diff --git a/doc/LectureNotes/DataFiles/cancer.dot b/doc/LectureNotes/DataFiles/cancer.dot index fb432c33d..2699d824e 100644 --- a/doc/LectureNotes/DataFiles/cancer.dot +++ b/doc/LectureNotes/DataFiles/cancer.dot @@ -10,19 +10,19 @@ edge [fontname="helvetica"] ; 2 -> 3 ; 4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139"] ; 3 -> 4 ; -5 [label="mean radius <= 12.265\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ; +5 [label="worst compactness <= 0.085\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ; 3 -> 5 ; 6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ; 5 -> 6 ; 7 [label="gini = 0.0\nsamples = 2\nvalue = [[2, 0]\n[0, 2]]", fillcolor="#e58139"] ; 5 -> 7 ; -8 [label="worst texture <= 29.455\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ; +8 [label="mean texture <= 20.84\ngini = 0.397\nsamples = 11\nvalue = [[8, 3]\n[3, 8]]", fillcolor="#fae9dd"] ; 2 -> 8 ; 9 [label="gini = 0.0\nsamples = 8\nvalue = [[8, 0]\n[0, 8]]", fillcolor="#e58139"] ; 8 -> 9 ; 10 [label="gini = 0.0\nsamples = 3\nvalue = [[0, 3]\n[3, 0]]", fillcolor="#e58139"] ; 8 -> 10 ; -11 [label="mean texture <= 16.22\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ; +11 [label="worst texture <= 24.785\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ; 1 -> 11 ; 12 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ; 11 -> 12 ; @@ -34,7 +34,7 @@ edge [fontname="helvetica"] ; 14 -> 15 ; 16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 0]\n[0, 11]]", fillcolor="#e58139"] ; 15 -> 16 ; -17 [label="symmetry error <= 0.014\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ; +17 [label="fractal dimension error <= 0.002\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ; 15 -> 17 ; 18 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ; 17 -> 18 ; @@ -42,16 +42,16 @@ edge [fontname="helvetica"] ; 17 -> 19 ; 20 [label="mean concave points <= 0.049\ngini = 0.088\nsamples = 151\nvalue = [[7, 144]\n[144, 7]]", fillcolor="#ea985d"] ; 14 -> 20 ; -21 [label="concave points error <= 0.01\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ; +21 [label="compactness error <= 0.016\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ; 20 -> 21 ; 22 [label="gini = 0.0\nsamples = 9\nvalue = [[0, 9]\n[9, 0]]", fillcolor="#e58139"] ; 21 -> 22 ; 23 [label="gini = 0.0\nsamples = 6\nvalue = [[6, 0]\n[0, 6]]", fillcolor="#e58139"] ; 21 -> 23 ; -24 [label="mean smoothness <= 0.079\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ; +24 [label="fractal dimension error <= 0.013\ngini = 0.015\nsamples = 136\nvalue = [[1, 135]\n[135, 1]]", fillcolor="#e6853f"] ; 20 -> 24 ; -25 [label="gini = 0.0\nsamples = 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"editable": true + }, + "source": [ + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "6f7356c3", + "metadata": { + "editable": true + }, + "source": [ + "# Exercises week 42\n", + "**October 9-13, 2023**\n", + "\n", + "Date: **Deadline is Sunday October 22 at midnight**\n", + "\n", + "You can hand in the exercises from week 41 and week 42 as one exercise and get a total score of two additional points." + ] + }, + { + "cell_type": "markdown", + "id": "aa378ef2", + "metadata": { + "editable": true + }, + "source": [ + "# Overarching aims of the exercises this week\n", + "\n", + "The aim of the exercises this week is to get started with implementing\n", + "gradient methods of relevance for project 2. The exercise this week is a simple\n", + "continuation from the previous week with the addition of automatic differentation.\n", + "Everything you develop here will be used in project 2. \n", + "\n", + "In order to get started, we will now replace in our standard ordinary\n", + "least squares (OLS) and Ridge regression codes (from project 1) the\n", + "matrix inversion algorithm with our own gradient descent (GD) and SGD\n", + "codes. You can use the Franke function or the terrain data from\n", + "project 1. **However, we recommend using a simpler function like**\n", + "$f(x)=a_0+a_1x+a_2x^2$ or higher-order one-dimensional polynomials.\n", + "You can obviously test your final codes against for example the Franke\n", + "function. Automatic differentiation will be discussed next week.\n", + "\n", + "You should include in your analysis of the GD and SGD codes the following elements\n", + "1. A plain gradient descent with a fixed learning rate (you will need to tune it) using automatic differentiation. Compare this with the analytical expression of the gradients you obtained last week. Feel free to use **Autograd** as Python package or **JAX**. You can use the examples form last week.\n", + "\n", + "2. Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate). Compare this with the analytical expression of the gradients you obtained last week.\n", + "\n", + "3. Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from week 39. Discuss the results as functions of the various parameters (size of batches, number of epochs etc)\n", + "\n", + "4. Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD using automatic differentiation..\n", + "\n", + "5. Add RMSprop and Adam to your library of methods for tuning the learning rate. Again using automatic differentiation.\n", + "\n", + "The lecture notes from weeks 39 and 40 contain more information and code examples. Feel free to use these examples.\n", + "\n", + "We recommend reading chapter 8 on optimization from the textbook of [Goodfellow, Bengio and Courville](https://www.deeplearningbook.org/). This chapter contains many useful insights and discussions on the optimization part of machine learning." + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/_sources/week42.ipynb b/doc/LectureNotes/_build/html/_sources/week42.ipynb new file mode 100644 index 000000000..702b9e719 --- /dev/null +++ b/doc/LectureNotes/_build/html/_sources/week42.ipynb @@ -0,0 +1,2888 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "50ce4eae", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "f46bd6b4", + "metadata": { + "editable": true + }, + "source": [ + "# Week 42 Constructing a Neural Network code with introduction to Tensor flow\n", + "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", + "\n", + "Date: **October 16-20, 2023**" + ] + }, + { + "cell_type": "markdown", + "id": "8c0fa4d7", + "metadata": { + "editable": true + }, + "source": [ + "## Plan for week 42\n", + "\n", + "**Material for the active learning sessions on Tuesday and Wednesday.**\n", + "\n", + " * Exercise on writing your own stochastic gradient and gradient descent codes. This exercise continues from the previous week but now with inclusion of automatic differentiation\n", + "\n", + " * Discussion of project 2\n", + "\n", + " * [See video on automatic differentiation from last year](https://www.youtube.com/watch?v=cWCebuNKrA8). This video will be updated before Tuesday.\n", + "\n", + " \n", + "\n", + "**Material for the lecture on Thursday October 12, 2023.**\n", + "\n", + " * Building our own Feed-forward Neural Network and discussion of project 2\n", + "\n", + " * Readings and Videos:\n", + "\n", + " * These lecture notes\n", + "\n", + " * [Aurelien Geron's chapters 10-11](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Textbooks/TensorflowML.pdf)\n", + "\n", + " * For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. \n", + "\n", + " * [Neural Networks demystified](https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs)\n", + "\n", + " * [Building Neural Networks from scratch](https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex)\n", + "\n", + " * [Video on Neural Networks](https://www.youtube.com/watch?v=CqOfi41LfDw)\n", + "\n", + " * [Video on the back propagation algorithm](https://www.youtube.com/watch?v=Ilg3gGewQ5U)\n", + "\n", + "I also recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at ." + ] + }, + { + "cell_type": "markdown", + "id": "89b6b637", + "metadata": { + "editable": true + }, + "source": [ + "## Lecture Thursday October 19" + ] + }, + { + "cell_type": "markdown", + "id": "3a32ad82", + "metadata": { + "editable": true + }, + "source": [ + "## Review of the back propagation algorithm\n", + "\n", + "During the last lecture we discussed in detail the back propagation\n", + "algorithm. This algorithm is based on a repeated application of the\n", + "chain rule. Let us bring back the basic equation and at the same time\n", + "link this with the basic mathematics of automatic differentiation." + ] + }, + { + "cell_type": "markdown", + "id": "4f9291ee", + "metadata": { + "editable": true + }, + "source": [ + "## Setting up the Back propagation algorithm\n", + "\n", + "The four equations derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.\n", + "\n", + "First, we set up the input data $\\boldsymbol{x}$ and the activations\n", + "$\\boldsymbol{z}_1$ of the input layer and compute the activation function and\n", + "the pertinent outputs $\\boldsymbol{a}^1$.\n", + "\n", + "Secondly, we perform then the feed forward till we reach the output\n", + "layer and compute all $\\boldsymbol{z}_l$ of the input layer and compute the\n", + "activation function and the pertinent outputs $\\boldsymbol{a}^l$ for\n", + "$l=2,3,\\dots,L$.\n", + "\n", + "Thereafter we compute the ouput error $\\boldsymbol{\\delta}^L$ by computing all" + ] + }, + { + "cell_type": "markdown", + "id": "7753981f", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_j^L = f'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8b093c71", + "metadata": { + "editable": true + }, + "source": [ + "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,2$ as" + ] + }, + { + "cell_type": "markdown", + "id": "96ca25bd", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a156d8bd", + "metadata": { + "editable": true + }, + "source": [ + "Finally, we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,2$ and update the weights and biases according to the rules" + ] + }, + { + "cell_type": "markdown", + "id": "f35c8afe", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "w_{jk}^l\\leftarrow = w_{jk}^l- \\eta \\delta_j^la_k^{l-1},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ffa6d322", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "7b6e59f6", + "metadata": { + "editable": true + }, + "source": [ + "The parameter $\\eta$ is the learning parameter discussed in connection with the gradient descent methods.\n", + "Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training." + ] + }, + { + "cell_type": "markdown", + "id": "e93ff00c", + "metadata": { + "editable": true + }, + "source": [ + "## Setting up a Multi-layer perceptron model for classification\n", + "\n", + "We are now gong to develop an example based on the MNIST data\n", + "base. This is a classification problem and we need to use our\n", + "cross-entropy function we discussed in connection with logistic\n", + "regression. The cross-entropy defines our cost function for the\n", + "classificaton problems with neural networks.\n", + "\n", + "In binary classification with two classes $(0, 1)$ we define the\n", + "logistic/sigmoid function as the probability that a particular input\n", + "is in class $0$ or $1$. This is possible because the logistic\n", + "function takes any input from the real numbers and inputs a number\n", + "between 0 and 1, and can therefore be interpreted as a probability. It\n", + "also has other nice properties, such as a derivative that is simple to\n", + "calculate.\n", + "\n", + "For an input $\\boldsymbol{a}$ from the hidden layer, the probability that the input $\\boldsymbol{x}$\n", + "is in class 0 or 1 is just. We let $\\theta$ represent the unknown weights and biases to be adjusted by our equations). The variable $x$\n", + "represents our activation values $z$. We have" + ] + }, + { + "cell_type": "markdown", + "id": "3c437395", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3d7b1140", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "e3df5aec", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "63345646", + "metadata": { + "editable": true + }, + "source": [ + "where $y \\in \\{0, 1\\}$ and $\\boldsymbol{\\theta}$ represents the weights and biases\n", + "of our network." + ] + }, + { + "cell_type": "markdown", + "id": "6ac465b3", + "metadata": { + "editable": true + }, + "source": [ + "## Defining the cost function\n", + "\n", + "Our cost function is given as (see the Logistic regression lectures)" + ] + }, + { + "cell_type": "markdown", + "id": "cf06b4a0", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n", + "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\boldsymbol{\\theta}) .\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "719f761f", + "metadata": { + "editable": true + }, + "source": [ + "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n", + "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$. \n", + "The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather\n", + "than maximizing a negative number. \n", + "\n", + "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector: \n", + "\n", + "$y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n", + "\n", + "$y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n", + "\n", + "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$).. \n", + "\n", + "If $\\boldsymbol{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n", + "output vector $\\boldsymbol{y}_i$. \n", + "The probability of $\\boldsymbol{x}_i$ being in class $c$ will be given by the softmax function:" + ] + }, + { + "cell_type": "markdown", + "id": "342de1d9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n", + "{\\sum_{c'=0}^{C-1} \\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_{c'})}} ,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "211a69ba", + "metadata": { + "editable": true + }, + "source": [ + "which reduces to the logistic function in the binary case. \n", + "The likelihood of this $C$-class classifier\n", + "is now given as:" + ] + }, + { + "cell_type": "markdown", + "id": "5f0cd5a2", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fe018e32", + "metadata": { + "editable": true + }, + "source": [ + "Again we take the negative log-likelihood to define our cost function:" + ] + }, + { + "cell_type": "markdown", + "id": "9d48faca", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "897c8b0c", + "metadata": { + "editable": true + }, + "source": [ + "See the logistic regression lectures for a full definition of the cost function.\n", + "\n", + "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!" + ] + }, + { + "cell_type": "markdown", + "id": "68347a7f", + "metadata": { + "editable": true + }, + "source": [ + "## Example: binary classification problem\n", + "\n", + "As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\\beta$ as" + ] + }, + { + "cell_type": "markdown", + "id": "8425d868", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "9108d4ac", + "metadata": { + "editable": true + }, + "source": [ + "where we had defined the logistic (sigmoid) function" + ] + }, + { + "cell_type": "markdown", + "id": "77e0ec3b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "64ed867c", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "51819578", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "db6532a5", + "metadata": { + "editable": true + }, + "source": [ + "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n", + "\n", + "Now we replace $x_i$ with the activation $z_i^l$ for a given layer $l$ and the outputs as $y_i=a_i^l=f(z_i^l)$, with $z_i^l$ now being a function of the weights $w_{ij}^l$ and biases $b_i^l$. \n", + "We have then" + ] + }, + { + "cell_type": "markdown", + "id": "24e5e213", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d398c961", + "metadata": { + "editable": true + }, + "source": [ + "with" + ] + }, + { + "cell_type": "markdown", + "id": "236d161c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "25e3004d", + "metadata": { + "editable": true + }, + "source": [ + "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n", + "Our cost function at the final layer $l=L$ is now" + ] + }, + { + "cell_type": "markdown", + "id": "9440c725", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "782f5282", + "metadata": { + "editable": true + }, + "source": [ + "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get" + ] + }, + { + "cell_type": "markdown", + "id": "0e8498a5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "68398b35", + "metadata": { + "editable": true + }, + "source": [ + "In case we use another activation function than the logistic one, we need to evaluate other derivatives." + ] + }, + { + "cell_type": "markdown", + "id": "19887152", + "metadata": { + "editable": true + }, + "source": [ + "## The Softmax function\n", + "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need" + ] + }, + { + "cell_type": "markdown", + "id": "80e8dc5d", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n", + "\\frac{\\partial f(z_i^l)}{\\partial z_j^l} \\frac{\\partial z_j^l}{\\partial w_{jk}^l}= \\frac{\\partial f(z_i^l)}{\\partial z_j^l}a_k^{l-1}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "68d33776", + "metadata": { + "editable": true + }, + "source": [ + "For the Softmax function we have" + ] + }, + { + "cell_type": "markdown", + "id": "3c86943c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "efe53876", + "metadata": { + "editable": true + }, + "source": [ + "Its derivative with respect to $z_j^l$ gives" + ] + }, + { + "cell_type": "markdown", + "id": "fce5b9b2", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "97210471", + "metadata": { + "editable": true + }, + "source": [ + "which in case of the simply binary model reduces to having $i=j$." + ] + }, + { + "cell_type": "markdown", + "id": "4f515591", + "metadata": { + "editable": true + }, + "source": [ + "## Developing a code for doing neural networks with back propagation\n", + "\n", + "One can identify a set of key steps when using neural networks to solve supervised learning problems: \n", + "\n", + "1. Collect and pre-process data \n", + "\n", + "2. Define model and architecture \n", + "\n", + "3. Choose cost function and optimizer \n", + "\n", + "4. Train the model \n", + "\n", + "5. Evaluate model performance on test data \n", + "\n", + "6. Adjust hyperparameters (if necessary, network architecture)" + ] + }, + { + "cell_type": "markdown", + "id": "ec34f212", + "metadata": { + "editable": true + }, + "source": [ + "## Collect and pre-process data\n", + "\n", + "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n", + "package. You may also find it for example [here](http://yann.lecun.com/exdb/mnist/). \n", + "The *MNIST* (Modified National Institute of Standards and Technology) database is a large database\n", + "of handwritten digits that is commonly used for training various image processing systems. \n", + "The MNIST dataset consists of 70 000 images of size $28\\times 28$ pixels, each labeled from 0 to 9. \n", + "The scikit-learn dataset we will use consists of a selection of 1797 images of size $8\\times 8$ collected and processed from this database. \n", + "\n", + "To feed data into a feed-forward neural network we need to represent\n", + "the inputs as a design/feature matrix $X = (n_{inputs}, n_{features})$. Each\n", + "row represents an *input*, in this case a handwritten digit, and\n", + "each column represents a *feature*, in this case a pixel. The\n", + "correct answers, also known as *labels* or *targets* are\n", + "represented as a 1D array of integers \n", + "$Y = (n_{inputs}) = (5, 3, 1, 8,...)$.\n", + "\n", + "As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from\n", + "measurements of height (in m) \n", + "and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example: \n", + "\n", + "$$ X = \\begin{bmatrix}\n", + "1.85 & 81\\\\\n", + "1.71 & 65\\\\\n", + "1.95 & 103\\\\\n", + "1.55 & 42\\\\\n", + "1.63 & 56\n", + "\\end{bmatrix} ,$$ \n", + "\n", + "and the targets would be: \n", + "\n", + "$$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$ \n", + "\n", + "Since each input image is a 2D matrix, we need to flatten the image\n", + "(i.e. \"unravel\" the 2D matrix into a 1D array) to turn the data into a\n", + "design/feature matrix. This means we lose all spatial information in the\n", + "image, such as locality and translational invariance. More complicated\n", + "architectures such as Convolutional Neural Networks can take advantage\n", + "of such information, and are most commonly applied when analyzing\n", + "images." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e389e60e", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn import datasets\n", + "\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# display images in notebook\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = (12,12)\n", + "\n", + "\n", + "# download MNIST dataset\n", + "digits = datasets.load_digits()\n", + "\n", + "# define inputs and labels\n", + "inputs = digits.images\n", + "labels = digits.target\n", + "\n", + "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n", + "print(\"labels = (n_inputs) = \" + str(labels.shape))\n", + "\n", + "\n", + "# flatten the image\n", + "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n", + "n_inputs = len(inputs)\n", + "inputs = inputs.reshape(n_inputs, -1)\n", + "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n", + "\n", + "\n", + "# choose some random images to display\n", + "indices = np.arange(n_inputs)\n", + "random_indices = np.random.choice(indices, size=5)\n", + "\n", + "for i, image in enumerate(digits.images[random_indices]):\n", + " plt.subplot(1, 5, i+1)\n", + " plt.axis('off')\n", + " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n", + " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9a264b82", + "metadata": { + "editable": true + }, + "source": [ + "## Train and test datasets\n", + "\n", + "Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions. \n", + "\n", + "We will reserve $80 \\%$ of our dataset for training and $20 \\%$ for testing. \n", + "\n", + "It is important that the train and test datasets are drawn randomly from our dataset, to ensure\n", + "no bias in the sampling. \n", + "Say you are taking measurements of weather data to predict the weather in the coming 5 days.\n", + "You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data\n", + "collected from 12.00 to 24.00." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "8750ea41", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "from sklearn.model_selection import train_test_split\n", + "\n", + "# one-liner from scikit-learn library\n", + "train_size = 0.8\n", + "test_size = 1 - train_size\n", + "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n", + " test_size=test_size)\n", + "\n", + "# equivalently in numpy\n", + "def train_test_split_numpy(inputs, labels, train_size, test_size):\n", + " n_inputs = len(inputs)\n", + " inputs_shuffled = inputs.copy()\n", + " labels_shuffled = labels.copy()\n", + " \n", + " np.random.shuffle(inputs_shuffled)\n", + " np.random.shuffle(labels_shuffled)\n", + " \n", + " train_end = int(n_inputs*train_size)\n", + " X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]\n", + " Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]\n", + " \n", + " return X_train, X_test, Y_train, Y_test\n", + "\n", + "#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)\n", + "\n", + "print(\"Number of training images: \" + str(len(X_train)))\n", + "print(\"Number of test images: \" + str(len(X_test)))" + ] + }, + { + "cell_type": "markdown", + "id": "d3897eca", + "metadata": { + "editable": true + }, + "source": [ + "## Define model and architecture\n", + "\n", + "Our simple feed-forward neural network will consist of an *input* layer, a single *hidden* layer and an *output* layer. The activation $y$ of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have \n", + "\n", + "$$ z = \\sum_{i=1}^n w_i a_i ,$$\n", + "\n", + "$$ y = f(z) ,$$\n", + "\n", + "where $f$ is the activation function, $a_i$ represents input from neuron $i$ in the preceding layer\n", + "and $w_i$ is the weight to input $i$. \n", + "The activation of the neurons in the input layer is just the features (e.g. a pixel value). \n", + "\n", + "The simplest activation function for a neuron is the *Heaviside* function:\n", + "\n", + "$$ f(z) = \n", + "\\begin{cases}\n", + "1, & z > 0\\\\\n", + "0, & \\text{otherwise}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "A feed-forward neural network with this activation is known as a *perceptron*. \n", + "For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer. \n", + "This activation can be generalized to $k$ classes (using e.g. the *one-against-all* strategy), \n", + "and we call these architectures *multiclass perceptrons*. \n", + "\n", + "However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and \n", + "Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function. \n", + "\n", + "Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU). \n", + "We will be using the sigmoid function $\\sigma(x)$: \n", + "\n", + "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n", + "\n", + "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions." + ] + }, + { + "cell_type": "markdown", + "id": "ad593a03", + "metadata": { + "editable": true + }, + "source": [ + "## Layers\n", + "\n", + "* Input \n", + "\n", + "Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons. \n", + "\n", + "* Hidden layer\n", + "\n", + "We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer. \n", + "Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer. \n", + "\n", + "* Output\n", + "\n", + "If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,\n", + "which could output 0 or 1 according to the Heaviside function. This would be an example of a *hard* classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a *soft* classifier, which outputs the probability of being in class 0 or 1. \n", + "\n", + "For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class. \n", + "\n", + "Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons $j = 0,1,...,9$. The activation of each output neuron $j$ will be according to the *softmax* function: \n", + "\n", + "$$ P(\\text{class $j$} \\mid \\text{input $\\boldsymbol{a}$}) = \\frac{\\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_j)}}\n", + "{\\sum_{c=0}^{9} \\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_c)}} ,$$ \n", + "\n", + "i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\\boldsymbol{a}$, with $\\boldsymbol{w}_j$ the weights of neuron $j$ to the inputs. \n", + "The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1. \n", + "The exponent is just the weighted sum of inputs as before: \n", + "\n", + "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i+b_j.$$ \n", + "\n", + "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n", + "weights to the output layer." + ] + }, + { + "cell_type": "markdown", + "id": "e37b3844", + "metadata": { + "editable": true + }, + "source": [ + "## Weights and biases\n", + "\n", + "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n", + "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless. \n", + "\n", + "Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range\n", + "of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron $j$, $b_j$: \n", + "\n", + "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i + b_j.$$ \n", + "\n", + "The bias weights $\\boldsymbol{b}$ are often initialized to zero, but a small value like $0.01$ ensures all neurons have some output which can be backpropagated in the first training cycle." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3d909fc7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# building our neural network\n", + "\n", + "n_inputs, n_features = X_train.shape\n", + "n_hidden_neurons = 50\n", + "n_categories = 10\n", + "\n", + "# we make the weights normally distributed using numpy.random.randn\n", + "\n", + "# weights and bias in the hidden layer\n", + "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n", + "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n", + "\n", + "# weights and bias in the output layer\n", + "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n", + "output_bias = np.zeros(n_categories) + 0.01" + ] + }, + { + "cell_type": "markdown", + "id": "b89c2d9f", + "metadata": { + "editable": true + }, + "source": [ + "## Feed-forward pass\n", + "\n", + "Denote $F$ the number of features, $H$ the number of hidden neurons and $C$ the number of categories. \n", + "For each input image we calculate a weighted sum of input features (pixel values) to each neuron $j$ in the hidden layer $l$: \n", + "\n", + "$$ z_{j}^{l} = \\sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},$$\n", + "\n", + "this is then passed through our activation function \n", + "\n", + "$$ a_{j}^{l} = f(z_{j}^{l}) .$$ \n", + "\n", + "We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron $j$ in the output layer: \n", + "\n", + "$$ z_{j}^{L} = \\sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.$$ \n", + "\n", + "Finally we calculate the output of neuron $j$ in the output layer using the softmax function: \n", + "\n", + "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n", + "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$" + ] + }, + { + "cell_type": "markdown", + "id": "435c0ced", + "metadata": { + "editable": true + }, + "source": [ + "## Matrix multiplications\n", + "\n", + "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n", + "layer have the dimensions \n", + "$W_{hidden} = (n_{features}, n_{hidden})$,\n", + "we can easily feed the network all our training data in one go by taking the matrix product \n", + "\n", + "$$ X W^{h} = (n_{inputs}, n_{hidden}),$$ \n", + "\n", + "and obtain a matrix that holds the weighted sum of inputs to the hidden layer\n", + "for each input image and each hidden neuron. \n", + "We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$: \n", + "\n", + "$$ \\boldsymbol{z}^{l} = \\boldsymbol{X} \\boldsymbol{W}^{l} + \\boldsymbol{b}^{l} ,$$\n", + "\n", + "meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image. \n", + "This is then passed through the activation: \n", + "\n", + "$$ \\boldsymbol{a}^{l} = f(\\boldsymbol{z}^l) .$$ \n", + "\n", + "This is fed to the output layer: \n", + "\n", + "$$ \\boldsymbol{z}^{L} = \\boldsymbol{a}^{L} \\boldsymbol{W}^{L} + \\boldsymbol{b}^{L} .$$\n", + "\n", + "Finally we receive our output values for each image and each category by passing it through the softmax function: \n", + "\n", + "$$ output = softmax (\\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3037d7ab", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# setup the feed-forward pass, subscript h = hidden layer\n", + "\n", + "def sigmoid(x):\n", + " return 1/(1 + np.exp(-x))\n", + "\n", + "def feed_forward(X):\n", + " # weighted sum of inputs to the hidden layer\n", + " z_h = np.matmul(X, hidden_weights) + hidden_bias\n", + " # activation in the hidden layer\n", + " a_h = sigmoid(z_h)\n", + " \n", + " # weighted sum of inputs to the output layer\n", + " z_o = np.matmul(a_h, output_weights) + output_bias\n", + " # softmax output\n", + " # axis 0 holds each input and axis 1 the probabilities of each category\n", + " exp_term = np.exp(z_o)\n", + " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n", + " \n", + " return probabilities\n", + "\n", + "probabilities = feed_forward(X_train)\n", + "print(\"probabilities = (n_inputs, n_categories) = \" + str(probabilities.shape))\n", + "print(\"probability that image 0 is in category 0,1,2,...,9 = \\n\" + str(probabilities[0]))\n", + "print(\"probabilities sum up to: \" + str(probabilities[0].sum()))\n", + "print()\n", + "\n", + "# we obtain a prediction by taking the class with the highest likelihood\n", + "def predict(X):\n", + " probabilities = feed_forward(X)\n", + " return np.argmax(probabilities, axis=1)\n", + "\n", + "predictions = predict(X_train)\n", + "print(\"predictions = (n_inputs) = \" + str(predictions.shape))\n", + "print(\"prediction for image 0: \" + str(predictions[0]))\n", + "print(\"correct label for image 0: \" + str(Y_train[0]))" + ] + }, + { + "cell_type": "markdown", + "id": "61c33a3f", + "metadata": { + "editable": true + }, + "source": [ + "## Choose cost function and optimizer\n", + "\n", + "To measure how well our neural network is doing we need to introduce a cost function. \n", + "We will call the function that gives the error of a single sample output the *loss* function, and the function\n", + "that gives the total error of our network across all samples the *cost* function.\n", + "A typical choice for multiclass classification is the *cross-entropy* loss, also known as the negative log likelihood. \n", + "\n", + "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector: \n", + "\n", + "$$ y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ \n", + "\n", + "$$ y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ \n", + "\n", + "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset. \n", + "\n", + "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector. \n", + "We define the cost function $\\mathcal{C}$ as a sum over the cross-entropy loss for each point $\\boldsymbol{x}_i$ in the dataset.\n", + "\n", + "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n", + "probability of the correct category $c'$ \n", + "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n", + "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\boldsymbol{\\theta}$ represents the parameters of our network, i.e. all the weights and biases." + ] + }, + { + "cell_type": "markdown", + "id": "665f44ff", + "metadata": { + "editable": true + }, + "source": [ + "## Optimizing the cost function\n", + "\n", + "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n", + "is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a *local* minimum of the cost function. \n", + "Each parameter $\\theta$ is iteratively adjusted according to the rule \n", + "\n", + "$$ \\theta_{i+1} = \\theta_i - \\eta \\nabla \\mathcal{C}(\\theta_i) ,$$\n", + "\n", + "where $\\eta$ is known as the *learning rate*, which controls how big a step we take towards the minimum. \n", + "This update can be repeated for any number of iterations, or until we are satisfied with the result. \n", + "\n", + "A simple and effective improvement is a variant called *Batch Gradient Descent*. \n", + "Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient\n", + "on a subset of the data called a *minibatch*. \n", + "If there are $N$ data points and we have a minibatch size of $M$, the total number of batches\n", + "is $N/M$. \n", + "We denote each minibatch $B_k$, with $k = 1, 2,...,N/M$. The gradient then becomes: \n", + "\n", + "$$ \\nabla \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n", + "\\frac{1}{M} \\sum_{i \\in B_k} \\nabla \\mathcal{L}_i(\\theta) ,$$\n", + "\n", + "i.e. instead of averaging the loss over the entire dataset, we average over a minibatch. \n", + "\n", + "This has two important benefits: \n", + "1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima. \n", + "\n", + "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient. \n", + "\n", + "The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html)." + ] + }, + { + "cell_type": "markdown", + "id": "2d0168d0", + "metadata": { + "editable": true + }, + "source": [ + "## Regularization\n", + "\n", + "It is common to add an extra term to the cost function, proportional\n", + "to the size of the weights. This is equivalent to constraining the\n", + "size of the weights, so that they do not grow out of control.\n", + "Constraining the size of the weights means that the weights cannot\n", + "grow arbitrarily large to fit the training data, and in this way\n", + "reduces *overfitting*.\n", + "\n", + "We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes: \n", + "\n", + "$$ \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n", + "\\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\boldsymbol{w} \\rvert \\rvert_2^2 \n", + "= \\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}(\\theta) + \\lambda \\sum_{ij} w_{ij}^2,$$ \n", + "\n", + "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n", + "\n", + "In order to train the model, we need to calculate the derivative of\n", + "the cost function with respect to every bias and weight in the\n", + "network. In total our network has $(64 + 1)\\times 50=3250$ weights in\n", + "the hidden layer and $(50 + 1)\\times 10=510$ weights to the output\n", + "layer ($+1$ for the bias), and the gradient must be calculated for\n", + "every parameter. We use the *backpropagation* algorithm discussed\n", + "above. This is a clever use of the chain rule that allows us to\n", + "calculate the gradient efficently." + ] + }, + { + "cell_type": "markdown", + "id": "9c0a8db3", + "metadata": { + "editable": true + }, + "source": [ + "## Matrix multiplication\n", + "\n", + "To more efficently train our network these equations are implemented using matrix operations. \n", + "The error in the output layer is calculated simply as, with $\\boldsymbol{t}$ being our targets, \n", + "\n", + "$$ \\delta_L = \\boldsymbol{t} - \\boldsymbol{y} = (n_{inputs}, n_{categories}) .$$ \n", + "\n", + "The gradient for the output weights is calculated as \n", + "\n", + "$$ \\nabla W_{L} = \\boldsymbol{a}^T \\delta_L = (n_{hidden}, n_{categories}) ,$$\n", + "\n", + "where $\\boldsymbol{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input. \n", + "Since we are going backwards we have to transpose the activation matrix. \n", + "\n", + "The gradient with respect to the output bias is then \n", + "\n", + "$$ \\nabla \\boldsymbol{b}_{L} = \\sum_{i=1}^{n_{inputs}} \\delta_L = (n_{categories}) .$$ \n", + "\n", + "The error in the hidden layer is \n", + "\n", + "$$ \\Delta_h = \\delta_L W_{L}^T \\circ f'(z_{h}) = \\delta_L W_{L}^T \\circ a_{h} \\circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,$$ \n", + "\n", + "where $f'(a_{h})$ is the derivative of the activation in the hidden layer. The matrix products mean\n", + "that we are summing up the products for each neuron in the output layer. The symbol $\\circ$ denotes\n", + "the *Hadamard product*, meaning element-wise multiplication. \n", + "\n", + "This again gives us the gradients in the hidden layer: \n", + "\n", + "$$ \\nabla W_{h} = X^T \\delta_h = (n_{features}, n_{hidden}) ,$$ \n", + "\n", + "$$ \\nabla b_{h} = \\sum_{i=1}^{n_{inputs}} \\delta_h = (n_{hidden}) .$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0bf3739e", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# to categorical turns our integer vector into a onehot representation\n", + "from sklearn.metrics import accuracy_score\n", + "\n", + "# one-hot in numpy\n", + "def to_categorical_numpy(integer_vector):\n", + " n_inputs = len(integer_vector)\n", + " n_categories = np.max(integer_vector) + 1\n", + " onehot_vector = np.zeros((n_inputs, n_categories))\n", + " onehot_vector[range(n_inputs), integer_vector] = 1\n", + " \n", + " return onehot_vector\n", + "\n", + "#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)\n", + "Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)\n", + "\n", + "def feed_forward_train(X):\n", + " # weighted sum of inputs to the hidden layer\n", + " z_h = np.matmul(X, hidden_weights) + hidden_bias\n", + " # activation in the hidden layer\n", + " a_h = sigmoid(z_h)\n", + " \n", + " # weighted sum of inputs to the output layer\n", + " z_o = np.matmul(a_h, output_weights) + output_bias\n", + " # softmax output\n", + " # axis 0 holds each input and axis 1 the probabilities of each category\n", + " exp_term = np.exp(z_o)\n", + " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n", + " \n", + " # for backpropagation need activations in hidden and output layers\n", + " return a_h, probabilities\n", + "\n", + "def backpropagation(X, Y):\n", + " a_h, probabilities = feed_forward_train(X)\n", + " \n", + " # error in the output layer\n", + " error_output = probabilities - Y\n", + " # error in the hidden layer\n", + " error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)\n", + " \n", + " # gradients for the output layer\n", + " output_weights_gradient = np.matmul(a_h.T, error_output)\n", + " output_bias_gradient = np.sum(error_output, axis=0)\n", + " \n", + " # gradient for the hidden layer\n", + " hidden_weights_gradient = np.matmul(X.T, error_hidden)\n", + " hidden_bias_gradient = np.sum(error_hidden, axis=0)\n", + "\n", + " return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient\n", + "\n", + "print(\"Old accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))\n", + "\n", + "eta = 0.01\n", + "lmbd = 0.01\n", + "for i in range(1000):\n", + " # calculate gradients\n", + " dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)\n", + " \n", + " # regularization term gradients\n", + " dWo += lmbd * output_weights\n", + " dWh += lmbd * hidden_weights\n", + " \n", + " # update weights and biases\n", + " output_weights -= eta * dWo\n", + " output_bias -= eta * dBo\n", + " hidden_weights -= eta * dWh\n", + " hidden_bias -= eta * dBh\n", + "\n", + "print(\"New accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))" + ] + }, + { + "cell_type": "markdown", + "id": "33e198f3", + "metadata": { + "editable": true + }, + "source": [ + "## Improving performance\n", + "\n", + "As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image. \n", + "In order to obtain a network that does something useful, we will have to do a bit more work. \n", + "\n", + "The choice of *hyperparameters* such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a *grid-search* is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates $\\eta = 10^{-6}, 10^{-5},...,10^{-1}$ with different regularization parameters $\\lambda = 10^{-6},...,10^{-0}$. \n", + "\n", + "Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an *iteration*, and a full training period\n", + "going through the entire dataset ($n/M$ batches) an *epoch*.