J0~LXCbO*`XP~J$vzBD<_o{otmZEhbFYwKZtACMC
z)SPtUdJXhfo4%il@LP}ZCv9Bd{!Z$)*IM$pSK~{BN!TQAd?A^A!Z2&H?IAfzWtL{8
zyEh2$FN64+`lf>IGkgVq>0G~PtXTD{?u~TX19;#4g_vmLlRJ0E!i^&3e8`_Nr(|Ec
z4ySA!E9iWE{MD`QnYZmH&+kRcU4IS|k_@VOAyOH|2xSYFL##Pm*hrt+Psr_Kdfr2p
z)OgN7QCrx^B+u8*K&a`&1g5bqI{Mvne8auYx@{xDmkS|Fp|&v+h#y~G$MjxAc(t^@
zi7MaRT(gSSPma$eZw;SqV~Z*m8YP8$`Z1koLD#ctOqdrc&kCP5x-5DFS%1qbhX_2+
zF4-58;>V%)<$dWxdwhyVSdj1WPqlVgX+@i4@eLaWk<I4evqOFmP2b&49)*_!accz&
zBRz%>U574ny+d2QB?JgqRJ6kv!UQW(cxiHV(>VM%>5I&JTV$g=4ua-}TsN1>9Ih_R
zQ1hsUr3a)aH&o&aJ|(gr@PDW22edOyhA!<e)(72Frc+!KT+Ype`<+}mQOhENfeSU2
zQkiXQJ}R;V!qJNdY#k$b#j=d%v(T>mpg_`o(@7^|l0+U!O8j@POfTVf5&<t&%Wzhi
z2dTwptR{`G?J807B2cZ=J`Hm*Sn(W3f2QpQ1rz?%mND|=*JZ~uPk%5{o$QGd!1H<5
zJn!@$w5N_|tc%UWHZw!|g89!Gy>2h4*}eYt;<0gny7SIL>aB`#*}bg&8^MB9Uq5~K
z_GEISzwvogMIo_ag5>e-uCl6!E}rq5MUg7<QrHB`aF;3J{zUdW8?tl<7pRIMq&KNZ
z^u#i5=M+o`a!z9NgnuG_lqSN?7=ib4xUBBGl$X^}TE^|iZ96FKInd-r@z8d~F(}gO
zcPBD>;OSo&+B7NUpYt&(=iN<(oqVujvbGVDK_2i_6SO@m=(yeC8Alx!H7=HY+@`8c
zL}!WCagPw@cV{LtGqeh74YttLTDz!v23C2b;zYPn=<$5CiGT0n{`Xj`1UOR0eM1?q
zu^DQwE5OvpeVrT<XK-wjet2nlfj+tSMFqc5u@67xbx)oE6@V{&iXP6fO(D>hcw>fb
ztc;IWP1b0j!YJDmx`nsda~Oo#I((Sg<Jo9NebJ%3dY-+{(klKy!MvIm!*2Y9olfIE
zgRb}WCEBl4Ga>FU2IkU<R*x^uVU~O6EM$O>+EFCdtA6|RGXDcg*Tg`RLDUlhH#nEU
zH~|wAGB_|X3NK7$ZfA68G9WWDIWRYuQS<{81v4}>Fg24==O=%(dSzIZ+uAjaG}6tY
zySux)8zdIZqPtr<6p%(bqy&^sDe3Mm>6V6Xx%W9o_j%9X@8Xi>xO2=g?>V0bl!{DM
zgGtQ7(F`c<2y$a$V`k+CC@QHtI+%jkSeev;R_^wuE&z6BR#r|#Dk=#VpsAaUBS_NJ
z4ag7RakB=fn7e<0bHNd;tbB-602v?%=mK_H0L;7rN<cSLO>ZY48-UjIFQDq^>c(Vd
z>I!xPK~^>(ARRbG!qLgw#m36o?N<#BCZ=DNer1a@1LRH3?HoN_?Q8(1APayzvl25v
z+0hehv;ojMf&gYfYg2nmfTJZq6Q~Q&(vVWu0LZATXsLf{&@qDxYq&c(IlBCdi-d-z
zmJB06QcPJ>3INn*1juM<X#V=H2?T-pTQLHZHNpO0eZYag(v_q%#WeL)rPx@0tpUIW
z@Bq5F+Wcz!U)-p{%mBZsfm1DA93B2@0HC#Yb93TnVe$0zWVUj5bz^pPv0`?z|BIid
zwT&yl)6sv$4gmgi0onuq62={50hZIv8u)jCU%LWOv@r*QT!Fumq#gfuI)J4FCxPv5
z{~-nz!tGa0`@h2hu0Y^F+E|;q{*|k!s;UTZFtq`>0YRo9b8w)Wshhhi;LTq)@E@QB
z&EEup010;&mtQ@U{_S%4Pn&;J7k31&%+TJ~-_(Eezjw?O<nHS8hc^FQwz(t7)yCD$
z_3w&6fTfK+@E3d6UwdW)`pc#yrYt8drJ>2B2p&8TlaeD?9T2mdm)l>_zv_ueD)Iw(
zS-Amhe4GGQ@Q_M@EF>Hq9Kfty5r4@iX#>{D&C$i1<^K-09mvrW<oiDymNp;@%U{}C
zxI2HbXn|~;-GOqF{|X125P#dOfNlU*0MHo#^fI?*`PJ~RdHH2#`(*|T;qU9@=mfAd
zwRZ*j+gJj@ABeuLrXE0mn~OWp-}g_)KM^7u55U64+zmYH;Nyb$S9Lj%r6YjvZ!?(5
zzg_<t0@}ZhDjoQoS~!C2y#W?LOGFlBM>l`)NYMWOIcfjZOWNJuUfI+ENc(>@{qI0i
z2OE3ue}?{7hz{@<TUupD7Y9@O|MJ<mO51n=EmUpX%&q^H_HVnKn<;qy#Xwf}K=8Kw
zWzza}r0l`73%-ABeqCPxCN@s)|MG#y(%cRNbae%A{+$K{3-Mo!!Rr6w3t-VulvjTd
z*I@X+WAj&>6v*7s!UkjoVCUinn7X)_dLy!eXMvrI3*gHJ9&8Js*I&Z|U||M1x`9&w
zPVR30082*~#9tfA%>`f)`(^qYaRXSye<L0Mi^Oll3t*A_jrag8QvX3btN<42--r#s
zBJ&%u16X8#BMtzI+;7AQV3Gfgz}<fpe<N^rrQZnLUHLZxcUSoj;stkC{f)r=)PEyz
zKaJlA+)wj20<T@`Hv)Ip{*A!hb^e3+z{vDB0&_9@jliola{*5;(9Irb>Gs>s@gMu&
z=iomMFnRO;ATDq*b4Ppdoc!Cu$@$CT;PAU48!LE)7Joo+OW^McVB)}kbl`vf<#%>B
zwf~QW155@y1@@*6e^dbrW%(PjgK1gX{I1IJ3wr#~=2y6*yUQO1z#&$DKrnCX->U$N
zYwhi14FvrW0k+xv0l~y=|A1hT?f!sZVeJ2aV0wR$X9FwpyD}Fz6$Cz4fB3-?IQ}LB
zPIml<8@w2&-)?X*CsXjF=O2F?$jSCE>p!;-e3)6BfG#$Uzc+*vEQFIi_@VZ@KG@>?
zdp~|5ccANE*TH{ceid?dcXR{(vpyReSjRt9W&?}%yD}GeC9XgRn}3cB*RL3$#~)gA
zfs44>c>SgbR>;-f)YbZr!r=bD+j4<d>t^i&{A0txs<?SN{*eH#;r@RI1aFYX9}vvU
z^N(=?XM6nt!R5XGfMET7ev<=N@&UU1-Rhs$pz5zzfxn({tiSKYf4w99g*Dt<9PNNQ
zHWuLb!#_flOu?tl%YYU9fMNsN!C(LWo6$cSQ2l<k{*f&%?&#&q#L2-5U}EP3U#Fbl
zrGsaN$NwL>=6}Dg{Pllu1Yh9)#=qVb06?G@&>V4L*3n!b%r@;yL|K4T!FV|=6(94_
zCmdm2`6QTyjPX`NJjuLGa-c|IaAQy=b)lo8EWc4eN-(Hcmnsa~{&}_OedXAdg_`J=
zX@F7yA*z(vP_8z!R!FAOd{B8iIo-Z|ZoXa#=VWGcQZoraYv_MKg0HpXE{=Wl<@H4>
zxnX(p@<&+DqG`6TST6P$Ui0V#ZG`jVZIEs+cUTFrrrlx-^iyy0BXEY~;hefUFt;IN
zi$oq{Xty)@Z!x84@0?c`wf5l+qFmdMh#-gqDT&IhWB@ep3=wfWGkTP8Q=s3Dp+Y7V
zy0*Iq=gW;t(ByxF9^f~;o|wPq<GA$G6V+S_Ns~HS>i&^tN6DY=AmgK+8DZ5T^3_WS
z$x|SOUJ8(y`SDQx^Su)9NG9X8`|bME=O6kGdP9iMo3Cyg7T&yyeoq3*JnUeG8Y+l*
zI$@DVl;TfC2^xeHuTxnkykW6IH->(#ghy=4mk6!Teg1#xRQg9)DIP08JW4?vE_>#!
zL0XN>luCz-)auQvh8>7K(oe<Ldc0kO>)ep%=uJ(aCK6O4-I@0_^q!<)LDG)PZoCrG
zNc=B&R^0v;s<@jagLY^wWq8@?MisDRm1mUqtsK@2OA)Zx#zuIUn*#D566e*I==+)6
zC641b2R45*-nz%1HE=6p+X|5hj3mB^V&u_WAJ{pXAJNxE&C@3MPLlY^$dhiZq;_n0
zFs_lV>+=B>nsS5UT5XK>LiFQQ^3|f;b8gn-drUvB`*2tB#P~5K2z(%%g$niS7iFuO
zWJ+9T>g{#Cx$ZKtJi>YR=StcLQCZ?u?PBML9yNag@10W-Y+-7Xc~Kb!%SP7k`Up~n
zAFJDIDPK5%l_82t8;H0y@%%EhjJsG!2$s`_AwvexN`1>l_U#~|bR4AGt5SEV?b)fL
z0M-um+nbC?H=LiDEyjiL8Yrp<&#4`@ofn>^1v(yh+}r6FWW_7{pAexd$4`^kK7%CK
z*-3v@X0p^8ur-hl2<qItF9~x%?{{PnkuG7NpBjkUWBp-;2u*I{OTR;2j)F+ybwrGR
zbce7L%6%2e7S8(C17UQiSdbqQ!xS^}N$#rZ-Wd|s7%=jo9w4QJ$mplQ$I%-63GIxC
zSZ&g5wo!ks$;lmgeD*>Wb*X}?NBYk84eftNbO)wl;Uf6%i7InZb~y$oiuXzrcTdQh
zH&<4LBy)vm2N5kZNEQaA0YaG{3J{<;TwmPfa3w4xF}shmU&$8Ub1>;L#k^dOPYADX
zCqW%;&Qj(To!mgc>M0td!7E)GLu-|D^mSg$Tys^uvt|xAAY8HE*D`YnYt2YXKYxGw
z#MsdOfp3M+VMlBt7}8<(Oq-uNoM2{a9ck7Slvjw8$i&}pl;;1CVLW`a_2zM^Hctg7
z#F3CX{4``eIfmD)lPkC?(C`67yD>4~kY#xc*{H=yzrBPO#Q2)d7OAa=le<7Kr2$#|
zU@DO=STSZ4f0Y<iy)NTXyvb{}PsV>p3L%>NI;@H-&e2eleW`3=%MdvZeIZj)fT)R1
zWnPim;GO&{oyzS*EI<9m!$H@PI6mne6b+pnzxf-ksCCHG%|;D3zv8h(6n09wKvU#`
z%g<&xn=Wf9tOX{0SnBLO-ZL60B4n&W1tZR7s!nCk5|!U4Z58315xfw?-l~5-WC}oq
z_untk7B~~Z(Fk}yOi9FK;q6}iQ0u;c=6`l5#QYd32*(b!dWEtc(jZx1?M!pvV32T~
z=c@K0K!fTajxM~~Hy7)G(N7J*GWe@AV=@hCaLm(V^esYG>&nQ>hVe#ji#K|-o=udt
zW+$QvYtb#_l2jT84;~M{Ktg|N43=nLQtiF7$NFe84N4@v0dTWORDvOGB+%x@s@UhU
zd7bfH;cTwYD;(ze2YWqbLVNV~i)GCazYOkBI4>kNZ=oLDXk1i%z-J`C0AIHm9}0H+
z`ArUTk4y5<F*IkJ6ZJL^FV3$*;mL#KjkJpP7U~9yb%&MSV}{cNIqH8~A`{Y1eU9)b
zu{V2fe5HR<J9irPIAiCcn10>hzROmLST7!W-jBH$CknctI>EYpO7I-7L}?x)9wbcc
zB5(j=bo-L5K2-_}TX8bLun(p_?z#%_5MI9F<TBXY+k4I=<J>xJ@3JeZLGX7;^mNsn
z5aq$_&E{|4jJYRS4|ad4?cTSbF7x)3ncm#l<Kl@%e-M1OG4#vujH_K?&@{PfdKbsM
z50yC!q#nvgf~KH0t`!+bEpruY%Z<!`=%+Lz?aC4{6B7?^Z4fN94K|(O?jDCEU|dv~
zn<G%e*+4QFb7$nvS{JBuGxeE-f-sM}+0x53tD&_GeU9+|!LfhH>-escg_6*)w87va
zt_{ZpsrDOVMq0bBCZp7uj%@A6j~qw-FT+&Eu!p9*5M1x=L99>~jw6t+(Vv<s)mz7B
zN3-_^$4mN{>`7ikOO|Q2JIO_b@hY?O7<4@wcx0y7sHeASo_w00^_@v>=)cjJtQ>GF
zpvH|B?<^P~3*>*WVU>SpLT(d3^hHNX=MaJr(~62#p8ob`<04daji=mw$@EZ;uEH#m
zsXBko`vZ>4^&CwY{<v^*1BuzFXt$9U+MA`2BT9{ahrF#*a*_=}^igT_$QoE3``Jhu
zXXVz#+I5=;Ee1+CvgQ1Wd<+wAaUN~d?|M`M9~W{tD7=5Hb5&~Hw)!|Vt3P9vzE>bm
zpEJ=~msS?9ozHW4avE8B=UDpn+`!tJy5U60;LYpl=P1IYxK2)f$XBqkLFC#G7&=%{
zXs!l%(ove~)q8V7Y5Lv*>SCVJNwVK<W&6`E6_baie?YVOce6|l&XbZp4X@xL+S?$y
ze*`{cBPV~anz`*YaT4-tmYQl|J7ANR%gpM}a6x&Dz<3Sg`aJ7Q7!Xkg1ojDxyhO^o
zJF84lKFwQ-DbJj(Fuq7TlqZE|L&whzwcEUFanl;&QIuwV5aXFK@p$zXKZw5bXjM8f
zytSwJy;8=m-AW(FDPjkZa7rJ+)$aTEJeu`0y54^|9_9<Vdnl_eQOq3nf&mtS5JKH{
z4XbcBDlV<^zAP1!MY4&_W)VSuITyh?)m*y742Voisu7Kx_Y($~t!^XjphwH(+9NFH
z2>U$~(zf^G1We>4LKfq)qnz4E9gyElHw#<%{W26NJLPg~O)&v-1hT7>(9ZXEP(=_)
z&((h#ibb?L^YKsNmQf<wpNUN1E>Snn!fWiF`PZrPG+9srtqITW`QR>IWBGoRo{Kg6
z!qQ%lClz}6O)7SAEbwFBOY~266n7}L2K9%;bMl&QUR>l8kC>t_ZL<?<s1J6hl=y>$
z6h9N+8-4noe3EE--&4BL=xJ~BoDK+RvSoj^Cr>+!(B8=jnQxq5==sq-5w;7oe|DfJ
zu<nob@y>^8(TBlyNu6W8du9=Mhw~`rX>@h*wx3YVcO-<iBd1#D6{*hB-JG%?E3O5e
zd8%MRg%RcuECjk;&ddY|N$P3H%6%Y0qda&miufwAsq#yesx#9oQBI(A+((N>CP9CZ
z4hJIN)UVX+IWXLdXp}B7=O$hQKPtW-)|f<ciL3O(FYltLwH7kc2rx^`L%qf{e>+OQ
zMCh8>2+_MLRiKvZ%v~Dd%#l98#;fv?Is?-L$WI-{_<`M%5&JOYhZW~b7Il*E`NaLt
z<h!xL*dkKg`Xg>Acf!(@s7>PdCtQF1zQuTGk;^r-<v<lH<73p%Ux9HyBL_>|7Y+nn
ztmL)v`JPxN%pd*P5$tUPlwT2>uK0*7@Q7ptDl9(E7__w?QE0)LR6qZ)k11iE-XFD;
z!dC98Lt=}v@^qXmLI@pNw?!mdN@r>dCP0w#?L_gTw%)Mhz^-SV7(ij-yN!R3oYoRe
z$)}1Q=66SZKQ_}nSuxAC82F6a=As@t3MrU_ki|dqre&~%UbQZl+exB1)*v+uvS1`Q
z&4EnxQ{TPF8{@43dGxZcYT|{rAex;H9mu=s`E6Xpo2L#z1RUmQmA(;~F4fY0p7wO?
zj#ow8Pe0)rNmy<3ZW3|^L*;+tvNCxbGBq-fAGSNvFa6{>i?g+9&{{?~;IW)PVP++c
z2FAhj$I485J>$Nu_DI-&=6B=V5uxoA3qYFe(EH{h(#+EJvAT@CR#qQ7lKat^A5?fO
zuf$`(B)&B96~)IGy8iLQp~j`_DP<}1^6{u@cCy{f*0-O#-6z)!(kg$u8tT^|ubG(h
z^<<W|skv5bDC+a62ohrNRN7$MNPEZT@>?2IXsqxJ;ctXuL>l~teVYy1b=<Pr{3xav
z6oZl7*@T&I`}8^%h6V0=2}Qlc5l}hP-^WXA40JZ|*qd;_ilT5@h3CiZwvmIHc&YDU
zcvt7pqw>-lz2fk|344EOfl%)$n0`Q+Pau}Ro-Gn;a&Ko*a+)m<H@;YF{K@Ty@7L{E
z)wHLh0FU>WlzTr!fa3krIdEu%?|KG%mK6<PSwzI~b(y5zXU6h-!<SIieGN7@npM4m
zX~yc=pPG5+@j*x6zE7bOx%1p~<p>=>CQ7FnKLmZzCUYSxwa0%Yl(E_uHB`BVy!NqH
zRfYCq^A&!m8lZ&zoSxdWg0!2c9dq43><3Y3r;UP%%GHa@x0yQU@0yjHvFiO}WEdj;
z1ftAecDhxJ@@91~28s^m<ECp;!ZamvmB>xpAp{j>I6WWnChHX~%scUxy}L<}s<)0K
zo7;*-$)fuWYQ}#)8YH;i;+IAi!>(L7%6o`h6}xDAC5VEaI6OCTOOP|p#4I<h)re7n
zHi}HlM5uMrF6I8!Sz(8D%&O0q*S)5qKk9pX8v5_UVkd&his&-G{2&;8jy8&6rEqlS
zxY1a>kgXRHB*na%?9lN3dTX6;vS`LQFA}ZHK6ujiwQYYxlBnSxuMJlU6n!!`#@>IX
zXCrXkGXNJ@5JreX=ys*UzDT=<)W`;ilB9eis4sThl8VUIfL<UljMZmdDR_hbfpp==
z;f_@?B#J+LX<O5a<mXR-l!7cbJQ1;NM@H?|hOFJHn|&O;1<d(3VGLEhhlXT<ec_$<
z`r9&t$^C!Ad`siKqlIIHtHzG5NAPufs}RSBHSvDSKB>yI*P$nOFo!mJwNnLYmfEbE
zpC?s~g9_us5-mp>-*V7fec-Z6-+!278n&;@w&gHj7%Lu!DCzY+0Nt_fDUggcmHXzR
zD%(rjbzXA{d7l}-Pj6NL$i(c&A<v5PBcFuu5tM(h{OE)h?2rt#2)gd17clI6O3-8P
zTa^FqY89(cF{2HYPa!9<Ok^5xqb-RRiBkA^ig@6}^lOLm7?qmW<m9)nH{k(+S{{r6
z?dPb)#I!OdY6d7xd_ENKu@5Nhh7;MZPVIV64Dg+%UbP6m8@^FpGSDN{`K-oMh`^!r
zsyKgZ2C+XE_%0JZ-}K8Ksc<VxoanNNzAVRNcX*DV<joF6)c5;?6QYRnlr>IY#1AbA
zo)e}&Cs9AQ(##zsVIps=A{B(hkI}vh;$;g)24%ugf72H!ef?GMuFuqp4!>|qy@)3;
z(>@nDsX@&)I<n>kvG5z-l?hYw*nx!)@Kt~5aVFg2gPt<luo***Wr58wrP~asY&@Z#
zJDnzd0$XczUQV1MW%;n&A98wxi_x+===|#C1wm-~&I?NAb855<%{pz&#Yf8U5H*Pe
z*t!E!Ydfwpc&6_i>R(#YaunBXV-lq4+yF0I*tXelC=wdi=^Iovl#u<oXIF7}>_2~a
zW#|(K-j@-?&rD+d=s*@uR_ri${vjnQ>qi`QnFNW_JPPR?28>qraXYam?{@VGhBqJ1
zQXWzEgcZH=Qbo%UGcfG<iT+l+le}OH;|a&@Qp2c14mAOmQ07f+^1jJ!@f)bHTQrQW
zi?<Av2i|8B2sE~bTh7EpM&$E=l`wyh5(U&-YBm=58|)=#$-qy9OX0{40Z%C=;UY14
zo#>W2^@h#4oE?-XFK+oan$HspmB(*h!F=_yC(B3#l#ZCOWFmWSo9m;G)#YreR-$dg
z23Z$cN7YO&_K)U>&a2>l`7{zKK?ln`kF{;i73Z|-+t>U&!s9DzE(8hx1t@>n|A~u7
z`J0c^5d2%#MY*a*q^E$v68nv>D2Z#Zs4$~S4W<3K6t!&hz!<8)itaIwDU-?`&Cz!@
zGmU}M+SD7h0?<QwJptWnZBn$bE{rhe83H1Lgv|6*{1a4-)Na)uM7k-8Ogc=FI`fhq
zo;q*@)TWZG%7jgyGR0tpzW9HhTa=>ii?hN!+iFRUK{aI0F}DRD${W|S$IPH9fOd_T
zzEo5NbM&_r<q7DX%vl;uvy`c`m?M{_7tKX;qax^;QD1GbuTR{aZ|7keT3{JTb}qCv
zk?@hF=FT$6orY-~v;r(bqRBO{wWH&5P|Rp#dn6P-jk<+3-R@!07E6B-`wqo8Ev|Bm
zd<o*9Etp|GZm*4-hmpo3u8d|PADiY1LBGQVVFMA0v~UTPK7T%UII3k(<<1$~T8)|<
zcO^vYCKhk>{3IrQIw2|!(=zHvreK?X@P1WAGOK<YS+hb>q;?fcJfQI~I&r|Ssj*M-
zI&kthrZD=I?*Y@x%m#n9Zx|deKKogn28OCV)On$oG!9uCN|^f9q-68Q><5B8%7Rki
zxM}?c4_e3VBQzyl2(8yO!DUXSJT1JB65mzy>MqwKp{&g=zU<**JP1KmNYb<%Cy%Gs
zK_<;WMZBSoa9kW<Q;s<K#IZfe!6exZ;F7p|?0l;+G6WTaZ?Jz$B#jT`eGdC6kXp^v
z67b&QeIl~9f&v0z!xy(2<e#6<tK6~sPq+o;DYZ*s-$puzpzNYJ7t(z_bWp}Zf+^-|
zB!;Pj?BmSR?jgBoT-P39E+bnUJao^(9rLdWEYSw46<@BjIZ@N*8hvGqWQtrLHw$Y_
z7&=6tXbozoNyUExiMwF;3!Ge_hD1wS6WT4GT9M|XwMa&7#Z4D=>v>s|ixPZMQCouB
zh;a!IE_XTNhe#%7-DVOh$IZ^oVW3*fA>(POQFROOS7XVtqO<?X^$kbPghi96%=|N7
z7yHEQlNhI=2}Kf0xj@+kwWe>&r3p-uQ8sl(81l$!(I<c7N{Ius6#2PvPPgJxrfOq?
zw%bubAoC=#Xv;xjC{~S>AC3JIS}K1o_PF<?4ZNt5BiqN~-iq@wn>B6+;n#A~X@Vdr
zp$VN@v!kSu?Wa?fYD3Ns6FK9bYxAWFz^}R9U)(_9pf$+P5@lw6)e6^}yI=1C=U#+`
zBm6A6JRW~N0;7_Jy1mz@I8dF$?4d*a;*o58t?z~>kYUuZdpOI<Bv^bS$9i~j_*yzK
z^RsuqHp<@^1oc}R;9Oqv>vex3baCpSRCB;f9MCprDf}{rl=y<UOMw1n(E8Pdhac=6
zd$JGWx0^AD{YqaLs3ZVaK&ZdM0QyDM;`=Z%DsH69<=2vbDSqn)s`9Zt{*bm`+{h*Y
z?^umYU!7LB^WN^m)BqZ{E*LjE`Q&Ac1tUZe=sG(e8NaEw>A@Do;hWsYs=AM2eAOW6
z^Gq7w4WoW%LB+m*w)Tlc!Gf%i=N$p~^xFFjkc#i~Fzr-Z+(#CcWVICK-DolfTSHyE
z4?h_vSOC6%%tB3>dn{(yS{{yEEm>)jyf3YzF$s(Jxxt52)f0S_UOnh+=c=DeV|r^q
zci%|RQ1>2R7S*Xh4(M9|v__H@HY0zt(NArPn{o@^n1QwgEP0;~Ytz!Z>dY`^i+^Y<
zOnBp%*!R-yt0^ztQBUoOxC2ZbV=F+K{YEE;hTNNfMCMZ=I{8ZSeSaCBvvz0>dR-me
zKAO-aQ-5VLk9ljt5@g!>(RW=!boy9Y5dpOHlp`df{R#U@)?>Ucx9r<GFgy80q&?|B
zNNG?dQ$i)uQzue8)K*kBM=|lYLT)tFsv9Ro{IWb35}!w6?^6#=uOu<3UsqcE)HIr_
z?~4|H@s?I3w%CHgmlGhj=R7inUYiSb+!OaQc*g;Hms5`zPlit&g~v0E?0eKs1ZwGk
zGo%&p^A#A62V~zk<vY0KUnVv(RvR20=0(0Ln5{idPP83KOdtr=Y7?d5Z;H4@eM7c|
zy;gtXeS+?XG?Y%u>eC976$G<M_~9Y0P`fpM$@3>`l-KRDlh*mgIjjFIaNkkbQAcbu
zh>i4%hMy^6z7(l6@eG3waa5cH5hUE|{E254&=i=xqyB+P0A)m(*K*B~N|xw-=U|$%
z90>_#aMsVl3K1_SU&z*$rmukdB|QwyDix`ExL2PUg+!ztJk=FYR!eI-%<anM=Shu!
zy^X)smx{<lDB)1LIcW|HTS)~s{)n=I`O&<&O#PzxQr{2XID88C{@RD#PaI8>w6CBK
zGh26mHrpX#&OVe$%(PmmB19%u!RfZS>mhIup9Gf|aL`yZ?LBSo!dNAd8eq9@ML>Y;
zx96KSpMcib%XwOI)o2Ja-%{&(`H|Lt=p@?)mE7<kH}3?-xLuxWy?up*Y7KBmvc^><
zrb!4{zo`;xG87SUz<jgcg${JJQehP;{a>2d7yHe%Tu>^b<C!>ke_J4?&H~A^ypc@|
z!zX>~$iUDxT9YR~e{iB>+Ca$8=BQ#)U7WB&UMWs%v-y@5)6dBcxo6u^<ESQoO5TUx
zLOV6Rt24ZA%)!x=b<9SVYRtS#Ky;K02;#|m{1R$g-sxXREw5}M!5-=JDTp1ja$cAb
zn&G=Ag$Fr)5ri#F?o^$s+q}VIhN+Puy9CtT|N4z2ER4+OqOOt6I=>(lRUKak%vUQ}
zVu}V9orO8CO*INU@Z-M}pD)&b<CF2o9&PyTQmAeX5_uph>HF&z+GyYfIhIw!{)mT;
z5GnSr@p0h{Qo|E>xSWPahDn~l9Djf0;-bXV3ULwY{;t?)yu%PE@<{T0%aK#i2T?RB
z!J7jQML*K-q<_ACkPv)p)KRF!l7+HqPl-Ea_KkS%1<r()1BvCp!@zofC&wuN+2|*+
zkakyX&2fn{p?hET(My<V(p6uBYp_0lnb*KW4WS}mkN=Kcz9lmmr?P9mm~7YSfX}x&
zH`eO61-EMKix5<#`pWzZIg)A^j|KW4SylxEuBnvuI)5|*-1`tKP~tQrM7bc-A${?X
zn+Ho+n2cWE!M}-Rb)D3IJ0e{V_l5O`%&hO}>Q_@#QBS3WQs&ZjMCJlLHDbW`_f%dG
zmlJFG7Z6B4nXvqLo~nm0Iof*XRE>!F^<HQr3<hOd@6+s9Zu6%xrKJYBK_OX}dpu*Y
z+dgip@(~1_LW`K|_ExpUCe@XG{k{q{t*g){evBU0YdNad^$YcXr$+j9&21weiUkt5
zRc~$g;i)FpIhem7j|T9DY-j&q8`=^MJKAVo#sh{<g=>dVY)JKeUg0%I`}y`uu59oE
zA$?9t2?uiXOe6>0XL-#bP)pGISeK4cq>xf?Lqw<Eg-u#==EQAeI+5DP)3wyR#c0lV
z<g^dMX}cCM;b+Ew=pLO*Qo6eB{R(Y8kMt_&=)=T29@1H`N0Vev*e-cT2?}_|?Lpcq
z9dM>@XBDUdd(tHfi=|W%HE?+Z=ozt;E+4HZ=naK!4($$;lRwy6wrLuU4kxoK4SxR8
ztuJsI7a&C)Nyw;r{n`8bUC_#qZ?ySVhnwF$tvG5koMC}~{+;;lSht0P>ihRplMuKN
zCVNezwr=QKl#m5${Rq!rU$ty$Z-wHf^^s|=H<6IBtM|t7sVQe(%Q@M|k&MF$cxSDh
z1f|?_ABsN#g-unp+2lf}u_MrF%U8m2Uq9TBz&Ks1E=-4gn79bcoXYXpVm79-eZjpM
zJq^&rP47g1t#Gpwwtbz6>Q|MdmEBiV*Zi3)q89n~r<MQrK%$hy(iiS>y{A4^jQNy=
z(ZZrgKnn2wq-%5?#rtYZj@e3qoM)GyvTOqbA;|AQE86sbJb&R6yZJc_jrAsGNc7*6
zu>`2y?}%L%+|SjO?E3r|#e4b5fF8^Ul48kY+1t5)&OO9t@|<`JFQ#Rp@G8w~W&>uJ
zZtrL#Fs*wIGArA^e!cb>$r`N&W@V6u6#-k!iS|q=m=^*rY20&FVc(*{Fs&=G)>@9`
z$QFZ1gPda`?o~XmzmdN=X^()oknO71CpB#kp&{i7&J|U9eXpSp-NyG#MuSgDA1Uvy
zt7w0JNcQy{+$@B}*uex0)WPYo?)e?hx}K$Y937m0k7V=ms~CUqFTBQUB&{sP!{T5t
zW3GoNi~XQTv6^U)k?K8`Z#6uo@($O|z2o_=ytLoBR4A(@;8~Q8ewy2VIl}o!c3WmZ
z{&nXF2bue^+<b9r$ubA|jAvL!8T7J#NcI<hvu{`NT03^l$STl<%31kN%luYHB#8dy
z^GNP$kQkB$8*X2(In#nutp=^CCTug=-BZ8HCJ|bOp#@VFzam-i5SOetoT?UO)Nm@L
z)jD!zpG(kqdB^N^@mX;{!URB=-a$yrKcXz9JsKFO%Ms)^ZbJ<zEG}jzZYcAmnz(R(
zO>is3HbS;UDRhFl-b6(TyYGfwP+<E4<Y8R>%<pAgyn9uqunqXI!TOlf{i((vAyCbC
zO@$MykCH6yGf;#1he#DCZ%8G4>dbI+@rA`X6CWx|r*4Y1t_91{4C34VF^Az~d1h7B
zfZR~>QHb<*ukw~1$nK&0L&qNo5}j#(aEYBz0RH*sCJIu0CKUSmc?j1IOlw}c$~1^N
zfW8DPP8z|5>>-s4U04Lon-nF+^-&oGeqHKSn1&x{Z5OZWohV*>eR7xZh%GwwITBCl
z4s5aQYi&h{dq1MgTs=(TiOSqwGr&h4Dmb;O>3+xJm(dZ&q@ak^)+p%6rTyN2HVPW@
z)G|%A8JYD-rGwgyvdB?C(;C|_jQT!A`(a~Skt&XXMm}r8pI0H?%`vD9{oOG-W^lY3
z*?qgxD53tAku&-Ev1ui}@8&CRJx)O0M^=uttlNcx-3zM26{ic9NZx1l5-LV=(zoYf
zX78@99VKm0r_YKOw0~wQFb^4jxF8uG7<e7?du~&jtj9-)^*~9sN-Ul9$vJF<+}>em
zV|b5UnD$R|e6HBcPTg@q%^7DfsPMi_AQj(P(!UY@%J0kd>@v@7PeJ#g$GQDf3Q~DL
za&_g*MX|Z3GwhOQ97mknaB)eEcY=DX<!mjzy@AcAU&1vl8J=O<4;8(CiM|yT%hO+m
z6Y1Xc^MaIIDe9E=w^7Zc)+&qwjk7^*p4bae7$>gva(RN>AlE($*Y`)NM!gYvY3w)L
z{4YZ*#%c6|FAHR5E<dd_LH@U&6HrI3A4IOgVtJ9hj+^P*!uC@0wktBe>R_*E+#F@j
z`w_jiV2=}Wsi}?8VJuI7yP(mGb9|KWf2HzsSv|3GvlZHP*&T8<`wMa<lh$bg936Zx
zZe-B3E(Ij1*Rz8r1@3SoL!yIj#St=Ac!#={5Ei09N_z2=Z^BI_{OkR>$i3-S*J3*O
zd4?kLoZL7HhWxk$Kbn)|WHyhCdz3qkI8{kP11#7U?8U%aer?l#5kLqE!axhWt$tN-
z!xr}UL=tKSPc}LIvg`;VBNL?Fm|p6kV{(3I!Up-lH<WWJmd|m8A2gh4zRJ)%)>>R(
z!QRDljd{v`e@ng~jV_}*8Pz`)y$BJ$S@D==q4?!)XlfSPCn8iM@r@V#eXn^;6~D`O
z$8E0s+Aw#fPa6e)Kj^{$y_c|0E2LO2w%y-CM+OAt*&YfH)Qr9!(le((L!Xa*fYTY?
