From 0abaf08d94f6422de3b0908b982560571ab607d2 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Wed, 25 Oct 2023 09:40:54 +0200 Subject: [PATCH] update of exercises week 43 --- .../_build/.doctrees/environment.pickle | Bin 540439 -> 540342 bytes .../_build/.doctrees/exercisesweek43.doctree | Bin 975676 -> 976077 bytes .../_build/.doctrees/week43.doctree | Bin 1488200 -> 1488381 bytes .../html/_sources/exercisesweek43.ipynb | 438 ++++++++----- .../_build/html/_sources/week43.ipynb | 581 ++++++++--------- .../_build/html/exercisesweek43.html | 12 +- doc/LectureNotes/_build/html/searchindex.js | 2 +- doc/LectureNotes/_build/html/week43.html | 14 +- .../jupyter_execute/exercisesweek43.ipynb | 431 +++++++++---- .../_build/jupyter_execute/exercisesweek43.py | 7 +- .../_build/jupyter_execute/week43.ipynb | 599 +++++++++--------- .../_build/jupyter_execute/week43.py | 7 +- doc/LectureNotes/week43.ipynb | 581 ++++++++--------- 13 files changed, 1484 insertions(+), 1188 deletions(-) diff 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zoVtFkB`?{fYVdi>0RtnnVXO6H7a@9^^~i_JOQld>k90ZUz1-)sIc~xMycFPT zb6id`t5*YjN2IWFl{~x@M4wS}eE0Y}?ZX#W_;ykgR``Cf%Vlxf7i@<|c*nSYOms_3 z>>Zur(Iv*>rToC@(+AZF)@$1?h%CTEFwY!Hui;!#a`&smID z*4w&7pP|=HIVZ&IdD;(Eoh+7 zmnwCoNT0K`d zA+4?zPDrbl3)2@1)9b`HgRr?q45jtnVkoUYC%#GR#qCzJez\n", @@ -12,8 +14,10 @@ }, { "cell_type": "markdown", - "id": "77f844d9", - "metadata": {}, + "id": "812b4e46", + "metadata": { + "editable": true + }, "source": [ "# Exercises weeks 43 and 44 \n", "**October 23-27, 2023**\n", @@ -25,8 +29,10 @@ }, { "cell_type": "markdown", - "id": "d5b983e3", - "metadata": {}, + "id": "3230cd2f", + "metadata": { + "editable": true + }, "source": [ "# Overarching aims of the exercises weeks 43 and 44\n", "\n", @@ -63,8 +69,10 @@ }, { "cell_type": "markdown", - "id": "7f6cc12f", - "metadata": {}, + "id": "e3617d4e", + "metadata": { + "editable": true + }, "source": [ "## The AND and XOR Gates\n", "\n", @@ -99,8 +107,10 @@ }, { "cell_type": "markdown", - "id": "c0b07e46", - "metadata": {}, + "id": "54e1e7fc", + "metadata": { + "editable": true + }, "source": [ "## Representing the Data Sets\n", "\n", @@ -109,8 +119,10 @@ }, { "cell_type": "markdown", - "id": "e0a9840a", - "metadata": {}, + "id": "6b3c15cb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}=\\begin{bmatrix} 0 & 0 \\\\\n", @@ -122,8 +134,10 @@ }, { "cell_type": "markdown", - "id": "ff95d379", - "metadata": {}, + "id": "acc25271", + "metadata": { + "editable": true + }, "source": [ "while the vector of outputs is $\\boldsymbol{y}^T=[0,1,1,0]$ for the XOR gate, $\\boldsymbol{y}^T=[0,0,0,1]$ for the AND gate and $\\boldsymbol{y}^T=[0,1,1,1]$ for the OR gate.\n", "\n", @@ -150,8 +164,10 @@ }, { "cell_type": "markdown", - "id": "36fa3466", - "metadata": {}, + "id": "ffe0a840", + "metadata": { + "editable": true + }, "source": [ "## Setting up dimensionalities by hand\n", "\n", @@ -160,8 +176,10 @@ }, { "cell_type": "markdown", - "id": "e2e5e808", - "metadata": {}, + "id": "46abf545", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{W_h}=\\begin{bmatrix} 1 & 1 \\\\\n", @@ -171,16 +189,20 @@ }, { "cell_type": "markdown", - "id": "419e3904", - "metadata": {}, + "id": "86e105cc", + "metadata": { + "editable": true + }, "source": [ "Multiplying $\\boldsymbol{X}$ and $\\boldsymbol{W}$ gives" ] }, { "cell_type": "markdown", - "id": "88a9712a", - "metadata": {}, + "id": "5e1d21f1", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{X}{W}_h=\\begin{bmatrix} 0 & 0 \\\\\n", @@ -192,16 +214,20 @@ }, { "cell_type": "markdown", - "id": "036eee14", - "metadata": {}, + "id": "692c6cbf", + "metadata": { + "editable": true + }, "source": [ "Assume also that the bias vector for the hidden layer is" ] }, { "cell_type": "markdown", - "id": "3c771918", - "metadata": {}, + "id": "5d81e641", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{b}_h=\\begin{bmatrix} 0 \\\\\n", @@ -211,16 +237,20 @@ }, { "cell_type": "markdown", - "id": "f5a4150d", - "metadata": {}, + "id": "a42bdee4", + "metadata": { + "editable": true + }, "source": [ "Adding it gives us the input to the activation function of the hidden layer" ] }, { "cell_type": "markdown", - "id": "e4eb7753", - "metadata": {}, + "id": "5116b854", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{z}_h=\\boldsymbol{X}\\boldsymbol{W}_h+\\boldsymbol{b}_h=\\begin{bmatrix} 0 & -1 \\\\\n", @@ -232,16 +262,20 @@ }, { "cell_type": "markdown", - "id": "b5442b32", - "metadata": {}, + "id": "8dd26d09", + "metadata": { + "editable": true + }, "source": [ "Let us then assume that our activation function is the RELU function, which simply means that we take the max of $0$ and the elements of the input argument $\\boldsymbol{z}_h$, that is we have" ] }, { "cell_type": "markdown", - "id": "64d99f85", - "metadata": {}, + "id": "ebf97c03", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{a}_h=\\mathrm{RELU}(\\boldsymbol{z}_h=\\boldsymbol{X}\\boldsymbol{W}_h+\\boldsymbol{b}_h)=\\begin{bmatrix} 0 & 0 \\\\\n", @@ -253,16 +287,20 @@ }, { "cell_type": "markdown", - "id": "2aee4b6b", - "metadata": {}, + "id": "262a4a3a", + "metadata": { + "editable": true + }, "source": [ "Assume also that the bias of the output layer is zero and that the weights of the output layer are" ] }, { "cell_type": "markdown", - "id": "884541eb", - "metadata": {}, + "id": "f03ad8e7", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{w}_o=\\begin{bmatrix} 1 \\\\\n", @@ -272,37 +310,46 @@ }, { "cell_type": "markdown", - "id": "3999a4d5", - "metadata": {}, + "id": "36fe00c0", + "metadata": { + "editable": true + }, "source": [ "and multiplying with $\\boldsymbol{a}_h$ gives the output" ] }, { "cell_type": "markdown", - "id": "a4896b4d", - "metadata": {}, + "id": "80ab43ac", + "metadata": { + "editable": true + }, "source": [ "$$\n", - "\\boldsymbol{a}_o=\\boldsymbol{w}_h^T\\begin{bmatrix} 0 & 0 \\\\\n", + "\\boldsymbol{a}_o=\\begin{bmatrix} 0 & 0 \\\\\n", " 1 & 0 \\\\\n", "\t\t 1 & 0 \\\\\n", - "\t\t 2 & 1 \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n", + "\t\t 2 & 1 \\end{bmatrix}\\begin{bmatrix} 1 \\\\\n", + " -2\\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n", "$$" ] }, { "cell_type": "markdown", - "id": "2c74e7c0", - "metadata": {}, + "id": "86bcfe49", + "metadata": { + "editable": true + }, "source": [ - "the wanted result." + "the wanted result. Pay attention to the dimensionalities as well." ] }, { "cell_type": "markdown", - "id": "249b9804", - "metadata": {}, + "id": "f19a899e", + "metadata": { + "editable": true + }, "source": [ "## Setting up the Neural Network\n", "\n", @@ -312,8 +359,11 @@ { "cell_type": "code", "execution_count": 1, - "id": "afdd3100", - "metadata": {}, + "id": "901ddca7", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "%matplotlib inline\n", @@ -379,16 +429,20 @@ }, { "cell_type": "markdown", - "id": "fb383164", - "metadata": {}, + "id": "53f22266", + "metadata": { + "editable": true + }, "source": [ "Not an impressive result, but this was our first forward pass with randomly assigned weights. Let us now add the full network with the back-propagation algorithm discussed above." ] }, { "cell_type": "markdown", - "id": "0d26394c", - "metadata": {}, + "id": "5f665ac6", + "metadata": { + "editable": true + }, "source": [ "## The Code using Scikit-Learn" ] @@ -396,8 +450,11 @@ { "cell_type": "code", "execution_count": 2, - "id": "befc368c", - "metadata": {}, + "id": "cb396cda", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# import necessary packages\n", @@ -458,8 +515,10 @@ }, { "cell_type": "markdown", - "id": "03895a9f", - "metadata": {}, + "id": "c5978471", + "metadata": { + "editable": true + }, "source": [ "## Building a neural network code\n", "\n", @@ -475,8 +534,10 @@ }, { "cell_type": "markdown", - "id": "6226915b", - "metadata": {}, + "id": "7b82dc46", + "metadata": { + "editable": true + }, "source": [ "### Learning rate methods\n", "\n", @@ -495,8 +556,11 @@ { "cell_type": "code", "execution_count": 3, - "id": "b6d5ea73", - "metadata": {}, + "id": "de4dedfb", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -633,8 +697,10 @@ }, { "cell_type": "markdown", - "id": "edb42bef", - "metadata": {}, + "id": "bb621fce", + "metadata": { + "editable": true + }, "source": [ "### Usage of the above learning rate schedulers\n", "\n", @@ -647,8 +713,11 @@ { "cell_type": "code", "execution_count": 4, - "id": "108c1209", - "metadata": {}, + "id": "34ddb829", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n", @@ -657,8 +726,10 @@ }, { "cell_type": "markdown", - "id": "d1c423f0", - "metadata": {}, + "id": "e43498d4", + "metadata": { + "editable": true + }, "source": [ "Here is a small example for how a segment of code using schedulers\n", "could look. Switching out the schedulers is simple." @@ -667,8 +738,11 @@ { "cell_type": "code", "execution_count": 5, - "id": "63c8c749", - "metadata": {}, + "id": "f05b9625", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "weights = np.ones((3,3))\n", @@ -686,8 +760,10 @@ }, { "cell_type": "markdown", - "id": "7cb80992", - "metadata": {}, + "id": "19cf9841", + "metadata": { + "editable": true + }, "source": [ "### Cost functions\n", "\n", @@ -700,8 +776,11 @@ { "cell_type": "code", "execution_count": 6, - "id": "a181dacb", - "metadata": {}, + "id": "993efa8d", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -735,8 +814,10 @@ }, { "cell_type": "markdown", - "id": "26a7fe37", - "metadata": {}, + "id": "011c734c", + "metadata": { + "editable": true + }, "source": [ "Below we give a short example of how these cost function may be used\n", "to obtain results if you wish to test them out on your own using\n", @@ -746,8 +827,11 @@ { "cell_type": "code", "execution_count": 7, - "id": "5894bd31", - "metadata": {}, + "id": "9e1b97f5", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "from autograd import grad\n", @@ -764,8 +848,10 @@ }, { "cell_type": "markdown", - "id": "71141fab", - "metadata": {}, + "id": "4acd87b2", + "metadata": { + "editable": true + }, "source": [ "### Activation functions\n", "\n", @@ -778,8 +864,11 @@ { "cell_type": "code", "execution_count": 8, - "id": "433e0886", - "metadata": {}, + "id": "befa86ae", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -833,8 +922,10 @@ }, { "cell_type": "markdown", - "id": "14c9d538", - "metadata": {}, + "id": "c20aa75e", + "metadata": { + "editable": true + }, "source": [ "Below follows a short demonstration of how to use an activation\n", "function. The derivative of the activation function will be important\n", @@ -846,8 +937,11 @@ { "cell_type": "code", "execution_count": 9, - "id": "4c3a44ef", - "metadata": {}, + "id": "e209f9e5", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "z = np.array([[4, 5, 6]]).T\n", @@ -864,8 +958,10 @@ }, { "cell_type": "markdown", - "id": "aa7f604e", - "metadata": {}, + "id": "524b409b", + "metadata": { + "editable": true + }, "source": [ "### The Neural Network\n", "\n", @@ -886,8 +982,11 @@ { "cell_type": "code", "execution_count": 10, - "id": "585a227b", - "metadata": {}, + "id": "083116d3", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import math\n", @@ -1355,8 +1454,10 @@ }, { "cell_type": "markdown", - "id": "7de704af", - "metadata": {}, + "id": "e4ba55d0", + "metadata": { + "editable": true + }, "source": [ "Before we make a model, we will quickly generate a dataset we can use\n", "for our linear regression problem as shown below" @@ -1365,8 +1466,11 @@ { "cell_type": "code", "execution_count": 11, - "id": "212b0a35", - "metadata": {}, + "id": "c72a22c6", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1406,8 +1510,10 @@ }, { "cell_type": "markdown", - "id": "1ff4ec7b", - "metadata": {}, + "id": "25b63b47", + "metadata": { + "editable": true + }, "source": [ "Now that we have our dataset ready for the regression, we can create\n", "our regressor. Note that with the seed parameter, we can make sure our\n", @@ -1420,8 +1526,11 @@ { "cell_type": "code", "execution_count": 12, - "id": "57d8eca3", - "metadata": {}, + "id": "b6b4e461", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "input_nodes = X_train.shape[1]\n", @@ -1432,8 +1541,10 @@ }, { "cell_type": "markdown", - "id": "f1977bae", - "metadata": {}, + "id": "d7860b74", + "metadata": { + "editable": true + }, "source": [ "We then fit our model with our training data using the scheduler of our choice." ] @@ -1441,8 +1552,11 @@ { "cell_type": "code", "execution_count": 13, - "id": "31ae2a1e", - "metadata": {}, + "id": "00522c73", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n", @@ -1453,8 +1567,10 @@ }, { "cell_type": "markdown", - "id": "96a64da4", - "metadata": {}, + "id": "a57bfb12", + "metadata": { + "editable": true + }, "source": [ "Due to the progress bar we can see the MSE (train_error) throughout\n", "the FFNN's training. Note that the fit() function has some optional\n", @@ -1467,8 +1583,11 @@ { "cell_type": "code", "execution_count": 14, - "id": "246499fc", - "metadata": {}, + "id": "35259e41", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n", @@ -1478,8 +1597,10 @@ }, { "cell_type": "markdown", - "id": "61d11e17", - "metadata": {}, + "id": "4a403370", + "metadata": { + "editable": true + }, "source": [ "We see that given more epochs to train on, the regressor reaches a lower MSE.\n", "\n", @@ -1491,8 +1612,11 @@ { "cell_type": "code", "execution_count": 15, - "id": "b5b91899", - "metadata": {}, + "id": "6c791130", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "from sklearn.datasets import load_breast_cancer\n", @@ -1514,8 +1638,11 @@ { "cell_type": "code", "execution_count": 16, - "id": "4bd01b3d", - "metadata": {}, + "id": "0ac0258d", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "input_nodes = X_train.shape[1]\n", @@ -1526,8 +1653,10 @@ }, { "cell_type": "markdown", - "id": "3a138d66", - "metadata": {}, + "id": "a9c74baa", + "metadata": { + "editable": true + }, "source": [ "We will now make use of our validation data by passing it into our fit function as a keyword argument" ] @@ -1535,8 +1664,11 @@ { "cell_type": "code", "execution_count": 17, - "id": "faf1534e", - "metadata": {}, + "id": "e5021bbf", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n", @@ -1547,8 +1679,10 @@ }, { "cell_type": "markdown", - "id": "33d2d346", - "metadata": {}, + "id": "ae0148bb", + "metadata": { + "editable": true + }, "source": [ "Finally, we will create a neural network with 2 hidden layers with activation functions." ] @@ -1556,8 +1690,11 @@ { "cell_type": "code", "execution_count": 18, - "id": "a8f0a61c", - "metadata": {}, + "id": "bb7e4340", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "input_nodes = X_train.shape[1]\n", @@ -1573,8 +1710,11 @@ { "cell_type": "code", "execution_count": 19, - "id": "d651702d", - "metadata": {}, + "id": "d0655afb", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n", @@ -1585,8 +1725,10 @@ }, { "cell_type": "markdown", - "id": "200b64c0", - "metadata": {}, + "id": "dc8a90af", + "metadata": { + "editable": true + }, "source": [ "### Multiclass classification\n", "\n", @@ -1598,8 +1740,11 @@ { "cell_type": "code", "execution_count": 20, - "id": "98b8d59b", - "metadata": {}, + "id": "9305c08a", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "from sklearn.datasets import load_digits\n", @@ -1632,8 +1777,10 @@ }, { "cell_type": "markdown", - "id": "cadd7e47", - "metadata": {}, + "id": "8e208051", + "metadata": { + "editable": true + }, "source": [ "## Testing the XOR gate and other gates\n", "\n", @@ -1643,8 +1790,11 @@ { "cell_type": "code", "execution_count": 21, - "id": "a40e5cfe", - "metadata": {}, + "id": "db016d41", + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n", @@ -1663,32 +1813,16 @@ }, { "cell_type": "markdown", - "id": "b635db73", - "metadata": {}, + "id": "d1384449", + "metadata": { + "editable": true + }, "source": [ "Not bad, but the results depend strongly on the learning reate. Try different learning rates." ] } ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.9.10" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/_sources/week43.ipynb b/doc/LectureNotes/_build/html/_sources/week43.ipynb index 8de3714cd..4c84cfe33 100644 --- a/doc/LectureNotes/_build/html/_sources/week43.ipynb +++ b/doc/LectureNotes/_build/html/_sources/week43.