\n", + "\n", + "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers. \n", + "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/)." + ] + }, + { + "cell_type": "markdown", + "id": "932f6c5e", + "metadata": { + "editable": true + }, + "source": [ + "## Full object-oriented implementation\n", + "\n", + "It is very natural to think of the network as an object, with specific instances of the network\n", + "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "91e351de", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "class NeuralNetwork:\n", + " def __init__(\n", + " self,\n", + " X_data,\n", + " Y_data,\n", + " n_hidden_neurons=50,\n", + " n_categories=10,\n", + " epochs=10,\n", + " batch_size=100,\n", + " eta=0.1,\n", + " lmbd=0.0):\n", + "\n", + " self.X_data_full = X_data\n", + " self.Y_data_full = Y_data\n", + "\n", + " self.n_inputs = X_data.shape[0]\n", + " self.n_features = X_data.shape[1]\n", + " self.n_hidden_neurons = n_hidden_neurons\n", + " self.n_categories = n_categories\n", + "\n", + " self.epochs = epochs\n", + " self.batch_size = batch_size\n", + " self.iterations = self.n_inputs // self.batch_size\n", + " self.eta = eta\n", + " self.lmbd = lmbd\n", + "\n", + " self.create_biases_and_weights()\n", + "\n", + " def create_biases_and_weights(self):\n", + " self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)\n", + " self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01\n", + "\n", + " self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)\n", + " self.output_bias = np.zeros(self.n_categories) + 0.01\n", + "\n", + " def feed_forward(self):\n", + " # feed-forward for training\n", + " self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias\n", + " self.a_h = sigmoid(self.z_h)\n", + "\n", + " self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias\n", + "\n", + " exp_term = np.exp(self.z_o)\n", + " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n", + "\n", + " def feed_forward_out(self, X):\n", + " # feed-forward for output\n", + " z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias\n", + " a_h = sigmoid(z_h)\n", + "\n", + " z_o = np.matmul(a_h, self.output_weights) + self.output_bias\n", + " \n", + " exp_term = np.exp(z_o)\n", + " probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n", + " return probabilities\n", + "\n", + " def backpropagation(self):\n", + " error_output = self.probabilities - self.Y_data\n", + " error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)\n", + "\n", + " self.output_weights_gradient = np.matmul(self.a_h.T, error_output)\n", + " self.output_bias_gradient = np.sum(error_output, axis=0)\n", + "\n", + " self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)\n", + " self.hidden_bias_gradient = np.sum(error_hidden, axis=0)\n", + "\n", + " if self.lmbd > 0.0:\n", + " self.output_weights_gradient += self.lmbd * self.output_weights\n", + " self.hidden_weights_gradient += self.lmbd * self.hidden_weights\n", + "\n", + " self.output_weights -= self.eta * self.output_weights_gradient\n", + " self.output_bias -= self.eta * self.output_bias_gradient\n", + " self.hidden_weights -= self.eta * self.hidden_weights_gradient\n", + " self.hidden_bias -= self.eta * self.hidden_bias_gradient\n", + "\n", + " def predict(self, X):\n", + " probabilities = self.feed_forward_out(X)\n", + " return np.argmax(probabilities, axis=1)\n", + "\n", + " def predict_probabilities(self, X):\n", + " probabilities = self.feed_forward_out(X)\n", + " return probabilities\n", + "\n", + " def train(self):\n", + " data_indices = np.arange(self.n_inputs)\n", + "\n", + " for i in range(self.epochs):\n", + " for j in range(self.iterations):\n", + " # pick datapoints with replacement\n", + " chosen_datapoints = np.random.choice(\n", + " data_indices, size=self.batch_size, replace=False\n", + " )\n", + "\n", + " # minibatch training data\n", + " self.X_data = self.X_data_full[chosen_datapoints]\n", + " self.Y_data = self.Y_data_full[chosen_datapoints]\n", + "\n", + " self.feed_forward()\n", + " self.backpropagation()" + ] + }, + { + "cell_type": "markdown", + "id": "e8c2feb6", + "metadata": { + "editable": true + }, + "source": [ + "## Evaluate model performance on test data\n", + "\n", + "To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data. \n", + "We measure the performance of the network using the *accuracy* score. \n", + "The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of $1$. \n", + "\n", + "$$ \\text{Accuracy} = \\frac{\\sum_{i=1}^n I(\\tilde{y}_i = y_i)}{n} ,$$ \n", + "\n", + "where $I$ is the indicator function, $1$ if $\\tilde{y}_i = y_i$ and $0$ otherwise." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1534af1b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "epochs = 100\n", + "batch_size = 100\n", + "\n", + "dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n", + " n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n", + "dnn.train()\n", + "test_predict = dnn.predict(X_test)\n", + "\n", + "# accuracy score from scikit library\n", + "print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n", + "\n", + "# equivalent in numpy\n", + "def accuracy_score_numpy(Y_test, Y_pred):\n", + " return np.sum(Y_test == Y_pred) / len(Y_test)\n", + "\n", + "#print(\"Accuracy score on test set: \", accuracy_score_numpy(Y_test, test_predict))" + ] + }, + { + "cell_type": "markdown", + "id": "85627e28", + "metadata": { + "editable": true + }, + "source": [ + "## Adjust hyperparameters\n", + "\n", + "We now perform a grid search to find the optimal hyperparameters for the network. \n", + "Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around $98\\%$ ($2\\%$ error rate)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "19382903", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)\n", + "# store the models for later use\n", + "DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + "\n", + "# grid search\n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n", + " n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n", + " dnn.train()\n", + " \n", + " DNN_numpy[i][j] = dnn\n", + " \n", + " test_predict = dnn.predict(X_test)\n", + " \n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n", + " print()" + ] + }, + { + "cell_type": "markdown", + "id": "12bc42df", + "metadata": { + "editable": true + }, + "source": [ + "## Visualization" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "ec0dc239", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# visual representation of grid search\n", + "# uses seaborn heatmap, you can also do this with matplotlib imshow\n", + "import seaborn as sns\n", + "\n", + "sns.set()\n", + "\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " dnn = DNN_numpy[i][j]\n", + " \n", + " train_pred = dnn.predict(X_train) \n", + " test_pred = dnn.predict(X_test)\n", + "\n", + " train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n", + " test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n", + "\n", + " \n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4dd39506", + "metadata": { + "editable": true + }, + "source": [ + "## scikit-learn implementation\n", + "\n", + "**scikit-learn** focuses more\n", + "on traditional machine learning methods, such as regression,\n", + "clustering, decision trees, etc. As such, it has only two types of\n", + "neural networks: Multi Layer Perceptron outputting continuous values,\n", + "*MPLRegressor*, and Multi Layer Perceptron outputting labels,\n", + "*MLPClassifier*. We will see how simple it is to use these classes.\n", + "\n", + "**scikit-learn** implements a few improvements from our neural network,\n", + "such as early stopping, a varying learning rate, different\n", + "optimization methods, etc. We would therefore expect a better\n", + "performance overall." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "d9dbb807", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "from sklearn.neural_network import MLPClassifier\n", + "# store models for later use\n", + "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + "\n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n", + " alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n", + " dnn.fit(X_train, Y_train)\n", + " \n", + " DNN_scikit[i][j] = dnn\n", + " \n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Accuracy score on test set: \", dnn.score(X_test, Y_test))\n", + " print()" + ] + }, + { + "cell_type": "markdown", + "id": "214af3ab", + "metadata": { + "editable": true + }, + "source": [ + "## Visualization" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "d57415ac", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# optional\n", + "# visual representation of grid search\n", + "# uses seaborn heatmap, could probably do this in matplotlib\n", + "import seaborn as sns\n", + "\n", + "sns.set()\n", + "\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " dnn = DNN_scikit[i][j]\n", + " \n", + " train_pred = dnn.predict(X_train) \n", + " test_pred = dnn.predict(X_test)\n", + "\n", + " train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n", + " test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n", + "\n", + " \n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "fe7af77c", + "metadata": { + "editable": true + }, + "source": [ + "## Testing our code for the XOR, OR and AND gates\n", + "\n", + "Last week we discussed three different types of gates, the so-called\n", + "XOR, the OR and the AND gates. Their inputs and outputs can be\n", + "summarized using the following tables, first for the OR gate with\n", + "inputs $x_1$ and $x_2$ and outputs $y$:\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
$x_1$ $x_2$ $y$
0 0 0
0 1 1
1 0 1
1 1 1
" + ] + }, + { + "cell_type": "markdown", + "id": "7e12b1cf", + "metadata": { + "editable": true + }, + "source": [ + "## The AND and XOR Gates\n", + "\n", + "The AND gate is defined as\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
$x_1$ $x_2$ $y$
0 0 0
0 1 0
1 0 0
1 1 1
\n", + "\n", + "And finally we have the XOR gate\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
$x_1$ $x_2$ $y$
0 0 0
0 1 1
1 0 1
1 1 0
" + ] + }, + { + "cell_type": "markdown", + "id": "4b5002b4", + "metadata": { + "editable": true + }, + "source": [ + "## Representing the Data Sets\n", + "\n", + "Our design matrix is defined by the input values $x_1$ and $x_2$. Since we have four possible outputs, our design matrix reads" + ] + }, + { + "cell_type": "markdown", + "id": "a44df1a3", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{X}=\\begin{bmatrix} 0 & 0 \\\\\n", + " 0 & 1 \\\\\n", + "\t\t 1 & 0 \\\\\n", + "\t\t 1 & 1 \\end{bmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "acdb4e08", + "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." + ] + }, + { + "cell_type": "markdown", + "id": "0567fd0f", + "metadata": { + "editable": true + }, + "source": [ + "## Setting up the Neural Network\n", + "\n", + "We define first our design matrix and the various output vectors for the different gates." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "412401df", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\"\"\"\n", + "Simple code that tests XOR, OR and AND gates with linear regression\n", + "\"\"\"\n", + "\n", + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn import datasets\n", + "\n", + "def sigmoid(x):\n", + " return 1/(1 + np.exp(-x))\n", + "\n", + "def feed_forward(X):\n", + " # weighted sum of inputs to the hidden layer\n", + " z_h = np.matmul(X, hidden_weights) + hidden_bias\n", + " # activation in the hidden layer\n", + " a_h = sigmoid(z_h)\n", + " \n", + " # weighted sum of inputs to the output layer\n", + " z_o = np.matmul(a_h, output_weights) + output_bias\n", + " # softmax output\n", + " # axis 0 holds each input and axis 1 the probabilities of each category\n", + " probabilities = sigmoid(z_o)\n", + " return probabilities\n", + "\n", + "# we obtain a prediction by taking the class with the highest likelihood\n", + "def predict(X):\n", + " probabilities = feed_forward(X)\n", + " return np.argmax(probabilities, axis=1)\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# Design matrix\n", + "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n", + "\n", + "# The XOR gate\n", + "yXOR = np.array( [ 0, 1 ,1, 0])\n", + "# The OR gate\n", + "yOR = np.array( [ 0, 1 ,1, 1])\n", + "# The AND gate\n", + "yAND = np.array( [ 0, 0 ,0, 1])\n", + "\n", + "# Defining the neural network\n", + "n_inputs, n_features = X.shape\n", + "n_hidden_neurons = 2\n", + "n_categories = 2\n", + "n_features = 2\n", + "\n", + "# we make the weights normally distributed using numpy.random.randn\n", + "\n", + "# weights and bias in the hidden layer\n", + "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n", + "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n", + "\n", + "# weights and bias in the output layer\n", + "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n", + "output_bias = np.zeros(n_categories) + 0.01\n", + "\n", + "probabilities = feed_forward(X)\n", + "print(probabilities)\n", + "\n", + "\n", + "predictions = predict(X)\n", + "print(predictions)" + ] + }, + { + "cell_type": "markdown", + "id": "53c52dab", + "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": "7d192a02", + "metadata": { + "editable": true + }, + "source": [ + "## The Code using Scikit-Learn" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "766d5af6", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.neural_network import MLPClassifier\n", + "from sklearn.metrics import accuracy_score\n", + "import seaborn as sns\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# Design matrix\n", + "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n", + "\n", + "# The XOR gate\n", + "yXOR = np.array( [ 0, 1 ,1, 0])\n", + "# The OR gate\n", + "yOR = np.array( [ 0, 1 ,1, 1])\n", + "# The AND gate\n", + "yAND = np.array( [ 0, 0 ,0, 1])\n", + "\n", + "# Defining the neural network\n", + "n_inputs, n_features = X.shape\n", + "n_hidden_neurons = 2\n", + "n_categories = 2\n", + "n_features = 2\n", + "\n", + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)\n", + "# store models for later use\n", + "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + "epochs = 100\n", + "\n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n", + " alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n", + " dnn.fit(X, yXOR)\n", + " DNN_scikit[i][j] = dnn\n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Accuracy score on data set: \", dnn.score(X, yXOR))\n", + " print()\n", + "\n", + "sns.set()\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " dnn = DNN_scikit[i][j]\n", + " test_pred = dnn.predict(X)\n", + " test_accuracy[i][j] = accuracy_score(yXOR, test_pred)\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9b182ae1", + "metadata": { + "editable": true + }, + "source": [ + "## Building neural networks in Tensorflow and Keras\n", + "\n", + "Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n", + "and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n", + "and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer. \n", + "\n", + "In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n", + "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n", + "NumPy arrays." + ] + }, + { + "cell_type": "markdown", + "id": "60683ec5", + "metadata": { + "editable": true + }, + "source": [ + "## Tensorflow\n", + "\n", + "Tensorflow is an open source library machine learning library\n", + "developed by the Google Brain team for internal use. It was released\n", + "under the Apache 2.0 open source license in November 9, 2015.\n", + "\n", + "Tensorflow is a computational framework that allows you to construct\n", + "machine learning models at different levels of abstraction, from\n", + "high-level, object-oriented APIs like Keras, down to the C++ kernels\n", + "that Tensorflow is built upon. The higher levels of abstraction are\n", + "simpler to use, but less flexible, and our choice of implementation\n", + "should reflect the problems we are trying to solve.\n", + "\n", + "[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n", + "in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n", + "to represent your model, and then create a Tensorflow *session* to run the graph.\n", + "\n", + "In this guide we will analyze the same data as we did in our NumPy and\n", + "scikit-learn tutorial, gathered from the MNIST database of images. We\n", + "will give an introduction to the lower level Python Application\n", + "Program Interfaces (APIs), and see how we use them to build our graph.\n", + "Then we will build (effectively) the same graph in Keras, to see just\n", + "how simple solving a machine learning problem can be.\n", + "\n", + "To install tensorflow on Unix/Linux systems, use pip as" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8a0c6901", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "pip3 install tensorflow" + ] + }, + { + "cell_type": "markdown", + "id": "b66e0227", + "metadata": { + "editable": true + }, + "source": [ + "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n", + "(current release of CPU-only TensorFlow)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "df994f58", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "conda create -n tf tensorflow\n", + "conda activate tf" + ] + }, + { + "cell_type": "markdown", + "id": "b9005559", + "metadata": { + "editable": true + }, + "source": [ + "To install the current release of GPU TensorFlow" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "7287b5eb", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "conda create -n tf-gpu tensorflow-gpu\n", + "conda activate tf-gpu" + ] + }, + { + "cell_type": "markdown", + "id": "c066b083", + "metadata": { + "editable": true + }, + "source": [ + "## Using Keras\n", + "\n", + "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n", + "that supports Tensorflow, CTNK and Theano as backends. \n", + "If you have Anaconda installed you may run the following command" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "6582adea", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "conda install keras" + ] + }, + { + "cell_type": "markdown", + "id": "7d305596", + "metadata": { + "editable": true + }, + "source": [ + "You can look up the [instructions here](https://keras.io/) for more information.\n", + "\n", + "We will to a large extent use **keras** in this course." + ] + }, + { + "cell_type": "markdown", + "id": "a4508850", + "metadata": { + "editable": true + }, + "source": [ + "## Collect and pre-process data\n", + "\n", + "Let us look again at the MINST data set." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "5f2256f6", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "from sklearn import datasets\n", + "\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# display images in notebook\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = (12,12)\n", + "\n", + "\n", + "# download MNIST dataset\n", + "digits = datasets.load_digits()\n", + "\n", + "# define inputs and labels\n", + "inputs = digits.images\n", + "labels = digits.target\n", + "\n", + "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n", + "print(\"labels = (n_inputs) = \" + str(labels.shape))\n", + "\n", + "\n", + "# flatten the image\n", + "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n", + "n_inputs = len(inputs)\n", + "inputs = inputs.reshape(n_inputs, -1)\n", + "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n", + "\n", + "\n", + "# choose some random images to display\n", + "indices = np.arange(n_inputs)\n", + "random_indices = np.random.choice(indices, size=5)\n", + "\n", + "for i, image in enumerate(digits.images[random_indices]):\n", + " plt.subplot(1, 5, i+1)\n", + " plt.axis('off')\n", + " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n", + " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "a5dfa0e9", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Sequential #This allows appending layers to existing models\n", + "from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer\n", + "from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n", + "from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)\n", + "from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function\n", + "\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "# one-hot representation of labels\n", + "labels = to_categorical(labels)\n", + "\n", + "# split into train and test data\n", + "train_size = 0.8\n", + "test_size = 1 - train_size\n", + "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n", + " test_size=test_size)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "dd935ce0", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "epochs = 100\n", + "batch_size = 100\n", + "n_neurons_layer1 = 100\n", + "n_neurons_layer2 = 50\n", + "n_categories = 10\n", + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)\n", + "def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n", + " model = Sequential()\n", + " model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(Dense(n_categories, activation='softmax'))\n", + " \n", + " sgd = optimizers.SGD(lr=eta)\n", + " model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n", + " \n", + " return model" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "67158cb2", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + " \n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n", + " eta=eta, lmbd=lmbd)\n", + " DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n", + " scores = DNN.evaluate(X_test, Y_test)\n", + " \n", + " DNN_keras[i][j] = DNN\n", + " \n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Test accuracy: %.3f\" % scores[1])\n", + " print()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "86d74ee3", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# optional\n", + "# visual representation of grid search\n", + "# uses seaborn heatmap, could probably do this in matplotlib\n", + "import seaborn as sns\n", + "\n", + "sns.set()\n", + "\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " DNN = DNN_keras[i][j]\n", + "\n", + " train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n", + " test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n", + "\n", + " \n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "563d3f68", + "metadata": { + "editable": true + }, + "source": [ + "## The Breast Cancer Data, now with Keras" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "34e6467a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "import tensorflow as tf\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Sequential #This allows appending layers to existing models\n", + "from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer\n", + "from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n", + "from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)\n", + "from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "from sklearn.model_selection import train_test_split as splitter\n", + "from sklearn.datasets import load_breast_cancer\n", + "import pickle\n", + "import os \n", + "\n", + "\n", + "\"\"\"Load breast cancer dataset\"\"\"\n", + "\n", + "np.random.seed(0) #create same seed for random number every time\n", + "\n", + "cancer=load_breast_cancer() #Download breast cancer dataset\n", + "\n", + "inputs=cancer.data #Feature matrix of 569 rows (samples) and 30 columns (parameters)\n", + "outputs=cancer.target #Label array of 569 rows (0 for benign and 1 for malignant)\n", + "labels=cancer.feature_names[0:30]\n", + "\n", + "print('The content of the breast cancer dataset is:') #Print information about the datasets\n", + "print(labels)\n", + "print('-------------------------')\n", + "print(\"inputs = \" + str(inputs.shape))\n", + "print(\"outputs = \" + str(outputs.shape))\n", + "print(\"labels = \"+ str(labels.shape))\n", + "\n", + "x=inputs #Reassign the Feature and Label matrices to other variables\n", + "y=outputs\n", + "\n", + "#%% \n", + "\n", + "# Visualisation of dataset (for correlation analysis)\n", + "\n", + "plt.figure()\n", + "plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)\n", + "plt.xlabel('Mean radius',fontweight='bold')\n", + "plt.ylabel('Mean perimeter',fontweight='bold')\n", + "plt.show()\n", + "\n", + "plt.figure()\n", + "plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)\n", + "plt.xlabel('Mean compactness',fontweight='bold')\n", + "plt.ylabel('Mean concavity',fontweight='bold')\n", + "plt.show()\n", + "\n", + "\n", + "plt.figure()\n", + "plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)\n", + "plt.xlabel('Mean radius',fontweight='bold')\n", + "plt.ylabel('Mean texture',fontweight='bold')\n", + "plt.show()\n", + "\n", + "plt.figure()\n", + "plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)\n", + "plt.xlabel('Mean perimeter',fontweight='bold')\n", + "plt.ylabel('Mean compactness',fontweight='bold')\n", + "plt.show()\n", + "\n", + "\n", + "# Generate training and testing datasets\n", + "\n", + "#Select features relevant to classification (texture,perimeter,compactness and symmetery) \n", + "#and add to input matrix\n", + "\n", + "temp1=np.reshape(x[:,1],(len(x[:,1]),1))\n", + "temp2=np.reshape(x[:,2],(len(x[:,2]),1))\n", + "X=np.hstack((temp1,temp2)) \n", + "temp=np.reshape(x[:,5],(len(x[:,5]),1))\n", + "X=np.hstack((X,temp)) \n", + "temp=np.reshape(x[:,8],(len(x[:,8]),1))\n", + "X=np.hstack((X,temp)) \n", + "\n", + "X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1) #Split datasets into training and testing\n", + "\n", + "y_train=to_categorical(y_train) #Convert labels to categorical when using categorical cross entropy\n", + "y_test=to_categorical(y_test)\n", + "\n", + "del temp1,temp2,temp\n", + "\n", + "# %%\n", + "\n", + "# Define tunable parameters\"\n", + "\n", + "eta=np.logspace(-3,-1,3) #Define vector of learning rates (parameter to SGD optimiser)\n", + "lamda=0.01 #Define hyperparameter\n", + "n_layers=2 #Define number of hidden layers in the model\n", + "n_neuron=np.logspace(0,3,4,dtype=int) #Define number of neurons per layer\n", + "epochs=100 #Number of reiterations over the input data\n", + "batch_size=100 #Number of samples per gradient update\n", + "\n", + "# %%\n", + "\n", + "\"\"\"Define function to return Deep Neural Network model\"\"\"\n", + "\n", + "def NN_model(inputsize,n_layers,n_neuron,eta,lamda):\n", + " model=Sequential() \n", + " for i in range(n_layers): #Run loop to add hidden layers to the model\n", + " if (i==0): #First layer requires input dimensions\n", + " model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))\n", + " else: #Subsequent layers are capable of automatic shape inferencing\n", + " model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))\n", + " model.add(Dense(2,activation='softmax')) #2 outputs - ordered and disordered (softmax for prob)\n", + " sgd=optimizers.SGD(lr=eta)\n", + " model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])\n", + " return model\n", + "\n", + " \n", + "Train_accuracy=np.zeros((len(n_neuron),len(eta))) #Define matrices to store accuracy scores as a function\n", + "Test_accuracy=np.zeros((len(n_neuron),len(eta))) #of learning rate and number of hidden neurons for \n", + "\n", + "for i in range(len(n_neuron)): #run loops over hidden neurons and learning rates to calculate \n", + " for j in range(len(eta)): #accuracy scores \n", + " DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)\n", + " DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)\n", + " Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]\n", + " Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]\n", + " \n", + "\n", + "def plot_data(x,y,data,title=None):\n", + "\n", + " # plot results\n", + " fontsize=16\n", + "\n", + "\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111)\n", + " cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)\n", + " \n", + " cbar=fig.colorbar(cax)\n", + " cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)\n", + " cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])\n", + " cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])\n", + "\n", + " # put text on matrix elements\n", + " for i, x_val in enumerate(np.arange(len(x))):\n", + " for j, y_val in enumerate(np.arange(len(y))):\n", + " c = \"${0:.1f}\\\\%$\".format( 100*data[j,i]) \n", + " ax.text(x_val, y_val, c, va='center', ha='center')\n", + "\n", + " # convert axis vaues to to string labels\n", + " x=[str(i) for i in x]\n", + " y=[str(i) for i in y]\n", + "\n", + "\n", + " ax.set_xticklabels(['']+x)\n", + " ax.set_yticklabels(['']+y)\n", + "\n", + " ax.set_xlabel('$\\\\mathrm{learning\\\\ rate}$',fontsize=fontsize)\n", + " ax.set_ylabel('$\\\\mathrm{hidden\\\\ neurons}$',fontsize=fontsize)\n", + " if title is not None:\n", + " ax.set_title(title)\n", + "\n", + " plt.tight_layout()\n", + "\n", + " plt.show()\n", + " \n", + "plot_data(eta,n_neuron,Train_accuracy, 'training')\n", + "plot_data(eta,n_neuron,Test_accuracy, 'testing')" + ] + }, + { + "cell_type": "markdown", + "id": "09879108", + "metadata": { + "editable": true + }, + "source": [ + "## Fine-tuning neural network hyperparameters\n", + "\n", + "The flexibility of neural networks is also one of their main\n", + "drawbacks: there are many hyperparameters to tweak. Not only can you\n", + "use any imaginable network topology (how neurons/nodes are interconnected),\n", + "but even in a simple FFNN you can change the number of layers, the\n", + "number of neurons per layer, the type of activation function to use in\n", + "each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you\n", + "know what combination of hyperparameters is the best for your task?\n", + "\n", + "* You can use grid search with cross-validation to find the right hyperparameters.\n", + "\n", + "However,since there are many hyperparameters to tune, and since\n", + "training a neural network on a large dataset takes a lot of time, you\n", + "will only be able to explore a tiny part of the hyperparameter space.\n", + "\n", + "* You can use randomized search.\n", + "\n", + "* Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly." + ] + }, + { + "cell_type": "markdown", + "id": "f8ec1769", + "metadata": { + "editable": true + }, + "source": [ + "## Hidden layers\n", + "\n", + "For many problems you can start with just one or two hidden layers and it will work just fine.\n", + "For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a\n", + "few hundred neurons.\n", + "You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of\n", + "neurons, in roughly the same amount of training time. \n", + "\n", + "For more complex problems, you can gradually\n", + "ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such\n", + "as large image classification or speech recognition, typically require networks with dozens of layers\n", + "and they need a huge amount\n", + "of training data. However, you will rarely have to train such networks from scratch: it is much more\n", + "common to reuse parts of a pretrained state-of-the-art network that performs a similar task." + ] + }, + { + "cell_type": "markdown", + "id": "43cc1fe5", + "metadata": { + "editable": true + }, + "source": [ + "## Which activation function should I use?\n", + "\n", + "The Back propagation algorithm we derived above works by going from\n", + "the output layer to the input layer, propagating the error gradient on\n", + "the way. Once the algorithm has computed the gradient of the cost\n", + "function with regards to each parameter in the network, it uses these\n", + "gradients to update each parameter with a Gradient Descent (GD) step.\n", + "\n", + "Unfortunately for us, the gradients often get smaller and smaller as the\n", + "algorithm progresses down to the first hidden layers. As a result, the\n", + "GD update leaves the lower layer connection weights\n", + "virtually unchanged, and training never converges to a good\n", + "solution. This is known in the literature as \n", + "**the vanishing gradients problem**. \n", + "\n", + "In other cases, the opposite can happen, namely the the gradients can grow bigger and\n", + "bigger. The result is that many of the layers get large updates of the \n", + "weights the\n", + "algorithm diverges. This is the **exploding gradients problem**, which is\n", + "mostly encountered in recurrent neural networks. More generally, deep\n", + "neural networks suffer from unstable gradients, different layers may\n", + "learn at widely different speeds" + ] + }, + { + "cell_type": "markdown", + "id": "a9cbce9f", + "metadata": { + "editable": true + }, + "source": [ + "## Is the Logistic activation function (Sigmoid) our choice?\n", + "\n", + "Although this unfortunate behavior has been empirically observed for\n", + "quite a while (it was one of the reasons why deep neural networks were\n", + "mostly abandoned for a long time), it is only around 2010 that\n", + "significant progress was made in understanding it.\n", + "\n", + "A paper titled [Understanding the Difficulty of Training Deep\n", + "Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio](http://proceedings.mlr.press/v9/glorot10a.html) found that\n", + "the problems with the popular logistic\n", + "sigmoid activation function and the weight initialization technique\n", + "that was most popular at the time, namely random initialization using\n", + "a normal distribution with a mean of 0 and a standard deviation of\n", + "1. \n", + "\n", + "They showed that with this activation function and this\n", + "initialization scheme, the variance of the outputs of each layer is\n", + "much greater than the variance of its inputs. Going forward in the\n", + "network, the variance keeps increasing after each layer until the\n", + "activation function saturates at the top layers. This is actually made\n", + "worse by the fact that the logistic function has a mean of 0.5, not 0\n", + "(the hyperbolic tangent function has a mean of 0 and behaves slightly\n", + "better than the logistic function in deep networks)." + ] + }, + { + "cell_type": "markdown", + "id": "2dfb3f9a", + "metadata": { + "editable": true + }, + "source": [ + "## The derivative of the Logistic funtion\n", + "\n", + "Looking at the logistic activation function, when inputs become large\n", + "(negative or positive), the function saturates at 0 or 1, with a\n", + "derivative extremely close to 0. Thus when backpropagation kicks in,\n", + "it has virtually no gradient to propagate back through the network,\n", + "and what little gradient exists keeps getting diluted as\n", + "backpropagation progresses down through the top layers, so there is\n", + "really nothing left for the lower layers.\n", + "\n", + "In their paper, Glorot and Bengio propose a way to significantly\n", + "alleviate this problem. We need the signal to flow properly in both\n", + "directions: in the forward direction when making predictions, and in\n", + "the reverse direction when backpropagating gradients. We don’t want\n", + "the signal to die out, nor do we want it to explode and saturate. For\n", + "the signal to flow properly, the authors argue that we need the\n", + "variance of the outputs of each layer to be equal to the variance of\n", + "its inputs, and we also need the gradients to have equal variance\n", + "before and after flowing through a layer in the reverse direction.\n", + "\n", + "One of the insights in the 2010 paper by Glorot and Bengio was that\n", + "the vanishing/exploding gradients problems were in part due to a poor\n", + "choice of activation function. Until then most people had assumed that\n", + "if Nature had chosen to use roughly sigmoid activation functions in\n", + "biological neurons, they must be an excellent choice. But it turns out\n", + "that other activation functions behave much better in deep neural\n", + "networks, in particular the ReLU activation function, mostly because\n", + "it does not saturate for positive values (and also because it is quite\n", + "fast to compute)." + ] + }, + { + "cell_type": "markdown", + "id": "f806c047", + "metadata": { + "editable": true + }, + "source": [ + "## The RELU function family\n", + "\n", + "The ReLU activation function suffers from a problem known as the dying\n", + "ReLUs: during training, some neurons effectively die, meaning they\n", + "stop outputting anything other than 0.\n", + "\n", + "In some cases, you may find that half of your network’s neurons are\n", + "dead, especially if you used a large learning rate. During training,\n", + "if a neuron’s weights get updated such that the weighted sum of the\n", + "neuron’s inputs is negative, it will start outputting 0. When this\n", + "happen, the neuron is unlikely to come back to life since the gradient\n", + "of the ReLU function is 0 when its input is negative.\n", + "\n", + "To solve this problem, nowadays practitioners use a variant of the ReLU\n", + "function, such as the leaky ReLU discussed above or the so-called\n", + "exponential linear unit (ELU) function" + ] + }, + { + "cell_type": "markdown", + "id": "ef9e2a08", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\ z & z \\ge 0.\\end{array}\\right.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "2e2750d8", + "metadata": { + "editable": true + }, + "source": [ + "## Which activation function should we use?\n", + "\n", + "In general it seems that the ELU activation function is better than\n", + "the leaky ReLU function (and its variants), which is better than\n", + "ReLU. ReLU performs better than $\\tanh$ which in turn performs better\n", + "than the logistic function. \n", + "\n", + "If runtime\n", + "performance is an issue, then you may opt for the leaky ReLU function over the \n", + "ELU function If you don’t\n", + "want to tweak yet another hyperparameter, you may just use the default\n", + "$\\alpha$ of $0.01$ for the leaky ReLU, and $1$ for ELU. If you have\n", + "spare time and computing power, you can use cross-validation or\n", + "bootstrap to evaluate other activation functions." + ] + }, + { + "cell_type": "markdown", + "id": "4e566f13", + "metadata": { + "editable": true + }, + "source": [ + "## More on activation functions, output layers\n", + "\n", + "In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).\n", + "\n", + "It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.\n", + "\n", + "**For the output layer:**\n", + "\n", + "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n", + "\n", + "* For regression tasks, you can simply use no activation function at all." + ] + }, + { + "cell_type": "markdown", + "id": "03205666", + "metadata": { + "editable": true + }, + "source": [ + "## Batch Normalization\n", + "\n", + "Batch Normalization\n", + "aims to address the vanishing/exploding gradients problems, and more generally the problem that the\n", + "distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.\n", + "\n", + "The technique consists of adding an operation in the model just before the activation function of each\n", + "layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new\n", + "parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model\n", + "learn the optimal scale and mean of the inputs for each layer.\n", + "In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and\n", + "standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current\n", + "mini-batch, from this the name batch normalization." + ] + }, + { + "cell_type": "markdown", + "id": "ad7c3e53", + "metadata": { + "editable": true + }, + "source": [ + "## Dropout\n", + "\n", + "It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but\n", + "excluding the output neurons) has a probability $p$ of being temporarily dropped out, meaning it will be\n", + "entirely ignored during this training step, but it may be active during the next step.\n", + "\n", + "The\n", + "hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.\n", + " It is viewed as one of the most popular regularization techniques." + ] + }, + { + "cell_type": "markdown", + "id": "c3b98a7c", + "metadata": { + "editable": true + }, + "source": [ + "## Gradient Clipping\n", + "\n", + "A popular technique to lessen the exploding gradients problem is to simply clip the gradients during\n", + "backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural\n", + "networks).\n", + "\n", + "This technique is called Gradient Clipping.\n", + "\n", + "In general however, Batch\n", + "Normalization is preferred." + ] + }, + { + "cell_type": "markdown", + "id": "e7f21477", + "metadata": { + "editable": true + }, + "source": [ + "## A very nice website on Neural Networks\n", + "\n", + "You may find this [website](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.29243&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false) very useful." + ] + }, + { + "cell_type": "markdown", + "id": "54968291", + "metadata": { + "editable": true + }, + "source": [ + "## A top-down perspective on Neural networks\n", + "\n", + "The first thing we would like to do is divide the data into two or three\n", + "parts. A training set, a validation or dev (development) set, and a\n", + "test set. The test set is the data on which we want to make\n", + "predictions. The dev set is a subset of the training data we use to\n", + "check how well we are doing out-of-sample, after training the model on\n", + "the training dataset. We use the validation error as a proxy for the\n", + "test error in order to make tweaks to our model. It is crucial that we\n", + "do not use any of the test data to train the algorithm. This is a\n", + "cardinal sin in ML. Then:\n", + "\n", + "* Estimate optimal error rate\n", + "\n", + "* Minimize underfitting (bias) on training data set.\n", + "\n", + "* Make sure you are not overfitting.\n", + "\n", + "If the validation and test sets are drawn from the same distributions,\n", + "then a good performance on the validation set should lead to similarly\n", + "good performance on the test set. \n", + "\n", + "However, sometimes\n", + "the training data and test data differ in subtle ways because, for\n", + "example, they are collected using slightly different methods, or\n", + "because it is cheaper to collect data in one way versus another. In\n", + "this case, there can be a mismatch between the training and test\n", + "data. This can lead to the neural network overfitting these small\n", + "differences between the test and training sets, and a poor performance\n", + "on the test set despite having a good performance on the validation\n", + "set. To rectify this, Andrew Ng suggests making two validation or dev\n", + "sets, one constructed from the training data and one constructed from\n", + "the test data. The difference between the performance of the algorithm\n", + "on these two validation sets quantifies the train-test mismatch. This\n", + "can serve as another important diagnostic when using DNNs for\n", + "supervised learning." + ] + }, + { + "cell_type": "markdown", + "id": "4500b85e", + "metadata": { + "editable": true + }, + "source": [ + "## Limitations of supervised learning with deep networks\n", + "\n", + "Like all statistical methods, supervised learning using neural\n", + "networks has important limitations. This is especially important when\n", + "one seeks to apply these methods, especially to physics problems. Like\n", + "all tools, DNNs are not a universal solution. Often, the same or\n", + "better performance on a task can be achieved by using a few\n", + "hand-engineered features (or even a collection of random\n", + "features). \n", + "\n", + "Here we list some of the important limitations of supervised neural network based models. \n", + "\n", + "* **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).\n", + "\n", + "* **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.\n", + "\n", + "* **Homogeneous data.** Almost all DNNs deal with homogeneous data of one type. It is very hard to design architectures that mix and match data types (i.e. some continuous variables, some discrete variables, some time series). In applications beyond images, video, and language, this is often what is required. In contrast, ensemble models like random forests or gradient-boosted trees have no difficulty handling mixed data types.\n", + "\n", + "* **Many problems are not about prediction.** In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a *wrong* model. The model might or might not be useful for understanding the underlying science.\n", + "\n", + "Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems." + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/chapter1.html b/doc/LectureNotes/_build/html/chapter1.html index 45bbddf08..2f2b2ea11 100644 --- a/doc/LectureNotes/_build/html/chapter1.html +++ b/doc/LectureNotes/_build/html/chapter1.html @@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output" Week 40: Gradient descent methods (continued) and start Neural networks +
  • + + Exercises week 41 + +
    • +
  • + + Week 41 Neural networks and constructing a neural network code + +
    • +
  • + + Exercises week 42 + +
    • +
  • + + Week 42 Constructing a Neural Network code with introduction to Tensor flow + +