zQMHY7o#+|#uUC@3)5)vHd>;S@?<1O8@A%FFr^G})mGQirDYT~eB3MGayDqX3#3vXc
z_htnpzx91*+|1GoyO!<97i33=pCjqJz2XMJ&s5=29vC)%tIEnMNhH<~s2|2l)0=3L
z^r5Ea4Uj23Y?g7K31lZxOS@$iVOCD(ak-3CB3-nh_*Xe*Pte<GxiAX4Fqnv=vGVl&
zTJLt2sspR~w$-?!MENMt)w$CYqo^$0$VlhpjOe1f8d$?#7Hb1xFezw#=-;x;7Hs~U
z6{Wu6;H_GJbe&XBwITg{+APC)7c?F($!cl5Y#;ociQ^7EsFOQrGG2jN|KOUrQ>N<G
zVYyiYly0NOxItIyqe-oKf+EIANHH8jD*DM0@)WH$`>Y`&-N5ZQ0jf+O^(Ytj`{+$Q
zEH0U`aGSEui7Stjnom7CM|T8#gh6T*l;W(xsV^6Q&qhWQJu4(TOGLseIGwN>y04=d
z0T(t}*Fm}QXIVQIsBljv?Q-~>=p()Fx5zpszaM4FOH+Q2->an1KfgvP3!fxC)lFOO
zKb4nz3yr4Zhd{J`%ak%%5vI0e&8An7+%~f_F(57QU1<-A7H$GkE{enh$>ZX6f+1vj
zdZ`G1vo(H3t#$yGGe)|KHR|#Ow*6Iv@aL?b$cYVG{o1PyU!A()2&dy68zB|^J&7nr
zdh1AwK_o7{9s*yd5NtpH+$iOOa3rkclTN<62V|d$MK#KEq(O{;+%7w!-YT6hP2%3Q
z;nL|kdz)7mJ$ChLY`bofG`1tjza4=}4_objI^n!T^}Ol9l|RUL&GU1p-B(ncc(d!V
z1=0Eii%$(QCzndT!k*q$WsZuAOI-R=fSDyw>G5E|dD^~n)X<NFYA`-I?VVU@xZfLg
zaR+`(dmW)3pU2yw=?j+64?k;Wf>oPGTtsmpJf)0czq6xZ$xW^I29d07543E`GKb`U
zBqUMlcBLBJwojLb2bg_rgNPeO^4kQVxbOME<sTtAzgrQLFU2&BC+^czvaHz95@M;Q
zJ{2`og4kZk4dp?kZGV{5on8NOXsh#8*}On4zTYwczS)4mkKEcQvhkn44tA?Q<4y3*
ztzyFIk8AS!p8j>j>vGkd=+PWq4^!-agd_^6(>tB?ve0|<DPC)htK(Y4c3~xM+R5bn
zT>T3}kJu|^LOiyX<Dw31R30wsF|88&!N9`6r@8r*S0oR_sqQ~~IjQdRk`<&zgXr|_
zssxL^vFT$xyg^DnIbz)WGKg1_XvO{G9r_f}9@_yAmCNS@v8rB3d?QY2B*hwk6j!84
z7a}-EHZ5UlY@z+<sk)zyk>j>!3b0=~eIF>i3H0WAJqgSP-;iJeeqs%magRe1Y3$Vr
z8K@rnUS45DT_v0h2wCU=Dcg|<v%O1z+>1`!_zBx8yzIf@n2g@`-9I&6P3A!MzvE9u
zd6mY#lCNBfk>Y-(W!6)+>Y&_zp(o4a<JzSyjPMDw>ZV{<d9J~DUIM+H5+c$FX6&4K
z7*yK!E=o=!T8ImMGKN3PCM?O{(<!PO!T-I!-VfJnT!JNBE~mtr<fw{)pZOf?^v(uf
zHl@{~9%Y(tlzh)rNLooN$7`xb+rK9T;41q~mrR9T7`8c6@^DGycZKnPEs@hu`mz=h
zxip3k&>WnljI|G;ys(hMS_+9LBeZBa%#ns%(7n!}Q7@;TWhkylGj=9NF%}|&VA0$<
zq^{HC;GK9%Cfjkis_h5Du|4jY)EH=NG`016bhNv*^sgi@h^?3ro?EI~=#kh;*sxo@
z?PQZP*f_Lu_7t*4oi4C{CJ38w63Zmc4l!X}OUXJ^V%@BtRF3HU)cCL{f>y9h=e@U6
z0BX3M_orTn<=^xpBZ^fi!en9)_YDti8687Oj8@*OJ~g?Qo5>0jhZ&YNU<8UlnaSLq
z_oWp-6_dSAnh$p<vCh3`#q3$vLDs{$I7r{%#hVl~g%QvVZm&Ln66H+{a{1;bAWsSN
z5$d@GmlFbBkOHckCk)w@PGy!x#FR21lMBh9`eZ?k9=ZU?6A|91|ABhwBN4<^Yq!mS
zjOI;;9{w|}(&Zsr>+R;8>?vzkrL0n2B$^kyn)j>gcw>CSZ8}_pm7|O3NqMA*0-|;D
zp~BpX$uAuUkM-YwnS#s2zfqEqTn$F`*Okc7RMHo-+DA=B<r%_lTJE3Y;uf>Ez>te$
zByuB!eM_I|zNWXiq#!0KwS*rI*vn=3f^2+Mjol+gQNkkrM8%x(8dzVkMe6VGXwon7
zdRuiUCgWpXQ#E&z<gOg7KJ~{)1j_vC&-0hvD_xEgZ2gyiQ2BQcz@y<xX`E!2ea_e^
z-)!x=@)(GO{m}3L7Az*_au|obLMR~+WHP~spzIybTO<dgZV_Gn*8?*HNq&@!Pz7u!
zw8%$QCC_Q7>ezEt7N+dbj7p^eT5FzFg|Z$-W)4Sr-7#E4vWu3l*N?N&S$g#%lXodp
zqRX0Q-{R1Jt(8G)LVIe9kPVnNma%emmVgA1b|7O<N*&t`7=)#raowJ~ZagsX_Sx`c
z&uc6q8Qi1Nt63;{V9|;ElQf9NjI-xwr;3(HXbT(Km+z_rB@w>WY;c+F#u8KIejjl<
z8$M^2jTRvn=ti>0;cu?ubea9J&^Anz&(@$3GmNZ%mFn$YH}GhrtNm?+qC3Osc8_Q)
zdH$&^uyz3fQ9;5|`K;EzPXM5=BatA12%VN9*Z+7zN{({sH+yZaxwiWb;(HHu%}U$!
za5#$wz*q4VlVJK3oHWmEA9N~Q(&Hx)A;>VfrD=l+*F3wh?jLbeWv4Fr+Yi#%Im6ZM
zfJ^;<=y@0No+DUPg8lW({kTFdIg9|d!iB-qtw%tSXf&^G3r8TTwfK=y7K#y7>ZkSq
zMKgAv+jyH?Hy)1nUhSei**Yt<NT*TB|LfltUInBnPLWciwb>~bdMF}ib%ej&f_xqi
zTXofld>4aVR=-ezmAfJDMzbYp30LvyDge)a>L_a~AoKns5=yj-_b1Vr6Z6(y+k}ND
z;=!L}T{@3i21;qdlrYFR{BBJ<0@rMqw#I8o$*KC^KdhVM^cqUixZ3BKE(M|u!!aqd
zH%$`N`K8OOaWb@`p+!B*_)%ge@|$k()r^0<vaerE7v9X*ceQNqdhh_C&@eg+6nw#d
z5^xHnGBeUxK5N?Kwd+8DSYLnrqw?V<!I;b}8H)2m*ebKu%f+kNIks>9roNJ=l%x@+
zQQzabPq&NVdk*F8;VKPXQ^r(J@D39LdN6G?r^_baPQDd!=J63t93YB9LH+Oq*I%AQ
z@0?)>Ik6Prmj^3ctABqWx`j`T5;p{YgYO%*Lf5SNIOm}Sv%P5FIkblTELtwks^vjo
zK}3N86N-Cfmf-F*wX|g*@`jHXv)i#o;p9C@I|*>XHs~gI)%?+)UOq<yR5m4WLs0K#
zs+1v)g;s^>6DV89KFzfDjV?Qqw$ZxjQNM<wj_Y7fFVowwGbG)t*Vx$u%j`LSmx%J5
zsYv7laCk@A9<Tu!^7fVQ>)D7Xv%XB5YS!)N9LcfM)0s|u?lVF5O;DP;c6dZ}f_0~e
zr}yhkl(S4FLI`Dq`tK2*WqL{eck?id&%F4x=^?HM#<wTX%y7Ivm$&glWw~M{iC~K5
zk;QHYFJ<9ZS1yohTiK-ZW0UEB;^0nC;t!|p?ODQtmBQ$*4!ORktIsK=-83_H1R;4m
zprFxBN)*)&=K<Rwue=lb(iztbYQ5)!lGm~IF5QkCxpvjj@h+q;`NhY`RoMMT>rD6k
zG@e^estwVPoaC)vD7lrLHr%pXnF}GG_%h22qEJ;*7E6WRwr1XBp|Kc$@C3KdoW|=f
znQJDF9K{tpG1ds}kA+g8^4#gNaD3kQ@J{^w4m~{;j>sChyfp~;$SlmF!@`j(d%@CH
zN65bE7Xdr(ZGT_p!cH+%t))D)oyHO)n((B7ydWo0bSj;3I(k%&$F^gK5??(0)vnb`
zIUX}MfWUfbkFS&1f!i8?gPQKLk2&i_F8crrK8tPEa3P_@rmdIPmfDJ^g14zbB`9Pi
zIizKDmGaG^T}sPpwy@Ow1t$AIq2uY$byREKRdeCY0#Ms-@L=J7i%7P^R3VgeK@QM&
z9O6(}m@IhPL<LZ$$P2Vb#f)6hydG$SCsNM!XGPRB&x3m)-&{3+^Q22}=^b^Yq?t93
z(@$PV<cL$WCap<kWi|0d(b+l4VhUY^?i~==zzqCCr>rAW?UTBvsrmH?)u-{z2HSDQ
zewA9pCi$sGFGsZiwMXGemaJPS5^1%RS(edADJKGp8n*+lPgZ?MK__t3xldkow23Mx
zUS}xPVcCO+XzCt+LE8Ret~TX|0@KIqVf;b$nDsh&q!OJNtdA>`jUZXz`4$5N1%6~I
zG&~@btOr<xu0n8dd)PWH|K_6kJwq6K*=L`his256T^(6JaO&hn1L&*@q8z53rkCY9
zi~_>nL4}+{?K;XI1>TN{!;v3y)^Dva+0FTjPoG=ZPZC6bS#E82o~cDS))Q=!uSHvp
z1R3|LQ5g3J<xxqA6+Fve)Q-Dm9vHwz9QUpJWMhXU&0X{C+Fsj}7sbVK?FgQBjX4So
zV9N20&{mVB*@@TKnmcDnN-!)3NCzvGp}|%Mr;Moc9Szuilvw1B6lo*&Z&(|nRHZ@s
zYJ!Ig^T@w{h)ti#9~Rq#O7yKq4Qq85-c<<!y$5B}nsHFdq0W4=17E%Bq#|P~D?FeX
z_c<S@76BW7ew00Wp76mMXW6SES~HtnElaoHVMzEQ&UtpL>zjh0FV8yv+Lh8N7gX24
zGeilaKMQ}Qm_aJ3`Vgvf7lqedzGgT?+e<gfJ=Ai4UZ76HIgUyNc`=Lf|M<~JJLi+s
ziNX?2Tys3lVRj*x*xY!|pgPR`7(uE9Lp!ecYmfCp&cxGYeY$)YJ4iO6p-tSga;mrE
z5$d!Fd!O9(=0|&4-_)=!Sf=jQaBYp>gJ!F%nf>Mo4upEQ*vhL93=>T{Cm2CPZ*G`y
zc0D|QTtLp@3N*Vo76Sq&c`3mksu0)LHI|trU{GhKn>P5R9Y5b5wIZuS=4w$JY6U5a
z?#qet4t&FM$Pq<kyn(T@&}Z>0IKmQVZ}OA8s-LCah5ZzI$msA2QsTIdB&g8Jf#MN0
z@r+Y@gM#Qm@Y_}~{3_k&^lDuS{7_>G(ReX`#Z9`bY18AAo+Whr06)^)LTnN3c`ilT
zwG^?>Lm9}@%?IsawaP<=l2Ey9;^J_wqBwL^@VZo-GiMj(_lgn!{(nU>^M^Somxgu{
z{R4zaT(LjZ{IbO2@>0^5b7l#3woWk45kJ1Pk|jcjWhD%;NC}jRQAwA%#{uGy`s{Om
zZYWW@865i6E|ntS3E?^%H|o3F`d&A)VZqvHTW1QPG9VDQLuDN`amu{LgD=%t)-;9}
z7n#dC<Zu?OZvY*JrHt(2h;e5P?>E@e!%SMI^X1-=sx-y_+@!6XWI_<M#Jxs-`yoe}
zKPD=8(OajfO;#qxmY@dGp_#ufx6`D5xGU+VRFGZ%%q)XCm(;Fzz&4ObKh@T=?)cG-
z<>4ddT`_rgr6Cdf_lf)A-V~EJD({;e>+xoPs=Sy68ZDRH@atearw$&LC=Q8YMvr%@
zu$F+#e7ehUp*goTg$Wg9F>>PbH+z?r;yZ5BeEZhiUiR6McWpQ;*t*~OloX<WaA6B_
z*z;_X2!~)Pa>Wp0Y-->t+u@oCn6rTbgX4uDnNBhwZf{S9h7i5=?Q5dX;^QOaarhOm
z>~Ud|ofuD}#NAB~y2g}ymFV)CmYUCzG|H>YoePZee}+nrh*p94&En!-t6};m95aUN
z9FZ}6u?W()Z5c<OH{=3-K4!*$5iv<>EZH0N>*(GZl^Wvp$miQ<aP$*oNF2U`Tz^em
z28Z=1QB_d9%<?nR-S5x_dui^bm7`AK^3Y<wp2R#qJ}vH)GtVa@gV!l;BN;|lI_jFQ
z!#*hMTIET&QDciK$31u&{&1_1rB;KZ(b77s>C^vs!xJ~bHiurb_3nXxT!(|G;LSrl
zFl9sHEI`<Vc51%qYM_Vnd8=?_0W1oZP2;7nl2uSgUBj+^%+s(8Qrm^yx2AH9RazRB
zDl_#ii}gqI5hzJA-puaUsN!Dg{Ga>w6nm5A(UAZeBs%L@@%w30u1W4f!au2SzpKQ4
zBwYU`zm$bjCf<)GTlR;4hZ@$Ash)5T3o@qy%7w1Cd5G#J%>x1^gQZ-+x>gn>hH%;=
zA-S~`CNTjqCGT)ca{SV*Lia^x!04!%rAKB{;T<8glUh||c1vIb3sq6kTA@+R(_NDa
zig5MB0_|t=NK(z3uWm!6?{4`6iJazp)*aK%9Hq0obaR(-diX<sosZspC+T`3iyX7x
zHP`u;sNnq-ra!$30ht-24Aw0^jz-P=O<4Q427ko<l+C$}Z;kU*R2;eGVLeEn6B!wu
z(a;;wzFckp+?BL|si8IW8N?hN5WKsD2qm4=&+r?AC<CGfV9y-N+RqE|#$tW&H;+4R
z@UX&}Iq6`3dbIg}ATw_BNDs6kwmg&~66B{Obvf){)I_UbluKD&6!vKUkk+=^Lxq5I
zz7;EO?gi`PkMuQ19r@&Dh1Kw;<1S?xux@o?C*uE%*m^)YE7aj8LFr$Iy|l?5!|#OS
zn;bh`8+F@q*p-wKgK^wEU<X};cjF&+&h_z?UAW9}U4Y$xTjuAL{ypu$*Or>6A7JV4
z-vk}w;|x;6#VAO-?|d-N%>kwAp=y(No9$#{@-tl>dGO2*DBo95HEV2pB#<2*`!_ek
z2tY?qC3Qg)jXraySg)}h+c>v>n=v+sB!vXP<Bj+Z>QduKcD^7xJopksoW7ii+tU?o
zk}<(kt&xy_zRPn~jbvl8qo79o!X9_Y?lre*nGq|;2-)ZDFo{h0#S?zpHLMokqIxC~
z0%i5;HN?9~U)Pd~bRng@ndC}oO)1}>8_fokWO$}%kU`<Ht^tCocX5wEmhuL}!!#v)
z&o5PyecKRds5i06yXXfFW3mPXWG85YUYz&&*kT=jQH9do_+*txg95{MRou2~(g0K)
zibQ3mPFC7d&y<x9P(&4JcRN-EIxGIiE6E>MYq#BLfZdqYq7$buk?)N+{V;DG(@9$Q
z92yfxn04`&h6`)6@o4yczE!vq;Wy%BUm0d%a?FQkev?vCCO?mh+c)wCcG{rc9@d~+
z&Y|sp(u9>UIYCB*`njRbXV5{XlCuRGJuyG5p=l_mZ!+boEgoM-^5Ou6)v>p^$G$<M
z9y1fg;i&B`xp*!2?dB#S69*jm>^yZ7y{2G4poY{49heq2S2T&om~R(2K^#u!eJv7*
z0#Wmg^o2x`jY-)&I%yKpeAJfaBzd{iycw#0Ka?f&5sq#n!U#&f_R54zl6<ofS+s8w
z<$laJjdMAte06+Wp#j&vXc6rMvfMw*H%O;Za9)l1rs#5Wm&ZbEL$6GmbI;lA4Uwn)
zJ>X22FS!`x$|WudxqWGE?m(;?OLdm(9P8non%$btc;XIk#>V?dSQPbRGakY48A}3x
zZwJ$1N=ss~Kf&HpL!6I%Sdi?7AwMJgI}L?14gpZq(fKtUU1A{pL%eNUTI+I|p8Xq3
z*ir(nmc65uMNnW{8?sIMd*=?0jRy4L$0yJYcikx6K8<jsetdAn{<ArO%JI;S>tMFb
zcn5R-QkA9ei~6Y++zu^*6fyW#Wqh}P2T$T?Kx20Hlj+So6{41iN^kaSf85dd_o-PO
z?*)zg9|3ZZWUQfeLei!{PCAtw6S6=B?Ya^9A<A6aLyR)~2yCAxiNqPoyaZ;R_ZV18
z{g;P2y$Kzu*AVk4KNk%X49g51$kiL03P%em_i|ZX=;~(NF$0Rk%2K}H3q#U>1CXQg
zB&HRt+}~Y~!{HGcmA8H@BK3GhQ*h8aY>cz#&l;fq4raV;kwO3kBRN#Ap*&#_?SnMb
zSkb}e)ayzJHP~AT>iZKv<m{e8=iw^C0qyRij}9va^gC^3OAqe~HdCNK*3Qq`nYqZl
zgmsA@7}lG=HQYnR5)%w!9^5m3WFJPzquhGSvBwbevq<^}R+Aufqh(>!kS~c0=9g|W
zlihcH27$L-nc4w~13+buOOq_r9P7un%WFoV>NjTlYy(2GH61snKqlSP;7;SwfF|`2
zA#&65Oc7T)o0Jjg4?V`}?a4~MJ$zE{dcR^#5J3&|POOM;x$%auoYXph5f#OY?RIQZ
zBYhXl#p0<NYb`EawtyN6m$rhHJyx?y<X`*_s0vqZuVt4_GvV;Pf*L<@5ld&6k?ew>
z8oBK$-6+l@9{)+{%5XG+G7)nHk%4Kw17B3LzKMR-O}tryt0nZqef0-p*hW8QtZ{>~
z-az$UzbL0hMt717vL%y$y2~S^uM)zPh4_I5O@WR0c!k<B4^m1I2*n%`RoPY1I+$<i
z%Fk!oAyKEGdG6Ll{3p#K+VQlY+xobK#KpP$Pv_lb+!CM^E3#LGS&xwY7Y5-ZzT@-j
zavww@OzF8FC`F?(@3F%aNs2tJZBNwgGMuM^v(jzmkt-xk6C4A7uRz^}Z_qA|jEn-j
zSztakZcXP{JfN3_;)z=EI)np4)5v_5o9Iy#-}DL*TZD|I=(Hb?`AL%Pe{OcV64k^_
z^-b^pIcejSK=`ED9vLG}u@YN;1ns)D;8I<2Ch4VS-)-3C>*&Ptl*321;lx<p1frIL
zNdA8SJV3+0dUxD^9{naM&%AzSs?Y9a%qcS?jS3scDJ9^^Ovn%4ue`HK8!mzUp~Z}&
ziy(Yc5~AtQ%if##Pivl&(WCJSNg{p(X|`*%fxAPo>jEhPDc!)Wz=sat^^eVmdL)4p
zON)__?Xkp_?IB#AJ6k0QjI(Dm8wKyJCzaM`)8v(TOD^JnfXioSUWufX^DTI1OA&{u
zJ4Ejx0<V_~&5*Kk65^!<b3EHLp~506Ofd13!@+xv26YCfbH80O!W4r%{^I~U6a@Qy
zSrpp<W(;Jo7b;0O_X`S0SRBmkIx*0Xqdp$|XTR+_l&^<i8-LrrIDt)U=qkRbM(LJ{
zWN#PbTIKS8n=j?^J*c9^e;W?PL^0<#%0dIG0V@m0ai^}kE6Ofwt9f6x6LJ_nr*>TK
zX;@fkP4v4P{SxQnIwZ6QF^RIa)9cfThsK~O4_(?XI)tsYjz-ao7$m6n%cnMDUeD*<
z#=VWl!6Ppr?Q^%sC&<=S*P?Zbe;<!RyJmz)5f{dPr@aoRpJ97x0h{R$$1I`&wa|2!
zIoHC>;tK{73|<J5(;TV?Z+eT11BlRCT$~|u9&3YF<HA#lef}N(s^(SUlJMNRYBy;u
zA$cq4M=iH`x96F>YO&`GL90?+7BRtKcC7SQb1yY?y?+S1L|&cAo#Vf<RVuu4iS8dd
zO;Wdi<RVFm**ki7g;c-W-(~TJtVn}s`R%TO@gqdCw)7xT%w#G1zO-IkE`#3_cVqCZ
zdPpQF=}l<h7*(te$s@3y=L%W6+A1kN$s7<{!AZ6yxo2ZiHR#eP-dAlxK-`y$lWCP>
zN3uf>0kT5}lj=Xa1fkSuGSe1vexUdvf>mjM)2lO$voKV@#L-usAobUcr}}b$Sf*<%
zG<)a9k(?`7G_@eQyY0^LYZ6Ra+@_WB1Xu3Cx}960`&PNItZ%)l(l27&sww^^WAqZK
z>;j6`R_8h%*N2EGh!g5xG~6@ry}Qi#?Cm!hwsYc_kA})To>!k!t{Wl3dvwge^eE<k
z{dyK8mheM!sneiN7P}gbvI^qwK-Mhw-eGx8j-MZTcvv^aBW)?-X`|`&dXpXy1mQ3(
zYC6FJY~~U`E!l6?J87<q?!Qtl+I@3S6j0q7`0lws927K(HZw5(7pKa{J0+?l8#`1=
z!dQHPk?>sAe{P&r(1&A~Rzn<D79*j5bZW8!R43!aDS9qkK7F3~{98Cd)W$giwq7Pb
z&OPG^!}UDDZSu2ZAY0T7@GA8-h-oQU_05lp<#@KZgr8l;S(YRf9!+7iA(;TKAdKNI
z;o@gbVD(D8Yo7rvOmMq&Xf)ModT`a6w>+jZ>D;o}Hk9ji<1C~oTqWl+$DAsE<@2V_
zkX-(a{pa`C^l2&m0YGsk)0aQuEYqw{Z@UWDxoaQ`LC%oZyJj=XNFBit{1mFV=_XHF
zn{Ql>Xm39zJHP_Sh)+24yKV_~jig^{zqb??w!t6Fxp0MLT@(RHQyouc6JTrr#b1Oe
zb-6Ula@HY2SmZX9FQw!NIq=bcOK2Z~PtXyE?{I}{*phD4>&cbRSGrp!J9ztPfsb8u
z<(nn(>iszWCxlK3vq5(p#)j!Q=m{>cIAN36`2tEx7w_yr)W~HBQL1CCN?2D827o?L
zQ97r<G^nirGH`cv+W_m9PqG>o+MZTzoRKQcw0e^4xiB4~^%uQeW<K$M)zJiVS-E!x
z(hUROOQ;K2wqO&?>iUg9G6U3XUvX$^xnT^x?P*cS0o_AUEs2adRN$vYJ(24AuYC?Q
z#81USA10XCsFVbD38LA(o#2)6{1-l~+%VN1UyV0fz<U$4*BpVDb_a<9St%tfF!*LU
z$h6$?Cq*@y;~L@aBTy-SFUh$%RhCq>wx$=-^=StTV(Saw_#u_y=7i0he{%!V*bvl_
zON#lYxJc_Zg*yyr(#K$qSx=kqd|Q1$bu#(Zr^PK4{ZoQ`gar?*Y_GuVshR+1^0qFN
z<7c{jNf?{*7eFgS+=ON&^SiH`P6!m@brQK80lxxsf<};vI<K97c_+m-El?-v)2W7b
zepMWk=i+@)CV)ojI<iyiM8hVAHmvy5^z#1qD0`cyIi1iAdoM5&+Q`&=X)OM~Lf?+H
z_;&*^6&gU};15N2J;DTl$kw}cb#MKTTz!Uf>~4Oq3H~6PqOR{q==(F=_&gH9RoWF^
zE7OLZM3>Lm2~%Q!VP0;h#Fpt{&bTB1CW@xm^O<DYTszqa5<9CCLr|f-SJM^tXhd?;
zh9wzu0Hw61*hBjwjD=qgH>{7zh3oB(nxOC+_+|*;Nc0p&_O{q+2nKut4Df%ZR|M{5
z1UqqYckGU2RI<}=+$zoq`O}0Ab_LGk>0`bY%#L0-n1ZT*na@{EySM?J3^bi(rF<xT
zs`d#TZq4$6qrkF@X)KqUMJ4D#Wn#y?Y%fHHW$fq?%4S<}T->_vzzO;--TKfxQ$WRu
z4+d7nQAT7+w1Y%4?4Ad*xvaX<OJVgT#SAY@!nzMe?4y`1R}XhJN;{SEy&w^C7oamL
zwrLcMy*^5RbTDH{hp;U=So+RkR(oE^U*WVd;`*S4!0{<WMoDrTZ}-B;Eg7-&@t@QK
z(9^sNUYqX%PjhHGAYF!42Pyiy(>qv2a=+#0q`xaHzfzCT*Dqd*5bk#Qiwc=ngb4QT
z{#do?BRht`hgnbd$<iM5(464&v^q&mVoy_;m(&q|gR1wFmS=tmlqma~awmFfUWZaM
zRf1fiRsm!HN}@+Z(~Ku?8vgms%WMho$r6zbF&G4BY;f-G{)s0f>~mP&&!)bchT?dP
zca>&6tst!CSU6KcipGl+F7_29{yy`n0g2ge1peTtZsPC2+wg`m+WLb^cmw22)Xwhx
zS9%?PULUKb6lTF>E(xm?@NDf&m}_0-0H~fcA3kEp6-!ulgbNn`@Hr8zJB+5=$G^GQ
zK%y%Z=Gw@|z%J!?`hsgsw;AOA+o$*gsX!lJY1UO;xWlIV+;qZM`5K7YQfgt0gw5OQ
zY1(*|B%4<v@{NwXYV2%QW>YvQ$G0z0#SfByta)+`D}7+TM9RQcr-~TZpjta%SkhZL
zRjoU)SAR+$DRD&nX?}h&0T2)J;~Hb>N#SKn-6xFugb0Za%UKKA3h8RrTABnK=EV3F
z43V=8V6HEn!|E&9xINIfsC#-^=)!0!0Rg7_!S##Vq9=dNLhJFIq~;z?&P?VVz&=`k
z>0X_B{mv4$kINISv}NFgWEg{hy*OLCTgsSJn!pt>`}0poh6$R?NL!3BbTr>5K|ZNM
zRjxYzY=c1+3A{e=F)!vMuU2QDH8TMDVgSK;ZL3g?r=baLU^KuwOC*tN`vF~3BjXb&
zQ1J*my9x-VZP;B~RnXK#$cil#yQ0p2*RE34lOP6qX9fmqb*Rl{a_SBMHvBx<;`sdk
zZtu0=l$LbEM`-W?f`1b6x_7RDXBuRC)`p+)TDs5(KLqduqT7l+Q|7R8nEy%}@<6AW
zb>edDO(BC{=K%2x=sSNv9GK?pSZ_|8L3GZE@@zhXcLo&D1b*%$?e|(NvKIG$?BCj!
zb7Ykufvh5@rw(<3M>SYzy+O@=7@|;<=nHE=e}EZXnqXOmR|{_ww+l6ERMxZLKHra?