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8d7cc066", + "id": "88f6e253", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "028dc8c6", + "id": "ebd16d73", "metadata": { "editable": true }, @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "15ef2310", + "id": "e9bc94b9", "metadata": { "editable": true }, @@ -73,7 +73,7 @@ }, { "cell_type": "markdown", - "id": "192aa783", + "id": "457d4421", "metadata": { "editable": true }, @@ -87,7 +87,7 @@ }, { "cell_type": "markdown", - "id": "22874f1a", + "id": "e86537af", "metadata": { "editable": true }, @@ -104,7 +104,7 @@ }, { "cell_type": "markdown", - "id": "29c53621", + "id": "14ffcfd0", "metadata": { "editable": true }, @@ -114,7 +114,7 @@ }, { "cell_type": "markdown", - "id": "c3ab8226", + "id": "5773ab41", "metadata": { "editable": true }, @@ -151,7 +151,7 @@ }, { "cell_type": "markdown", - "id": "d686af76", + "id": "fdcb6f1e", "metadata": { "editable": true }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "9e6ae224", + "id": "7bc3e18a", "metadata": { "editable": true }, @@ -201,7 +201,7 @@ }, { "cell_type": "markdown", - "id": "ee5e7e34", + "id": "b82f5167", "metadata": { "editable": true }, @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "da275174", + "id": "1ff6327f", "metadata": { "editable": true }, @@ -246,7 +246,7 @@ }, { "cell_type": "markdown", - "id": "78669a54", + "id": "fd88cb2a", "metadata": { "editable": true }, @@ -258,7 +258,7 @@ }, { "cell_type": "markdown", - "id": "453ff3ab", + "id": "277ccf21", "metadata": { "editable": true }, @@ -271,7 +271,7 @@ }, { "cell_type": "markdown", - "id": "9d82c2f1", + "id": "69024cd6", "metadata": { "editable": true }, @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "a22ab766", + "id": "3739f7f4", "metadata": { "editable": true }, @@ -296,7 +296,7 @@ }, { "cell_type": "markdown", - "id": "abfc4274", + "id": "891fbfbd", "metadata": { "editable": true }, @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "2b7b0970", + "id": "0befa9f2", "metadata": { "editable": true }, @@ -319,7 +319,7 @@ }, { "cell_type": "markdown", - "id": "d1e78b4a", + "id": "8b87520f", "metadata": { "editable": true }, @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "0ee46428", + "id": "0c36a6e9", "metadata": { "editable": true }, @@ -344,7 +344,7 @@ }, { "cell_type": "markdown", - "id": "bac66371", + "id": "6a5ebf2f", "metadata": { "editable": true }, @@ -354,7 +354,7 @@ }, { "cell_type": "markdown", - "id": "77606059", + "id": "5c2cce0f", "metadata": { "editable": true }, @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "b1a1f219", + "id": "6700bff0", "metadata": { "editable": true }, @@ -379,7 +379,7 @@ }, { "cell_type": "markdown", - "id": "a46fd0d7", + "id": "c9deb439", "metadata": { "editable": true }, @@ -392,7 +392,7 @@ }, { "cell_type": "markdown", - "id": "01e41f6f", + "id": "bca3d76a", "metadata": { "editable": true }, @@ -402,32 +402,33 @@ }, { "cell_type": "markdown", - "id": "371a2c47", + "id": "0fd2b2d0", "metadata": { "editable": true }, "source": [ "$$\n", - "\\boldsymbol{a}_o=\\boldsymbol{w}_h^T\\begin{bmatrix} 0 & 0 \\\\\n", + "\\boldsymbol{a}_o=\\begin{bmatrix} 0 & 0 \\\\\n", " 1 & 0 \\\\\n", "\t\t 1 & 0 \\\\\n", - "\t\t 2 & 1 \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n", + "\t\t 2 & 1 \\end{bmatrix}\\begin{bmatrix} 1 \\\\\n", + " -2\\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n", "$$" ] }, { "cell_type": "markdown", - "id": "8ab62ed9", + "id": "aef5937c", "metadata": { "editable": true }, "source": [ - "the wanted result." + "the wanted result. Pay attention to the dimensionalities as well." ] }, { "cell_type": "markdown", - "id": "ee45366d", + "id": "784de267", "metadata": { "editable": true }, @@ -440,7 +441,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "43b32c8a", + "id": "1529f64e", "metadata": { "collapsed": false, "editable": true @@ -510,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "ce3f8d7b", + "id": "6c344985", "metadata": { "editable": true }, @@ -520,7 +521,7 @@ }, { "cell_type": "markdown", - "id": "0a60227f", + "id": "dda91d6e", "metadata": { "editable": true }, @@ -531,7 +532,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "0574c4c7", + "id": "dc12224d", "metadata": { "collapsed": false, "editable": true @@ -596,7 +597,7 @@ }, { "cell_type": "markdown", - "id": "c3db2190", + "id": "7c9b27ed", "metadata": { "editable": true }, @@ -615,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "3b6e8500", + "id": "e8e28114", "metadata": { "editable": true }, @@ -637,7 +638,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "ee32fb88", + "id": "37a2ec80", "metadata": { "collapsed": false, "editable": true @@ -778,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "6477d18f", + "id": "38ea41a5", "metadata": { "editable": true }, @@ -794,7 +795,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "5a396095", + "id": "869cf239", "metadata": { "collapsed": false, "editable": true @@ -807,7 +808,7 @@ }, { "cell_type": "markdown", - "id": "28bd1ab9", + "id": "b9b25144", "metadata": { "editable": true }, @@ -819,7 +820,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "fb5d04e9", + "id": "7d2dc23b", "metadata": { "collapsed": false, "editable": true @@ -841,7 +842,7 @@ }, { "cell_type": "markdown", - "id": "f1229684", + "id": "83b5e35f", "metadata": { "editable": true }, @@ -857,7 +858,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "f4a50c76", + "id": "4c217329", "metadata": { "collapsed": false, "editable": true @@ -895,7 +896,7 @@ }, { "cell_type": "markdown", - "id": "3d646164", + "id": "a0515ac9", "metadata": { "editable": true }, @@ -908,7 +909,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "b0057b55", + "id": "5eb41a10", "metadata": { "collapsed": false, "editable": true @@ -929,7 +930,7 @@ }, { "cell_type": "markdown", - "id": "37f67196", + "id": "0535d6fd", "metadata": { "editable": true }, @@ -945,7 +946,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "ae3c2dad", + "id": "c55d6d5f", "metadata": { "collapsed": false, "editable": true @@ -1003,7 +1004,7 @@ }, { "cell_type": "markdown", - "id": "5be7f268", + "id": "b820a2a1", "metadata": { "editable": true }, @@ -1018,7 +1019,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "5296db7b", + "id": "43974d31", "metadata": { "collapsed": false, "editable": true @@ -1039,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "fa62814a", + "id": "ec754834", "metadata": { "editable": true }, @@ -1063,7 +1064,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "08db6527", + "id": "505e52ab", "metadata": { "collapsed": false, "editable": true @@ -1535,7 +1536,7 @@ }, { "cell_type": "markdown", - "id": "464f4548", + "id": "00aa7046", "metadata": { "editable": true }, @@ -1547,7 +1548,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "ea3d3c51", + "id": "b0b45dd4", "metadata": { "collapsed": false, "editable": true @@ -1591,7 +1592,7 @@ }, { "cell_type": "markdown", - "id": "a6b49446", + "id": "cf9645c3", "metadata": { "editable": true }, @@ -1607,7 +1608,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "4f0f50b6", + "id": "a792c324", "metadata": { "collapsed": false, "editable": true @@ -1622,7 +1623,7 @@ }, { "cell_type": "markdown", - "id": "8ae3f1e4", + "id": "e11ed70e", "metadata": { "editable": true }, @@ -1633,7 +1634,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "4d206fa2", + "id": "dfd03f3c", "metadata": { "collapsed": false, "editable": true @@ -1648,7 +1649,7 @@ }, { "cell_type": "markdown", - "id": "27ffcb75", + "id": "99b1bd91", "metadata": { "editable": true }, @@ -1664,7 +1665,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "8cf19432", + "id": "864038bb", "metadata": { "collapsed": false, "editable": true @@ -1678,7 +1679,7 @@ }, { "cell_type": "markdown", - "id": "97abfa15", + "id": "24d5f3cc", "metadata": { "editable": true }, @@ -1693,7 +1694,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "5aa3cb16", + "id": "14df9a52", "metadata": { "collapsed": false, "editable": true @@ -1719,7 +1720,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "793cb2e9", + "id": "adb3edf2", "metadata": { "collapsed": false, "editable": true @@ -1734,7 +1735,7 @@ }, { "cell_type": "markdown", - "id": "7b47a35a", + "id": "fa885022", "metadata": { "editable": true }, @@ -1745,7 +1746,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "e34123b4", + "id": "1b862f90", "metadata": { "collapsed": false, "editable": true @@ -1760,7 +1761,7 @@ }, { "cell_type": "markdown", - "id": "413243c9", + "id": "e86e60dc", "metadata": { "editable": true }, @@ -1771,7 +1772,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "aa7b9e8f", + "id": "9e578191", "metadata": { "collapsed": false, "editable": true @@ -1791,7 +1792,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "c66ee57f", + "id": "bbfc34f4", "metadata": { "collapsed": false, "editable": true @@ -1806,7 +1807,7 @@ }, { "cell_type": "markdown", - "id": "aca7922f", + "id": "2ac7ad43", "metadata": { "editable": true }, @@ -1821,7 +1822,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "1503f15a", + "id": "f4a821cd", "metadata": { "collapsed": false, "editable": true @@ -1858,7 +1859,7 @@ }, { "cell_type": "markdown", - "id": "838cf72d", + "id": "0fcf8bf2", "metadata": { "editable": true }, @@ -1871,7 +1872,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "a4444105", + "id": "d91608cf", "metadata": { "collapsed": false, "editable": true @@ -1894,7 +1895,7 @@ }, { "cell_type": "markdown", - "id": "8bbdf09c", + "id": "494009be", "metadata": { "editable": true }, @@ -1904,7 +1905,7 @@ }, { "cell_type": "markdown", - "id": "c5cffe73", + "id": "db70a4fe", "metadata": { "editable": true }, @@ -1914,7 +1915,7 @@ }, { "cell_type": "markdown", - "id": "e88dc6ab", + "id": "e5fc9732", "metadata": { "editable": true }, @@ -1943,7 +1944,7 @@ }, { "cell_type": "markdown", - "id": "8ec227a0", + "id": "1f986c86", "metadata": { "editable": true }, @@ -1993,7 +1994,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "5336138a", + "id": "0f845fb5", "metadata": { "collapsed": false, "editable": true @@ -2046,7 +2047,7 @@ }, { "cell_type": "markdown", - "id": "da4f9c76", + "id": "fbab1656", "metadata": { "editable": true }, @@ -2067,7 +2068,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "3d4a38d4", + "id": "3ecd3028", "metadata": { "collapsed": false, "editable": true @@ -2105,7 +2106,7 @@ }, { "cell_type": "markdown", - "id": "bc7c43bb", + "id": "b45412df", "metadata": { "editable": true }, @@ -2149,7 +2150,7 @@ }, { "cell_type": "markdown", - "id": "60a15786", + "id": "e90b1e65", "metadata": { "editable": true }, @@ -2189,7 +2190,7 @@ }, { "cell_type": "markdown", - "id": "d9b2c952", + "id": "92bff738", "metadata": { "editable": true }, @@ -2210,7 +2211,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "a6dfcaaf", + "id": "8eb225e4", "metadata": { "collapsed": false, "editable": true @@ -2236,7 +2237,7 @@ }, { "cell_type": "markdown", - "id": "623ec89c", + "id": "da1e7ad6", "metadata": { "editable": true }, @@ -2264,7 +2265,7 @@ }, { "cell_type": "markdown", - "id": "391b8f09", + "id": "52ea3780", "metadata": { "editable": true }, @@ -2301,7 +2302,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "a3a7a56e", + "id": "8ec12507", "metadata": { "collapsed": false, "editable": true @@ -2347,7 +2348,7 @@ }, { "cell_type": "markdown", - "id": "6a467f9c", + "id": "518a6c33", "metadata": { "editable": true }, @@ -2378,7 +2379,7 @@ }, { "cell_type": "markdown", - "id": "824f2150", + "id": "9e4fe561", "metadata": { "editable": true }, @@ -2416,7 +2417,7 @@ }, { "cell_type": "markdown", - "id": "ad801a4f", + "id": "331db754", "metadata": { "editable": true }, @@ -2450,7 +2451,7 @@ }, { "cell_type": "markdown", - "id": "adbd5bf5", + "id": "94f8797f", "metadata": { "editable": true }, @@ -2491,7 +2492,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "03850373", + "id": "6cc0ad5a", "metadata": { "collapsed": false, "editable": true @@ -2570,7 +2571,7 @@ }, { "cell_type": "markdown", - "id": "5c4ce702", + "id": "66341fe5", "metadata": { "editable": true }, @@ -2591,7 +2592,7 @@ }, { "cell_type": "markdown", - "id": "f54c055f", + "id": "4654bdd2", "metadata": { "editable": true }, @@ -2605,7 +2606,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "05fadefb", + "id": "84200c9e", "metadata": { "collapsed": false, "editable": true @@ -2715,7 +2716,7 @@ }, { "cell_type": "markdown", - "id": "6d6bba32", + "id": "2fade818", "metadata": { "editable": true }, @@ -2734,7 +2735,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "5605c90f", + "id": "da2d74fa", "metadata": { "collapsed": false, "editable": true @@ -2761,7 +2762,7 @@ }, { "cell_type": "markdown", - "id": "f22bb889", + "id": "45f911b8", "metadata": { "editable": true }, @@ -2775,7 +2776,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "a097c9e1", + "id": "b21a2c19", "metadata": { "collapsed": false, "editable": true @@ -2806,7 +2807,7 @@ }, { "cell_type": "markdown", - "id": "bc02f298", + "id": "80801250", "metadata": { "editable": true }, @@ -2817,7 +2818,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "970ba03e", + "id": "303e085a", "metadata": { "collapsed": false, "editable": true @@ -2861,7 +2862,7 @@ }, { "cell_type": "markdown", - "id": "e4ff0700", + "id": "9358790a", "metadata": { "editable": true }, @@ -2884,7 +2885,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "8bc77d1c", + "id": "a238def8", "metadata": { "collapsed": false, "editable": true @@ -2911,7 +2912,7 @@ }, { "cell_type": "markdown", - "id": "76d38bcf", + "id": "2ef943ac", "metadata": { "editable": true }, @@ -2922,7 +2923,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "d22894cb", + "id": "afeabf8f", "metadata": { "collapsed": false, "editable": true @@ -2967,7 +2968,7 @@ }, { "cell_type": "markdown", - "id": "d4efa31d", + "id": "3dd5dfb4", "metadata": { "editable": true }, @@ -2985,7 +2986,7 @@ }, { "cell_type": "markdown", - "id": "d6caddb7", + "id": "72754d13", "metadata": { "editable": true }, @@ -3020,7 +3021,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "96f112a6", + "id": "9fc42ba6", "metadata": { "collapsed": false, "editable": true @@ -3032,7 +3033,7 @@ }, { "cell_type": "markdown", - "id": "2dee5b42", + "id": "35795551", "metadata": { "editable": true }, @@ -3044,7 +3045,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "29e13f69", + "id": "1dabca19", "metadata": { "collapsed": false, "editable": true @@ -3057,7 +3058,7 @@ }, { "cell_type": "markdown", - "id": "4695192d", + "id": "be829505", "metadata": { "editable": true }, @@ -3068,7 +3069,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "573fade6", + "id": "7d92ce1c", "metadata": { "collapsed": false, "editable": true @@ -3081,7 +3082,7 @@ }, { "cell_type": "markdown", - "id": "0d8ced47", + "id": "057049d7", "metadata": { "editable": true }, @@ -3096,7 +3097,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "28886e64", + "id": "0837641b", "metadata": { "collapsed": false, "editable": true @@ -3108,7 +3109,7 @@ }, { "cell_type": "markdown", - "id": "298e5186", + "id": "19d5a72d", "metadata": { "editable": true }, @@ -3120,7 +3121,7 @@ }, { "cell_type": "markdown", - "id": "ea131902", + "id": "4ae0b49b", "metadata": { "editable": true }, @@ -3133,7 +3134,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "686215bb", + "id": "429afe53", "metadata": { "collapsed": false, "editable": true @@ -3188,7 +3189,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "fa9efbca", + "id": "887c06b9", "metadata": { "collapsed": false, "editable": true @@ -3217,7 +3218,7 @@ { "cell_type": "code", "execution_count": 39, - "id": "5a6a0547", + "id": "a4d8f64e", "metadata": { "collapsed": false, "editable": true @@ -3247,7 +3248,7 @@ { "cell_type": "code", "execution_count": 40, - "id": "9df608ec", + "id": "b8fb8fa0", "metadata": { "collapsed": false, "editable": true @@ -3274,7 +3275,7 @@ { "cell_type": "code", "execution_count": 41, - "id": "8d20fdf7", + "id": "7777faa8", "metadata": { "collapsed": false, "editable": true @@ -3316,7 +3317,7 @@ }, { "cell_type": "markdown", - "id": "bd641a2a", + "id": "bb6d1d3e", "metadata": { "editable": true }, @@ -3327,7 +3328,7 @@ { "cell_type": "code", "execution_count": 42, - "id": "a6d8bf75", + "id": "d8c0caf4", "metadata": { "collapsed": false, "editable": true @@ -3504,7 +3505,7 @@ }, { "cell_type": "markdown", - "id": "505033e6", + "id": "2631b51d", "metadata": { "editable": true }, @@ -3532,7 +3533,7 @@ }, { "cell_type": "markdown", - "id": "d138fcf8", + "id": "357644b3", "metadata": { "editable": true }, @@ -3555,7 +3556,7 @@ }, { "cell_type": "markdown", - "id": "df986885", + "id": "06854c7f", "metadata": { "editable": true }, @@ -3586,7 +3587,7 @@ }, { "cell_type": "markdown", - "id": "67ccb46b", + "id": "bb26a6da", "metadata": { "editable": true }, @@ -3618,7 +3619,7 @@ }, { "cell_type": "markdown", - "id": "a043bdea", + "id": "0277931e", "metadata": { "editable": true }, @@ -3656,7 +3657,7 @@ }, { "cell_type": "markdown", - "id": "ac370685", + "id": "93a45265", "metadata": { "editable": true }, @@ -3681,7 +3682,7 @@ }, { "cell_type": "markdown", - "id": "68411972", + "id": "7feb8c33", "metadata": { "editable": true }, @@ -3693,7 +3694,7 @@ }, { "cell_type": "markdown", - "id": "68d05dd2", + "id": "1f55cf23", "metadata": { "editable": true }, @@ -3716,7 +3717,7 @@ }, { "cell_type": "markdown", - "id": "55c89a89", + "id": "7cea0ca3", "metadata": { "editable": true }, @@ -3736,7 +3737,7 @@ }, { "cell_type": "markdown", - "id": "20f0b6de", + "id": "086014d5", "metadata": { "editable": true }, @@ -3758,7 +3759,7 @@ }, { "cell_type": "markdown", - "id": "8f0a4e60", + "id": "9bc419af", "metadata": { "editable": true }, @@ -3776,7 +3777,7 @@ }, { "cell_type": "markdown", - "id": "ee9f6778", + "id": "a9198ed4", "metadata": { "editable": true }, @@ -3795,7 +3796,7 @@ }, { "cell_type": "markdown", - "id": "8ec34edc", + "id": "75c023d8", "metadata": { "editable": true }, @@ -3807,7 +3808,7 @@ }, { "cell_type": "markdown", - "id": "4cb4f14f", + "id": "2d2e4666", "metadata": { "editable": true }, @@ -3852,7 +3853,7 @@ }, { "cell_type": "markdown", - "id": "3ceba030", + "id": "23dc45c2", "metadata": { "editable": true }, @@ -3882,7 +3883,7 @@ }, { "cell_type": "markdown", - "id": "fad4c7c0", + "id": "8d80aba5", "metadata": { "editable": true }, @@ -3909,7 +3910,7 @@ }, { "cell_type": "markdown", - "id": "92edec9a", + "id": "b8d6cf49", "metadata": { "editable": true }, @@ -3923,7 +3924,7 @@ }, { "cell_type": "markdown", - "id": "07153151", + "id": "ba566ae5", "metadata": { "editable": true }, @@ -3940,7 +3941,7 @@ }, { "cell_type": "markdown", - "id": "31a707ec", + "id": "fddca9d2", "metadata": { "editable": true }, @@ -3956,7 +3957,7 @@ }, { "cell_type": "markdown", - "id": "d0cbacbc", + "id": "11ed9eb7", "metadata": { "editable": true }, @@ -3968,7 +3969,7 @@ }, { "cell_type": "markdown", - "id": "88e6378a", + "id": "ab228680", "metadata": { "editable": true }, @@ -3986,7 +3987,7 @@ }, { "cell_type": "markdown", - "id": "a85abfe5", + "id": "a620d020", "metadata": { "editable": true }, @@ -4007,7 +4008,7 @@ }, { "cell_type": "markdown", - "id": "28e312e0", + "id": "4de72e77", "metadata": { "editable": true }, @@ -4024,7 +4025,7 @@ }, { "cell_type": "markdown", - "id": "7e562a52", + "id": "60ef63bb", "metadata": { "editable": true }, @@ -4036,7 +4037,7 @@ }, { "cell_type": "markdown", - "id": "ca872cb5", + "id": "6c719d5b", "metadata": { "editable": true }, @@ -4047,7 +4048,7 @@ }, { "cell_type": "markdown", - "id": "3f5aaf97", + "id": "3a6248cc", "metadata": { "editable": true }, @@ -4064,7 +4065,7 @@ }, { "cell_type": "markdown", - "id": "ea91ec87", + "id": "937fbb4d", "metadata": { "editable": true }, @@ -4075,7 +4076,7 @@ }, { "cell_type": "markdown", - "id": "23d4791e", + "id": "985098ad", "metadata": { "editable": true }, @@ -4091,7 +4092,7 @@ }, { "cell_type": "markdown", - "id": "645d3042", + "id": "7a2ade22", "metadata": { "editable": true }, @@ -4103,7 +4104,7 @@ }, { "cell_type": "markdown", - "id": "1957cac1", + "id": "4b50fe09", "metadata": { "editable": true }, @@ -4120,7 +4121,7 @@ }, { "cell_type": "markdown", - "id": "7ba994c2", + "id": "310ac762", "metadata": { "editable": true }, @@ -4132,7 +4133,7 @@ }, { "cell_type": "markdown", - "id": "0b4d1e86", + "id": "8ce2620f", "metadata": { "editable": true }, @@ -4150,7 +4151,7 @@ }, { "cell_type": "markdown", - "id": "7c000d4f", + "id": "78459d15", "metadata": { "editable": true }, @@ -4160,7 +4161,7 @@ }, { "cell_type": "markdown", - "id": "5c6e9896", + "id": "d40f94e2", "metadata": { "editable": true }, @@ -4172,7 +4173,7 @@ }, { "cell_type": "markdown", - "id": "c610b5a3", + "id": "c5f2c97d", "metadata": { "editable": true }, @@ -4189,7 +4190,7 @@ }, { "cell_type": "markdown", - "id": "7b156ba0", + "id": "bb30f7cc", "metadata": { "editable": true }, @@ -4201,7 +4202,7 @@ }, { "cell_type": "markdown", - "id": "6332b4fb", + "id": "a5d8512c", "metadata": { "editable": true }, @@ -4212,7 +4213,7 @@ }, { "cell_type": "markdown", - "id": "dadb48a5", + "id": "1c888249", "metadata": { "editable": true }, @@ -4224,7 +4225,7 @@ }, { "cell_type": "markdown", - "id": "14979de9", + "id": "477dada7", "metadata": { "editable": true }, @@ -4234,7 +4235,7 @@ }, { "cell_type": "markdown", - "id": "b15978ac", + "id": "8e5e2b68", "metadata": { "editable": true }, @@ -4254,7 +4255,7 @@ }, { "cell_type": "markdown", - "id": "ab70d7dc", + "id": "84150e8d", "metadata": { "editable": true }, @@ -4271,7 +4272,7 @@ }, { "cell_type": "markdown", - "id": "3158ad88", + "id": "3f25aabb", "metadata": { "editable": true }, @@ -4290,7 +4291,7 @@ }, { "cell_type": "markdown", - "id": "424ea4cd", + "id": "ce6c0a98", "metadata": { "editable": true }, @@ -4302,7 +4303,7 @@ }, { "cell_type": "markdown", - "id": "9875f210", + "id": "17805209", "metadata": { "editable": true }, @@ -4312,7 +4313,7 @@ }, { "cell_type": "markdown", - "id": "c317c081", + "id": "f9984101", "metadata": { "editable": true }, @@ -4329,7 +4330,7 @@ }, { "cell_type": "markdown", - "id": "850d7062", + "id": "4abcf7b3", "metadata": { "editable": true }, @@ -4339,7 +4340,7 @@ }, { "cell_type": "markdown", - "id": "05b6c21e", + "id": "3a4b99d7", "metadata": { "editable": true }, @@ -4355,7 +4356,7 @@ }, { "cell_type": "markdown", - "id": "52090d6f", + "id": "261d5f57", "metadata": { "editable": true }, @@ -4367,7 +4368,7 @@ }, { "cell_type": "markdown", - "id": "f4f56b6e", + "id": "0c7e0ed7", "metadata": { "editable": true }, @@ -4379,7 +4380,7 @@ }, { "cell_type": "markdown", - "id": "e76317e2", + "id": "410091f0", "metadata": { "editable": true }, @@ -4391,7 +4392,7 @@ }, { "cell_type": "markdown", - "id": "cf1ff27d", + "id": "17f0e1e7", "metadata": { "editable": true }, @@ -4401,7 +4402,7 @@ }, { "cell_type": "markdown", - "id": "c6558ca7", + "id": "acac4ddf", "metadata": { "editable": true }, @@ -4413,7 +4414,7 @@ }, { "cell_type": "markdown", - "id": "eb10b3cf", + "id": "0b3bdcec", "metadata": { "editable": true }, @@ -4430,7 +4431,7 @@ }, { "cell_type": "markdown", - "id": "95040138", + "id": "8b71f89e", "metadata": { "editable": true }, @@ -4440,7 +4441,7 @@ }, { "cell_type": "markdown", - "id": "efbb37df", + "id": "b1a4b8b2", "metadata": { "editable": true }, @@ -4452,7 +4453,7 @@ }, { "cell_type": "markdown", - "id": "ce339463", + "id": "bb3f35b1", "metadata": { "editable": true }, @@ -4466,7 +4467,7 @@ }, { "cell_type": "markdown", - "id": "51d1021d", + "id": "bb8eac7a", "metadata": { "editable": true }, @@ -4482,7 +4483,7 @@ }, { "cell_type": "markdown", - "id": "5471c13f", + "id": "23361eba", "metadata": { "editable": true }, @@ -4494,7 +4495,7 @@ }, { "cell_type": "markdown", - "id": "ca1015ba", + "id": "94bf3ada", "metadata": { "editable": true }, @@ -4516,7 +4517,7 @@ }, { "cell_type": "markdown", - "id": "325048d9", + "id": "ff0afe4b", "metadata": { "editable": true }, @@ -4528,7 +4529,7 @@ }, { "cell_type": "markdown", - "id": "5c6b185f", + "id": "393ee959", "metadata": { "editable": true }, @@ -4551,7 +4552,7 @@ }, { "cell_type": "markdown", - "id": "eddea0e3", + "id": "f2df5cfc", "metadata": { "editable": true }, @@ -4567,7 +4568,7 @@ }, { "cell_type": "markdown", - "id": "39eeb7a1", + "id": "f6358bb7", "metadata": { "editable": true }, @@ -4579,7 +4580,7 @@ }, { "cell_type": "markdown", - "id": "25477c00", + "id": "ef56bb84", "metadata": { "editable": true }, @@ -4603,7 +4604,7 @@ }, { "cell_type": "markdown", - "id": "dbdce765", + "id": "acd41944", "metadata": { "editable": true }, @@ -4615,7 +4616,7 @@ }, { "cell_type": "markdown", - "id": "3b833783", + "id": "1a2a7e92", "metadata": { "editable": true }, @@ -4636,7 +4637,7 @@ }, { "cell_type": "markdown", - "id": "98103cac", + "id": "a082637c", "metadata": { "editable": true }, @@ -4648,7 +4649,7 @@ }, { "cell_type": "markdown", - "id": "01de1e28", + "id": "dfc24dff", "metadata": { "editable": true }, @@ -4667,7 +4668,7 @@ }, { "cell_type": "markdown", - "id": "3d50cf6a", + "id": "90f81e55", "metadata": { "editable": true }, @@ -4677,7 +4678,7 @@ }, { "cell_type": "markdown", - "id": "221269b0", + "id": "3693fc3b", "metadata": { "editable": true }, @@ -4691,7 +4692,7 @@ }, { "cell_type": "markdown", - "id": "b736af88", + "id": "2bb540dd", "metadata": { "editable": true }, @@ -4703,7 +4704,7 @@ }, { "cell_type": "markdown", - "id": "ea505169", + "id": "5fad7cc5", "metadata": { "editable": true }, @@ -4715,7 +4716,7 @@ }, { "cell_type": "markdown", - "id": "515470a3", + "id": "c9a47e0a", "metadata": { "editable": true }, @@ -4732,7 +4733,7 @@ }, { "cell_type": "markdown", - "id": "f9eaeace", + "id": "f579f1d0", "metadata": { "editable": true }, @@ -4744,7 +4745,7 @@ }, { "cell_type": "markdown", - "id": "e6488f9b", + "id": "f980cb6a", "metadata": { "editable": true }, @@ -4766,7 +4767,7 @@ }, { "cell_type": "markdown", - "id": "f2bc476e", + "id": "de47a73d", "metadata": { "editable": true }, @@ -4781,7 +4782,7 @@ }, { "cell_type": "markdown", - "id": "2d7b7d19", + "id": "5eacb34e", "metadata": { "editable": true }, @@ -4792,7 +4793,7 @@ { "cell_type": "code", "execution_count": 43, - "id": "4aad6e10", + "id": "77235f88", "metadata": { "collapsed": false, "editable": true @@ -4947,7 +4948,7 @@ }, { "cell_type": "markdown", - "id": "f8c418c1", + "id": "0147790d", "metadata": { "editable": true }, @@ -4962,7 +4963,7 @@ { "cell_type": "code", "execution_count": 44, - "id": "96758ada", + "id": "59eb96af", "metadata": { "collapsed": false, "editable": true @@ -5131,7 +5132,7 @@ }, { "cell_type": "markdown", - "id": "c62fedb8", + "id": "dc02c291", "metadata": { "editable": true }, @@ -5144,7 +5145,7 @@ }, { "cell_type": "markdown", - "id": "1f962431", + "id": "c8fff51e", "metadata": { "editable": true }, @@ -5161,7 +5162,7 @@ }, { "cell_type": "markdown", - "id": "71b1d885", + "id": "3751edf7", "metadata": { "editable": true }, @@ -5177,7 +5178,7 @@ }, { "cell_type": "markdown", - "id": "0b96a028", + "id": "a502c731", "metadata": { "editable": true }, @@ -5190,7 +5191,7 @@ }, { "cell_type": "markdown", - "id": "311ae3d3", + "id": "eb73f07e", "metadata": { "editable": true }, @@ -5207,7 +5208,7 @@ }, { "cell_type": "markdown", - "id": "98cb3d44", + "id": "9ab9d930", "metadata": { "editable": true }, @@ -5219,7 +5220,7 @@ }, { "cell_type": "markdown", - "id": "3e8e134d", + "id": "9cb8689a", "metadata": { "editable": true }, @@ -5246,7 +5247,7 @@ }, { "cell_type": "markdown", - "id": "a1844ff9", + "id": "d21e3a14", "metadata": { "editable": true }, @@ -5259,7 +5260,7 @@ { "cell_type": "code", "execution_count": 45, - "id": "4410b99e", + "id": "833da16b", "metadata": { "collapsed": false, "editable": true @@ -5433,7 +5434,7 @@ }, { "cell_type": "markdown", - "id": "f0ab0e0f", + "id": "0fdcf8c5", "metadata": { "editable": true }, @@ -5453,7 +5454,7 @@ }, { "cell_type": "markdown", - "id": "333b0a8d", + "id": "0a057338", "metadata": { "editable": true }, @@ -5468,7 +5469,7 @@ }, { "cell_type": "markdown", - "id": "5b358fbf", + "id": "6721bcf2", "metadata": { "editable": true }, @@ -5482,7 +5483,7 @@ }, { "cell_type": "markdown", - "id": "c5d60864", + "id": "dc3db9fd", "metadata": { "editable": true }, @@ -5498,7 +5499,7 @@ }, { "cell_type": "markdown", - "id": "bcce6eb8", + "id": "9af3fd6a", "metadata": { "editable": true }, @@ -5508,7 +5509,7 @@ }, { "cell_type": "markdown", - "id": "e6497fd7", + "id": "4c2da445", "metadata": { "editable": true }, @@ -5530,7 +5531,7 @@ }, { "cell_type": "markdown", - "id": "31b650fc", + "id": "93b58380", "metadata": { "editable": true }, @@ -5544,7 +5545,7 @@ { "cell_type": "code", "execution_count": 46, - "id": "6e267e72", + "id": "cb73915d", "metadata": { "collapsed": false, "editable": true @@ -5620,7 +5621,7 @@ }, { "cell_type": "markdown", - "id": "8b054a85", + "id": "c9d250c7", "metadata": { "editable": true }, @@ -5632,7 +5633,7 @@ }, { "cell_type": "markdown", - "id": "f637dd9d", + "id": "0d67bc8c", "metadata": { "editable": true }, @@ -5649,7 +5650,7 @@ }, { "cell_type": "markdown", - "id": "ac088e86", + "id": "fe4ee5a8", "metadata": { "editable": true }, @@ -5661,7 +5662,7 @@ }, { "cell_type": "markdown", - "id": "14afd7fa", + "id": "62b400ca", "metadata": { "editable": true }, @@ -5676,7 +5677,7 @@ }, { "cell_type": "markdown", - "id": "0a2680eb", + "id": "7d4723f2", "metadata": { "editable": true }, @@ -5688,7 +5689,7 @@ }, { "cell_type": "markdown", - "id": "7e30575f", + "id": "97889b0e", "metadata": { "editable": true }, @@ -5700,7 +5701,7 @@ }, { "cell_type": "markdown", - "id": "3b30e08a", + "id": "236028bc", "metadata": { "editable": true }, @@ -5712,7 +5713,7 @@ }, { "cell_type": "markdown", - "id": "be7d958b", + "id": "a4334818", "metadata": { "editable": true }, @@ -5722,7 +5723,7 @@ }, { "cell_type": "markdown", - "id": "d6a52e39", + "id": "8330dd77", "metadata": { "editable": true }, @@ -5739,7 +5740,7 @@ }, { "cell_type": "markdown", - "id": "488d0a14", + "id": "78522018", "metadata": { "editable": true }, @@ -5751,7 +5752,7 @@ }, { "cell_type": "markdown", - "id": "59834674", + "id": "943956e4", "metadata": { "editable": true }, @@ -5763,7 +5764,7 @@ }, { "cell_type": "markdown", - "id": "af640638", + "id": "3c7b57e2", "metadata": { "editable": true }, @@ -5773,7 +5774,7 @@ }, { "cell_type": "markdown", - "id": "8d83ea23", + "id": "55173c99", "metadata": { "editable": true }, @@ -5785,7 +5786,7 @@ }, { "cell_type": "markdown", - "id": "4d4e4ea8", + "id": "a6d078e4", "metadata": { "editable": true }, @@ -5796,7 +5797,7 @@ { "cell_type": "code", "execution_count": 47, - "id": "ad4cc32f", + "id": "452c599c", "metadata": { "collapsed": false, "editable": true @@ -5957,7 +5958,7 @@ }, { "cell_type": "markdown", - "id": "ceb283ce", + "id": "8ca2348f", "metadata": { "editable": true }, @@ -5979,7 +5980,7 @@ }, { "cell_type": "markdown", - "id": "a68e0e56", + "id": "0ccc174e", "metadata": { "editable": true }, @@ -5996,7 +5997,7 @@ }, { "cell_type": "markdown", - "id": "8441e4e6", + "id": "d4601257", "metadata": { "editable": true }, @@ -6006,7 +6007,7 @@ }, { "cell_type": "markdown", - "id": "1d343e68", + "id": "9ec01889", "metadata": { "editable": true }, @@ -6021,7 +6022,7 @@ }, { "cell_type": "markdown", - "id": "1c566531", + "id": "71993d6c", "metadata": { "editable": true }, @@ -6031,7 +6032,7 @@ }, { "cell_type": "markdown", - "id": "7a06b755", + "id": "f6acfae4", "metadata": { "editable": true }, @@ -6046,7 +6047,7 @@ }, { "cell_type": "markdown", - "id": "2e88c504", + "id": "6540422f", "metadata": { "editable": true }, @@ -6057,7 +6058,7 @@ }, { "cell_type": "markdown", - "id": "7299b0d3", + "id": "fd8c2326", "metadata": { "editable": true }, @@ -6077,7 +6078,7 @@ }, { "cell_type": "markdown", - "id": "c849f0cc", + "id": "74eabad7", "metadata": { "editable": true }, @@ -6089,7 +6090,7 @@ }, { "cell_type": "markdown", - "id": "f19b2ed7", + "id": "f9d16e2f", "metadata": { "editable": true }, @@ -6126,7 +6127,7 @@ }, { "cell_type": "markdown", - "id": "96581350", + "id": "68c24098", "metadata": { "editable": true }, @@ -6136,7 +6137,7 @@ }, { "cell_type": "markdown", - "id": "2c5aa09d", + "id": "02c1e06d", "metadata": { "editable": true }, @@ -6149,7 +6150,7 @@ { "cell_type": "code", "execution_count": 48, - "id": "9b979206", + "id": "972b8e94", "metadata": { "collapsed": false, "editable": true @@ -6350,7 +6351,7 @@ }, { "cell_type": "markdown", - "id": "ec7cab35", + "id": "734d97bc", "metadata": { "editable": true }, @@ -6367,7 +6368,7 @@ }, { "cell_type": "markdown", - "id": "7366658f", + "id": "2c2d0e2c", "metadata": { "editable": true }, @@ -6384,7 +6385,7 @@ }, { "cell_type": "markdown", - "id": "b6557284", + "id": "9de00307", "metadata": { "editable": true }, @@ -6394,7 +6395,7 @@ }, { "cell_type": "markdown", - "id": "df2d7d07", + "id": "cb659253", "metadata": { "editable": true }, @@ -6409,7 +6410,7 @@ }, { "cell_type": "markdown", - "id": "aad0506a", + "id": "909d23ae", "metadata": { "editable": true }, @@ -6423,7 +6424,7 @@ }, { "cell_type": "markdown", - "id": "9e5776d1", + "id": "e3607f9e", "metadata": { "editable": true }, @@ -6436,7 +6437,7 @@ }, { "cell_type": "markdown", - "id": "7fad71c5", + "id": "e0254d92", "metadata": { "editable": true }, @@ -6456,7 +6457,7 @@ }, { "cell_type": "markdown", - "id": "d98bd52b", + "id": "7a787737", "metadata": { "editable": true }, @@ -6468,7 +6469,7 @@ }, { "cell_type": "markdown", - "id": "3f6cb731", + "id": "42cfda53", "metadata": { "editable": true }, @@ -6480,7 +6481,7 @@ }, { "cell_type": "markdown", - "id": "0efeb6a7", + "id": "41fdd74a", "metadata": { "editable": true }, @@ -6492,7 +6493,7 @@ }, { "cell_type": "markdown", - "id": "b3367fd8", + "id": "9a43a5c3", "metadata": { "editable": true }, @@ -6502,7 +6503,7 @@ }, { "cell_type": "markdown", - "id": "f5cdf037", + "id": "2deb98de", "metadata": { "editable": true }, @@ -6514,7 +6515,7 @@ }, { "cell_type": "markdown", - "id": "39090b0c", + "id": "367f7d4b", "metadata": { "editable": true }, @@ -6526,7 +6527,7 @@ }, { "cell_type": "markdown", - "id": "306f52ce", + "id": "4ace8d41", "metadata": { "editable": true }, @@ -6538,7 +6539,7 @@ }, { "cell_type": "markdown", - "id": "4dddd0e4", + "id": "014d9b72", "metadata": { "editable": true }, @@ -6548,7 +6549,7 @@ }, { "cell_type": "markdown", - "id": "19ba57a3", + "id": "91cb0d4f", "metadata": { "editable": true }, @@ -6564,7 +6565,7 @@ }, { "cell_type": "markdown", - "id": "3f4b369e", + "id": "7015c1df", "metadata": { "editable": true }, @@ -6574,7 +6575,7 @@ }, { "cell_type": "markdown", - "id": "01054c66", + "id": "a170f9bf", "metadata": { "editable": true }, @@ -6586,7 +6587,7 @@ }, { "cell_type": "markdown", - "id": "48250dfa", + "id": "f79c87b0", "metadata": { "editable": true }, @@ -6603,7 +6604,7 @@ }, { "cell_type": "markdown", - "id": "830538cd", + "id": "7b00c2c7", "metadata": { "editable": true }, @@ -6613,7 +6614,7 @@ }, { "cell_type": "markdown", - "id": "1e05f3d1", + "id": "1da2ec1f", "metadata": { "editable": true }, @@ -6629,7 +6630,7 @@ }, { "cell_type": "markdown", - "id": "278b7644", + "id": "d048b2b0", "metadata": { "editable": true }, @@ -6643,7 +6644,7 @@ }, { "cell_type": "markdown", - "id": "08bf068d", + "id": "2a5423c6", "metadata": { "editable": true }, @@ -6662,7 +6663,7 @@ { "cell_type": "code", "execution_count": 49, - "id": "fb15b704", + "id": "39978a3f", "metadata": { "collapsed": false, "editable": true @@ -6717,7 +6718,7 @@ }, { "cell_type": "markdown", - "id": "ca43eaaa", + "id": "d86acd9a", "metadata": { "editable": true }, @@ -6747,7 +6748,7 @@ }, { "cell_type": "markdown", - "id": "8cb99e50", + "id": "219af542", "metadata": { "editable": true }, @@ -6776,7 +6777,7 @@ { "cell_type": "code", "execution_count": 50, - "id": "2c311458", + "id": "0300f83e", "metadata": { "collapsed": false, "editable": true @@ -6823,7 +6824,7 @@ }, { "cell_type": "markdown", - "id": "6ce6fcdb", + "id": "63ff2d7d", "metadata": { "editable": true }, @@ -6849,7 +6850,7 @@ { "cell_type": "code", "execution_count": 51, - "id": "975ad28f", + "id": "504a8a89", "metadata": { "collapsed": false, "editable": true @@ -7083,7 +7084,7 @@ }, { "cell_type": "markdown", - "id": "a85b7bc6", + "id": "2154560c", "metadata": { "editable": true }, @@ -7095,7 +7096,7 @@ }, { "cell_type": "markdown", - "id": "913742fb", + "id": "36990efc", "metadata": { "editable": true }, @@ -7107,7 +7108,7 @@ }, { "cell_type": "markdown", - "id": "9b936d66", + "id": "d4e6e7d4", "metadata": { "editable": true }, @@ -7119,7 +7120,7 @@ }, { "cell_type": "markdown", - "id": "a0cd719f", + "id": "cca6cfed", "metadata": { "editable": true }, @@ -7136,7 +7137,7 @@ }, { "cell_type": "markdown", - "id": "8a8ddb73", + "id": "19f73071", "metadata": { "editable": true }, @@ -7146,7 +7147,7 @@ }, { "cell_type": "markdown", - "id": "460bb8e2", + "id": "3e637804", "metadata": { "editable": true }, @@ -7158,7 +7159,7 @@ }, { "cell_type": "markdown", - "id": "619814ea", + "id": "1a3ef69a", "metadata": { "editable": true }, @@ -7175,7 +7176,7 @@ }, { "cell_type": "markdown", - "id": "833fef22", + "id": "b9206a11", "metadata": { "editable": true }, @@ -7186,7 +7187,7 @@ }, { "cell_type": "markdown", - "id": "72df2582", + "id": "3050dcc1", "metadata": { "editable": true }, @@ -7206,7 +7207,7 @@ }, { "cell_type": "markdown", - "id": "efc2be56", + "id": "2adca788", "metadata": { "editable": true }, @@ -7216,7 +7217,7 @@ }, { "cell_type": "markdown", - "id": "8bee39ce", + "id": "9d36478f", "metadata": { "editable": true }, @@ -7242,7 +7243,7 @@ }, { "cell_type": "markdown", - "id": "e133bda5", + "id": "f5a39291", "metadata": { "editable": true }, @@ -7258,7 +7259,7 @@ }, { "cell_type": "markdown", - "id": "8cc804aa", + "id": "2090b5b8", "metadata": { "editable": true }, @@ -7269,7 +7270,7 @@ { "cell_type": "code", "execution_count": 52, - "id": "8e3fb51d", + "id": "0598530e", "metadata": { "collapsed": false, "editable": true @@ -7500,7 +7501,7 @@ }, { "cell_type": "markdown", - "id": "a77decf5", + "id": "518138c8", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/html/exercisesweek43.html b/doc/LectureNotes/_build/html/exercisesweek43.html index 120ef889f..5c1994bb7 100644 --- a/doc/LectureNotes/_build/html/exercisesweek43.html +++ b/doc/LectureNotes/_build/html/exercisesweek43.html @@ -750,12 +750,13 @@ inputs \(x_1\) and and multiplying with \(\boldsymbol{a}_h\) gives the output