    • @@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output" Project 1 on Machine Learning, deadline October 9 (midnight), 2023 +

  • + + Project 2 on Machine Learning, deadline November 13 (Midnight) + +
    • @@ -1041,13 +1066,13 @@ example of the functionality of Scikit-Learn.

    The intercept alpha: 
- [2.04292593]
+ [2.04828291]
 Coefficient beta : 
- [[5.00440395]]
+ [[4.85601654]]
 Mean squared error: 0.27
-Variance score: 0.88
+Variance score: 0.89
 Mean squared log error: 0.01
-Mean absolute error: 0.41
+Mean absolute error: 0.40
    _images/chapter1_19_1.png @@ -1147,7 +1172,7 @@ a linear \(x\)-dependence we s
    _images/chapter1_33_0.png -
    0.004999999999999994
+
    0.005000000000000001
    diff --git a/doc/LectureNotes/_build/html/chapter10.html b/doc/LectureNotes/_build/html/chapter10.html index 0ca2b6130..2796f090c 100644 --- a/doc/LectureNotes/_build/html/chapter10.html +++ b/doc/LectureNotes/_build/html/chapter10.html @@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output" Week 40: Gradient descent methods (continued) and start Neural networks +
  • + + Exercises week 41 + +
    • +
  • + + Week 41 Neural networks and constructing a neural network code + +
    • +
  • + + Exercises week 42 + +
    • +
  • + + Week 42 Constructing a Neural Network code with introduction to Tensor flow + +

    • @@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output" Project 1 on Machine Learning, deadline October 9 (midnight), 2023 +

  • + + Project 2 on Machine Learning, deadline November 13 (Midnight) + +
    • @@ -1358,7 +1383,7 @@ the Hadamard product, meaning element-wise multiplication.

    Old accuracy on training data: 0.1440501043841336
    -
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_18986/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1592,30 +1617,345 @@ Lambda =  1e-05
 Accuracy score on test set:  0.5305555555555556
    -
    ---------------------------------------------------------------------------
-KeyboardInterrupt                         Traceback (most recent call last)
-Input In [8], in <cell line: 7>()
-      8 for j, lmbd in enumerate(lmbd_vals):
-      9     dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,
-     10                         n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)
----> 11     dnn.train()
-     13     DNN_numpy[i][j] = dnn
-     15     test_predict = dnn.predict(X_test)
-
-Input In [6], in NeuralNetwork.train(self)
-     95 self.X_data = self.X_data_full[chosen_datapoints]
-     96 self.Y_data = self.Y_data_full[chosen_datapoints]
----> 98 self.feed_forward()
-     99 self.backpropagation()
-
-Input In [6], in NeuralNetwork.feed_forward(self)
-     36 def feed_forward(self):
-     37     # feed-forward for training
----> 38     self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias
-     39     self.a_h = sigmoid(self.z_h)
-     41     self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias
-
-KeyboardInterrupt: 
+
    Learning rate  =  0.0001
+Lambda =  0.0001
+Accuracy score on test set:  0.5944444444444444
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.001
+Accuracy score on test set:  0.5888888888888889
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.01
+Accuracy score on test set:  0.6111111111111112
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.1
+Accuracy score on test set:  0.5222222222222223
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  1.0
+Accuracy score on test set:  0.5555555555555556
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  10.0
+Accuracy score on test set:  0.8055555555555556
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1e-05
+Accuracy score on test set:  0.85
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.0001
+Accuracy score on test set:  0.85
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.001
+Accuracy score on test set:  0.875
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.01
+Accuracy score on test set:  0.8666666666666667
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.1
+Accuracy score on test set:  0.8638888888888889
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1.0
+Accuracy score on test set:  0.9555555555555556
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  10.0
+Accuracy score on test set:  0.925
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1e-05
+Accuracy score on test set:  0.9472222222222222
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.0001
+Accuracy score on test set:  0.9277777777777778
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.001
+Accuracy score on test set:  0.9472222222222222
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.01
+Accuracy score on test set:  0.9305555555555556
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.1
+Accuracy score on test set:  0.9555555555555556
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1.0
+Accuracy score on test set:  0.7694444444444445
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  10.0
+Accuracy score on test set:  0.19166666666666668
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  1e-05
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.0001
+Accuracy score on test set:  0.08611111111111111
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.01
+Accuracy score on test set:  0.08888888888888889
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.1
+Accuracy score on test set:  0.08611111111111111
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  10.0
+Accuracy score on test set:  0.09166666666666666
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  1e-05
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.0001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.01
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.1
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  10.0
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1e-05
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.01
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.1
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1.0
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  10.0
+Accuracy score on test set:  0.07777777777777778
    @@ -1661,6 +2001,22 @@ Accuracy score on test set: 0.5305555555555556
    +
    +
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    +
    +_images/chapter10_59_1.png +_images/chapter10_59_2.png +
    @@ -1696,6 +2052,329 @@ performance overall.

    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  1e-05
+Accuracy score on test set:  0.18333333333333332
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  0.0001
+Accuracy score on test set:  0.18611111111111112
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  0.001
+Accuracy score on test set:  0.13055555555555556
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  0.01
+Accuracy score on test set:  0.24444444444444444
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  0.1
+Accuracy score on test set:  0.23333333333333334
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  1.0
+Accuracy score on test set:  0.12777777777777777
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  1e-05
+Lambda =  10.0
+Accuracy score on test set:  0.1527777777777778
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  1e-05
+Accuracy score on test set:  0.9111111111111111
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  0.0001
+Accuracy score on test set:  0.8888888888888888
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  0.001
+Accuracy score on test set:  0.8722222222222222
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  0.01
+Accuracy score on test set:  0.8305555555555556
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  0.1
+Accuracy score on test set:  0.8888888888888888
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  1.0
+Accuracy score on test set:  0.8805555555555555
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.0001
+Lambda =  10.0
+Accuracy score on test set:  0.8944444444444445
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  1e-05
+Accuracy score on test set:  0.975
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  0.0001
+Accuracy score on test set:  0.9777777777777777
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  0.001
+Accuracy score on test set:  0.9805555555555555
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  0.01
+Accuracy score on test set:  0.9861111111111112
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  0.1
+Accuracy score on test set:  0.9805555555555555
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  1.0
+Accuracy score on test set:  0.9777777777777777
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.001
+Lambda =  10.0
+Accuracy score on test set:  0.9444444444444444
+
    +
    +
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    +
    +
    Learning rate  =  0.01
+Lambda =  1e-05
+Accuracy score on test set:  0.9861111111111112
+
    +
    +
    Learning rate  =  0.01
+Lambda =  0.0001
+Accuracy score on test set:  0.9888888888888889
+
    +
    +
    Learning rate  =  0.01
+Lambda =  0.001
+Accuracy score on test set:  0.9888888888888889
+
    +
    +
    Learning rate  =  0.01
+Lambda =  0.01
+Accuracy score on test set:  0.9861111111111112
+
    +
    +
    Learning rate  =  0.01
+Lambda =  0.1
+Accuracy score on test set:  0.9888888888888889
+
    +
    +
    Learning rate  =  0.01
+Lambda =  1.0
+Accuracy score on test set:  0.9722222222222222
+
    +
    +
    Learning rate  =  0.01
+Lambda =  10.0
+Accuracy score on test set:  0.9527777777777777
+
    +
    +
    Learning rate  =  0.1
+Lambda =  1e-05
+Accuracy score on test set:  0.9027777777777778
+
+Learning rate  =  0.1
+Lambda =  0.0001
+Accuracy score on test set:  0.8583333333333333
+
    +
    +
    Learning rate  =  0.1
+Lambda =  0.001
+Accuracy score on test set:  0.8722222222222222
+
+Learning rate  =  0.1
+Lambda =  0.01
+Accuracy score on test set:  0.9055555555555556
+
    +
    +
    Learning rate  =  0.1
+Lambda =  0.1
+Accuracy score on test set:  0.8805555555555555
+
+Learning rate  =  0.1
+Lambda =  1.0
+Accuracy score on test set:  0.8722222222222222
+
    +
    +
    Learning rate  =  0.1
+Lambda =  10.0
+Accuracy score on test set:  0.8666666666666667
+
+Learning rate  =  1.0
+Lambda =  1e-05
+Accuracy score on test set:  0.08611111111111111
+
+Learning rate  =  1.0
+Lambda =  0.0001
+Accuracy score on test set:  0.10555555555555556
+
    +
    +
    Learning rate  =  1.0
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
+Learning rate  =  1.0
+Lambda =  0.01
+Accuracy score on test set:  0.17777777777777778
+
+Learning rate  =  1.0
+Lambda =  0.1
+Accuracy score on test set:  0.08333333333333333
+
    +
    +
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
+Learning rate  =  1.0
+Lambda =  10.0
+Accuracy score on test set:  0.09444444444444444
+
    +
    +
    Learning rate  =  10.0
+Lambda =  1e-05
+Accuracy score on test set:  0.17222222222222222
+
+Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on test set:  0.11666666666666667
+
+Learning rate  =  10.0
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
+Learning rate  =  10.0
+Lambda =  0.01
+Accuracy score on test set:  0.1388888888888889
+
    +
    +
    Learning rate  =  10.0
+Lambda =  0.1
+Accuracy score on test set:  0.11388888888888889
+
    +
    +
    Learning rate  =  10.0
+Lambda =  1.0
+Accuracy score on test set:  0.10555555555555556
+
+Learning rate  =  10.0
+Lambda =  10.0
+Accuracy score on test set:  0.09444444444444444
+
    +
    +
    @@ -1739,6 +2418,10 @@ performance overall.

    +
    +_images/chapter10_63_0.png +_images/chapter10_63_1.png +
    @@ -1777,6 +2460,14 @@ and/or if you use anaconda, just write (or install from the gra
    +
    +
      Input In [12]
+    conda create -n tf tensorflow
+          ^
+SyntaxError: invalid syntax
+
    +
    +

    To install the current release of GPU TensorFlow

    diff --git a/doc/LectureNotes/_build/html/chapter11.html b/doc/LectureNotes/_build/html/chapter11.html index 99a6d7ba8..aecd5c6bf 100644 --- a/doc/LectureNotes/_build/html/chapter11.html +++ b/doc/LectureNotes/_build/html/chapter11.html @@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output" Week 40: Gradient descent methods (continued) and start Neural networks +
  • + + Exercises week 41 + +
    • +
  • + + Week 41 Neural networks and constructing a neural network code + +
    • +
  • + + Exercises week 42 + +
    • +
  • + + Week 42 Constructing a Neural Network code with introduction to Tensor flow + +

    • @@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output" Project 1 on Machine Learning, deadline October 9 (midnight), 2023 +

  • + + Project 2 on Machine Learning, deadline November 13 (Midnight) + +
    • @@ -2612,173 +2637,38 @@ Using TensorFlow results in a much better execution time. Try it!

    19 x = tuple(args[i] for i in argnum) ---> 20 return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25, in grad(fun, x) - 18 @unary_to_nary - 19 def grad(fun, x): - 20 """ - 21 Returns a function which computes the gradient of `fun` with respect to - 22 positional argument number `argnum`. The returned function takes the same - 23 arguments as `fun`, but returns the gradient instead. The function `fun` - 24 should be scalar-valued. The gradient has the same type as the argument.""" ----> 25 vjp, ans = _make_vjp(fun, x) - 26 if not vspace(ans).size == 1: - 27 raise TypeError("Grad only applies to real scalar-output functions. " - 28 "Try jacobian, elementwise_grad or holomorphic_grad.") - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10, in make_vjp(fun, x) - 8 def make_vjp(fun, x): - 9 start_node = VJPNode.new_root() ----> 10 end_value, end_node = trace(start_node, fun, x) - 11 if end_node is None: - 12 def vjp(g): return vspace(x).zeros() - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10, in trace(start_node, fun, x) - 8 with trace_stack.new_trace() as t: - 9 start_box = new_box(x, t, start_node) ----> 10 end_box = fun(start_box) - 11 if isbox(end_box) and end_box._trace == start_box._trace: - 12 return end_box._value, end_box._node - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f(x) - 13 else: - 14 subargs = subvals(args, zip(argnum, x)) ----> 15 return fun(*subargs, **kwargs) - -Input In [9], in cost_function(P, x, t) - 78 g_t = g_trial(point,P) - 79 g_t_jacobian = g_t_jacobian_func(point,P) ----> 80 g_t_hessian = g_t_hessian_func(point,P) - 82 g_t_dt = g_t_jacobian[1] - 83 g_t_d2x = g_t_hessian[0][0] - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f(*args, **kwargs) - 18 else: - 19 x = tuple(args[i] for i in argnum) ----> 20 return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:78, in hessian(fun, x) - 75 @unary_to_nary - 76 def hessian(fun, x): - 77 "Returns a function that computes the exact Hessian." ----> 78 return jacobian(jacobian(fun))(x) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f(*args, **kwargs) - 18 else: - 19 x = tuple(args[i] for i in argnum) ----> 20 return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:57, in jacobian(fun, x) - 47 @unary_to_nary - 48 def jacobian(fun, x): - 49 """ - 50 Returns a function which computes the Jacobian of `fun` with respect to - 51 positional argument number `argnum`, which must be a scalar or array. Unlike - (...) - 55 (out1, out2, ...) then the Jacobian has shape (out1, out2, ..., in1, in2, ...). - 56 """ ----> 57 vjp, ans = _make_vjp(fun, x) - 58 ans_vspace = vspace(ans) - 59 jacobian_shape = ans_vspace.shape + vspace(x).shape - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10, in make_vjp(fun, x) - 8 def make_vjp(fun, x): - 9 start_node = VJPNode.new_root() ----> 10 end_value, end_node = trace(start_node, fun, x) - 11 if end_node is None: - 12 def vjp(g): return vspace(x).zeros() - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10, in trace(start_node, fun, x) - 8 with trace_stack.new_trace() as t: - 9 start_box = new_box(x, t, start_node) ----> 10 end_box = fun(start_box) - 11 if isbox(end_box) and end_box._trace == start_box._trace: - 12 return end_box._value, end_box._node - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f(x) - 13 else: - 14 subargs = subvals(args, zip(argnum, x)) ----> 15 return fun(*subargs, **kwargs) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20, in unary_to_nary.<locals>.nary_operator.<locals>.nary_f(*args, **kwargs) - 18 else: - 19 x = tuple(args[i] for i in argnum) ----> 20 return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:61, in jacobian(fun, x) - 59 jacobian_shape = ans_vspace.shape + vspace(x).shape - 60 grads = map(vjp, ans_vspace.standard_basis()) ----> 61 return np.reshape(np.stack(grads), jacobian_shape) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88, in stack(arrays, axis) - 83 def stack(arrays, axis=0): - 84 # this code is basically copied from numpy/core/shape_base.py's stack - 85 # we need it here because we want to re-implement stack in terms of the - 86 # primitives defined in this file ----> 88 arrays = [array(arr) for arr in arrays] - 89 if not arrays: - 90 raise ValueError('need at least one array to stack') - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88, in <listcomp>(.0) - 83 def stack(arrays, axis=0): - 84 # this code is basically copied from numpy/core/shape_base.py's stack - 85 # we need it here because we want to re-implement stack in terms of the - 86 # primitives defined in this file ----> 88 arrays = [array(arr) for arr in arrays] - 89 if not arrays: - 90 raise ValueError('need at least one array to stack') +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:29, in grad(fun, x) + 26 if not vspace(ans).size == 1: + 27 raise TypeError("Grad only applies to real scalar-output functions. " + 28 "Try jacobian, elementwise_grad or holomorphic_grad.") +---> 29 return vjp(vspace(ans).ones()) File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14, in make_vjp.<locals>.vjp(g) ---> 14 def vjp(g): return backward_pass(g, end_node) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21, in backward_pass(g, end_node) - 19 for node in toposort(end_node): - 20 outgrad = outgrads.pop(node) ----> 21 ingrads = node.vjp(outgrad[0]) +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:23, in backward_pass(g, end_node) + 21 ingrads = node.vjp(outgrad[0]) 22 for parent, ingrad in zip(node.parents, ingrads): - 23 outgrads[parent] = add_outgrads(outgrads.get(parent), ingrad) +---> 23 outgrads[parent] = add_outgrads(outgrads.get(parent), ingrad) + 24 return outgrad[0] -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67, in defvjp.<locals>.vjp_argnums.<locals>.<lambda>(g) - 64 raise NotImplementedError( - 65 "VJP of {} wrt argnum 0 not defined".format(fun.__name__)) - 66 vjp = vjpfun(ans, *args, **kwargs) ----> 67 return lambda g: (vjp(g),) - 68 elif L == 2: - 69 argnum_0, argnum_1 = argnums +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:165, in add_outgrads(prev_g_flagged, g) + 163 if mutable: + 164 if sparse: +--> 165 return sparse_add(vs, prev_g, g), True + 166 else: + 167 return vs.mut_add(prev_g, g), True -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:701, in <lambda>(g) - 699 return A - 700 return SparseObject(vs, mut_add) ---> 701 defvjp(func(ArrayBox.__getitem__), lambda ans, A, idx: lambda g: untake(g, idx, vspace(A))) - 702 defvjp(untake, lambda ans, x, idx, _: lambda g: g[idx]) - 704 def _unpad(array, width): - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:44, in primitive.<locals>.f_wrapped(*args, **kwargs) - 42 parents = tuple(box._node for _ , box in boxed_args) - 43 argnums = tuple(argnum for argnum, _ in boxed_args) ----> 44 ans = f_wrapped(*argvals, **kwargs) - 45 node = node_constructor(ans, f_wrapped, argvals, kwargs, argnums, parents) - 46 return new_box(ans, trace, node) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45, in primitive.<locals>.f_wrapped(*args, **kwargs) - 43 argnums = tuple(argnum for argnum, _ in boxed_args) - 44 ans = f_wrapped(*argvals, **kwargs) ----> 45 node = node_constructor(ans, f_wrapped, argvals, kwargs, argnums, parents) +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48, in primitive.<locals>.f_wrapped(*args, **kwargs) 46 return new_box(ans, trace, node) 47 else: +---> 48 return f_raw(*args, **kwargs) -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36, in VJPNode.__init__(self, value, fun, args, kwargs, parent_argnums, parents) - 33 fun_name = getattr(fun, '__name__', fun) - 34 raise NotImplementedError("VJP of {} wrt argnums {} not defined" - 35 .format(fun_name, parent_argnums)) ----> 36 self.vjp = vjpmaker(parent_argnums, value, args, kwargs) - -File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:56, in defvjp.<locals>.vjp_argnums(argnums, ans, args, kwargs) - 53 argnums = kwargs.get('argnums', count()) - 54 vjps_dict = {argnum : translate_vjp(vjpmaker, fun, argnum) - 55 for argnum, vjpmaker in zip(argnums, vjpmakers)} ----> 56 def vjp_argnums(argnums, ans, args, kwargs): - 57 L = len(argnums) - 58 # These first two cases are just optimizations +File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:186, in sparse_add(vs, x_prev, x_new) + 183 @primitive + 184 def sparse_add(vs, x_prev, x_new): + 185 x_prev = x_prev if x_prev is not None else vs.zeros() +--> 186 return x_new.mut_add(x_prev) KeyboardInterrupt: diff --git a/doc/LectureNotes/_build/html/chapter12.html b/doc/LectureNotes/_build/html/chapter12.html index 623a6403e..9f5dbc2f8 100644 --- a/doc/LectureNotes/_build/html/chapter12.html +++ b/doc/LectureNotes/_build/html/chapter12.html @@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output" Week 40: Gradient descent methods (continued) and start Neural networks +
  • + + Exercises week 41 + +
    • +
  • + + Week 41 Neural networks and constructing a neural network code + +
    • +
  • + + Exercises week 42 + +
    • +
  • + + Week 42 Constructing a Neural Network code with introduction to Tensor flow + +

    • @@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output" Project 1 on Machine Learning, deadline October 9 (midnight), 2023 +

  • + + Project 2 on Machine Learning, deadline November 13 (Midnight) + +
    • @@ -1272,7 +1297,7 @@ labels = (n_inputs) = (1797,) 
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/keras/optimizer_v2/gradient_descent.py:102: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
   super(SGD, self).__init__(name, **kwargs)
-2023-10-02 06:54:12.770204: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz
+2023-10-15 21:48:58.909327: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz
 
    ---------------------------------------------------------------------------
diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html
index a9f62202b..e53fbcecc 100644
--- a/doc/LectureNotes/_build/html/chapter13.html
+++ b/doc/LectureNotes/_build/html/chapter13.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    •
    @@ -675,267 +700,321 @@ systems such as automatic translation and speech-to-text.

    Epoch 1/100
    -
    2023-10-02 06:54:48.552042: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz
+
    2023-10-15 21:49:35.228942: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz
 
    
 
    
-
    50/50 - 4s - loss: 1.7644 - 4s/epoch - 84ms/step
+
    50/50 - 3s - loss: 0.5276 - 3s/epoch - 66ms/step
 
    
 
    
 
    Epoch 2/100
 
    
 
    
-
    50/50 - 0s - loss: 0.4353 - 499ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.4234 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 3/100
 
    
 
    
-
    50/50 - 0s - loss: 0.4066 - 479ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.4043 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 4/100
 
    
 
    
-
    50/50 - 1s - loss: 0.4033 - 740ms/epoch - 15ms/step
+
    50/50 - 0s - loss: 0.4010 - 460ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 5/100
 
    
 
    
-
    50/50 - 1s - loss: 0.4014 - 596ms/epoch - 12ms/step
+
    50/50 - 0s - loss: 0.3979 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 6/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3999 - 561ms/epoch - 11ms/step
+
    50/50 - 0s - loss: 0.3967 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 7/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3996 - 515ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3962 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 8/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3975 - 495ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3957 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 9/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3970 - 473ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3929 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 10/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3944 - 687ms/epoch - 14ms/step
+
    50/50 - 0s - loss: 0.3920 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 11/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3948 - 500ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3918 - 454ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 12/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3932 - 501ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3898 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 13/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3923 - 499ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3921 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 14/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3919 - 484ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3911 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 15/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3928 - 556ms/epoch - 11ms/step
+
    50/50 - 0s - loss: 0.3888 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 16/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3901 - 497ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3871 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 17/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3907 - 456ms/epoch - 9ms/step
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    50/50 - 0s - loss: 0.3894 - 458ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 18/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3893 - 456ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3873 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 19/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3878 - 458ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3855 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 20/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3877 - 455ms/epoch - 9ms/step
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    50/50 - 0s - loss: 0.3871 - 453ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 21/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3873 - 462ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3802 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 22/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3865 - 468ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3856 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 23/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3856 - 487ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3804 - 453ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 24/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3853 - 473ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3842 - 453ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 25/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3838 - 492ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3815 - 452ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 26/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3840 - 477ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3782 - 454ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 27/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3836 - 643ms/epoch - 13ms/step
+
    50/50 - 0s - loss: 0.3798 - 454ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 28/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3834 - 484ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3804 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 29/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3838 - 483ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3812 - 452ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 30/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3837 - 468ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3780 - 454ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 31/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3821 - 671ms/epoch - 13ms/step
+
    50/50 - 0s - loss: 0.3800 - 453ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 32/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3816 - 832ms/epoch - 17ms/step
+
    50/50 - 0s - loss: 0.3767 - 467ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 33/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3812 - 581ms/epoch - 12ms/step
+
    50/50 - 0s - loss: 0.3787 - 493ms/epoch - 10ms/step
 
    
 
    
 
    Epoch 34/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3770 - 515ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3758 - 464ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 35/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3814 - 654ms/epoch - 13ms/step
+
    50/50 - 0s - loss: 0.3784 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 36/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3789 - 522ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3766 - 461ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 37/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3799 - 488ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3733 - 456ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 38/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3795 - 450ms/epoch - 9ms/step
+
    50/50 - 0s - loss: 0.3749 - 455ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 39/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3786 - 692ms/epoch - 14ms/step
+
    50/50 - 0s - loss: 0.3756 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 40/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3773 - 741ms/epoch - 15ms/step
+
    50/50 - 0s - loss: 0.3737 - 458ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 41/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3765 - 555ms/epoch - 11ms/step
+
    50/50 - 0s - loss: 0.3743 - 459ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 42/100
 
    
 
    
-
    50/50 - 0s - loss: 0.3799 - 485ms/epoch - 10ms/step
+
    50/50 - 0s - loss: 0.3730 - 460ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 43/100
 
    
 
    
-
    50/50 - 1s - loss: 0.3786 - 665ms/epoch - 13ms/step
+
    50/50 - 0s - loss: 0.3706 - 457ms/epoch - 9ms/step
 
    
 
    
 
    Epoch 44/100
 
    
 
    
+
    50/50 - 0s - loss: 0.3724 - 459ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 45/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3716 - 456ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 46/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3713 - 459ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 47/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3705 - 458ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 48/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3703 - 460ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 49/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3701 - 459ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 50/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3676 - 470ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 51/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3679 - 464ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 52/100
+
    
+
    
+
    50/50 - 0s - loss: 0.3689 - 460ms/epoch - 9ms/step
+
    
+
    
+
    Epoch 53/100
+
    
+
    
 
    ---------------------------------------------------------------------------
 KeyboardInterrupt                         Traceback (most recent call last)
 Input In [1], in <cell line: 58>()
diff --git a/doc/LectureNotes/_build/html/chapter2.html b/doc/LectureNotes/_build/html/chapter2.html
index 67ba10971..8baccf5d0 100644
--- a/doc/LectureNotes/_build/html/chapter2.html
+++ b/doc/LectureNotes/_build/html/chapter2.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1290,10 +1315,10 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    -0.033790755027115954
-3.888577549915147
-[[ 1.2697447   3.97644118]
- [ 3.97644118 13.38465596]]
+
    0.12765651865754318
+4.348676117830458
+[[0.98073929 2.88442538]
+ [2.88442538 9.24128917]]
 
    
 
    
 
    
@@ -1330,10 +1355,10 @@ a more brute force way. Here we scale the mean values for each column of the des
 
    
 
    
 
    
-
    0.08238863600759742
-1.795225339396409
-[[1.         0.64391062]
- [0.64391062 1.        ]]
+
    0.08652153831327969
+1.7893215781870513
+[[1.         0.70344416]
+ [0.70344416 1.        ]]
 
    
 
    
 
    
@@ -1363,30 +1388,30 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
    
 
    