zMW0}_B<U1a6)X`T4+dx9l{A!&KsNj&s~we4rz_L%#DCKiGdtH7?m&Xio2dgANHan1
zh?2fN|8jc$AP>TsQ$0*j^1QQuiT1eU+Tg4_eX&B-^z+|D3=BBNj|I;aAEK{y`tL3`
zk3OG?D_Q()QtX6V<OaQ1{V~NJO9x(qMMCS3F*nW9o|GT>H`z9PiT$_n^%6h+Z@13z
z0Ipc<{3W2^%h`7%{>UMnCT%vg;V69HX$uZzyz;8=!YrE?OVhVo{C^dHoyJsB`&!X$
zsEX)_o0Pio`sQt9uC<&jWWxNB(Dh)e^@os;$22t$)nHbu5hgQNO15{~h%(6s1rQL0
zGaX5IsP8oGpV?jAVadg2<eR^c;`@swI0Z9Y?*^y*FVE;<(xwhZo#MqX^G>}sPq|>a
z`iEhgx17gFdkU#?TK49DeBhc&LvZA+iqr}sJB$}2a7x&DcU)ZHu5v<B>|U|ZLuaA&
zIM0Iwk~z3AOhQLj;3;qFtJKQ7pcK2)5k9InSU&5Y4v)S%!~-UhG}wcWwcTrnzGYA|
z^rBjPGqUK)#v6#r#^d}OdyKzW%rXND!AOe7t=HEsCI{L*vICxfKw;t;DRHCXeujk*
z=J5)JcO{?9ZQpi=^_QlPicnh?`iy7IEFFz%MQ3|xki+U-+Q=GlI+5%^Gx(0aruD?7
z>`snD&b7q7rJ$4all2=?c#B0Pr3@S#+_7oD+OzF(jL5HjA372ztoD|W?RKSgxXM<o
zsj9}RH;`8b5c33o2l^K;am%0Kp_xFI|3?U9{#yHj*VrX1UmQY)0mr%(-#@o2eH3Q{
zRD;e-9^o0Ig~2WE$~-+cxmYoepgEJ=+qy&v7AN>6*{KNtkeH;l;8uER$*W_A6>(jB
z3T{}E3HB5rG}tuaG~l7Nu@pQ18f)KvQ`<kzsh)XPFk{w#oAHwA30jaQ;z_oYSU|O_
za1PPIy-(<%RskEf3WRO`ch|W!V#<yg5E%rf)t|A`(sL&41$!8S-24e#&JB_R;gA>u
z=8SJMf&K>IJE`%!+ofs~lN{fROF^rAhTHb63V5@xW_4om{lVuT3>2Tg3R23B+6vIG
zRX2<%5eZ;_35_Xy`hQza;?*;nJ)+zXa!hd6Jz)x1rsA_RuUjwN<}O0Fau8l=x}gd&
zeg`%;EKtfoezu(s5TL3X!IB%=slrA0LFYuabSg*Ll)hqXhtCS|ArQqX-0auOmaI%c
zG%QIBACEXu-S2ne5?9d`0?<{|IKi>{%h@zJ^om@6?3Q|i3B1KE(#~_?9wB#k1j}&8
zIxv?Dveh97as3F9I3G%}3eX*e?|9v4wW1zZ3)qK%PvHSmMt{Js$x*gN;||QL##Q82
zV1-Jh9sbH#*5jHGe$I+MzJ6q1#S?S_k)V0wpgEh=)yhHB?8El?Yasr|K^U(+vNgrE
zrvz<(J9A36B6+Zov6BSa2;p5*;9eW0V>RG*S7@y_?oIY<wOs#a;l0!KrbSSP6jxdE
zhqCBZ8%FaS>4ept)18e#b)M<72s>4sV2beOgbhrguLM)GgPQ<%lfq?scOlR_nU<!g
z-USgHf_$`56$!`!m901O7YCLLqjYr4vNlJ58orMtzd1nzS0Of`v!P4~0YdQ<k5MPM
znX56lGFQRW0Li1ZSBZO8%rj;>q<$;hT2ZAYVviZVUSMnoop5QLjZG>0a@=ltUkaOU
z9Tb;JZ%?_LhfZ{l(F-9*bJS=P@elqSm>#eaEHxFsCw8^CGx`z=<5sQcBeI?2E~dGE
zKv`}AB_8dlU;+WF@{B<hbM?)?CHY3f5<;G`!u1|x?sLf0k{R9UKV|@tBR^G2foIEs
zOJwk>88HfJi!Nt0d|j3D+Z_BT5aEuJTI5RO-F?dGz#|aRL*#85LZ1A2o!eAR*&h~8
zlO7^gHks5X`)b9O*<R#+4o^rc#DZ&ohA9By{;Vgfn`}jXl{6NipdEr*wOO%?l;RIa
z1w<Ch#YNBSyw1uP&cQ20nj~Qh<(}HUh#p9a07+rF*LHK=A0|Vo36#?#Jw$$dEsq^Z
zQdfEFktXky`L&~Iv4m~_?5iWxm6MT-h`c6pLG_<xKM+C3v50iARN~DjD&&%XjZZgQ
z5|;bAv*0_1lMI2%H?1yW%0aM?F<8+kvJpGU!70ho)P@zy+i=Flp-IcdpIK32Tve?I
z#CNUwW_RE#5z1ge3SA~d=kdg-u(VGJzT2LQ4t$y^*(%Le-hfnmk~**_=Z44L?AKBw
zz_PZvb&F2LCILlqAU$>m^5Q^$BotG;-n%X6<yKzCngX=waKqGxAVpQdoxFhk<jKw*
zOo<Ybuk84sRqE&*eJhQGT|bif>7ae6X9?-ji=W0nDUJ9%pEPj4;L0WSIFg^VoRT|r
zw*hxZg8=}=bs_^r6NVqon0V{t^oclX!KZ0z2)pl|epYxK`a91f%sY~QS`60qNd?=p
z1h9%!rAYbnyUt+l&g(0C5GzV7+_#qF)9TvWC5T_NuO}{zq?L=3@ZDh+0m81bRO-<m
zw4c%58cfi4OUa`;5ClkA;0u)9o#^HHivGM4k*OOH3#W)m<TGzS>(GmPleJLHZ647e
zt82jVEBxqmuJ4$lbtyD|WJrXbX!ZW=K9~c=QeMVlk#;5l&?w606rpu4)fV!qpx2)9
z3IA8fnU|_VD^}87)aiQ-_RP}hULe=lG_Y>@!2&^{3CIm>$=%xQP#B`JL&)Rb65#4Y
zNhJHnV5Q?MlYd=tmGF1$4%C{XAEWt79A$U@1u5=Q7V@<V25*0VU}=+qm|9AF>+4a*
z)^LEZtdB0)C<&804aqyOh#Xn;BW;H|^w9VBaO?P&9g=K#Y*EjfWy6;j_^)7+BM&K*
zbEc?Z(#&si`R5c?IJB+sKoEfkOn6BF(+AzZQsR4c2C}bvTXXh?tsXY8Kh673M6JZb
z|7bXSuVt1yU}HajCv))m;NWlm&cDox+IZi_?cCBG1TT*Gu0}r{GKTh&m=T?{<w8}v
zd9H;)(?JfkvFatBKS%G{wW%V`<-dEmr&)4U|46%aD-c7Q9GW8b^1vy7CiUd@7HTS)
z`0{bGvFw0@EI{Ql{7T8hi18|U1d3)~|FSkzu!nY&jr=`-&hNXdZ+Ymw%c?nYysN7Q
z6@9<4iaK;}qYy5tt!go+VJxE&7L;<0C8lL&b|}IndZgN;cE>KAm8vV2H)=bBH=B!!
z%dFJT{Kg%i#Jvxl`b9xKvAo0Dk6Jw$Odc{(sbH<(W;8KiGc~B)N!gxuo7Xr~sPY2)
zh^U=IaQ7&G*l%6hm_Fn{Abw}5+l!ZC5Jhhj{LxbXkpgjz55<1PwT_%H*sBg;G%$Q;
zO_WftHgLq|t&L4CL!8#C#uj)@k+YiEQUEj?OEVIFon}dcJEAQrkP;|;i>SoQLkFQ4
zip&ov_^s(P&J^!Uo0$Y5WX3bO|6{ziM`eb4Mycn28CbAZ0uQR3zi?3eLLMbe92o(4
zYAyTN(2RY=*PJ>S^V3Bjn#GkneLDROT@8&zSC@0SQFB<I0^3Auz8SA{99ha=`VWG7
zmU*VE#28VG!7OFgR#bp&oU9F8Mi`0FaH+{-Pfdp)rBy3hKNmv`G7Ah_Ob((g66`w_
z1`JhyH8!uIt5pX;_bSS3muCF>0H*9LWrasbf5NteLkKqxAi&&D6yBkCHqcXBi-dv%
zamu4g(=;hd=b%Yt@{+K?pQ@XiAt+q%R8HsMMBkUQ(@QN`)Uu;_t`kSaq5e5kES^Qd
z_iA#Lhf>XXR;<X&lPQ5`&Ko~7(I|DB9>oxUJ5cY!)ZX3dj$8tA$JB7+T(CNbHO$UY
zwGL8&a0KMjw@wVBEDS0VvBsW4rk!NAFAjZ=ep~DA+zIDhSxRy=J0)SH&=8}QA@cfU
zzs_YccWLN7OyTOFmxFY?FWi;6liALB!wO837~8<aNF1h5PJzCNq8><^WVh~|A#faj
zc(9U|TFRK<V;09e)NujeVY=AfD;m(Vjdt_C+{zO_w`20eOqVBbZR+c1JfT}K4NfFN
zpETOea}0f&jlS4e{O`UQhs$iT;Q?y+KxNb^dpU|0-&Pmz%!}fgvpc<#I{YsR<xB)w
z0WTzQ=wdf#<P)<*kxai4nzB|>VsBu7de3i$DBl65*1Y3~3bwH0)~eub)h9KrI2hbZ
z@*zIYj3?_#iT8yHAqe<?ah{hL5l@ktpDDzl)VqzFn3My%3JgusD>$|;qA#rB(Rt2A
zP5+Z&ksJs20LqhnO^}Fpl}P%?o@T|>YO&U|>1X1^05-Lk;EqF9EKOzT00UruG&El)
zbyi-p@wU!88S0pVIRw13hWRRnVa{$so#3;k64uS&J=^6!Qu$XD(Of1PI_nsFq1-E=
z6QbQAQXLYR{HY_aBSz$D)V^Q@32{2B?fa4hg2%w|IpXqRyNtZpO*!um3#N3-{Lrg6
z3tM0Sk~96_vy3Dj{F({qYdn&F|Cy`$lCU|ODZ9`FXf8^GlWeIlkbrZe2`%hJOG&T(
zToa;$DVCm2dXuUFTTB`?-D!IcS6!@n10*_bq4C5w#Hp*sBK21b`i6?6u4iBC#ZFI)
znJ7H_^Ozlkqs^m#G6hmd)8})rrB9sb)q4qZEpd!-#&J^c*z=F8g3o$?zOwy@#+t?E
zuO=C#7_-G(f4#Txo<X8WpYm!r6WFEjwRUy3p*2a+EJ!WVgNXz?L~-r`7_>`P9~p5&
z!Lo{V5+FIIe4|RV&}c>X8plFcKuO%7{avNO5iu7;w|eWPXHNC}r*Lwg?+(LV*xj2J
z*{$3#%X+$YGJU~5C@2|!$|~@pQ<=Jq->6<5n}K7pG(bgrh+`BH^)gStAu|9=x6HDm
ztv^S^YYQZHY?s<iNrBxCGqpx260faFmjV3p`xLUQ?3HgsVViy%ZX&=)m12JYR-xaa
zg-hzU#`f23*=)#h=ct4IcP-8*;(}0~JliknVl7a5IA|m(Op4=wv@xN&|GJ1<4o=xY
zeDKjzT@7bj-OrVSPuGBlQ<IYFH5~oo09g+O<k~+lEpSi0kA}#l^3e3d#!tQV+BFrU
z1fSO-6BGb!K$E{cTmL*3lJvo@&r<87^~0@48EcNIp88p(hWimVWPT0iJ|U6MOMl#L
zW^B>(>N+1yI*LEWeV;a)f9+t#;~}M7xo^PNq$`bD`+DgfI=Ux>xwRJiVsbV;Ef08Z
zH{ER;o#pzm&8CcYbGb^)IQVw3a!!3Uy%=;|;+aB_C>Wz&7Ky~whuf%=F~LqIJQW9z
z%Ww8k^jyPW&e<+dRc?-T_l6Mmq<xB7cAW-E&s^d$G@X3K__p4Hf7=MFqRELwIivlZ
zc?A9KnQ7=F{r0WT7U(Yt_sJX!>l9Xm-!Mp{8(oUFE@)`047U$yGJYP;G%8N4_8Lg-
z2h~cL=kqh9ra(f^l&4NhvSm?op|t(}em(ahEi6*=UHW#|y(qHX7Q!o33)17*_-r;J
z6E+74f!0dI7)6|Ff5pr730FQiX09<{*=FCzdv|HeXMJAB`21Hm9a9ZM+{dg{zPnh_
zbsX{^0&rux;MA5>iJOC!%CT+vgP)>gYwdu5)Ivk&M1}i;BVtSl&%GLF%o%)Vb)grx
zwg<kdeEESd-NS_rF?lfGp^D$Q9FDhJ3;Q}PFdqF(W0Wxte@ubd*E!#a##I(v6pW=@
zdKhpRJaPl==5A$I=e@nZGcw_wzY*(jj$E59Ps}olK|c|rmKn}+*Ly>yUkLH8?YwT`
zLmC_ZmzPLq(X*Um_Y2&jM1CV2bHAVTXiAzQ4=D&u*lgO=c%1vFSNiOiyCrkQJkiZr
zJ!9VYbP+`uf87XoXzWC&lc(;>ZI#1YxP79xGBXbhJ?zgV4fmgGk)gyowTJQ_>yv42
z+XS}58Q$J5$35hqKog+celC-6hQNCX+7J4#sg1#ze0{ifkf&MVtrsI0O6?%;&qXl5
z$VeQ-X|{ekpeRS6_VqO3IjX^3EHR(~qq;<*{u0DSe|}^ABHhWV@OI9v7S%s3dV+a{
zQ41gBPU~u+wGJi+lw9hono(gsK59nEx3L8*3RIC34lyp$gR6V|Mhfw4TCjsUnQv&7
z!m@Y-*q~Fsem=ZS8z)h$f7n`%mnGQKs;<Fa!JBV&$C>mu=T8n8TGbf0<VM2;70y=J
zM;x2ue-Hu@6o;1HmXuZEM5UW2@;^i{PC0B{GKsNL&KWXC$$$;3C=+hJDSCCsN#oI5
z(-rnZiUkOaLUDWUqdq6|Xi5<*qBD-qUZ5WOp|qTz-l6*7(q3&#D_{bkKQ!Iik(+B7
z3ztZ*R_OXnn>Kx8rVPg7sm4(DTd6^j;k^`!e}TxV{bV>Lu{c&`RrS<>2`>9k%Vs6K
zFZlci7^g;hBv@ICt}H(}(vnL`rmJDTTgfn3xyb{Sn5$#h1>Ntj#fdqky1I&IO{~3^
zHhu0rkcd3F@!GXJJa%a2{YZ~2f!(_v(9u8Cy7FulR>~opcEq!EFt3QC_)#+203{z<
ze@;5to<YcY+u+Bp^Du^(9(PL!E9W`1DD-c;f#=|8<y&!vg-~OYOjj1|!}SGg+K>l~
zSQS1@EeUrfSa9mV6{87h1&3+|dt_oCEg^(@a3qPcjP@sJWf7M5SHRpoNPH6wj9K{R
zyb3*PA*x_hKQwT@+Oc1Y;)+4&BsK}De};&BeYo22^hM-kOdTpDW;&*+ZM|3EaSU@9
z!BS~_ZT9#3Y@*6n8otg2W9@|IG>+MPRDo1w^WiB3rW_UYZ_{dVDFxae3)+Fd;Twy%
zpVQ&2i`;ek8sI1fE>jR&l3e{R)kj54rX~MMb@jA%eiZ(y=`1O=^#CYRNtTQ8e=cAj
z;GRgb?eL;MS+tx;m)_9A35ezZnxYwsOkaf^I`<~$B4hvTC=t0n1irM)<<bHhpKzeP
z0zNV&j8Y7jpiS82uOB{4Z7^R;=6tvax~Jyc)K1MGHq$c}Z+uK74S3^~A>jgxTjR@&
zuUl+h^NnJ?+0Srt@^Ma=M^9T-f5}t#ds|x9;4I1#q)e*d+ZBArj7mW+!_SV8K|HY@
zkMV6{3CT~A#~#6g?d-c%Jdm{a`;?u~l<&t>zx*5uwm&M<&x3^36~NiNf^HAuVKbDO
zef{ok2Q@iSfNasNR(W>tOo^_Mbx*7jjfQwiTzBm96(ZTb#-OJLq)EF$e<a{YcrQU+
zp#beSS<qJF^bEZ*LL(H8s-g#9XH_<%@LH>~m9F4oEK%j}>29Z^(CiFu!;7Wijmjt>
zy#q(DgE%d~DX`o~tpi{kNH7gg1+0|2jX*=VSR~jDtHjqfK^a23sLu!$e<9X97A720
z$|bZa?&oQtwVf5y3v!bEe}lH+*HClU&gWZ^vu(2o7;(+Bm~m-GoI*&Gi8j#iG%n{a
z>NON#YC8j{z7Ka|E=7kaDYx+H&6}5g4_Y$q`h=f`X~XezF)=FI_GQ7VJ_#z81_DlX
zY3W{uf>`JWZ9+JS=#4g_d&+^t{t4)ncf1D#8<0EmuiZt(#Vj{ye>2RS2hp3bidLVv
z(yAZ0*V?a+eoLyk-c`spYj{&Bo&Q<BY?@gu>rs`1nq!URk^bao_KhXVQ5Cn}BCxHR
zP|crId5XXmQR^l`_<D9$u<k27cThFxLIw0Kg&)c=q|Y{bH9k!cW4)d5GO2Fuld@5<
z8jxisdGjsE(L{iRf18E;#e?l@$3w@f4veAVp<zK(c$Z!!(dj6~hI&a~h*n#s!1=1x
zLS2tHOvN9|6$TO+DX_-S&#n3P_il?&{5T3~kI0#i{rItN{Z-?SiZkjuT@S_pjO7P@
zllb9@j0&aO%g}R<HQLzb3em>bVD(fn`2xTY+|o#iY$xNsf9*I3)DG%Am6)h9Hv7MS
zn-i-u(qLXm-rId+O-xmaj{2J!-0Mh_the9X<un36^y7*`HHI>ERYqyTm???EpUy}5
zPuR=M`9vZST6J!Jqy0)`mo1bY#f2bz4hrcAf@)Zlm1k$G8qO_v4^|}4Q{Dt>Ht(}r
zQt(sKXjV*yf35a?M^vilwE`WUu_HLGvm7=fB4r;ELB`^^om!T=ZLRot?~nE4XH;QW
zpM=tp-zkherVr!GatGyZam7Iy)l2RG9cn|H%S$_Wm8`d~e#kAsXCXp|YDZw&7Sqy8
zKrdpvX?3@P824`bp`P}5Mvx>wM`cf~nhTFeR384(e<?s;P$D$fCtq}$#+-O2rSE7u
z)W_UUzMvOyhC5%;*3GP&njNiJ1g*bY`Zwg5eA|a-#A3!d7N?j{)Xck@X5D>Bcj^^<
zw#2?1Ik(#47c58k>TaIP7_;^Ohh~SjeKXh&y@mt3xMC8P4$hhVfJtm86fxKLFhOs}
zlm=+`e<JU<=<Lon)DwV$(>-;UUI<O_Oo5fpZgR+yol*kUqe|Xah#OR51TwN_q>UDe
zdli{CH@*&Oo2K{MP$#_HMLYqAg7i!Md81asMLmVJ?KpUuGo{k3=ArcN<&;y*!ALti
zVxUoU^424A9XR9g*oP;9f_E`NZEQzqKgx*-e}?9_m&FsFvDkgViDT{-I3D}sS<j^p
z-aNHUJSJwVy&usC4}4WuA<|gej7`Tf?7Pc%AHK4Ki`ZlH#$}toO(}6^Jqox+A@N)o
zYy<O=;e&%J_N-E$xVm4p*nt2Qdi6S5m<=LOK@W;w`743p=MGrPX2uSv{Sve4+V9)g
ze|WOTzjywd>?=@}DN~sP!3|l7H{KaWYN`zZP;rsCMb3_HnuI@Tj6JO$<bOf5%sM(+
z)qbsFrb73;QqTrXVr!*KUu6CFQKz1!#HmRp+8!UuJL}<iise+78waMOct>z``p3kZ
zf`d(W^(cXK5_Wu|oAzn6OaMe=<2G~ce{N^?OE$%fHcyK9#@IeP{4dQ0sMBM}zkoJ3
z^%AO-&XWMgsM#&!*~hr*AydAaij8aQ4AUr9GS*xysi>0(m?zh;$CFnE28XVo9$_6S
zoLmaBREDf^0ZQ@W7L}iImi$Q>@<=|IXdHj3+XYdxB%@)K=8UZse%A+yPi5pje-53i
zDB2F&lw<zF2&apd7AK|w3K0vl_nE5Q=|^>pGHS`|Rng00M6s@hT544sD3l^u8lk;F
zhIQ{7A#ECT@0>DTps??0{R-pmIHfLcK`%OvZfw&|s&E9$g<&ja^=7|D!d`+1D9vpB
zAlF23s(x0u1qpU&*Kc$u`o8FCe{LDfxp_GA;1aLR<WE<+Gc8xgUfOBS0(Rd-xFBRZ
zsbBBUJ<Qy*rzJr$yii3b5cxEl37R-iA0rgp@P&Az3S|YG6*l2?cugV7lZ!Ff5__9u
zV#t`K7Y5bu00Vk-SUL83%A%|4@Q|rFh!U&|b%s6zdr*-ehfASDbOmnbe?jqU7h`_W
z9ALqq$)AhqY|8ta-8J3;3Z2V5A3ae*nEHH)EmmsChS|c=f1D%6j6*8Wo`L}+gs*l<
z!}^D#u0+{Cx1iTvXE>{ms(Dt^Ov|k`+qACo1w<j~P&$lA1Vo^`3oxadkI27j--jAl
zg?be@SeKZGdrDAXcqt(`e~OzeMvRto3;R@K`V^n-#!(n=X>U}}WmToHyM}U|Vt-*#
zHj&(L5KvqX9Gl(obbO-uaFaywbSWtb?s@(xMVPorKbeu<lgj?e0oQH)9cLT};pbm>
zmBT)WUfso~Q)b~=q)y^69AKDnWEVCIx*<cq+;#l(k#C~=Q9Uk-e<Thnf{hbl>7ao$
zjN))Bl6{*c!FJ>GoHa<bBJ!)4m#s*#dxXb(SNl3L**(BiS)*%*^urm>LG}KT8B|V~
z7cUrJ$dD0eM)vFgbxS29;q=oRn|eG*8@S2!JDKMqj@NCkVe{4E=>5_B92K&I;+3C1
z6O{HLE}YfTAPPb$f3y*#H@*f!EgT13gw<mgo5jR+TzmWfzz#~$y=F;1*>oe~!JQv#
z*g7-9ab-WF!TQWb%;48PUGHE$m{7zuZ0ilP+zm(v{`RxFM1TQ9p)c%#2F1^vg8I)H
zS3=dU=>jAVekTB_5|kQJGjD}K2evahmaQPm+PNjI%&nt6f0r82o3qV73w)_vo&4SW
z6y6vnv<ESXvbNLft&j%Xt91xN171Wh2<g<Tg=?I=b?)ztcijC<*7c=xp|s|<@>noc
zcMkt&No)YG(B!nqFmOj^g&e9w6k!Is7Q`U?K5oS14Fj)!%&24|mx3Fvq$4zztmHep
ze3^<MN<XV*e{e8)Gn8KiCs*G1fr?K}zAwGIPM2MoX?=+7QBmh4lnD)${VqQIOT`~~
zoMNcBYJIkge%!eyg0M}&#cJ(-K7+Ss<mqT2OFOF3pWMI`uTAg|hWyF~x89Oag)w~3
zhGzQ{wBa+w+NVZ=zA(h*jcK8_&*eIq0z?|p#157Nf1I4#SFhHg`0?-XBPMidy?73=
zM+F<^G}bR~7C?pT1XVTUN^ATLHdM-U@B^IfI7430VICmk1fCYOG`b8v_Ebm1xwsxz
z+I7ph>DFkOfB)*!P*3jUK{2r#D-`V$w;*vxxg$^7>+p6lgFDg>Wae;IKfq%S2Y-5G
zdq_tpfAZP!Mpw4Ew#3jRdh4$o5W{z(LBtq{DW4pR3-?oop&5jX{|f@XhW#cj_$}N=
z*@_Hie9lJ~w+9Q82m}D)U2vgg%|o@~_|~AsNSH{){O&Kf(WoeD<`A|7s11YyQ~3yg
z>(2Axcw&Y8p?N!h@?uEjs-d!q^?XxE&`1fyf0&lxi3#l1i7Wjp4RfNJTM$GuoFF&P
zXf*3WmKVb|W}*+2UX^TAcQQDHPhB52;!rI59SjezIi4nq-e<;P+ESHv{Ipf|*4BUe
zp(`a~5hIxtDGCQSI?ivN(@gdK9Dyk<e#7DU)s0V#yZ{-S9wu8oz!d_TL5bw`Aelpz
ze-HCmH|?9vedXx%8PP4P(CkK7q#hR!LfQ3@P|sKIA~Z)M0;Hk*hFyxXHLS{YRc2)p
zi<!a*NT;@IN1(AplCVHiTKR!1Y*$ZEWSYE8wY_T;dTyC$==FmuRg2%P8c+cop8nA3
ztb9tAnU3uxzZ#WMzrx}4eTnLCTx&kne^#7aR&%(GCFBSzWNoAS{AJVuE6*T2RbpsT
z>u<bsEW4PmZ3qJ#{{XKtUR9=Rpr{4UF1{pGF<f)!)~F<5tM4g;v^{uDoL6U6dJp>L
z;(m91uGa@Mk&)soV4c!(4vW4=9TS|XJe!OG?e60z8%B2;Gj#n<Sbyz*b+3%-f8`A_
zMo*(^?hiPYqExXcLPf~Ksn-dT!Sfx)buuD_4$noJd*)2nNYk%QttSKZe8Bip)-_KK
zskA_j7C^Tk=-oKteFf+Nu%VjawV8^a^%EW?nfv%h;|VhCiPx?%!BTcv3cN;ciAA}t
zD$n~jLPv5+IRX7tZAM#4Nlt}Yf2@@!|2mP@@A+|NZ{37P9VmYs4f2jaJ-9cf=IdKh
zRGR@0vIhJ@ts611<0*G=*l5gIZgYB4H0d6x#VUsLnkCL{`lwdsOWOb=6Oz7&LK-P>
zTErPgh<^{qohV@L5Ha5nf#^9`{zG5|55RjpBX&D>y^n$O7pIp@S}DVGe<mNu*bVI|
ztc{kGFpeP%ZEWXTkO2RbK3ow*x``@Sx?w0S!{l%*H_)dhU&AhL%90POn?zqdDQf!*
zYB(8n>7W*prUU<-5Jw}s0wzWjb$c>0L2t*D259#p##>~&h3zaNTZg*gFNb0^L+7FR
zHiN}kBr$OrpKB~{^t1B}f1P})afu%8fXIjPPiDhMe|;|IalZh0L?BY4vw=X6HOMF|
zp_()F@rRUG3;;IN6U|Eb*>$Tuj}#k~^CcT?tJQ?@e03yvV`Kpw+=LX>>|_|*fqC!u
zfJvjoj|>mmKy+iJzJ{FZhu#qHVH<!hTQtqmg)X6y;;R0t*m;50f7)_2LcAm${gS3I
zIO22koV0?_^wUNM>Am<0Zsg`xiz%TqG+aZ+PKc<X<tMP`d#+-JgM!+8d`MLx%#hTj
zfBngXZ-)A#aYtct3;uA<ozKvP|H1%b`-*o}To3|f*esk8mEH^*>YNVDUKfX$RYWH~
z%(8o35gL;`kO!k3e=5G!F|ntZayGcN*|LN`;i%@gm&tY!C-Nh0X_F?N+$~>%Lv6OD
zDBvIqbV$wY4t;Varj-muFWTIqC?joIEmVt74hpsFfgw#^#jMTpz$+-;p(X(<y2`X}
zTMBWLkQ`+he)t}YelveJ5oFDSc0)d$C05A&6|oTHHKxM>e{u>gLB~$jWtqwwAU1LG
z-@rR19f3|I60xtkOaV$QN80sEx9Td6jnn=wm=_7Q>G{OWP<FD<MsU7m`_EBf6oe?m
z5m8R!EBk}TabXl+z~uZDS2OVq!D%`ZS|<;)=skz?qm=wO=9y=MJOR_&h+#@6#5@SM
zw<EdhFi(GXf5jR_3QW70*btm8E{62izuNMp6&5}#?LB|<HLU=>@ke!R7kw}Ps)Lro
z3Wa_poP6vK)S9CoqxtOmd{D~W638IS<+dX}#H^eUwv{W@s5ASSZ|5BL(dk07$-ssf
zy4?9BIis%p@jgXvc|^!yUk<5eaB8do)Za?WE2;q~f0<sl#G4#ocQ8pQQ<BuYq?Pn`
zh5sS*Vo|aQz}qBa6In!5z{!D>$ULOc)96dM!4P13-YLJw9ndS(FU@0v@g9nI;|Nf-
zRFE~oqf0Sd#7xiUUIW!j<XGE3^#gQK$96$Ax_<WVdfvM#%%KzaO?_4d%XB-OEAE#I
z`RFojfA@2l7-Q5|4Ni&l&9Mh_u{H=siETRXtrs1pqd6e@*{AmgbAX`!_qTG9!abcb
zF)FiFP_V@*YUoG8u*|E$<E0bO03YOQdZ+G8WbTp?$Rd(=6nn=9jgnbQZ?AG>s25FS
z`6FA?ECjhW&C`90NM!0|1e)EFDmzi`upzoEf1wr>>a*Lae(q+xD7oGVuiK?RCWaep
z7>r&1X=YzCeV{yZuEC)JBv5<+6Y^qRiLbbn34QT(b<VZMKZN~t%Qo^nr$UJPlY1w_
zbqG4Y6bz*45d|Rs1%%nd4Tp5?`FaGcjF=!xG;e?vkUOn!5lJv3fJzc#at&lbnvN~5
zfB8*DgZ2?-2dd`(-E-SB5yV*vIQTz|Wq}dCo+eCrvt!tnIo=DQrD_c#B>2KW+l^u8
zl>jd#n``=}7_7w6yAWk33z{c=h1hpe6MXCJWrCA;NmDw2!p-_|^O34&%B*9fwSFKj
zMFr>CyY<U;-~8=T!E6_t=pK_V)QK_Je>t}6oW4f~MHHSY=94RuY(luq+;k&>;X#`j
zl0@JZ0;*)ZQ<e@sf&Jy)sgExzf7=*GvmwlV<Ecb2D>I-I_uY-nV^oCiWnUGtAcZCY
zz<lYdY3axgUH2^UGvX?eE?1k6-LoO^9R6^Y3suwpS(qsV2<|i$_QQR4Ai~boe@S+9
zG@$EjZj3WdT=gwSEe=4DUYWK?qLCE7wx4vCR?K*h6KpZ8%GS?tpEaT>cMSO)Qf<b&
z?YE$vD&yXPcxXx(fqt*kLpyguol+tAKRY=O5N})QV1af4*~jXF@Cu;$i&9`1`>tjM
zV{{H{DB9W3vs}C*u<N#7{U%Gne}FgWo}6$#;t>bH$z-%-ebf@BaqyloA*FNC5-U_?
zv@NGfrZ%jviW5|@@W4{pBSO7VvoP_O+sdA&?<cC!Y_r!0BU{c(Qz;y7>R0#2kNA?U
zX%4fab9p}oR%XQc2AR>^UhA4>K{xIfMnPyiBiRE=E^bkV3+U?`RukGce;6AKgHdKd
zaOM+x>vU$gdm)CltKEiIm^vS0I@J^VQ*5ir1^eb;Cc5O(FrirJ%e>_<A#2~qe~W&L
zy3J}+{n3w}u(oy;N4AFl^^(TlDDEwM#|`~hOd4@mycj+mnU-(;WF76hDK=Ye2hfO6
z-eQEm89+MR8ZR79j4!i3f31G9;~Hm`92V#deAS8wO$nh0D6KfSjg*FL)LG^T-Y^ye
z7n4+OEY4*?YrtY{YxZRMAX<gj*<2L_s^(qGU*3GG9nL%`NtI@|Gx5b=K4}LtrSgDG
zd6aU(oC|t~T<J#t&t}zV0@k`>BH_3=F<&H1CjV>Q-YcH0;A|JWe}WT&nZQ3=(_`U1
z&Ym+!Bez@9WSRSS>$2^n_BS0<8E%#@arX=`b5tWyP$bLTv;F^315(xMro&7G%OABi
z+&&Qm!~)x&!2t`2gHdD^Yfs3V->cA2-I2cUe#W|-@oMm)?7+E#f+kvt#Ej3_?&m#J
zQQ~x}%2GA*_-lQye>;ZD58i6(gjM!?8Av%G?LYg(R{RvQUb*&}*4hm|?E-jU1v-yP
zpr1ev^p~=u0rCeBfY_(f*4*a0V+)%@M^pcEkvRgV?igiitUYrTq$NFYd@zm16Ei;_
zAmQ7}l?}~ioXY`?EPf7ov?C@mg3Yg?R%J|o;01Ad7KQ7@f0<UnfinMvC!*j7R=)f8
zF{YCdLfX@p2CT$Xs<O693gxYhub{(tJzCFa&Z5KlJx=c#X-ipe?G{K1!c4@m+6|3V
zq6ejpQe3dx?AB9ZBI4NNToNp%%L1tJ3f!G%#(f7o@Uvs0uLY#Zki-_-vDP(HgLSs)
zey3nA5A<|Sf19}t#-MHlWxDW(ZfOeS-^kVNlN*_6muU?8c-;u5c;Nif!V?YxOd+^J
zyEPj0@xwj*L6&mm?S|%MWV&h3w{zkcDY62wy9SNhRG3xkRt%E&in$_l{!^?)@VCT<
zs$rjD7dyh)DbeaYkvCy`zx2}&9$m+wggCxqMp+f_e-0R-!q92z%w_{-oO3?fUj^{f
zzK7p+1yUH|BcfwLs#?O_;!DAP+(&DX*oFaU&wnm*Zcw_`>02jas<qFzmla<*^+6!}
zSfh;Hq0i!H|6-!?VWALB=@{QqPQ)WyqpA@0**Oj@1YA?VaSQ${B`5IR>I@2Luf9`4
zQw6GIe_ttc{Z3>&og+A%k|K8xf1w3KG0iB}9a|@gvP1v8<nWXG6&xHn*><U3ke-+1
z2K5g-L3^1NxeR9Bsb}a`Wo#gdaD+W#37{s3`1i&poFz(H`o6+1nz<SJ@JQQ7ickZa
z?y$xV{pP(G!bEB@xi4VosO1ymqg@e_O;nP}e~S#Tc?U10(7%&xv_I{)$Q{Qk?tgQ;
z==n$d48?_X;bYvo>HFsG-=npPH2;)a-nXahR?$`oYM?>m$jJj6)9rPp-^_oaZt%ca
z38NvBZ<y6k1!!|&6z7DpQ)Isa@+>Q?{mB)*9q1e3_H22wrvuD8p8u65OXq~k`JIFX
zf2iKN4nKPH5q6so>C={#Z19)s&q}{NhXD;SiZ_;Fg%%qb{-_rzUh@ZBul852KN#$U
zQ>!NY=dKj?$8kKv(VD#4Z17PsundL2poA@015*Z%rn*r~;-+KiMj&xvGp{|Iq#9Xl
zzf*~UJmAreuh8ePK3B>9;M1+N<3h4Af8p`kw4)WQh;moce(YehZNeJYlA1{3w33%*
z8PK|GE)0POSy?&}1m@4X64dzmnWZr#DQ<e*15|&2SfGk<l6A!n`k8HgFF~U}Mc-zG
z)7&8H%X?0{d7NzrP2<!vL$?|EW-D`<I+l&G$XoYQ-*rlyOn(xo$SQzN4Rt5we@MUm
zXZn&ERwrk=3B>dozcz9Mi`zBsAE{UhM-WS(=kh^zHNO+U;XL7K39R|AL&-!(xMei4
zX_LiN!E^jVyDth#CpT0ildwWcwwSo1VL{{xR5^RPQ8QhFepqEekbiBylnBOuahJ$R
zGZA(yfct|oH#vvj8Pc4%;`?zre>}<UJ+G)8-TzA?h1@XmdXXAYch&-5UT$CirvS&q
zdO<zc<dZ+MA!0oyn82Kff<w)o@PD0^db0MH7L1XtSz(rJ>`hI3l5i|N4U=>9N=T1P
zkQ&?{K!pXFl56{56{}tpK=s@bC6qb3Rq4+9XC%)+oc(W%+5c6N)jy3xe{FgDOAt=_
zHC@(NS=Qenb=1U?*RA6yXpg6gweW(HJ*X{ZTb~fgj)N^NNwdHBHc1W;ZhUp^_bkmz
zvDoTI@Nh2>@gT(yHhZOhJLSd2eR2mdq8Gtjw1;_z&qj%Oa}3Yt=sC5*g6Oq(-`U-R
z@Ag_yjU%r2o>mLCGj)MWf9L+>E^QtO(bwrbud!fsXayZ0FzIV^oNn#aa`@c#flbVC
zXTJVn+y<oibK~^o@u5z4P5u_+7ZWz1oU^trcq`V>wbzbtSt~b2z1%tRt^|J6t?D{4
zOu%OI*LGgJQ4Qp%oL1lb0F25(21XwQRzv?2S+|-@)EUccanXdte-oPl5x<B)UU0rC
zW9<K@jH#DWB1rTQ`T&)O6rdo-q{LW5e>L&80?&$FYahLMlH80x9@DM}c=vd~8wB&p
zObpHgAHZ@A<vr6^@IS$toQ)fgq-7+6&2-xo(l61CgS2lPUGC;kRAV$vbaDq|iZPN^
znvWEg%$IcOcd}%Kf4d93g*yvycigvtIB9W<)hE|ysqE$y!N%jGmDr#vn{D$|L29Jj
z#n7Z~J1yfc>NIKs*KOs-??nblb{h&p=5{DqV;SICdIK=x^Ado+sIqpFS<oBX;^x&~
zW#qG0e_ybl3p=&9hy;2dI%zgp)}lI1a$S+khaH~4uR=LLfBD}}2IU>u-+o@$CreZZ
z_$<4cR`z<QQ@e*X?jkIHiWZjtG^AcL>;HiqIf!yzhU`)cLFTqYH70lLF2H`CIH%&j
zqxQWVSaJ)a4UV2N_5g{AqCCly+1*GLs=?BZ<VPa~dmqaQ|9lyVimK3Z?ormY;|}Ra
z;yfhE(Y%X)f4CzP9!KW=P;=rQL_)`T8rM^=_SPg4$w^Ebda+YD-)XR**WXFj#;H1P
zB>8xp+BvU24y>4sU;?wk`@C^T)P**IY1L2#=-Ic2X8g96)mFWEAv+a$AsihJLG=%=
z=ozweo)sEMd!LQWy-~fNdXx(&us`$nPoP-67~*eke`BmgKk;a$Fw_Im5vi#|XLM5e
zCIWviLcaIk!ot8Bvy}^Y7X#Y$#CNnKB&zH|;?_2MN1BT{8V$Uza)~W@e<6kez3hKo
zWAiuujJqOcJ)2?<WbJ94y~<T5aE7t#pyV8W`1?<L@vwaAsw0BESO?aigr8N=Ym<2{
zo;<xoe}6)R6?BR6jxIz#^P#OBkn)K(Ds)}%?bx0~xS4IDuoC?S#hVS?b)prJT8|b?