\[\begin{split} -\boldsymbol{a}_o=\boldsymbol{w}_h^T\begin{bmatrix} 0 & 0 \\ +\boldsymbol{a}_o=\begin{bmatrix} 0 & 0 \\ 1 & 0 \\ 1 & 0 \\ - 2 & 1 \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix}, + 2 & 1 \end{bmatrix}\begin{bmatrix} 1 \\ + -2\end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix}, \end{split}\]
-

the wanted result.

+

the wanted result. Pay attention to the dimensionalities as well.

 
Adam: Eta=0.0001, Lambda=0
-
-  [----------------------------------------] 0.000% | train_error: 11.3 | train_acc: 0.453 | val_error: 10.4 | val_acc: 0.497 
+
+
+
  [----------------------------------------] 0.000% | train_error: 11.3 | train_acc: 0.453 | val_error: 10.4 | val_acc: 0.497 
 
  [----------------------------------------] 0.1000% | train_error: 11.4 | train_acc: 0.448 | val_error: 10.4 | val_acc: 0.497 
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index 848be62de..3f4072a76 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
+++ b/doc/LectureNotes/_build/html/searchindex.js
@@ -1 +1 @@
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:[9,10],agorithm:10,agre:[5,6,29,34,35],agreement:[13,21,37,38],ahead:9,ai:[0,27,31],aid:[11,20],aim:[0,1,4,6,7,11,14,15,16,24,25,26,27,33,35,36,40,41],ainv:5,airplan:3,aka:[5,34,35],al:[0,2,4,15,16,17,27,31,32,33,34,35,36,37,38,39,40,41],alarm:[5,7,34,35],algebra:[0,3,5,13,21,24,33,34,35,37,38],algorithm:[0,1,2,4,5,6,7,8,13,14,22,23,24,25,26,29,31,32,34,35,36,41],align:[0,2,5,6,7,8,13,26,29,32,33,34,35,36,37,41],all:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],allevi:[1,13,36,37,40,41],alloc:[3,25],allow:[0,1,2,3,5,6,8,10,13,15,16,23,24,25,26,32,33,34,35,36,37,38,39,40,41],almost:[0,1,6,8,11,13,21,29,32,35,36,37,38,40,41],alon:[2,9,41],along:[2,3,4,5,6,9,10,11,23,24,25,32,33,34,35,36,41],alpha:[0,1,2,3,4,6,7,8,9,10,13,14,23,29,32,33,35,36,37,39,40,41],alpha_0:3,alpha_1:3,alpha_2:3,alpha_:10,alpha_i:[3,13,37],alpha_k:[13,37],alpha_m:10,alpha_n:3,alpha_opt:[13,37],alreadi:[2,3,4,5,6,10,12,24,25,29,32,33,34,35,38,39,41],also:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,23,24,25,26,27,28,29,32,33,34,35,36,37,38,39,40,41],alter:[1,39,40,41],altern:[0,1,4,5,6,7,8,9,11,13,25,26,32,33,34,35,36,37,38,39,40,41],although:[0,1,5,6,8,10,13,16,21,23,32,34,35,37,38,40,41],alwai:[0,3,5,6,12,13,16,21,29,32,33,34,35,36,37,38,39],am:[4,33],ame2016:[0,32],american:[0,33],among:[0,3,5,9,10,12,25,32,33,34,38,39],amongst:[5,34,35],amount:[0,1,3,4,6,8,10,14,23,24,35,40,41],an:[1,2,3,5,6,7,8,9,11,12,13,14,15,16,17,19,20,21,23,24,25,26,27,29,30,31,33,34,35,36,37,38,39,40,41],an_:29,anaconda:[0,1,15,24,26,32,40,41],analog:[13,37,38],analys:[6,34,35],analysi:[1,3,4,7,14,15,16,17,19,21,22,25,31,36,39,40,41],analyt:[2,3,5,6,7,12,13,15,22,24,26,27,32,33,34,35,36,37,38,39],analytical_gradi:21,analyz:[0,1,3,4,5,6,16,17,26,27,29,32,33,34,39,40,41],andrew:[1,39,40,41],angl:[0,3,9,33],anharmon:3,ani:[0,1,2,3,4,5,6,7,8,9,10,12,14,18,23,29,32,33,34,35,38,39,40,41],anim:[4,12,38,39],ann:[12,38,39],annot:[0,1,3,7,8,23,32,33,36,39,40,41],announc:32,anoth:[0,1,3,4,5,6,7,8,10,11,12,13,25,26,27,29,32,33,36,37,38,39,40,41],ans_vspac:[],ansatz:[0,32],answer:[0,1,3,5,6,25,26,27,30,32,34,35,39,40,41],antialias:[2,6,26,41],anticip:4,anymor:[1,8,40,41],anyon:[4,8],anyth:[1,29,40,41],anytim:[30,32],apach:[1,40,41],apart:[11,13,36,37],api:[1,24,32,40,41],appar:[2,41],appear:[0,1,3,13,16,23,25,29,32,37,38,39,40,41],append:[1,3,4,8,9,13,21,23,32,37,40,41],appendix:26,appl:[3,4],appli:[0,1,2,3,4,6,7,8,9,10,11,12,13,15,16,26,27,29,31,32,33,34,35,36,37,38,39,40,41],applic:[0,1,3,4,5,6,7,9,12,13,21,25,26,29,31,32,33,35,36,37,38,39,40,41],apply_gradi:4,approach:[1,2,4,5,6,9,10,11,12,13,17,21,23,24,29,31,33,36,39,40,41],appropri:[2,6,9,12,13,24,29,35,37,38,39,41],approv:32,approx:[0,2,3,6,10,11,13,29,32,35,36,37,38,41],approxim:[0,1,2,3,4,5,6,7,10,11,13,18,19,26,29,32,33,34,35,36,37,38,40,41],apt:[0,15,24,26,32],aq:29,ar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],aragorn:32,arang:[1,3,4,6,7,9,10,12,13,23,26,32,36,37,38,39,40,41],arbitrari:[1,4,6,8,12,13,29,35,36,37,38,39,40,41],arbitrarili:[0,1,11,32,39,40,41],arc:[6,26],architectur:[3,4,12,23],archiv:27,area:[0,3,6,9,26,31,32],arg:[0,2,3,4,13,32,38],argmax:[1,11,39,40,41],argmin:[4,10,14],argnum:[2,13,38],argnum_0:[],argnum_1:[],args_with_tang:[3,4],argsort:11,argu:[1,13,37,38,40,41],argument:[0,2,3,5,6,11,12,13,21,23,26,32,33,34,35,39,41],argval:[],aris:[0,6,12,13,29,32,35,36,37,39],arithmet:[0,13,25,32,37,38],arm:[6,34],armadillo:25,around:[0,1,4,5,6,11,29,32,34,35,39,40,41],arr:[],arrai:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,21,23,24,26,29,33,34,35,36,37,38,39,40,41],arrang:[3,32],arraybox:[13,37,38],arriv:[0,6,9,11,25,29,32,35],arrow:[12,23,38,39,41],arrowprop:8,art3d:[13,37],art:[0,1,15,24,32,40,41],articl:[0,3,4,6,10,18,27,32,33,34,35],artifici:[0,2,7,12,31,32,36,41],artificialneuron:[12,38,39],arug:[13,37,38],arxiv:[3,4,21,27,37,38],as_fram:33,asap:32,asarrai:[0,2,6,9,21,33,34,37],ashort:20,asid:33,ask:[5,6,11,12,34,35,39],aspect:[0,6,24,26,32,33,34],assembl:[0,3,32],assert:[4,23,41],assess:[0,6,26,32,33,34,35],assici:4,assign:[0,7,8,9,12,13,14,23,28,30,31,32,33,36,37,38,39,40,41],associ:[0,6,9,12,14,29,32,35,38,39],assum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,23,25,26,29,32,33,34,35,36,37,38,39,40,41],assumpt:[0,3,5,6,9,11,18,26,29,32,33],ast:[0,5,6,18,26,32,34,35,36],astronomi:[32,33,34,35,36,37,38,39,40,41],astyp:[4,9,10],asymmetri:[0,32],asymptot:[4,6,35],async_wait:[3,4],atla:32,atom:[0,32],attempt:[0,4,6,7,8,10,32,34,36],attend:28,attent:[0,25,32],attr:[3,4,34],attract:[0,10,32],attribut:[0,9,13,23,27,32,34,35,41],attributeerror:[13,34],audi:[0,32],audio:[3,4],august:[15,16,32],aurelien:[0,15,28,31,32,38,40,41],austfjel:[6,26],author:[0,1,10,29,32,40,41],authour:32,auto:[6,9,10,23,29,41],autocor:29,autocorrelation_tim:29,autocorrelform:29,autocovari:29,autoencod:[4,24,32],autoencond:24,autograd:[22,23,24,27,32],autom:[0,24,31,32],automac:25,automag:32,automat:[0,1,2,3,4,11,16,22,23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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations  with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Exercises weeks 43 and 44","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 13 (Midnight)","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with introduction to Tensor flow","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"],titleterms:{"1":[0,15,16,17,18,26,32,33],"12":39,"13":27,"14":35,"19":40,"2":[0,15,16,17,18,27,32,33],"2023":[26,30],"21":36,"23":36,"26":41,"3":[0,15,16,32,33],"31":33,"34":[15,32],"35":[16,33],"36":[17,34],"37":[18,35],"38":[19,36],"39":[20,21,37],"4":[0,33],"40":[21,38],"41":[21,39],"42":[22,40],"43":[23,41],"44":[23,41],"5":0,"7":34,"9":26,"case":[8,10,29,33,34,36,37],"class":36,"do":[1,32,34,35,37,38,39,40,41],"final":[12,21,27,33,34,37,38,39,41],"function":[0,1,6,7,8,10,11,12,13,21,23,26,27,29,32,33,34,35,36,37,38,39,40,41],"import":[5,21,25,32,33,34],"new":[4,34,35],A:[0,1,4,8,9,21,32,34,35,36,40,41],AND:[23,38,39,40,41],And:[21,32,33,34,36,37,38],But:[21,37,38],In:30,Is:[40,41],Ising:6,OR:[38,39,40,41],The:[0,1,2,3,5,6,7,8,9,11,12,17,23,24,32,33,34,35,36,37,38,39,40,41],To:[32,33],With:[4,34],about:[32,33],abov:[23,34,41],activ:[1,12,23,27,34,38,39,40,41],ad:[0,6,17,26,32,33,38,39],adaboost:10,adagrad:[13,21,37,38],adam:[13,21,37,38],adapt:[10,21,37,38],adjust:[1,39,40,41],advanc:21,adversari:4,again:[3,9,36],ai:32,aim:[8,9,17,18,19,20,21,22,23,32],aka:[32,33],al:21,algebra:[25,32],algorithm:[9,10,11,12,21,27,33,37,38,39,40],algortithm:[13,36,37],all:8,an:[0,4,10,32],analys:[5,33],analysi:[0,5,6,11,24,26,27,29,32,33,34,35],analyt:[0,16,17,21,41],ani:[13,36,37],anoth:[9,34,35],appli:24,approach:[0,8,14,32,35,37,38],approxim:[12,39],architectur:[1,39,40,41],argument:[37,38],arrai:[25,32],artifici:[38,39],assist:30,assumpt:[34,35],august:33,autocorrel:29,autograd:[2,13,21,37,38,41],automat:[13,21,37,38,41],avoid:[37,38],b:[17,26,27,37,38],back:[1,11,12,39,40,41],background:[24,26,27,35],bag:10,base:[13,21,35,37,38],basic:[0,5,7,9,10,11,25,33,34,35,36],batch:[1,37,38,40,41],bay:[5,34,35],befor:11,beta:[34,35],better:[8,38,39],bia:[6,26,35],bias:[39,40,41],binari:[1,39,40],bind:32,bird:10,boldsymbol:[33,34,35],boost:10,bootstrap:[6,10,35],boston:[0,33],breast:[1,40,41],brief:[32,35,36,37],bring:[12,39],build:[1,3,9,23,40,41],c:[26,27,32],calcul:33,can:[21,32,35,37,38],cancer:[1,7,9,11,36,40,41],cart:9,center:33,central:[13,24,29,35,36,37],chain:[12,39],challeng:36,chang:10,channel:32,chi:[0,32],choic:[40,41],choos:[1,39,40,41],cifar01:3,classic:11,classif:[1,9,10,23,27,36,39,40,41],classifi:[8,36],clip:[1,40,41],cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,21,23,27,32,33,34,35,36,37,38,39,40,41],collect:[1,3,39,40,41],come:36,commun:32,compact:36,compar:[2,10,41],comparison:34,compet:[21,37,38],complet:33,complex:[0,6,26,33],complic:[6,37,38],compon:11,comput:[9,37,38],computation:35,computerlab:32,con:9,concept:29,condit:[34,35,36,37],confid:35,conjug:[13,37],construct:[39,40,41],continu:38,contn:32,convex:[8,13,36,37],convolut:[3,12,38,39],correctli:[34,35],correl:[11,33,36],correspond:[36,37],cost:[1,10,23,33,34,35,36,37,39,40,41],cours:[24,31,32],covari:[5,11,29,33],cover:32,critic:27,cross:[6,26,35,36],cython:32,d:[26,27],data:[0,1,3,6,7,9,11,15,16,23,24,26,29,32,33,34,36,39,40,41],dataset:[1,3,39,40,41],deadlin:[26,27,32],decai:[2,37,38,41],decis:[9,10],decomposit:[5,11,17,25,33],deep:[1,2,36,40,41],defin:[1,32,39,40,41],definit:39,degre:[0,33],deliveri:[26,27],delta:35,dens:[0,32],deriv:[5,12,33,34,35,36,37,39,40,41],descent:[2,10,13,21,27,36,37,38,41],descript:26,design:33,detail:[3,32,41],develop:[1,39,40,41],diagon:11,differ:[8,27,37,38],different:21,differenti:[2,13,37,38,41],diffus:[2,41],dimension:[2,3,8,23,26,33,41],directli:[37,38],disadvantag:9,discret:29,discuss:36,distribut:[5,29,34,35],distrubut:[34,35],doe:[33,34,38,39],domain:29,dot:[37,38],down:[1,40,41],dropout:[1,40,41],e:[26,27],each:36,economi:33,electron:[26,27],element:[0,29,32,37,38],elimin:25,energi:32,ensembl:10,entropi:[9,36],environ:[0,15,32],equat:[0,2,12,32,33,34,36,37,39,41],error:[0,10,32,33,35],essenti:32,estim:[34,35],et:21,etc:32,euler:[2,41],evalu:[1,27,39,40,41],exampl:[0,1,2,3,4,6,7,8,9,10,21,32,33,34,35,36,37,38,39,40,41],exercis:[0,6,15,16,17,18,19,20,21,22,23,32,33,35,41],expect:[18,29,34,35],expens:35,experi:29,explor:[0,15,16,32],exponenti:[2,41],express:[17,18,32,33,36,37],extend:[36,37],extrapol:4,extrem:[10,32],ey:10,f:[26,27],fall:30,famili:[1,32,33,40,41],famou:25,fantast:33,featur:[9,25,33],feed:[1,12,38,39,40,41],find:[35,37,38],fine:[1,40,41],first:[4,12,27,32,33,34,36,37,39,41],fit:[0,10,32,34],fix:33,flow:40,fold:[35,36],forc:3,forest:10,format:[26,27,32],forward:[1,2,12,38,39,40,41],fourier:3,frank:[6,26,33],freedom:[0,33],frequent:33,frequentist:[0,32],fridai:36,from:[5,10,12,21,27,33,34,35,36,37,38,39],full:[2,39,40,41],funtion:[40,41],further:[3,5,33],g:26,gan:4,gate:[23,38,39,40,41],gaussian:25,gd:[13,21,37,38],gener:[4,9,32],geometr:[11,36,37],get:21,gini:9,good:[0,32],goodfellow:21,grade:[30,32],gradient:[1,2,10,13,21,27,36,37,38,40,41],grid:36,group:36,growth:[2,41],ha:24,hand:[23,41],handl:[25,32,33],happen:[34,35],have:32,heard:32,hessian:[33,36,37],hidden:[2,40,41],histogram:35,homework:[36,37],hous:[0,33],how:36,hyperbol:[38,39],hyperparamet:[1,39,40,41],hyperplan:8,i:[1,40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:[9,10],agorithm:10,agre:[5,6,29,34,35],agreement:[13,21,37,38],ahead:9,ai:[0,27,31],aid:[11,20],aim:[0,1,4,6,7,11,14,15,16,24,25,26,27,33,35,36,40,41],ainv:5,airplan:3,aka:[5,34,35],al:[0,2,4,15,16,17,27,31,32,33,34,35,36,37,38,39,40,41],alarm:[5,7,34,35],algebra:[0,3,5,13,21,24,33,34,35,37,38],algorithm:[0,1,2,4,5,6,7,8,13,14,22,23,24,25,26,29,31,32,34,35,36,41],align:[0,2,5,6,7,8,13,26,29,32,33,34,35,36,37,41],all:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],allevi:[1,13,36,37,40,41],alloc:[3,25],allow:[0,1,2,3,5,6,8,10,13,15,16,23,24,25,26,32,33,34,35,36,37,38,39,40,41],almost:[0,1,6,8,11,13,21,29,32,35,36,37,38,40,41],alon:[2,9,41],along:[2,3,4,5,6,9,10,11,23,24,25,32,33,34,35,36,41],alpha:[0,1,2,3,4,6,7,8,9,10,13,14,23,29,32,33,35,36,37,39,40,41],alpha_0:3,alpha_1:3,alpha_2:3,alpha_:10,alpha_i:[3,13,37],alpha_k:[13,37],alpha_m:10,alpha_n:3,alpha_opt:[13,37],alreadi:[2,3,4,5,6,10,12,24,25,29,32,33,34,35,38,39,41],also:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,23,24,25,26,27,28,29,32,33,34,35,36,37,38,39,40,41],alter:[1,39,40,41],altern:[0,1,4,5,6,7,8,9,11,13,25,26,32,33,34,35,36,37,38,39,40,41],although:[0,1,5,6,8,10,13,16,21,23,32,34,35,37,38,40,41],alwai:[0,3,5,6,12,13,16,21,29,32,33,34,35,36,37,38,39],am:[4,33],ame2016:[0,32],american:[0,33],among:[0,3,5,9,10,12,25,32,33,34,38,39],amongst:[5,34,35],amount:[0,1,3,4,6,8,10,14,23,24,35,40,41],an:[1,2,3,5,6,7,8,9,11,12,13,14,15,16,17,19,20,21,23,24,25,26,27,29,30,31,33,34,35,36,37,38,39,40,41],an_:29,anaconda:[0,1,15,24,26,32,40,41],analog:[13,37,38],analys:[6,34,35],analysi:[1,3,4,7,14,15,16,17,19,21,22,25,31,36,39,40,41],analyt:[2,3,5,6,7,12,13,15,22,24,26,27,32,33,34,35,36,37,38,39],analytical_gradi:21,analyz:[0,1,3,4,5,6,16,17,26,27,29,32,33,34,39,40,41],andrew:[1,39,40,41],angl:[0,3,9,33],anharmon:3,ani:[0,1,2,3,4,5,6,7,8,9,10,12,14,18,23,29,32,33,34,35,38,39,40,41],anim:[4,12,38,39],ann:[12,38,39],annot:[0,1,3,7,8,23,32,33,36,39,40,41],announc:32,anoth:[0,1,3,4,5,6,7,8,10,11,12,13,25,26,27,29,32,33,36,37,38,39,40,41],ans_vspac:[],ansatz:[0,32],answer:[0,1,3,5,6,25,26,27,30,32,34,35,39,40,41],antialias:[2,6,26,41],anticip:4,anymor:[1,8,40,41],anyon:[4,8],anyth:[1,29,40,41],anytim:[30,32],apach:[1,40,41],apart:[11,13,36,37],api:[1,24,32,40,41],appar:[2,41],appear:[0,1,3,13,16,23,25,29,32,37,38,39,40,41],append:[1,3,4,8,9,13,21,23,32,37,40,41],appendix:26,appl:[3,4],appli:[0,1,2,3,4,6,7,8,9,10,11,12,13,15,16,26,27,29,31,32,33,34,35,36,37,38,39,40,41],applic:[0,1,3,4,5,6,7,9,12,13,21,25,26,29,31,32,33,35,36,37,38,39,40,41],apply_gradi:4,approach:[1,2,4,5,6,9,10,11,12,13,17,21,23,24,29,31,33,36,39,40,41],appropri:[2,6,9,12,13,24,29,35,37,38,39,41],approv:32,approx:[0,2,3,6,10,11,13,29,32,35,36,37,38,41],approxim:[0,1,2,3,4,5,6,7,10,11,13,18,19,26,29,32,33,34,35,36,37,38,40,41],apt:[0,15,24,26,32],aq:29,ar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],aragorn:32,arang:[1,3,4,6,7,9,10,12,13,23,26,32,36,37,38,39,40,41],arbitrari:[1,4,6,8,12,13,29,35,36,37,38,39,40,41],arbitrarili:[0,1,11,32,39,40,41],arc:[6,26],architectur:[3,4,12,23],archiv:27,area:[0,3,6,9,26,31,32],arg:[0,2,3,4,13,32,38],argmax:[1,11,39,40,41],argmin:[4,10,14],argnum:[2,13,38],argnum_0:[],argnum_1:[],args_with_tang:[3,4],argsort:11,argu:[1,13,37,38,40,41],argument:[0,2,3,5,6,11,12,13,21,23,26,32,33,34,35,39,41],argval:[],aris:[0,6,12,13,29,32,35,36,37,39],arithmet:[0,13,25,32,37,38],arm:[6,34],armadillo:25,around:[0,1,4,5,6,11,29,32,34,35,39,40,41],arr:[],arrai:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,21,23,24,26,29,33,34,35,36,37,38,39,40,41],arrang:[3,32],arraybox:[13,37,38],arriv:[0,6,9,11,25,29,32,35],arrow:[12,23,38,39,41],arrowprop:8,art3d:[13,37],art:[0,1,15,24,32,40,41],articl:[0,3,4,6,10,18,27,32,33,34,35],artifici:[0,2,7,12,31,32,36,41],artificialneuron:[12,38,39],arug:[13,37,38],arxiv:[3,4,21,27,37,38],as_fram:33,asap:32,asarrai:[0,2,6,9,21,33,34,37],ashort:20,asid:33,ask:[5,6,11,12,34,35,39],aspect:[0,6,24,26,32,33,34],assembl:[0,3,32],assert:[4,23,41],assess:[0,6,26,32,33,34,35],assici:4,assign:[0,7,8,9,12,13,14,23,28,30,31,32,33,36,37,38,39,40,41],associ:[0,6,9,12,14,29,32,35,38,39],assum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,23,25,26,29,32,33,34,35,36,37,38,39,40,41],assumpt:[0,3,5,6,9,11,18,26,29,32,33],ast:[0,5,6,18,26,32,34,35,36],astronomi:[32,33,34,35,36,37,38,39,40,41],astyp:[4,9,10],asymmetri:[0,32],asymptot:[4,6,35],async_wait:[3,4],atla:32,atom:[0,32],attempt:[0,4,6,7,8,10,32,34,36],attend:28,attent:[0,23,25,32,41],attr:[3,4,34],attract:[0,10,32],attribut:[0,9,13,23,27,32,34,35,41],attributeerror:[13,34],audi:[0,32],audio:[3,4],august:[15,16,32],aurelien:[0,15,28,31,32,38,40,41],austfjel:[6,26],author:[0,1,10,29,32,40,41],authour:32,auto:[6,9,10,23,29,41],autocor:29,autocorrelation_tim:29,autocorrelform:29,autocovari:29,autoencod:[4,24,32],autoencond:24,autograd:[22,23,24,27,32],autom:[0,24,31,32],automac:25,automag:32,automat:[0,1,2,3,4,11,16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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations  with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Exercises weeks 43 and 44","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 13 (Midnight)","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with introduction to Tensor flow","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"],titleterms:{"1":[0,15,16,17,18,26,32,33],"12":39,"13":27,"14":35,"19":40,"2":[0,15,16,17,18,27,32,33],"2023":[26,30],"21":36,"23":36,"26":41,"3":[0,15,16,32,33],"31":33,"34":[15,32],"35":[16,33],"36":[17,34],"37":[18,35],"38":[19,36],"39":[20,21,37],"4":[0,33],"40":[21,38],"41":[21,39],"42":[22,40],"43":[23,41],"44":[23,41],"5":0,"7":34,"9":26,"case":[8,10,29,33,34,36,37],"class":36,"do":[1,32,34,35,37,38,39,40,41],"final":[12,21,27,33,34,37,38,39,41],"function":[0,1,6,7,8,10,11,12,13,21,23,26,27,29,32,33,34,35,36,37,38,39,40,41],"import":[5,21,25,32,33,34],"new":[4,34,35],A:[0,1,4,8,9,21,32,34,35,36,40,41],AND:[23,38,39,40,41],And:[21,32,33,34,36,37,38],But:[21,37,38],In:30,Is:[40,41],Ising:6,OR:[38,39,40,41],The:[0,1,2,3,5,6,7,8,9,11,12,17,23,24,32,33,34,35,36,37,38,39,40,41],To:[32,33],With:[4,34],about:[32,33],abov:[23,34,41],activ:[1,12,23,27,34,38,39,40,41],ad:[0,6,17,26,32,33,38,39],adaboost:10,adagrad:[13,21,37,38],adam:[13,21,37,38],adapt:[10,21,37,38],adjust:[1,39,40,41],advanc:21,adversari:4,again:[3,9,36],ai:32,aim:[8,9,17,18,19,20,21,22,23,32],aka:[32,33],al:21,algebra:[25,32],algorithm:[9,10,11,12,21,27,33,37,38,39,40],algortithm:[13,36,37],all:8,an:[0,4,10,32],analys:[5,33],analysi:[0,5,6,11,24,26,27,29,32,33,34,35],analyt:[0,16,17,21,41],ani:[13,36,37],anoth:[9,34,35],appli:24,approach:[0,8,14,32,35,37,38],approxim:[12,39],architectur:[1,39,40,41],argument:[37,38],arrai:[25,32],artifici:[38,39],assist:30,assumpt:[34,35],august:33,autocorrel:29,autograd:[2,13,21,37,38,41],automat:[13,21,37,38,41],avoid:[37,38],b:[17,26,27,37,38],back:[1,11,12,39,40,41],background:[24,26,27,35],bag:10,base:[13,21,35,37,38],basic:[0,5,7,9,10,11,25,33,34,35,36],batch:[1,37,38,40,41],bay:[5,34,35],befor:11,beta:[34,35],better:[8,38,39],bia:[6,26,35],bias:[39,40,41],binari:[1,39,40],bind:32,bird:10,boldsymbol:[33,34,35],boost:10,bootstrap:[6,10,35],boston:[0,33],breast:[1,40,41],brief:[32,35,36,37],bring:[12,39],build:[1,3,9,23,40,41],c:[26,27,32],calcul:33,can:[21,32,35,37,38],cancer:[1,7,9,11,36,40,41],cart:9,center:33,central:[13,24,29,35,36,37],chain:[12,39],challeng:36,chang:10,channel:32,chi:[0,32],choic:[40,41],choos:[1,39,40,41],cifar01:3,classic:11,classif:[1,9,10,23,27,36,39,40,41],classifi:[8,36],clip:[1,40,41],cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,21,23,27,32,33,34,35,36,37,38,39,40,41],collect:[1,3,39,40,41],come:36,commun:32,compact:36,compar:[2,10,41],comparison:34,compet:[21,37,38],complet:33,complex:[0,6,26,33],complic:[6,37,38],compon:11,comput:[9,37,38],computation:35,computerlab:32,con:9,concept:29,condit:[34,35,36,37],confid:35,conjug:[13,37],construct:[39,40,41],continu:38,contn:32,convex:[8,13,36,37],convolut:[3,12,38,39],correctli:[34,35],correl:[11,33,36],correspond:[36,37],cost:[1,10,23,33,34,35,36,37,39,40,41],cours:[24,31,32],covari:[5,11,29,33],cover:32,critic:27,cross:[6,26,35,36],cython:32,d:[26,27],data:[0,1,3,6,7,9,11,15,16,23,24,26,29,32,33,34,36,39,40,41],dataset:[1,3,39,40,41],deadlin:[26,27,32],decai:[2,37,38,41],decis:[9,10],decomposit:[5,11,17,25,33],deep:[1,2,36,40,41],defin:[1,32,39,40,41],definit:39,degre:[0,33],deliveri:[26,27],delta:35,dens:[0,32],deriv:[5,12,33,34,35,36,37,39,40,41],descent:[2,10,13,21,27,36,37,38,41],descript:26,design:33,detail:[3,32,41],develop:[1,39,40,41],diagon:11,differ:[8,27,37,38],different:21,differenti:[2,13,37,38,41],diffus:[2,41],dimension:[2,3,8,23,26,33,41],directli:[37,38],disadvantag:9,discret:29,discuss:36,distribut:[5,29,34,35],distrubut:[34,35],doe:[33,34,38,39],domain:29,dot:[37,38],down:[1,40,41],dropout:[1,40,41],e:[26,27],each:36,economi:33,electron:[26,27],element:[0,29,32,37,38],elimin:25,energi:32,ensembl:10,entropi:[9,36],environ:[0,15,32],equat:[0,2,12,32,33,34,36,37,39,41],error:[0,10,32,33,35],essenti:32,estim:[34,35],et:21,etc:32,euler:[2,41],evalu:[1,27,39,40,41],exampl:[0,1,2,3,4,6,7,8,9,10,21,32,33,34,35,36,37,38,39,40,41],exercis:[0,6,15,16,17,18,19,20,21,22,23,32,33,35,41],expect:[18,29,34,35],expens:35,experi:29,explor:[0,15,16,32],exponenti:[2,41],express:[17,18,32,33,36,37],extend:[36,37],extrapol:4,extrem:[10,32],ey:10,f:[26,27],fall:30,famili:[1,32,33,40,41],famou:25,fantast:33,featur:[9,25,33],feed:[1,12,38,39,40,41],find:[35,37,38],fine:[1,40,41],first:[4,12,27,32,33,34,36,37,39,41],fit:[0,10,32,34],fix:33,flow:40,fold:[35,36],forc:3,forest:10,format:[26,27,32],forward:[1,2,12,38,39,40,41],fourier:3,frank:[6,26,33],freedom:[0,33],frequent:33,frequentist:[0,32],fridai:36,from:[5,10,12,21,27,33,34,35,36,37,38,39],full:[2,39,40,41],funtion:[40,41],further:[3,5,33],g:26,gan:4,gate:[23,38,39,40,41],gaussian:25,gd:[13,21,37,38],gener:[4,9,32],geometr:[11,36,37],get:21,gini:9,good:[0,32],goodfellow:21,grade:[30,32],gradient:[1,2,10,13,21,27,36,37,38,40,41],grid:36,group:36,growth:[2,41],ha:24,hand:[23,41],handl:[25,32,33],happen:[34,35],have:32,heard:32,hessian:[33,36,37],hidden:[2,40,41],histogram:35,homework:[36,37],hous:[0,33],how:36,hyperbol:[38,39],hyperparamet:[1,39,40,41],hyperplan:8,i:[1,40,41],id3:9,idea:11,ideal:[36,37],ident:[34,35],identifi:35,ii:[32,41],iid:[34,35],iii:41,illustr:[34,38,39],implement:[1,39,40,41],implic:[5,33],improv:[1,37,39,40,41],includ:[13,21,36,37,38],increment:11,independ:[34,35],index:9,inform:30,input:[2,41],instal:[24,26,32],instructor:30,intercept:33,interpret:[5,11,32,33,34,35,36,37],interv:35,introduc:[11,13,21,33,37,38],introduct:[0,6,24,25,26,27,32,38,39,40],invers:[5,25,34],invert:33,iter:[10,37],its:33,iv:41,jacobian:[33,41],jax:[13,21,37,38],job:[38,39],julia:32,jungl:10,k:[35,36],kera:[1,3,40,41],kernel:[8,11],l:39,lagrangian:8,lambda:36,lasso:[5,6,26,33,34,35,36],last:[33,35,36,38],later:[5,33],layer:[1,2,3,12,39,40,41],learn:[0,1,2,11,13,14,15,16,21,23,24,26,27,32,33,34,35,36,37,38,39,40,41],least:[5,6,18,26,32,33,34],lectur:[32,33,34,35,36,39,40,41],level:10,librari:[24,32],likelihood:[7,34,35,36],limit:[1,13,29,35,36,37,38,40,41],linear:[0,8,13,25,27,32,33,34,36],link:[5,11,28,31,33,34,35],literatur:[26,27],logist:[7,27,32,36,37,38,39,40,41],loop:[37,38],loss:[33,36,37],lu:25,machin:[0,8,13,24,26,27,32,36,37],made:[34,35],mai:32,main:29,make:[0,9,10,15,16,32,33],mani:[10,12,39],manipul:33,margin:[34,35],mass:32,materi:[28,32,33,34,35,36,41],math:[5,33],mathemat:[3,5,8,33,37,38,39],matric:[5,25,32,34],matrix:[1,5,11,12,25,32,33,34,36,37,38,39,40,41],matter:[0,32],max:33,maximum:[34,35,36],mean:[0,32,33,34,36],measur:36,meet:[5,10,29,32,33],mercer:8,method:[6,9,10,13,21,23,26,35,36,37,38,41],midnight:[26,27],min:33,mini:[37,38],minibatch:[21,37,38],minim:[32,36,41],ml:32,mle:[34,35],mlp:[12,39],mnist:[3,4],model:[0,1,4,6,12,32,38,39,40,41],moment:[37,38],momentum:[13,21,37,38],moon:[8,9],more:[3,6,21,25,26,32,33,34,35,36,37,38,40,41],multi:[38,39,40],multiclass:[23,41],multilay:[12,38,39],multipl:[1,3,39,40,41],multipli:8,need:[26,32],network:[1,2,3,4,7,12,23,27,32,36,38,39,40,41],neural:[1,2,3,4,7,12,23,27,32,38,39,40,41],neuron:[38,39],newton:[21,36,37,38],nice:[40,41],noen:[21,37,38],non:8,normal:[0,1,35,40,41],notat:[12,38,39],note:[21,33,34,35],novemb:27,now:[1,9,13,21,34,35,37,38,40,41],nuclear:[0,32],nueral:36,numba:32,number:[0,2,21,29,33,37,38,41],numer:[2,26,27,29,41],numpi:[21,25,32,37,38],object:[3,39,40,41],obtain:11,octob:[26,39,40,41],od:[2,41],off:[6,26],ol:[5,6,21,26,34,35,37,38],one:[2,12,36,37,39,41],ones:[38,39],oper:25,optim:[1,8,13,24,32,33,36,37,38,39,40,41],order:[13,21,37,38],ordinari:[5,6,18,26,32,33,34,41],organ:[0,32],orient:[39,40,41],oslo:31,other:[4,9,11,12,23,25,32,33,36,38,39,41],our:[0,4,5,11,13,32,33,36,37,39,40,41],outcom:[24,32],output:[2,40,41],overarch:[0,4,8,9,17,18,19,20,21,22,23,32,33],overview:[10,32,37,38],own:[0,10,11,15,16,27,32,33],packag:[25,32],panda:[32,33],paper:26,paramet:[32,33,36,37,38],part:[13,24,26,27,33,36,37],partial:[2,41],pass:[1,39,40,41],pca:11,pdf:29,pencil:26,perceptron:[12,38,39,40],perform:[1,9,39,40,41],period:3,perspect:[1,40,41],plan:[33,34,35,36,37,38,39,40,41],plot:[35,36],point:4,poisson:[2,41],polynomi:[3,34],popul:[2,41],possibl:41,practic:[13,21,30,32,37,38],pre:[1,3,39,40,41],predict:4,predictor:36,preprocess:33,prerequisit:[3,24,32],princip:11,principl:3,pro:9,probabl:[5,29,34,35],problem:[1,2,13,21,32,33,34,36,37,38,39,40,41],procedur:[9,32],process:[1,3,39,40,41],product:[37,38],program:[2,13,26,27,36,37,41],project:[6,26,27,32,36],prop:[13,37,38],propag:[1,12,39,40,41],properti:[5,29,33,36],python:[0,9,15,24,25,32],quick:8,r:32,random:[10,11,29,36],raphson:[36,37],rate:[21,23,37,38,41],read:[9,32,33,35],real:[6,26,32],recommend:[32,33,37,38],rectangular:34,recurr:[4,12,38,39],recurs:[37,38],reduc:[0,33],reduct:3,reformul:[2,41],regress:[0,5,6,7,9,10,13,17,18,26,27,32,33,34,35,36,37,38,39],regular:[1,36,39,40,41],relat:33,relev:[31,33,35,36,38,39],relu:[1,40,41],remark:3,remind:[6,8,32,36,37],repeat:33,replac:[13,37,38],report:[26,27],repositori:35,repres:[23,39,40,41],requir:[2,24,41],resampl:[6,26,34,35],rescal:[6,34],residu:33,resourc:[2,41],result:[33,34],review:40,revisit:[13,36,37],rewrit:[32,33,35],rewritten:36,ridg:[0,5,6,17,18,26,33,34,35,36,37],rm:[13,37,38],rmsprop:[21,37,38],rule:[12,39],s:[8,10,21,35,36,37,38],same:[13,21,35,37,38],sampl:11,scale:[33,35],schedul:[23,28,32,41],schemat:9,scheme:[2,41],scienc:32,scikit:[0,1,11,15,16,23,32,33,34,35,36,37,39,40,41],search:36,second:[13,21,37,38],select:36,semest:30,sensit:[36,37],septemb:[34,35,36],session:34,set:[0,2,3,9,12,15,23,32,33,36,39,40,41],setup:41,sgd:[13,37,38],should:[1,40,41],sigmoid:[40,41],similar:[13,21,37,38],simpl:[0,4,9,13,32,33,34,36,37,38],singl:[10,38,39],singular:[5,11,17,33],size:33,slightli:[37,38],soft:8,softmax:[1,39,40],softwar:[26,32],solut:41,solv:[2,34,36,37,41],solver:13,some:[13,25,32,33,36,37],specif:41,specifi:[2,41],split:[0,15,16,32,33],squar:[0,5,6,10,18,26,32,33,34],standard:[13,33,35,37],start:[21,38],state:[0,32],statement:32,statist:[5,6,24,29,32,34,35],steepest:[10,13,36,37],step:[27,35,36,37,38],still:33,stochast:[13,21,27,29,37,38],stop:[37,38],strongli:32,studi:36,subtract:33,suggest:32,sum:35,summari:[30,32,38],superposit:3,supervis:[1,40,41],support:8,svd:[5,33,34],syntax:[37,38],systemat:3,t:[33,34],taken:21,teach:[28,30],teacher:[30,32],technic:[34,41],techniqu:[6,11,26,34],technolog:24,tensor:40,tensorflow:[1,3,40,41],tent:32,term:[35,39],test:[0,1,15,16,23,27,32,33,34,39,40,41],textbook:[31,32],than:[36,37],thei:32,theorem:[5,8,11,12,29,34,35,39],theori:29,thi:[17,18,19,20,21,22,32],think:33,thursdai:[33,34,35,36,39,40,41],time:[37,38],tip:[13,21,37,38],togeth:[12,39],tool:32,top:[1,40,41],topic:32,toward:11,trade:[6,26],tradeoff:[6,35],train:[0,1,4,15,16,32,33,39,40,41],transform:3,tree:[9,10],trial:41,tuesdai:34,tune:[1,40,41],two:[3,8,24,26,33,36],type:[2,4,12,32,38,39,41],uio:32,understand:35,univers:[12,31,39],unsupervis:14,unsupport:[37,38],up:[0,2,9,12,15,21,23,32,33,35,36,39,40,41],us:[0,1,2,3,7,13,21,23,24,27,32,33,36,37,38,39,40,41],usag:[23,34,35,41],valid:[6,26,35,36],valu:[5,11,17,18,29,33,34,35,36],vari:[21,37,38],variabl:[29,36,37],varianc:[6,26,34,35],variou:[0,15,27,32,35,36],vector:[8,12,25,32,33,38,39],veri:[40,41],video:[37,38],view:[0,4,10,33],visual:[1,9,39,40,41],vs:3,wai:[9,21,35],warm:21,wave:[2,41],we:[21,32,37,38,40,41],websit:[40,41],wednesdai:34,week:[15,16,17,18,19,20,21,22,23,32,33,34,35,36,37,38,39,40,41],weekend:36,weekli:[28,35],weight:[39,40,41],what:[0,32,33,34,35],when:[37,38],which:[1,21,37,38,40,41],why:[32,33,35,38,39,41],wisconsin:[7,36],wrap:[33,35],write:[4,11,27,34,41],x:[33,34],xgboost:10,xor:[23,38,39,40,41],yet:34,you:32,your:[0,10,15,16,27,32,33],yourself:36,z_j:39}})
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/week43.html b/doc/LectureNotes/_build/html/week43.html
index 8771fb53b..a51bd6a44 100644
--- a/doc/LectureNotes/_build/html/week43.html
+++ b/doc/LectureNotes/_build/html/week43.html
@@ -1689,12 +1689,13 @@ inputs \(x_1\) and and multiplying with \(\boldsymbol{a}_h\) gives the output