-
    [[ 1.29135778  4.3399612 ]
- [ 0.08815506 -1.48140137]
- [ 0.34149655  1.18571316]
- [-1.00375475 -2.69226802]
- [ 0.42198678  2.56858701]
- [ 0.53278871  2.8969113 ]
- [-1.38020451 -4.26263837]
- [-0.64969451 -2.00778523]
- [-0.32632463 -1.7413913 ]
- [ 0.68419351  1.19431161]]
+
    [[ 1.71727268  5.22388434]
+ [ 0.31027702  0.17469167]
+ [-0.26149831 -0.93082933]
+ [ 0.04107874  1.47244548]
+ [-2.10812381 -5.28818554]
+ [-1.62910047 -4.07706814]
+ [ 0.92136836  2.27309401]
+ [-0.3175938  -1.42457498]
+ [ 0.68037392  0.16481217]
+ [ 0.64594566  2.41173033]]
           0         1
-0  1.291358  4.339961
-1  0.088155 -1.481401
-2  0.341497  1.185713
-3 -1.003755 -2.692268
-4  0.421987  2.568587
-5  0.532789  2.896911
-6 -1.380205 -4.262638
-7 -0.649695 -2.007785
-8 -0.326325 -1.741391
-9  0.684194  1.194312
+0  1.717273  5.223884
+1  0.310277  0.174692
+2 -0.261498 -0.930829
+3  0.041079  1.472445
+4 -2.108124 -5.288186
+5 -1.629100 -4.077068
+6  0.921368  2.273094
+7 -0.317594 -1.424575
+8  0.680374  0.164812
+9  0.645946  2.411730
           0         1
-0  1.000000  0.943439
-1  0.943439  1.000000
+0  1.000000  0.962653
+1  0.962653  1.000000
 
    
 
    
 
    
@@ -1443,40 +1468,37 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
         0         1         2         3         4         5         6         7   \
 0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.089710  0.084075  0.088697  0.086518  0.084247  0.079455  0.077756   
-2   0.0  0.084075  0.079226  0.082189  0.080406  0.078545  0.073008  0.071611   
-3   0.0  0.088697  0.082189  0.093408  0.090365  0.087247  0.087250  0.084843   
-4   0.0  0.086518  0.080406  0.090365  0.087603  0.084764  0.083853  0.081680   
-5   0.0  0.084247  0.078545  0.087247  0.084764  0.082205  0.080411  0.078467   
-6   0.0  0.079455  0.073008  0.087250  0.083853  0.080411  0.083988  0.081246   
-7   0.0  0.077756  0.071611  0.084843  0.081680  0.078467  0.081246  0.078707   
-8   0.0  0.076125  0.070275  0.082517  0.079581  0.076592  0.078593  0.076249   
-9   0.0  0.074545  0.068987  0.080256  0.077542  0.074772  0.076012  0.073858   
-10  0.0  0.070597  0.064412  0.079882  0.076354  0.072805  0.078656  0.075758   
-11  0.0  0.068974  0.063055  0.077650  0.074330  0.070986  0.076136  0.073422   
-12  0.0  0.067437  0.061775  0.075523  0.072404  0.069257  0.073728  0.071191   
-13  0.0  0.065982  0.060567  0.073494  0.070569  0.067611  0.071423  0.069055   
-14  0.0  0.064602  0.059427  0.071554  0.068816  0.066042  0.069213  0.067009   
+1   0.0  0.082246  0.081621  0.082225  0.081617  0.081120  0.073421  0.072973   
+2   0.0  0.081621  0.081679  0.081960  0.081804  0.081742  0.073498  0.073387   
+3   0.0  0.082225  0.081960  0.087271  0.086900  0.086636  0.081057  0.080755   
+4   0.0  0.081617  0.081804  0.086900  0.086868  0.086932  0.080935  0.080903   
+5   0.0  0.081120  0.081742  0.086636  0.086932  0.087311  0.080906  0.081136   
+6   0.0  0.073421  0.073498  0.081057  0.080935  0.080906  0.077455  0.077330   
+7   0.0  0.072973  0.073387  0.080755  0.080903  0.081136  0.077330  0.077429   
+8   0.0  0.072637  0.073376  0.080571  0.080980  0.081466  0.077313  0.077630   
+9   0.0  0.072410  0.073465  0.080502  0.081164  0.081896  0.077403  0.077931   
+10  0.0  0.064640  0.064948  0.073406  0.073471  0.073618  0.071662  0.071685   
+11  0.0  0.064320  0.064896  0.073187  0.073476  0.073840  0.071579  0.071792   
+12  0.0  0.064101  0.064938  0.073080  0.073586  0.074161  0.071601  0.072000   
+13  0.0  0.063980  0.065069  0.073079  0.073797  0.074577  0.071726  0.072305   
+14  0.0  0.063953  0.065289  0.073184  0.074108  0.075089  0.071951  0.072707   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.076125  0.074545  0.070597  0.068974  0.067437  0.065982  0.064602  
-2   0.070275  0.068987  0.064412  0.063055  0.061775  0.060567  0.059427  
-3   0.082517  0.080256  0.079882  0.077650  0.075523  0.073494  0.071554  
-4   0.079581  0.077542  0.076354  0.074330  0.072404  0.070569  0.068816  
-5   0.076592  0.074772  0.072805  0.070986  0.069257  0.067611  0.066042  
-6   0.078593  0.076012  0.078656  0.076136  0.073728  0.071423  0.069213  
-7   0.076249  0.073858  0.075758  0.073422  0.071191  0.069055  0.067009  
-8   0.073980  0.071773  0.072953  0.070795  0.068734  0.066762  0.064874  
-9   0.071773  0.069746  0.070228  0.068241  0.066344  0.064532  0.062797  
-10  0.072953  0.070228  0.074969  0.072310  0.069766  0.067328  0.064987  
-11  0.070795  0.068241  0.072310  0.069822  0.067440  0.065158  0.062967  
-12  0.068734  0.066344  0.069766  0.067440  0.065214  0.063081  0.061034  
-13  0.066762  0.064532  0.067328  0.065158  0.063081  0.061092  0.059182  
-14  0.064874  0.062797  0.064987  0.062967  0.061034  0.059182  0.057406  
-
    
-
    
-
    
+1   0.072637  0.072410  0.064640  0.064320  0.064101  0.063980  0.063953  
+2   0.073376  0.073465  0.064948  0.064896  0.064938  0.065069  0.065289  
+3   0.080571  0.080502  0.073406  0.073187  0.073080  0.073079  0.073184  
+4   0.080980  0.081164  0.073471  0.073476  0.073586  0.073797  0.074108  
+5   0.081466  0.081896  0.073618  0.073840  0.074161  0.074577  0.075089  
+6   0.077313  0.077403  0.071662  0.071579  0.071601  0.071726  0.071951  
+7   0.077630  0.077931  0.071685  0.071792  0.072000  0.072305  0.072707  
+8   0.078041  0.078548  0.071805  0.072098  0.072486  0.072967  0.073541  
+9   0.078548  0.079255  0.072022  0.072495  0.073059  0.073712  0.074455  
+10  0.071805  0.072022  0.067420  0.067457  0.067591  0.067820  0.068141  
+11  0.072098  0.072495  0.067457  0.067660  0.067955  0.068340  0.068815  
+12  0.072486  0.073059  0.067591  0.067955  0.068407  0.068945  0.069570  
+13  0.072967  0.073712  0.067820  0.068340  0.068945  0.069634  0.070406  
+14  0.073541  0.074455  0.068141  0.068815  0.069570  0.070406  0.071323  
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/chapter3.html b/doc/LectureNotes/_build/html/chapter3.html
index 1baea9f8b..7253cd0f1 100644
--- a/doc/LectureNotes/_build/html/chapter3.html
+++ b/doc/LectureNotes/_build/html/chapter3.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -844,10 +869,10 @@ number \(i\) is left out. Usin
 
    
 
    
 
    
-
    Runtime: 0.179404 sec
+
    Runtime: 0.136236 sec
 Jackknife Statistics :
 original           bias      std. error
- 100.039        100.029        0.150726
+  99.979         99.969         0.14845
 
    
 
    
 
    
@@ -1066,7 +1091,7 @@ theorem.
    
 
    
 
    Bootstrap Statistics :
 original           bias      std. error
- 100.092  14.9578        100.093        0.149299
+ 99.8342  14.8306        99.8351         0.14857
 
    
 
    
 
    
@@ -1288,14 +1313,14 @@ Error: 0.06844519414009445
 Bias^2: 0.06453579006728322
 Var: 0.003909404072811221
 0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444
-
    
-
    
-
    Polynomial degree: 5
+Polynomial degree: 5
 Error: 0.05227921801205679
 Bias^2: 0.04818727730430286
 Var: 0.004091940707753925
 0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679
-Polynomial degree: 6
+
    
+
    
+
    Polynomial degree: 6
 Error: 0.03781367141738902
 Bias^2: 0.03365768507152769
 Var: 0.0041559863458613296
@@ -1569,12 +1594,12 @@ Mean squared error on test data: 5.98822371
 Degree of polynomial:   6
 Mean squared error on training data: 3.66204648
 Mean squared error on test data: 8.14812206
-
    
-
    
-
    Degree of polynomial:   7
+Degree of polynomial:   7
 Mean squared error on training data: 0.47075725
 Mean squared error on test data: 2.00607783
-Degree of polynomial:   8
+
    
+
    
+
    Degree of polynomial:   8
 Mean squared error on training data: 0.04912436
 Mean squared error on test data: 0.21596432
 Degree of polynomial:   9
@@ -1589,15 +1614,15 @@ Mean squared error on test data: 1.35533773
 Degree of polynomial:  12
 Mean squared error on training data: 0.00813803
 Mean squared error on test data: 0.17446471
-
    
-
    
-
    Degree of polynomial:  13
+Degree of polynomial:  13
 Mean squared error on training data: 0.00759119
 Mean squared error on test data: 1.08131003
 Degree of polynomial:  14
 Mean squared error on training data: 0.00472199
 Mean squared error on test data: 0.81333804
-Degree of polynomial:  15
+
    
+
    
+
    Degree of polynomial:  15
 Mean squared error on training data: 0.00410478
 Mean squared error on test data: 92.09172409
 Degree of polynomial:  16
@@ -1609,9 +1634,7 @@ Mean squared error on test data: 1271.35771826
 Degree of polynomial:  18
 Mean squared error on training data: 0.00228742
 Mean squared error on test data: 108.27092910
-
    
-
    
-
    Degree of polynomial:  19
+Degree of polynomial:  19
 Mean squared error on training data: 0.00156376
 Mean squared error on test data: 1371.99051150
 Degree of polynomial:  20
@@ -1620,7 +1643,9 @@ Mean squared error on test data: 1887.86252988
 Degree of polynomial:  21
 Mean squared error on training data: 0.00118508
 Mean squared error on test data: 14859.69908626
-Degree of polynomial:  22
+
    
+
    
+
    Degree of polynomial:  22
 Mean squared error on training data: 0.00092647
 Mean squared error on test data: 876.51191552
 Degree of polynomial:  23
@@ -1629,9 +1654,7 @@ Mean squared error on test data: 5594.60815105
 Degree of polynomial:  24
 Mean squared error on training data: 0.00084705
 Mean squared error on test data: 1277.61702282
-
    
-
    
-
    Degree of polynomial:  25
+Degree of polynomial:  25
 Mean squared error on training data: 0.00079129
 Mean squared error on test data: 128664.31650694
 Degree of polynomial:  26
@@ -1640,7 +1663,9 @@ Mean squared error on test data: 19003.94822514
 Degree of polynomial:  27
 Mean squared error on training data: 0.00068946
 Mean squared error on test data: 2379.66219404
-Degree of polynomial:  28
+
    
+
    
+
    Degree of polynomial:  28
 Mean squared error on training data: 0.00062595
 Mean squared error on test data: 4082.19983530
 Degree of polynomial:  29
@@ -1648,9 +1673,9 @@ Mean squared error on training data: 0.00060705
 Mean squared error on test data: 3250.17647619
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(testerror), label='Test Error')
 
    
 
    
@@ -1884,7 +1909,7 @@ cross-validation (LOOCV).
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
 
    
 
    
@@ -2772,6 +2797,15 @@ linear system as an equation would reduce this down to
 
    
 
    
 
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
+
    
+
    
+_images/chapter3_154_1.png
+
    
 
    
 
    It is interesting to note that OLS
 considers both \(J_{j, j + 1} = -0.5\) and \(J_{j, j - 1} = -0.5\) as
@@ -2909,6 +2943,15 @@ with the form utilized in linear regression, viz.
    
 
    
 
    
 
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
+  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
+
    
+
    
+_images/chapter3_172_1.png
+
    
 
    
 
    The results agree perfectly with our previous discussion where we used our own code.
    
 
    Having explored the ordinary least squares we move on to ridge
@@ -2942,6 +2985,15 @@ cost function is given by
    
 
    
 
    
 
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
+  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
+
    
+
    
+_images/chapter3_175_1.png
+
    
 
    
 
    In the Least Absolute Shrinkage and Selection Operator (LASSO)-method we get a third cost function.
    
 
@@ -2970,6 +3022,15 @@ cost function is given by
    
 
    
 
    
 
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  cb = fig.colorbar(im)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
+  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
+
    
+
    
+_images/chapter3_179_1.png
+
    
 
    
 
    It is quite striking how LASSO breaks the symmetry of the coupling
 constant as opposed to ridge and OLS. We get a sparse solution with
@@ -3016,6 +3077,51 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 
    
 
    
 
    
+
    
+
      0%|                                                                                                                          | 0/10 [00:00<?, ?it/s]
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00
+  model = cd_fast.enet_coordinate_descent(
+
+ 10%|███████████▍                                                                                                      | 1/10 [00:00<00:08,  1.06it/s]
+
    
+
    
+
     20%|██████████████████████▊                                                                                           | 2/10 [00:01<00:07,  1.04it/s]
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+
    
+
    
+
    100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:06<00:00,  1.62it/s]
+
    
+
    
+
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+
    
+
    
+
    
+
    
+
    
+_images/chapter3_181_13.png
+
    
 
    
 
    We see that LASSO reaches a good solution for low
 values of \(\lambda\), but will “wither” when we increase \(\lambda\) too
@@ -3062,6 +3168,9 @@ testing set that is close to the accuracy of the training set.
    
 
    
 
    
 
    
+
    
+_images/chapter3_183_0.png
+
    
 
    
 
    From the above figure we can see that LASSO with \(\lambda = 10^{-2}\)
 achieves a very good accuracy on the test set. This by far surpasses the
@@ -3151,6 +3260,15 @@ which polynomial fits the data best.
    
 
    
 
    
 
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+  ax = fig.gca(projection='3d')
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
+  fig.colorbar(surf, shrink=0.5, aspect=5)
+
    
+
    
+_images/chapter3_188_1.png
+
    
 
    
 
    
 
    5.8.1. Exercise: Ordinary Least Square (OLS) on the Franke function
    
@@ -3303,6 +3421,16 @@ Python program using
    
 
    
 
    
 
    
+
    
+
    ---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [31], in <cell line: 1>()
+----> 1 scipy.misc.imread
+
+NameError: name 'scipy' is not defined
+
    
+
    
+
    
 
    
 
    Here is a simple part of a Python code which reads and plots the data
 from such files
    
diff --git a/doc/LectureNotes/_build/html/chapter4.html b/doc/LectureNotes/_build/html/chapter4.html
index 78e7812bd..dbd68ef30 100644
--- a/doc/LectureNotes/_build/html/chapter4.html
+++ b/doc/LectureNotes/_build/html/chapter4.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1182,6 +1207,10 @@ Based on this we can then define the accuracy score as the sum of correctly pred
 
    (426, 30)
 (143, 30)
 Test set accuracy with Logistic Regression: 0.94
+Test set accuracy Logistic Regression with scaled data: 0.96
+[1.         1.         1.         1.         1.         1.
+ 1.         1.         0.92857143 0.92857143]
+Test set accuracy with Logistic Regression  and scaled data: 0.96
 
    
 
    
 
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
@@ -1194,15 +1223,9 @@ Please also refer to the documentation for alternative solver options:
   n_iter_i = _check_optimize_result(
 
    
 
    
-
    Test set accuracy Logistic Regression with scaled data: 0.96
-[1.         1.         1.         1.         1.         1.
- 1.         1.         0.92857143 0.92857143]
-Test set accuracy with Logistic Regression  and scaled data: 0.96
-
    
-
    
+_images/chapter4_64_2.png
 _images/chapter4_64_3.png
 _images/chapter4_64_4.png
-_images/chapter4_64_5.png
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/chapter5.html b/doc/LectureNotes/_build/html/chapter5.html
index bb667d505..7ba11d262 100644
--- a/doc/LectureNotes/_build/html/chapter5.html
+++ b/doc/LectureNotes/_build/html/chapter5.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapter6.html b/doc/LectureNotes/_build/html/chapter6.html
index cc64ec13a..a928e6651 100644
--- a/doc/LectureNotes/_build/html/chapter6.html
+++ b/doc/LectureNotes/_build/html/chapter6.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -772,9 +797,9 @@ predicting the target features of query instances is as follows:
    
 
    
 
    
 
    2nd degree coefficients:
-zero power:  -1.3439564710454786
-first power:  0.020404272938413143
-second power:  0.0001539814498783133
+zero power:  -0.2774877574815404
+first power:  0.11112589053037751
+second power:  -0.00033136014047192484
 
    
 
    
 _images/chapter6_1_1.png
diff --git a/doc/LectureNotes/_build/html/chapter7.html b/doc/LectureNotes/_build/html/chapter7.html
index 28c213e50..19c6f4426 100644
--- a/doc/LectureNotes/_build/html/chapter7.html
+++ b/doc/LectureNotes/_build/html/chapter7.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapter8.html b/doc/LectureNotes/_build/html/chapter8.html
index efe2d38c7..88ecb4d12 100644
--- a/doc/LectureNotes/_build/html/chapter8.html
+++ b/doc/LectureNotes/_build/html/chapter8.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -726,10 +751,10 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    -0.026250840755899812
-3.9783319210079595
-[[ 1.06075426  3.40216748]
- [ 3.40216748 11.8635085 ]]
+
    -0.10776220958055382
+3.743189104728408
+[[0.82379443 2.29894362]
+ [2.29894362 7.75174305]]
 
    
 
    
 
    
@@ -769,10 +794,10 @@ a more brute force way. Here we scale the mean values for each column of the des
 
    
 
    
 
    
-
    0.08076969085177746
-1.9295763474254684
-[[1.        0.7135487]
- [0.7135487 1.       ]]
+
    0.0704374681593734
+1.3273472571412799
+[[1.         0.58076367]
+ [0.58076367 1.        ]]
 
    
 
    
 
    
@@ -801,30 +826,30 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
    
 
    
-
    [[ 1.52944573  4.65218729]
- [ 0.12050822  0.97069774]
- [ 0.40413036  1.80861057]
- [-0.07004211  0.30763135]
- [-1.27793476 -4.21460652]
- [-0.14670413 -1.48950243]
- [-0.41506637 -1.52573941]
- [ 1.75627883  5.73410729]
- [-0.47187428 -1.10927588]
- [-1.42874148 -5.13410999]]
+
    [[-0.92200223 -1.78838813]
+ [-0.90854751 -2.66047048]
+ [ 0.83618601  2.91748202]
+ [-0.88821402 -4.10035098]
+ [ 0.44781662  2.48685204]
+ [ 1.20493234  2.32729105]
+ [ 1.02509184  2.42265837]
+ [-0.84210141 -3.82012236]
+ [-0.01031541  1.40111899]
+ [ 0.05715377  0.81392948]]
           0         1
-0  1.529446  4.652187
-1  0.120508  0.970698
-2  0.404130  1.808611
-3 -0.070042  0.307631
-4 -1.277935 -4.214607
-5 -0.146704 -1.489502
-6 -0.415066 -1.525739
-7  1.756279  5.734107
-8 -0.471874 -1.109276
-9 -1.428741 -5.134110
+0 -0.922002 -1.788388
+1 -0.908548 -2.660470
+2  0.836186  2.917482
+3 -0.888214 -4.100351
+4  0.447817  2.486852
+5  1.204932  2.327291
+6  1.025092  2.422658
+7 -0.842101 -3.820122
+8 -0.010315  1.401119
+9  0.057154  0.813929
           0         1
-0  1.000000  0.988835
-1  0.988835  1.000000
+0  1.000000  0.920619
+1  0.920619  1.000000
 
    
 
    
 
    
@@ -881,37 +906,37 @@ this matrix we easily see that it is a positive definite matrix.
    
 
    
 
         0         1         2         3         4         5         6         7   \
 0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.076825  0.078868  0.077705  0.077226  0.076504  0.071258  0.070157   
-2   0.0  0.078868  0.083096  0.081976  0.082506  0.082577  0.076127  0.075513   
-3   0.0  0.077705  0.081976  0.085023  0.085454  0.085391  0.081955  0.081126   
-4   0.0  0.077226  0.082506  0.085454  0.086441  0.086843  0.082760  0.082255   
-5   0.0  0.076504  0.082577  0.085391  0.086843  0.087642  0.083000  0.082781   
-6   0.0  0.071258  0.076127  0.081955  0.082760  0.083000  0.081584  0.080933   
-7   0.0  0.070157  0.075513  0.081126  0.082255  0.082781  0.080933  0.080505   
-8   0.0  0.069033  0.074780  0.080163  0.081570  0.082347  0.080105  0.079878   
-9   0.0  0.067915  0.073984  0.079124  0.080773  0.081772  0.079165  0.079121   
-10  0.0  0.064634  0.069384  0.076833  0.077710  0.078029  0.078187  0.077613   
-11  0.0  0.063407  0.068403  0.075582  0.076662  0.077171  0.076996  0.076587   
-12  0.0  0.062221  0.067419  0.074327  0.075587  0.076266  0.075779  0.075521   
-13  0.0  0.061084  0.066453  0.073088  0.074509  0.075342  0.074560  0.074439   
-14  0.0  0.060001  0.065517  0.071879  0.073445  0.074419  0.073354  0.073362   
+1   0.0  0.076527  0.079731  0.075684  0.075421  0.075030  0.066467  0.065808   
+2   0.0  0.079731  0.084207  0.080233  0.080607  0.080750  0.071252  0.070964   
+3   0.0  0.075684  0.080233  0.079381  0.079948  0.080284  0.072483  0.072285   
+4   0.0  0.075421  0.080607  0.079948  0.080953  0.081677  0.073541  0.073640   
+5   0.0  0.075030  0.080750  0.080284  0.081677  0.082746  0.074340  0.074708   
+6   0.0  0.066467  0.071252  0.072483  0.073541  0.074340  0.068082  0.068257   
+7   0.0  0.065808  0.070964  0.072285  0.073640  0.074708  0.068257  0.068650   
+8   0.0  0.065215  0.070694  0.072098  0.073720  0.075030  0.068406  0.068997   
+9   0.0  0.064696  0.070461  0.071942  0.073802  0.075331  0.068551  0.069320   
+10  0.0  0.057462  0.062071  0.064444  0.065735  0.066768  0.061869  0.062273   
+11  0.0  0.056898  0.061747  0.064145  0.065645  0.066870  0.061826  0.062390   
+12  0.0  0.056418  0.061484  0.063905  0.065593  0.066992  0.061813  0.062523   
+13  0.0  0.056019  0.061281  0.063722  0.065582  0.067139  0.061833  0.062675   
+14  0.0  0.055697  0.061138  0.063597  0.065614  0.067315  0.061888  0.062852   
 
           8         9         10        11        12        13        14  
 0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.069033  0.067915  0.064634  0.063407  0.062221  0.061084  0.060001  
-2   0.074780  0.073984  0.069384  0.068403  0.067419  0.066453  0.065517  
-3   0.080163  0.079124  0.076833  0.075582  0.074327  0.073088  0.071879  
-4   0.081570  0.080773  0.077710  0.076662  0.075587  0.074509  0.073445  
-5   0.082347  0.081772  0.078029  0.077171  0.076266  0.075342  0.074419  
-6   0.080105  0.079165  0.078187  0.076996  0.075779  0.074560  0.073354  
-7   0.079878  0.079121  0.077613  0.076587  0.075521  0.074439  0.073362  
-8   0.079434  0.078845  0.076857  0.075984  0.075058  0.074108  0.073152  
-9   0.078845  0.078412  0.075980  0.075249  0.074457  0.073630  0.072790  
-10  0.076857  0.075980  0.076105  0.074970  0.073802  0.072624  0.071452  
-11  0.075984  0.075249  0.074970  0.073972  0.072931  0.071872  0.070811  
-12  0.075058  0.074457  0.073802  0.072931  0.072009  0.071062  0.070107  
-13  0.074108  0.073630  0.072624  0.071872  0.071062  0.070220  0.069365  
-14  0.073152  0.072790  0.071452  0.070811  0.070107  0.069365  0.068606  
+1   0.065215  0.064696  0.057462  0.056898  0.056418  0.056019  0.055697  
+2   0.070694  0.070461  0.062071  0.061747  0.061484  0.061281  0.061138  
+3   0.072098  0.071942  0.064444  0.064145  0.063905  0.063722  0.063597  
+4   0.073720  0.073802  0.065735  0.065645  0.065593  0.065582  0.065614  
+5   0.075030  0.075331  0.066768  0.066870  0.066992  0.067139  0.067315  
+6   0.068406  0.068551  0.061869  0.061826  0.061813  0.061833  0.061888  
+7   0.068997  0.069320  0.062273  0.062390  0.062523  0.062675  0.062852  
+8   0.069522  0.070009  0.062631  0.062894  0.063159  0.063434  0.063723  
+9   0.070009  0.070645  0.062963  0.063359  0.063747  0.064134  0.064527  
+10  0.062631  0.062963  0.057231  0.057361  0.057502  0.057657  0.057831  
+11  0.062894  0.063359  0.057361  0.057613  0.057864  0.058121  0.058388  
+12  0.063159  0.063747  0.057502  0.057864  0.058216  0.058567  0.058921  
+13  0.063434  0.064134  0.057657  0.058121  0.058567  0.059004  0.059439  
+14  0.063723  0.064527  0.057831  0.058388  0.058921  0.059439  0.059949  
 
    
 
    
 
    
@@ -1100,10 +1125,10 @@ We can write our own code or simply use either the functionaly of numpy<
 
    
 
    
 
              0         1
-0  3.942604  1.984308
-1  1.984308  1.984182
-[[3.94260358 1.98430782]
- [1.98430782 1.98418221]]
+0  3.949162  1.987722
+1  1.987722  2.004480
+[[3.94916237 1.98772232]
+ [1.98772232 2.00447992]]
 
    
 
    
 
    
@@ -1130,8 +1155,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
 
    
 
    
 
    Centered covariance using own code
-[[3.94260358 1.98430782]
- [1.98430782 1.98418221]]
+[[3.94916237 1.98772232]
+ [1.98772232 2.00447992]]
 
    
 
    
 _images/chapter8_65_1.png
@@ -1191,16 +1216,16 @@ questions.
    
 
    
 
    
 
    Eigenvalues of Covariance matrix
-5.17615838052499
-0.7506274061293645
+5.189621963782685
+0.7640203256838339
 First eigenvector
-[0.84927263 0.52795454]
+[0.84835621 0.52942586]
 Second eigenvector
-[-0.52795454  0.84927263]
+[-0.52942586  0.84835621]
 
    
 
    
 
    Eigenvector of largest eigenvalue
-[0.84927263 0.52795454]
+[0.84835621 0.52942586]
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/chapter9.html b/doc/LectureNotes/_build/html/chapter9.html
index f8975bba7..06ab0b886 100644
--- a/doc/LectureNotes/_build/html/chapter9.html
+++ b/doc/LectureNotes/_build/html/chapter9.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/chapteroptimization.html b/doc/LectureNotes/_build/html/chapteroptimization.html
index 39ae43a02..4dca7d07f 100644
--- a/doc/LectureNotes/_build/html/chapteroptimization.html
+++ b/doc/LectureNotes/_build/html/chapteroptimization.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1022,11 +1047,11 @@ which equals
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19294/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31672/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection="3d")
 
    
 
    
-
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x127e425e0>
+
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x1183f2640>
 
    
 
    
 _images/chapteroptimization_61_2.png
@@ -1084,7 +1109,7 @@ which equals
    
 
    
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x16c9a8880>]
+
    [<matplotlib.lines.Line2D at 0x118c9b1c0>]
 
    
 
    
 _images/chapteroptimization_69_1.png
@@ -1341,11 +1366,11 @@ when \(||\nabla_\beta C(\beta_k) || \
 
    
 
    
 
    
-
    [0.31022577 4.45255977]
-[[3.8942133 ]
- [3.04191629]]
-[[3.8942133 ]
- [3.04191629]]
+
    [0.29633889 4.15119514]
+[[3.90793019]
+ [3.18761375]]
+[[3.90793019]
+ [3.18761375]]
 
    
 
    
 _images/chapteroptimization_123_1.png
@@ -1374,9 +1399,9 @@ when \(||\nabla_\beta C(\beta_k) || \
 
    
 
    
 
    
-
    [[4.13542726]
- [2.97804446]]
-[4.07929472] [2.96841776]
+
    [[3.96783837]
+ [3.23305112]]
+[3.95982273] [3.21682143]
 
    
 
    
 
    
@@ -1447,10 +1472,10 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
 
    
 
    
 
    
-
    [[3.9208878 ]
- [3.21055226]]
-[[3.84859258]
- [3.26931499]]
+
    [[3.91619855]
+ [3.20101684]]
+[[3.85813693]
+ [3.24679418]]
 
    
 
    
 _images/chapteroptimization_132_1.png
@@ -1700,15 +1725,15 @@ function.
    
 
    
 
    
 
    Own inversion
-[[3.87533278]
- [2.94854992]]
-Eigenvalues of Hessian Matrix:[0.31803769 4.15962297]
+[[3.70224083]
+ [3.16389131]]
+Eigenvalues of Hessian Matrix:[0.29022057 4.66510547]
 theta from own gd
-[[3.87533278]
- [2.94854992]]
+[[3.70224083]
+ [3.16389131]]
 theta from own sdg
-[[3.90803422]
- [2.93820524]]
+[[3.67541155]
+ [3.1532465 ]]
 
    
 
    
 _images/chapteroptimization_148_1.png
diff --git a/doc/LectureNotes/_build/html/clustering.html b/doc/LectureNotes/_build/html/clustering.html
index 0a8aeb607..d3392881a 100644
--- a/doc/LectureNotes/_build/html/clustering.html
+++ b/doc/LectureNotes/_build/html/clustering.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek34.html b/doc/LectureNotes/_build/html/exercisesweek34.html
index ba7f5313e..51bd0a4e7 100644
--- a/doc/LectureNotes/_build/html/exercisesweek34.html
+++ b/doc/LectureNotes/_build/html/exercisesweek34.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek35.html b/doc/LectureNotes/_build/html/exercisesweek35.html
index 55938c67f..ae0dcb919 100644
--- a/doc/LectureNotes/_build/html/exercisesweek35.html
+++ b/doc/LectureNotes/_build/html/exercisesweek35.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek36.html b/doc/LectureNotes/_build/html/exercisesweek36.html
index 69c65a108..14a1a71a1 100644
--- a/doc/LectureNotes/_build/html/exercisesweek36.html
+++ b/doc/LectureNotes/_build/html/exercisesweek36.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek37.html b/doc/LectureNotes/_build/html/exercisesweek37.html
index 875234ca6..cf05619c1 100644
--- a/doc/LectureNotes/_build/html/exercisesweek37.html
+++ b/doc/LectureNotes/_build/html/exercisesweek37.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek38.html b/doc/LectureNotes/_build/html/exercisesweek38.html
index abebba2b0..9786b5333 100644
--- a/doc/LectureNotes/_build/html/exercisesweek38.html
+++ b/doc/LectureNotes/_build/html/exercisesweek38.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek39.html b/doc/LectureNotes/_build/html/exercisesweek39.html
index 0d129dd19..c9e6c99bd 100644
--- a/doc/LectureNotes/_build/html/exercisesweek39.html
+++ b/doc/LectureNotes/_build/html/exercisesweek39.html
@@ -311,6 +311,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -323,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/exercisesweek41.html b/doc/LectureNotes/_build/html/exercisesweek41.html
index ce03ed498..d53e81fd9 100644
--- a/doc/LectureNotes/_build/html/exercisesweek41.html
+++ b/doc/LectureNotes/_build/html/exercisesweek41.html
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 41 Neural networks and constructing a neural network code
   
  
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -335,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -789,15 +804,15 @@ regression.
    
 
    
 
    
 
    Own inversion
-[[3.83505053]
- [3.09726322]]
-Eigenvalues of Hessian Matrix:[0.27717261 4.34154132]
+[[3.89481038]
+ [3.13155259]]
+Eigenvalues of Hessian Matrix:[0.28194659 4.81122914]
 theta from own gd
-[[3.83505053]
- [3.09726322]]
+[[3.89481038]
+ [3.13155259]]
 theta from own sdg
-[[3.77589027]
- [3.07286416]]
+[[3.88291866]
+ [3.19123037]]
 
    
 
    
 _images/exercisesweek41_5_1.png
@@ -919,14 +934,14 @@ first example shows results with ordinary leats squares.
    