z4qhY(fPglZNQDl={RKs+AK3z3wNJM05D+SuXPScOIcV6yJ~^~3KAGoqN3l}($B)DQ
zL=7-w!kJ<Pq#|hPy`nlDVTxq|#ww7$fR<IEe<bn2pcPZf1WCy{$z1G8V*Kpts6@?a
z`Fd;gkW;U<J+{iML=Q>)!lWlpKJPT8JrOcB?WRF)gb*jG*4EOR2c?8D&gCUlG0D2Y
zPcy%lhp|Xfyd^R<8BDjq?WIMm%x)T&bG=s~)oETEjYIoF8QkI8opPTA21nqr24N99
ze_J1<zY8E-0;8l;k@ldq3sU?UpW<6+tI?;~#t)TYjwrh%hK-Oi!%N~!d0pRxa^4n1
z4m&;+SL!64JqT_Th2VBQiUXQV7*Kr=8s;mov3>du6Ecj@nvDjba05t|0$Fwlp;sq}
zraz2C_yK6HDOAFR6xkX&H3e!~cvzJle-v$OF59<4Pj%_TUt#h-8>u94vz|AS=XRFM
zTU>(yBzKMmT1q#QLsvzDk<@Unu+iPFHIqyLao)5-R4EijfEu9MT+AN}7AbffIsS6S
zOb<UU>ID*Jj=`2`E(7O<bK97BC-jzFks6nV1=Rc1hqHd10w2oHy`H4HA2va3e<6^w
zY%r3vP$Og=lZs7L5)h%zrgFz{gO4XxI36iv^W$NyI$u-{oK!3q7v|78(74)*DB;3<
zQ5o1lPTse}OMJeX3!kHl)$5|ZN9r!+bxN`>Q%_K2<%8!d*<V4TjQ6(xqBk208o;hP
ziEisXii9Q#xmB8pf_sT4hK%sEe{}vbs_&|y5KLl^5tpXiJRru|F?n9B14wXftq<>O
zV}$@iJJmwe7pD(q7SFYh;^<C`XSvd6u4yo4lS(BL0MqP)@rr4em}+d1rWliQgBY9l
zQvdx#7l;@EIfH-2+NRxIRFcXUqan8+<#E2hU67jYTg9iw6aB>ijwN+Bf1WfXdJ!XT
zf^GG)t6DIduolJ-F*T9|CJPWT7m;*wF~qbA86>leOk4_SKi>-jluC*+D?_@O$!~1|
zCIs30xWB>P4so6H5dNdV)59|t!20G32$h=qF3Y}5T|uhKYGRq1ZC*l)`7m|2=0#uW
z(TbRAwO(aH+oaSl-yD*qe{ycTeF?w}MuUSegd)yU0}=#&Gz5JF2>%k$Y5=MVV)=W`
zXM3d#zrqxf%EHZkX9d=vZrO<e1lo#yHF@1$2djlj(LfA&V6$I*MTeDLJY<LdZO}_Q
z>mn_)SxqhF5cK!NH$Bv$qqc5XuMipv)<Yn5_Y^t!P|WODk%Ua2e^;fdk|7{Fc$Wdc
z>a>!W<b(Njv4NKfcOp1{Hr%_bCe24lC|Tg_h^aE9>&2-ps1#;DoR+`d#%W^bD3ka9
znL4CtL>u&*saS`yhQY-bvqHl|o0NBxn-E)xs!`Rl_Ol1++YGVcPG1joQ}BFnec~o4
zpo6G6-@G+s0kzbue-%8@|D1Ct_&7e~XR5|w)<}KkEvV@1%&lzc@E0Caj4QZ~{NPfn
z!CJGi9h&c8eUHoLm=qA9U(D35UTyRsQcS0ne}>>Q2T{@2A#^=CI@_M@J7nd7PZJxT
zqGsrXPU%2jVhq7{&S?4_R!v-D3RC)6Dfiine4$%$Skc6Df8Ir!Mnd{xhtmHR`orIy
zaRx(1hyD}lJd{ib!!G$8sDTr{AI&J4i=#gBiE;w119Ke4Z{xBiDQeIcE+ySdYvAxV
z6dKYsnb@cwLQ5hKz-85Lxq~3-a@kcX+ELlpIA{EPj5ahfeW89?k(&(K4NdK<&hNVj
z|HCv3X`6H^e>O-0Lrijwi|%C9{7|)ti|LN@20{9y%%T{hZ+Leydd6=GRxGel#$Vb_
zU&MXAR2qXys?6cc&DyyUMew^<LDgAHk<^dtU(R2wu$cYOY5${?J``1cFErLc&$%{x
zU2I>_<;-UeKo4Gp8i(#-m$|S6KEW0<(Y~^B#5Z@dfAS02Mf?#@>|CFH;wl)c3s+v>
zxlc%3AiD@f9lZ-AZh~LIx(&T#+QldY36+-V5<r<W0DEJvb@zQ>GZDGP5F~ha&^OA{
zTtBK0IVD_aC4?=1PGU#20IMe%n5{zDt8)i$Fq48+p1LFaQ_`SAOso-|ovRKEN3a2X
z8Ywule>h1MeKn&*O=LS7&AsLp*`=knRJh(PRwH9OW<{Tg3QKPcQeEnbjPlT%n6k@e
zG)|&J_|`7JWM)bT@;0#XJ6Z0r^?m(H7~NL-dJQB;W)_=CJ}#<d{!)Y5l$8%YE%ZOt
z<rIdm2Ybks(VTunC6JL-#tPG?5}L$aHGm+He{r<H_B!&aod$0V7TC86C)tj+BCR_X
zj;u2MNVzjBv3PxHzMR_Kr7V&~-dAB6MPero|HY2EfihktIvLlfbF{|`VxWo7IQo0E
zP>&AIZlwuj2DkOJxln=tv<p!paBH8N{WqPHY8QQ~l9Ve-BR2|VZe(+Ga%Ev{3T19&
zlTXwI0yr?Yp(+D_L<2H7GMB+P0Tj15Zv%)*12Q-?m!T>H6}Q;A15i2xGB`Gu!8idF
z5;-$B3NK7$ZfA68G9WTCH90qzQS<{91T!}{IFnK5Cx5hgWmp_-vNrA#++lDC?(XjH
z7TkSsm*DQM0fI|#cXxLP1b27xk$3m(ySwN7{jRyDd+IK`yPm42XQs)C6;<ejOze$J
z#qI5YbWHS&+yGfQWqVsgI}SQ!Q*##^Lni<;JtHG4967m&lc^!l(%w$g5NOH`-~d_x
z6pVo%u74jEjEr1x<Nyg%J5#3*r3t{u10ZJ#G*tC)Fl7Qz8U7_G+B*a3j0~MW)TVak
zmUgDpA1)&H4jxXH<`%#|F<9v6{zUrYEldxPHZ-=jcXPJ31Q^<x0Ho>V=mGNfZXci}
zfXdzuU}S1xXk!MjHv_1eY68?$#FSM463Pl{ihnB9^dEs$TpS$io&L#1L`79if)*eu
zB(Ew4Fjc1oNT{i({yD0e+I{dhrv=EXe(3+?`7r$BE+?icq^hMT#>DXF8URcHS5qfv
z%Rg!ViyOrUGr-@}K3vV5>}~%_0HCq}0v)&+7~I_4=*?Z6f%NuH=JXCWfALebuyh8v
z*?&7(13u19rZ%R36~@KR<fEKG3)6oD__HVgSxaM6J7?2BPU80eP}+W!^26x^2mXuL
zM<IZJV%q$}9N=tf`X6a544wb-l~q)f1=t!|+5t`N4DF0R41tC~7iYkizp#(DsR`vj
z2$}*!T%4T#<dFLxmD9h{{10_u`;RNrwSV#QF?9Ry6*IJRarXST+WhBb8{6ACTRH=s
z{}Is?U}kA!`iH&qpEa|z`wNp3l9v(}Q&FXp{b)QpIyw7~>e$f(-GP5u|A{9gD$5Pv
zWMl_0aj^mzKblm`&P2rC*7k$7Gu)r@iCTWt325)+!SKKO+S<<E&Cct8<7Sq2CVyss
zDsSTAz@TPl>F8oACHhb64+!pW%-j?RU<8;t0!-bFEg1f!`>R|2z)XMOk23gpIoLY@
z%nWUuO?@oQOg~O=Ue1QDrU0Omi>Z&-zbpPzf@9(Um{=MEKN|gGSm6GOE@fwC58(O-
z{K4dZRR3%Ns=o%6`eRB>?Coqk0DmT?W^fGh_P~#Zp!)waXaAK;+{MO5-q6;R>c30+
z-*$$!mNp*$VfkMc8m51^Qpwvp*&5pXm(J2z+|u3DM9~sxZ1Io6{sWf+8h-S?ke#`W
z>Bpk{1*!cRC!3GH{n&df|7=|VIwnTu|I&T5q_MS~sk1YHh4n9$=|>s<i+}J(?f=jP
zFlfnZ%4=)U{I8z*%S_D9*xtm_&K$tZ#ttxaax(OQWBh0YW;Ql}7t=>io0z)))hPf5
zdOLgIhYP^L1?U4Xvv-2~vzkndi~t6cKiEG-CIEx!zr>G_41ZPSUkLjjy`zhv&EGaG
z00uKlSJQus@qw8Co5%)Wuz&nFkrTl1w>J~hM}E7%gK>OFANBb+{YOIke~GMIAJV_6
zSwFlT3_tb@8&k8tNwPBi6LtCz?yMiY9Be+eoxg*#0vMeBPW}-L=w|<K>W^%0f4hGW
z_cV3-hyFj;O7YKL_173O{=Inr+{FKqRe(<R)}|VkCLcGje>0IY1b;eNy6Z50%n;KD
z{_*;sPkR56fc)?A|2J=8VS9HkI#x~=039<IGk}SW{o}yI%<A(WzQ+I9Pyd?Vk1qQk
z`OjtsFg0~IHHKSRv^VAnwn}XbDfJaAoGybT=b}HYz~tAIj)z#um~O|z7R}osF%|e0
z(CnW{@y%XVl3UL=Ie);eSd%;$!{&XnC8=`i)<j8g*U(qa7Y|8HXe?KqUM(<FZrQ)A
zlZ5(6I=4WpgmpHvHNKS)pf+|a!qwjO6wN&O8|6BMM7OMUJs;AoXr8GF-N^>kefbk^
z2j22@2Pp9O6MAfvVXx52=eaKhA(&&*P!2s^X!|*>hx|MCzJHU7N6oC+xUQntM*>eq
zN|=m#+!0L|M~xGwepl5M)ab!tjy-(~DyU@o$@oCJ(yavohyXM1?aQvpLxjC#MX}L_
zCMF-}<7eP5*J(d5R{?Au#9oIByETYa{Jb5Zcj*2jQG+zghG?}8-y<#yFIX^L7RUtB
z!oZ=IKt{K5!+#Pi*7gdRV7X|}XcainUb~Ek;R?**Q1{e8$A&=HxRmd_=nVEWUCBcB
zJs&UxfzcTr1G<=;%%X&y31i@zlTtZ{NU3tL|9P;3g+kJ>hgxT7GVlo_hmEvV{lfZ2
z6pX2MN_3@CVYeD_V-h#X=}71pd{T1Dv8#M#=LdD8j(=~)*5cc&ym!Jkd}UStHn#OZ
ztmrLF+3Z<~J3uEuft7|3Nd^W;J0z(mK(V&TYt^1vte~Cw=vsJ{@D2qPqe|8+%;mPZ
zrvizZ6z`-*Lv@LnPs3X-!it;=P%os7M^FDG>W8L`TZG;vD7%H`&*CS1@s3ca!Tw6M
zOPLBlF@H?|l<i!rq;YVcCknL0fqFOw;><&+W;pFS$~96%n0*n4>7pGl)yQFWn(HM`
z^K9P`IXRBDJUm5qs2TwpT<LEua|a&97gjXSRq`8BrFtf(M4EXLlfIP!S8lO?C%!j6
zK<5e*WNk9OTX}o5ZZTu?UbRFl3Xg4BbQqie4u4@GgJMxswk9E9DFsXW>bi>7GA^Ww
z^aPunz#=mQl4~DI{443_87)yZ?&B1^&;2D$9uJQ-r3%$pQUllObo&d)Y>!TR5egkC
zT{AYZIkt{OIICJFN6KC_1A`s-S{{X=MU~zCZGsdCeBYJT%<nqQ(!>&opU&bia+|j{
z4}UKM&zfH*C|3jgj3bee>UUX$v>!{0%T0#Raaii?YV~G7B49s#Cph`c^#j)yjU3Nc
zUyih#4OZR;zNY3{p(;hJv2I%=zjM7;B{y1Mu^yS}lZQFbR;R11<0zwZWwE8BEemD&
zSB92=NY`&(`K@PvPLPJVJAc^A5!`;|h=2QrUFf{8v(_D2*eotomx_q~6e86lqj}OE
zcG@pV(C7d;sQN`<ZhuX~2*@`&R2ggMS<ugP(Aw64o#9fbI*o%)QzS+v+qPUp$J@)h
zEI+^A?(oBzZOrIw&OG<|w-CjuczCJo%L%IKkJz~)1d8QX<|@XJj%Uo2f-XAf!hgri
zT{5w!Ts09|7Hnynb)H*yXp>&E`J|J1e%EO~ReDTo)&RhJp!U2cP%lLwV08{W1}uSz
zY3`mlUE&Ff3TSxIrWf7n!K(#st`1eFrqFjzZV+$Yeuf)!)<lG<%*ijA3~z4*+Q_Ab
zn+AvN_&bfhvs%&+rnxO)NW#;$qkjbKm+C+seP*)7BevJrm-0tPX<<jJ`m{fE%9KIl
zIK;#knbiQd&3&Fs*M<9<z10o>E3~z0MPkChXF1SB{(4g@T~tuUx6Ij;B9lJPcY&D`
zhNUf9484QmQaDZKsT{srB+4M8#@4<#tUt<U^v7K|sDLm8xM0q6z<t9ZD1SPqp0)DM
zm;(7-qzxCxL*X)}{+29otkH;yzhLw`t^H|*cG>HLV$i*YP%Wr$$~eAlKH<t(U5=8t
z*1Qf{Ml(++8J_*NOk4)ace37A{|zc(n<k@H4Cnp6pI4tiCIk&dgO?Zzy(#)pL{a%5
zuiWI=soM}Z6K;NIVZGZJlz&^W#o*6Njh>v68`^Zct~+@&3*?h8ZV0mpw%;~kv(9$e
zJ@<|GBl6$W?Z6<T2MgO5A^ez_hXmPRL|@=%c1#RNw5b6uafA-U_g$B@CL*Q?n{kDu
zRf{yB$KH;G=_kR}dW^8??g@12NQ5N7h%wJwSA0{Mi<GeO@+jj*>VKMy(Bi&QUt~O4
zkRaFrHc9GtO~XE(=#C(<5vC4(!Ydy}9&|EJsY84gJhK|?VK0OqlZ6jQl8<mpQRz9d
z!>SA%)bscpJqx?B25VA;7S?Dvkcy7GI_{c;1G(IXm&N3c#t~RCC$6hoFt2M7rpmNj
zuIEC>6q7Gm_K@REvVSupv-ufaT!HNF*U#_is!hJXMSl(rG^x`d@^i$7Ygu+XdkeD|
zt`$)Y7GCw5VBX~|a5|EiS}=t$T;h*~_<{K*U-r0viqNtQS6A(ZGhi%w1YHwLW#J&a
zV27=h>H4&9Wb#I6SB0e&I*z!<HGY{fgna{j2u~fRv)tl1Y=4f_sP1D`;AE7Yc|H?E
zzcb=IF+eTpvLOaGy+3h^rJ>5@KHd%-svs4{(_AWI+auGZ(!nAqvp#_Qt)VD6?i$&A
zB~U4#B*a469;g^cV9M<<@9JnC6|0ZYnExCTojpIi{T{%_9&UKG9qgSjVRrfcf(yQq
zlL4zL=B{fjK!1WheYKK1%G+qEEAw;v{*hs|!oYy!6Z!$AW}#;V_a6Sm{3wOM)Ji?B
z%+=B-et6j`GYL)Fki)}wZ+W~a9Sh62&TfsHFrqK%HWl2_zapTb@e}WbTHWC&J5xpD
zu6y&(t{fYR9?r;q@X_+`uG!#}+7d{fOUtdunTUvc8-Gr`Pqu@`0q{Ag*GRTMZkua4
zwC8zO&y7dKg6kk}2KHFwRhaWKv4^t!sC3e{5zN@>0cdIdP@@Jb(XbWaJ~&%W%Ikxi
z44;HB164X0MPy#`PF3Q0kK}tb>SgDKWj~8zXMBzmwt>EP;E}5=`tlaX%3N4lB<+Zp
z#1LU4M1OU!GDC|ro)>FP9clxeE>djBhz^N~oa?5I?aje4H$!zEE#mq41w|-mRqV$J
zmaj*e8jD;7$CqO~%}h0;oB0rpE<Yj`*0Lga^=UoomZ)qDIvd21uup9Q6-Kj=_~YG$
z;Y*Cii#6J_(Gs?om`z~I7e+Iqh3wAsdw1@P0Dp?#tYNwh=Hc3(&Kio5X^gdFLBopW
zWxZ*-vCob|rV#}!y2l0}iCL{e3y3bZZgohZNH@}jQ1TD!yPl34_74@AoBdlIod?2K
z4b@vhkj4p*X0xBo`k_N;W9wkHs@b<;V><79J%`0uagV51Sw&8%=F$Q1uOM$=?AIrt
z<$vIi;Qj(!toHHhf#!-O9-G||u3!f<fZ70%&V6C3bR;cb;#cFgLkj~Y{KFi?8(nLW
zp<%puwy1k0?<}F{yi~{cS{SdAFUAyM_}csR^f1ADPctv*v5nXluN+aqQ5iG%TLA)@
zp!UlV;Kd%hJjH9}M7G91sDJ%tpHc1foqunBtH@{Y2o?Q;=G2DkE~Qn^ubEse&9Q#k
z5bK{j#}kA<&3oj-TFY-+5kT(+r0;2inLHSjbBL|u)+dis8HkGBDW44Ozc7uT&eijz
z2{|XyF}P`JS`n-(e6zM#6B~5}Cn0!E*dyUDT4^HCKvTrFPp#UE&VF@63q{1+%YUs@
zx)f)5FAxv9=77iTY8I-O*90jkJ3J0$iwu!kHNBG@Jj2C%x`u08UaYx!ir%NIqOVrc
zdckQu7`7FcY7wQNX8L}0B3a>|xvkhbmxi`}9eU7A(z)?S{d@K9Kt!mSXPf*S{pKy!
zZMwvC1_Ddab1-is|G<Z%BIq(5SAV{i;jTRK_L~cNi}_tUyPJw}MDmp>GgL<ZROWcr
z9W%3-40?~QKI4`qsw>>nI-NCGcZ%*hV*D1aq-R^(&Q7?oY<Bu1%hKoVusgZ#j(MSD
z{f7LP=!L~Y;gVEUzmz9{C7VRF5=+a0p|H+{RdB*3U>^uQ#Y_l#9!rH%+J9Z5Cq2Z~
zFf+|e12g!^Aq4Azot+P(Qe}?`k2ji7(A<!Gpx^io1y#1N+y+UYyS5rT9`uqdjT)JQ
zsJN!6FcW0#wHEXn;*iCHivEeJd5lB#0-cTpZbWbEhUThNCoE9nm%h%9yL_T=1B9VS
zi#$uHKU?0XT<4a<6Qu!0^?%-th2V}mKCpqUYV_hGv!|<j^QO0vB#<OW5K_z}_$R-M
zqgC`att9vg!F>uf^mr=K+so`b@*xdBO1JL!5R|^4g*Dxw?ube6RZh31)r&U=6E4>3
zPg8a)za9N|+=d+6hNT&ylZub#&WzXv%(^#LAfE5bLBD_2CxwOlVSg2rE@<s(o1%p1
zMqk&tM6qy1BN|#Qj#v{3_N0FiOF*ij&HD(-K9pXz;E+_Zs-}kkVI}Ojg&J+8X&l48
zOr!A|W|7XUT?Yx1iBKv<zE345zP$&`XtFG^0VWo93obL`7#%u`X;F6txx}ab9j8SV
zm#eZawL_0>1s<G_8-JdBU{bAI?lIc7UW9S|F;**m1Lv{p@u|~17YD=fxK1%3Vz2K2
z3xuk&`P(<Yh&-og!pIQ+NS|M#%qJ1xnsX~_aNlt19xE(aM4FVVQ3^a-p&p5q^`>v#
zf>2z8r+!X*<S2(Y=!$a*0(LW8vlG~+oV72tXKD6yBvWXEWq-??I_Jal<7N(3(iA&#
zCDCf~2p%6@&&Cxv1=Zd-23(ws>JCgUMrxxRz#a@0n~*#>{i0YRN~WGi$~jg2emfL3
zZgu(GM|Pc)i&<9=JbQn;I-7t^=L2+$!(^l#>o{!N99e7>-R~<ZXQ;=Tl{lYSs)a4Z
zOT%{KhoS~E6@L-?xKZov9lJ6FhvCzbPhCI6nMhZLS!Q;O%)P^&{mPJ$_*#7RQkC8?
zkU_+bX)fGI6U35VA8ZzZmgTH58!yB#{Ui}YLad*wwV#;Mr`-?hEsOfqlbzrD^~($2
z$*hQD?(kwras`!>o|%W;-tNju2S#mC&q|lppi%uv6n}c%w{sf@DH3K!gdZbuVXgf7
z>E8t~8xjI}M>G*|pY_%>KV89Pcu~AVwa!crjATJ-``iCEJ0)y(lt#wEXs}C^<YA)<
zB-TtW5joa}u3Y{qjRvC39%pSWRk|}D#tz7xmoKrw;>x}qIU{^G<D5AAN#`;~l=#T)
zhwrcsR(~;;K57lyDxzBbI9<O3%CP5e&XzZBEooJ(=z8+d1{IYt_3Lwj_B>Tk8a2q;
zyH=Ad&OK~I`x?~Fg8e*V)Wx?-i2>vEt%OV6f|i@kGKxcqZy>=TII-n;RV~Vpyn<QJ
z^W34H-ohYIll(aln@a<aFbahXSx>SplXc@38h_5y5n;M)?KF5AUu89(hz>!-dw!2X
z;S!q?L)^xPC_{|JBqoiC-QO|dHGm^#OW6eO!=$|DtD*>X|K10+j9ot>JxWN=&B~)@
zwDTntJIi?ygLR0ax>0D9cu-UTOF*>0j0ADr!pgl<SWjvQg{dagpT?8Bj-q4Lc!O~A
zdWYs{ZI6FJqbf(KXP(%^ySZHZHF8f#p7QccsB30nLMV$NOk^8CqP7xEADfa&6D#+o
zFj0nAlM3kG*toeUhr}s771Unk$Gc?Q_x6gM@aK`unH^Oec@_r$MM^O9Q~Kww0&Dy4
zFKX=~h*SQp%L!@A(6bdqo(&`_8_YZ|SjY`t1eAX<i@!JVIo-r_2&uM`&IabnWH@6~
ztKTMyT-@!_h-l7Z2f^AF&(7^<aL9@TBJJT^Yzk6|7u}^pZuUbQ$Pg+<J41&OSAC6x
z!VGg-TLx(xh)PHYu4$ll7(ml>rudQ)E60C068IR!ZAg6Cv?Hylu6xKT%r<00q!7_>
z0Xcu&vC)29TnHo=oU^VQVkc1o)8He1g9lH^EV#{qTVWO2VPGt$K!xhk?ijIF7!6*k
zaUbLyI%3%z$g>nBemJC<pVe63EYU?`jth=?M5!;+!^oi337yKz+8*<Bl(F0_;^deT
zeu^2FbfZasY0b8{F;l`4k>Y6eo#aWe|5ksfa}Hqtouw<xO#zQEE)7s7CVOn!tSH@o
zVW!D6+ti@eb~h+y3EMvB7^c8(zwSi2wM6;BoFS0%t1t?~b>uwmJqIpVzds>@sTso%
zW2`<&%(L<R3{SrdepQ*G&8t+(==7w{3RCAnIsU>97@qN?beU{Y10HOE3toOtH&uW4
zL6LgkybyLMDLq_@An-&31@h4<D+R2GF*@86k~aT7Kib=L29$yn6eFfS;^8uA2r}JI
zgRA+=HMV7{0zTN9#NFLcb=H}%2qi&<sZ00^(sy72e06hLI5ZYDw5^LGv07qjq&#W9
z15B`>WFx6L6NniyCqKlC!AW0XcL9GWOp5UgXlu_33i`OC@jKv*?|TTxFm~;fWhCVB
zC7z0KvkOggu8ts(E>jmw6;h(G(@B67xE@H8kz^38zS<i-|GOCH0M$A~O60=j^kf2r
z!-fJ4)W12q|JMGA*dAZxR!GJhwGn-e`g^Nng0pPtHoiqGKe3#vk|3SF7IJ^h7$E|F
zId2v<6p7glCU0-h^|B+#66V5If{m!!yWiMPvN4I?XwXtTO9a|$q@Hjy4L0zo-tT%Q
z{Gb)LX`P7{xtVA02mafF!hGxcJd&=j5joI}S$GiL5hCy=Ja%)oqj{M^?{6(gpN1>;
zZ^pPd=kHO$(K?~SzonF%G1-5v#N&{JG%D91XoHl8LXvxi?4_%i(Am&YA}UHoVDEBj
zgj0?U*+W@o)&yTl?J|^$h+T7Ek4Hrs5#}&E8bPy-4E5j>+gyQ3$GC|#McNpxq^RA0
z%OvCO^Os{S@?@PZ;O4C|rP6#2omNi|5MDyn(iuSKP%s;j4?exUF|>a!F_<AP?-a{B
z`9WOh7Nt|^?Dd%r6)%Cxeos4`+aS}6!)2o!Gy&VI)HyUrhIoxtHrQ3v@OC?J=OoPk
z?zCT~s_s>c2Sl}$1C4c}oAAXUWZ_3?G7)R|7fAx*`_NvD<LCG-n*aycMZ<taeHoB9
z0ADp+orGopr?7{CICp>2XJUdaKP8X+YvUAYe@-<%hZ?$q+ce7Y%bU#Y5!vb-sAZjN
zc4v~19w+SlzPlMRN7j0u9>9p@JE7NA-Od(Tf1_;Xn-UmE@3ugmy0lwH)pi$bA<py3
z=8li$Y6}%ucl^QA!O*Z}N{g;mEBf4C>Pm;i-rNr?AUZLUg6V%33)n*hA1CWV0e@2L
zJg}sQ+x+u{Y$ONLFXA#$tSGg_uFI^4k0yI`x}G_|>X#ZOjP3!vOe>>x7-olEL)Kd`
z&VE9b(LWJ|o4&_GK{+7eHt#iW<eC=W*>$^!l|%l(Qe`>avX5QIQaT|i889HUr0if>
zug$e(Ey@bHR40EjR2Q;>lEjv>{Mk&XK5f#1X9%!iC<Unu%)a;KC=edle!H)pY=a{H
zUU{I#J7O^re8c>rsQ05#@5p%aajH<x?CkTs?3Vn}w3v1Dj}wB0Xn5jG2jiqNQ#j(v
zN9as93w4f-v;d_+bl4fuKn$45GgytfeBSZM#NS>6uik&29958{=f$(dT}<Q41Eo?g
z4QrZ6t0tm!g+_)c&EKE`&SF6J`NBt;tDr*HNr~O_d@n=i9a!3+MAT8u!Uee$Rn}hd
zSyW_b`g%iVoMXOp0|$G;LR16!RosSYVJ24;Gwu?{#=PJuaL9u<P`?cNcxJwSWqIrM
zP_Bv4UWI=c*;x0*eZKIZ_<|9d+B((Yz4%g3^w4JfP~T!8JIt3@y~!o*m;6kDl+P!%
z0}&|tW=?k}+0XSo2*w`$7AFvyiGg_w>r%;DDqVQb?!}NxDLRm@+Za}_U3#i>L`1?u
zDPUsshA;eHd0|jk))v<A7OrnW{`aEQoi+hU3u%AyA)MQp5%5UCTBxzAUT{@HAB_w`
zY~GxrcwQ-%wXCg+mxn2-tn1j26<@0n6&pz&-^HzOKh+X^PXffLS(@BPfss{PQ>F;C
zO!f^e2UH)CfGxgLi?L6Azq#kz<@cm<(IrbQd2qD2cJq$3&$&EZAd$)TT*VQ$DcWq7
zIl+IcvuzY46efjcJyAg&2`Q{1DS`p*hdX`>wVPqeWWU4`p8MF{2>aBPxb(qM1YT*+
zU^d0WFOJKfw|?wi7(G1fx+7eYM<m>`EEgV3{8*%ei%qt%+nocWsfgdt?NEN@*4$T5
zf~vaGvLeNi;7%^5au69Pq#+!~p=PXpZo7ZxA$qXupljuFJ>d_VqN9{I47&=Ubxsa(
z{egDfx8redz0u&{@P(iQj73eZ5mJP>G<xZseB%V(TqKVEip?hJYsEPMXSA+ZFPgif
zo{O2k|1Z=>ZVSV}SR<uts1`K*WCFr@cIm81mEg>1`r=X5A@9}>@dNo)zJ|+SO(1_l
z1+G~WqI=*rDlTf&%}v9;a14=M*V8xvU0X4NiM!>*P71}lrkh=Lr*m5q$;kMyWCKj|
z;w6PP480!%$&r5Embish5B^Ft9s1Vlo>ARuhnu@S+U_TZQw-r?_UupG3k)KQQg>71
z)XNvdTw6?jLD+|;x(eiY?eKDP{%3zve(H%%uM>k|2QjNhX-j1Fyo}(J+Q|haUG{6A
zmHX$FO(lLrTlB&-5cKCySqW?<3mO>8zEcAp{I&gRBjJ@`@|#TzNO7760l)kqgISVk
zEWeT)0s^UHk?h!0qN2G>M{gkZ)$g?ilcKO;xNaWu{I8=b-(yYoa6e(K#b<vVH+*e@
zZj;z=0(odN!x2iJ)fhohix%a0^~2@m`!t!Zq1HE&Yjpi0>Li{yEN;fw-Q3r!_w%Qn
zM@iwc<@Q@(o`lvsCI)erITspkMPd-}a~*cxY}!QJ$$avTE;Jt^=F#Fqj1tY{xD^oi
zy5T)6F!j~8D-Igs#1K2vW6gg@NU~=Ip5r3M!|1?ojC~5`a_D?A>Wc&~X?Cl_r@4{F
zhfLH#5S=t8=>CS10Ow0zfu($4KQgJ=_jETi+R>KQ2y?lLjudvEbH2DR-j=J?1|F^>
z*z17=gw$G18D9{kPre84wMe}KBvzCNC944sqR>f(*bwaP3HC6HxiNpe3kBXFcF)q5
zK5rn<P)iC};NDwBl`Y`J5x)0_mt+OR9x^V&HP+HH)2zFX-nRDgT0!#|=jR-VWbo8G
zioz}TWMB5xu37kAZ&p0hUQ4BFR~^eK!<2%SyNWYZHM++g8X^?2uR$5*AULM_%b*#5
zYG)`C>8@lS_%(o>(Z_!p9K7p!&H?Zl@9A#9ynSK#f8F8M%EK68t;>i-OFbDxQgvcd
zVvQMLY>|8hyo3ILPC=^XTZq`iD@KhpaRP?*7?EjmA|nR{CU)qKuufI)UlVUmuM~@r
z{md<&sG#GlS(kc^pogETD<Y8w4D={$t49n))#6*JMAS!lKLURr48@F?>DR173tb)k
zsc6*ogYg8@NMaio>xp9bK4E?%EV9jr7dDl(<%LTH?T)?}=S4)Rz9|=el6WA~!=}+S
zt$<kAXQ)1X_a>U@%vA3J9mk5U<YO~OCXdqNBIY~@_C00Hc+@}-lut}BC&{SZ%!=al
z!?-kgr~~16*{FXJQr*C(#1sz8FE6(GvTYlne~17w{Syy6NB<SX3z@e1V!Z?8=C{;K
zUR&f38Ksf>Do=K1D;*iVI@^UGMHt%;`<Mv5wP<%Ex3VvsskS~KU$WSaTxQ}&IY?%A
zlc57o6pSYn9p}V*mR2=u&XvV&Z8uqLWejqIlEu@wNNj(x>r`5fT-WGvzVFj(HwxA`
zeczGdi^9d@({My0xq1pCtG?l}P|ezv-ncecpT~i4V)I|}PkQ3tqMF0nIs6{V?uZW|
za-bGbM%*pFHe4mEwxM(qOOvJ>s=#brn|ls6e+Pw8p>XpAb+jD!9RNagQDFvN4*|UY
z*1{eV-3Navg;Dy+d1clS^uA&jL}~G05iUy@I~>Z2q#SIeV|dh{RbD>*djNQ%c6{ll
z#tI9#nAUexJvua;YDd7SimKVe8OcLOR9P1<g4pzrqI}H#75aUadHo9GB>+9cmY%9m
ze<d`^(NgHad<S(0GH>T6nzHxmud;XxF56T-;<tYU46TxtNSgd`4fu3fM?WF^AJM_*
zmH=Pu$0C9QHAb9=E<b;Zo8;ixJl3~1&`cH8kw8n{vgeu=J06&SJ@rHVY;3^kAeGmr
zMI5VaF;WnA9M{hFR?T=!nZ`}NqJDEHw(#m+6)gMB%b-wKpRpvD{?_U#_Lhf$^o(*6
zY<7R|gt~J*5#8A?PP}R^_Zb7qdIjOYcO9NCof6z4P24^^9JV5$vu)w6c@5FgJ;lkm
zMoOj?yf*fr;rFt}!B}GyM>_T}xD1SD#2#czQB53SAM{z*ZSh1@@3YxxpA4qGP)5d^
ziLxmuzoQp_euM3Jp5VwMXF`V4xA`Bo82o=aSV7TJK2hbuLUhq)R1xWukWt^#6|Cmo
z5(`e|ID4bk+w!;i&R7LZ21f_=0<jPDCrYS4BQvx~MhMmmClZ7gEXrqHyj<>jd?wD8
zh>q6@jgU=VIuY<&(-&&PhZBFlvTK7&W#h)vv+P;uE!#p$fmEJ-r#w(b+pP;C;TM0O
z=DnSD=p6+2?lXOCGW@RWdUp!JS&(vTf_mvb8)e!~@ZB+@N#6Cn>ClIVt4rqMccPA@
z7E%o~MYlPUE39%w%n1O#ZD3R}LJlbAKjdNH#RtVVnBpZgv#KBt8a`^WN*B?mHv<>?