 

 \[\begin{split}
-\boldsymbol{a}_o=\boldsymbol{w}_h^T\begin{bmatrix} 0 & 0 \\
+\boldsymbol{a}_o=\begin{bmatrix} 0 & 0 \\
                        1 & 0 \\
 		       1 & 0 \\
-		       2 & 1 \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
+		       2 & 1 \end{bmatrix}\begin{bmatrix} 1 \\
+                       -2\end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
 \end{split}\]

-
the wanted result.

+
the wanted result.  Pay attention to the dimensionalities as well.

Setting up the Neural Network¶

@@ -6362,6 +6363,9 @@ case.

Adam: Eta=0.001, Lambda=0
+

+
+
  [----------------------------------------] 0.000% | train_error: 12.9 | train_acc: 0.376 | val_error: 12.6 | val_acc: 0.392
@@ -18823,9 +18827,7 @@ This is then passed through the activation:

probabilities = (n_inputs, n_categories) = (1437, 10)
-
-
-
probability that image 0 is in category 0,1,2,...,9 = 
+probability that image 0 is in category 0,1,2,...,9 = 
 [5.41511965e-04 2.17174962e-03 8.84355903e-03 1.44970586e-03
  1.10378326e-04 5.08318298e-09 2.03256632e-04 1.92507116e-03
  9.84443254e-01 3.11507992e-04]
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
index 4b0831142..f0fcf3cea 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "ae832182",
-   "metadata": {},
+   "id": "d5ebb4c0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77f844d9",
-   "metadata": {},
+   "id": "812b4e46",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Exercises weeks 43 and 44 \n",
     "**October 23-27, 2023**\n",
@@ -25,8 +29,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5b983e3",
-   "metadata": {},
+   "id": "3230cd2f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Overarching aims of the exercises weeks 43 and 44\n",
     "\n",
@@ -63,8 +69,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f6cc12f",
-   "metadata": {},
+   "id": "e3617d4e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The AND and XOR Gates\n",
     "\n",
@@ -99,8 +107,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0b07e46",
-   "metadata": {},
+   "id": "54e1e7fc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Representing the Data Sets\n",
     "\n",
@@ -109,8 +119,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0a9840a",
-   "metadata": {},
+   "id": "6b3c15cb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{X}=\\begin{bmatrix} 0 & 0 \\\\\n",
@@ -122,8 +134,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff95d379",
-   "metadata": {},
+   "id": "acc25271",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "while the vector of outputs is $\\boldsymbol{y}^T=[0,1,1,0]$ for the XOR gate, $\\boldsymbol{y}^T=[0,0,0,1]$ for the AND gate and $\\boldsymbol{y}^T=[0,1,1,1]$ for the OR gate.\n",
     "\n",
@@ -150,8 +164,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36fa3466",
-   "metadata": {},
+   "id": "ffe0a840",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up dimensionalities by hand\n",
     "\n",
@@ -160,8 +176,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2e5e808",
-   "metadata": {},
+   "id": "46abf545",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{W_h}=\\begin{bmatrix} 1 & 1 \\\\\n",
@@ -171,16 +189,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "419e3904",
-   "metadata": {},
+   "id": "86e105cc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Multiplying $\\boldsymbol{X}$ and $\\boldsymbol{W}$ gives"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "88a9712a",
-   "metadata": {},
+   "id": "5e1d21f1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{X}{W}_h=\\begin{bmatrix} 0 & 0 \\\\\n",
@@ -192,16 +214,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "036eee14",
-   "metadata": {},
+   "id": "692c6cbf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Assume also that the bias vector for the hidden layer is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3c771918",
-   "metadata": {},
+   "id": "5d81e641",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{b}_h=\\begin{bmatrix} 0 \\\\\n",
@@ -211,16 +237,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5a4150d",
-   "metadata": {},
+   "id": "a42bdee4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Adding it gives us the input to the activation function of the hidden layer"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e4eb7753",
-   "metadata": {},
+   "id": "5116b854",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{z}_h=\\boldsymbol{X}\\boldsymbol{W}_h+\\boldsymbol{b}_h=\\begin{bmatrix} 0 & -1 \\\\\n",
@@ -232,16 +262,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5442b32",
-   "metadata": {},
+   "id": "8dd26d09",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Let us then assume that our activation function is the RELU function, which simply means that we take the max of $0$ and the elements of the input argument $\\boldsymbol{z}_h$, that is we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "64d99f85",
-   "metadata": {},
+   "id": "ebf97c03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{a}_h=\\mathrm{RELU}(\\boldsymbol{z}_h=\\boldsymbol{X}\\boldsymbol{W}_h+\\boldsymbol{b}_h)=\\begin{bmatrix} 0 & 0 \\\\\n",
@@ -253,16 +287,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2aee4b6b",
-   "metadata": {},
+   "id": "262a4a3a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Assume also that the bias of the output layer is zero and that the weights of the output layer are"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "884541eb",
-   "metadata": {},
+   "id": "f03ad8e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{w}_o=\\begin{bmatrix} 1 \\\\\n",
@@ -272,37 +310,46 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3999a4d5",
-   "metadata": {},
+   "id": "36fe00c0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and multiplying with $\\boldsymbol{a}_h$ gives the output"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a4896b4d",
-   "metadata": {},
+   "id": "80ab43ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
-    "\\boldsymbol{a}_o=\\boldsymbol{w}_h^T\\begin{bmatrix} 0 & 0 \\\\\n",
+    "\\boldsymbol{a}_o=\\begin{bmatrix} 0 & 0 \\\\\n",
     "                       1 & 0 \\\\\n",
     "\t\t       1 & 0 \\\\\n",
-    "\t\t       2 & 1 \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
+    "\t\t       2 & 1 \\end{bmatrix}\\begin{bmatrix} 1 \\\\\n",
+    "                       -2\\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2c74e7c0",
-   "metadata": {},
+   "id": "86bcfe49",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "the wanted result."
+    "the wanted result.  Pay attention to the dimensionalities as well."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "249b9804",
-   "metadata": {},
+   "id": "f19a899e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the Neural Network\n",
     "\n",
@@ -312,8 +359,11 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "afdd3100",
-   "metadata": {},
+   "id": "901ddca7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -390,16 +440,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb383164",
-   "metadata": {},
+   "id": "53f22266",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not an impressive result, but this was our first forward pass with randomly assigned weights. Let us now add the full network with the back-propagation algorithm discussed above."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "0d26394c",
-   "metadata": {},
+   "id": "5f665ac6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Code using Scikit-Learn"
    ]
@@ -407,8 +461,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "befc368c",
-   "metadata": {},
+   "id": "cb396cda",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -712,8 +769,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03895a9f",
-   "metadata": {},
+   "id": "c5978471",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building a neural network code\n",
     "\n",
@@ -729,8 +788,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6226915b",
-   "metadata": {},
+   "id": "7b82dc46",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Learning rate methods\n",
     "\n",
@@ -749,8 +810,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "b6d5ea73",
-   "metadata": {},
+   "id": "de4dedfb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -887,8 +951,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edb42bef",
-   "metadata": {},
+   "id": "bb621fce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Usage of the above learning rate schedulers\n",
     "\n",
@@ -901,8 +967,11 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "108c1209",
-   "metadata": {},
+   "id": "34ddb829",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
@@ -911,8 +980,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1c423f0",
-   "metadata": {},
+   "id": "e43498d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here is a small example for how a segment of code using schedulers\n",
     "could look. Switching out the schedulers is simple."
@@ -921,8 +992,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "63c8c749",
-   "metadata": {},
+   "id": "f05b9625",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -956,8 +1030,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7cb80992",
-   "metadata": {},
+   "id": "19cf9841",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Cost functions\n",
     "\n",
@@ -970,8 +1046,11 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "a181dacb",
-   "metadata": {},
+   "id": "993efa8d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1005,8 +1084,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26a7fe37",
-   "metadata": {},
+   "id": "011c734c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below we give a short example of how these cost function may be used\n",
     "to obtain results if you wish to test them out on your own using\n",
@@ -1016,8 +1097,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "5894bd31",
-   "metadata": {},
+   "id": "9e1b97f5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1045,8 +1129,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71141fab",
-   "metadata": {},
+   "id": "4acd87b2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -1059,8 +1145,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "433e0886",
-   "metadata": {},
+   "id": "befa86ae",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1114,8 +1203,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14c9d538",
-   "metadata": {},
+   "id": "c20aa75e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below follows a short demonstration of how to use an activation\n",
     "function. The derivative of the activation function will be important\n",
@@ -1127,8 +1218,11 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "4c3a44ef",
-   "metadata": {},
+   "id": "e209f9e5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1166,8 +1260,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa7f604e",
-   "metadata": {},
+   "id": "524b409b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### The Neural Network\n",
     "\n",
@@ -1188,8 +1284,11 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "585a227b",
-   "metadata": {},
+   "id": "083116d3",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import math\n",
@@ -1657,8 +1756,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7de704af",
-   "metadata": {},
+   "id": "e4ba55d0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Before we make a model, we will quickly generate a dataset we can use\n",
     "for our linear regression problem as shown below"
@@ -1667,8 +1768,11 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "212b0a35",
-   "metadata": {},
+   "id": "c72a22c6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1708,8 +1812,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ff4ec7b",
-   "metadata": {},
+   "id": "25b63b47",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now that we have our dataset ready for the regression, we can create\n",
     "our regressor. Note that with the seed parameter, we can make sure our\n",
@@ -1722,8 +1828,11 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "57d8eca3",
-   "metadata": {},
+   "id": "b6b4e461",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -1734,8 +1843,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1977bae",
-   "metadata": {},
+   "id": "d7860b74",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We then fit our model with our training data using the scheduler of our choice."
    ]
@@ -1743,8 +1854,11 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "31ae2a1e",
-   "metadata": {},
+   "id": "00522c73",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -2573,8 +2687,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96a64da4",
-   "metadata": {},
+   "id": "a57bfb12",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Due to the progress bar we can see the MSE (train_error) throughout\n",
     "the FFNN's training. Note that the fit() function has some optional\n",
@@ -2587,8 +2703,11 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "246499fc",
-   "metadata": {},
+   "id": "35259e41",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -10616,8 +10735,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61d11e17",
-   "metadata": {},
+   "id": "4a403370",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
     "\n",
@@ -10629,8 +10750,11 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "b5b91899",
-   "metadata": {},
+   "id": "6c791130",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_breast_cancer\n",
@@ -10652,8 +10776,11 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "4bd01b3d",
-   "metadata": {},
+   "id": "0ac0258d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -10664,8 +10791,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a138d66",
-   "metadata": {},
+   "id": "a9c74baa",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We will now make use of our validation data by passing it into our fit function as a keyword argument"
    ]
@@ -10673,8 +10802,11 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "faf1534e",
-   "metadata": {},
+   "id": "e5021bbf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -18703,8 +18835,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33d2d346",
-   "metadata": {},
+   "id": "ae0148bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Finally, we will create a neural network with 2 hidden layers with activation functions."
    ]
@@ -18712,8 +18846,11 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "a8f0a61c",
-   "metadata": {},
+   "id": "bb7e4340",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -18729,14 +18866,23 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "d651702d",
-   "metadata": {},
+   "id": "d0655afb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Adam: Eta=0.0001, Lambda=0\n",
+      "Adam: Eta=0.0001, Lambda=0\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "\r",
       "  [----------------------------------------] 0.000% | train_error: 11.3 | train_acc: 0.453 | val_error: 10.4 | val_acc: 0.497 "
      ]
@@ -26759,8 +26905,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "200b64c0",
-   "metadata": {},
+   "id": "dc8a90af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Multiclass classification\n",
     "\n",
@@ -26772,8 +26920,11 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "98b8d59b",
-   "metadata": {},
+   "id": "9305c08a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -34830,8 +34981,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cadd7e47",
-   "metadata": {},
+   "id": "8e208051",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Testing the XOR gate and other gates\n",
     "\n",
@@ -34841,8 +34994,11 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "a40e5cfe",
-   "metadata": {},
+   "id": "db016d41",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -42879,19 +43035,16 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b635db73",
-   "metadata": {},
+   "id": "d1384449",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
    ]
   }
  ],
  "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.py b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.py
index 3b297c7b7..5ff7f5114 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.py
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.py
@@ -160,13 +160,14 @@
 # and multiplying with $\boldsymbol{a}_h$ gives the output
 
 # $$
-# \boldsymbol{a}_o=\boldsymbol{w}_h^T\begin{bmatrix} 0 & 0 \\
+# \boldsymbol{a}_o=\begin{bmatrix} 0 & 0 \\
 #                        1 & 0 \\
 # 		       1 & 0 \\
-# 		       2 & 1 \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
+# 		       2 & 1 \end{bmatrix}\begin{bmatrix} 1 \\
+#                        -2\end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
 # $$
 
-# the wanted result.
+# the wanted result.  Pay attention to the dimensionalities as well.
 