 
    
 
    
 
    Own inversion
-[[3.81651921]
- [3.10399758]]
-Eigenvalues of Hessian Matrix:[0.30971881 4.52950417]
+[[4.23636536]
+ [2.77184871]]
+Eigenvalues of Hessian Matrix:[0.30125775 4.66878535]
 
    
 
    
 
    theta from own gd
-[[3.81651921]
- [3.10399758]]
+[[4.23636536]
+ [2.77184871]]
 
    
 
    
 _images/exercisesweek41_16_2.png
@@ -997,73 +1012,73 @@ Eigenvalues of Hessian Matrix:[0.30971881 4.52950417]
 
    Own inversion
 [[4.]
  [3.]]
-Eigenvalues of Hessian Matrix:[0.28641189 4.39287528]
-0 [-15.65565751] [-18.44347438]
-1 [-0.02618169] [0.02215597]
-2 [-0.02447466] [0.02071142]
-3 [-0.02287894] [0.01936105]
-4 [-0.02138725] [0.01809873]
-5 [-0.01999282] [0.01691871]
-6 [-0.0186893] [0.01581562]
-7 [-0.01747077] [0.01478446]
-8 [-0.01633169] [0.01382052]
-9 [-0.01526688] [0.01291943]
-10 [-0.01427149] [0.0120771]
-11 [-0.013341] [0.01128968]
-12 [-0.01247118] [0.0105536]
-13 [-0.01165807] [0.00986552]
-14 [-0.01089797] [0.00922229]
-15 [-0.01018743] [0.00862101]
-16 [-0.00952322] [0.00805892]
-17 [-0.00890232] [0.00753349]
-18 [-0.00832189] [0.00704231]
-19 [-0.00777931] [0.00658316]
-20 [-0.00727211] [0.00615394]
-21 [-0.00679797] [0.00575271]
-22 [-0.00635475] [0.00537764]
-23 [-0.00594042] [0.00502702]
-24 [-0.00555311] [0.00469926]
-25 [-0.00519105] [0.00439287]
-26 [-0.0048526] [0.00410646]
-27 [-0.00453622] [0.00383872]
-28 [-0.00424046] [0.00358844]
-29 [-0.00396398] [0.00335448]
+Eigenvalues of Hessian Matrix:[0.35058127 4.29679459]
+0 [-8.31895514] [-8.15055258]
+1 [-0.75472506] [0.63957747]
+2 [-0.69314603] [0.58739348]
+3 [-0.63659131] [0.53946725]
+4 [-0.58465096] [0.49545139]
+5 [-0.5369485] [0.45502684]
+6 [-0.49313815] [0.41790059]
+7 [-0.45290234] [0.38380352]
+8 [-0.41594943] [0.35248847]
+9 [-0.38201155] [0.32372846]
+10 [-0.35084272] [0.29731502]
+11 [-0.32221699] [0.27305669]
+12 [-0.29592687] [0.25077762]
+13 [-0.2717818] [0.23031634]
+14 [-0.24960675] [0.21152452]
+15 [-0.229241] [0.19426595]
+16 [-0.21053692] [0.17841553]
+17 [-0.19335893] [0.16385836]
+18 [-0.17758251] [0.15048894]
+19 [-0.16309331] [0.13821034]
+20 [-0.14978631] [0.12693357]
+21 [-0.13756504] [0.11657689]
+22 [-0.12634093] [0.10706523]
+23 [-0.1160326] [0.09832963]
+24 [-0.10656534] [0.09030678]
+25 [-0.09787053] [0.08293853]
+26 [-0.08988514] [0.07617146]
+27 [-0.08255129] [0.06995653]
+28 [-0.07581582] [0.06424868]
+29 [-0.06962991] [0.05900655]
 theta from own gd
-[[3.98706221]
- [3.01094846]]
-0 [-0.00370554] [0.00313577]
-1 [-0.00346394] [0.00293132]
-2 [-0.00316561] [0.00267887]
-3 [-0.00286972] [0.00242847]
-4 [-0.00259385] [0.00219502]
-5 [-0.00234197] [0.00198187]
-6 [-0.00211371] [0.00178871]
-7 [-0.00190742] [0.00161414]
-8 [-0.00172117] [0.00145652]
-9 [-0.00155308] [0.00131428]
-10 [-0.00140139] [0.00118591]
-11 [-0.00126452] [0.00107008]
-12 [-0.00114101] [0.00096557]
-13 [-0.00102956] [0.00087126]
-14 [-0.000929] [0.00078616]
-15 [-0.00083826] [0.00070937]
-16 [-0.00075639] [0.00064009]
-17 [-0.00068251] [0.00057757]
-18 [-0.00061585] [0.00052115]
-19 [-0.0005557] [0.00047025]
-20 [-0.00050142] [0.00042432]
-21 [-0.00045244] [0.00038288]
-22 [-0.00040825] [0.00034548]
-23 [-0.00036838] [0.00031174]
-24 [-0.0003324] [0.00028129]
-25 [-0.00029993] [0.00025381]
-26 [-0.00027064] [0.00022902]
-27 [-0.0002442] [0.00020665]
-28 [-0.00022035] [0.00018647]
-29 [-0.00019883] [0.00016826]
+[[3.81759234]
+ [3.15457792]]
+0 [-0.06394871] [0.05419212]
+1 [-0.05873105] [0.04977051]
+2 [-0.0523738] [0.04438319]
+3 [-0.04619338] [0.03914571]
+4 [-0.04057027] [0.03438051]
+5 [-0.03557316] [0.0301458]
+6 [-0.03117156] [0.02641575]
+7 [-0.02730775] [0.02314144]
+8 [-0.02392053] [0.020271]
+9 [-0.02095266] [0.01775594]
+10 [-0.01835274] [0.01555268]
+11 [-0.01607534] [0.01362274]
+12 [-0.01408051] [0.01193226]
+13 [-0.01233322] [0.01045155]
+14 [-0.01080274] [0.00915458]
+15 [-0.00946219] [0.00801855]
+16 [-0.00828799] [0.0070235]
+17 [-0.0072595] [0.00615193]
+18 [-0.00635865] [0.00538851]
+19 [-0.00556958] [0.00471983]
+20 [-0.00487843] [0.00413413]
+21 [-0.00427304] [0.00362111]
+22 [-0.00374279] [0.00317175]
+23 [-0.00327833] [0.00277816]
+24 [-0.00287151] [0.00243341]
+25 [-0.00251517] [0.00213144]
+26 [-0.00220306] [0.00186694]
+27 [-0.00192967] [0.00163526]
+28 [-0.00169021] [0.00143234]
+29 [-0.00148047] [0.00125459]
 theta from own gd wth momentum
-[[3.9993736 ]
- [3.00053008]]
+[[3.99630114]
+ [3.00313452]]
 
    
 
    
 
    
@@ -1116,17 +1131,17 @@ theta from own gd wth momentum
 
    
 
    
 
    Own inversion
-[[3.92351924]
- [3.025027  ]]
-Eigenvalues of Hessian Matrix:[0.33104875 3.95055425]
-0 [-11.75315452] [-11.48461009]
-1 [3.84783351e-15] [-1.7484672e-15]
-2 [-4.8897518e-16] [-4.48356153e-16]
-3 [4.61653285e-16] [3.79106945e-16]
-4 [-4.8897518e-16] [-4.48356153e-16]
+[[4.08185019]
+ [2.82781715]]
+Eigenvalues of Hessian Matrix:[0.32244056 3.90871918]
+0 [-14.19393543] [-14.29174301]
+1 [-6.35255737e-15] [-1.10851799e-14]
+2 [-5.89805982e-17] [-2.66490332e-16]
+3 [9.81853487e-16] [1.10741066e-15]
+4 [-5.89805982e-17] [-2.66490332e-16]
 beta from own Newton code
-[[3.92351924]
- [3.025027  ]]
+[[4.08185019]
+ [2.82781715]]
 
    
 
    
 
    
@@ -1215,20 +1230,20 @@ beta from own Newton code
 
    
 
    
 
    Own inversion
-[[4.08928088]
- [2.79578306]]
-Eigenvalues of Hessian Matrix:[0.31588332 4.45642521]
+[[3.41716708]
+ [3.50046106]]
+Eigenvalues of Hessian Matrix:[0.24252405 4.30774404]
 
    
 
    
 
    theta from own gd
-[[4.08928088]
- [2.79578306]]
+[[3.41716708]
+ [3.50046106]]
 
    
 
    
 _images/exercisesweek41_22_2.png
 
    theta from own sdg
-[[4.10188623]
- [2.87242312]]
+[[3.38135654]
+ [3.49216685]]
 
    
 
    
 
    
@@ -1310,15 +1325,15 @@ Eigenvalues of Hessian Matrix:[0.31588332 4.45642521]
 
    
 
    
 
    Own inversion
-[[3.84094234]
- [3.01300561]]
-Eigenvalues of Hessian Matrix:[0.26776828 4.97262227]
+[[4.12427537]
+ [2.85355539]]
+Eigenvalues of Hessian Matrix:[0.33486875 3.91080327]
 theta from own gd
-[[3.83774539]
- [3.01544605]]
+[[4.12417157]
+ [2.85365229]]
 theta from own sdg with momentum
-[[3.8186717 ]
- [3.06511966]]
+[[4.25050227]
+ [2.8249367 ]]
 
    
 
    
 
    
@@ -1393,9 +1408,9 @@ theta from own sdg with momentum
 
    
 
    
 
    theta from own AdaGrad
-[[2.00019432]
- [2.99888222]
- [4.00105497]]
+[[1.99999773]
+ [3.0000164 ]
+ [3.99998703]]
 
    
 
    
 
    
@@ -1477,9 +1492,9 @@ theta from own sdg with momentum
 
    
 
    
 
    theta from own RMSprop
-[[1.9996357 ]
- [3.00788598]
- [3.99589367]]
+[[2.01023308]
+ [2.95235306]
+ [4.04597076]]
 
    
 
    
 
    
@@ -1565,9 +1580,9 @@ theta from own sdg with momentum
 
    
 
    
 
    theta from own ADAM
-[[2.0001042 ]
- [2.99949077]
- [4.00048049]]
+[[1.99998193]
+ [3.0000747 ]
+ [3.99992263]]
 
    
 
    
 
    
@@ -1640,7 +1655,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
   return asarray(x, dtype=self.dtype)
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x1268ba940>]
+
    [<matplotlib.lines.Line2D at 0x10febc640>]
 
    
 
    
 _images/exercisesweek41_39_2.png
@@ -1679,7 +1694,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
   return asarray(x, dtype=self.dtype)
 
    
 
    
-
    <matplotlib.collections.PathCollection at 0x1162c32b0>
+
    <matplotlib.collections.PathCollection at 0x10febcf10>
 
    
 
    
 _images/exercisesweek41_41_2.png
diff --git a/doc/LectureNotes/_build/html/exercisesweek42.html b/doc/LectureNotes/_build/html/exercisesweek42.html
new file mode 100644
index 000000000..f8ba3c845
--- /dev/null
+++ b/doc/LectureNotes/_build/html/exercisesweek42.html
@@ -0,0 +1,567 @@
+
+
+
+
+  
+    
+    
+    Exercises week 42 — Applied Data Analysis and Machine Learning
+    
+  
+  
+
+    
+  
+  
+  
+
+    
+      
+
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
+
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+
+    
+    
+  
+  
+    
+    
+
+    
+
+    
    
+      
    
+          
+
+
+
+          
+
+
+          
+
    
+    
+    
    
+    
    
+        
    
+        
    
+            
+            
+            
+            
+
    
+    
+
+    
    
+        
+        
+        
+        
+        
+        
+    
    
+
    
+
+            
+
+            
+
+
+
+            
+
+        
    
+
+        
+        
    
+            
+            
    
+                 Contents
+            
    
+            
+        
    
+    
    
+
    
+    
    
+        
    
+            
+            
    
+                
    Exercises week 42
    
+                
+                
    
+                    
+                
    
+            
    
+            
+              
    
+                
+  
+
    
+
    Exercises week 42
    
+
    October 9-13, 2023
    
+
    Date: Deadline is Sunday October 22 at midnight
    
+
    You can hand in the exercises from week 41 and week 42 as one exercise and get a total score of two additional points.
    
+
    
+
    
+
    Overarching aims of the exercises this week
    
+
    The aim of the exercises this week is to get started with implementing
+gradient methods of relevance for project 2. The exercise this week is a simple
+continuation from the  previous week with the addition of automatic differentation.
+Everything you develop here will be used in project 2.
    
+
    In order to get started, we will now replace in our standard ordinary
+least squares (OLS) and Ridge regression codes (from project 1) the
+matrix inversion algorithm with our own gradient descent (GD) and SGD
+codes.  You can use the Franke function or the terrain data from
+project 1. However, we recommend using a simpler function like
+\(f(x)=a_0+a_1x+a_2x^2\) or higher-order one-dimensional polynomials.
+You can obviously test your final codes against for example the Franke
+function. Automatic differentiation will be discussed next week.
    
+
    You should include in your analysis of the GD and SGD codes the following elements
    
+
      
+
    1. A plain gradient descent with a fixed learning rate (you will need to tune it) using automatic differentiation. Compare this with the analytical expression of the gradients you obtained last week. Feel free to use Autograd as Python package or JAX. You can use the examples form last week.
      2. 
+
    2. Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate). Compare this with the analytical expression of the gradients you obtained last week.
      3. 
+
    3. Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from week 39. Discuss the results as functions of the various parameters (size of batches, number of epochs etc)
      4. 
+
    4. Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD using automatic differentiation..
      5. 
+
    5. Add RMSprop and Adam to your library of methods for tuning the learning rate. Again using automatic differentiation.
      6. 
+
    
+
    The lecture notes from weeks 39 and 40 contain more information and code examples. Feel free to use these examples.
    
+
    We recommend reading chapter 8 on optimization from the textbook of Goodfellow, Bengio and Courville. This chapter contains many useful insights and discussions on the optimization part of machine learning.
    
+
    
+
+    
+    
+
+              
    
+              
+            
+                
+
     
+    
+        
+        
    
+            
    previous
    
+            
    Week 41 Neural networks and constructing a neural network code
    
+        
    
+        
+    
+    
    
+        
    next
    
+        
    Week 42 Constructing a Neural Network code with introduction to Tensor flow
    
+    
    
+    
+        
+
    
+            
+        
    
+    
    
+    
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    
+
    
+
+
+      
    
+    
    
+  
+  
+
+  
+
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html
index 81a1b3fb1..78397021b 100644
--- a/doc/LectureNotes/_build/html/genindex.html
+++ b/doc/LectureNotes/_build/html/genindex.html
@@ -319,6 +319,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 41 Neural networks and constructing a neural network code
   
  
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -331,6 +341,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/intro.html b/doc/LectureNotes/_build/html/intro.html
index 286ca1691..54b20091b 100644
--- a/doc/LectureNotes/_build/html/intro.html
+++ b/doc/LectureNotes/_build/html/intro.html
@@ -320,6 +320,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 41 Neural networks and constructing a neural network code
   
  
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -332,6 +342,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/linalg.html b/doc/LectureNotes/_build/html/linalg.html
index 7d59c9b51..764e896f7 100644
--- a/doc/LectureNotes/_build/html/linalg.html
+++ b/doc/LectureNotes/_build/html/linalg.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -628,8 +653,8 @@ matrices and vectors.
    
 
    
 
    
 
    
-
    [ 0.31579721  1.74724767 -0.89609007  2.48464841 -0.36051635 -2.41246325
-  0.28008933  0.45134965 -0.52204004 -0.48145226]
+
    [-1.0526992  -0.18065292  0.78521833  0.80074264  0.59327016 -1.16492688
+  0.85276246 -0.04581197 -0.65825344 -0.87931006]
 
    
 
    
 
    
@@ -850,26 +875,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
 
    
 
    
 
    
-
    [[0.69873514 0.39457095 0.31927572 0.01704432 0.11837671 0.15047127
-  0.56465688 0.50274255 0.69818111 0.82296251]
- [0.45308692 0.37112277 0.77794957 0.43043913 0.95327702 0.89793609
-  0.29401213 0.08245909 0.1520039  0.59511582]
- [0.98004227 0.101058   0.57572321 0.61394448 0.963198   0.49616116
-  0.83488328 0.05432856 0.12814914 0.03856554]
- [0.283078   0.19166136 0.29275129 0.39300201 0.59004971 0.29199381
-  0.40644745 0.9036573  0.44729805 0.34447052]
- [0.57670824 0.6568551  0.84380376 0.86221134 0.28908491 0.25663096
-  0.62862896 0.1937079  0.15673992 0.44921888]
- [0.25139357 0.11197884 0.26514544 0.11896755 0.13404683 0.21059098
-  0.86012593 0.67890723 0.97948913 0.30567713]
- [0.51845286 0.76010633 0.71640333 0.75282841 0.47447472 0.78882958
-  0.84159521 0.3729492  0.80152684 0.04084872]
- [0.38088413 0.63567272 0.82909728 0.13829298 0.26037366 0.92772833
-  0.74577867 0.42239354 0.20594513 0.72328506]
- [0.38831624 0.44520102 0.17305512 0.0106014  0.94866246 0.84929103
-  0.81753152 0.06664867 0.96750421 0.50462474]
- [0.32584888 0.58948347 0.22729927 0.01919702 0.74280244 0.73448544
-  0.33995567 0.61197218 0.5320148  0.34517495]]
+
    [[0.80207897 0.22885848 0.14526269 0.91022359 0.76135601 0.52687741
+  0.68711054 0.01455922 0.70967214 0.47297104]
+ [0.87431418 0.15724663 0.06301519 0.41894238 0.47364408 0.06406913
+  0.31588043 0.87953769 0.74731872 0.10490195]
+ [0.87533326 0.71038664 0.29726695 0.34011629 0.51741855 0.32185967
+  0.58793527 0.0510594  0.81948868 0.5914397 ]
+ [0.96850702 0.53558374 0.40512793 0.83443463 0.96618584 0.54644868
+  0.1871257  0.28585116 0.79035184 0.2171263 ]
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+ [0.17829104 0.30129931 0.77203046 0.2707158  0.09391542 0.82988221
+  0.61480907 0.29282684 0.37667238 0.91086026]]
 
    
 
    
 
    
@@ -929,13 +954,13 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    0.1388976715362099
-4.3703468543933255
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- [ 3.28607817 10.56366546 16.19343949]]
-[25.58818643  0.05982961  3.17136288]
+
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+ [ 3.69519297 12.18993003 19.00431775]
+ [ 6.31082439 19.00431775 65.3283771 ]]
+[72.14421971  0.08339896  6.5092982 ]
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/objects.inv b/doc/LectureNotes/_build/html/objects.inv
index 7c8b3c1e8..cf4ce901e 100644
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index 0cb5bbb41..e736e8ce4 100644
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@@ -55,7 +55,8 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
-    
+    
+    
     
     
     
@@ -312,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -324,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -674,7 +700,7 @@ which polynomial fits the data best.
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19329/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31707/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection='3d')
 
    
 
    
@@ -1033,13 +1059,20 @@ of code developers and contributors keeps increasing.
    
             
                 
 
     
-    
+    
         
         
    
             
    previous
    
-            
    Week 40: Gradient descent methods (continued) and start Neural networks
    
+            
    Week 42 Constructing a Neural Network code with introduction to Tensor flow
    
         
    
         
+    
+    
    
+        
    next
    
+        
    Project 2 on Machine Learning, deadline November 13 (Midnight)
    
+    
    
+    
+        
 
    
             
         
    
diff --git a/doc/LectureNotes/_build/html/project2.html b/doc/LectureNotes/_build/html/project2.html
index 73c9a483a..5800974b8 100644
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+++ b/doc/LectureNotes/_build/html/project2.html
@@ -55,6 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
+    
     
     
     
@@ -321,18 +322,33 @@ const thebe_selector_output = ".output, .cell_output"
    Week 41 Neural networks and constructing a neural network code
   
  
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
   Projects
  
 
    
-
    
@@ -758,7 +774,14 @@ we encourage you to collaborate. Optimal working groups consist of
               
             
                 
-
    
+
     
+    
+        
+        
    
+            
    previous
    
+            
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
    
+        
    
+        
 
    
             
         
    
diff --git a/doc/LectureNotes/_build/html/schedule.html b/doc/LectureNotes/_build/html/schedule.html
index d7b226b7e..817725adb 100644
--- a/doc/LectureNotes/_build/html/schedule.html
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@@ -311,6 +311,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
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    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -323,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/search.html b/doc/LectureNotes/_build/html/search.html
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+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
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+ 
    • 
 
 
    
  
@@ -337,6 +347,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
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+ 
    • 
 
 
     
    
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No:[3,4,6,9,30,32,34,36],Not:[0,1,5,6,30,31,32,33,36,37],OR:27,Of:27,On:[0,3,15,26,27,28,29,30],One:[0,1,3,4,5,6,7,8,11,12,13,17,20,21,24,27,31,33,34,35,36,37],Or:[0,1,6,24,30,34],Such:[0,6,12,16,27,33,34,35,36,37],That:[0,5,7,10,11,12,14,19,24,27,30,32,33,34,37],The:[4,10,13,14,15,16,18,19,20,21,23,24,25,26,27,28,29],Their:37,Then:[0,1,6,8,9,10,11,12,13,14,23,24,30,31,33,34,35,36,37],There:[0,3,4,5,6,8,9,11,12,14,23,24,26,27,28,30,31,32,34,35,36,37],These:[0,2,3,4,5,8,9,10,11,12,13,14,15,16,23,24,25,27,28,30,31,32,35,36,37],To:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,21,23,24,25,27,32,33,34,35,36,37],With:[0,5,6,8,9,10,11,12,14,18,23,24,25,27,30,31,33,36,37],_0:[5,8,10,11,13,31,34,35],_1:[2,5,6,8,10,11,12,13,14,23,31,32,33,34,35,36,37],_2:[2,5,8,11,12,13,23,31,35,36,37],_3:23,_4:23,_9:[13,35,36],_:[0,1,2,4,5,6,7,8,9,10,11,12,13,17,18,19,21,23,24,30,31,32,33,34,35,36,37],_________________________________________________________________:4,__call__:[3,4],__class__:10,__doc__:[6,33],__future__:[8,9],__getattr__:32,__getitem__:2,__init__:[1,2,3,32,37],__main__:2,__name__:[2,10,32],__traceback__:[3,4],_auto10:[6,12,36,37],_auto11:[6,36],_auto12:[6,36],_auto1:[2,3,4,5,6,7,12,13,21,23,27,31,34,35,36,37],_auto2:[2,3,4,5,6,12,13,23,27,35,36,37],_auto3:[3,4,5,6,12,13,23,35,36,37],_auto4:[4,6,12,13,23,35,36,37],_auto5:[4,6,12,13,23,35,36,37],_auto6:[4,6,12,23,36,37],_auto7:[4,6,12,23,36,37],_auto8:[6,12,36,37],_auto9:[6,12,36,37],_base:8,_build:[0,17,19,22,24,29,30],_build_call_output:[3,4],_c:[1,37],_call:[3,4],_call_flat:[3,4],_check_optimize_result:[7,11,34],_compon:11,_decor:[0,30],_depth:9,_distn_infrastructur:34,_eagerdefinedfunct:[3,4],_fraction:9,_handl:[3,4],_i:[0,1,2,5,6,7,8,11,12,13,15,16,17,19,24,30,31,32,33,34,35,36,37],_inference_funct:[3,4],_interpolatefunctionerror:[3,4],_j:[0,1,2,3,5,6,8,13,17,19,24,31,32,33,35,37],_jit_compil:[3,4],_k:[13,34,35,36],_l:[12,36,37],_lambda:[6,30],_leaf:9,_lock:[3,4],_logist:[7,11,34],_m:10,_make_vjp:[2,13,36],_maybe_define_funct:[3,4],_multilayer_perceptron:37,_n:[2,5,8,11,13,31,34,35],_node:[2,9,13,36],_notokstatusexcept:[3,4],_num_output:[3,4],_p:[5,8,31],_process_traceback_fram:[3,4],_r:[3,4],_ratio:11,_sampl:9,_select_forward_and_backward_funct:[3,4],_split:[6,9,24],_src:21,_stateful_fn:[3,4],_stateless_fn:[3,4],_t:[13,21,35,36],_test:[6,24],_trace:[2,13,36],_unpad:2,_valu:[2,13,36],_varianc:11,_weight:9,a0:3,a0faa0:[9,10],a1:[0,30],a2:[0,30],a3:[0,30],a4:[0,30],a_0:[0,21,25,30],a_1a:[0,30],a_1x:[21,25],a_2a:[0,30],a_2x:[21,25],a_3:[0,30],a_3a:[0,30],a_4:[0,30],a_4a:[0,30],a_:[0,1,16,23,30,31,37],a_h:[1,37],a_i:[0,1,2,12,30,37],a_j:[1,12,37],a_k:[0,1,12,37],aaron:29,ab:[0,2,5,13,14,21,30,31,32,35,36],ab_channel:22,abandon:1,abbrevi:26,abid:27,abil:[0,10,30],abl:[0,1,4,5,6,7,10,12,13,16,24,31,34,35,36,37],about:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,22,23,24,25,28,32,33,34,35,36,37],abov:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,21,23,24,25,27,29,30,31,33,34,35,36,37],abovement:[6,33],abscissa:[13,34,35],absolut:[0,2,5,6,13,30,31,32,33,35,36],absorb:[31,32],acceler:[13,21,35,36],accept:[0,3,6,9,24,30,31],access:[0,3,11,27,31],accid:[4,6,33,34],accompani:[0,30,31],accomplish:[8,9,13,35,36],accord:[0,1,2,5,6,9,12,13,14,15,16,27,30,32,33,34,35,36,37],accordingli:11,account:[0,3,5,13,15,27,30,32,33,35,36],accumul:[12,13,21,27,35,36,37],accur:[0,3,4,6,10,13,33,35,36],accuraci:[0,1,3,4,5,6,7,9,10,11,12,25,30,31,34,36,37],accuracy_scor:[0,1,10,30,37],accuracy_score_numpi:[1,37],achiev:[0,1,5,6,8,12,23,30,32,33,36,37],aco:27,acquaint:[22,30],acquir:[1,22,30],acr:[0,31],across:[1,3,6,9,22,30,33,37],act:[1,3,23,37],action:27,activ:[0,2,3,4,9,26,28,30,33,34,35],actual:[0,1,4,5,6,8,11,16,23,27,30,31,32,33],ad:[1,3,4,5,8,13,15,16,23,32,33,34,35],ada_clf:10,adaboostclassifi:10,adadelta:[13,35,36],adagrad:25,adam:[1,3,4,25,28,30],adapt:[4,6,13,29,31,33,34],add:[0,1,2,3,4,5,6,8,10,11,12,15,16,17,21,24,25,27,30,31,32,33,35,37],add_outgrad:2,add_subplot:[1,7,12,14,34,36,37],addendum:5,addit:[0,2,3,5,6,7,8,9,10,12,13,15,17,21,22,23,24,27,28,29,30,31,32,33,34,35,36,37],addition:[12,13,34,35,36,37],address:[1,9,11,13,30,35,36],adjac:[3,12,36,37],adjoint:[5,31,32],adjust:[0,5,12,13,34,35,36],admir:[0,30],advanc:[4,6,12,29,30,33,36,37],advantag:[1,3,5,6,10,13,23,32,33,34,35,36,37],adversari:30,afecionado:30,affect:3,affin:[0,3,8,11,31],afford:3,aficionado:30,aforement:14,african:[0,31],after:[0,1,2,4,5,6,9,11,12,13,15,20,21,22,23,24,25,27,30,31,32,33,35,36,37],afterward:[0,30],ag:[0,7,26,30,31,34],ag_0:2,again:[0,1,4,5,6,7,8,10,11,12,13,15,16,21,24,25,27,30,31,32,33,35,36,37],against:[1,4,7,10,21,25,34,37],agegroup:[7,34],agegroupmean:[7,34],aggreg:[9,10],agorithm:10,agre:[5,6,27,32,33],agreement:[13,21,35,36],ahead:9,ai:[0,25,29],aid:[11,20],aim:[0,1,4,6,7,11,14,15,16,22,23,24,25,31,33,34],ainv:5,airplan:3,aka:[5,32,33],al:[0,2,4,15,16,17,25,29,30,31,32,33,34,35,36,37],alarm:[5,7,32,33],algebra:[0,3,5,13,21,22,31,32,33,35,36],algorithm:[0,1,2,4,5,6,7,8,13,14,22,23,24,27,29,30,32,33,34],align:[0,2,5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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","Applied Data Analysis and Machine Learning","2. 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4,35,36,37,38,39],alarm:[5,7,33,34],algebra:[0,3,5,13,21,23,32,33,34,36,37],algorithm:[0,1,2,4,5,6,7,8,13,14,22,23,24,25,28,30,31,33,34,35],align:[0,2,5,6,7,8,13,25,28,31,32,33,34,35,36],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],allevi:[1,13,35,36,39],alloc:[3,24],allow:[0,1,2,3,5,6,8,10,13,15,16,23,24,25,31,32,33,34,35,36,37,38,39],almost:[0,1,6,8,11,13,21,28,31,34,35,36,37,39],alon:[2,9],along:[2,3,4,5,6,9,10,11,23,24,31,32,33,34,35],alpha:[0,1,2,3,4,6,7,8,9,10,13,14,28,31,32,34,35,36,38,39],alpha_0:3,alpha_1:3,alpha_2:3,alpha_:10,alpha_i:[3,13,36],alpha_k:[13,36],alpha_m:10,alpha_n:3,alpha_opt:[13,36],alreadi:[2,3,4,5,6,10,12,23,24,28,31,32,33,34,37,38],also:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,23,24,25,26,27,28,31,32,33,34,35,36,37,38,39],alter:[1,38,39],altern:[0,1,4,5,6,7,8,9,11,13,24,25,31,32,33,34,35,36,37,38,39],although:[0,1,5,6,8,10,13,16,21,31,33,34,36,37,39],alwai:[0,3,5,6,12,13,16,21,28,31,32,33,34,35,36,37,38],am:[4,32],ame2016:[0,31],american:[0,32],among:[0,3,5,9,10,12,24,31,32,33,37,38],amongst:[5,33,34],amount:[0,1,3,4,6,8,10,14,23,34,39],an:[1,2,3,5,6,7,8,9,11,12,13,14,15,16,17,19,20,21,23,24,25,26,28,29,30,32,33,34,35,36,37,38,39],an_:28,anaconda:[0,1,15,23,25,31,39],analog:[13,36,37],analys:[6,33,34],analysi:[1,3,4,7,14,15,16,17,19,21,22,24,30,35,38,39],analyt:[2,3,5,6,7,12,13,15,22,23,25,26,31,32,33,34,35,36,37,38],analytical_gradi:21,analyz:[0,1,3,4,5,6,16,17,25,26,28,31,32,33,38,39],andrew:[1,38,39],angl:[0,3,9,32],anharmon:3,ani:[0,1,2,3,4,5,6,7,8,9,10,12,14,18,28,31,32,33,34,37,38,39],anim:[4,12,37,38],ann:[12,37,38],annot:[0,1,3,7,8,31,32,35,38,39],announc:31,anoth:[0,1,3,4,5,6,7,8,10,11,12,13,24,25,26,28,31,32,35,36,37,38,39],ans_vspac:[],ansatz:[0,31],answer:[0,1,3,5,6,24,25,26,29,31,33,34,38,39],antialias:[2,6,25],anticip:4,anymor:[1,8,39],anyon:[4,8],anyth:[1,28,39],anytim:[29,31],apach:[1,39],apart:[11,13,35,36],api:[1,23,31,39],appar:2,appear:[0,1,3,13,16,24,28,31,36,37,38,39],append:[1,3,4,8,9,13,21,31,36,39],appendix:25,appl:[3,4],appli:[0,1,2,3,4,6,7,8,9,10,11,12,13,15,16,25,26,28,30,31,32,33,34,35,36,37,38,39],applic:[0,1,3,4,5,6,7,9,12,13,21,24,25,28,30,31,32,34,35,36,37,38,39],apply_gradi:4,approach:[1,2,4,5,6,9,10,11,12,13,17,21,23,28,30,32,35,38,39],appropri:[2,6,9,12,13,23,28,34,36,37,38],approv:31,approx:[0,2,3,6,10,11,13,28,31,34,35,36,37],approxim:[0,1,2,3,4,5,6,7,10,11,13,18,19,25,28,31,32,33,34,35,36,37,39],apt:[0,15,23,25,31],aq:28,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],aragorn:31,arang:[1,3,4,6,7,9,10,12,13,25,31,35,36,37,38,39],arbitrari:[1,4,6,8,12,13,28,34,35,36,37,38,39],arbitrarili:[0,1,11,31,38,39],arc:[6,25],architectur:[3,4,12],archiv:26,area:[0,3,6,9,25,30,31],arg:[0,2,3,4,13,31,37],argmax:[1,11,38,39],argmin:[4,10,14],argnum:[2,13,37],argnum_0:[],argnum_1:[],args_with_tang:[3,4],argsort:11,argu:[1,13,36,37,39],argument:[0,2,3,5,6,11,12,13,21,25,31,32,33,34,38],argval:[],aris:[0,6,12,13,28,31,34,35,36,38],arithmet:[0,13,24,31,36,37],arm:[6,33],armadillo:24,around:[0,1,4,5,6,11,28,31,33,34,38,39],arr:[],arrai:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,21,23,25,28,32,33,34,35,36,37,38,39],arrang:[3,31],arraybox:[13,36,37],arriv:[0,6,9,11,24,28,31,34],arrow:[12,37,38],arrowprop:8,art3d:[13,36],art:[0,1,15,23,31,39],articl:[0,3,4,6,10,18,26,31,32,33,34],artifici:[0,2,7,12,30,31,35],artificialneuron:[12,37,38],arug:[13,36,37],arxiv:[3,4,21,26,36,37],as_fram:32,asap:31,asarrai:[0,2,6,9,21,32,33,36],ashort:20,asid:32,ask:[5,6,11,12,33,34,38],aspect:[0,6,23,25,31,32,33],assembl:[0,3,31],assert:4,assess:[0,6,25,31,32,33,34],assici:4,assign:[0,7,8,9,12,13,14,27,29,30,31,32,35,36,37,38,39],associ:[0,6,9,12,14,28,31,34,37,38],assum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,19,24,25,28,31,32,33,34,35,36,37,38,39],assumpt:[0,3,5,6,9,11,18,25,28,31,32],ast:[0,5,6,18,25,31,33,34,35],astronomi:[31,32,33,34,35,36,37,38,39],astyp:[4,9,10],asymmetri:[0,31],asymptot:[4,6,34],async_wait:[3,4],atla:31,atom:[0,31],attempt:[0,4,6,7,8,10,31,33,35],attend:27,attent:[0,24,31],attr:[3,4,33],attract:[0,10,31],attribut:[0,9,13,26,31,33,34],attributeerror:[13,33],audi:[0,31],audio:[3,4],august:[15,16,31],aurelien:[0,15,27,30,31,37,39],austfjel:[6,25],author:[0,1,10,28,31,39],authour:31,auto:[6,9,10,28],autocor:28,autocorrelation_tim:28,autocorrelform:28,autocovari:28,autoencod:[4,23,31],autoencond:23,autograd:[22,23,26,31],autom:[0,23,30,31],automac:24,automag:31,automat:[0,1,2,3,4,11,16,22,23,24,31,38,39],automobil:3,autonom:4,avail:[0,1,4,6,10,11,15,20,21,23,24,25,26,27,29,30,31,34,38,39],averag:[0,1,3,6,9,10,13,14,21,28,29,31,32,33,34,35,36,37,38,39],avoid:[0,4,5,6,9,11,13,21,24,31,32,34,35],awai:[2,3,6,32,33,34],awar:[2,10],award:[29,31],ax:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,24,25,26,31,32,34,35,36,37,38,39],axes3d:[2,6,13,25,35,36],axes_grid1:6,axessubplot:32,axhlin:8,axi:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,21,24,25,28,31,32,33,34,35,36,37,38,39],axiom:[5,33,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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","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 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,34,35,36],interv:34,introduc:[11,13,21,32,36,37],introduct:[0,6,23,24,25,26,31,37,38,39],invers:[5,24,33],invert:32,iter:[10,36],its:32,jacobian:32,jax:[13,21,36,37],job:[37,38],julia:31,jungl:10,k:[34,35],kera:[1,3,39],kernel:[8,11],l:38,lagrangian:8,lambda:35,lasso:[5,6,25,32,33,34,35],last:[32,34,35,37],later:[5,32],layer:[1,2,3,12,38,39],learn:[0,1,2,11,13,14,15,16,21,23,25,26,31,32,33,34,35,36,37,38,39],least:[5,6,18,25,31,32,33],lectur:[31,32,33,34,35,38,39],level:10,librari:[23,31],likelihood:[7,33,34,35],limit:[1,13,28,34,35,36,37,39],linear:[0,8,13,24,26,31,32,33,35],link:[5,11,27,30,32,33,34],literatur:[25,26],logist:[7,26,31,35,36,37,38,39],loop:[36,37],loss:[32,35,36],lu:24,machin:[0,8,13,23,25,26,31,35,36],made:[33,34],mai:31,main:28,make:[0,9,10,15,16,31,32],mani:[10,12,38],manipul:32,margin:[33,34],mass:31,materi:[27,31,32,33,34,35],math:[5,32],mathemat:[3,5,8,32,36,37,38],matric:[5,24,31,33],matrix:[1,5,11,12,24,31,32,33,35,36,37,38,39],matter:[0,31],max:32,maximum:[33,34,35],mean:[0,31,32,33,35],measur:35,meet:[5,10,28,31,32],mercer:8,method:[6,9,10,13,21,25,34,35,36,37],midnight:[25,26],min:32,mini:[36,37],minibatch:[21,36,37],minim:[31,35],ml:31,mle:[33,34],mlp:[12,38],mnist:[3,4],model:[0,1,4,6,12,31,37,38,39],moment:[36,37],momentum:[13,21,36,37],moon:[8,9],more:[3,6,21,24,25,31,32,33,34,35,36,37,39],multi:[37,38,39],multilay:[12,37,38],multipl:[1,3,38,39],multipli:8,need:[25,31],network:[1,2,3,4,7,12,26,31,35,37,38,39],neural:[1,2,3,4,7,12,26,31,37,38,39],neuron:[37,38],newton:[21,35,36,37],nice:39,noen:[21,36,37],non:8,normal:[0,1,34,39],notat:[12,37,38],note:[21,32,33,34],novemb:26,now:[1,9,13,21,33,34,36,37,39],nuclear:[0,31],nueral:35,numba:31,number:[0,2,21,28,32,36,37],numer:[2,25,26,28],numpi:[21,24,31,36,37],object:[3,38,39],obtain:11,octob:[25,38,39],od:2,off:[6,25],ol:[5,6,21,25,33,34,36,37],one:[2,12,35,36,38],ones:[37,38],oper:24,optim:[1,8,13,23,31,32,35,36,37,38,39],order:[13,21,36,37],ordinari:[5,6,18,25,31,32,33],organ:[0,31],orient:[38,39],oslo:30,other:[4,9,11,12,24,31,32,35,37,38],our:[0,4,5,11,13,31,32,35,36,38,39],outcom:[23,31],output:[2,39],overarch:[0,4,8,9,17,18,19,20,21,22,31,32],overview:[10,31,36,37],own:[0,10,11,15,16,26,31,32],packag:[24,31],panda:[31,32],paper:25,paramet:[31,32,35,36,37],part:[13,23,25,26,32,35,36],partial:2,pass:[1,38,39],pca:11,pdf:28,pencil:25,perceptron:[12,37,38,39],perform:[1,9,38,39],period:3,perspect:[1,39],plan:[32,33,34,35,36,37,38,39],plot:[34,35],point:4,poisson:2,polynomi:[3,33],popul:2,practic:[13,21,29,31,36,37],pre:[1,3,38,39],predict:4,predictor:35,preprocess:32,prerequisit:[3,23,31],princip:11,principl:3,pro:9,probabl:[5,28,33,34],problem:[1,2,13,21,31,32,33,35,36,37,38,39],procedur:[9,31],process:[1,3,38,39],product:[36,37],program:[2,13,25,26,35,36],project:[6,25,26,31,35],prop:[13,36,37],propag:[1,12,38,39],properti:[5,28,32,35],python:[0,9,15,23,24,31],quick:8,r:31,random:[10,11,28,35],raphson:[35,36],rate:[21,36,37],read:[9,31,32,34],real:[6,25,31],recommend:[31,32,36,37],rectangular:33,recurr:[4,12,37,38],recurs:[36,37],reduc:[0,32],reduct:3,reformul:2,regress:[0,5,6,7,9,10,13,17,18,25,26,31,32,33,34,35,36,37,38],regular:[1,35,38,39],relat:32,relev:[30,32,34,35,37,38],relu:[1,39],remark:3,remind:[6,8,31,35,36],repeat:32,replac:[13,36,37],report:[25,26],repositori:34,repres:[38,39],requir:[2,23],resampl:[6,25,33,34],rescal:[6,33],residu:32,resourc:2,result:[32,33],review:39,revisit:[13,35,36],rewrit:[31,32,34],rewritten:35,ridg:[0,5,6,17,18,25,32,33,34,35,36],rm:[13,36,37],rmsprop:[21,36,37],rule:[12,38],s:[8,10,21,34,35,36,37],same:[13,21,34,36,37],sampl:11,scale:[32,34],schedul:[27,31],schemat:9,scheme:2,scienc:31,scikit:[0,1,11,15,16,31,32,33,34,35,36,38,39],search:35,second:[13,21,36,37],select:35,semest:29,sensit:[35,36],septemb:[33,34,35],session:33,set:[0,2,3,9,12,15,31,32,35,38,39],sgd:[13,36,37],should:[1,39],sigmoid:39,similar:[13,21,36,37],simpl:[0,4,9,13,31,32,33,35,36,37],singl:[10,37,38],singular:[5,11,17,32],size:32,slightli:[36,37],soft:8,softmax:[1,38,39],softwar:[25,31],solv:[2,33,35,36],solver:13,some:[13,24,31,32,35,36],specifi:2,split:[0,15,16,31,32],squar:[0,5,6,10,18,25,31,32,33],standard:[13,32,34,36],start:[21,37],state:[0,31],statement:31,statist:[5,6,23,28,31,33,34],steepest:[10,13,35,36],step:[26,34,35,36,37],still:32,stochast:[13,21,26,28,36,37],stop:[36,37],strongli:31,studi:35,subtract:32,suggest:31,sum:34,summari:[29,31,37],superposit:3,supervis:[1,39],support:8,svd:[5,32,33],syntax:[36,37],systemat:3,t:[32,33],taken:21,teach:[27,29],teacher:[29,31],technic:33,techniqu:[6,11,25,33],technolog:23,tensor:39,tensorflow:[1,3,39],tent:31,term:[34,38],test:[0,1,15,16,26,31,32,33,38,39],textbook:[30,31],than:[35,36],thei:31,theorem:[5,8,11,12,28,33,34,38],theori:28,thi:[17,18,19,20,21,22,31],think:32,thursdai:[32,33,34,35,38,39],time:[36,37],tip:[13,21,36,37],togeth:[12,38],tool:31,top:[1,39],topic:31,toward:11,trade:[6,25],tradeoff:[6,34],train:[0,1,4,15,16,31,32,38,39],transform:3,tree:[9,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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/statistics.html b/doc/LectureNotes/_build/html/statistics.html
index 668a13d43..4534a0d41 100644
--- a/doc/LectureNotes/_build/html/statistics.html
+++ b/doc/LectureNotes/_build/html/statistics.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1000,27 +1025,27 @@ uncorrelated.
    