zm2*bPJy5K+v3l7SqW@8$Wh}Eg5DR}~Ur=3Fxm2l5exfw(0Qg*ODxBw42n$&>Q0rbx
zJQsD4!@Wek3qtjaIVDduI*@~JYzOPIj67^QM42k~pu$CKd9vTgs$Qo|((3D4@2#2{
ziEU0^q$E2W)e)&vW+l*a$S4_j&6yFAjm2<6P51LSTvG(84foAYV#1KR?k#`!2FYa1
zdkq;fQ^45gbX%LX{Uw#Ck$3VCJhLu5+x-B9FX0=Ba(A1SIlALRG2KzI4GRvn(vLES
zuR{IiSe*IW<Cx=un1VV;hG|a69#szApj*tRTbB$k==iB_tt$gUBNX}(TWgWBB@^<N
z2XHmed^QO;o)Q1YPjTvROt61W=iRL(C&PJ)B0pn{mHZm*Sa=p!exu?!T#!bA1xpXH
zCQ*XR3%;@m7?=Ma&jQqau%Tbw1WGvyBo|w7?Q8VL!HPY9&oT^sCkcihe&z>TX#hMN
zy6e4PldshYMcItsTvH)3X%?tllbMw~Xug&o^E}ls^^b4HF#gttVoQH_3M(U%;Ucf_
zoVt8#wNrr6s$P<J!t~_hS+?gSoE`jf1Bw0^6FVOZZ*D+s6;y%4`MR@}o<W<sLF}y1
zIECc;4wuN`>OM&1oOp2J9Uo0G?D*`(a@lBEeW?EfQ7TYGyIs84f`Wo{u^3sE4-H$d
zV}!Gz(61o0+dD4nll_0I>P5G`>i}vX_)`vQ$3!DKTEhE%-}%KAVhO01)16O$Dz2o#
z^98}T(MI|boA%|kRs25bK67vj>a@Ct2VcycTZVNwi0BY+qdnFc1Jz(g{a#<32RSXP
zTh<8MA3u>V-gFr~y#pt1Hj}UJpx=8?;{?dKdbXp($yzTO>Dzz6xM98yYOV9cD_#^A
z*Y`h6o7=WQG2-bQIhE{9%E&)dzn-8?$K*z^>OR#Sp`s8onkJ4_7B{@<P>vt?9Cx0y
z|5BL#28s>yo3K{UgFwxv5Lf)ofS&v4)}MOKy5h!UYP%KQjYFkP!|&8*07Ym>wraF1
z1hX>vEoZJ4KR$o*M>P5?%j`C;t!DqciEDsC+Hft@8^x2B)DP(C-~-S=h;L?F6AN_~
zejz%aAG44ouo0?r+cNK8<}(|8|J4tkp-=eVE`sQNY;TUXdB%@t!OB`4rG6I11wQxj
z)thMS^VT^5){#d7*2m0QTnlrl;!;I7J|lgVbL!RfvZ;ThKGj)x&`VfaNe!mG8MS@>
z#W4+pf*c>gc4_J_2=z}1V%j{#6$%Q3%tl%Q`?_YE-sO=s+w;jfGdtn-qSN5l&S`V}
zDZ@3^;63Jn;fQ##<fFOsUP2CD?R*aa(w${4e^weDVerb8V)P9>CX4}c`~s{twwP>c
zOsKyC5Ga4%lZv9SWndAWFCh^8Jmd&B%^s~vA7PZ)&TB{a^=y!k*;_%d<;QhSpvt{+
zt1%``0<P$!uUhlYMl1|1KGbR(bNicbW#6;5lnytK|3Kgcx5vn(d2P?a$PtDXgJ1bW
zN`A>PPwLxR4Q0B&8Z)tVJwof(;kVk1LC9S00@{DKb!x$kO_oIy_^%<9!j~<u41JI8
zwJ_M?>?q`kGc|?!(Kkj9$-^O?b+bM(OD{|e{TO+zh7$Xx5DcR<c#S<o<1G$fO*i%+
z{2nDUH&r$pXwq0&xzw|HqhNN+tYeOd(ZBQ_us16UIy3CF5?QT%PF^sn&0u8P@iTjj
z5;}jV<X*RNX0baJ#}8;mjWWu)JhaRII@1%6I%xU$Xs~|qIlRKoD#kHZEg*r1<(m%Y
zgcS)7adx`<T+1`ZA!H0ybD`jEy=vSf$wk~3kB#ZrJ7PuaNw>(%C0e@!)9b^695hzi
zl3FfpsDAjZYwDRnyZW<2F=d1K*EV_GCX|28fYq~YaaOxwctb~&M7Md(nZ(*h!ooJU
z&-4X2Wv|`OWV+@|1&4cvgFIe+=pOuHiRD!ds<E@wB*>9c<Nh&P$UqIWR!9(v^0;%2
zb}Sr1pnA$^LvMS+-l?=+?lwF>n{;gamgwcPsIrP>;w2Y@WYP%62%)hj2{*De8jODx
zOIn2O^JCge&v;j#Cx!MMRFiJ=ZCboM)^J23h7U1jf7jlpEB`^>X|B2S+LeAl<Yq1j
z>@EXSz>`0hiMq&7J@R-z&aJn|S(E-Q-C^vTXVtS!tVqH9+QpqG5O!Vh5mliTWx%st
z7yT8S>x&@J-y}Kjo8-}*5D&_02DE?DNQj)116pIXM>OwZ1r76>5ey8**NF@!8dwh=
ze4;#c4q=T-7*2ni6lE$$ZMNm1FmG25S$ts`_#iP*<gx1;@(T~uqQhTeZ)pI+2|Bio
zPnB3k$*YRwb&`tHUyK^+)_TJRmpEW>IGj3nzRGA2Wu&P=Ur4v(`dzhfS?Yf%OWQ!3
z5$z}Q)OVjhLO$e?X~vck9PARME8i-rD?p9bLRQ+#0<&K;($nVLfF`tUp!pNR{IwEK
zI@(hg=%OXPB%H=hP$fzDmlH|g9brFLhxFBVhsDD&>FY~`epxNy^D`t|r12vB&ZQVq
zYO2N~i`>$Dn|}XHj-jug@vMI)HrZRV2-`P*_&ukhVrU9cRsb>+1bahlBoWPPl3q>)
zCM!X_athML9Y?-fGysyPgO=KdyuOnqVoy8dsbh^?a*)kg&m=q_3>49?_Is1f(P%z-
zY^QidaYcmrfkG1zfP5{e&OfUC-ofJ5<qP(g>PO~gR{!O8CoN_wFmr!NFOXM8;zF5E
zr$%~_uVV$&;SCqe4k6IC`Pw&M&s;s^AvIP&zAjgHpW2K3KzoZ6aG2XQljNkG_<gn`
zI3Fa8;2(ZS@WOLsP%*Hr3MIpj#fwhO?O~$p$Iq6%w_D^$wRUBmJr-&NW<+BA8V%lZ
zBrH_Oj@-`+cG5JEA+djBf;rtyGw#5{XNMJy4U{qR?Cl}EUsWG5(i-W$%6S1{V~%{q
zr~Ss*Ok^#P*Flmc_my9MSGWBqFwABG=ywB(0XKj+URY}$!%1wc7Z$6F^JVV^<!u&A
zo+!a`D<U}m;0L_*5^ZQ79|%pF<yenfhfn%;dH%_*oZpJy8(n`r$QINPc&Z}bz4xbj
zXSdRv_Gg6vA{5uBq&~hcbkZ^wnP5BfU|&HY&}@G1%xrRJ$r+?s>!8T~QpGldoPnV@
z5J%W&yZU+&zT$>+*VZ@0>y~~gfa&i8B_baBj&{ro_Ox#M3Lx6C?7c9L;1k`z0gyeg
zS~wj_BtvGyp<aLPagoI&e!pR50GDV!1@kYvO$gsqkTk}=W3pm&CPi*h&YBVIF4l>4
z4n$7xKZl#duU=h#X@H^v?-QLKXHLx^JnwshcJfF0wtYSA37R)l=N(d16oD)bFP%z(
ztgOR|*fUIYrcIhJ&|%gi1x`$#t#8AG_Eo$sx+tibts{Rnni_sNdD?L4|9H@+R<bET
z06HV-C&<K+-7sWkucjz8@`Q@exjUoxs6ASIrfpqk_!;VGmDiVTTC5Bso$NRUa#J$S
z`r7s8D#!13Gvw9)F1uMMMfmCG8~Y5-a72w7Fo*;i4NG`9(LC+78n=FG#v=pMjlsi^
zfU_s?)H;99kl_Y%P3WrzOU-2K%L8o(??L8R6zL;FAu4lMHp0_D>MX-ud_kmN+;0b~
zlTz$NEzb~ps!W&0LDG%x9o(FrqoLA}Df)B3Io%YNP#7mt5pcp2`H1sABTjDOT>aSn
z9mYKMK_T=DRbEF!1ClbtKI(UQ!&Sf~#76BgknexERy_fSl<{a3ZKcoSe!j~hV)W_W
zlie$(lz-9`@;uy0Lw4c98@1|Fd5zhSZUFyY(F~eAiVx>7B}CReLR`b{kot;T@>(S<
zO%v?v)$A>UJ%L}@Hh&Rs!ve7t$UN`y>WJZII(P`pgu$=Ni$=g$+u^m}o`CXnhbdu-
zW?6rABTDJ**y^Rs@9|Ex`P`DE`(hm7TD#wp<C$0bz14^(@I5>Oyab?^#(JUEI=?%6
zT+ctqZG%67y|+u?E)K5oE_QacYVq#MVkHnqp9`A@+V6yu!G6i;6?u7yo-5fV`+OZD
zF^AieV=3xXfH8ZUymDRleLrBP57U~M_{@Kd>nRN{eti|i;T`uAks<cHZf~i+@hI=y
zv3zk<P)AP@4p!p?Yvg=!RqnYZg0^<aV2-PF)TOeR`<YqTW?@}E!KJEpC7Nhbb>~~Q
z(vF8L{6rTk`$Jj}CW+s`PX=@l6Yndb=&D(p3iNmzl-k$)9>=EIptHwpkR0U#JB5F>
z`VhLhWOLfi$8LAHnaLS8lCwtU@SK?yb5DinuVilF$yMlVP8gD#iVna8Vi*E^mzyks
z&1qUMm83nkXfdB7y_1rC29{;C+Bq7R@<}V}8b&uC$hF_m4mQPm+&@rc+J7m1`h}F!
zi!&bdlRFJU!ENLMZKzh-MPYi|+oFFINwyYH`9%6){Qc%2r(&V6iuiDQZ{w4e)}1*U
zekx}2<%O9}oPiAZ+yd~mSnWMd5Ti`J%1K}QJP`T0TRnt7oaZrq<RPO0Yz6z|6C=E$
zCytXSM%)ScwH3AgMX3E6d%O|mk8coVG+w%ppN}DsH<o$?lc{6YpS3}QfscPEt)&nY
zo<$NI7_zvzh31J9)wF3ZC6vwWYdsaQ;!wRl@3X#qm6Q2_GXu_jVcbtX>>l+oHCU0%
zlmUq8^+AScJgUW8>!FmQBy29-ojAhLldAfzFH<9DGdOzj=MvomVrx`UHaxtz_13Q&
z`Ef@_ywQ*N8$tR32kNSlhq-^Pw`qivz#Tzb?!2J99!R{7j*=v*5Nv|*$78R29HZSa
z_t-X+xq>WUQ7Y;3Th=_23-U24N0>yh->F@sY$<V1*(*}tjx1-Ft;tcZE+1guE;c-%
z+70@=kM7l9Fxmwi;^<k=ZMhakz2Eia`O^$xXfeS%6L>XZ>BEwZ<*|Q{^$Dff1Ay{M
zM=C6kB{B$HgNUk{=H#1mxflSu_3(6|u274ab=ONyOpq7hU`;ELz(Lo0%UIY|DbZ!%
z0_lBssFZ@sr6o;9L%337Fr69`qA1LT@T~_S-{jV4lw>2{ZfkMPHK7nO?8y)*=KO1Q
ziJ0Q*1V>OiTT9A3*DrtOV*$+Q0h7{4_$U{tSq8>$l2-*KRrKbRt?|xvKgjw^&HU68
zejvhLG$LSk3mT|o@;3_WK_zE6psZHSJ^Oc|fvTm^Rc9bBYkCzRA&hQ~NM_x4G0)~n
z2u_)`$%5FSqk*-Jeti9Ni((Cz$DMgADP4>&;+Yf3IAb&H-}Zm+E0`o4oIak~*FxtE
z7sQ69hMk6HULrC!ixmr8wJsy@zfz~k&lW9(7|8@cKKmkrSi$BC-l^zWJs93{Yy&G$
zusI8Ye6g8Mp8F7%1AABC!?@s@96$F7pQ(q5j&Uz8THHvOJi+TnnD9mw)LqeZoGwL|
z-ImgIoZ#)v{W^dD(c)$tHJO$NGQ{YG^g|BsLUQ<3AwPV%)Tl~J%&uqmd&EH~Uz;E$
z98Tu#Pm|Ul{pIiO&RV719bMeUj@d!JjZ{W%B0UG#Hm}|tlGwWs8vBX%HP!uuUm+G$
ze)p(ZaojYNMc-k1jB#I?*5**gECU~Z85_-&kA+0YN_>AeiBR_pS3|zN{C-vaBmZII
zDDzNs0sSZGTibl@uGRPGr@eUS;Y7EPmtX~>`4DVFBBCm1uh|4$)%N-F(Q2(7^YB{w
z4LgmoWfn=QD7RQ-sfDXA=PUlJb@4xw)|vxeML6C{$gtxKg>MnC%@%{~)iiE{SDbl{
z$y;Z7x>tWjv#jeOM$6+ki!3EOmEWYWNj7@kKvT%~1p<()7(otGkQ|%%<G?BHNS;Og
zsJE{xy|>?YN0-zpNK+Jk<h`f%ke1`Fg9-DbYYy=-S}&Et#il9^zYY(3SUaXu$E1~`
z>K1_2<lRplqlXXpilx*bp8GlqY}Fziv0<5MQsjRT<|1T@e6J3cq40A3R6L_`%)RP;
z&tHYV*}1q=?lBXCMFesG)1-GaSG`?Np5K_yR!H*y_(zLhhAVL|tyPJc0aCI=x|i6)
z{(=hIb8{9yS@U~827XOz8HwCppq5-*NLPNAv83~QbYyg{)>KJK*oFRq$uBlq0%dxw
zFQb18nKC@A@#3ABE$kpy<O;2OyJyw&%^(X=ugo0T0Q%fRhXwvVksfTx<mkI$1N>j~
zoQpA3<in-P2_@blVkS1L#4@-GCwMv{aM#*^yhirl=O`<eVA;j1{&Rd+=5-4v{)HfZ
zZPoBgM1$`!&E)bb9_3O`Z|d`ltK7^y3X6YbVmEMc(R?Rt(=qhb@|y?<Cg1c0M9vL{
zhJv~KQ-;pJuBoEkF>73j)cSx;>+8Qylfq;=<3u&sbGA+?imrsWSB-b!V*0&A7f-)3
zDu1GgNO}m}J)qd(i%826v9#wO<&vcm3hi?7!DbWJYZ?Y|OLTEztoEE!R%bNMFK&M_
zxwqLT_=Fo;5kU`wO<x{CuDoDH>YEyFwi%9mirOg-<&VVvhIv>`YoeRm4U{+&3@J#q
z-rZ>C=^64h!ro@0oC0n6F^A7t&9Iogqh`&xLcOrv7j3IJph6OWeZJu7v?zhSEcCjc
zVd(hNMUEpXp&CGWws`bfJYBCxR$G5UlA7TrhikMD<{@E{y+uiodu*R{&r?z<36gu-
zHUw)?_2MTstVkctq%GuRF~Dl(-CdSUCAuYbKfpXsy*F$hKC_?tdTO(PA!fq)KJ$a+
zHH_gHYf^ty@tv?FVSPR^IGl7J+1vct>N^y9(iO?KC`ApnNji~bK^bRk?(~1T88{NH
z?9yZomMawwU-W`df@eI2=f_sq_#o2&<;iWHolB`fj`kx95>i!zjVg23<BJ&5RibF4
zyNjD$#zOBTrpLewZ08@XI!EHppYp17-W=E4jfx>wgrq?tFMpZvPu*(K+-tPee(q@~
zrX9(&vD%N;?@XANrausUM4W$jcCNdhc^;`Nc+{Wrj}cIC7Sc9CjwMJoe&wmrVFI(3
z5@AUgPJ~}E!z1lIMS}0^o(mVt4M9$AHEL}?w7Efb2z%#VA0Xz8l9+dY#|o=<jXiqj
z2D0u6P<6}o!g!z$CD#lU!slQw+YzRpb}0Ja5k}x3m*$Ug5g;~S=H`E%FGsK<1esP#
zi74!ze%4w!7r$XKGFC{{4D`auo%W6?#<0^pBI+;@z1)#l(MbLxR%^(F_N2i;tj>&D
zm)@Hqi2wEVVk|RZw$6Nlr4>0SkGN%bPlvn9cD~Z=SsC|g_K<_5yIhk1`C@W3-%x)W
zquv3_W0^Fi;L5{bJ4k={MWN`CC854SUZlLLx5hKl9K|&Wjhk6ggAknIyMs82jzbXW
z_slt|=DLbrVuf*o0y(dhcNhO7SUGY(bqtWB%H~czmXI`R&Vb*fzVU2(1bjd1_&elz
z{pli)eNT3T4u)0<g*dIqysablHy8shBK3VYD;ss)j?A#QAf<n?WN_)rs#g!&8f0@F
z65PV1TEcvHqmrH3^=R(I6b>DyM11Qd+q$_(!=P}<O#9=Sxi@}`Dj4>&gDY#K4%W&>
z-Q-C<3?|=<BxVp0>j!xBV&qUei*E?-s;P^%YpKpiv#_tk*A=u?$98MUdhuEZBx_$x
zBqY)wnc2n8btHe3(e>gq%Oy=FEBMxT5hTrw*+QmbpTigtbVl)|T(`ddRHj^(pd}4m
z(<3JW7PIZ)xbo5%&Nfct3ASwYv^{wq4E76a!jh5NVvO+iM7O6kEVAQ+x!bpk3ZqJT
z$N86dLKsO#6^eqml#g!yc2lPO1)lta2cU)^KBUzyJl=m~k>(=T1FT>FjO9lWXm&xm
zxt#EZkBpjt)HT}z`Ut<qUN{3J2DheJD1(x(IwOjS#5IQv12jH9(51VmrRiY)s$ju0
zu61|FQ9GNeZd04QxEf8llcDd?-LxQR!=X-WP=Scj956r<Mx4x}%RE>9{jaA9A-k&A
z*{15{&~JY_aTy@i%?nCy%F^m3&J72BK5B7Ki5!mIziBdh>-<Irj<WmC3*FX29h9`x
zjE;{~L}?>zFq?h7lV#pJFfNJ{VXkQ%3}vhA@-v!CF6Rh_Uo~4ya)TC!D1N$~4W$4T
z;i_&P;y^BA6_D%Z-FjX<tu9cg4Cl&ZjijXZbbEgb+CmSH)<oAl2=K+LciI5@@!@tx
zxnT_$;-R2SN@BFV=gzy<a!jAK^7tLKdziBwLaY2r)J>I&Z&u7=j#D&cAgFfDPm?Mv
zN9dC%QX1g8;ilH{BJK^`y=c@m#Ct`z2w7TrNZ2vb+ocxvaIq-Yate)ixU09%B~KUA
z6^nnh%^&iqk6xqfg9KMY_<N1UxfAs9!;?#rn#72+YSi%qxeB0gW;FGC1AKe#5-%mL
z#%f~hJpD*D-I~U=xxd={8vg1SxMv22!i(Kemv~tJxKCQn=Jjn@!LnvVPob7{@A`zg
zuq<~(ATqd59I+H->_>;j9pcFbRyO4wy7qrCX#jU-iT}vkPXlA_X!Je}Vl#SVBm1w{
z;*>{4ocVgYk2;~IB-%7{c>TEow(Lbu9<Pt`>#}mmZ#Lw0pAVe!<jOlOqF9i&>CO}`
zXv{~4GDg?m@~4<fkNnp?#2vW{8a+2*_aHulIq$;J$@~9ac#ITjD{KE8aU<iEale1~
zJ``d#!=>z+==<H4l^H{f*kut;JQwQL>c=Nh{njOE6LHgl$RZ!_Pv6a5mZxnVES!{Q
zY-=AkZCI`1YlCeqiYH&9_t~{vl5C*4#b&c!snQA(=C6GB7Qx`W8pJoe#;9EgG}_H?
zl7v!AWo+h@LQZ9zaj}oeDt%7~xS4-U!XjR3(G&P$s9v=QtL)AWOd`^kbP(*+O}B8E
zSzg3h-fOW8O!&>MP<5+>kLdd7{GA-xT+Ljm8H3t$8LdT2I_3<FeGF|Jz`<l-_Q+{X
z&(MW1ZQTOqml1@wFrE=e1Wq7hI#i4DHn+Us)9AYbr{fj8S?;9fAaz3&?|OfhFQB+r
zjc?cp^dmp(jL!y3!WrRK*OY3jiZ%En!f$hg!&VI<tIBdgsoDvsjb7ghWxD_7YN0j)
zQuP%(TM8yHKXRUj>}JbGKgWv5p%VYn4{SWo!c~Add(*tudTJ@@8}j5vWA69_63w~y
ztwGFwF*vM)Iu9I457@LUDm8zr#JTQn#?bbh(Zu&{iTosFJNx%?n784t_(Z5z7F3HK
zp0Q_pk}|Pw!h`n>Dg&}i%6Zo8J+T%#Zh<Fm@3roy8W@JNH^)fryi+V5qcGt}Pg#FM
zj2+)=%-7SH6V8Ypmi<=<oLzO<dGL#}{g+0)h0a<7H4>G&#$C<=$#Q>a4k5-B2r;tK
zTSje0j>y>yFkvu)uLDT8m(RY@t0mi6Y(mvZ-`dP>k!M3zT+<A<ep>L;w!JgL+a)x)
z)I#ZaK)!$<kcI|Yq0a<#R-KrD$Mvb)njF8R$*-vBUqC9tC`f?XX@lpKwtn@d(1?m=
zS1dkb79ygk5A-%eij;qX?ejjVICpY5hBm}FbQQMUKDFeo#3N_T>E|m9zzw?E6Yn0w
zl#1;|GzRVOzh72X&Q}0;s8_hV&}}uvmWJuw8L%rFek2))7eW!8blSES#7+9{t55ud
z3mSl-T_tV&K#;?X+vn<gGIkr2&0Ue2Ru%{Y56_!d^Kc5b^jd$g)0~JhJjZxhX~z|!
zlB{AuwHiK=YzN+6gKk>a4nd7cvn^<xOMle;oZ{={-A(;MS2E(yx0JULb~$)8!G)~X
zK7zUWg$7J_3CFMQY=;D_Ip39W9?zS>UtvKJ!C>BvjlA?HHR@trf$1h}J-2Lb!wqFH
zjW_h!*0`z8fG&TPgEoo;NZoZ5t~KS<0W0};h<Zq?y)Rcvnr?L{4X^h#SmgrV{%`^N
zM)RH(^ObIwP0iO)CEc^;6)@;!ZdMG=_z-qptn{c-FbSv!6CfD{L$@R0uA~hV2{ojB
zL#Qv3+yAdkd+Lh>P@n*wJ=u1fZB2G<_GY`ywvEa5X4ijaZ5t<>8#hkajC)`1+x-gX
z>HN>{SZW=ylhI<4f^I9yHbcFh$NeIFh*5)&(xOo0D#<fR+nW+Ls^8>A{@*31rns5O
z{VY<;gZ?#fGIDlp$oF&uuQ<l0XA`9!c~sChFl`?jI;tyi!tv4plMPmCFMHA|0*`wK
zM)Es}Z%KbO%iG_5x1YUr1kHIbT`i|_FBkpjOA{~E2o*C^l~7Vq`6K)49v169&5=pp
z1R#_9Zu(4JddB(R$=iz9D=I46_h47y-fWq;X%(XW*jEcW**W)R9A8riP3j`8-~(cp
zHYPfo?s(#eUmE25WA^qPlDOIYzReBRK-7^`Wmta@)j7-)OFiG!6kSPk%Z}ubac#w%
zy8tM%1su#d4YmBN(Sz%Wk)$BTZl4#-S*AfrBOk#WA{C%|(H56Wn`#%ST}k43o81yX
zu!`Eajydr}lX*V>eI+e&z}=*U@nx(@^3%dZ__|b_47~sVzpE_0Ac7Ep`y%hW;jtG`
z+QWaF9Vs#4^61&y_8Q>QrN2gNz^3cp-D?FH{|@FHo`L9nn5*vM%<31w^Pt)5klj@{
z!b|c_8T^-IUfY8X)$~IJEo$JctQuAjo1;#7TW0NdO)NwaXvU?&pxn2bhtbe>k0tGj
z4rUcxmG2Y-ndj5-XsO2Y>FH$PtFYp%WEX!<vK-_f3h!q+VY7`)Hj!o*0!oFeKW|+E
zrqiNbYK^=ziMjWR8W^wUQo<yBt!2;~2p`tON^?2yZ*52mL$Zx60bG54leGTs#lXro
z3T6CquC6Q0Qg0gzsx)fVk4Z-4pv?*wn%J=_(dZfnKyIgVTmo$sC)>$kfy5U?>e7Ei
zMp^^KccBC3hQxRMZ7Oq>Abac@tls`K63fu>XswQb#a!JEDn`Yi6<%6)K>i>*$)$<u
zzlp5CFm%^x*5rr2u$k(@ThaWo4<V_@^ABHzE})9Egm~xwgsifpF__s<uHk6z>W`ef
zak)tzVnVF+9S`}y$H`F+w49C}MFW2`NJ}z}!%?_&T_G*ciBGS%l{&XdIV)fVsB+$d
zwrPXbo>I`7pbBn(!D8=D=Ft3Uj;e*RmJLl_Qq=p2rNP_7t<}2|c%&Tpc!`L^;ReS4
zB%w02&;Nq<B={3Hhsa*!hi3v?Kat4cXEh8-lbsh-L>A6D+Gjio&k?fy;fjA{dvJV>
zKuH#lKw*^k(}b`E5k%6O=)(lq=5Vq=ReCsjQayVfH9sh4!)xT+3J_TGzwSP(nD2`L
z6?_W}fCTl`mnm_}W_eyjqKQs#%tL2xK#RqHZS>e_^i(n<3`5UjxKW-mb{Ok4M12)v
z<sg5{d469bT1peRvu&UX^Z$SBr~EZ=DeLLms(S$oyY+zFd-ZM+G11lg@u_&mxq&^e
zQ?OgpI0=BZ1azCa_LTmN@LnZ6X6TX<p0SJnRLX{LdO6ozzdR2qbbmejEX4VXkWvkJ
zz`a#15JZ2Ba-uNAJ^FOR9GF<%lgQm>HyRquT}kQ{hrU;JmZIt#z}|ma3Pt*he6n5_
z2#9L+Se|1w#O=*)PJ#Zeu5yWiJ2q3;wt0)MlKWK9bI=CDA0rR5;xAm=$u%~&d&OXf
z(xFcNli0G051(^TBSVcN<o}OLjeH|D%dxg=VZCmmTSV80PrOFpSrD3E!K51COkqZp
zPQABIA8nu2m|sYTA7y`M?<YFCxrY;;F6l&)iY%T(f;Ynr3mpj7NtO2qbr3ZHp9I)N
z$_%%srxU(r1?;bv0kYp|nlXUo1i98J)?W&#pucdk9jdwdD&e7rbAR5qPZUQSWtZX%
z5oQEATj{4mgY!vCIBE-XRul8iGp38cf2_7F1J%TT4uP)S^V)w0fJ!l^N%*-H-&vL=
zp#mg$xvR5=<;|~o<M@fJbuhIa!R-Y)`f;=`XVjMU`F@>IJshJ@o&t`^_<3_a6>ybZ
z8u3NUi6J5qp=<`4XsEM#zifl?Mt|GsLMKWlKF}&sbkw9$cd_}%D)5Xq{b;#Vp9|jH
zP1km*vNf_s|FeHc%-r3qpr{kn4((j#C<8$l@V^@9(_psxcD@utY%a)BCnj^k@5Z#{
zm(vM>!=*B-a>Yt}(9@23Gu~)cAsXIkFR<_wuXRznUu`vpJ}Ak?6XsRG?P9@Rp=)7r
zw;VQ0jq=o-XQ|LXSfOlw_-~Whh}TtHcDS#ZYTRWe=^KAewsx(;n|1DjnzxY|JAG93
z4o$c~&??O0%L^=o0bv9Hphad8IJNc=E<^{`F`dz{x7L7zn_;_WQcmY`8FgzklW~|;
zk?{1yHIC5f&6zu8eERe5;vTAp&`py_O3f>Ipt)dHv!J#9lv6y5@jfZnX_n!9!(i5J
zr)5l4xKn>j?j(PC!)+D#BkM|djm?!ZnB%_BQaAw!p{!gN)KK4&OMPvrgBJIqGSfMt
zDQ5(E@t0mBK4})peVJ^?Kv~ByG)V+Q1QsSGc=>qRfe0QK)n362YV=zw5`^(M8h`v4
zI<6VAv`Dvh3l7XldA{c}aCW9@Mp0S}>04Y24(fkI2|;a{Mb-A!`}A(!lp`F198=tz
zQERMUjjvZH5Jn8s&<0q&<kaEh+STo3=ZP;@El*2ML>JTNFt~3qp&~3F)?!7iVImaS
zk#~UQ!Jg*JEBQTIxwuQHBf1tI^BUa`ybIYKmT4C!j?4JdTdfNcz-&X(;eatVtnh6)
zK~aDET~%1#fnO=TTcmWaboQv>Y11w)NZ~^Qg;?M;v-Jr@lv0m-o;07-%`@0`D*np?