 # ## Setting up the Neural Network
 # 
diff --git a/doc/LectureNotes/_build/jupyter_execute/week43.ipynb b/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
index 1643c5670..bedb76abd 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "8d7cc066",
+   "id": "88f6e253",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "028dc8c6",
+   "id": "ebd16d73",
    "metadata": {
     "editable": true
    },
@@ -29,7 +29,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15ef2310",
+   "id": "e9bc94b9",
    "metadata": {
     "editable": true
    },
@@ -73,7 +73,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "192aa783",
+   "id": "457d4421",
    "metadata": {
     "editable": true
    },
@@ -87,7 +87,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22874f1a",
+   "id": "e86537af",
    "metadata": {
     "editable": true
    },
@@ -104,7 +104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29c53621",
+   "id": "14ffcfd0",
    "metadata": {
     "editable": true
    },
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3ab8226",
+   "id": "5773ab41",
    "metadata": {
     "editable": true
    },
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d686af76",
+   "id": "fdcb6f1e",
    "metadata": {
     "editable": true
    },
@@ -189,7 +189,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e6ae224",
+   "id": "7bc3e18a",
    "metadata": {
     "editable": true
    },
@@ -201,7 +201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee5e7e34",
+   "id": "b82f5167",
    "metadata": {
     "editable": true
    },
@@ -216,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da275174",
+   "id": "1ff6327f",
    "metadata": {
     "editable": true
    },
@@ -246,7 +246,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78669a54",
+   "id": "fd88cb2a",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "453ff3ab",
+   "id": "277ccf21",
    "metadata": {
     "editable": true
    },
@@ -271,7 +271,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d82c2f1",
+   "id": "69024cd6",
    "metadata": {
     "editable": true
    },
@@ -281,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a22ab766",
+   "id": "3739f7f4",
    "metadata": {
     "editable": true
    },
@@ -296,7 +296,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abfc4274",
+   "id": "891fbfbd",
    "metadata": {
     "editable": true
    },
@@ -306,7 +306,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7b0970",
+   "id": "0befa9f2",
    "metadata": {
     "editable": true
    },
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1e78b4a",
+   "id": "8b87520f",
    "metadata": {
     "editable": true
    },
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ee46428",
+   "id": "0c36a6e9",
    "metadata": {
     "editable": true
    },
@@ -344,7 +344,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bac66371",
+   "id": "6a5ebf2f",
    "metadata": {
     "editable": true
    },
@@ -354,7 +354,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77606059",
+   "id": "5c2cce0f",
    "metadata": {
     "editable": true
    },
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1a1f219",
+   "id": "6700bff0",
    "metadata": {
     "editable": true
    },
@@ -379,7 +379,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a46fd0d7",
+   "id": "c9deb439",
    "metadata": {
     "editable": true
    },
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01e41f6f",
+   "id": "bca3d76a",
    "metadata": {
     "editable": true
    },
@@ -402,32 +402,33 @@
   },
   {
    "cell_type": "markdown",
-   "id": "371a2c47",
+   "id": "0fd2b2d0",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\boldsymbol{a}_o=\\boldsymbol{w}_h^T\\begin{bmatrix} 0 & 0 \\\\\n",
+    "\\boldsymbol{a}_o=\\begin{bmatrix} 0 & 0 \\\\\n",
     "                       1 & 0 \\\\\n",
     "\t\t       1 & 0 \\\\\n",
-    "\t\t       2 & 1 \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
+    "\t\t       2 & 1 \\end{bmatrix}\\begin{bmatrix} 1 \\\\\n",
+    "                       -2\\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8ab62ed9",
+   "id": "aef5937c",
    "metadata": {
     "editable": true
    },
    "source": [
-    "the wanted result."
+    "the wanted result.  Pay attention to the dimensionalities as well."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "ee45366d",
+   "id": "784de267",
    "metadata": {
     "editable": true
    },
@@ -440,7 +441,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "43b32c8a",
+   "id": "1529f64e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -521,7 +522,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce3f8d7b",
+   "id": "6c344985",
    "metadata": {
     "editable": true
    },
@@ -531,7 +532,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a60227f",
+   "id": "dda91d6e",
    "metadata": {
     "editable": true
    },
@@ -542,7 +543,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "0574c4c7",
+   "id": "dc12224d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -850,7 +851,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3db2190",
+   "id": "7c9b27ed",
    "metadata": {
     "editable": true
    },
@@ -869,7 +870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b6e8500",
+   "id": "e8e28114",
    "metadata": {
     "editable": true
    },
@@ -891,7 +892,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "ee32fb88",
+   "id": "37a2ec80",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1032,7 +1033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6477d18f",
+   "id": "38ea41a5",
    "metadata": {
     "editable": true
    },
@@ -1048,7 +1049,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "5a396095",
+   "id": "869cf239",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1061,7 +1062,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28bd1ab9",
+   "id": "b9b25144",
    "metadata": {
     "editable": true
    },
@@ -1073,7 +1074,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "fb5d04e9",
+   "id": "7d2dc23b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1111,7 +1112,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1229684",
+   "id": "83b5e35f",
    "metadata": {
     "editable": true
    },
@@ -1127,7 +1128,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "f4a50c76",
+   "id": "4c217329",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1165,7 +1166,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d646164",
+   "id": "a0515ac9",
    "metadata": {
     "editable": true
    },
@@ -1178,7 +1179,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "b0057b55",
+   "id": "5eb41a10",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1210,7 +1211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37f67196",
+   "id": "0535d6fd",
    "metadata": {
     "editable": true
    },
@@ -1226,7 +1227,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "ae3c2dad",
+   "id": "c55d6d5f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1284,7 +1285,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5be7f268",
+   "id": "b820a2a1",
    "metadata": {
     "editable": true
    },
@@ -1299,7 +1300,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "5296db7b",
+   "id": "43974d31",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1341,7 +1342,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa62814a",
+   "id": "ec754834",
    "metadata": {
     "editable": true
    },
@@ -1365,7 +1366,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "08db6527",
+   "id": "505e52ab",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1837,7 +1838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "464f4548",
+   "id": "00aa7046",
    "metadata": {
     "editable": true
    },
@@ -1849,7 +1850,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "ea3d3c51",
+   "id": "b0b45dd4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1893,7 +1894,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6b49446",
+   "id": "cf9645c3",
    "metadata": {
     "editable": true
    },
@@ -1909,7 +1910,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "4f0f50b6",
+   "id": "a792c324",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1924,7 +1925,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ae3f1e4",
+   "id": "e11ed70e",
    "metadata": {
     "editable": true
    },
@@ -1935,7 +1936,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "4d206fa2",
+   "id": "dfd03f3c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2768,7 +2769,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27ffcb75",
+   "id": "99b1bd91",
    "metadata": {
     "editable": true
    },
@@ -2784,7 +2785,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "8cf19432",
+   "id": "864038bb",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -10816,7 +10817,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97abfa15",
+   "id": "24d5f3cc",
    "metadata": {
     "editable": true
    },
@@ -10831,7 +10832,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "5aa3cb16",
+   "id": "14df9a52",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -10857,7 +10858,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "793cb2e9",
+   "id": "adb3edf2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -10872,7 +10873,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b47a35a",
+   "id": "fa885022",
    "metadata": {
     "editable": true
    },
@@ -10883,7 +10884,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "e34123b4",
+   "id": "1b862f90",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -10893,7 +10894,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Adam: Eta=0.001, Lambda=0\n"
+      "Adam: Eta=0.001, Lambda=0"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
      ]
     },
     {
@@ -18922,7 +18930,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "413243c9",
+   "id": "e86e60dc",
    "metadata": {
     "editable": true
    },
@@ -18933,7 +18941,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "aa7b9e8f",
+   "id": "9e578191",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -18953,7 +18961,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "c66ee57f",
+   "id": "bbfc34f4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -26992,7 +27000,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aca7922f",
+   "id": "2ac7ad43",
    "metadata": {
     "editable": true
    },
@@ -27007,7 +27015,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "1503f15a",
+   "id": "f4a821cd",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -35068,7 +35076,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "838cf72d",
+   "id": "0fcf8bf2",
    "metadata": {
     "editable": true
    },
@@ -35081,7 +35089,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "a4444105",
+   "id": "d91608cf",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43122,7 +43130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bbdf09c",
+   "id": "494009be",
    "metadata": {
     "editable": true
    },
@@ -43132,7 +43140,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5cffe73",
+   "id": "db70a4fe",
    "metadata": {
     "editable": true
    },
@@ -43142,7 +43150,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e88dc6ab",
+   "id": "e5fc9732",
    "metadata": {
     "editable": true
    },
@@ -43171,7 +43179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ec227a0",
+   "id": "1f986c86",
    "metadata": {
     "editable": true
    },
@@ -43221,7 +43229,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "5336138a",
+   "id": "0f845fb5",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43298,7 +43306,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4f9c76",
+   "id": "fbab1656",
    "metadata": {
     "editable": true
    },
@@ -43319,7 +43327,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "3d4a38d4",
+   "id": "3ecd3028",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43366,7 +43374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc7c43bb",
+   "id": "b45412df",
    "metadata": {
     "editable": true
    },
@@ -43410,7 +43418,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60a15786",
+   "id": "e90b1e65",
    "metadata": {
     "editable": true
    },
@@ -43450,7 +43458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9b2c952",
+   "id": "92bff738",
    "metadata": {
     "editable": true
    },
@@ -43471,7 +43479,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "a6dfcaaf",
+   "id": "8eb225e4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43497,7 +43505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "623ec89c",
+   "id": "da1e7ad6",
    "metadata": {
     "editable": true
    },
@@ -43525,7 +43533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "391b8f09",
+   "id": "52ea3780",
    "metadata": {
     "editable": true
    },
@@ -43562,7 +43570,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "a3a7a56e",
+   "id": "8ec12507",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43572,14 +43580,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "probabilities = (n_inputs, n_categories) = (1437, 10)"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
+      "probabilities = (n_inputs, n_categories) = (1437, 10)\n",
       "probability that image 0 is in category 0,1,2,...,9 = \n",
       "[5.41511965e-04 2.17174962e-03 8.84355903e-03 1.44970586e-03\n",
       " 1.10378326e-04 5.08318298e-09 2.03256632e-04 1.92507116e-03\n",
@@ -43638,7 +43639,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a467f9c",
+   "id": "518a6c33",
    "metadata": {
     "editable": true
    },
@@ -43669,7 +43670,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "824f2150",
+   "id": "9e4fe561",
    "metadata": {
     "editable": true
    },
@@ -43707,7 +43708,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad801a4f",
+   "id": "331db754",
    "metadata": {
     "editable": true
    },
@@ -43741,7 +43742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adbd5bf5",
+   "id": "94f8797f",
    "metadata": {
     "editable": true
    },
@@ -43782,7 +43783,7 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "03850373",
+   "id": "6cc0ad5a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -43883,7 +43884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c4ce702",
+   "id": "66341fe5",
    "metadata": {
     "editable": true
    },
@@ -43904,7 +43905,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f54c055f",
+   "id": "4654bdd2",
    "metadata": {
     "editable": true
    },
@@ -43918,7 +43919,7 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "05fadefb",
+   "id": "84200c9e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -44028,7 +44029,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d6bba32",
+   "id": "2fade818",
    "metadata": {
     "editable": true
    },
@@ -44047,7 +44048,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "5605c90f",
+   "id": "da2d74fa",
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@@ -44074,7 +44075,7 @@
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@@ -44088,7 +44089,7 @@
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@@ -44119,7 +44120,7 @@
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@@ -44130,7 +44131,7 @@
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@@ -44174,7 +44175,7 @@
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@@ -44197,7 +44198,7 @@
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@@ -44224,7 +44225,7 @@
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@@ -44235,7 +44236,7 @@
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@@ -44280,7 +44281,7 @@
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@@ -44298,7 +44299,7 @@
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@@ -44333,7 +44334,7 @@
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@@ -44345,7 +44346,7 @@
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@@ -44357,7 +44358,7 @@
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@@ -44370,7 +44371,7 @@
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@@ -44381,7 +44382,7 @@
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@@ -44394,7 +44395,7 @@
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@@ -44409,7 +44410,7 @@
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@@ -44421,7 +44422,7 @@
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@@ -44433,7 +44434,7 @@
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@@ -44446,7 +44447,7 @@
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@@ -44501,7 +44502,7 @@
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@@ -44530,7 +44531,7 @@
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@@ -44560,7 +44561,7 @@
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@@ -44587,7 +44588,7 @@
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@@ -44629,7 +44630,7 @@
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@@ -44640,7 +44641,7 @@
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@@ -44817,7 +44818,7 @@
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@@ -44845,7 +44846,7 @@
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@@ -44868,7 +44869,7 @@
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@@ -44899,7 +44900,7 @@
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@@ -44931,7 +44932,7 @@
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@@ -44969,7 +44970,7 @@
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@@ -44994,7 +44995,7 @@
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@@ -45006,7 +45007,7 @@
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@@ -45029,7 +45030,7 @@
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@@ -45049,7 +45050,7 @@
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@@ -45071,7 +45072,7 @@
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@@ -45089,7 +45090,7 @@
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@@ -45108,7 +45109,7 @@
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@@ -45120,7 +45121,7 @@
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@@ -45165,7 +45166,7 @@
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@@ -45195,7 +45196,7 @@
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@@ -45222,7 +45223,7 @@
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@@ -45236,7 +45237,7 @@
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@@ -45253,7 +45254,7 @@
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@@ -45269,7 +45270,7 @@
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@@ -45281,7 +45282,7 @@
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@@ -45299,7 +45300,7 @@
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@@ -45320,7 +45321,7 @@
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@@ -45337,7 +45338,7 @@
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@@ -45349,7 +45350,7 @@
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@@ -45360,7 +45361,7 @@
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@@ -45377,7 +45378,7 @@
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@@ -45388,7 +45389,7 @@
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@@ -45404,7 +45405,7 @@
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@@ -45416,7 +45417,7 @@
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@@ -45433,7 +45434,7 @@
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@@ -45445,7 +45446,7 @@
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@@ -45463,7 +45464,7 @@
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@@ -45473,7 +45474,7 @@
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@@ -45485,7 +45486,7 @@
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@@ -45502,7 +45503,7 @@
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@@ -45514,7 +45515,7 @@
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@@ -45525,7 +45526,7 @@
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@@ -45537,7 +45538,7 @@
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@@ -45547,7 +45548,7 @@
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@@ -45567,7 +45568,7 @@
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@@ -45584,7 +45585,7 @@
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@@ -45603,7 +45604,7 @@
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@@ -45615,7 +45616,7 @@
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@@ -45625,7 +45626,7 @@
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@@ -45642,7 +45643,7 @@
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@@ -45652,7 +45653,7 @@
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@@ -45668,7 +45669,7 @@
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@@ -45680,7 +45681,7 @@
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@@ -45692,7 +45693,7 @@
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@@ -45704,7 +45705,7 @@
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@@ -45714,7 +45715,7 @@
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@@ -45726,7 +45727,7 @@
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@@ -45743,7 +45744,7 @@
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@@ -45753,7 +45754,7 @@
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@@ -45765,7 +45766,7 @@
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@@ -45779,7 +45780,7 @@
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@@ -45795,7 +45796,7 @@
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@@ -45807,7 +45808,7 @@
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@@ -45829,7 +45830,7 @@
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@@ -45841,7 +45842,7 @@
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@@ -45864,7 +45865,7 @@
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@@ -45880,7 +45881,7 @@
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@@ -45892,7 +45893,7 @@
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@@ -45916,7 +45917,7 @@
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@@ -45928,7 +45929,7 @@
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@@ -45949,7 +45950,7 @@
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@@ -45961,7 +45962,7 @@
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@@ -45980,7 +45981,7 @@
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@@ -45990,7 +45991,7 @@
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@@ -46004,7 +46005,7 @@
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@@ -46016,7 +46017,7 @@
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@@ -46028,7 +46029,7 @@
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@@ -46045,7 +46046,7 @@
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@@ -46057,7 +46058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6488f9b",
+   "id": "f980cb6a",
    "metadata": {
     "editable": true
    },
@@ -46079,7 +46080,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2bc476e",
+   "id": "de47a73d",
    "metadata": {
     "editable": true
    },
@@ -46094,7 +46095,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d7b7d19",
+   "id": "5eacb34e",
    "metadata": {
     "editable": true
    },
@@ -46105,7 +46106,7 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "4aad6e10",
+   "id": "77235f88",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -46260,7 +46261,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8c418c1",
+   "id": "0147790d",
    "metadata": {
     "editable": true
    },
@@ -46275,7 +46276,7 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "96758ada",
+   "id": "59eb96af",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -46444,7 +46445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c62fedb8",
+   "id": "dc02c291",
    "metadata": {
     "editable": true
    },
@@ -46457,7 +46458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f962431",
+   "id": "c8fff51e",
    "metadata": {
     "editable": true
    },
@@ -46474,7 +46475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71b1d885",
+   "id": "3751edf7",
    "metadata": {
     "editable": true
    },
@@ -46490,7 +46491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b96a028",
+   "id": "a502c731",
    "metadata": {
     "editable": true
    },
@@ -46503,7 +46504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "311ae3d3",
+   "id": "eb73f07e",
    "metadata": {
     "editable": true
    },
@@ -46520,7 +46521,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98cb3d44",
+   "id": "9ab9d930",
    "metadata": {
     "editable": true
    },
@@ -46532,7 +46533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e8e134d",
+   "id": "9cb8689a",
    "metadata": {
     "editable": true
    },
@@ -46559,7 +46560,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1844ff9",
+   "id": "d21e3a14",
    "metadata": {
     "editable": true
    },
@@ -46572,7 +46573,7 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "4410b99e",
+   "id": "833da16b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -46746,7 +46747,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0ab0e0f",
+   "id": "0fdcf8c5",
    "metadata": {
     "editable": true
    },
@@ -46766,7 +46767,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "333b0a8d",
+   "id": "0a057338",
    "metadata": {
     "editable": true
    },
@@ -46781,7 +46782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b358fbf",
+   "id": "6721bcf2",
    "metadata": {
     "editable": true
    },
@@ -46795,7 +46796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5d60864",
+   "id": "dc3db9fd",
    "metadata": {
     "editable": true
    },
@@ -46811,7 +46812,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcce6eb8",
+   "id": "9af3fd6a",
    "metadata": {
     "editable": true
    },
@@ -46821,7 +46822,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6497fd7",
+   "id": "4c2da445",
    "metadata": {
     "editable": true
    },
@@ -46843,7 +46844,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31b650fc",
+   "id": "93b58380",
    "metadata": {
     "editable": true
    },
@@ -46857,7 +46858,7 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "6e267e72",
+   "id": "cb73915d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -46933,7 +46934,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b054a85",
+   "id": "c9d250c7",
    "metadata": {
     "editable": true
    },
@@ -46945,7 +46946,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f637dd9d",
+   "id": "0d67bc8c",
    "metadata": {
     "editable": true
    },
@@ -46962,7 +46963,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac088e86",
+   "id": "fe4ee5a8",
    "metadata": {
     "editable": true
    },
@@ -46974,7 +46975,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14afd7fa",
+   "id": "62b400ca",
    "metadata": {
     "editable": true
    },
@@ -46989,7 +46990,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a2680eb",
+   "id": "7d4723f2",
    "metadata": {
     "editable": true
    },
@@ -47001,7 +47002,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e30575f",
+   "id": "97889b0e",
    "metadata": {
     "editable": true
    },
@@ -47013,7 +47014,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b30e08a",
+   "id": "236028bc",
    "metadata": {
     "editable": true
    },
@@ -47025,7 +47026,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be7d958b",
+   "id": "a4334818",
    "metadata": {
     "editable": true
    },
@@ -47035,7 +47036,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6a52e39",
+   "id": "8330dd77",
    "metadata": {
     "editable": true
    },
@@ -47052,7 +47053,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "488d0a14",
+   "id": "78522018",
    "metadata": {
     "editable": true
    },
@@ -47064,7 +47065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59834674",
+   "id": "943956e4",
    "metadata": {
     "editable": true
    },
@@ -47076,7 +47077,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af640638",
+   "id": "3c7b57e2",
    "metadata": {
     "editable": true
    },
@@ -47086,7 +47087,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d83ea23",
+   "id": "55173c99",
    "metadata": {
     "editable": true
    },
@@ -47098,7 +47099,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d4e4ea8",
+   "id": "a6d078e4",
    "metadata": {
     "editable": true
    },
@@ -47109,7 +47110,7 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "ad4cc32f",
+   "id": "452c599c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -47270,7 +47271,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ceb283ce",
+   "id": "8ca2348f",
    "metadata": {
     "editable": true
    },
@@ -47292,7 +47293,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a68e0e56",
+   "id": "0ccc174e",
    "metadata": {
     "editable": true
    },
@@ -47309,7 +47310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8441e4e6",
+   "id": "d4601257",
    "metadata": {
     "editable": true
    },
@@ -47319,7 +47320,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d343e68",
+   "id": "9ec01889",
    "metadata": {
     "editable": true
    },
@@ -47334,7 +47335,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c566531",
+   "id": "71993d6c",
    "metadata": {
     "editable": true
    },
@@ -47344,7 +47345,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a06b755",
+   "id": "f6acfae4",
    "metadata": {
     "editable": true
    },
@@ -47359,7 +47360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e88c504",
+   "id": "6540422f",
    "metadata": {
     "editable": true
    },
@@ -47370,7 +47371,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7299b0d3",
+   "id": "fd8c2326",
    "metadata": {
     "editable": true
    },
@@ -47390,7 +47391,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c849f0cc",
+   "id": "74eabad7",
    "metadata": {
     "editable": true
    },
@@ -47402,7 +47403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f19b2ed7",
+   "id": "f9d16e2f",
    "metadata": {
     "editable": true
    },
@@ -47439,7 +47440,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96581350",
+   "id": "68c24098",
    "metadata": {
     "editable": true
    },
@@ -47449,7 +47450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c5aa09d",
+   "id": "02c1e06d",
    "metadata": {
     "editable": true
    },
@@ -47462,7 +47463,7 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "9b979206",
+   "id": "972b8e94",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -47663,7 +47664,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec7cab35",
+   "id": "734d97bc",
    "metadata": {
     "editable": true
    },
@@ -47680,7 +47681,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7366658f",
+   "id": "2c2d0e2c",
    "metadata": {
     "editable": true
    },
@@ -47697,7 +47698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6557284",
+   "id": "9de00307",
    "metadata": {
     "editable": true
    },
@@ -47707,7 +47708,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df2d7d07",
+   "id": "cb659253",
    "metadata": {
     "editable": true
    },
@@ -47722,7 +47723,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aad0506a",
+   "id": "909d23ae",
    "metadata": {
     "editable": true
    },
@@ -47736,7 +47737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e5776d1",
+   "id": "e3607f9e",
    "metadata": {
     "editable": true
    },
@@ -47749,7 +47750,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fad71c5",
+   "id": "e0254d92",
    "metadata": {
     "editable": true
    },
@@ -47769,7 +47770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98bd52b",
+   "id": "7a787737",
    "metadata": {
     "editable": true
    },
@@ -47781,7 +47782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f6cb731",
+   "id": "42cfda53",
    "metadata": {
     "editable": true
    },
@@ -47793,7 +47794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0efeb6a7",
+   "id": "41fdd74a",
    "metadata": {
     "editable": true
    },
@@ -47805,7 +47806,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3367fd8",
+   "id": "9a43a5c3",
    "metadata": {
     "editable": true
    },
@@ -47815,7 +47816,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5cdf037",
+   "id": "2deb98de",
    "metadata": {
     "editable": true
    },
@@ -47827,7 +47828,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39090b0c",
+   "id": "367f7d4b",
    "metadata": {
     "editable": true
    },
@@ -47839,7 +47840,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "306f52ce",
+   "id": "4ace8d41",
    "metadata": {
     "editable": true
    },
@@ -47851,7 +47852,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4dddd0e4",
+   "id": "014d9b72",
    "metadata": {
     "editable": true
    },
@@ -47861,7 +47862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19ba57a3",
+   "id": "91cb0d4f",
    "metadata": {
     "editable": true
    },
@@ -47877,7 +47878,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f4b369e",
+   "id": "7015c1df",
    "metadata": {
     "editable": true
    },
@@ -47887,7 +47888,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01054c66",
+   "id": "a170f9bf",
    "metadata": {
     "editable": true
    },
@@ -47899,7 +47900,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48250dfa",
+   "id": "f79c87b0",
    "metadata": {
     "editable": true
    },
@@ -47916,7 +47917,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "830538cd",
+   "id": "7b00c2c7",
    "metadata": {
     "editable": true
    },
@@ -47926,7 +47927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e05f3d1",
+   "id": "1da2ec1f",
    "metadata": {
     "editable": true
    },
@@ -47942,7 +47943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "278b7644",
+   "id": "d048b2b0",
    "metadata": {
     "editable": true
    },
@@ -47956,7 +47957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08bf068d",
+   "id": "2a5423c6",
    "metadata": {
     "editable": true
    },
@@ -47975,7 +47976,7 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "fb15b704",
+   "id": "39978a3f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -48030,7 +48031,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca43eaaa",
+   "id": "d86acd9a",
    "metadata": {
     "editable": true
    },
@@ -48060,7 +48061,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cb99e50",
+   "id": "219af542",
    "metadata": {
     "editable": true
    },
@@ -48089,7 +48090,7 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "2c311458",
+   "id": "0300f83e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -48136,7 +48137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ce6fcdb",
+   "id": "63ff2d7d",
    "metadata": {
     "editable": true
    },
@@ -48162,7 +48163,7 @@
   {
    "cell_type": "code",
    "execution_count": 51,
-   "id": "975ad28f",
+   "id": "504a8a89",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -48396,7 +48397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a85b7bc6",
+   "id": "2154560c",
    "metadata": {
     "editable": true
    },
@@ -48408,7 +48409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "913742fb",
+   "id": "36990efc",
    "metadata": {
     "editable": true
    },
@@ -48420,7 +48421,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b936d66",
+   "id": "d4e6e7d4",
    "metadata": {
     "editable": true
    },
@@ -48432,7 +48433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a0cd719f",
+   "id": "cca6cfed",
    "metadata": {
     "editable": true
    },
@@ -48449,7 +48450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a8ddb73",
+   "id": "19f73071",
    "metadata": {
     "editable": true
    },
@@ -48459,7 +48460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "460bb8e2",
+   "id": "3e637804",
    "metadata": {
     "editable": true
    },
@@ -48471,7 +48472,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "619814ea",
+   "id": "1a3ef69a",
    "metadata": {
     "editable": true
    },
@@ -48488,7 +48489,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "833fef22",
+   "id": "b9206a11",
    "metadata": {
     "editable": true
    },
@@ -48499,7 +48500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72df2582",
+   "id": "3050dcc1",
    "metadata": {
     "editable": true
    },
@@ -48519,7 +48520,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc2be56",
+   "id": "2adca788",
    "metadata": {
     "editable": true
    },
@@ -48529,7 +48530,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bee39ce",
+   "id": "9d36478f",
    "metadata": {
     "editable": true
    },
@@ -48555,7 +48556,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e133bda5",
+   "id": "f5a39291",
    "metadata": {
     "editable": true
    },
@@ -48571,7 +48572,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cc804aa",
+   "id": "2090b5b8",
    "metadata": {
     "editable": true
    },
@@ -48582,7 +48583,7 @@
   {
    "cell_type": "code",
    "execution_count": 52,
-   "id": "8e3fb51d",
+   "id": "0598530e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -48813,7 +48814,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a77decf5",
+   "id": "518138c8",
    "metadata": {
     "editable": true
    },
diff --git a/doc/LectureNotes/_build/jupyter_execute/week43.py b/doc/LectureNotes/_build/jupyter_execute/week43.py
index 341d8504e..6aec0a7bd 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week43.py
+++ b/doc/LectureNotes/_build/jupyter_execute/week43.py
@@ -210,13 +210,14 @@
 # and multiplying with $\boldsymbol{a}_h$ gives the output
 
 # $$
-# \boldsymbol{a}_o=\boldsymbol{w}_h^T\begin{bmatrix} 0 & 0 \\
+# \boldsymbol{a}_o=\begin{bmatrix} 0 & 0 \\
 #                        1 & 0 \\
 # 		       1 & 0 \\
-# 		       2 & 1 \end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
+# 		       2 & 1 \end{bmatrix}\begin{bmatrix} 1 \\
+#                        -2\end{bmatrix}=\begin{bmatrix} 0 \\ 1 \\ 1 \\0\end{bmatrix},
 # $$
 
-# the wanted result.
+# the wanted result.  Pay attention to the dimensionalities as well.
 