 
    
 
    
 
    
-
    2.226296567359957
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-   1.30630294  1.25561567  0.96804366  0.79787771]
- [15.76004012  3.00305172 13.98127617  9.04778116 10.53542722 10.34685874
-   6.08174081  5.84575663  4.50691065  3.71467081]
- [10.19888258  1.94338159  9.04778116  5.85514104  6.81784973  6.69582036
-   3.93571082  3.78299706  2.9165822   2.40389562]
- [11.875794    2.26291451 10.53542722  6.81784973  7.93884803  7.79675445
-   4.5828247   4.40500157  3.39612983  2.79914677]
- [11.66323494  2.22241171 10.34685874  6.69582036  7.79675445  7.65720414
-   4.50079895  4.32615859  3.33534416  2.7490462 ]
- [ 6.85548858  1.30630294  6.08174081  3.93571082  4.5828247   4.50079895
-   2.64550753  2.54285633  1.96046928  1.61585143]
- [ 6.58948138  1.25561567  5.84575663  3.78299706  4.40500157  4.32615859
-   2.54285633  2.44418822  1.884399    1.55315304]
- [ 5.08030109  0.96804366  4.50691065  2.9165822   3.39612983  3.33534416
-   1.96046928  1.884399    1.45281756  1.19743643]
- [ 4.18726877  0.79787771  3.71467081  2.40389562  2.79914677  2.7490462
-   1.61585143  1.55315304  1.19743643  0.98694705]]
+
    1.3329671101137754
+[[ 5.35146218  5.08271388  8.11911824  8.05880359  2.9797317   2.96911909
+   7.59642735  1.24785221  3.14389839  8.36403046]
+ [ 5.08271388  4.827462    7.71137935  7.65409368  2.83009076  2.82001111
+   7.21493779  1.18518557  2.98601306  7.94399217]
+ [ 8.11911824  7.71137935 12.31814386 12.22663583  4.52078202  4.5046808
+  11.52512898  1.89321335  4.76985203 12.68971917]
+ [ 8.05880359  7.65409368 12.22663583 12.13580759  4.4871984   4.4712168
+  11.43951204  1.8791492   4.73441814 12.59545081]
+ [ 2.9797317   2.83009076  4.52078202  4.4871984   1.65913552  1.65322635
+   4.22974406  0.69481287  1.75054469  4.65715086]
+ [ 2.96911909  2.82001111  4.5046808   4.4712168   1.65322635  1.64733822
+   4.21467941  0.69233822  1.74430995  4.64056395]
+ [ 7.59642735  7.21493779 11.52512898 11.43951204  4.22974406  4.21467941
+  10.78316665  1.77133246  4.4627795  11.8727831 ]
+ [ 1.24785221  1.18518557  1.89321335  1.8791492   0.69481287  0.69233822
+   1.77133246  0.29097377  0.7330932   1.9503219 ]
+ [ 3.14389839  2.98601306  4.76985203  4.73441814  1.75054469  1.74430995
+   4.4627795   0.7330932   1.84698999  4.91373404]
+ [ 8.36403046  7.94399217 12.68971917 12.59545081  4.65715086  4.64056395
+  11.8727831   1.9503219   4.91373404 13.07250301]]
 
    
 
    
 
    
@@ -1288,15 +1313,15 @@ more practically oriented methods like the blocking technique.
    
 
    
 
    
 
    
-
    -0.09327269724691106
-3.904648525660773
--0.17022089147584388
-0.9481513127527335 9.562888614232874 10.71437567912473
-2.845716766413386 2.3597516959642966 7.019140656913589
-[[ 0.94815131  2.84571677  2.3597517 ]
- [ 2.84571677  9.56288861  7.01914066]
- [ 2.3597517   7.01914066 10.71437568]]
-[17.97062694  0.08221578  3.17257288]
+
    -0.02582613386840159
+3.8311393813043355
+-0.30339081517583943
+1.1608179281668718 12.374777250972322 24.97606135399951
+3.6353716266230895 4.038211969489939 12.83140314044099
+[[ 1.16081793  3.63537163  4.03821197]
+ [ 3.63537163 12.37477725 12.83140314]
+ [ 4.03821197 12.83140314 24.97606135]]
+[33.84671508  0.08066381  4.58427764]
 
    
 
    
 
    
@@ -1626,7 +1651,7 @@ assumption for approximating \(\sigma
 
    
 
    
 
    
-
    -0.0071642501586093735 0.9871776311306221
+
    0.01229732982000352 0.93003138502386
 
    
 
    
 _images/statistics_188_1.png
diff --git a/doc/LectureNotes/_build/html/teachers.html b/doc/LectureNotes/_build/html/teachers.html
index 22da5cded..79d903759 100644
--- a/doc/LectureNotes/_build/html/teachers.html
+++ b/doc/LectureNotes/_build/html/teachers.html
@@ -311,6 +311,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -323,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/textbooks.html b/doc/LectureNotes/_build/html/textbooks.html
index 656476636..1baf3794e 100644
--- a/doc/LectureNotes/_build/html/textbooks.html
+++ b/doc/LectureNotes/_build/html/textbooks.html
@@ -311,6 +311,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -323,6 +343,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/week34.html b/doc/LectureNotes/_build/html/week34.html
index 93e1b4d9e..4f07987a3 100644
--- a/doc/LectureNotes/_build/html/week34.html
+++ b/doc/LectureNotes/_build/html/week34.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1790,8 +1815,8 @@ developed in the 1970s, namely EISPACK and LINPACK.  We describe them shortly he
 
    
 
    
 
    
-
    [ 0.5829913  -0.55086461  0.15975618 -0.92729959 -1.95190644  0.60383004
- -1.02308518 -1.48134747 -0.38259375 -1.42172457]
+
    [ 0.27919014 -0.36550376 -0.86282204  1.31714002 -1.99484719 -0.63837812
+  1.45062284 -0.33079132 -0.58182803 -0.7207467 ]
 
    
 
    
 
    
@@ -2016,26 +2041,26 @@ lowercase letters for vectors and uppercase letters for matrices)
    
 
    
 
    
 
    
-
    [[0.56364308 0.01989549 0.24569547 0.52482437 0.47701204 0.48629506
-  0.20695722 0.77646856 0.42578415 0.29153991]
- [0.6037092  0.87458904 0.84082439 0.87795661 0.53250091 0.08505008
-  0.17540272 0.59895188 0.7664107  0.06488406]
- [0.706833   0.71285447 0.27650338 0.43496417 0.69009002 0.76771975
-  0.74818082 0.94697839 0.73293298 0.04555073]
- [0.86015267 0.02183021 0.05852973 0.64299732 0.9129629  0.9142491
-  0.85615662 0.90223115 0.90325763 0.52518625]
- [0.32708194 0.14023656 0.86341536 0.45610021 0.22130126 0.67640036
-  0.76084455 0.08703034 0.86619181 0.37917253]
- [0.67189384 0.95117099 0.12695501 0.12155548 0.82410428 0.11352187
-  0.18433544 0.18824315 0.01344196 0.99215828]
- [0.83657122 0.48423285 0.81071342 0.64147722 0.09076319 0.38787447
-  0.62919818 0.22574374 0.78556129 0.17733642]
- [0.05966593 0.28096517 0.75719828 0.92717417 0.33860497 0.0401585
-  0.22328509 0.67035174 0.97488151 0.19463967]
- [0.00844667 0.65704027 0.50721349 0.75631027 0.50697511 0.96183456
-  0.28490569 0.09308274 0.65628888 0.30478013]
- [0.80802836 0.88305878 0.23392132 0.83793362 0.43490863 0.04448923
-  0.6289054  0.31705377 0.22001043 0.99268332]]
+
    [[0.23516186 0.40009482 0.40666305 0.26318493 0.37335014 0.7865355
+  0.11587186 0.81840893 0.38046294 0.17138811]
+ [0.70506522 0.56475572 0.02507163 0.57935482 0.33537181 0.32382849
+  0.37266855 0.00348543 0.11400145 0.84991754]
+ [0.27152452 0.88901776 0.95166414 0.82292185 0.09524714 0.92630576
+  0.29374695 0.55867377 0.10959669 0.71647328]
+ [0.15913825 0.89604286 0.80447153 0.59412285 0.30990916 0.94642209
+  0.20494446 0.7215423  0.03049638 0.55649207]
+ [0.70899024 0.80389541 0.60883945 0.7803213  0.43466245 0.33078483
+  0.86852099 0.19772911 0.93022647 0.45253585]
+ [0.5810785  0.94823368 0.73379189 0.09408163 0.14549142 0.8353591
+  0.46754435 0.29732036 0.7698352  0.39200159]
+ [0.77265782 0.37376184 0.43647835 0.38782352 0.97449977 0.02276062
+  0.36802977 0.43941514 0.99006712 0.98316168]
+ [0.89897156 0.04956816 0.52067151 0.52180619 0.21275991 0.86420934
+  0.50653545 0.49057373 0.77067609 0.16043757]
+ [0.22616902 0.70408916 0.43902948 0.68992377 0.5608253  0.84132082
+  0.95661705 0.7082333  0.33600213 0.44116407]
+ [0.96459246 0.32141575 0.95679388 0.44595818 0.1875353  0.47700752
+  0.03321947 0.55865092 0.96543101 0.63227278]]
 
    
 
    
 
    
@@ -2090,13 +2115,13 @@ covariance matrix through the np.linalg.eig() function.
    
 
    
 
    
 
    
-
    0.042044382097756156
-4.034169230664804
-0.4600624385659884
-[[ 1.22368396  3.61504341  4.56171141]
- [ 3.61504341 11.96611032 13.21879159]
- [ 4.56171141 13.21879159 31.04223754]]
-[38.67554897  0.10440776  5.45207509]
+
    -0.022210866177877393
+3.7588118737641243
+0.5615739502773949
+[[ 1.30150056  3.81953844  7.0377961 ]
+ [ 3.81953844 12.2361161  19.72546953]
+ [ 7.0377961  19.72546953 73.31248389]]
+[79.90960269  0.08394792  6.85654993]
 
    
 
    
 
    
@@ -2319,7 +2344,7 @@ Name: Aragorn, dtype: object
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19344/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31718/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
   data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/week35.html b/doc/LectureNotes/_build/html/week35.html
index cffd2608b..3dcc25cbf 100644
--- a/doc/LectureNotes/_build/html/week35.html
+++ b/doc/LectureNotes/_build/html/week35.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1671,7 +1696,7 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    0.9963311287748658
+
    0.995840825550726
 
    
 
    
 
    
@@ -1688,7 +1713,7 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    0.007891914573161948
+
    0.007607459165915922
 
    
 
    
 
    
@@ -1703,23 +1728,23 @@ Since we are not using Scikit-Learn here we can define our own
 
    
 
    
 
    
-
    [0.00712321 0.05126901 0.00172452 0.00104613 0.01477821 0.06642248
- 0.04547353 0.0207306  0.01552289 0.01492    0.0200568  0.01097423
- 0.02400359 0.04111096 0.02126208 0.00799998 0.00976647 0.0447389
- 0.0006527  0.02468681 0.03543039 0.00627535 0.04259402 0.02635835
- 0.04362755 0.00478655 0.01989299 0.01508632 0.04372783 0.00324969
- 0.01508966 0.08185315 0.01214101 0.01130932 0.00186362 0.02809859
- 0.00480371 0.08481871 0.01881546 0.04314342 0.11022363 0.01288591
- 0.03370315 0.00858536 0.00202679 0.00229911 0.00446979 0.0496375
- 0.00426531 0.02593026 0.03063575 0.03119091 0.05459089 0.01916913
- 0.00183869 0.00015239 0.01347636 0.01267006 0.02702978 0.02944425
- 0.01424197 0.00354492 0.06026294 0.00148709 0.02061026 0.03616508
- 0.03543958 0.02079171 0.00595615 0.01765474 0.01268892 0.00225484
- 0.01135167 0.03894328 0.04426647 0.03717939 0.01502518 0.03195835
- 0.00474485 0.06331463 0.01671556 0.01762067 0.00219624 0.07358383
- 0.01038358 0.0002364  0.04669463 0.00048325 0.00012934 0.01529503
- 0.0093869  0.00952586 0.0154222  0.01463052 0.0296969  0.01372375
- 0.02536494 0.00472549 0.04225015 0.04690007]
+
    [0.00552246 0.00115669 0.02017377 0.01896127 0.01389847 0.01591021
+ 0.02816083 0.0100949  0.02757522 0.00182747 0.00584432 0.02081274
+ 0.01365363 0.0191717  0.01068907 0.02763182 0.02950229 0.02485679
+ 0.01456159 0.00644939 0.0297291  0.08272096 0.01335857 0.00825399
+ 0.04478101 0.05834444 0.04198166 0.034985   0.00562524 0.01524072
+ 0.01529708 0.02083512 0.01161357 0.01708691 0.02279888 0.02912421
+ 0.00076617 0.02329285 0.00626773 0.01054509 0.00460405 0.01476097
+ 0.0036718  0.00569405 0.07804489 0.03894873 0.02103178 0.00726135
+ 0.00353575 0.00857028 0.00923278 0.01616709 0.02881357 0.00550379
+ 0.02942218 0.00946636 0.03982972 0.0149713  0.04103307 0.05526765
+ 0.00463639 0.00254359 0.00915433 0.02588522 0.00090992 0.00739382
+ 0.02075115 0.024632   0.00115506 0.01963203 0.00086063 0.01580414
+ 0.01059601 0.03376827 0.02745507 0.02109939 0.05977068 0.04662395
+ 0.00283853 0.03903968 0.0001225  0.02385515 0.02089297 0.04214702
+ 0.01289962 0.00798188 0.04746791 0.04822955 0.02066371 0.01045774
+ 0.01164198 0.03633213 0.00183398 0.0105301  0.00880924 0.015244
+ 0.01596986 0.01176096 0.01448147 0.00610607]
 
    
 
    
 
    
@@ -1788,15 +1813,15 @@ but now splitting the data into a training set and a test set.
    
 
    
 
    
 
    
-
    [ 1.95558642  0.77265448  2.8784267   1.83384573 -0.41219619]
+
    [ 2.04899609 -0.34193915  5.64527549 -0.69997503  0.31290684]
 Training R2
-0.9969332511584248
+0.9952222065466447
 Training MSE
-0.006829400694106674
+0.008897354602673473
 Test R2
-0.9950597269547777
+0.9915165982451293
 Test MSE
-0.011917343246903285
+0.009442796383765939
 
    
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/week36.html b/doc/LectureNotes/_build/html/week36.html
index a59e1bf7a..4ff957ced 100644
--- a/doc/LectureNotes/_build/html/week36.html
+++ b/doc/LectureNotes/_build/html/week36.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
diff --git a/doc/LectureNotes/_build/html/week37.html b/doc/LectureNotes/_build/html/week37.html
index 1fe998ab7..a322bccac 100644
--- a/doc/LectureNotes/_build/html/week37.html
+++ b/doc/LectureNotes/_build/html/week37.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1792,7 +1817,7 @@ theorem.
    
 
    
 
    Bootstrap Statistics :
 original           bias      std. error
- 99.8182  15.0632        99.8197        0.152701
+ 100.115  15.1213        100.117        0.151517
 
    
 
    
 
    
@@ -2027,14 +2052,14 @@ Error: 0.06844519414009445
 Bias^2: 0.06453579006728322
 Var: 0.003909404072811221
 0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444
-Polynomial degree: 5
+
    
+
    
+
    Polynomial degree: 5
 Error: 0.05227921801205679
 Bias^2: 0.04818727730430286
 Var: 0.004091940707753925
 0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679
-
    
-
    
-
    Polynomial degree: 6
+Polynomial degree: 6
 Error: 0.03781367141738902
 Bias^2: 0.03365768507152769
 Var: 0.0041559863458613296
@@ -2049,9 +2074,7 @@ Error: 0.017355848195593312
 Bias^2: 0.010331721306655165
 Var: 0.007024126888938144
 0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331
-
    
-
    
-
    Polynomial degree: 9
+Polynomial degree: 9
 Error: 0.026605727637184558
 Bias^2: 0.010018312644139219
 Var: 0.016587414993045335
@@ -2066,19 +2089,23 @@ Error: 0.07160048164232538
 Bias^2: 0.014436800088896381
 Var: 0.05716368155342902
 0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254
-Polynomial degree: 12
+
    
+
    
+
    Polynomial degree: 12
 Error: 0.11547777218876518
 Bias^2: 0.016285782696017142
 Var: 0.09919198949274803
 0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518
-Polynomial degree: 13
+
    
+
    
+
    Polynomial degree: 13
 Error: 0.2284246870217162
 Bias^2: 0.01975416527168255
 Var: 0.20867052175003364
 0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162
 
    
 
    
-_images/week37_162_3.png
+_images/week37_162_4.png
 
    
 
    
 
    
@@ -2531,9 +2558,9 @@ Mean squared error on training data: 0.00063862
 Mean squared error on test data: 3073.63180447
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(testerror), label='Test Error')
 
    
 
    
@@ -2618,7 +2645,7 @@ Mean squared error on test data: 3073.63180447
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
   plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
 
    
 
    
diff --git a/doc/LectureNotes/_build/html/week38.html b/doc/LectureNotes/_build/html/week38.html
index b784da4b8..234a63f80 100644
--- a/doc/LectureNotes/_build/html/week38.html
+++ b/doc/LectureNotes/_build/html/week38.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -2009,7 +2034,7 @@ case under study.
    
 
    
 
    
 
    RandomizedSearchCV(estimator=Ridge(), n_iter=100,
-                   param_distributions={'alpha': <scipy.stats._distn_infrastructure.rv_frozen object at 0x13ef4e1c0>})
+                   param_distributions={'alpha': <scipy.stats._distn_infrastructure.rv_frozen object at 0x156346610>})
 Best estimated lambda-value: 0.9849967686928113
 MSE score: 1.0853136633465326
 R2 score: -0.0002382102844775691
diff --git a/doc/LectureNotes/_build/html/week39.html b/doc/LectureNotes/_build/html/week39.html
index 553fbe981..bfba01344 100644
--- a/doc/LectureNotes/_build/html/week39.html
+++ b/doc/LectureNotes/_build/html/week39.html
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1773,11 +1798,11 @@ which equals
    
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19394/3838917029.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31749/3838917029.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection="3d")
 
    
 
    
-
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x127a38670>
+
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11ada9670>
 
    
 
    
 _images/week39_80_2.png
@@ -1835,7 +1860,7 @@ which equals
    
 
    
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x13eaa7490>]
+
    [<matplotlib.lines.Line2D at 0x11f5f6520>]
 
    
 
    
 _images/week39_88_1.png
diff --git a/doc/LectureNotes/_build/html/week40.html b/doc/LectureNotes/_build/html/week40.html
index 82188042e..f78b3b9ba 100644
--- a/doc/LectureNotes/_build/html/week40.html
+++ b/doc/LectureNotes/_build/html/week40.html
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
-    
+    
     
     
     
@@ -313,6 +313,26 @@ const thebe_selector_output = ".output, .cell_output"
    Week 40: Gradient descent methods (continued) and start Neural networks
   
  
+ 
  • 
+  
+   Exercises week 41
+  
+ 
    • 
+ 
  • 
+  
+   Week 41 Neural networks and constructing a neural network code
+  
+ 
    • 
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -325,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -1421,15 +1446,15 @@ function.
    
 
    
 
    
 
    Own inversion
-[[4.06481015]
- [2.84666445]]
-Eigenvalues of Hessian Matrix:[0.28638913 4.44842116]
+[[4.42484459]
+ [2.65626992]]
+Eigenvalues of Hessian Matrix:[0.30361418 4.06484621]
 theta from own gd
-[[4.06481015]
- [2.84666445]]
+[[4.42484459]
+ [2.65626992]]
 theta from own sdg
-[[4.02231445]
- [2.89996783]]
+[[4.53049637]
+ [2.68581655]]
 
    
 
    
 _images/week40_25_1.png
@@ -3407,10 +3432,10 @@ become the most popular for deep neural networks
    
             
    Week 39: Optimization and  Gradient Methods
    
         
    
     
-    
+    
     
    
         
    next
    
-        
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
    
+        
    Exercises week 41
    
     
    
     
         
diff --git a/doc/LectureNotes/_build/html/week41.html b/doc/LectureNotes/_build/html/week41.html
index 5ee70bd52..108ca6ee0 100644
--- a/doc/LectureNotes/_build/html/week41.html
+++ b/doc/LectureNotes/_build/html/week41.html
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
     
     
     
-    
+    
     
     
     
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
    Week 41 Neural networks and constructing a neural network code
   
  
+ 
  • 
+  
+   Exercises week 42
+  
+ 
    • 
+ 
  • 
+  
+   Week 42 Constructing a Neural Network code with introduction to Tensor flow
+  
+ 
    • 
 
 
    
  
@@ -335,6 +345,11 @@ const thebe_selector_output = ".output, .cell_output"
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
   
  
+ 
  • 
+  
+   Project 2 on Machine Learning, deadline November 13 (Midnight)
+  
+ 
    • 
 
 
     
    
@@ -2780,7 +2795,7 @@ the Hadamard product, meaning element-wise multiplication.
    
 
    Old accuracy on training data: 0.1440501043841336
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3116,7 +3131,7 @@ Lambda =  10.0
 Accuracy score on test set:  0.19166666666666668
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3125,7 +3140,7 @@ Lambda =  1e-05
 Accuracy score on test set:  0.10555555555555556
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3134,7 +3149,7 @@ Lambda =  0.0001
 Accuracy score on test set:  0.08611111111111111
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3143,7 +3158,7 @@ Lambda =  0.001
 Accuracy score on test set:  0.10555555555555556
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3152,7 +3167,7 @@ Lambda =  0.01
 Accuracy score on test set:  0.08888888888888889
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3161,7 +3176,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.08611111111111111
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3170,7 +3185,7 @@ Lambda =  1.0
 Accuracy score on test set:  0.08888888888888889
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3179,11 +3194,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.09166666666666666
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3192,11 +3207,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3205,11 +3220,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3218,11 +3233,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3231,11 +3246,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3244,7 +3259,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3253,11 +3268,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.10555555555555556
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3266,11 +3281,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3279,11 +3294,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3292,11 +3307,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3305,11 +3320,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3318,11 +3333,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3331,11 +3346,11 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3344,11 +3359,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.07777777777777778
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -3401,15 +3416,15 @@ Accuracy score on test set:  0.07777777777777778
 
    
 
    
 
    
-
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -3730,13 +3745,13 @@ Accuracy score on test set:  0.17777777777777778
 Learning rate  =  1.0
 Lambda =  0.1
 Accuracy score on test set:  0.08333333333333333
-
-Learning rate  =  1.0
-Lambda =  1.0
-Accuracy score on test set:  0.08888888888888889
 
    
 
    
 
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
+Learning rate  =  1.0
 Lambda =  10.0
 Accuracy score on test set:  0.09444444444444444
 
@@ -3756,9 +3771,8 @@ Accuracy score on test set:  0.10555555555555556
 Learning rate  =  10.0
 Lambda =  0.01
 Accuracy score on test set:  0.1388888888888889
-
    
-
    
-
    Learning rate  =  10.0
+
+Learning rate  =  10.0
 Lambda =  0.1
 Accuracy score on test set:  0.11388888888888889
 
    
@@ -4284,10 +4298,10 @@ Accuracy score on data set:  0.5
             
    Exercises week 41
    
         
    
     
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    next
    
-        
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
    
+        
    Exercises week 42
    
     
    
     
         
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+    Week 42 Constructing a Neural Network code with introduction to Tensor flow — Applied Data Analysis and Machine Learning
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    Week 42 Constructing a Neural Network code with introduction to Tensor flow
    
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     Contents 
    
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+
    Week 42 Constructing a Neural Network code with introduction to Tensor flow
    
+
    Morten Hjorth-Jensen, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University
    
+
    Date: October 16-20, 2023
    
+
    
+
    Plan for week 42
    
+
    Material for the active learning sessions on Tuesday and Wednesday.
    