z1187amw4DRJQO<2e<eprAz3?Cs?N?rWH64u6cj)#k7=yVD4P_%Q7{@VHG{#p99X%(
z=^)E+1uq^YMFKssz_;FT8sdnxfg&l{s{nsIWuDHh5grS<m|5#yhrxuz?RJTFH_{Bm
z>~&-ILek9a7NE;wN=V9+>D+4g;*$<GiQe10SUDLM@a!=B?{6@b$y$w?*|<!sr@UAf
zk@~YP7Jm}eVai^rxwbO&o<^j+4mC^tPj(3sY0UOP7hzQ)RF+3?4Nzn>jo^DeC*pqw
z4g3CUny65}52G-|;`I<?2}`_yC5jBRetY6H1v6Bt0U2ZsdTkLsegeiG?^XEOFVnTX
z$`+{YMqh?|mEYdz=fZ$?p%WR20akqsRA1`ch+NBociF)MgSL5xgTSC{q7U0Q7FCL3
zjw%nar88<5ao5+SI_6)>r+!99d}n`zf~C|^&#))xXA+{y$=Cy0dFGN_Z0BbLu-}vs
zJ}_)2`Kwy>ak^fOBU8NEf1HBSD^!>OP^IG$?30&l{OqWyJ;r^qWiYDTl6qIK*{}q{
z=LiikqE-!~O%DcyLWSK1RkDL|KR!EvJ`Z*LMPx8$8#6LiKWJeO_`rB1DGPsdz1bQC
z<H{h)#3;#M(i>`7@b-TM8f^LO^*h8o-sp^R#O?4{Gk*I?*5D>}FZ-iIYW>lpve$wW
z&RsMd#hjO2)U5M2tUTD}l4R92KLw#Ww!ho~bmn(B5){(>_LR}eOu%_3W`FrRGH&gV
z7s`}AUHRjQQ}I`r&t!_*$BlmtX=l1Rab+b#*++)E%j>I3w0PpSLv^CJy9+jAZvKqL
zcq7gz@}{6qi~Ou#7d_5)!<ra@o6<J6{!*2{IXRtL8e)7nXW@%;<@_+`l0=oKUG~vj
z@Ap3WkEjh?#3B&m)Jhl(?H2$njdejo`+1BN-FWr=X3_4FKs-V9^cH_|tK#(R=!>wW
zA|5K`IwMRxdz9Q*G{=-^2vWc$>Bp4ITwX^h*Bbg;5Q&Mm(wNFRdPysUW(CdHbv2Q*
zk^bBt_YJ;iOb$;fzt!q1VkS0?Z?hgrujeY|hxBgMzhTq2d_2C&*-ZsOuV#3B>CM0H
zfg1(CLY(t5b*JQ|k;H$<3A3{MRW{gM<EC>GNZKzC$_+YWLFXCcF0;@rohLhwf6NaU
zft&R&KL?ZU-S0Ykgsi9)-C5|H!`-fzKsS`|jq`};(IM)^e6A~~DfMof37y3lf~AX9
z<MP%jfV+*RG1(0E7=JXTAMyPb2rJFgJCf=re8<gGb19w@D3pKLZM?&_zj`PaOJnxP
znNz=O`_C0EY*HcZ*%J6@5W1eCoiRoKSe`cN{JRoF;tc*V9qt{R->UYO3hNYYhE!?m
z-kAI7x-uk(X>R{R7(mGVK9E2>WBVyi+QE=FKig3DT!iw~vp``wc`16}^u(V4+2ovN
zfH`W1?%T%$^LBrxTFlqJll3vXf{6#A(QZ0v^Ky0xfOf|}Aj6OzqlNn}LhNeVSJ)nl
zQFG9TCW`?3B^YkZjE#}Yd;6K>N5e5OGsifE)IGimeJ_-CL-o*5noYelUg&DM*a(;M
zr)X^uuIlX6(=eU!;UMn<hft-{KP&oj(q<s@Ih9HR_K<(>Uj`QBg|7m)Me1LcEY+g7
zrmq$lxJO@bh}GW#DzHq`2ec$@x?(#*k?_>_;Q@3@Wdp4}uRr)gZt+;t+#Q7J@DAmZ
zPwBSYZydYwO6j1*ja7&7?28)_L+Q0p7nXSE>K$unIHikq&z~O7Q+wPC&tq^B<Je7H
zj4lZ7ci?~XN2NPb8PxnE?MzH4eWB2PRaX9ty3v;ky$GKZ|H>9PK*?O8*LKc8s+-36
zb!aEgP%)K=ySg|LHDj|RT${8{SC@iXiU|~?wnVyZx^jpEpR4zx?R>|nB*({mr=6m6
zK>WxB2&18PzSJ;x9{E?7GqjKmw{VA}oK0|VvT%QW-c2X-01Jc(i-i4pVkwtvO(Z2@
z=S;LQ9sa?11nVZEVeEkYyH{esl9+eialvLs<Ms(d%~Bd?__6>=o|e5KuAz=V6^HMd
z-DGS!hN{W+karmyE!8YqEccyfjevQ?rM3IX6vb;qCIy=_J19DwRJv$i$G}GLi^6&w
z*x!FAZ<@0sMOLT{Xq$@vuTzaz>%#<pvyrGBit?TN)QmlQ{mT2AEb={G8=kJyXy8*0
zo1;2|#Q}-uHL4zNYK{ihN>zohF8Y})8|{~KWB2}_!q;^OQ37I@Q%nh3VLt2cD)1oX
z`@_4F>HWWome7l09w%t8rxEcBK!k~Vf2w~xf`5k)$Q#So+f(~#l-kVyPd*ux&vFK9
z;R;N|>!NlvLmM29iyg_n7V*Kc(s7un(c#%f^p&<7#xIvCs{=xoCaacyC>~9#_%A7a
zY#;8ye6C3|PReCjQtOCx9o!XJfDCX|&-z)~!S<wHYb5OJg~54Tz>1>BN!Ep1OWc1k
zkChT@!(|w4!{A?Mo-gM}>ouB56e|2ScF@SE3{giBiGc}Vm9|}n{dp;npeMDhadej|
zm`>eiVPUlMF)}Dv+cmhhHsB|mB+LF)-t5BjC1F>oS@eUa=?&2{0RP*~aIt-!C)BTc
zLPH5WZ@+jQ8;5~a90}ZRRCzCwUSEHH=2NOpt$akaWO4bwf=-wD&AJ4hCTK8<ynE#A
zrSebAdB(M7wCX+#3KTsMJ`S@<krsaDKPP7jKYn^PT#aq-uMODBi-=O9YfPSOw|t1+
zHC3op-V&PoSzm-z8-D-7gHQb#$L1sb3g@Arp>iC$UUe`PdEn{Qy?(Y^yo`V8UAI$E
z#RW@lp3Mn~f_XvIELWX43T@y^9b|Zg?%yf$^wZ&ktb!N+2|Bo2k7?jsGGKdKmRU3g
z%t;k}M<LxWt;a?$)^c-3kTz1{qh(L@o=>=bt`;#|?`6^LJqymYjheU-n}9tHSDccf
zDdJ-0`EtM(F1{YKY%LLFB!GWP49Lg2VKIr*-{^8Yk@M24M4IwUrZiN=Lc6m37{WfH
z>lE}!{~?-QScPSm$BE;G#eA52+*7tbXOHHM#nhcU<0=LF$A(dXuLu-^4CY|?Mt_qf
zJH?sJ<Fk^@o8s|Or@eE6HfFj~XQ|sh#*AsPbgUh@tt&B*Tw!Kpvvq&qfew`q+og>5
zl}z@O$`hmUC+QsmCTXCKh}79VxFlKMk;x+QMTiL<7=y?pQphJoq@xiR5tL5D0xN6z
zXH@h)r(XbbBu-VtyaKiDs5x45irks-9cch+kE}z%wW7gu&p*nA{p6i1<HowM#$WjA
ze3}{?Ubn4Mz<kBv{&asS!%Vk{?E?@7<;01M%lwp(5HiY=hJoT!S`Z&gX<-EVv~+Ua
zMn5{TFq>h3rB|}+qpO&QDwj=fdQ$62Dx*Xfx2u0vh!jBDx4=irWc)uX@^1(Cv=j2i
zMQpN2?{o<FezK{u{XrL$^8|MmcjD26S?dqi4eCE?#wLM~E1Q3R{^daA|HVGJ-Ll~_
zW=oip(Y|S1j#ul?8?*z`6GqpW<fmN~#`JxBfgf{bg4fI-Vojr$sPEqq@YE35{lpNa
zkITUSD2kjAux80zAQvHCG)4OWf%)TG9Q<opO=89N01^tnt@Ai;J76y54ARFIuqj(4
zz9^zFZA~nKuVsIK&$CZ|$4Ul<=_|+glw3okX##5b>1PThF({+MDue@L!fH8zxNY?S
zc0h^0I8V<8-EHQN6`4@76Qk7=lh&!4=M{%F<W)T0otoV00Et4mpdezmsYO|g!VocF
ziq*c}hJp@YAjMR*N39C`n7`>*dNpL?^-<0ZKXq-W{+b!;n85*m0q!_(nb)mC;{Dn;
zrX~k4de!<b`+gFKLQ`PRjs6i)u-emG%g3z4?B9mn#}FT;rA?96!mlHB6(B1#@ZaZU
zwa{60#EJsd)=BK}1vhgft~&Ojt$e{EJ?LX{pV83Fg#Sh`VE+zgT|H)y|M;^hU3qXv
zC6`*cVnB&8Qu45W{?B4kDWgPlSr3q7rNkkqc34DT3fb`HlquyhO)p0G*PE5+=(^vR
zOo8fw&Q>o4kmJb4Ia$sgn~YRPi6A;!1-pR&Tm{1m;nBEXY<*-c<q6f^rd~q`PwOPy
zDdA_L?2c!|15%nyAO808>{|7!E2lR7L=%~Tek~NxY*)2^J{sPK`xz`!KmZJf*hRu%
z1jgdD{ndJ9H2k)#kf3PW$qlRqbX3f6EgO^_lT98S`4tE)?kwG$$8eAl)k#&dp1he!
z->ANzJVY$8E1pU8g(ECSOsd<{8>DjCDcw{~IDyZ@Svu=wt_QeN2x~u-a2sO4XmhmA
zbO6dZw6AS{Pj!E22_ezieUipd^ULkR&*tKw_Fo%SvZ4JPqsMMDpe*r3{-HwBB8~2G
zR7ygCtpoe~EL5W5=JtouN>1J%80;vAs!Q41rW~N{@G~U*IpvmM^QLNpl%>Jy@(l`s
z%zQ5@RJnMYx+{;~?w#Uvu)^rFUfl->?=KRgH5$u*?;-PK)u3F)W=bOQJoPTcH}A;q
z1|<x9kjDRu=w9C+drqBIOh;9KO0Vnh)oS&VyG!5+!=t00gUg&aLr-Bh;Z5d;r2pUJ
zl1BS~m;s0kPZEdtQW){l$gy~)CDOo6svlKug<GFB4Bc6dzq8cJiH+|fMn1j_5}chI
zRbR+|XQfd5d>ljUpiN!Agcl-S|J{^aXyoE=l6DQkGfdxUH&5~Pn4JLkl5D^$Nr{aM
z2D6l@equV$v=ip-<*pZXe=7}b(8wYkj7s39_-9QqG2PD<WZH#h06fEOC6LbSJS{z@
zk341wnqIrIcnp4U1@L%9CdU&<a|GM}J@dkUWcF-~VWJMj6ZK;`?x0}PV3)A%mNOtE
z97Fj&AgS>QhV(0TWx~Y}XYQ(t{@4EA0+?4a0kUV`aoS1kaYx2c{zR<ueSW{XzfNPV
zbKaNr7G+-X?CUPOZ79^et7069*ORhQt>E&rfK=6?p0ztlmg#tTN=f7ye+?I&ogFQI
zgTN&gRMtp-U<8p4I|->Sm@D2@sYqj1%|B8<XkK~Qs8(-~tu<e=_(v8ycrVHvH$<>n
zJ2o+3^dM2f>~7FFC93+%PYi<}rT-Ep(@)Z#U7F{7ml11;>q~D!br<mz_<3QKc^gzO
zM*m41f`(Kmdq>L~cnYwbTy%^5Jr=`%PZBn36%wS#vU>0^>^>varmqotk)4K;mkW`8
z*0SHyAVQQqifU5!qq#5o_v<!kwVaD{8?VoUE1au{8p0+zS1yr19mXgpNc=<_!nuRU
z@}XR7a}o4(rvkP6a~1?wYPf{x?Xdi6V41O1#YUA)(#}PL_t~?VCb<w|J1%X14Dab>
z>cg0Aa&c*!Ah28;cEntfk$LgSLe%v0ZtVe!!Q|o~48#w|%5qW1oLdUbUD<?gPC?&H
z^DQ^y&c@ssXa1l<rE&cw6OF;$BII?Ek?<qa`J|zF*HyB5D`~%`yBAEqEnk>C7%~?z
zqDU``i$ir%d6Fyg6TO6Btmy-PvUPfGbV!-PZ4h^vv$$%^sf$ENb+fx4kU9@ADbyWy
z{V_lt<4*VjLziw2JS$%fAW^OeucWSR-dg|#DkItyf7%F0`l}qY4ITUzH%1fOD(DSj
z7XsuizpAPl@})62MevHX1s|Lr$(oG<x)-U1!H0y~)3m({NIFl4Dd~HEy?M;+Y=;{B
z@&O$3K*2+ZBLwt_z)$G2ZGa7bS&n1}txC>>gO`y{-xVLn@`*LjQe<qeP(X@i$|JN9
zffv6Z5_*j%opuIz@rH5v<6ex16tg!RiQl;Q16qpD58^8?1A2eWkmDdwSoS{OfgABy
zgsLenXJw72O=vM$I!~g1r+;3{JWk>fB&U;1IRj0meSEVX?oO5=7LMblCAofr3Lw%<
zz3r11jI6!hG)+>7Q}7;KQTP_h;JP2K<~`N+d@TQg5I>PbY3ApKeMMhLt&p_+x-qMf
zaEEhI!E8|IgMzpaGM68yxr=+-3y^&Bix6O_ge-ZFbd1qiSzDohLTxn)bm0WEtqY`$
zx>Pc_a@3FLzI{PomZ;ZN($Wn$-gzWkf6d3N(=b&EG`96j@l9t{BA@-0>)Wec<oXn$
zRGj8|mLa@TEFW1s>~Ew|#Hq1}IVh!QFQCXhUaC9d))pOKLXfF29-CYAWM00rst@*i
z-w+8R_<JJ^g5^Gc{TK>`3GGe@l6K!ZhYHpakg|z3D>&ea)S2Zy#lCEDYWa+dXjGa7
zTe}Vo$aC+OyiCnSwRWET4^dx`iOufnWzMV7m{6AITJKc9BaX_UklZQ#M&2IE6Y<f{
zv#%ek%At_cx-nQ4@BV5lG1*T*Ag6;kmLS!B3rmPA<!1eVpdTw9<qhJ9P{xK5TcPM@
zgZvfT%q?^X4SlO3YK^#1_VsuqSi>j$n3&f=x-0$EqeG$`0R?hWnKtpT6~QM5d37=f
zelMMoDZP3zWWikYFuAoc4s?^h{O3*c3+$h1R2vP(AUW7NBw;@eQqe4Yk-B_UpQ7Pz
zO<?IudWi2OtLKHMa<D#gK^TP~pG3}f47LqgP3v@S_w`s76He0n2T>EUJd;7x69PCm
zm%%sz6Sw$M1WsrJGC44p!8idEw_LjfL}mjrIWm`_DgzY}I5`S0Ol59obZ9alF)%qW
zH<wZL0~7@@GB7eZlTqg<f3>(}R2)jyH5^=nTYy00?(XjH5FpS%<4)u5?(XhRa1S0_
zgF6WxoZx)q-kEo1?(_Rwy;_dd*|lq*>eWp_qO8UsVq#|mlC-l0Gq5l+^8(}*RPAhl
zwk*sHGGL&!g)xAYk(rqtk%B_Z5d;KV*x8B$!604$7uX!2WDI^Qe{}?~GBfiaQUIht
zwjjs1pb5ap9iRXL1J&K_K`a1j;9rKaofDYB2<Y?{2HBcf*n()@O2q8!-5o8=%)x)w
zU}IqTv(lexQAU6)(Adh()yc{N0JJp$$TBK00u=3B-<%czYCBti5y%{9Z3?h61*n6x
z0UBx&s%ii!RV58&e>ED$w}sW5?d|Ox|Aj?NO<hBZ9w08Fs4f8jY0?9vG}P4pysCq2
z-|(B!0~FQY;(z+QCH^T_kWd#<*HM;WVfwQN01Lnc<mhDar|mzmQNAGq{0G`wsi~u#
z&0h@w)aGEYJuefJtE(%cnX?m^(azC~(cbzmeCp;FP5@Use@838+q)yk8uS-2&bB6R
zbb`%6e=qRoPyq54#vofK(4QhnyT5}rZ&bb&z4^ia57-+K;6H0x|D6tS0)hUgjXBWi
zuUdI!WqE)N(83lBvIW{2za@f!U}q<Q;a|SDC&+~AZ-5|xn6snfpB@VT4mtk6Hvfh$
zYWKD?J!?;If1v9>PYh`5?BwxZ-2CshjqPlmES$hjf3FAvm|9qa{-AgIb7mH{fB6(d
z6lEkO)YKW|--Kt&pkVjLjx8hD4g6R3pY=q<<#_?z%$xug9(Dlpn@A;WO~mYMY~D~i
zA^xFH+~SQVu$`kj)Bn-6m93qtt>^#sn_AeKnEqkjf5h3INyFB{!5JhY{;%ve7vg_>
zW*{(t831wsfZUADnf|o<OD%ugEPvc@G<bX3+t~w5f!0nSZwph<+Z&>%6VL?&06RK^
zygmOr@V^!!3m3q|!WjG}^tWL_{A+a?TT?p#&)@DhB>xWmO9Iq?4Jyssl$zMtTDt>G
zK&FUHe~NbCH$hPU|1)R*=q2fFZLJ8j0a5>x(tqXwZ7i(a|2Oj=DO#XEV5t@D9BqKs
z|A<*QNm{spOq4Ca#^!%B`?vq^ULv+;)*t`_3p*n-8z<}E5sg1%W&Nh#w>!w<&lUD3
z&iRknn>3BBY(Y*=0CwiTLZCM~{sH{$4F13de=teOs_00F()}Op{FNqQYiws?VQU6p
z<=_MW9UX!0h|F(-VCCQdc(S}{+XUqHmtp`+jJ9^*w-SK8GuRtoYUhaf=TupkSpZC+
zKfZsN8~`SZ|1x<1Og8^9SvUbq;J?iO#j5;gX8)2S^MAnq>oWVxRs%cQS%I`HOx`Z?
zfB#BR0D>JY+;o}Ww8Zk}e|!A<lm7oSp!m-i{8zQ8sGXZ913L#dfPt0gZPRSrZ==b=
z%HjP#wZ?znD}U+ujpcvae})<W0=a>V5tqN)8S@2MrZ$I^`$!Z{SHMv4FrHN52x`m5
zLoa7ccM{-<=k1V!go^xI{W2+w?Bu0+fAxKm{cTIMDT1)AUpCs3s;90^RD^edJ_<er
zC=w!Lxtfd`0htO*eihxMG>5Xe1v;hdvzhJj?L+{Lu_G~_&Yt^d*2!1&%M?<*iuSd9
z7}w%?mKH2WYYev~H2f}trRgpR@asKRY!t9hWSMr(upk6yOcvJuYY*lgL{zcRe^Vs&
zUMBOwJ6bHH2IkEqD4hPX==PUOnFnB#uAJsz+B~H##_zgwSS%rpYg7NceY<TuURMB4
zt+6E?Gy66jM#nKfsrO_@V4CGS#qMy1cy^xiZ3yFHtx;30Mvfnp=m)|gG~9gn=2|Cm
zGL(-)1^ZF~_Z)?fsH-qzc+Zhjf3f(rm5#k^!bh5$j;lJC1Zcc#gPx&`9=+}<3a7o(
z?XZkI2*Zm<L2!f10F|Q@ml{<6a9aW4;3+AQ&tLu3D&wqP2W(EC2-g@V3a8y1Qg0iJ
zS`+naWXY$batsoSW=4>EfK|0ssn=tY$^_2L;-W+XVL`+|0Z|~6lRt!He-_%}0$1Jq
zTtZ5Dr4S}Vd10eY-JSA|KfYyPlIKDYGA!2ThDRnXzZ?vtG(HhgwzR!e_LQ-?>e8kf
z1evH%sFa7td;G2HRtx=iY^FELKW<(@`_pJy<D;$L0_f-^`vVAJk8hr#z7p&Y_idES
zv0%c^Ty3)S$d%7Xh(}H6fBhhFb(H7#Ab^-llWu>US59S0Ld$~l6t;?CYXDd0PIjOB
z)8@;}&G|z1`Mm>}iS7xArk<xtX^0CZx21S93F^K4_957RWqbB*ZN&n?c=yqS&sAOH
zH$3OPv{!8O<vGD7)KjYVb>!Nn7!u&SWp0TW1dm04_*W~*$<daoe{o#IWxSS=rc)S<
z3@ANz?xJrL$W3if(DO5qaB>JRVcou0qzJ85tHnj@N?DB*n>ShJdpN{m4u7=2(viBS
zjJa9Lp$tZq`_@TY-xGo`SE4{D)=?k&#MQWIh=fjglTB&IqjlB8#V$P~Pu_v}x=iOX
z(M^Q*<q67J^%M-Pe+M7>(Y|+pK^Bej9Z@$@*ZXXtUPObH&U2a~Ju((d?t&iJ9$oNf
zbYH~79P-+I8Pv1>N7fH1Tch!raqAtOaN((Wjnzd_?<?z4tnwBr2c`B_9Lt@P3_48w
zeGt+I%{efbpHr*-Uy`NV-?w8ncDDuhKaZ~$PRrL8R5{c|f6fIHBmcA|nJ#>XCFC7`
zQyOP;yEwiyZz^}wW%Ur@w>aUujoAr|rc>Jvss7ZD-HGy5PcBd>=0LidM%Q<9a1;(}
zPu6f$S=~#C3S_FvB~mI@{^Bi`IHc+hA-CbuM*=%4W;so&QEHwMAg3v3ku9wfO5X`F
zx&Hk`Qq?)Wf2U1cG!M%rHnC7YqJS8rLljkoUZ(IOgka2vx&kXkqN908Te|x_rOn$q
z8s8^ZzF{&fAS@?}`q6))j6U*0JEgQfP;!FU$M2MRein<vj!9y*rcDzT?VvL>$<#z=
z5?=7sy2|wR0Tnmd3Ev_Fg@-?@V=^ASES_l?VxM&Je?c$|lAH(PVvF0d`)kUXV`fv2
zuw2+d3{FO|6a9iH+=@n#C$~m`amqECtV|xMUsz)MX2=o9RJiRqdU580We%fn3hd4C
z7`!1br;4(PUHg=$X6mQ%6XwvI!YN87WsD7GNiRu@^|-AUvL)AC2Xb~l^IhAKy0qc<
zu)~SVf6r+yxhp{rX)DD#XPT7uHJ9U#a>tV@j#UeNH@G25Hb0E=jcW8>k=Kh{cxx{$
zNGKa0Hub-eFzZUxx4v%BB1{=WTnCS|tkF%0LrYRLh49toGBC=Vun5(BG(fz~bX9XD
zmNU!@{A85qMwhl}1H=G8i8de+r88%A4Up7xe=eI7^~UvJ$;*8_qP9CkW(>6a3fCFN
z%cksX_|kv0-ANH&=8gQLW`%i03H{d*8VeWDpADNZBA>e{=cL7}sXHnIjK`g2wLZ(`
z|2^kO&J=1Z%x9XbzMcCcCTbeOgI<u(Rn4m}VeI+IFEdN<y8ppJ&`d8HHt%cu>xTCv
zf8qC=tsId^^8u>5YLA-1-4qo`^jAS`Q6|@yO~pr0m+1|WwvqQ|O43<6=NAZN{1|sX
zhfyX?{p>8P#LM#XIOxy~2JTAFx`o4X5uuIUoRxk9%|a7-Dl;MBErv;Et~#4VXCAL0
zNw>7DIDpxSzx-tGknBv8b2!yRGpmnFf7#NAguG8immd@Y0kzdY@5}D(eO-U7agK)(
zNY!-Q`uVgkZIf}>-Zs~DBu`E?Yw&@A3dglhz|#R?aVLyMg-iGD@Puk4aHb!}iiG6U
zl;=K;AbxEH-Tnn14KHqbx-})LXw%VCD0$9ggu9Vc5-%7M_Z0+o#uZPYNz&>bf1ThI
zR!DWHbjZ(9P`Q$YYsiI&%k+eDA-;q|-iDEXebp~=jJ%%w7!FXiCy;I>*1m1^U9+RS
zplRSQoRiqG6LJXXS}B^N+Xp<|d^$q$>L#1AN$}Ds_VcDpYHZ$-!O&ctPo=J8!q$Lh
zR9)z)JRBa)n{b?^%mx=#j;-&mf2SQaD6maXH<Yk5`pyaxykLbcQHG;uwrV=gGw?e!
z{gfDCOgPs%HVDrAMYd9|jm3DZLhWuVIfi)M#Fgg7xS;yQJE#PQ^cj}(i27;s=^Z1R
zFFZ`;iK+t8=Gn=n6(O~6QLz7%QVZD*Swxc_g6pQ(AueonepAbE%ZIPXf1e0+1=MS}
zR%f$XbEQYQl7y|Bd;ve*Hcf4})l3M!GpuH*;F9`?-;K*5Fl4BLmGu}@uSmxww9tF8
zyjtv}$T}b?<<K~R4NGe#NU`KeCoGnFT4IU6)e|UC<g02H66jbJ`ejiCbe5t^3?jom
zjW*$&wu-^XImq(fk;`0de>G*)y|WvDVGu|uoa8)jd3S6Ey%#yRmG|S+UQY;OV)Hc3
zE3&MG!F<$81|=OHs<TO+LG2TwrSw)34t25M@A}G82OO5B5eRNdzL@v<PXlDp4l3UH
z#*#Xv@&K!CH`ezMjhk5dHiOtBQKMX?8^v)yj#1~>*{{OCmXbXIf4QfwM_@WgR_>24
zFs_g(n^O0~T@Gl{@JMs6d$k+#0C=ZRWeV+<bz$=QACf<=8FWN?;q8<*eR2q}hg(oI
z6bK{1d$9WoRT;;78khfDhN~@H$)8|oaXRVns3iQjKc`S);*P&+cF7*k5Tk)L*;;TN
zrW-u2^|Ly$q)a_yf8z*gtd7?4C|Dg#`4~MKJh}AM{a^(<FC6{MkzOAY^Fv=<<go-E
z=W78X=~}q}0V6F1?+isNCAc<CsE@4Jpa=NAm<lvGy_lQkox<Orz^VIX{Wk|9UHRl{
z%`?_x4pf)TWD9mg<dr7WP?$VXw`QcmVwXmN3PZR)Z;nL}e_7+hmV5GI>~fY?P(#b`
zAi`lA-#87&z}~wg3d#$LxTOM~)++nm50tdGMYumP*B2{;`qroP%R{fI*IDwHV~Oq6
zEW8yt%uu}abz!?#(&HSnoSWJOo<TcBIkjoV+ReaM9Keh-)fq}3Q1OYybx-_}&E`sX
z{tIdN@0Tdkf08l=Z)dBU@Mt&h+pJhw=U{1$i|IsGEA8YE1%&ID`%`jU9ex#9OoZ9{
zA~3@k+zZFkI?%#IPv?V9&<Cb;+3)<ANFx=-TyI|!*qkuJOju14DqOLumsu^-@~LIF
z>Lyy=n*+d~RlgeastKT5rhc-kc*{Ft?R0PMx232!f4q`j;ch42kWXfG9yV=$Kjf&N
z=W^KOshInj^%}#6yl+m9iV}7BnwTSpZwxXOr8At3Fb|#lrDY?6zWO|M_(dX?iVB|2
zkyEET?UxBVUq@ZD(X|4e)p|bwmj?}MeX6v;EXIV#`eeV&0)8hne&s_-u*jkCPKy4~
z{BJY#e@Uxsa4Q=ODgxYYGeP#O>Qf|kla0qOgK>v)vclJGVKaIY31?eHvC)W<Z|tYi
zv*lRD$^*#ZD#~4Y0~<P2Q(Oy4ZFCX>Fvu#M=WNtFwP11p)&{p>Mq7OarnZooZk|Nh
zQpRAUD*zE;$azoAU90DV&3tKTpN`F_{#|Yye*y6o;3KV!v{1rx=b7AP^s;<9rcp9j
z&Xm<h!CC#N@UXd1+z*Ws*yEme(dVnaJdJqT9PDE)UG<84=<;QQ@2hSx<n2YLoJ1r7
zM6$lxBAjOJg8cidC;=cGo_WzEZ>i4lR3f<ODooj@elQ*@dF`|5=QY?W=OQU%Vqti`
zf5`AT&^?KdUnM8(G$XE>?^O?+iQKNlc3Lh(k6rRmw{<x}hakomfsp&2R#JK$YAKQ(
z$Xd-SI9R{TzT1^%{#gmCyb|q?xm*EMe#@3RpRix<(>21Z#gzg%_4WvUcNJrMwO4Ye
z8xLW&d-lZ9e!$2xt*ogiQt~(Vkh^^bf8#*SY;6ZS%&iz{ctE-I?c<QoT(g+p|2)HC
zp=%DU5Uhoi2-DL$8wi@LMyg5CuYsTtUf$H*$W_vZoVWU+t6;{;IYH*Cr@%&{c<72P
zLv`;${T*AwRzIL42ZrbUuVITJ9<$$xIx`LNkAbL?Rw+k0oUae`+|I+{Qzgnre=ZId
zj6e^Yp;=S0bZ`Ot*@UhwO0q_%$qNFaMC*)Ki`+_4&+SSR_uJ0|$1AUTptjlc5xeB|
z11<;`i@^Co<u+SgD&lZA2N+^Dm{XMA0*?<b-n@pUp-<(X6`PVffX@ZcOTFG%IV^`B
z`10-=PN$#|PYfK(U@#QNd_{E0f1t?LLbr5EQ%b?4&mDklp<MQbtiIJGhWDkF%8r5X
zLXLMK3})>eU?n-{hP<^~>cSckV{)fp#_mc_Al6{c^P`p_??rVrm+4a@nhX_I$GvLN
znJebmFocJ3c(TUA`m=5K#bjQyCCGooINCr#mT;GC;}$mQm2ZZ-P9s}Te>=40C@V|-
zj?F-0oP!!B?@6S<EQy7p)W$8O=;x1H@NLbA6XDlm9~FI{+4@360Rs78YS1<A;qx*1
z<q}HMcoqZScX=Ae*h-OZmKzk+(74zN<KN|oU#+Tf<_V|9a?|!rXbJh`IrER2d<2qG
z@YN`tKHRG4a-QX2a5|f2e~LI~U)uF@9_wG4Ve(bm*hS=sexxh*RnZd#r=j?oee(2H
zIMpEjg@S@b<2RyWfml;3OH^)>*$`R<l}Ec&ZMR5-h|`&>5DRa%o?9^&A?YbsArX+0
zDMDRLs<JBB^$@G`I{Mjngb{Gv5gqW9QL7UbHhGz^Z-v>Wnb0Tcf3x!4=Bhy*Ug@2y
zL|A4nPap~5y-85Idmw(-j%?-c9=MUg^mCOvJmP|tnC4MRf5D7cEAsKALZ8JKuEl9)
zN@Z*61f*DW*!$3Q8T}4km|nT>GB853iGDw&YZ{moLvc0YKgQOS3UVB~aXb*(;k(P9
z*SE!B)sOE9#Mg8Ee~L@-+jDF_shHl6;_!Om0Ii&}{GwP&G_&~usefDF@>@(-ISRFz
z&(2oUeO3%0(b@IH9GZ*dP((Bv{S_+93JHRP5@br;Wl8lAYpo>I5OKxuw3rzgsCc(U
z>mM7-2hZV<3&>?JZ_$%w!kLJUHS8UJ4?i<eSX^A(3uN8Be`m_@?yUh}i?4a`XxRtA
zh74fz3`dFj#J~`wAL;`>Eq_-cikk~pP}ChEe<#ym>df~+o~DgOfF-liCB!<ysByZZ
zyI#F$IVi(x%m3ZF7)n)I_~WI;05jpIxhzBCRvY2CVg^5Ff*9lkm34V@Qaeg7NW!At
z!>kh7LFK?He}T^!B<&1{-OqHB9fIF~gs>wT)^7OU>SccUN*sd)J6%ugDlsO^V=fCo
zrlskZ{Yjxaoat19)#g{)uVqgB3>{jFz(>g=aYp(xWU!;*`O%>d{$cX-BOf<rSo}7e
zzhR;*+zc;YmgP>6Wg2#+&@tD(KkO(XyNJ`Ls+`8Ge-X9XX05|GJ@s$RiTW8fGcP3h
zDi)Cexi|DPgZ{)JTCw6kx?Ap3odZ}~&VIP&j06l9@3=&hpq7xz5XzBChqcobmny95
zKhPMbTQYxNYmJ7m37xBFfqUjvcxY7AP5G)pq5QCD9IIeJC94Kdf|u|A0E<`tRc4#M
zWk1;&e@U{X)IIFeaSc*6;7VOvJL%{ciDnv8Q@58dFo^_Jo6*=Xtk4^4ru^2`TBW<p
zZD`O!+Hi5Nv_}BX-~`?h-~Eb)9tyw6--M~~V>-2W7HcyOG2wzh{hqN=o}IJCGlQ(A
zc5NXO<tXfKD1nnmNGvY)&~|W0>GW3oIF^Y~e-1+X40-a%4b4Quh>L>!-BbnVL-<lf
zv!SEdy!bqoLL=70C)#<XP#NCdcZ`@dz2qI;gDlnsM^XTduP;7^_qvIXnhN`beJ3Rk
z{16a#KaSRl9W8cG4SBLzU3tjht>H&Q#a-`r6ci}771@MdC(;JnO@4s87#~RGn)ZOJ
ze_~hj0h3eBXLO;0coA_|;rtC-jl-WDgv9ya-D#D>35E)WOP}fa-vOTNyT4B>GzOrq
z^g@aTvgrO&=W_yVFv%<lKZTD)6fg9$n}I6jp+vbK!9LA9oQ0-K&?c_airwn2r{5NZ
z=v_k5Rz3@Fl7$)VeYVITMP#Y?K>E~Hf6|_Gg5$@~dK!hDf+XR70nw1}ym-JsE!lW~
zpwZb>5}}+$=RKXfEIn7NSWN|W<JEho`kg}wrMyu%v~_x?<1nb+_mEi#Q#8W-dwz04
z*lRP_Nl=YUBaA3)tq5g-P}}!JL$}}eR74isHG>E0wrcMe6M_Wa`zmpt^ry{Qe>syl
zb&K#jxO~>O#1}W^##~l}EU~%oqsb1XZZ&Uv`cy~uh2v;ZC(~VTFl6?Em+eL7W!^9!