 # ## Setting up the Neural Network
 # 
diff --git a/doc/LectureNotes/week43.ipynb b/doc/LectureNotes/week43.ipynb
index 8de3714cd..4c84cfe33 100644
--- a/doc/LectureNotes/week43.ipynb
+++ b/doc/LectureNotes/week43.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "8d7cc066",
+   "id": "88f6e253",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "028dc8c6",
+   "id": "ebd16d73",
    "metadata": {
     "editable": true
    },
@@ -29,7 +29,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15ef2310",
+   "id": "e9bc94b9",
    "metadata": {
     "editable": true
    },
@@ -73,7 +73,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "192aa783",
+   "id": "457d4421",
    "metadata": {
     "editable": true
    },
@@ -87,7 +87,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22874f1a",
+   "id": "e86537af",
    "metadata": {
     "editable": true
    },
@@ -104,7 +104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29c53621",
+   "id": "14ffcfd0",
    "metadata": {
     "editable": true
    },
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3ab8226",
+   "id": "5773ab41",
    "metadata": {
     "editable": true
    },
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d686af76",
+   "id": "fdcb6f1e",
    "metadata": {
     "editable": true
    },
@@ -189,7 +189,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e6ae224",
+   "id": "7bc3e18a",
    "metadata": {
     "editable": true
    },
@@ -201,7 +201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee5e7e34",
+   "id": "b82f5167",
    "metadata": {
     "editable": true
    },
@@ -216,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da275174",
+   "id": "1ff6327f",
    "metadata": {
     "editable": true
    },
@@ -246,7 +246,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78669a54",
+   "id": "fd88cb2a",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "453ff3ab",
+   "id": "277ccf21",
    "metadata": {
     "editable": true
    },
@@ -271,7 +271,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d82c2f1",
+   "id": "69024cd6",
    "metadata": {
     "editable": true
    },
@@ -281,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a22ab766",
+   "id": "3739f7f4",
    "metadata": {
     "editable": true
    },
@@ -296,7 +296,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abfc4274",
+   "id": "891fbfbd",
    "metadata": {
     "editable": true
    },
@@ -306,7 +306,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7b0970",
+   "id": "0befa9f2",
    "metadata": {
     "editable": true
    },
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1e78b4a",
+   "id": "8b87520f",
    "metadata": {
     "editable": true
    },
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ee46428",
+   "id": "0c36a6e9",
    "metadata": {
     "editable": true
    },
@@ -344,7 +344,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bac66371",
+   "id": "6a5ebf2f",
    "metadata": {
     "editable": true
    },
@@ -354,7 +354,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77606059",
+   "id": "5c2cce0f",
    "metadata": {
     "editable": true
    },
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1a1f219",
+   "id": "6700bff0",
    "metadata": {
     "editable": true
    },
@@ -379,7 +379,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a46fd0d7",
+   "id": "c9deb439",
    "metadata": {
     "editable": true
    },
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01e41f6f",
+   "id": "bca3d76a",
    "metadata": {
     "editable": true
    },
@@ -402,32 +402,33 @@
   },
   {
    "cell_type": "markdown",
-   "id": "371a2c47",
+   "id": "0fd2b2d0",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\boldsymbol{a}_o=\\boldsymbol{w}_h^T\\begin{bmatrix} 0 & 0 \\\\\n",
+    "\\boldsymbol{a}_o=\\begin{bmatrix} 0 & 0 \\\\\n",
     "                       1 & 0 \\\\\n",
     "\t\t       1 & 0 \\\\\n",
-    "\t\t       2 & 1 \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
+    "\t\t       2 & 1 \\end{bmatrix}\\begin{bmatrix} 1 \\\\\n",
+    "                       -2\\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 1 \\\\ 1 \\\\0\\end{bmatrix},\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8ab62ed9",
+   "id": "aef5937c",
    "metadata": {
     "editable": true
    },
    "source": [
-    "the wanted result."
+    "the wanted result.  Pay attention to the dimensionalities as well."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "ee45366d",
+   "id": "784de267",
    "metadata": {
     "editable": true
    },
@@ -440,7 +441,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "43b32c8a",
+   "id": "1529f64e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -510,7 +511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce3f8d7b",
+   "id": "6c344985",
    "metadata": {
     "editable": true
    },
@@ -520,7 +521,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a60227f",
+   "id": "dda91d6e",
    "metadata": {
     "editable": true
    },
@@ -531,7 +532,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "0574c4c7",
+   "id": "dc12224d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -596,7 +597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3db2190",
+   "id": "7c9b27ed",
    "metadata": {
     "editable": true
    },
@@ -615,7 +616,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b6e8500",
+   "id": "e8e28114",
    "metadata": {
     "editable": true
    },
@@ -637,7 +638,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "ee32fb88",
+   "id": "37a2ec80",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -778,7 +779,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6477d18f",
+   "id": "38ea41a5",
    "metadata": {
     "editable": true
    },
@@ -794,7 +795,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "5a396095",
+   "id": "869cf239",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -807,7 +808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28bd1ab9",
+   "id": "b9b25144",
    "metadata": {
     "editable": true
    },
@@ -819,7 +820,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "fb5d04e9",
+   "id": "7d2dc23b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -841,7 +842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1229684",
+   "id": "83b5e35f",
    "metadata": {
     "editable": true
    },
@@ -857,7 +858,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "f4a50c76",
+   "id": "4c217329",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -895,7 +896,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d646164",
+   "id": "a0515ac9",
    "metadata": {
     "editable": true
    },
@@ -908,7 +909,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "b0057b55",
+   "id": "5eb41a10",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -929,7 +930,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37f67196",
+   "id": "0535d6fd",
    "metadata": {
     "editable": true
    },
@@ -945,7 +946,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "ae3c2dad",
+   "id": "c55d6d5f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1003,7 +1004,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5be7f268",
+   "id": "b820a2a1",
    "metadata": {
     "editable": true
    },
@@ -1018,7 +1019,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "5296db7b",
+   "id": "43974d31",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1039,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa62814a",
+   "id": "ec754834",
    "metadata": {
     "editable": true
    },
@@ -1063,7 +1064,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "08db6527",
+   "id": "505e52ab",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1535,7 +1536,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "464f4548",
+   "id": "00aa7046",
    "metadata": {
     "editable": true
    },
@@ -1547,7 +1548,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "ea3d3c51",
+   "id": "b0b45dd4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1591,7 +1592,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6b49446",
+   "id": "cf9645c3",
    "metadata": {
     "editable": true
    },
@@ -1607,7 +1608,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "4f0f50b6",
+   "id": "a792c324",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1622,7 +1623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ae3f1e4",
+   "id": "e11ed70e",
    "metadata": {
     "editable": true
    },
@@ -1633,7 +1634,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "4d206fa2",
+   "id": "dfd03f3c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1648,7 +1649,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27ffcb75",
+   "id": "99b1bd91",
    "metadata": {
     "editable": true
    },
@@ -1664,7 +1665,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "8cf19432",
+   "id": "864038bb",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1678,7 +1679,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97abfa15",
+   "id": "24d5f3cc",
    "metadata": {
     "editable": true
    },
@@ -1693,7 +1694,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "5aa3cb16",
+   "id": "14df9a52",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1719,7 +1720,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "793cb2e9",
+   "id": "adb3edf2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1734,7 +1735,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b47a35a",
+   "id": "fa885022",
    "metadata": {
     "editable": true
    },
@@ -1745,7 +1746,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "e34123b4",
+   "id": "1b862f90",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1760,7 +1761,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "413243c9",
+   "id": "e86e60dc",
    "metadata": {
     "editable": true
    },
@@ -1771,7 +1772,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "aa7b9e8f",
+   "id": "9e578191",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1791,7 +1792,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "c66ee57f",
+   "id": "bbfc34f4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1806,7 +1807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aca7922f",
+   "id": "2ac7ad43",
    "metadata": {
     "editable": true
    },
@@ -1821,7 +1822,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "1503f15a",
+   "id": "f4a821cd",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1858,7 +1859,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "838cf72d",
+   "id": "0fcf8bf2",
    "metadata": {
     "editable": true
    },
@@ -1871,7 +1872,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "a4444105",
+   "id": "d91608cf",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1894,7 +1895,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bbdf09c",
+   "id": "494009be",
    "metadata": {
     "editable": true
    },
@@ -1904,7 +1905,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5cffe73",
+   "id": "db70a4fe",
    "metadata": {
     "editable": true
    },
@@ -1914,7 +1915,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e88dc6ab",
+   "id": "e5fc9732",
    "metadata": {
     "editable": true
    },
@@ -1943,7 +1944,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ec227a0",
+   "id": "1f986c86",
    "metadata": {
     "editable": true
    },
@@ -1993,7 +1994,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "5336138a",
+   "id": "0f845fb5",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2046,7 +2047,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4f9c76",
+   "id": "fbab1656",
    "metadata": {
     "editable": true
    },
@@ -2067,7 +2068,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "3d4a38d4",
+   "id": "3ecd3028",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2105,7 +2106,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc7c43bb",
+   "id": "b45412df",
    "metadata": {
     "editable": true
    },
@@ -2149,7 +2150,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60a15786",
+   "id": "e90b1e65",
    "metadata": {
     "editable": true
    },
@@ -2189,7 +2190,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9b2c952",
+   "id": "92bff738",
    "metadata": {
     "editable": true
    },
@@ -2210,7 +2211,7 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "a6dfcaaf",
+   "id": "8eb225e4",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2236,7 +2237,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "623ec89c",
+   "id": "da1e7ad6",
    "metadata": {
     "editable": true
    },
@@ -2264,7 +2265,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "391b8f09",
+   "id": "52ea3780",
    "metadata": {
     "editable": true
    },
@@ -2301,7 +2302,7 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "a3a7a56e",
+   "id": "8ec12507",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2347,7 +2348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a467f9c",
+   "id": "518a6c33",
    "metadata": {
     "editable": true
    },
@@ -2378,7 +2379,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "824f2150",
+   "id": "9e4fe561",
    "metadata": {
     "editable": true
    },
@@ -2416,7 +2417,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad801a4f",
+   "id": "331db754",
    "metadata": {
     "editable": true
    },
@@ -2450,7 +2451,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adbd5bf5",
+   "id": "94f8797f",
    "metadata": {
     "editable": true
    },
@@ -2491,7 +2492,7 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "03850373",
+   "id": "6cc0ad5a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2570,7 +2571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c4ce702",
+   "id": "66341fe5",
    "metadata": {
     "editable": true
    },
@@ -2591,7 +2592,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f54c055f",
+   "id": "4654bdd2",
    "metadata": {
     "editable": true
    },
@@ -2605,7 +2606,7 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "05fadefb",
+   "id": "84200c9e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2715,7 +2716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d6bba32",
+   "id": "2fade818",
    "metadata": {
     "editable": true
    },
@@ -2734,7 +2735,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "5605c90f",
+   "id": "da2d74fa",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2761,7 +2762,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f22bb889",
+   "id": "45f911b8",
    "metadata": {
     "editable": true
    },
@@ -2775,7 +2776,7 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "a097c9e1",
+   "id": "b21a2c19",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2806,7 +2807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc02f298",
+   "id": "80801250",
    "metadata": {
     "editable": true
    },
@@ -2817,7 +2818,7 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "970ba03e",
+   "id": "303e085a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2861,7 +2862,7 @@
   },
   {
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@@ -2884,7 +2885,7 @@
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@@ -2911,7 +2912,7 @@
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@@ -2922,7 +2923,7 @@
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@@ -2967,7 +2968,7 @@
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@@ -2985,7 +2986,7 @@
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@@ -3020,7 +3021,7 @@
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@@ -3032,7 +3033,7 @@
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@@ -3044,7 +3045,7 @@
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@@ -3057,7 +3058,7 @@
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@@ -3068,7 +3069,7 @@
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@@ -3081,7 +3082,7 @@
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@@ -3096,7 +3097,7 @@
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@@ -3108,7 +3109,7 @@
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@@ -3120,7 +3121,7 @@
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@@ -3133,7 +3134,7 @@
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@@ -3188,7 +3189,7 @@
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@@ -3217,7 +3218,7 @@
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@@ -3247,7 +3248,7 @@
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@@ -3274,7 +3275,7 @@
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@@ -3316,7 +3317,7 @@
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@@ -3327,7 +3328,7 @@
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@@ -3504,7 +3505,7 @@
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@@ -3532,7 +3533,7 @@
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@@ -3555,7 +3556,7 @@
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@@ -3586,7 +3587,7 @@
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@@ -3618,7 +3619,7 @@
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@@ -3656,7 +3657,7 @@
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@@ -3681,7 +3682,7 @@
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@@ -3693,7 +3694,7 @@
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@@ -3716,7 +3717,7 @@
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@@ -3736,7 +3737,7 @@
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@@ -3758,7 +3759,7 @@
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@@ -3776,7 +3777,7 @@
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@@ -3795,7 +3796,7 @@
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@@ -3807,7 +3808,7 @@
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@@ -3852,7 +3853,7 @@
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@@ -3882,7 +3883,7 @@
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@@ -3909,7 +3910,7 @@
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@@ -3923,7 +3924,7 @@
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@@ -3940,7 +3941,7 @@
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@@ -3956,7 +3957,7 @@
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@@ -3968,7 +3969,7 @@
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@@ -3986,7 +3987,7 @@
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@@ -4007,7 +4008,7 @@
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@@ -4024,7 +4025,7 @@
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@@ -4036,7 +4037,7 @@
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@@ -4047,7 +4048,7 @@
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@@ -4064,7 +4065,7 @@
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@@ -4075,7 +4076,7 @@
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@@ -4091,7 +4092,7 @@
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@@ -4103,7 +4104,7 @@
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@@ -4120,7 +4121,7 @@
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@@ -4132,7 +4133,7 @@
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@@ -4150,7 +4151,7 @@
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@@ -4160,7 +4161,7 @@
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@@ -4172,7 +4173,7 @@
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@@ -4189,7 +4190,7 @@
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@@ -4201,7 +4202,7 @@
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@@ -4212,7 +4213,7 @@
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@@ -4224,7 +4225,7 @@
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@@ -4234,7 +4235,7 @@
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@@ -4254,7 +4255,7 @@
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@@ -4271,7 +4272,7 @@
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@@ -4290,7 +4291,7 @@
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@@ -4302,7 +4303,7 @@
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@@ -4312,7 +4313,7 @@
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@@ -4329,7 +4330,7 @@
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@@ -4339,7 +4340,7 @@
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@@ -4355,7 +4356,7 @@
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@@ -4367,7 +4368,7 @@
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@@ -4379,7 +4380,7 @@
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@@ -4391,7 +4392,7 @@
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@@ -4401,7 +4402,7 @@
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@@ -4413,7 +4414,7 @@
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@@ -4430,7 +4431,7 @@
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@@ -4440,7 +4441,7 @@
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@@ -4452,7 +4453,7 @@
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@@ -4466,7 +4467,7 @@
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@@ -4482,7 +4483,7 @@
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@@ -4494,7 +4495,7 @@
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@@ -4516,7 +4517,7 @@
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@@ -4528,7 +4529,7 @@
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@@ -4551,7 +4552,7 @@
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@@ -4567,7 +4568,7 @@
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@@ -4579,7 +4580,7 @@
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@@ -4603,7 +4604,7 @@
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@@ -4615,7 +4616,7 @@
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@@ -4636,7 +4637,7 @@
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@@ -4648,7 +4649,7 @@
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@@ -4667,7 +4668,7 @@
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@@ -4677,7 +4678,7 @@
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@@ -4691,7 +4692,7 @@
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@@ -4703,7 +4704,7 @@
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@@ -4715,7 +4716,7 @@
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@@ -4732,7 +4733,7 @@
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@@ -4744,7 +4745,7 @@
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@@ -4766,7 +4767,7 @@
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@@ -4781,7 +4782,7 @@
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@@ -4792,7 +4793,7 @@
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@@ -4947,7 +4948,7 @@
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+   "id": "0147790d",
    "metadata": {
     "editable": true
    },
@@ -4962,7 +4963,7 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "96758ada",
+   "id": "59eb96af",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5131,7 +5132,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c62fedb8",
+   "id": "dc02c291",
    "metadata": {
     "editable": true
    },
@@ -5144,7 +5145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f962431",
+   "id": "c8fff51e",
    "metadata": {
     "editable": true
    },
@@ -5161,7 +5162,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71b1d885",
+   "id": "3751edf7",
    "metadata": {
     "editable": true
    },
@@ -5177,7 +5178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b96a028",
+   "id": "a502c731",
    "metadata": {
     "editable": true
    },
@@ -5190,7 +5191,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "311ae3d3",
+   "id": "eb73f07e",
    "metadata": {
     "editable": true
    },
@@ -5207,7 +5208,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98cb3d44",
+   "id": "9ab9d930",
    "metadata": {
     "editable": true
    },
@@ -5219,7 +5220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e8e134d",
+   "id": "9cb8689a",
    "metadata": {
     "editable": true
    },
@@ -5246,7 +5247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1844ff9",
+   "id": "d21e3a14",
    "metadata": {
     "editable": true
    },
@@ -5259,7 +5260,7 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "4410b99e",
+   "id": "833da16b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5433,7 +5434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0ab0e0f",
+   "id": "0fdcf8c5",
    "metadata": {
     "editable": true
    },
@@ -5453,7 +5454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "333b0a8d",
+   "id": "0a057338",
    "metadata": {
     "editable": true
    },
@@ -5468,7 +5469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b358fbf",
+   "id": "6721bcf2",
    "metadata": {
     "editable": true
    },
@@ -5482,7 +5483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5d60864",
+   "id": "dc3db9fd",
    "metadata": {
     "editable": true
    },
@@ -5498,7 +5499,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcce6eb8",
+   "id": "9af3fd6a",
    "metadata": {
     "editable": true
    },
@@ -5508,7 +5509,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6497fd7",
+   "id": "4c2da445",
    "metadata": {
     "editable": true
    },
@@ -5530,7 +5531,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31b650fc",
+   "id": "93b58380",
    "metadata": {
     "editable": true
    },
@@ -5544,7 +5545,7 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "6e267e72",
+   "id": "cb73915d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5620,7 +5621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b054a85",
+   "id": "c9d250c7",
    "metadata": {
     "editable": true
    },
@@ -5632,7 +5633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f637dd9d",
+   "id": "0d67bc8c",
    "metadata": {
     "editable": true
    },
@@ -5649,7 +5650,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac088e86",
+   "id": "fe4ee5a8",
    "metadata": {
     "editable": true
    },
@@ -5661,7 +5662,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14afd7fa",
+   "id": "62b400ca",
    "metadata": {
     "editable": true
    },
@@ -5676,7 +5677,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a2680eb",
+   "id": "7d4723f2",
    "metadata": {
     "editable": true
    },
@@ -5688,7 +5689,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e30575f",
+   "id": "97889b0e",
    "metadata": {
     "editable": true
    },
@@ -5700,7 +5701,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b30e08a",
+   "id": "236028bc",
    "metadata": {
     "editable": true
    },
@@ -5712,7 +5713,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be7d958b",
+   "id": "a4334818",
    "metadata": {
     "editable": true
    },
@@ -5722,7 +5723,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6a52e39",
+   "id": "8330dd77",
    "metadata": {
     "editable": true
    },
@@ -5739,7 +5740,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "488d0a14",
+   "id": "78522018",
    "metadata": {
     "editable": true
    },
@@ -5751,7 +5752,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59834674",
+   "id": "943956e4",
    "metadata": {
     "editable": true
    },
@@ -5763,7 +5764,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af640638",
+   "id": "3c7b57e2",
    "metadata": {
     "editable": true
    },
@@ -5773,7 +5774,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d83ea23",
+   "id": "55173c99",
    "metadata": {
     "editable": true
    },
@@ -5785,7 +5786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d4e4ea8",
+   "id": "a6d078e4",
    "metadata": {
     "editable": true
    },
@@ -5796,7 +5797,7 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "ad4cc32f",
+   "id": "452c599c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5957,7 +5958,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ceb283ce",
+   "id": "8ca2348f",
    "metadata": {
     "editable": true
    },
@@ -5979,7 +5980,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a68e0e56",
+   "id": "0ccc174e",
    "metadata": {
     "editable": true
    },
@@ -5996,7 +5997,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8441e4e6",
+   "id": "d4601257",
    "metadata": {
     "editable": true
    },
@@ -6006,7 +6007,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d343e68",
+   "id": "9ec01889",
    "metadata": {
     "editable": true
    },
@@ -6021,7 +6022,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c566531",
+   "id": "71993d6c",
    "metadata": {
     "editable": true
    },
@@ -6031,7 +6032,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a06b755",
+   "id": "f6acfae4",
    "metadata": {
     "editable": true
    },
@@ -6046,7 +6047,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e88c504",
+   "id": "6540422f",
    "metadata": {
     "editable": true
    },
@@ -6057,7 +6058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7299b0d3",
+   "id": "fd8c2326",
    "metadata": {
     "editable": true
    },
@@ -6077,7 +6078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c849f0cc",
+   "id": "74eabad7",
    "metadata": {
     "editable": true
    },
@@ -6089,7 +6090,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f19b2ed7",
+   "id": "f9d16e2f",
    "metadata": {
     "editable": true
    },
@@ -6126,7 +6127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96581350",
+   "id": "68c24098",
    "metadata": {
     "editable": true
    },
@@ -6136,7 +6137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c5aa09d",
+   "id": "02c1e06d",
    "metadata": {
     "editable": true
    },
@@ -6149,7 +6150,7 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "9b979206",
+   "id": "972b8e94",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6350,7 +6351,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec7cab35",
+   "id": "734d97bc",
    "metadata": {
     "editable": true
    },
@@ -6367,7 +6368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7366658f",
+   "id": "2c2d0e2c",
    "metadata": {
     "editable": true
    },
@@ -6384,7 +6385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6557284",
+   "id": "9de00307",
    "metadata": {
     "editable": true
    },
@@ -6394,7 +6395,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df2d7d07",
+   "id": "cb659253",
    "metadata": {
     "editable": true
    },
@@ -6409,7 +6410,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aad0506a",
+   "id": "909d23ae",
    "metadata": {
     "editable": true
    },
@@ -6423,7 +6424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e5776d1",
+   "id": "e3607f9e",
    "metadata": {
     "editable": true
    },
@@ -6436,7 +6437,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fad71c5",
+   "id": "e0254d92",
    "metadata": {
     "editable": true
    },
@@ -6456,7 +6457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98bd52b",
+   "id": "7a787737",
    "metadata": {
     "editable": true
    },
@@ -6468,7 +6469,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f6cb731",
+   "id": "42cfda53",
    "metadata": {
     "editable": true
    },
@@ -6480,7 +6481,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0efeb6a7",
+   "id": "41fdd74a",
    "metadata": {
     "editable": true
    },
@@ -6492,7 +6493,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3367fd8",
+   "id": "9a43a5c3",
    "metadata": {
     "editable": true
    },
@@ -6502,7 +6503,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5cdf037",
+   "id": "2deb98de",
    "metadata": {
     "editable": true
    },
@@ -6514,7 +6515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39090b0c",
+   "id": "367f7d4b",
    "metadata": {
     "editable": true
    },
@@ -6526,7 +6527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "306f52ce",
+   "id": "4ace8d41",
    "metadata": {
     "editable": true
    },
@@ -6538,7 +6539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4dddd0e4",
+   "id": "014d9b72",
    "metadata": {
     "editable": true
    },
@@ -6548,7 +6549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19ba57a3",
+   "id": "91cb0d4f",
    "metadata": {
     "editable": true
    },
@@ -6564,7 +6565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f4b369e",
+   "id": "7015c1df",
    "metadata": {
     "editable": true
    },
@@ -6574,7 +6575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01054c66",
+   "id": "a170f9bf",
    "metadata": {
     "editable": true
    },
@@ -6586,7 +6587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48250dfa",
+   "id": "f79c87b0",
    "metadata": {
     "editable": true
    },
@@ -6603,7 +6604,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "830538cd",
+   "id": "7b00c2c7",
    "metadata": {
     "editable": true
    },
@@ -6613,7 +6614,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e05f3d1",
+   "id": "1da2ec1f",
    "metadata": {
     "editable": true
    },
@@ -6629,7 +6630,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "278b7644",
+   "id": "d048b2b0",
    "metadata": {
     "editable": true
    },
@@ -6643,7 +6644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08bf068d",
+   "id": "2a5423c6",
    "metadata": {
     "editable": true
    },
@@ -6662,7 +6663,7 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "fb15b704",
+   "id": "39978a3f",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6717,7 +6718,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca43eaaa",
+   "id": "d86acd9a",
    "metadata": {
     "editable": true
    },
@@ -6747,7 +6748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cb99e50",
+   "id": "219af542",
    "metadata": {
     "editable": true
    },
@@ -6776,7 +6777,7 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "2c311458",
+   "id": "0300f83e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6823,7 +6824,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ce6fcdb",
+   "id": "63ff2d7d",
    "metadata": {
     "editable": true
    },
@@ -6849,7 +6850,7 @@
   {
    "cell_type": "code",
    "execution_count": 51,
-   "id": "975ad28f",
+   "id": "504a8a89",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -7083,7 +7084,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a85b7bc6",
+   "id": "2154560c",
    "metadata": {
     "editable": true
    },
@@ -7095,7 +7096,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "913742fb",
+   "id": "36990efc",
    "metadata": {
     "editable": true
    },
@@ -7107,7 +7108,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b936d66",
+   "id": "d4e6e7d4",
    "metadata": {
     "editable": true
    },
@@ -7119,7 +7120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a0cd719f",
+   "id": "cca6cfed",
    "metadata": {
     "editable": true
    },
@@ -7136,7 +7137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a8ddb73",
+   "id": "19f73071",
    "metadata": {
     "editable": true
    },
@@ -7146,7 +7147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "460bb8e2",
+   "id": "3e637804",
    "metadata": {
     "editable": true
    },
@@ -7158,7 +7159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "619814ea",
+   "id": "1a3ef69a",
    "metadata": {
     "editable": true
    },
@@ -7175,7 +7176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "833fef22",
+   "id": "b9206a11",
    "metadata": {
     "editable": true
    },
@@ -7186,7 +7187,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72df2582",
+   "id": "3050dcc1",
    "metadata": {
     "editable": true
    },
@@ -7206,7 +7207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc2be56",
+   "id": "2adca788",
    "metadata": {
     "editable": true
    },
@@ -7216,7 +7217,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bee39ce",
+   "id": "9d36478f",
    "metadata": {
     "editable": true
    },
@@ -7242,7 +7243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e133bda5",
+   "id": "f5a39291",
    "metadata": {
     "editable": true
    },
@@ -7258,7 +7259,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cc804aa",
+   "id": "2090b5b8",
    "metadata": {
     "editable": true
    },
@@ -7269,7 +7270,7 @@
   {
    "cell_type": "code",
    "execution_count": 52,
-   "id": "8e3fb51d",
+   "id": "0598530e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -7500,7 +7501,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a77decf5",
+   "id": "518138c8",
    "metadata": {
     "editable": true
    },

Setting up the Neural Network¶

@@ -8456,8 +8457,9 @@ case.