+
      
+
    • Exercise on writing your own stochastic gradient and gradient descent codes. This exercise continues from the previous  week but now with inclusion of automatic differentiation
      • 
+
    • Discussion of project 2
      • 
+
    • See video on automatic differentiation from last year. This video will be updated before Tuesday.
      • 
+
    
+
    Material for the lecture on Thursday October 12, 2023.
    
+
+
    I also  recommend Michael Nielsen’s intuitive approach to the neural networks and the universal approximation theorem, see the slides at http://neuralnetworksanddeeplearning.com/chap4.html.
    
+
    
+
    
+
    Lecture Thursday October 19
    
+
    
+
    
+
    Review of the back propagation algorithm
    
+
    During the last lecture we discussed in detail the back propagation
+algorithm. This algorithm is based on a repeated application of the
+chain rule. Let us bring back the basic equation and at the same time
+link this with the basic mathematics of automatic differentiation.
    
+
    
+
    
+
    Setting up the Back propagation algorithm
    
+
    The four equations  derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.
    
+
    First, we set up the input data \(\boldsymbol{x}\) and the activations
+\(\boldsymbol{z}_1\) of the input layer and compute the activation function and
+the pertinent outputs \(\boldsymbol{a}^1\).
    
+
    Secondly, we perform then the feed forward till we reach the output
+layer and compute all \(\boldsymbol{z}_l\) of the input layer and compute the
+activation function and the pertinent outputs \(\boldsymbol{a}^l\) for
+\(l=2,3,\dots,L\).
    
+
    Thereafter we compute the ouput error \(\boldsymbol{\delta}^L\) by computing all
    
+
    
+\[
+\delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
+\]
    
+
    Then we compute the back propagate error for each \(l=L-1,L-2,\dots,2\) as
    
+
    
+\[
+\delta_j^l = \sum_k \delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l).
+\]
    
+
    Finally, we update the weights and the biases using gradient descent for each \(l=L-1,L-2,\dots,2\) and update the weights and biases according to the rules
    
+
    
+\[
+w_{jk}^l\leftarrow  = w_{jk}^l- \eta \delta_j^la_k^{l-1},
+\]
    
+
    
+\[
+b_j^l \leftarrow b_j^l-\eta \frac{\partial {\cal C}}{\partial b_j^l}=b_j^l-\eta \delta_j^l,
+\]
    
+
    The parameter \(\eta\) is the learning parameter discussed in connection with the gradient descent methods.
+Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training.
    
+
    
+
    
+
    Setting up a Multi-layer perceptron model for classification
    
+
    We are now gong to develop an example based on the MNIST data
+base. This is a classification problem and we need to use our
+cross-entropy function we discussed in connection with logistic
+regression. The cross-entropy defines our cost function for the
+classificaton problems with neural networks.
    
+
    In binary classification with two classes \((0, 1)\) we define the
+logistic/sigmoid function as the probability that a particular input
+is in class \(0\) or \(1\).  This is possible because the logistic
+function takes any input from the real numbers and inputs a number
+between 0 and 1, and can therefore be interpreted as a probability. It
+also has other nice properties, such as a derivative that is simple to
+calculate.
    
+
    For an input \(\boldsymbol{a}\) from the hidden layer, the probability that the input \(\boldsymbol{x}\)
+is in class 0 or 1 is just. We let \(\theta\) represent the unknown weights and biases to be adjusted by our equations). The variable \(x\)
+represents our activation values \(z\). We have
    
+
    
+\[
+P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} ,
+\]
    
+
    and
    
+
    
+\[
+P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) ,
+\]
    
+
    where \(y \in \{0, 1\}\)  and \(\boldsymbol{\theta}\) represents the weights and biases
+of our network.
    
+
    
+
    
+
    Defining the cost function
    
+
    Our cost function is given as (see the Logistic regression lectures)
    
+
    
+\[
+\mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n
+y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) .
+\]
    
+
    This last equality means that we can interpret our cost function as a sum over the loss function
+for each point in the dataset \(\mathcal{L}_i(\boldsymbol{\theta})\).
    
+The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
+than maximizing a negative number.
    
+
    In multiclass classification it is common to treat each integer label as a so called one-hot vector:
    
+
    \(y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,\) and
    
+
    \(y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,\)
    
+
    i.e. a binary bit string of length \(C\), where \(C = 10\) is the number of classes in the MNIST dataset (numbers from \(0\) to \(9\))..
    
+
    If \(\boldsymbol{x}_i\) is the \(i\)-th input (image), \(y_{ic}\) refers to the \(c\)-th component of the \(i\)-th
+output vector \(\boldsymbol{y}_i\).
    
+The probability of \(\boldsymbol{x}_i\) being in class \(c\) will be given by the softmax function:
    
+
    
+\[
+P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}}
+{\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} ,
+\]
    
+
    which reduces to the logistic function in the binary case.
    
+The likelihood of this \(C\)-class classifier
+is now given as:
    
+
    
+\[
+P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+\]
    
+
    Again we take the negative log-likelihood to define our cost function:
    
+
    
+\[
+\mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}.
+\]
    
+
    See the logistic regression lectures for a full definition of the cost function.
    
+
    The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!
    
+
    
+
    
+
    Example: binary classification problem
    
+
    As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters \(\beta\) as
    
+
    
+\[
+\mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right),
+\]
    
+
    where we had defined the logistic (sigmoid) function
    
+
    
+\[
+p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+\]
    
+
    and
    
+
    
+\[
+p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}).
+\]
    
+
    The parameters \(\boldsymbol{\beta}\) were defined using a minimization method like gradient descent or Newton-Raphson’s method.
    
+
    Now we replace \(x_i\) with the activation \(z_i^l\) for a given layer \(l\) and the outputs as \(y_i=a_i^l=f(z_i^l)\), with \(z_i^l\) now being a function of the weights \(w_{ij}^l\) and biases \(b_i^l\).
+We have then
    
+
    
+\[
+a_i^l = y_i = \frac{\exp{(z_i^l)}}{1+\exp{(z_i^l)}},
+\]
    
+
    with
    
+
    
+\[
+z_i^l = \sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,
+\]
    
+
    where the superscript \(l-1\) indicates that these are the outputs from layer \(l-1\).
+Our cost function at the final layer \(l=L\) is now
    
+
    
+\[
+\mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+\]
    
+
    where we have defined the targets \(t_i\). The derivatives of the cost function with respect to the output \(a_i^L\) are then easily calculated and we get
    
+
    
+\[
+\frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.
+\]
    
+
    In case we use another activation function than the logistic one, we need to evaluate other derivatives.
    
+
    
+
    
+
    The Softmax function
    
+
    In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation \(z_i^l\), that is we need
    
+
    
+\[
+\frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
+\frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
+\]
    
+
    For the Softmax function we have
    
+
    
+\[
+f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.
+\]
    
+
    Its derivative with respect to \(z_j^l\) gives
    
+
    
+\[
+\frac{\partial f(z_i^l)}{\partial z_j^l}= f(z_i^l)\left(\delta_{ij}-f(z_j^l)\right),
+\]
    
+
    which in case of the simply binary model reduces to  having \(i=j\).
    
+
    
+
    
+
    Developing a code for doing neural networks with back propagation
    
+
    One can identify a set of key steps when using neural networks to solve supervised learning problems:
    
+
      
+
    1. Collect and pre-process data
      2. 
+
    2. Define model and architecture
      3. 
+
    3. Choose cost function and optimizer
      4. 
+
    4. Train the model
      5. 
+
    5. Evaluate model performance on test data
      6. 
+
    6. Adjust hyperparameters (if necessary, network architecture)
      7. 
+
    
+
    
+
    
+
    Collect and pre-process data
    
+
    Here we will be using the MNIST dataset, which is readily available through the scikit-learn
+package. You may also find it for example here.
    
+The MNIST (Modified National Institute of Standards and Technology) database is a large database
+of handwritten digits that is commonly used for training various image processing systems.
    
+The MNIST dataset consists of 70 000 images of size \(28\times 28\) pixels, each labeled from 0 to 9.
    
+The scikit-learn dataset we will use consists of a selection of 1797 images of size \(8\times 8\) collected and processed from this database.
    
+
    To feed data into a feed-forward neural network we need to represent
+the inputs as a design/feature matrix \(X = (n_{inputs}, n_{features})\).  Each
+row represents an input, in this case a handwritten digit, and
+each column represents a feature, in this case a pixel.  The
+correct answers, also known as labels or targets are
+represented as a 1D array of integers
+\(Y = (n_{inputs}) = (5, 3, 1, 8,...)\).
    
+
    As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from
+measurements of height (in m)
    
+and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example:
    
+
    
+\[\begin{split} X = \begin{bmatrix}
+1.85 & 81\\
+1.71 & 65\\
+1.95 & 103\\
+1.55 & 42\\
+1.63 & 56
+\end{bmatrix} ,\end{split}\]
    
+
    and the targets would be:
    
+
    
+\[ Y = (23.7, 22.2, 27.1, 17.5, 21.1) \]
    
+
    Since each input image is a 2D matrix, we need to flatten the image
+(i.e. “unravel” the 2D matrix into a 1D array) to turn the data into a
+design/feature matrix. This means we lose all spatial information in the
+image, such as locality and translational invariance. More complicated
+architectures such as Convolutional Neural Networks can take advantage
+of such information, and are most commonly applied when analyzing
+images.
    
+
    
+
    
+
    %matplotlib inline
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# flatten the image
+# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
+n_inputs = len(inputs)
+inputs = inputs.reshape(n_inputs, -1)
+print("X = (n_inputs, n_features) = " + str(inputs.shape))
+
+
+# choose some random images to display
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
    
+
    
+
    
+
    
+
    inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)
+labels = (n_inputs) = (1797,)
+X = (n_inputs, n_features) = (1797, 64)
+
    
+
    
+_images/week42_51_1.png
+
    
+
    
+
    
+
    
+
    Train and test datasets
    
+
    Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.
    
+
    We will reserve \(80 \%\) of our dataset for training and \(20 \%\) for testing.
    
+
    It is important that the train and test datasets are drawn randomly from our dataset, to ensure
+no bias in the sampling.
    
+Say you are taking measurements of weather data to predict the weather in the coming 5 days.
+You don’t want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data
+collected from 12.00 to 24.00.
    
+
    
+
    
+
    from sklearn.model_selection import train_test_split
+
+# one-liner from scikit-learn library
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
+# equivalently in numpy
+def train_test_split_numpy(inputs, labels, train_size, test_size):
+    n_inputs = len(inputs)
+    inputs_shuffled = inputs.copy()
+    labels_shuffled = labels.copy()
+    
+    np.random.shuffle(inputs_shuffled)
+    np.random.shuffle(labels_shuffled)
+    
+    train_end = int(n_inputs*train_size)
+    X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]
+    Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]
+    
+    return X_train, X_test, Y_train, Y_test
+
+#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)
+
+print("Number of training images: " + str(len(X_train)))
+print("Number of test images: " + str(len(X_test)))
+
    
+
    
+
    
+
    
+
    Number of training images: 1437
+Number of test images: 360
+
    
+
    
+
    
+
    
+
    
+
    
+
    Define model and architecture
    
+
    Our simple feed-forward neural network will consist of an input layer, a single hidden layer and an output layer. The activation \(y\) of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have
    
+
    
+\[ z = \sum_{i=1}^n w_i a_i ,\]
    
+
    
+\[ y = f(z) ,\]
    
+
    where \(f\) is the activation function, \(a_i\) represents input from neuron \(i\) in the preceding layer
+and \(w_i\) is the weight to input \(i\).
    
+The activation of the neurons in the input layer is just the features (e.g. a pixel value).
    
+
    The simplest activation function for a neuron is the Heaviside function:
    
+
    
+\[\begin{split} f(z) = 
+\begin{cases}
+1,  &  z > 0\\
+0,  & \text{otherwise}
+\end{cases}
+\end{split}\]
    
+
    A feed-forward neural network with this activation is known as a perceptron.
    
+For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer.
    
+This activation can be generalized to \(k\) classes (using e.g. the one-against-all strategy),
+and we call these architectures multiclass perceptrons.
    
+
    However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and
    
+Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function.
    
+
    Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU).
    
+We will be using the sigmoid function \(\sigma(x)\):
    
+
    
+\[ f(x) = \sigma(x) = \frac{1}{1 + e^{-x}} ,\]
    
+
    which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.
    
+
    
+
    
+
    Layers
    
+
      
+
    • Input
      • 
+
    
+
    Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons.
    
+
      
+
    • Hidden layer
      • 
+
    
+
    We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer.
    
+Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer.
    
+
      
+
    • Output
      • 
+
    
+
    If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,
+which could output 0 or 1 according to the Heaviside function. This would be an example of a hard classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a soft classifier, which outputs the probability of being in class 0 or 1.
    
+
    For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class.
    
+
    Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons \(j = 0,1,...,9\). The activation of each output neuron \(j\) will be according to the softmax function:
    
+
    
+\[ P(\text{class $j$} \mid \text{input $\boldsymbol{a}$}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}}
+{\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,\]
    
+
    i.e. each neuron \(j\) outputs the probability of being in class \(j\) given an input from the hidden layer \(\boldsymbol{a}\), with \(\boldsymbol{w}_j\) the weights of neuron \(j\) to the inputs.
    
+The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.
    
+The exponent is just the weighted sum of inputs as before:
    
+
    
+\[ z_j = \sum_{i=1}^n w_ {ij} a_i+b_j.\]
    
+
    Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500
+weights to the output layer.
    
+
    
+
    
+
    Weights and biases
    
+
    Typically weights are initialized with small values distributed around zero, drawn from a uniform
+or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless.
    
+
    Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range
+of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron \(j\), \(b_j\):
    
+
    
+\[ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.\]
    
+
    The bias weights \(\boldsymbol{b}\) are often initialized to zero, but a small value like \(0.01\) ensures all neurons have some output which can be backpropagated in the first training cycle.
    
+
    
+
    
+
    # building our neural network
+
+n_inputs, n_features = X_train.shape
+n_hidden_neurons = 50
+n_categories = 10
+
+# we make the weights normally distributed using numpy.random.randn
+
+# weights and bias in the hidden layer
+hidden_weights = np.random.randn(n_features, n_hidden_neurons)
+hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+
+# weights and bias in the output layer
+output_weights = np.random.randn(n_hidden_neurons, n_categories)
+output_bias = np.zeros(n_categories) + 0.01
+
    
+
    
+
    
+
    
+
    
+
    
+
    Feed-forward pass
    
+
    Denote \(F\) the number of features, \(H\) the number of hidden neurons and \(C\) the number of categories.
    
+For each input image we calculate a weighted sum of input features (pixel values) to each neuron \(j\) in the hidden layer \(l\):
    
+
    
+\[ z_{j}^{l} = \sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},\]
    
+
    this is then passed through our activation function
    
+
    
+\[ a_{j}^{l} = f(z_{j}^{l}) .\]
    
+
    We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron \(j\) in the output layer:
    
+
    
+\[ z_{j}^{L} = \sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.\]
    
+
    Finally we calculate the output of neuron \(j\) in the output layer using the softmax function:
    
+
    
+\[ a_{j}^{L} = \frac{\exp{(z_j^{L})}}
+{\sum_{c=0}^{C-1} \exp{(z_c^{L})}} .\]
    
+
    
+
    
+
    Matrix multiplications
    
+
    Since our data has the dimensions \(X = (n_{inputs}, n_{features})\) and our weights to the hidden
+layer have the dimensions
    
+\(W_{hidden} = (n_{features}, n_{hidden})\),
+we can easily feed the network all our training data in one go by taking the matrix product
    
+
    
+\[ X W^{h} = (n_{inputs}, n_{hidden}),\]
    
+
    and obtain a matrix that holds the weighted sum of inputs to the hidden layer
+for each input image and each hidden neuron.
    
+We also add the bias to obtain a matrix of weighted sums to the hidden layer \(Z^{h}\):
    
+
    
+\[ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,\]
    
+
    meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.
    
+This is then passed through the activation:
    
+
    
+\[ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .\]
    
+
    This is fed to the output layer:
    
+
    
+\[ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .\]
    
+
    Finally we receive our output values for each image and each category by passing it through the softmax function:
    
+
    
+\[ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .\]
    
+
    
+
    
+
    # setup the feed-forward pass, subscript h = hidden layer
+
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
+
+def feed_forward(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    exp_term = np.exp(z_o)
+    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+    
+    return probabilities
+
+probabilities = feed_forward(X_train)
+print("probabilities = (n_inputs, n_categories) = " + str(probabilities.shape))
+print("probability that image 0 is in category 0,1,2,...,9 = \n" + str(probabilities[0]))
+print("probabilities sum up to: " + str(probabilities[0].sum()))
+print()
+
+# we obtain a prediction by taking the class with the highest likelihood
+def predict(X):
+    probabilities = feed_forward(X)
+    return np.argmax(probabilities, axis=1)
+
+predictions = predict(X_train)
+print("predictions = (n_inputs) = " + str(predictions.shape))
+print("prediction for image 0: " + str(predictions[0]))
+print("correct label for image 0: " + str(Y_train[0]))
+
    
+
    
+
    
+
    
+
    probabilities = (n_inputs, n_categories) = (1437, 10)
+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]
+probabilities sum up to: 1.0
+
+predictions = (n_inputs) = (1437,)
+prediction for image 0: 8
+correct label for image 0: 6
+
    
+
    
+
    
+
    
+
    
+
    
+
    Choose cost function and optimizer
    
+
    To measure how well our neural network is doing we need to introduce a cost function.
    
+We will call the function that gives the error of a single sample output the loss function, and the function
+that gives the total error of our network across all samples the cost function.
+A typical choice for multiclass classification is the cross-entropy loss, also known as the negative log likelihood.
    
+
    In multiclass classification it is common to treat each integer label as a so called one-hot vector:
    
+
    
+\[ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,\]
    
+
    
+\[ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,\]
    
+
    i.e. a binary bit string of length \(C\), where \(C = 10\) is the number of classes in the MNIST dataset.
    
+
    Let \(y_{ic}\) denote the \(c\)-th component of the \(i\)-th one-hot vector.
    
+We define the cost function \(\mathcal{C}\) as a sum over the cross-entropy loss for each point \(\boldsymbol{x}_i\) in the dataset.
    
+
    In the one-hot representation only one of the terms in the loss function is non-zero, namely the
+probability of the correct category \(c'\)
    
+(i.e. the category \(c'\) such that \(y_{ic'} = 1\)). This means that the cross entropy loss only punishes you for how wrong
+you got the correct label. The probability of category \(c\) is given by the softmax function. The vector \(\boldsymbol{\theta}\) represents the parameters of our network, i.e. all the weights and biases.
    
+
    
+
    
+
    Optimizing the cost function
    
+
    The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is gradient descent and its generalizations. The idea behind gradient descent
+is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a local minimum of the cost function.
    
+Each parameter \(\theta\) is iteratively adjusted according to the rule
    
+
    
+\[ \theta_{i+1} = \theta_i - \eta \nabla \mathcal{C}(\theta_i) ,\]
    
+
    where \(\eta\) is known as the learning rate, which controls how big a step we take towards the minimum.
    
+This update can be repeated for any number of iterations, or until we are satisfied with the result.
    
+
    A simple and effective improvement is a variant called Batch Gradient Descent.
    
+Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient
+on a subset of the data called a minibatch.
    
+If there are \(N\) data points and we have a minibatch size of \(M\), the total number of batches
+is \(N/M\).
    
+We denote each minibatch \(B_k\), with \(k = 1, 2,...,N/M\). The gradient then becomes:
    
+
    
+\[ \nabla \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \nabla \mathcal{L}_i(\theta) \quad \rightarrow \quad
+\frac{1}{M} \sum_{i \in B_k} \nabla \mathcal{L}_i(\theta) ,\]
    
+
    i.e. instead of averaging the loss over the entire dataset, we average over a minibatch.
    
+
    This has two important benefits:
    
+
      
+
    1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima.
      2. 
+
    2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient.
      3. 
+
    
+
    The various optmization  methods, with codes and algorithms,  are discussed in our lectures on Gradient descent approaches.
    
+
    
+
    
+
    Regularization
    
+
    It is common to add an extra term to the cost function, proportional
+to the size of the weights.  This is equivalent to constraining the
+size of the weights, so that they do not grow out of control.
+Constraining the size of the weights means that the weights cannot
+grow arbitrarily large to fit the training data, and in this way
+reduces overfitting.
    
+
    We will measure the size of the weights using the so called L2-norm, meaning our cost function becomes:
    
+
    
+\[  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
+\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 
+= \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,\]
    
+
    i.e. we sum up all the weights squared. The factor \(\lambda\) is known as a regularization parameter.
    
+
    In order to train the model, we need to calculate the derivative of
+the cost function with respect to every bias and weight in the
+network.  In total our network has \((64 + 1)\times 50=3250\) weights in
+the hidden layer and \((50 + 1)\times 10=510\) weights to the output
+layer (\(+1\) for the bias), and the gradient must be calculated for
+every parameter.  We use the backpropagation algorithm discussed
+above. This is a clever use of the chain rule that allows us to
+calculate the gradient efficently.
    
+
    
+
    
+
    Matrix  multiplication
    
+
    To more efficently train our network these equations are implemented using matrix operations.
    
+The error in the output layer is calculated simply as, with \(\boldsymbol{t}\) being our targets,
    
+
    
+\[ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .\]
    
+
    The gradient for the output weights is calculated as
    
+
    
+\[ \nabla W_{L} = \boldsymbol{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,\]
    
+
    where \(\boldsymbol{a} = (n_{inputs}, n_{hidden})\). This simply means that we are summing up the gradients for each input.
    
+Since we are going backwards we have to transpose the activation matrix.
    
+
    The gradient with respect to the output bias is then
    
+
    
+\[ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .\]
    
+
    The error in the hidden layer is
    
+
    
+\[ \Delta_h = \delta_L W_{L}^T \circ f'(z_{h}) = \delta_L W_{L}^T \circ a_{h} \circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,\]
    
+
    where \(f'(a_{h})\) is the derivative of the activation in the hidden layer. The matrix products mean
+that we are summing up the products for each neuron in the output layer. The symbol \(\circ\) denotes
+the Hadamard product, meaning element-wise multiplication.
    
+
    This again gives us the gradients in the hidden layer:
    
+
    
+\[ \nabla W_{h} = X^T \delta_h = (n_{features}, n_{hidden}) ,\]
    
+
    
+\[ \nabla b_{h} = \sum_{i=1}^{n_{inputs}} \delta_h = (n_{hidden}) .\]
    
+
    
+
    
+
    # to categorical turns our integer vector into a onehot representation
+from sklearn.metrics import accuracy_score
+
+# one-hot in numpy
+def to_categorical_numpy(integer_vector):
+    n_inputs = len(integer_vector)
+    n_categories = np.max(integer_vector) + 1
+    onehot_vector = np.zeros((n_inputs, n_categories))
+    onehot_vector[range(n_inputs), integer_vector] = 1
+    
+    return onehot_vector
+
+#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)
+Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)
+
+def feed_forward_train(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    exp_term = np.exp(z_o)
+    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+    
+    # for backpropagation need activations in hidden and output layers
+    return a_h, probabilities
+
+def backpropagation(X, Y):
+    a_h, probabilities = feed_forward_train(X)
+    
+    # error in the output layer
+    error_output = probabilities - Y
+    # error in the hidden layer
+    error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)
+    
+    # gradients for the output layer
+    output_weights_gradient = np.matmul(a_h.T, error_output)
+    output_bias_gradient = np.sum(error_output, axis=0)
+    
+    # gradient for the hidden layer
+    hidden_weights_gradient = np.matmul(X.T, error_hidden)
+    hidden_bias_gradient = np.sum(error_hidden, axis=0)
+
+    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient
+
+print("Old accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))
+
+eta = 0.01
+lmbd = 0.01
+for i in range(1000):
+    # calculate gradients
+    dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)
+    
+    # regularization term gradients
+    dWo += lmbd * output_weights
+    dWh += lmbd * hidden_weights
+    
+    # update weights and biases
+    output_weights -= eta * dWo
+    output_bias -= eta * dBo
+    hidden_weights -= eta * dWh
+    hidden_bias -= eta * dBh
+
+print("New accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))
+
    
+
    
+
    
+
    
+
    Old accuracy on training data: 0.1440501043841336
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    New accuracy on training data: 0.09951287404314545
+
    
+
    
+
    
+
    
+
    
+
    
+
    Improving performance
    
+
    As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.
    
+In order to obtain a network that does something useful, we will have to do a bit more work.
    
+
    The choice of hyperparameters such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a grid-search is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates \(\eta = 10^{-6}, 10^{-5},...,10^{-1}\) with different regularization parameters \(\lambda = 10^{-6},...,10^{-0}\).
    
+
    Next, we haven’t implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an iteration, and a full training period
+going through the entire dataset (\(n/M\) batches) an epoch.
    
+
    If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers.
    
+Andrew Ng goes through some of these considerations in this video. You can find a summary of the video here.
    
+
    
+
    
+
    Full object-oriented implementation
    
+
    It is very natural to think of the network as an object, with specific instances of the network
+being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below.
    
+
    
+
    
+
    class NeuralNetwork:
+    def __init__(
+            self,
+            X_data,
+            Y_data,
+            n_hidden_neurons=50,
+            n_categories=10,
+            epochs=10,
+            batch_size=100,
+            eta=0.1,
+            lmbd=0.0):
+
+        self.X_data_full = X_data
+        self.Y_data_full = Y_data
+
+        self.n_inputs = X_data.shape[0]
+        self.n_features = X_data.shape[1]
+        self.n_hidden_neurons = n_hidden_neurons
+        self.n_categories = n_categories
+
+        self.epochs = epochs
+        self.batch_size = batch_size
+        self.iterations = self.n_inputs // self.batch_size
+        self.eta = eta
+        self.lmbd = lmbd
+
+        self.create_biases_and_weights()
+
+    def create_biases_and_weights(self):
+        self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)
+        self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01
+
+        self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)
+        self.output_bias = np.zeros(self.n_categories) + 0.01
+
+    def feed_forward(self):
+        # feed-forward for training
+        self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias
+        self.a_h = sigmoid(self.z_h)
+
+        self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias
+
+        exp_term = np.exp(self.z_o)
+        self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
+    def feed_forward_out(self, X):
+        # feed-forward for output
+        z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias
+        a_h = sigmoid(z_h)
+
+        z_o = np.matmul(a_h, self.output_weights) + self.output_bias
+        
+        exp_term = np.exp(z_o)
+        probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+        return probabilities
+
+    def backpropagation(self):
+        error_output = self.probabilities - self.Y_data
+        error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)
+
+        self.output_weights_gradient = np.matmul(self.a_h.T, error_output)
+        self.output_bias_gradient = np.sum(error_output, axis=0)
+
+        self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)
+        self.hidden_bias_gradient = np.sum(error_hidden, axis=0)
+
+        if self.lmbd > 0.0:
+            self.output_weights_gradient += self.lmbd * self.output_weights
+            self.hidden_weights_gradient += self.lmbd * self.hidden_weights
+
+        self.output_weights -= self.eta * self.output_weights_gradient
+        self.output_bias -= self.eta * self.output_bias_gradient
+        self.hidden_weights -= self.eta * self.hidden_weights_gradient
+        self.hidden_bias -= self.eta * self.hidden_bias_gradient
+
+    def predict(self, X):
+        probabilities = self.feed_forward_out(X)
+        return np.argmax(probabilities, axis=1)
+
+    def predict_probabilities(self, X):
+        probabilities = self.feed_forward_out(X)
+        return probabilities
+
+    def train(self):
+        data_indices = np.arange(self.n_inputs)
+
+        for i in range(self.epochs):
+            for j in range(self.iterations):
+                # pick datapoints with replacement
+                chosen_datapoints = np.random.choice(
+                    data_indices, size=self.batch_size, replace=False
+                )
+
+                # minibatch training data
+                self.X_data = self.X_data_full[chosen_datapoints]
+                self.Y_data = self.Y_data_full[chosen_datapoints]
+
+                self.feed_forward()
+                self.backpropagation()
+
    
+
    
+
    
+
    
+
    
+
    
+
    Evaluate model performance on test data
    
+
    To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.
    
+We measure the performance of the network using the accuracy score.
    
+The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of \(1\).
    
+
    
+\[ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,\]
    
+
    where \(I\) is the indicator function, \(1\) if \(\tilde{y}_i = y_i\) and \(0\) otherwise.
    
+
    
+
    
+
    epochs = 100
+batch_size = 100
+
+dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,
+                    n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)
+dnn.train()
+test_predict = dnn.predict(X_test)
+
+# accuracy score from scikit library
+print("Accuracy score on test set: ", accuracy_score(Y_test, test_predict))
+
+# equivalent in numpy
+def accuracy_score_numpy(Y_test, Y_pred):
+    return np.sum(Y_test == Y_pred) / len(Y_test)
+
+#print("Accuracy score on test set: ", accuracy_score_numpy(Y_test, test_predict))
+
    
+
    
+
    
+
    
+
    Accuracy score on test set:  0.9444444444444444
+
    
+
    
+
    
+
    
+
    
+
    
+
    Adjust hyperparameters
    
+
    We now perform a grid search to find the optimal hyperparameters for the network.
    
+Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around \(98\%\) (\(2\%\) error rate).
    
+
    
+
    
+
    eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+# store the models for later use
+DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+
+# grid search
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,
+                            n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)
+        dnn.train()
+        
+        DNN_numpy[i][j] = dnn
+        
+        test_predict = dnn.predict(X_test)
+        
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on test set: ", accuracy_score(Y_test, test_predict))
+        print()
+
    
+
    
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  1e-05
+Accuracy score on test set:  0.11666666666666667
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.0001
+Accuracy score on test set:  0.20833333333333334
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.001
+Accuracy score on test set:  0.12222222222222222
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.01
+Accuracy score on test set:  0.14722222222222223
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.1
+Accuracy score on test set:  0.17777777777777778
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  1.0
+Accuracy score on test set:  0.16111111111111112
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  10.0
+Accuracy score on test set:  0.20277777777777778
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  1e-05
+Accuracy score on test set:  0.5305555555555556
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.0001
+Accuracy score on test set:  0.5944444444444444
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.001
+Accuracy score on test set:  0.5888888888888889
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.01
+Accuracy score on test set:  0.6111111111111112
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.1
+Accuracy score on test set:  0.5222222222222223
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  1.0
+Accuracy score on test set:  0.5555555555555556
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  10.0
+Accuracy score on test set:  0.8055555555555556
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1e-05
+Accuracy score on test set:  0.85
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.0001
+Accuracy score on test set:  0.85
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.001
+Accuracy score on test set:  0.875
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.01
+Accuracy score on test set:  0.8666666666666667
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.1
+Accuracy score on test set:  0.8638888888888889
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1.0
+Accuracy score on test set:  0.9555555555555556
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  10.0
+Accuracy score on test set:  0.925
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1e-05
+Accuracy score on test set:  0.9472222222222222
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.0001
+Accuracy score on test set:  0.9277777777777778
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.001
+Accuracy score on test set:  0.9472222222222222
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.01
+Accuracy score on test set:  0.9305555555555556
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.1
+Accuracy score on test set:  0.9555555555555556
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1.0
+Accuracy score on test set:  0.7694444444444445
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  10.0
+Accuracy score on test set:  0.19166666666666668
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  1e-05
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.0001
+Accuracy score on test set:  0.08611111111111111
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.01
+Accuracy score on test set:  0.08888888888888889
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.1
+Accuracy score on test set:  0.08611111111111111
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  10.0
+Accuracy score on test set:  0.09166666666666666
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  1e-05
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.0001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.01
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.1
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  10.0
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1e-05
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.001
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.01
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.1
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1.0
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+  exp_term = np.exp(self.z_o)
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  10.0
+Accuracy score on test set:  0.07777777777777778
+
    
+
    
+
    
+
    
+
    
+
    
+
    Visualization
    
+
    
+
    
+
    # visual representation of grid search
+# uses seaborn heatmap, you can also do this with matplotlib imshow
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_numpy[i][j]
+        
+        train_pred = dnn.predict(X_train) 
+        test_pred = dnn.predict(X_test)
+
+        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)
+        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    
+
    
+
    
+
    
+
    /var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp
+  return 1/(1 + np.exp(-x))
+
    
+
    
+_images/week42_74_1.png
+_images/week42_74_2.png
+
    
+
    
+
    
+
    
+
    scikit-learn implementation
    
+
    scikit-learn focuses more
+on traditional machine learning methods, such as regression,
+clustering, decision trees, etc. As such, it has only two types of
+neural networks: Multi Layer Perceptron outputting continuous values,
+MPLRegressor, and Multi Layer Perceptron outputting labels,
+MLPClassifier. We will see how simple it is to use these classes.
    
+
    scikit-learn implements a few improvements from our neural network,
+such as early stopping, a varying learning rate, different
+optimization methods, etc. We would therefore expect a better
+performance overall.
    