zvVr1NrGIpRs;r9>yNK@?$Y|HUc0>A0%&+;{IYU$M3CqKaF;^ejt9BheAZy?G>&<Kd
zuFTJmN3aEKz}|J(fT&0Jcuw8-e_O<SqE}>*{C9J6hq!dB$_UnpG9-YA7{2B*SHALM
z>?(aLgUC-<kbMJd5CqW7rl&|-Fi&o)ot|`M-%*P)j$Afe)^mM`tKj0(Kh@&a`x=x8
zJ5i8&tRk5VPr!~942i8scP)7jn9d%IN~C<>8?C$(qu8<!i*S|V54td*f14ncS%f)D
zC{J_u?9;0)ISt+WIQL87G_L>4U12V#xMy@waMB~(JiRI9b<IXbHGL?~WX6|$=6s@#
z*%yU=gK~*_ge|&n)1$FW>Vpr>TQ1U{h^5~ZGxJWv@%=VSC~HZibk`-Wu{;$66=O4c
zpz=P$UN(FvndHuv^zfz)e~v*&N9Xd}r<nVIy-EO(dCf&dQ=k377uj!VP5GF*VN2w8
z9Nuf%DR1!G<Gp!BH?Jmf=7+<*YmhUaDMCW*0n?V`5OxF0v#u)(1PXld`+3WVdpegV
znF<g)OX9u2B~Lz0!hzvP`ZoqfiVBFD5OE{o1AH;KHWU8mUI}h!f8E*NEKO2w!WT~j
z1*dp?DzNOfy)&bd;)m2^(z~$nJdIe7A`V9;8aU7Or;tr5AuuT@bBf7GzY?EbCra16
zw188pmB9OlZ*C*^FUK((DzzNywF$dboQ)_p%Lneko>n~jYs4k#V#^C=mEA60%=BN=
zd9WXhobWXw7my_Hf5|mtYPgX%;BgpI@n$3M4`G*eFzuaKc-$^$MMs95nmf3^)#@Z6
zS8Dnd*us8fGECSSw7~_chS|UK8s!cAz>r!`t&$@@p4zj&ieSg~JE=~DDu%ezc_4HD
zveF5JXELT9xOjt21_%)sv9T+@=~rSu2BstixldA~=aQ9je_co!K9N;jrL{vO{`gF~
z2(uVDVS64Av$Fym;f>lk<{rT%wMnrwOY1@Mvs)c6Qi-1VA+kueU+R>a=c`wz{rp%}
z*&3YcUlxp49kr>wS1r@@3-N`|#JmEca^&ne6UmOaI^Od_mh<<}1T*JIk#-%xDrR(5
zou>+OXq?0ge{@5?Q(<z?PLa<bl>VT3V0x7E{z}hEY<Pqqo+Ij3#VboBIxhiP@8|Y$
zO`X7LbCu&I9?~dxtw99Oi=Yk}VMhLamCQMjX4Y8IGU^ed*KiKWJM@S`eEz*9U@Kz#
zh~X)KZ|LG%)WcMo23kt^iI|pCq!&tKYuD$DZ<Ha#e~?)q>G2D1=d$rKVEtwUql6y0
z2bvB8w`z_c2pL^L;R{RC`=>i`N0JC#%TuM6faS;JbPr-<v0t~n-rBd-9A6}Q3JW=+
zf+0J*E>OT!r(T${4cU{E#oPr+g4vsDLM;mkI}ze6+x>{D0%I~YW27$hRU5m3Km|<&
z!TO^0e{6Zlw$*R##hLO<r*pfx4#dXWp8~Gut2BC=*cHG1Gyw!%z#XZj<3+qwiA!mT
zD^Rs%FH4scz!{ina2B3d%w#ck@gQCrMCa!EukDeYnk~Wk42b6B+U;gr53I&NGu|f1
zWta>@qw%c*&J5|RnD<_CL~Sa?BeQBB<i6@Mf6Id<OYwEiHNW^mHzR+kaMdBD&DA(^
z#pr-)de;d(SQTmfo<Q-PR~9WHOi2ATPaz!^6ndN@mY`B7&Dq%EK`Gq8nu!xpiaeqU
zrHQi5#QtaC=V`zyj3<8oX>#MT=m2XAYkiMfqANbbDwcRaM)v5y@@_P)z3pcQq_}Fv
ze=w|b&?r>;Nc055rWv4)hJE;!%_r5RrioA@yQ%F;FyY%!Fuv4Rd_>N#(LbPL8l4~J
zJp}M}ln76iIzX?N<l@IfZjDM*0m2ci3dJh`2aG3Q9}?lBS2YMnH$eLSF8%O1-<q&Z
zJ|Zr;cZMHtgVmD}z#nEfenPJ<>l+h;f6#l0>}@WHqWSr6c8bu1zAU0lnxE{O6MJyS
zJ`zv@NySX1vj}f1>u9OV$e9Gt)<CyhIdqGq^C#AHE4#hWVQoAMy-r~sI{;4=B-U6$
z4B3li9^NUzZTeI7y^}66<h}Wps|ZKj(UwW*-Qw6TnC4w_UqWA>F@O{K&L?Baf1dW!
zS@;z+*A3@;*1|Nc&lp+dha$}O5#Y}^(g?l5RSbp?>{T2V;(WL^E+85=FN?^Uqu&)X
zl>8Z9oXJM8Lh0~}lwBVjs(F#YW8Z1-gW8&Ww6gQ#ON1&#JtQU-njZZ)-gh)`B9>P~
z+PVf?@>_axeaT7aC>|gQm<1G$f2&e;=4&TID=Tax%vAJerdASP2XbLL#c(*0;yBr1
z?C#r$*zB<cFarxdO1@b9WOHy8C0AwfW@1=X&3-AcL|f(D(5&$>74&ze$L1*pvQeyE
z=rp)B(&oG1@ciVS%nl!zLaZU+E(r7?I!bYz$MJ5n(vkBGNO{@~`n>dTf06V18<inS
zY%nI=5J1+I8G;c`d{2fu_KVnozt;>Hp@vz-LS0dMqD$_lG4Qt*P4FV5g!b;S<2iw_
zxR917eR}b=KK%HlRhPhGI4~Wdq+72I-68#PmWw04ld4u01>Y1@1&cv`Z5?xfe|FNu
z!cT|6G})QLqTxb|_Tj}cf5~jsN8RLhBx(+(c`=v+?@pC2TaPp=d?Cf;mBa?C>Rz(c
zlkkW{d(%?beVI<#XZ`dPo_mz@tHe0Po%XJr4b?WUqAOpt5dp=dTKvt>3c)R8!K2P)
z;?&XH4+BsSy{NG~tr#OVmZ_+4yO$fOjbhBWF81l|HR4z0JtO*-f3AAxRwde>7${wf
z2`+IQ<<LB^U<ThNLlGx(qOIYfGQrQK{bDX{d#V^p)nP$cX*V50)~D6yN?UlJl0P~g
zq!Z7dduX$`9}8e2%t`@y+7_9|#SOu3tr4~{&}O~AM>@S~OrRee>#XIrXmf`I8-z#V
z)=SI>L)>*tBNC;AfAsa^iQzm_JJ|$!HeHJH4as6rHg)&3>EzQ|IGNkb_OSdpmoqkC
zD0jM`U2Z>@%GZ@68s&XPF;^=~=DG@=>~@Eu#_Fgn6+Jmn>>oxB@P9cyAlKqs)$=?)
zY4{wqhQJE7dK#lK6<f6h&A1KY9xoNO5IP;~a;7VrR0na9f3{T+N>6lbHGAo_EQn%2
zNSAPcL{#_CPepDj<Floa1%V-$`b0o#Zie|0|05ZK90{AgFwxQk`Lvlt>w=*HBUcev
z4qI^7!Wccm5H+w?=mX?f?rHDZOeR4HJ}>2yMFrF;b1Zd%(0=Kruj0>Hs}Sy_<+fzI
z1mx13JC78oe@^Rp$h^?P;!wgHxquj56eb7UUXleOC1`EG!lDywbDoNdgzn%Mst_?B
zyHcbgYB)9}S#Q+jK5+*!Uo2=6Kh(#kYc4tr-Y?!?b|L&OSRZ#i`pGO0v)jZM8(TRZ
z=zbv7rOi~j(MJ@1Y};NX5>sKOu|68_hUaSYv(6DIe~vgS)#M!Og4JCtT11`}O;Ro(
z%*hkU;?2$x#u~@n_Cd}MdA=$-p*#io*OoOeR4Y-h>q3&ry!ZrEH?yPP*%ztu9&Fo*
z($;y0z5BYVD<_q6mIZZ}18HF#hy;JwJ^g$qxE4S;Vawj&2f5}0?juRSqu1yA3DMi2
z%3DbWfAvJ7tINS3`H|cD6pEw*9qM|Rl%)O!#l4wc$!41-t)#dyQ*@&m>)F^oj|kJ$
zGHCO7uy_r+r+z;3rn`ZM;zIKNgqA;V8hZDWOJTdGAq^;2m?t3fohm%OryQ<w(t-&j
zv_XboEQ7VK6O4VEtx@08C-`<D3%P6Y%jo<Of9m6!s0ppO)$#AXG!#MYv{D~n=e;Og
zC`D3*8pu$a!_QYg6GvUV3hS%#Ey2M%ukbIvnsUutv$q*tL$C5%_2ZpsVK@mTQT7F~
zTIJ0z>-OoA(>s;06s9Yoq`+aA&rQS+1$IUil0t4CLmyWVbu$a&@Ki`Yvin5n61|6!
zf16N>x3BOCcT5)R(k7+rfH<iZgkXv*MW_n57t78^A9_$dWMzr}-OAq}Il(BmAdCx$
z(bOt=8T*m1gJ@gEVr)R<E_r{-?(WO}3d_#uTmB+<oQg7F;GqeQj^53}VeBh{f98$N
z{pM_C$eGnRX^5W%2tMEGUx_KuiZ!+}e-P;?pH;_C%FzyH8uX@u$o|5h;P1_eIB?LF
z%IQq4h%06;JLbT&)#LL`#168rAKilTvA~d|nE-jpfgTyTb4)Q@hIYlF4JXR7e2+pY
z=4(ixl6p43(7iDP7kZ^*i?!o<PD^7WuGhijSnRRw;204ZM8n$GkD)QnP;o`ve+alK
z^mu1aX5iaZ_?Gm+6x;XET@_?Da?Ru0X<uC==OG1+l)(u>Qadqg@5)5<?Yq>C*G#6H
zR@BH7lM~AN;4}{t9X-Z)Miz!qkruyJY)gpklc07sj^%~TB{2SSP)76Nl|1^L5Ye`7
z_TigJCoZ-hg$Ik~vzwV>gez=Of1_`!2nnGfU!Yta|8+0Lk*%pMwnjeY$JWKV(A3Em
zmX3ihjii{jVv|Ug1h;&;9l{90GZb*GWbJ98dhf_s7ZOBM?0e?n{BHGsL#acJqB`!4
z_2II0?HVsgyx)s+fE};jPmRe^rI1wff+pS`8vfyKg5?Q0FscL(+pc<7e->XB$)u7P
zK&o(0n8`oNyL&~5p4KB|1f9guaT!b6_R;E|wM=d5d(i6di=@zlzIqR}<!+Sz;Lj<d
zpNcP#^UoyVUrZFrPr68gPhD8w`T70Ne=+l?Hn<{{&0V7y$FK9;N`qdF=DEGE;WycH
zGOZ0&eI!cb1_cV9%P-D;e}@QiQeWg{b+T8R6*Rql@vwd<ci?S?bh{-;ll9;`4@bC8
z(lv5Mc*RN^=l16{da;2x1$KyToywnMiEVgbSw11OM)BP`yfnIie$9eIkooTX)|jmQ
zCI`xCC(@BveL#e;6@B3zjDb14q!hmre~B~^8_{DDPL+~UT4H+Be}Fzq`y92H5aDDa
zi#ETClWGPvp$?kHckq5BwPu9)Avee}qXT6=M_+oh<ZXkI7!`%x<`m=vb`tY~ZDk9t
zN<#0S_YN1LeOa?$6v3+!*AH6;W%}p4^H5#suq0Sa=SHx<XRos<dVKfWm`aj55R-j-
zpX%iow0-1rEd1w(e}W)GRzYCD6xmZS%{4J5)@|JI6yeg84GJbl5ljrl?J_Vkv-hbH
zMUAZ3c^fY9cW&GXJ)M}rY#ixkL560G5Y=YbukVTy>uKN;Y_eIFqzm%n1DiB5d9w_{
zd}YC-0Z`PAlJ`ONJ(pSjTwbl`I7QE79@-XJ!6Ukt)TN{dfB%7@q_<aZ%?-UdQq+Zu
zJNBH`u1H%2W$%Mss3>kEc9<gD{3Nc77g+*9$R=|17b9GvpGgLueB6A?Ea;19XnGIC
zQ*Cas>|6N<SWa}(<jR_4K@^IyM`o#rJQvF0{E{duU7=c#y_&+ukFKU26CwD;ckoDR
zwrUla3YorKe}$If#FquuUtv0@Fs4wT72}D)oECuxhii}!1U)3s`n_4n-)iI(e{&Rz
zD5QNdr3-Y9{`hGxP9o02Cj>*v+BKjDee!*yL!_uRpouzSn%&*pF9w;VIDFbZiK{_U
zKJ>@OUWCAVlkPMXawV5u?9ly<n#^?{pxo<zv{8s;e?R@l<ldF#D~(_2T4+)_-Fd&K
z0mSTdC~5?kf*GDAMaQfYs?X_N{oOdk^2F_#!P4nn&HT>_{_<-TBh2eIbYyA}Sy7#5
zTxpcX(jU}&Oo$IUPP$?PuejXtm`&4!h{7|16Ki)2?|<ABAxdUJn+RKZ;2)To{M=N2
zY*f1Ie{+1oO1vn~US%YH@h~P~ELkVg*e}LBYoz#+cYn&}f}%PM=r7%>98ccbif|ON
z^}Bd4r9N%;Bs}mF6*D9?xs*))oH)xS?&0Uc*=2Znoohks=Gh9yLiUfcor2o$e5|3)
zyN%NP5lnbBiZxJrG0CQc-923FVeKg6WJI$#fA|P@A9HObu@L}U*fv{=@N(^=p7&RX
z2wDjDGS|>?x6Z_Mhg5_W%iB!=Wu2ZcHx*PfC~Wp2Sh95qA>G{M*VL2Zp+Xm~&;xVk
z>pN}C^Hbez&nRNsy3bwNxafoW!75JSjph$W9_(M-MI^hi3rojUuqpw>roRZFPKjF@
zf3BzOZ~a>QLl&>%C*qq)8N+%zUrhmF7_|8Fzi%X3sEpz}&C_Qg(Z(?#7^Hfsf59uT
z;BrTJ4&s*3xzFeV`5oM^$qij?)-jy4-xHkVgwZj1-~(O#JAV8etjiQ{Vb_>VMCV&W
zo-%2tO3|m|F5|qje5i!c`jvR+J6yb?e{a-aIuyiyIa6~<sqWcvWdI$opG}z&ggmiP
zT&36BQSLWWD&M$YI?<xIupJ>^u>D(vavx?%UO!y2{iSO;u2cJ`S_P7`*%n0`<<L|*
z$IQ{QbW+JXINEXhZv>&1@;VQUVZ?gv@v$@+LAjr&VJlP%Sg@Y0;=M;Sp;zS)e}@X@
z(6wkXAj0+6q8afttn2-F-iu8s>mu7=V2lr6r8Q<2#y|6V3P`Clz3PNg#u)BDo7CZ+
zSVo(7%XB*7R*^D*1`{^Y&`va|l9V(rfu67tr{}N7-b+Zd=hcvcW3iE@A*bKZrH{nj
zf1Wcq?>r$URk2IAujmB@&`#wIe~xb!sDMa?>g1WfV~Nx)aU&bGm-xd3;<h;-xUK7@
zTSCaEM@o9wsWiZ+4lak=(LKLMBZk^$-xgsmLSR$cem0a0HnV=cmCvPQ9_?WYoZ*_K
z?06~s_RQ}>60Y?*Fk|$%Obwbk=a@t=k8A9y-TTw_`E6`Yql7+@r|^-cf6Mur4aY<i
zUpX&!YxovfK7lnY$3s8;VXJ3el-ig{X`VlW3?d;1Ryx;@1{RA{FUPR(Um7XBpAiK0
zRIP^j;rI575Hi`*(&6_Wg;v<0es=nFMhV58{8;(%S#=5FzG`~}$Mb2}<3L0YbtgEs
z9sYZ5rcBk7113(=0L+zjf2;$Nq{kO9Z7eZB^25GYXwT0V<qdTY`MKelz)n)t0tcoh
zg&Pp#CRJotB1(mtGfqiOLWs8PFi+FWG%Fqa5So1m?r%;`0qnfh@+L=H6<8b*I#1(0
zk}CQj=4WjF0Gn;1Z-xw#>Kk8TVv<PpV?z|(iApR{KOv~@(m$BQe_2uMahv$YkYX80
z<&si;k6&;edVk$q<{6qZHUJxao2NKxp*&-xAkkKY%H9SIyz5XF{Fd~oY!p9NbEKB=
zL-=^r2`)4-WT_si!d%pi;fed%lpL2?YAm@$uG91EH239wfB?kZGhu(<EA&szTb-e#
zsI>GQtsJ)9>5tzfe`8-YCpV%)0cG#os{J5#m2OjXFrZzQDG)wPGs-QEjvBn5P~1E#
zJWoz^5W5o}{fK(1wJxT;k>yGmSW>!-e)m{F)0*}}wm5KTZH4T#!gVDFAbyS}$$u`w
zxL({=S$cEK=-%R>Tf18V@!<NA=)9nQ_sqncYyp$P%x*?US@Ilb_R8L_aIJ4Kk)!8u
z=K~&F2J_(tJ@r;Iq*AuO7kyYmnof$5s%{J+(t0R>U-Juyf*JP(g^Ap=Sr!FKiuaLz
z^7KTr^Grcfx+?3=EU^>s{{v$iI|P$K)Dr?ZG?&3R0TU83F)%p_FHB`_XLM*XAT%>F
zIhRrN0~7=`HZnMqaqlUARe3y=>-!F&WG52om3^6EEF(l&rm^p9MP|&4Vaza#vA2+f
zvSmxilBGpxlPql{6|(PZmSii^g8IIrb55N;zw_tsGoP7vp6gzo>$#unzF%nxYde@e
zj)VmdlZaFp0<NMBm|Iw2sNQzLepnKLf>43kf?hNNh72I!swygf9MaN;WDrBelZZwb
zDyR)0kW_EL4)mvjeprwUKrUJw(f}GHf@H{!1F*q>1xUr%2m6BvKn}CHuqIKcFf4`w
znL(l#o(RfAA%-OXU^3pzo65+c27@s&F`^CNfGNhqmqe%d;sFd12bjVw;D9BG4uN<;
zjzk2opf`r#36MO00ejFHaIiz!+5u==D+g;kc{r5Vj^^)ABLBt3(9Yfgtpph9TiT-l
z&`}9MJJ{JXe(gab#NSH^u(XHljC~+SMz{saUf<ru8ii11oB==pfgqWJXKeciHyMZ-
z@QWH0>PaT~ZEgU_c~hzW+RDmwIvwssqfp@_vKQQ+u*uJV-WyK==p?c)06obd0o*JM
zjfjKFN%aPQCSY6-V2<|yi4>3#beQzh=m(V&3W9LzKg6IyP#HN1KivTe2>xpuZwzHK
z*4*0K9Pq>7iByn?A$mZLR1B3y0o*q+=nLXxe-Z=%LmHXP*u&y)6ZxNQ{-$m~f=+gf
z5E_o5|9NA77$S`l@>^~GeQXaBk%FgCDL*rUfG3^+GT2iXcZMf!Vix+ACWldW_Aqlu
zdqkK8391eeP7R`NdNcCr8<}eZNG){$0eu-dMG<j^BtJihHHCvwJ|jF-Cn|{?to&aJ
z_a&0(#L)jVd*X>WPsTmqX#UC$M0@}ZG%@-s2!c3&eqml96;J`d000c~@K$DQzNsAs
zj9|b}QNlz0N&bK*hCl(s@tz>`;0UE)0zrUErh(z1zZ?F&;y`EuIJ^fHl0DQq9Glrq
zh@K=s>n98``P=lDAmmixP)Er_ZHprj3Bdpk^yE;sBvB!G$o>Cx-5+}$rV$917(Y<%
zKPvlwr#r?EPYC|M0{(Dx0vXKZEJ<WP4B-zOo^lu;1mdjmR1fc;W&VkqP%%(n=o7sN
zAOJ(C!&TIfsy{6bjE*Bf(uT$po-yDUcH|#6NVOimM36!O)KxZ3AXJ+_=tCF6AP*=T
zAF(=O<*fK$dfN0x5j{vaJkbkK)j$FmG8q$p%%K8_L{&or2t`2Z$ALkcDgu<@L=qJW
z0sLvyaKMv9=3v}3QWH=%WI&rM&HaF~<v%OLeic9&<L^%<1%UxH4B?kSi(w#>N%Wsr
z{|~OJ4k%+GX1@S62q0rTpsD2fyPw8i@E`H&S`ZFhHuwuuRe=~n;fy}~<%onFAx`*z
zKnww7OrC!Xnowph#tQ}{|C_U_3KCGp6QLf&Q-go=hZsZCg7U`!H6h-9cxdYUibp`1
z{b&R#-k<O*UR50dC=)SQ0_HbI1_XL-zT+qa48{Amf<kHip+l2!jDZVL#Qnw(%I{Cc
z`~7y9{Rjp`f+8q1Eak7F{97#6jCs0$IUH1espqd3&F0#UN+$V&PIw&jn*GfMQWO~<
zbW{cEYy^ZupTGaP{%Zs2Uqk7)XafUMP$*1Q3xH`MA+;e8NI+9lBm7^H9zQ4k=1hS^
z{`Z<OZUGPs0zEkTx=9{7Q9kMSqDv!C1#Q<@rM2L5H-z+@O_R3vU23Zl-DPxtWqcoa
zu<%sX$t;;dlDV<AYeecPVv)0S)K0?p;RhFQwyxl84ozSpEFwg?QTi`)9pMhAvn+Z~
zUaQ+D|IRcw-=$c+J*zsYS{!hAIcum@Q~&k6YReD4k7@gkU8^3<W2Im1MBEo76ZnIA
zd3V=}_O{hBQGa|DOo+!k(eG1#=y1=E7J6yQ=Kr{!_vkk<vukO-(+TaXyPm{pjF(=&
z)%til=fUzsTia*5%Q{Zlzo9cFOMmjQ-ZAMOlatBMG-{RQevE5hV9ucZWYPptb8=&v
zz1HB-BPo<c{;Jkzg-ec#$M&c;uAF$}%NL#)Eo8SlGI(&zfA5K1#x59tSZ>r;?up%t
z!5RFeN$8T-DqUZ`EU9(VTU{uD`+|n2<7xZarCDk_qja9PE0PZ;tmTyLMjr1f1g&?k
ztz@%2JXUu1$s?}ho{O9fnXVV>OWDr8AQxb-)kug(w9G^_`klDeAo$vePp;9dKvdUH
zeEgF0cI(Gp-K*#M_ei~eGk7XJ6glxi*r)&K9eFj^INZYdq9IuVoM-nZ`SI`+>;kEd
zq&~4o*)jU!jGrWo`A1w`=w&SyHE$+Qv%PG_X@l1aufcP(e1<sH;iJ-Y7ixYU{=ATg
zo`kmfrKcaeR_yes^KYCke))(ZwGVc&r*(ZT-iTK2yQ^<T;LZqth@DkpqvZC9Xtm2q
z0TF^`ejyVq0(=1><s4nQ2eLw3xk+O^!UhuPp#T_`gtdyhdK-QCsGVv^vebGV49wki
zRx&S#@7X9<vj1H!U3;TLrrQj}#JX66ID2jLoe#APycm1+X{gwQo)fZ1D>>}Jtgx*3
z?lmP5&2!=jrZ5qI>u#8$vDG2g7$<C+Q!ZX3RaOcGJ0(iJG$n=w1H_k@&3!7}zKh4K
ze~G<9PK~Fn3iSoNo#D$+Td6DU6?<Muf_>iAaj%%AHt6F^e>QivoZ<Ai&qG1tjR&{G
z@94tTTcd)zrNTqD&YvwwwUx@yI**q?g|oFM#1DOu$WK*&UVPQZTXIV22wbe69d;?a
zartRl25d4<Qa|+;cp~_juD$M4(RYQNWlUwk(ynnG+?`=?-MDVteQ<Yohru@PI=H*L
zyX)ZY?hXSCE|+t@FZceusbr<Av$8s!PF5;!RX-K6|M8539yZzwOI4P5NnTS(8Jaa^
zzUm@s8ft#xCBB?2%|J^%?TznZo4gn3f=Q`a5uwC39Ba;X>TS(t+8lZ+N?i6=uXYbr
z6dAAQPEmoBTg&UWHz<x5G^L|^$HK#)Se;H|wYQC$>1|Vo$+4kY(hT@<-i-Q-N6c4t
zqu$7S0z;psIP$Gl&&s?)?E@f^=4Omn_b#J3S{v@8J+vZauzs02h?Il8qIE1gU$jx-
zGL&u3FoZN!l5u&fEf%ukystUTN;!QCRK}`G(X4Y<*yyGpiD{h$6*<LG91vT_2+5jy
zUSz+dD3`nL%Gueks?g11<khe0F7a^+&>(k}^Bs(?4?zf|iZswn;Ik-edV3!GF;`7G
zB0Dri)o&C8OU~MBuhu!&)kUa(i@x-7Ux>rde02-!S~L}o@e;ZPWE8g9&~vvpJG(<R
zSAL%C^A4R#6b>_kPM$uLW%e>rew>}LLTD50BuE~z)D>pCE69hZiYHAmOlirG$q!cU
zlC^Dal9=ahBQ|iFMqB1^wR3*P1@x`OpU%!agk3*P=QC?T11oOtfPZNdyDzS5N5e|`
z&07}3tmOC&U%Vk2(J%}{bs0aFB<Rl28aQ<zwGQ_@{t+01R1YE5YE*#F*ck1OIucS&
zJ{&s?6~Xv#P2j!iac=xA&r;tmn=O;#qpLEMl)|fAZvt;N@~<TZ5buEUmhW)oO=Gz-
z{%eD0T`CyP3oG8ew#7@t8hzEp@=#01j*r#TktRLi1Sr;Qq4Zq)a!`wD$&ipFF+m^$
z`@8LNYw;#fmG@R#l@+4;Zg&h$OHcN!ed;Zzf(=P`%X*RYE<Dq7>R8Mhdpuck8?RS-
zSY3@_aB|oZgSzhoJ64NpmRs5a2jtWI>9i{={s@6A7k}gyZ|6SGpND@tO^92!vu=BS
zf{ch}XZ)m@Wu<nidiY(g1;>k)NWuHnC-&_+&EoVRXXNb7tR#B@D^4ag`)Dq6OEqO&
z7FdFZYBXx-*rqRlC*K+Z{^Gdw2Y^+@x%ylM2%>_rp33A9D)k+1Y`@HR*-rH97OTY)
z$E0%2T8?>?^f+lGoKFE$l%js97jz)!-Ck-RNlIBxELj>B`n~?!%V9e8C@q*p>Vcc#
zfo>I~W&!@sWO-<|5NwxqYv1mU2?AruhCdRL{i<X;M_h-`wa<P7Di@a@$>&kf%n*?F
z-rkQGGaaUuJnL$nzSlSVqEe7Gtgl=Az$dLiCpFf18ddG3@;AQdN#`0*!FAP4^*jFA
z&n;mYFCcys1MsGdSnS1wzsY<&4{Ix;=Hdkun{*VpLMOJ(x;%ZvhiToE6OAk6Y}Go%
z!Nc=Kuz7>CK2yt{+@|-a_c%XY@P3)JIY;W5OA9SwR2Zy5{x%Gyi$e3mx;li+MRzFF
z-dNt76gO-c_eWw>U*TAH`-F&WQY++AC>^=RdKKn_I5bbd)*D9Au@}ZhV;W6(2^S8?
zqfFsB{?xezR2W<6ord8Nx9Y@QpvtfOEEF`3ZT9PSH8w<C(5mI`;Z@9^)U1S@m+H6y
zX`*()_F_jIp`Fjth&nYxpzIyf9Qig3AkZ^bcg&>ESK3r9`;iy5ubEL4w#L#z*b?z!
z#R>q>+)N&v@-E4k?VhVz@`}5}@m7EaBAm5r?6%>~qy-Z_9+T(FUL_^ci|H9)z4RkE
zy#8o6UZ2;1IB%^??cTgU@1B@+b=7#Uus597g~#C*`t<hF@vWVi<H~irJ|&N2Q>^#F
z5r;4{UMr{K`ydgq_2+^27g0I5H!7wmXOfLX8}6?*zI<0rItK{@S;Fn51MncM<TiDm
zn;=LMo^!Zc<v0Bi>G!EL)()#|W^<f%<!G$5&gOX^iNp`cAq+Vm^F_of6ePY!>#J0Z
zg~BX$A|=bUXc?0<ytpps_#Of94zaG+i#`%*c)Qs1K;tgR*f59EYKsa63w8U!ylWzL
zo7q%Lo?Lwj4R*ExS1z{aJ2?=YK8>;rQlbOzT~s*j_q}x>@#B^~fHHU`?>QfkdjOB~
zD0|iYAZ5;z<7F*1J`Pt>a&2-KL~q6(?{Q4<gAANKOG-&c4ly4e9<Pfz$9~9!nqm8=
zChHt-Ute6)6EB%*kh#JMwunp@Rgk&-Qd(Er%Df6$uhgxgv)9`7WfG`fAjtDAgNkL)
z2^G-k&+~C{deV&be$*CbGiOBD@g31hYEKRKldL_((oY+LVdxQ>`>$;&9-ad=V44EP
z?FGQ9o+1CCGvD}hW?Ugc@$r{)-RED*vyrfdIQAT^JJ@Lh^qKxlDcoadfQjwlLxgU5
zJ@m-6-u!u2Tl#5##u+Goe{gYmjm$0sXL=f_>ee9Hzrpz08($k|I~sXR@@y+`FW#cr
z@zzv3rr~g#&Hu&`8qWGfj2v%4Cd?f7>RL-zBC-D7?LbVlwDP_1mgt?&-ZoKc*CWVf
zR14iT{{gZFq>+EMC7;o#U5V)4fY_#^Ail{I+ZrW3Rk~)*mJU+ATD3i&_kHiheHK4X
zJ6+*4{P{8r!Qx0$96^FjDIj4W2HmQ#jvXy3>hsCy`Py~KYaOgY)zg*2TeB`{^RJ|%
z&p7KMeU>-JQ70OqN0EvAg#6CZ?;zk<z+NMRy8KV!9{GSc1IksxeJgoGsU}1RNlnQj
z87RMtW}&umJrgwbKw3OU$6FLv{^UfnMOt(ty60PLwpvA)Pbd#8Dh&P+L6swgd07NS
zHd)PGAbv5wQ9FH^l4$ND6Rb;hv<2pFQM#xD_G8lI2FCEOd=w7Hr0FEnf;bJ^H#2nR
zy>QR-liRlkjV@tt-g=drZf);4VnD2!W;&4Pl3soPZz^b7QcjC@XozO-^+Wh_1$9?e
zHE&enWBnJsG!qXR`QI!{Z2OA`)t<#EpeLd1bN0NFo6Xwzqlm%VIj!^7qJnmhZkx%#
z#z~yl`RjXl*PC7X8auaK8f`Vd&0?ZX6!7z;H@L(7r`+x09Q?HmJFw@vyt{rYZxWr;
z2{OaS+8(5TxVhx5Fkr21vKoolm`Fd;0jO&9R;97>W-4)WGS`&&`#rLv>X-Ey3)3Mn
zH}*}@NdbMzq+OEo&lpUV#i_b>hU*Mo-mTC+IU|@2F4HE@*H8!^mK2BPi_97r-p=s_
z*;8Gu$CZSR1r**hII(+PS~yAHF?l|kSwl=mI&aXMxA8Tt&($Q-hq24Ku-8CU;@iKN
z^F#INS<uGQl1+v`O&d_RVOy8$>WB3k?>_fS;M~h|ljI77^!5ADYCdPfSstV~Z?DI6
zLvd^Z_e2V-8c1}!OKFuC<EQq$SqB10RwR|fqsx`Syk4nqN&Ph9Rg5T!Ka{A1DABVd
z=MgmC0Lw&RJAm-uiq*69#j2_MZkai}FC9i~r=ZUpN0zH3?;5UkVC)G=iD|HW@0s$i
z_<>C&QzU>1TEn8!Q;RNu)4E|9G7OVSXe_Jm=+`^Em2V0iqoojhwaVb0HdTCLh4>M2
zCa|_-Pe*1JYdgbE&Z~OciNLt2t!uNLsuol+n;nJ!j|1lowawAWJ>nuV$OnaNNamoZ
z#djki{~qdc#;tNEIhUE$O$PU6_0SVG$8u?9rgOy0{LvRO{&rcW1F>-&isYgER>D;S
zDBv<ANycdzRl>u&J;}w~y207r!=k8odA0%FUQ>7%Mr#gy#09+prh7w&;0xZ}=s^fI
z)J?0%7xSY0#J6);&r28mS+eI{s&lmyCnb%w<D5^&3VZp<Ye3<<mSal!e@H1lNGBgg
zC#rVtHL==%3IB~oAeB@7a4=Svl3Yr8ZTCp?6q{lop+LuBBg9zJmM?bs?(g|t(5!OE
zDJwm|wU3xB`*uE|);MfRysX8Kwgn1bE@NRzaee6*H`s4EU>g7C<{9PfY2o7)bQjY+
zH0P>cvAC}3liy%h!-9D7qJw}nTys&cJ{I*u7dkbOWrsqUDvfn0M2uWyn7xNXC6z4*
zjd8FWKHNUn-g+Tw$_M<yp$0n^xB`LlTR8$)T~^)O0o9}biux1Z{HuvAp%>_%)KyWZ
z@2X4YsH+p36LhvV<v?2=+9<X@t+rY7bwHfQt;T@sB$-qB<$GuU5_EPN#q(@f$FfOT
zXYs7}(LpGS?C8Y>;g;0>Z62SU?xr!>LrTHo!NS;8N9Qso#(fz<)JSEHX+@O8=gIK&
z^(q0yXH)YMUXLx%3%82q4h@uWY{tmEtU(0S$ux=gly8Xfz6!5j4yD~5{D|=Pik<b<
zi&ZG{$+Ca_X!F72&+K8YyI&*Ejlwhks_6AyFnmb83L3V!Qw&LPZ>LiTa!BXvke7#c
zkLbp^{-SFswESybx(_U?+bhz%WYyx!D#}`A?ijIfa+bFtxztf|n*{N-7wZ*ZVhj%2
zXFh>-JL{<%P5kN>pu7tBFwl$)H@=^bij61ixP;JuhC3H8u4H3Bt2@f=`JBNpeqC_B
zS%2*>K3x(LidEVEU4bmdc-=GFp{hgM-}j&&rK|r1n9)@h%Rc)>frjc9PQokH+f4!_
z7}<5emVmF7?D%C}_X6^*AJ2`mk=u#U3T@GyH`}D6fy5(9Id#u8=)=N-+|(9J?Ch`_
znyrE<G2QOEZ~v*o85gV_N%vC6h6&5}n+F`Fb&tN2U9zppzP@#5Kt^W*9*{&FAuC|p
zVAH&r(KA2Zg>L@xAb!<Y%5-L+rcoiPR^Xid6`&YqP<5Pl)lfjMuiZmvY<2&sN3sny
zr)@<h%**lGEf%}M8Qm#2EBZw75+wfdKaw)Xe<Wqh78Gabn{QvB7q0(;URrScpv~YR
z0RKyY`5g}ZX#xRY`5z`s@fGxM7YM-rXwfZl#xTO_5P<)F1`8Fy@&9ybW>z-#|LD?K
zkjz|w1Vc<}P_!~4m&!T*R^9qV_|%rJ*r~$m&xyrR28Df=t0EyK+VKhehEz@KiArY5
zpVhpDy75Y9C-Q}oE5XuYQgFIK^T~>Hj4ircDCS7*7CFb<$7#o!cc0sj-P@nKTMD4?
zj!@>v(B}c0Z$r_RCgso$ceRcMKf#m6NR`W6es_0MfdUYB72JM*z-W+(0T%Y?f~ufG
z9Qw^*ccn=~Ak5QHXK?+@tc0{pg^D0}lB_=9!=&i_h%f_g{0Q*4jH&4<PS=f$f}!A1
zcd&Qv&~P1)z$Z7nlV-VyYDH_Ic7>@O0v*8V$@C6{g?IcN(Qwse;SCKadL8SagUM3H
z|HMg3gNDh$m%akum>q~-|DsxQs3UOGKL!ls0aP+S67Ky=z~be(_yGKjq2vJ4Z^A){
z1xf*ABEM>(P-`GjsMKrazZGB@EW`VurP?6p##`nL$kiwLqq<~%b8JhM{Fa9Rg#_j;
z3K!^Vqs~GcK>!YSNaG);7=h+Z4J8~DCjgGC03w30S@Hx!!;)X3I+R9bW~7io%c~cU
zVEHy{=9Oq387>NlkdYdDyFi7Xpm?dyl||-+8#=I9DIp*c`sHnk$CsA67fja2vhv3c
zT_jaf-v%6joT>sdxe<lDV*nQF1dVwJnT^2AcU4F;DT=gfXe9gXNfgh4t3NbcKq(ay
z0pt(P7~i*RsLxxxCCP@r^IeDVX#gBf`UO1;Fz^=6%M5}?N8nI~f1U+XeSY;`6Q+&|
z%@ZENd3p+?IltuVvL#ZJPkvjqG!6_702otZ;AYIgXR*lQ_GWSgDMarhe^2=3J>)9<
zjH|&O&p2D6Kocr!)ob7+^sR3}!<t#R4Fmu@k-6y8CX7+=H-2hg?I(T~JDDba(%jp#
z8jT0_JNEQJ?b!QD2Ek!rz<H&iCVL~^giv8GAsu~ZnQhUdA|!M33x<IcXhDguk5^1R
zj@i-a3z8ka1mt~`>3AhZ{!O$NHcy9;B=g54r_F=rVXg(>*D3IEx#)!W35zplf^xy?
zzM;T+%L*&S1kKO{7qG<_2OW-)qZ{!KQ%Q6_pYnG{00<GBrQ~9nt4(DMd}aTP$j}qD
zIZ7aHiZ<jk847N`7QF|=RsZ|htS0gvr5vuH$%)U45&Dt(FC?2=4YSdanBC(1j>s|`
z`z{?py7=yWJ=$$yQVaMdenwm14r<rw>HZVze+zNcMR&B3gi>h<$h61YSpQ4?-W0gV
zG}K1I2)9+nz;yB5x^#h@qTDhqjhRiwNLur>sEy-SWyml~iRoN7JG*@XPMtnV(Po>1
zd3ULY+m;3XTypXJW)+Pap5%2i|6BQn%KA_ZGTTWHeakZbsyQmVB07fU4v4AhLF4kq
z{O0hy#*Y0DF%qXJOv@{07V%;P59`T(<uAjktF^_uO1wTKp>etFa(4R-yj1TGsrSsY
z0DOIn=t^wZo`pCnFZZeDA)`?t1shAT4@(K>7zCC_eY4p287np?^CC}t?)b8+YzZ^%
zRds9D%nS&OwX-Xq114#13($wJz^kftWa6hco09e-<|^^=OU!C!Ta|p03h}{8V}&4^
z{+53FqFYn_=|h*vX6NC>*=vch!vJK~IT>LN@N;}!0c!+%<LM;hm(EHnG~MH4gbOPP
zm$BBoGs_br!`{Js9d$D{6?=y(*x35rtL|k~W53>!<kY#*Ke~f3IZ!0*J`aq0=3Qm|
zrs}NcOBZ89*C^$;OX6hhI0+6d;-ja9iB|6V^Y7NPlovLq6Q&a(*9%pZN_PT0S5hc{
z;D9c+Og}XIvJ8_Elq6ajk4SpRB3VrCCtMWNn+QKP->HBl4a;`0FRG>Fd^Z2)zg_QF
z8jRGquVsfno<9|-5rNu9FXwUxP2FRBGNA`EGaAN?D=N>7x09Rn*K${X7fN$y?c^r0
zSu9@6zoW=)@s9+)w=wbH=rQbry|7Gg9QI6Vno7y5MgJNo<9jV<kPub<V^@((N8D99
zp5<tK8t*Y;+4XP9<@MB)gsZ{)?c7B3T3Csq=RxA}KyIVeXAQK0m4Y*raz9p*_Htn7
z%o*cRzhBiqdSqs;cssr~Nt?;qpe!4Z4Wn3f<@?#5h*hR&uR^ZF43Fbp3f;@8-gxKg
z<AY5&WoDzPtj<6yfA-5VjR`68Bx=p4%cJu2J%05d{@qjJ%0mtIXMe-_WytywPwdC*
zU)CCg_Qzka;vb;y{!DI0J^KjQyv=`0ELP7=lQ>w;fqd3dZ9HaF1wXK<pe5Q}qPxi>
zT_QcI1+tU{Zc7)>VzC~t1h~o*4teYyZQNV`ZL!NB6XAa=J3VrVs|YIC)eJRCfhoyp
zHNcjL{dbn0GzT&sk1%`8e>9AfDCjet9!Itn(V~(bdJhC$XJ3vwtfZ?yPvb~E1fT=;
zRbwAVDp~v8-q+YcKdJkfThlF$_D;JB5C7a7*LdMiyHl8>lmR0V+^ySKB%+*Suqrp&
zr-;4cBI4Yz<Ph)i#uqOlDmQ5?S1Z+fIE3OH_iQhTe&A>W<F^(2jOFyjg)FCT!h@qQ
zS>KSION2l!-esn5eM;)#5?Itr4*?4ZBth)oaN3W>C61xG5p4C;(wt^V^#)IQUCYiV
zbJ%wrt%e?Z%!Y_+z`1$iX52FVZq1@qCrE!$F8q$PfyIO`m!V=MED?9(w-;qiM+Bmj
zS&mLw#y?*I4a0{?&=;2feYjPMygP2Bhl-`jwKsqUa9Pzv&;gf$1y?AlFfGzn5)Ol!
zUG|=r(f&Z)9yo4ny$kvRU@&IvdPkGO$h&u@zzsFaOO)7D2g&B-8q6z-dIR=jRs;uV
zJx;Uhd#a{o88CAz&bR8Q*Z;EQ2;05Zq`u?U)VX`!ba7gC<qUF6>ET<BGo5rR&!^()
zbSO2=B|Zbl7HRf;vUS<<Rp2U0YYM^C&cxZp$<)yHKO=i1D+E?nj+D(!m=HJs2MaSh
zCmVB$^%e}l|MOzDV4@&dIM`Em24M*Bx!4ex#4VkiT}U}O|8Gv7l#PX(?Y|LEmyWhF
zL0hx$vHFQ4SBGF#hf0&RIyB1x3%rS+EQInez>HuH?s}aZ<!aAICB>iSLbvtQR{2HZ
z4W)`Admn2{-G#1!CUUIZHPj-aHy)$E%YgpY5CU;jGx9)0F|LZ6<nKBTPsX`<^e)=s
zqK5{xSfXKLR}Lpw2s!m3a0T2T9WF9Dq(Gt{O1+gE@MKK^+VW_Yj-IfjZ#+|IML{8&
zct6FpTTw;Tr7y#z(W-X3OTRHEHTa2P4Ez;lHi`-u38rXf0W?5aLM=Od7ovyBcQC4A
z31Z%(Rr9wPWM*(nMID5Pf#|D&f|JE4f&S)@$pyJrTTV9RFIn0DNehMqqSgquhC{|d
zCuO<#NlL-$VcNQ7h|Wkq(`$$t1;KAXxQ_)EqAg2$hs`MHM2428CWu@)VFOKCI|A+x
z0pkqgfj2SLw#%zW7(Qnh3qhe#!v^`|-6Bw$4S-<*uG06nnzfWpL&1YOSAo)ihb-<}
zE<!1c-Oeu<9Y}3i>TOtS5Ip1_e4>N~7z1ipWiEpsJtf|WGAaKIV`ZNKQkjZaoGK-f
z1C1i>=?=HQ2Bw9*1S!K90kYzB;zF(~IgCb-rXrgu^j0vt%VAD1J6nwdzlI3nCw*mJ
zk&u%iQk5U%cLO9On+v#wSdMO#r5Wr->bUQhicbD(Zb}z#Rczbppi)9;ZDE8&Y~CQu
zSC~rq>p--A;M+8OgTN~RF~;v}>skxF`>+1E*MN+B+q5W+4UD@Ahhz1RVZ3+!^MmgD
z^B_73+|j-Dxjvu$4gQNX0CqO^AROYptm%W}h@`+;o_DUCy;XAnRpZZBi<32!JIKn!
z8E7x;lG|l9uGYvx5Z*XiNV0F{olc--==hDgHmgJxwhc8qi2OkkNqN5zfxhpP1)Mst
z8Uk`9!%C66&fZvICIV!~&#{q$pdSAL--dg54IR?&`lhX_@AmP2P2~CEtb*amMkuSl
zlyL6InvOie+wHUA<;P3H$Rv-l{dWFU616L0-&@`lX!r>Og1Pr{#~>RR4Gi2xxqZxT
zOuxuehYB3IWExB%dNFd+MJeu$-O3B?nmuoC>xh-pLA}0YhQ;Vgdw7}r7ul!VL%E0y
z%veGJ^^rRqJ9|q?TM%wN4x9f=d=uB75%Cn&pKrMb0*lNWC2CICyX=OSV^Lb(UtqiP
z*t?2aTJB>&Tl23u1+Sih1TQ^}3M40f$fsd3XO66$dB!|>$}f^V^Cb7jc5$br;Dm&3
zu43};A9p!aj;`MKX9t^qGwHe`=mK?w91O=is%6KLCfa^0?3X*yweo;9>&<QZ*Qxie
z^6p%uX3wBxw>iJW`=<Zpyg-4ydECuAhOdO>?E2#a+WFf|Q}&krdzD~0(AS3-N!@sm
z+1O(NlsRL6zitdn;{bfNjO;cd|A>2&B3Xu`eS%FA{LHB6v&#<=kXO*}=>lW#yq3EL
zeKJ?UVrXE<J~noHT|5qtvqMY~M5z~4sP71U)29|yE8{O0C1@|_Y0OhLg-fR0x7z6V
z&{Bv8l~){HF<L9kW3M>OrN@{tDCoRcoTQpf4h?j3%VE0AY?wwDx-K3>cZjCljhIz6
z{#wMW;^p}T^+VWon=RpI&!h7!_)c+J!1p!#+#MYAYXwH8f&j?Z^G3uxmsk;%P}yPh
zf^w6VHlvns)ec(}BBcd~#j@R1H<8EtVSA1ZkVVdk`HD%`#|d%Enkw+}`8|Xe>0#Ak
zu6N29b8}G_h4*^c6~ztyqP2C=6Gfd9xK=}j(R11<ULscmn(sZzylkXg|9LX!%T|R1
zEp<dmaCTVHuw28^y(ryYA=&Il?#yeVy(;yvti#e4ZUSo`%f#<HLC#u%6fQQ4OCGrn
zLPJv8W1O9dm?|jp;BAX828^nF{xCNvNOgU<y8P3piN38a%>-S(l$S7=i0AZ=&896A
z?6I)6ssCs4&vT@~7q^2Ky5Z_URkLg+1q7|XlPG09z=xN{4@V>~`e7b8w-3<v_i$YP
zm=3b-T)YL;kC2<kWnqK&87P~C7v4%{kfrYg=ihr@on@DoX#i5(ea}CSR65@R>R-Mt
zo*!o{Qfg{+*#(eIttDCXSl3QN9aOY>uC&CWljIEq!J)BVZBdD*D6}uj9xw|%yflhg
z;hw2eKTIP-+Vhp`2>=-e45d@a2$$l%&wEcb3ONGPP>a@3!T2sH(*(6U_d|P3AjAm9
zYLO{wL&nSv+1BZi6dcywB@a{hAvU;B_O=JD#2)(0(+3%`==gTjYo@DSk$c4L+6C5J
z8C)-!C-ZOyn}d;QCdN;`Cui{#U6GWzc*fIa6GZVEhyBnxSzeeDARVg{?1k>dZ(4>T
z0K-xMtBrGWJYpx8=lkx!X%uS<D1?=pmAMkdkM(stv(1XaoGHP;9mc=fgb}k@PAPx^
zVYM^LmEd_=-Tt%l>77&x9^#2nxt{q4szGg!k+hU_VS98Lj6aEm9<VjK^XPm$VLV})
z`Iz_h*@68+VF^1l=HhuRjyXEC2@&r*the48RYwvCPWn1pe1A7~N5yj=^!Fxbho#!n
zIA>$wj*aRFRXz6I7fG*FU!ZsHBs%@N%NN*MZSE?XT7kF05oq=@pMsWmo`>g0;^}dr
zkn!`Ais-)j1;|r+?OlfL6j%GGNSzAnl;(H`M&QI3^zmnZ@$3F)U3`H6@WaK$H~HLH
z7aciof`$)AjZopZIWNWz<i4F@kk9dq&~*Nuxf8%PEh*nGe)T#u^n5<<&JAy!$yK~3
zzpGiOYLH+@Kz@?MT%)g#A|WsmT+iv$MwRo~%I6d5gbX|2KEHSzzGMD)Gqb&u=T3nR
z|K27;W|%}g=3vI5pb_9Kw|TbwmWz7KXcVU~PI9`x1Jm61&p}57gv&&0`_neLomiic
z@Ez?`6DQ69@?!TjLJ(zMp(ymO8kcc-us|`a%M!~FG&_BdKFzTwAHJxuE>%T6Ti<?R
zwgTJ6JKj)8txfnFb7=J~^*{<st9<iU5e)R&r0Qo|l9mznrdUQPM}#g@%ydkQe7;X*
z<iyl^C`<*@rN|)`C}WJaIoYSsT<<*6wGpK;M$A8ZUF@5I0!yGLVmb*Qzm7j~dPkp`
zsb|V<OYUuS|9%eBv;a}}%kpbO;A7<(^(85xv>qBGse~&Zcj9j?H!}lWs%1^1e6jNV
zd7T&vw5!Lye>cT=8+|O3mki{HaelI++nGZ+@Ie_jl;Ff8AXaR$LD>%HF^p(20aQ+E
zG{(gdCH5(~Njer>rN-FO-CVAPu})+Zo_n`LhKciKYn~?(d&vf%!20{vM1aqftfO12
zNTZgU2ejB+zbpE9!;i{oMPxq=xd#|WvUTFYvcdi^R+#{`59uRqCA5hNX2*#Jow@0c
zL#c?$<WAaDP}UPhaZ0E0s6G+>uc{eO*g4NSa3awg(;E6Cd$O={wN5%sw!0MiA+LnD
zEE(@eVVk6$R??+rJzKtLzG1VHPmla_lxKM5y8;kI2YKdS4933;z6+?P=4J%4s|32W
zI~FdY;}-y~H6ms#AX!Mkp;(8=*F|MCx>N2t%2eG((2ppzHi}(3u|^8|^AkAzVHmIe
z#01~aiw*>ie=76v+|EB`CX`RuCPS=P#<}8)6?ak1=JrCsLc}N%)Odm_D#N5Ju<m&x
z^CKh)=+b{VVm5f^o9Mxz*`9n?A-u;G$kR+e*!fFh$Doi>Q<N<pTbazm2G_8a^nJ8>
znoQaw76grThoCOTh8Q#UN+EgIi}j1u;cJUhQ*B`ltm=XK2(vH($oW2REYz*|Z>VAN
zHyJrQ7Tt{l1cNCf6=n8DROBeIT~g8RUwZ#&e*Whg;tyn?)o=n$2n8G!@4YS)2X3g8
z06XXWD|{4|;YF0)XW!ynYX^eHGTl3Rsx`PV2oI1Amaq=iyw@e?KiSG&NU@T*3DbO4
zunv)KdzxTaR^J<vcKj`)vf01tHM4PWDIZCoOfokusJW`N@s+FI4<`Iw+TxT$(T-rI
zJr+vFBEM?Zh6>QtOF6+&>q<;>FmsbJ0g-;P0sGq?Qq!DWpUgU*QZz)CVswQg&UGms
zM8VPoquDOdvgeR<^H=_KTgy{UH>~N8o`t1qow-BH(Rl*8o|lA62+ZOZ>H{8T^@mQu
zV96RU$2yMc-bv6pOfS2>ZX(#aP=Gm<nv{*{dT+}ElF;e>0xjZ1K&ldj;3)@e>(yxI
zpt;(vGCZh!4W`pIbd{o0t<W?r0S%rXREOk!7%zQ#ujR73uw#QymA$*0oprtki!mP9
zY4eOk^9fRx)^xR%Dr)h!9a^R}-C9C`EgxSiT7zl4nwFC`sgfkMJ)%;IUb7WE{}3z;
zTDmoO;<ur(Y+pmJH&20UD`QR(+*j~_$a7a$a68$(LEBEe5cIm3#;%ZjCYeM6CGKxo
z_07F2NUBJsMhCG41ZmtIawmjNGf4s9(4EXGD+ZVl-3>zpyugQTQ-2g1Jhkb)McZO6
ze_Qk3!spqGo&yjp*E-tbT*H2LTOrLh!Nlq~5Z^d`Uz!Xavi0Vw6bPg+3DO>-arXS%
zNJRW{d3fV_ZL>z8;4bvT_rTsBRQzv%f1P4?d~D@thC@nQaGlZ?-ZrIikuf_yh~l*4
zC@&4WVlt!&_1QN%w&a}PA`DDi5Ddb_vOyTU9{d|gyd?@;Un{lHBz7i>l@J1_pb2HU
z3x7C}<5H+j#1wEYBxS+@BL*KnTRC#I_o-e!$gc0oUk;f%FrqvwB%l2oG!Rdipwt&n
zm;rGp86z{aPwgOCyjHt$WwhX=LAbJ;hmeH??dDO8hJ4|W?bPQ_#5hMR_+81+V6C=F
zJJ(@oHT5tR%ujkb^w3orf<Ai|Dx!`CJC4WhZkzHSdv?Odbho(^4Y39T(NaKTE9^^r
zbtVp_TGf!CjC4wtU_6T{h$=2m%Ne53fixvx(!nH9T~Pc?OVCeX69R(VO4|)0p<Oi8
zY<!I0&qRgOs4D~IN<50vzQV~<V?Nm^cXwUs8yll`gg>^ewh<Vmx~s4_;pz@noWH`d
z5!90l!>C0X1<wX|QE&gNl-@%=ntDD#!|J4jyD|2OL^(F*J%#EYP@*90m=>zfg~jBK
zh_E$`OL6CVKAIedC$z(Tf9Hk+L>3*>Da=OxLZqnKde>+r^>ec1Z->p=OFRB{f@V=O
z<MQNtvId3}vUp9^TZZ`6WaW5%*`y9ZGN~~)2nn{;6RcjJ74#tpKgC2I#ZjB_U}}@*
zLlI0CYb{n%DRK7!kXy&|iQNi98aoBk*MlK!w35NKAWm~VAZ(&pCtmnB;W<={Mg8n%
zFL)%qYE8VR`k5eW)JD;ymCLlMb!G3ClIW!|sAYYsvpKm!(RfNRsnKGBpj-(a-#Ik-
zd=}eFhIbY@Q0@<`ENRD|B~3y7LmAoNh7?+kQ93$PX8sFMQa$cL(;*bn?V3{n4ENq9
z+K7qaW+lS;FqH{Im?XWukf_lwL^AYonJ|D#GK^_Fc^!nC8HJmwP0QDA9wE?IFUxJP
zLld$v#%R#w#6^GffgHZS-9FLn)##`m(vN@cLCo@tHh%q(1x2eOOU>(q8-DdC4~Msk
zPn6tj+rydmpt-=Medyc4^}K{L0-Lf|@zFS26jV$z&Mlb8is{J8mEb<e?GoVimoRXt
zgm*KSCqug|YXmyi;i2#IACQ;GMZGJ+-M3NftzI0Ja`@z5C&4N%6Mh0cc2j=bi6nnQ
z{)t6$Nx1|;lcpr@!C-?}xpWbjlr23?Nm*IB5SY|SwV6p-NtwSUmF(?Zz9!j80i;R@
zOj34c_Fo>y|9YaN+I$@B!kj{)oI>nE0HLn|fD6D5;NW6q6BiTb;1p%%;3xh6zk>9&
zkgTblxr+rU*H=pF=Qa!th+=_TR>crAWY^j3iYN#z)KurEqUcxgt`3+GxMq?ZG|q-d
z$&!^}Bde9sF-=rmZCwMqn$<;gcpX4(c(5pLaLaTn_UKPq+vj`R_;_mC`*`XQAgXs4
zy{ru=8TIG;u^F__gdm5pUN`!g0c>Nhn+8&aMhbv^0Gq#9mLL}##L+L0OdrJ3a_jjX
z4XucbMXw24RU3VMs|cB7Hzbr*2Zx{ty;zHBwRuKjDHV^z!O9RqQHy_On5I1rtkOoN
z%SCoc$w+mPV3^ryHdl)zFl4Cor__L*tR>bmgtc)ve=ncs2;f+RKHar}-pnQ5V=P8q
zIpyFfnZMU1xCjA)YH=Qfc<%*E*6-ie*HCmXN-jIn(sR*Vc42qEvP?DW6P#J=u%Wpm
zFb0Gn8;o0v==oCNl&WkJ2AIPJ2$UPuI<tFHTnHmOT$v%3E!OHy2T++o$~yYM6W{5+
zsP)NbSVx$tehRK@x8nq49luDGOu@3fP+dYeTI99p%JpjyjgLBb+4??*&x8=(jQ*FY
z9&Bc3&!Y20OP2-*th08_<hJLwm+q$j0t$)zbn*HSl__N`WrSl*?sLLcmQplYXzNl@
zuS17pEM>*_t2T;WUsu->_WWv-Ey*OwRLYvZxg}>2?naqTUG$izupMvw-$lL_LY17+
zw}AykAboHLhU8CP-r3sbdj04k{U2L8IS6n`w8$U7)Q*%thtWdRLgb0oBW)mUzzqOz
zY5ShVJgVktAd!0C8%7sKN6k!W@VmfsWf1E>rcAiA&0U;!zd}P#O)n4rKJ+b4B~E2V
zD-+fVVbLWVX~KE`M^WL&2Y|o*6=aiC9Q8V~oL+w=pv_K^U3R{t@&avJy_k3>Yo1>=
z!D`=ap|!JGuPJw!os}t|wY&P7!hQ&R-R~+6&X#SqEWbY(f|QHod(O6^^|*a(FQ!$v
zYhhFM(t0Z>8=favOt%8Q{}Wc8b$*AIi!@}q2y{CE>l%O0)kl5zAoL5Ip@r<4`S0-x
zGTFn07(yWjZXHrb^>NAi>FxiVjy{x`e(tw@Md|k_(@s8yA^OJ5#mvcxKtUm<Adc{V
E03y&<2mk;8

diff --git a/doc/src/Splines/Splines.do.txt b/doc/src/Splines/Splines.do.txt
index 8e8a86700..c95505d03 100644
--- a/doc/src/Splines/Splines.do.txt
+++ b/doc/src/Splines/Splines.do.txt
@@ -1712,3 +1712,162 @@ over the scalar $\alpha > 0$.
 !eblock
 
 
+
+!split
+===== Using gradient descent methods, limitations =====
+
+* _Gradient descent (GD) finds local minima of our function_. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our energy function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.
+
+* _GD is sensitive to initial conditions_. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.
+
+* _Gradients are computationally expensive to calculate for large datasets_. In many cases in statistics and ML, the energy function is a sum of terms, with one term for each data point. For example, in linear regression, $E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2$; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over *all* $n$ data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called ``mini batches''. This has the added benefit of introducing stochasticity into our algorithm.
+
+* _GD is very sensitive to choices of learning rates_. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would *adaptively* choose the learning rates to match the landscape.
+
+* _GD treats all directions in parameter space uniformly._ Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. 
+	
+* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.
+	
+
+!split
+===== Momentum based GD =====
+
+The stochastic gradient descent (SGD) is almost always used with a *momentum* or inertia term that serves as a memory of the direction we are moving in parameter space.  This is typically 
+implemented as follows
+!bt
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\end{align}
+!et
+where we have introduced a momentum parameter $\gamma$, with $0\le\gamma\le 1$, and for brevity we dropped the explicit notation to indicate the gradient is to be taken over a different mini-batch at each step. We call this algorithm gradient descent with momentum (GDM). From these equations, it is clear that $\mathbf{v}_t$ is a running average of recently encountered gradients and $(1-\gamma)^{-1}$ sets the characteristic time scale for the memory used in the averaging procedure. Consistent with this, when $\gamma=0$, this just reduces down to ordinary SGD as discussed earlier. An equivalent way of writing the updates is
+!bt
+\[
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+\]
+!et
+where we have defined $\Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1}$.
+
+!split
+===== More on momentum based approaches =====
+
+Let us try to get  more intuition from these equations. It is helpful to consider a simple physical analogy with a particle of mass $m$ moving in a viscous medium with drag coefficient $\mu$ and potential 
+$E(\mathbf{w})$. If we denote the particle's position by $\mathbf{w}$, then its motion is described by 
+!bt
+\[
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+\]
+!et
+We can discretize this equation in the usual way to get
+!bt
+\[
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+\]
+!et
+Rearranging this equation, we can rewrite this as
+!bt
+\[
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+\]
+!et
+
+!split
+===== Momentum parameter =====
+Notice that this equation is identical to previous one if we identify the position of the particle, $\mathbf{w}$, with the parameters $\boldsymbol{\theta}$. This allows
+us to identify the momentum parameter and learning rate with the mass of the particle and the viscous drag as:
+!bt
+\[
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+\]
+!et
+Thus, as the name suggests, the momentum parameter is proportional to the mass of the particle and effectively provides inertia.  Furthermore, in the large viscosity/small learning rate limit, our memory time scales as $(1-\gamma)^{-1} \approx  m/(\mu \Delta t)$.
+
+Why is momentum useful? SGD momentum helps the gradient descent algorithm gain speed in directions with persistent but small gradients even in the presence of stochasticity, while suppressing oscillations in high-curvature directions. This becomes especially important in situations where the landscape is shallow and flat in some directions and narrow and steep in others. It has been argued that first-order methods (with appropriate initial conditions) can perform comparable to more expensive second order methods, especially in the context of complex deep learning models. 
+
+These beneficial properties of momentum can sometimes become even more pronounced by using a slight modification of the classical momentum algorithm called Nesterov Accelerated Gradient (NAG). 
+
+In the NAG algorithm, rather than calculating the gradient at the current parameters, $\nabla_\theta E(\boldsymbol{\theta}_t)$, one calculates the gradient at the expected value of the parameters given our current momentum,   $\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1})$. This yields the NAG update rule
+!bt
+\begin{align}
+\mathbf{v}_{t}&=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber \\
+\boldsymbol{\theta}_{t+1}&= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\end{align}
+!et
+One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\gamma$.
+
+
+!split
+===== Second moment of the gradient =====
+
+
+In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates $\eta_t$
+as a function of time.  As discussed in the context of Newton's
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.
+
+Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and ADAM.
+
+!split
+===== RMS prop =====
+
+In RMS prop, in addition to keeping a running average of the first moment of the gradient, we also keep track of the second moment denoted by $\mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2]$. The update rule for RMS prop is given by
+!bt
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) \\
+\mathbf{s}_t &=\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber \\
+\boldsymbol{\theta}_{t+1}&=&\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\end{align}
+!et
+where $\beta$ controls the averaging time of the second moment and is typically taken to be about $\beta=0.9$, $\eta_t$ is a learning rate typically chosen to be $10^{-3}$, and $\epsilon\sim 10^{-8} $ is a small regularization constant to prevent divergences. Multiplication and division by vectors is understood as an element-wise operation. It is clear from this formula that the learning rate is reduced in directions where the norm of the gradient is consistently large. This greatly speeds up the convergence by allowing us to use a larger learning rate for flat directions.
+
+
+!split
+===== ADAM optimizer =====
+
+A related algorithm is the  ADAM optimizer. In ADAM, we keep a running average of both the first and second moment of the gradient and use this information to adaptively change the learning rate for different parameters. In addition to keeping a running average of the first and second moments of the gradient (i.e. $\mathbf{m}_t=\mathbb{E}[\mathbf{g}_t]$ and $\mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t]$, respectively), ADAM performs an additional bias correction to account for the fact that we are estimating the first two moments of the gradient using a running average (denoted by the hats in the update rule below). The update rule for ADAM is given by (where multiplication and division are once again understood to be element-wise operations below)
+!bt
+\begin{align}
+\mathbf{g}_t &= \nabla_\theta E(\boldsymbol{\theta}) \\
+\mathbf{m}_t &= \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber \\
+\mathbf{s}_t &=\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber \\
+\hat{\mathbf{m}}_t&={\mathbf{m}_t \over 1-\beta_1^t} \nonumber \\
+\hat{\mathbf{s}}_t &={\mathbf{s}_t \over1-\beta_2^t} \nonumber \\
+\boldsymbol{\theta}_{t+1}&=\boldsymbol{\theta}_t - \eta_t { \hat{\mathbf{m}}_t \over \sqrt{\hat{\mathbf{s}}_t} +\epsilon}, \nonumber \\
+\end{align}
+!et
+where $\beta_1$ and $\beta_2$ set the memory lifetime of the first and second moment and are typically taken to be $0.9$ and $0.99$ respectively, and $\eta$ and $\epsilon$ are identical to RMSprop.
+
+Like in RMSprop, the effective step size of a parameter depends on the magnitude of its gradient squared.  To understand this better, let us rewrite this expression in terms of the variance $\boldsymbol{\sigma}_t^2 = \hat{\mathbf{s}}_t - (\hat{\mathbf{m}}_t)^2$. Consider a single parameter $\theta_t$. The update rule for this parameter is given by
+!bt
+\[
+\Delta \theta_{t+1}= -\eta_t { \hat{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+\]
+!et
+
+
+
+
+!split
+===== Practical tips =====
+
+* _Randomize the data when making mini-batches_. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.
+
+* _Transform your inputs_. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the energy matrix is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.
+
+* _Monitor the out-of-sample performance._ Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.
+	
+* _Adaptive optimization methods don't always have good generalization._ Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.
+
+Geron's text, see chapter 11, has several interesting discussions.
+