+
    
+
    
+
    from sklearn.neural_network import MLPClassifier
+# store models for later use
+DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
+                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
+        dnn.fit(X_train, Y_train)
+        
+        DNN_scikit[i][j] = dnn
+        
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on test set: ", dnn.score(X_test, Y_test))
+        print()
+
    
+
    
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  1e-05
+Accuracy score on test set:  0.18333333333333332
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.0001
+Accuracy score on test set:  0.18611111111111112
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.001
+Accuracy score on test set:  0.13055555555555556
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.01
+Accuracy score on test set:  0.24444444444444444
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  0.1
+Accuracy score on test set:  0.23333333333333334
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  1.0
+Accuracy score on test set:  0.12777777777777777
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  10.0
+Accuracy score on test set:  0.1527777777777778
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  1e-05
+Accuracy score on test set:  0.9111111111111111
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.0001
+Accuracy score on test set:  0.8888888888888888
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.001
+Accuracy score on test set:  0.8722222222222222
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.01
+Accuracy score on test set:  0.8305555555555556
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  0.1
+Accuracy score on test set:  0.8888888888888888
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  1.0
+Accuracy score on test set:  0.8805555555555555
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.0001
+Lambda =  10.0
+Accuracy score on test set:  0.8944444444444445
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1e-05
+Accuracy score on test set:  0.975
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.0001
+Accuracy score on test set:  0.9777777777777777
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.001
+Accuracy score on test set:  0.9805555555555555
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.01
+Accuracy score on test set:  0.9861111111111112
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  0.1
+Accuracy score on test set:  0.9805555555555555
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  1.0
+Accuracy score on test set:  0.9777777777777777
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.001
+Lambda =  10.0
+Accuracy score on test set:  0.9444444444444444
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1e-05
+Accuracy score on test set:  0.9861111111111112
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.0001
+Accuracy score on test set:  0.9888888888888889
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.001
+Accuracy score on test set:  0.9888888888888889
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.01
+Accuracy score on test set:  0.9861111111111112
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  0.1
+Accuracy score on test set:  0.9888888888888889
+
    
+
    
+
    Learning rate  =  0.01
+Lambda =  1.0
+Accuracy score on test set:  0.9722222222222222
+
+Learning rate  =  0.01
+Lambda =  10.0
+Accuracy score on test set:  0.9527777777777777
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  1e-05
+Accuracy score on test set:  0.9027777777777778
+
+Learning rate  =  0.1
+Lambda =  0.0001
+Accuracy score on test set:  0.8583333333333333
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.001
+Accuracy score on test set:  0.8722222222222222
+
+Learning rate  =  0.1
+Lambda =  0.01
+Accuracy score on test set:  0.9055555555555556
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  0.1
+Accuracy score on test set:  0.8805555555555555
+
+Learning rate  =  0.1
+Lambda =  1.0
+Accuracy score on test set:  0.8722222222222222
+
    
+
    
+
    Learning rate  =  0.1
+Lambda =  10.0
+Accuracy score on test set:  0.8666666666666667
+
+Learning rate  =  1.0
+Lambda =  1e-05
+Accuracy score on test set:  0.08611111111111111
+
+Learning rate  =  1.0
+Lambda =  0.0001
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
+Learning rate  =  1.0
+Lambda =  0.01
+Accuracy score on test set:  0.17777777777777778
+
+Learning rate  =  1.0
+Lambda =  0.1
+Accuracy score on test set:  0.08333333333333333
+
    
+
    
+
    Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on test set:  0.08888888888888889
+
+Learning rate  =  1.0
+Lambda =  10.0
+Accuracy score on test set:  0.09444444444444444
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1e-05
+Accuracy score on test set:  0.17222222222222222
+
+Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on test set:  0.11666666666666667
+
+Learning rate  =  10.0
+Lambda =  0.001
+Accuracy score on test set:  0.10555555555555556
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  0.01
+Accuracy score on test set:  0.1388888888888889
+
+Learning rate  =  10.0
+Lambda =  0.1
+Accuracy score on test set:  0.11388888888888889
+
    
+
    
+
    Learning rate  =  10.0
+Lambda =  1.0
+Accuracy score on test set:  0.10555555555555556
+
+Learning rate  =  10.0
+Lambda =  10.0
+Accuracy score on test set:  0.09444444444444444
+
    
+
    
+
    
+
    
+
    
+
    
+
    Visualization
    
+
    
+
    
+
    # optional
+# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_scikit[i][j]
+        
+        train_pred = dnn.predict(X_train) 
+        test_pred = dnn.predict(X_test)
+
+        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)
+        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    
+
    
+
    
+
    
+_images/week42_78_0.png
+_images/week42_78_1.png
+
    
+
    
+
    
+
    
+
    Testing our code for the XOR, OR and AND gates
    
+
    Last week we discussed three different types of gates, the so-called
+XOR, the OR and the AND gates.  Their inputs and outputs can be
+summarized using the following tables, first for the OR gate with
+inputs \(x_1\) and \(x_2\) and outputs \(y\):
    
+
+
+
+
+
+
+
+
+
+
+
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            1       
    
+
    
+
    The AND and XOR Gates
    
+
    The AND gate is defined as
    
+
+
+
+
+
+
+
+
+
+
+
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            0       
       1            0            0       
       1            1            1       
    
+
    And finally we have the XOR gate
    
+
+
+
+
+
+
+
+
+
+
+
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            0       
    
+
    
+
    Representing the Data Sets
    
+
    Our design matrix is defined by the input values \(x_1\) and \(x_2\). Since we have four possible outputs, our design matrix reads
    
+
    
+\[\begin{split}
+\boldsymbol{X}=\begin{bmatrix} 0 & 0 \\
+                       0 & 1 \\
+		       1 & 0 \\
+		       1 & 1 \end{bmatrix},
+\end{split}\]
    
+
    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.
    
+
    
+
    
+
    Setting up the Neural Network
    
+
    We define first our design matrix and the various output vectors for the different gates.
    
+
    
+
    
+
    """
+Simple code that tests XOR, OR and AND gates with linear regression
+"""
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
+
+def feed_forward(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    probabilities = sigmoid(z_o)
+    return probabilities
+
+# we obtain a prediction by taking the class with the highest likelihood
+def predict(X):
+    probabilities = feed_forward(X)
+    return np.argmax(probabilities, axis=1)
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
+
+# Defining the neural network
+n_inputs, n_features = X.shape
+n_hidden_neurons = 2
+n_categories = 2
+n_features = 2
+
+# we make the weights normally distributed using numpy.random.randn
+
+# weights and bias in the hidden layer
+hidden_weights = np.random.randn(n_features, n_hidden_neurons)
+hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+
+# weights and bias in the output layer
+output_weights = np.random.randn(n_hidden_neurons, n_categories)
+output_bias = np.zeros(n_categories) + 0.01
+
+probabilities = feed_forward(X)
+print(probabilities)
+
+
+predictions = predict(X)
+print(predictions)
+
    
+
    
+
    
+
    
+
    [[0.80625657 0.36420967]
+ [0.90297441 0.30170017]
+ [0.89823921 0.28566769]
+ [0.93420126 0.25920793]]
+[0 0 0 0]
+
    
+
    
+
    
+
    
+
    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.
    
+
    
+
    
+
    The Code using Scikit-Learn
    
+
    
+
    
+
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.neural_network import MLPClassifier
+from sklearn.metrics import accuracy_score
+import seaborn as sns
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
+
+# Defining the neural network
+n_inputs, n_features = X.shape
+n_hidden_neurons = 2
+n_categories = 2
+n_features = 2
+
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+# store models for later use
+DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+epochs = 100
+
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
+                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
+        dnn.fit(X, yXOR)
+        DNN_scikit[i][j] = dnn
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on data set: ", dnn.score(X, yXOR))
+        print()
+
+sns.set()
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_scikit[i][j]
+        test_pred = dnn.predict(X)
+        test_accuracy[i][j] = accuracy_score(yXOR, test_pred)
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    
+
    
+
    
+
    
+
    Learning rate  =  1e-05
+Lambda =  1e-05
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  0.0001
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  0.001
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  0.01
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  1e-05
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  1e-05
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  0.0001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  0.001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  0.01
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.0001
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  1e-05
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  0.0001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  0.001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  0.01
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.001
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.01
+Lambda =  1e-05
+Accuracy score on data set:  0.25
+
+Learning rate  =  0.01
+Lambda =  0.0001
+Accuracy score on data set:  0.75
+
+Learning rate  =  0.01
+Lambda =  0.001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.01
+Lambda =  0.01
+Accuracy score on data set:  0.75
+
+Learning rate  =  0.01
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.01
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.01
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.1
+Lambda =  1e-05
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.1
+Lambda =  0.0001
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.1
+Lambda =  0.001
+Accuracy score on data set:  1.0
+
+Learning rate  =  0.1
+Lambda =  0.01
+Accuracy score on data set:  1.0
+
+Learning rate  =  0.1
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.1
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  0.1
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  1.0
+Lambda =  1e-05
+Accuracy score on data set:  0.75
+
+Learning rate  =  1.0
+Lambda =  0.0001
+Accuracy score on data set:  0.75
+
+Learning rate  =  1.0
+Lambda =  0.001
+Accuracy score on data set:  0.75
+
+Learning rate  =  1.0
+Lambda =  0.01
+Accuracy score on data set:  0.5
+
+Learning rate  =  1.0
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  1.0
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  1.0
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  1e-05
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  0.0001
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  0.001
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  0.01
+Accuracy score on data set:  0.5
+
    
+
    
+
    Learning rate  = 
+
    
+
    
+
    /Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
+  warnings.warn(
+
    
+
    
+
     10.0
+Lambda =  0.1
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  1.0
+Accuracy score on data set:  0.5
+
+Learning rate  =  10.0
+Lambda =  10.0
+Accuracy score on data set:  0.5
+
    
+
    
+_images/week42_88_4.png
+
    
+
    
+
    
+
    
+
    Building neural networks in Tensorflow and Keras
    
+
    Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn
+and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
+and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
    
+
    In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
+clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
+NumPy arrays.
    
+
    
+
    
+
    Tensorflow
    
+
    Tensorflow is an open source library machine learning library
+developed by the Google Brain team for internal use. It was released
+under the Apache 2.0 open source license in November 9, 2015.
    
+
    Tensorflow is a computational framework that allows you to construct
+machine learning models at different levels of abstraction, from
+high-level, object-oriented APIs like Keras, down to the C++ kernels
+that Tensorflow is built upon. The higher levels of abstraction are
+simpler to use, but less flexible, and our choice of implementation
+should reflect the problems we are trying to solve.
    
+
    Tensorflow uses so-called graphs to represent your computation
+in terms of the dependencies between individual operations, such that you first build a Tensorflow graph
+to represent your model, and then create a Tensorflow session to run the graph.
    
+
    In this guide we will analyze the same data as we did in our NumPy and
+scikit-learn tutorial, gathered from the MNIST database of images. We
+will give an introduction to the lower level Python Application
+Program Interfaces (APIs), and see how we use them to build our graph.
+Then we will build (effectively) the same graph in Keras, to see just
+how simple solving a machine learning problem can be.
    
+
    To install tensorflow on Unix/Linux systems, use pip as
    
+
    
+
    
+
    pip3 install tensorflow
+
    
+
    
+
    
+
    
+
      Input In [14]
+    pip3 install tensorflow
+         ^
+SyntaxError: invalid syntax
+
    
+
    
+
    
+
    
+
    and/or if you use anaconda, just write (or install from the graphical user interface)
+(current release of CPU-only TensorFlow)
    
+
    
+
    
+
    conda create -n tf tensorflow
+conda activate tf
+
    
+
    
+
    
+
    
+
    To install the current release of GPU TensorFlow
    
+
    
+
    
+
    conda create -n tf-gpu tensorflow-gpu
+conda activate tf-gpu
+
    
+
    
+
    
+
    
+
    
+
    
+
    Using Keras
    
+
    Keras is a high level neural network
+that supports Tensorflow, CTNK and Theano as backends.
    
+If you have Anaconda installed you may run the following command
    
+
    
+
    
+
    conda install keras
+
    
+
    
+
    
+
    
+
    You can look up the instructions here for more information.
    
+
    We will to a large extent use keras in this course.
    
+
    
+
    
+
    Collect and pre-process data
    
+
    Let us look again at the MINST data set.
    
+
    
+
    
+
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+import tensorflow as tf
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# flatten the image
+# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
+n_inputs = len(inputs)
+inputs = inputs.reshape(n_inputs, -1)
+print("X = (n_inputs, n_features) = " + str(inputs.shape))
+
+
+# choose some random images to display
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
    
+
    
+
    
+
    
+
    
+
    
+
    from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+
+from sklearn.model_selection import train_test_split
+
+# one-hot representation of labels
+labels = to_categorical(labels)
+
+# split into train and test data
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
    
+
    
+
    
+
    
+
    
+
    
+
    epochs = 100
+batch_size = 100
+n_neurons_layer1 = 100
+n_neurons_layer2 = 50
+n_categories = 10
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
+    model = Sequential()
+    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_categories, activation='softmax'))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
+
    
+
    
+
    
+
    
+
    
+
    
+
    DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
+                                         eta=eta, lmbd=lmbd)
+        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = DNN.evaluate(X_test, Y_test)
+        
+        DNN_keras[i][j] = DNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
+
    
+
    
+
    
+
    
+
    
+
    
+
    # optional
+# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        DNN = DNN_keras[i][j]
+
+        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    
+
    
+
    
+
    
+
    
+
    
+
    The Breast Cancer Data, now with Keras
    
+
    
+
    
+
    import tensorflow as tf
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+from sklearn.model_selection import train_test_split as splitter
+from sklearn.datasets import load_breast_cancer
+import pickle
+import os 
+
+
+"""Load breast cancer dataset"""
+
+np.random.seed(0)        #create same seed for random number every time
+
+cancer=load_breast_cancer()      #Download breast cancer dataset
+
+inputs=cancer.data                     #Feature matrix of 569 rows (samples) and 30 columns (parameters)
+outputs=cancer.target                  #Label array of 569 rows (0 for benign and 1 for malignant)
+labels=cancer.feature_names[0:30]
+
+print('The content of the breast cancer dataset is:')      #Print information about the datasets
+print(labels)
+print('-------------------------')
+print("inputs =  " + str(inputs.shape))
+print("outputs =  " + str(outputs.shape))
+print("labels =  "+ str(labels.shape))
+
+x=inputs      #Reassign the Feature and Label matrices to other variables
+y=outputs
+
+#%% 
+
+# Visualisation of dataset (for correlation analysis)
+
+plt.figure()
+plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean perimeter',fontweight='bold')
+plt.show()
+
+plt.figure()
+plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)
+plt.xlabel('Mean compactness',fontweight='bold')
+plt.ylabel('Mean concavity',fontweight='bold')
+plt.show()
+
+
+plt.figure()
+plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean texture',fontweight='bold')
+plt.show()
+
+plt.figure()
+plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean perimeter',fontweight='bold')
+plt.ylabel('Mean compactness',fontweight='bold')
+plt.show()
+
+
+# Generate training and testing datasets
+
+#Select features relevant to classification (texture,perimeter,compactness and symmetery) 
+#and add to input matrix
+
+temp1=np.reshape(x[:,1],(len(x[:,1]),1))
+temp2=np.reshape(x[:,2],(len(x[:,2]),1))
+X=np.hstack((temp1,temp2))      
+temp=np.reshape(x[:,5],(len(x[:,5]),1))
+X=np.hstack((X,temp))       
+temp=np.reshape(x[:,8],(len(x[:,8]),1))
+X=np.hstack((X,temp))       
+
+X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1)   #Split datasets into training and testing
+
+y_train=to_categorical(y_train)     #Convert labels to categorical when using categorical cross entropy
+y_test=to_categorical(y_test)
+
+del temp1,temp2,temp
+
+# %%
+
+# Define tunable parameters"
+
+eta=np.logspace(-3,-1,3)                    #Define vector of learning rates (parameter to SGD optimiser)
+lamda=0.01                                  #Define hyperparameter
+n_layers=2                                  #Define number of hidden layers in the model
+n_neuron=np.logspace(0,3,4,dtype=int)       #Define number of neurons per layer
+epochs=100                                   #Number of reiterations over the input data
+batch_size=100                              #Number of samples per gradient update
+
+# %%
+
+"""Define function to return Deep Neural Network model"""
+
+def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
+    model=Sequential()      
+    for i in range(n_layers):       #Run loop to add hidden layers to the model
+        if (i==0):                  #First layer requires input dimensions
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))
+        else:                       #Subsequent layers are capable of automatic shape inferencing
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
+    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)
+    sgd=optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
+    return model
+
+    
+Train_accuracy=np.zeros((len(n_neuron),len(eta)))      #Define matrices to store accuracy scores as a function
+Test_accuracy=np.zeros((len(n_neuron),len(eta)))       #of learning rate and number of hidden neurons for 
+
+for i in range(len(n_neuron)):     #run loops over hidden neurons and learning rates to calculate 
+    for j in range(len(eta)):      #accuracy scores 
+        DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)
+        DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)
+        Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]
+        Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]
+               
+
+def plot_data(x,y,data,title=None):
+
+    # plot results
+    fontsize=16
+
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)
+    
+    cbar=fig.colorbar(cax)
+    cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)
+    cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])
+    cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])
+
+    # put text on matrix elements
+    for i, x_val in enumerate(np.arange(len(x))):
+        for j, y_val in enumerate(np.arange(len(y))):
+            c = "${0:.1f}\\%$".format( 100*data[j,i])  
+            ax.text(x_val, y_val, c, va='center', ha='center')
+
+    # convert axis vaues to to string labels
+    x=[str(i) for i in x]
+    y=[str(i) for i in y]
+
+
+    ax.set_xticklabels(['']+x)
+    ax.set_yticklabels(['']+y)
+
+    ax.set_xlabel('$\\mathrm{learning\\ rate}$',fontsize=fontsize)
+    ax.set_ylabel('$\\mathrm{hidden\\ neurons}$',fontsize=fontsize)
+    if title is not None:
+        ax.set_title(title)
+
+    plt.tight_layout()
+
+    plt.show()
+    
+plot_data(eta,n_neuron,Train_accuracy, 'training')
+plot_data(eta,n_neuron,Test_accuracy, 'testing')
+
    
+
    
+
    
+
    
+
    
+
    
+
    Fine-tuning neural network hyperparameters
    
+
    The flexibility of neural networks is also one of their main
+drawbacks: there are many hyperparameters to tweak. Not only can you
+use any imaginable network topology (how neurons/nodes are interconnected),
+but even in a simple FFNN you can change the number of layers, the
+number of neurons per layer, the type of activation function to use in
+each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you
+know what combination of hyperparameters is the best for your task?
    
+
      
+
    • You can use grid search with cross-validation to find the right hyperparameters.
      • 
+
    
+
    However,since there are many hyperparameters to tune, and since
+training a neural network on a large dataset takes a lot of time, you
+will only be able to explore a tiny part of the hyperparameter space.
    
+
      
+
    • You can use randomized search.
      • 
+
    • Or use tools like Oscar, which implements more complex algorithms to help you find a good set of hyperparameters quickly.
      • 
+
    
+
    
+
    
+
    Hidden layers
    
+
    For many problems you can start with just one or two hidden layers and it will work just fine.
+For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a
+few hundred neurons.
+You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of
+neurons, in roughly the same amount of training time.
    
+
    For more complex problems, you can gradually
+ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such
+as large image classification or speech recognition, typically require networks with dozens of layers
+and they need a huge amount
+of training data. However, you will rarely have to train such networks from scratch: it is much more
+common to reuse parts of a pretrained state-of-the-art network that performs a similar task.
    
+
    
+
    
+
    Which activation function should I use?
    
+
    The Back propagation algorithm we derived above works by going from
+the output layer to the input layer, propagating the error gradient on
+the way. Once the algorithm has computed the gradient of the cost
+function with regards to each parameter in the network, it uses these
+gradients to update each parameter with a Gradient Descent (GD) step.
    
+
    Unfortunately for us, the gradients often get smaller and smaller as the
+algorithm progresses down to the first hidden layers. As a result, the
+GD update leaves the lower layer connection weights
+virtually unchanged, and training never converges to a good
+solution. This is known in the literature as
+the vanishing gradients problem.
    
+
    In other cases, the opposite can happen, namely the the gradients can grow bigger and
+bigger. The result is that many of the layers get large updates of the
+weights the
+algorithm diverges. This is the exploding gradients problem, which is
+mostly encountered in recurrent neural networks. More generally, deep
+neural networks suffer from unstable gradients, different layers may
+learn at widely different speeds
    
+
    
+
    
+
    Is the Logistic activation function (Sigmoid)  our choice?
    
+
    Although this unfortunate behavior has been empirically observed for
+quite a while (it was one of the reasons why deep neural networks were
+mostly abandoned for a long time), it is only around 2010 that
+significant progress was made in understanding it.
    
+
    A paper titled Understanding the Difficulty of Training Deep
+Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio found that
+the problems with the popular logistic
+sigmoid activation function and the weight initialization technique
+that was most popular at the time, namely random initialization using
+a normal distribution with a mean of 0 and a standard deviation of
+1.
    
+
    They showed that with this activation function and this
+initialization scheme, the variance of the outputs of each layer is
+much greater than the variance of its inputs. Going forward in the
+network, the variance keeps increasing after each layer until the
+activation function saturates at the top layers. This is actually made
+worse by the fact that the logistic function has a mean of 0.5, not 0
+(the hyperbolic tangent function has a mean of 0 and behaves slightly
+better than the logistic function in deep networks).
    
+
    
+
    
+
    The derivative of the Logistic funtion
    
+
    Looking at the logistic activation function, when inputs become large
+(negative or positive), the function saturates at 0 or 1, with a
+derivative extremely close to 0. Thus when backpropagation kicks in,
+it has virtually no gradient to propagate back through the network,
+and what little gradient exists keeps getting diluted as
+backpropagation progresses down through the top layers, so there is
+really nothing left for the lower layers.
    
+
    In their paper, Glorot and Bengio propose a way to significantly
+alleviate this problem. We need the signal to flow properly in both
+directions: in the forward direction when making predictions, and in
+the reverse direction when backpropagating gradients. We don’t want
+the signal to die out, nor do we want it to explode and saturate. For
+the signal to flow properly, the authors argue that we need the
+variance of the outputs of each layer to be equal to the variance of
+its inputs, and we also need the gradients to have equal variance
+before and after flowing through a layer in the reverse direction.
    
+
    One of the insights in the 2010 paper by Glorot and Bengio was that
+the vanishing/exploding gradients problems were in part due to a poor
+choice of activation function. Until then most people had assumed that
+if Nature had chosen to use roughly sigmoid activation functions in
+biological neurons, they must be an excellent choice. But it turns out
+that other activation functions behave much better in deep neural
+networks, in particular the ReLU activation function, mostly because
+it does not saturate for positive values (and also because it is quite
+fast to compute).
    
+
    
+
    
+
    The RELU function family
    
+
    The ReLU activation function suffers from a problem known as the dying
+ReLUs: during training, some neurons effectively die, meaning they
+stop outputting anything other than 0.
    
+
    In some cases, you may find that half of your network’s neurons are
+dead, especially if you used a large learning rate. During training,
+if a neuron’s weights get updated such that the weighted sum of the
+neuron’s inputs is negative, it will start outputting 0. When this
+happen, the neuron is unlikely to come back to life since the gradient
+of the ReLU function is 0 when its input is negative.
    
+
    To solve this problem, nowadays practitioners use a  variant of the ReLU
+function, such as the leaky ReLU discussed above or the so-called
+exponential linear unit (ELU) function
    
+
    
+\[\begin{split}
+ELU(z) = \left\{\begin{array}{cc} \alpha\left( \exp{(z)}-1\right) & z < 0,\\  z & z \ge 0.\end{array}\right.
+\end{split}\]
    
+
    
+
    
+
    Which activation function should we use?
    
+
    In general it seems that the ELU activation function is better than
+the leaky ReLU function (and its variants), which is better than
+ReLU. ReLU performs better than \(\tanh\) which in turn performs better
+than the logistic function.
    
+
    If runtime
+performance is an issue, then you may opt for the  leaky ReLU function  over the
+ELU function If you don’t
+want to tweak yet another hyperparameter, you may just use the default
+\(\alpha\) of \(0.01\) for the leaky ReLU, and \(1\) for ELU. If you have
+spare time and computing power, you can use cross-validation or
+bootstrap to evaluate other activation functions.
    
+
    
+
    
+
    More on activation functions, output layers
    
+
    In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).
    
+
    It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.
    
+
    For the output layer:
    
+
      
+
    • For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).
      • 
+
    • For regression tasks, you can simply use no activation function at all.
      • 
+
    
+
    
+
    
+
    Batch Normalization
    
+
    Batch Normalization
+aims to address the vanishing/exploding gradients problems, and more generally the problem that the
+distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.
    
+
    The technique consists of adding an operation in the model just before the activation function of each
+layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new
+parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model
+learn the optimal scale and mean of the inputs for each layer.
+In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and
+standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current
+mini-batch, from this the name batch normalization.
    
+
    
+
    
+
    Dropout
    
+
    It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but
+excluding the output neurons) has a probability \(p\) of being temporarily dropped out, meaning it will be
+entirely ignored during this training step, but it may be active during the next step.
    
+
    The
+hyperparameter \(p\) is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.
+It is viewed as one of the most popular regularization techniques.
    
+
    
+
    
+
    Gradient Clipping
    
+
    A popular technique to lessen the exploding gradients problem is to simply clip the gradients during
+backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural
+networks).
    
+
    This technique is called Gradient Clipping.
    
+
    In general however, Batch
+Normalization is preferred.
    
+
    
+
    
+
    A very nice website on Neural Networks
    
+
    You may find this website very useful.
    
+
    
+
    
+
    A top-down perspective on Neural networks
    
+
    The first thing we would like to do is divide the data into two or three
+parts. A training set, a validation or dev (development) set, and a
+test set. The test set is the data on which we want to make
+predictions. The dev set is a subset of the training data we use to
+check how well we are doing out-of-sample, after training the model on
+the training dataset. We use the validation error as a proxy for the
+test error in order to make tweaks to our model. It is crucial that we
+do not use any of the test data to train the algorithm. This is a
+cardinal sin in ML. Then:
    
+
      
+
    • Estimate optimal error rate
      • 
+
    • Minimize underfitting (bias) on training data set.
      • 
+
    • Make sure you are not overfitting.
      • 
+
    
+
    If the validation and test sets are drawn from the same distributions,
+then a good performance on the validation set should lead to similarly
+good performance on the test set.
    
+
    However, sometimes
+the training data and test data differ in subtle ways because, for
+example, they are collected using slightly different methods, or
+because it is cheaper to collect data in one way versus another. In
+this case, there can be a mismatch between the training and test
+data. This can lead to the neural network overfitting these small
+differences between the test and training sets, and a poor performance
+on the test set despite having a good performance on the validation
+set. To rectify this, Andrew Ng suggests making two validation or dev
+sets, one constructed from the training data and one constructed from
+the test data. The difference between the performance of the algorithm
+on these two validation sets quantifies the train-test mismatch. This
+can serve as another important diagnostic when using DNNs for
+supervised learning.
    
+
    
+
    
+
    Limitations of supervised learning with deep networks
    
+
    Like all statistical methods, supervised learning using neural
+networks has important limitations. This is especially important when
+one seeks to apply these methods, especially to physics problems. Like
+all tools, DNNs are not a universal solution. Often, the same or
+better performance on a task can be achieved by using a few
+hand-engineered features (or even a collection of random
+features).
    
+
    Here we list some of the important limitations of supervised neural network based models.
    
+
      
+
    • Need labeled data. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).
      • 
+
    • Supervised neural networks are extremely data intensive. DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.
      • 
+
    • Homogeneous data. Almost all DNNs deal with homogeneous data of one type. It is very hard to design architectures that mix and match data types (i.e. some continuous variables, some discrete variables, some time series). In applications beyond images, video, and language, this is often what is required. In contrast, ensemble models like random forests or gradient-boosted trees have no difficulty handling mixed data types.
      • 
+
    • Many problems are not about prediction. In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a wrong model. The model might or might not be useful for understanding the underlying science.
      • 
+
    
+
    Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems.
    
+
    
+
    
+
+    
+    
+
+              
    
+              
+            
+                
+
     
+    
+        
+        
    
+            
    previous
    
+            
    Exercises week 42
    
+        
    
+        
+    
+    
    
+        
    next
    
+        
    Project 1 on Machine Learning, deadline October 9 (midnight), 2023
    
+    
    
+    
+        
+
    
+            
+        
    
+    
    
+    
    
+  
    
+    
+      By Morten Hjorth-Jensen
    
+    
+        © Copyright 2021.
    
+  
    
+
    
+
    
+
+
+      
    
+    
    
+  
+  
+
+  
+
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
index a355ce8bd..8b1257c93 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
@@ -343,7 +343,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -515,7 +515,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -583,18 +583,18 @@
      "output_type": "stream",
      "text": [
       "The intercept alpha: \n",
-      " [1.9480732]\n",
+      " [2.04828291]\n",
       "Coefficient beta : \n",
-      " [[4.96645032]]\n",
-      "Mean squared error: 0.20\n",
-      "Variance score: 0.91\n",
+      " [[4.85601654]]\n",
+      "Mean squared error: 0.27\n",
+      "Variance score: 0.89\n",
       "Mean squared log error: 0.01\n",
-      "Mean absolute error: 0.35\n"
+      "Mean absolute error: 0.40\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -822,7 +822,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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ITk4mJCTETSWUpqB/axFpFqrnoJTnlXhh101d9Xd1akERERHxZD6UV+II5aCIiIh4Oh/JK3GEWlBERETE4yhAEREREY+jAEVEREQ8jsMByurVqxk9ejRt2rTBYrHwySefVHl/woQJWCyWKo+BAwdW2aeoqIhJkyYRGxtLeHg4Y8aM4cCBA436IiIiIuI7HA5Q8vLy6NOnD88//3yt+1x00UUcPny44vH5559Xef/OO+9k4cKFzJ8/n6+//prc3FwuvfRSysrKavlEERERaU4cHsUzatQoRo0aVec+wcHBJCQk2HwvKyuL119/nbfffpvhw4cD8M4775CUlMSyZcu48MILHS2SiIiI+BiX5KCsXLmS1q1b07VrVyZOnMjRo0cr3tuwYQMlJSWMHDmyYlubNm1ISUnhm2++sfl5RUVFZGdnV3mIiIiI73J6gDJq1CjmzZvHV199xVNPPcW6des4//zzKSoqAiA9PZ2goCBatmxZ5bj4+HjS09NtfubMmTOJioqqeCQlJTm72CIiIuJBnB6gjBs3jksuuYSUlBRGjx7N4sWL2blzJ5999lmdxxmGgaWWlX8feOABsrKyKh779+93drE9QuUE48DAQOLj4xkxYgRvvPEGVqvV7s+ZO3cu0dHRriuoiIiIi7l8mHFiYiIdOnRg165dACQkJFBcXMzJkyer7Hf06FHi4+NtfkZwcDCRkZFVHr6qPMF4z549LF68mGHDhjF58mQuvfRSSktL3V08ERGRJuHyAOX48ePs37+fxMREAPr3709gYCBLly6t2Ofw4cNs3bqVQYN8e10Be5QnGLdt25Z+/frx4IMP8umnn7J48WLmzp0LwNNPP02vXr0IDw8nKSmJ2267jdzcXMDM/7npppvIysqqaI2ZPn06YCYjp6amEhERQUJCAtddd12V/CARERFP4XCAkpuby+bNm9m8eTMAaWlpbN68mX379pGbm8uUKVP49ttv2bNnDytXrmT06NHExsZy+eWXAxAVFcXNN9/M3XffzfLly9m0aRPXX389vXr1qhjV4zEy1sKKUbCwnfmcsdYtxTj//PPp06cPH3/8MQB+fn48++yzbN26lTfffJOvvvqKe++9F4BBgwbx73//m8jIyIph3lOmTAGguLiYRx99lB9//JFPPvmEtLQ0JkyY4JbvJCIiUheHhxmvX7+eYcOGVby+6667ABg/fjwvvfQSW7Zs4a233iIzM5PExESGDRvGggULiIiIqDjmX//6FwEBAVxzzTUUFBRwwQUXMHfuXPz9/Z3wlZyk+vLWhemQvsxcUTJucJMXp3v37vz000+AOY9MueTkZB599FH+8pe/8OKLLxIUFERUVBQWi6XGUO8//elPFT936tSJZ599lnPOOYfc3FxatGjRJN9DRETEHg4HKEOHDsUwjFrfX7JkSb2fERISwnPPPcdzzz3n6OmbztbHqAhOwHy2+Jvb3bCiZOUk4hUrVvDEE0+wbds2srOzKS0tpbCwkLy8PMLDw2v9jE2bNjF9+nQ2b97MiRMnKhJv9+3bR48ePZrke4iIiNhDa/HUJnPL6eCknFFmbneD7du3k5yczN69e7n44otJSUnho48+YsOGDbzwwgsAlJSU1Hp8Xl4eI0eOpEWLFrzzzjusW7eOhQsXAmbXj4iIiCdxuAWl2YjuZXbrVA5SLP7m9ib21VdfsWXLFv72t7+xfv16SktLeeqpp/DzM+PL999/v8r+QUFBNZYN2LFjB8eOHWPWrFkV88isX7++ab6AiIiIg9SCUpuUqYDFDErg1LMFUh526WmLiopIT0/n4MGDbNy4kSeeeILLLruMSy+9lBtvvJHOnTtTWlrKc889x+7du3n77bd5+eWXq3xGx44dyc3NZfny5Rw7doz8/Hzat29PUFBQxXGLFi3i0Ucfdel3ERERaSgFKLWJG2wmxCaMgNC25vPwVRDn2qHQX3zxBYmJiXTs2JGLLrqIFStW8Oyzz/Lpp5/i7+9P3759efrpp/nHP/5BSkoK8+bNY+bMmVU+Y9CgQdx6662MGzeOuLg4Zs+eTVxcHHPnzuWDDz6gR48ezJo1i3/+858u/S4iIiINZTHqynj1UNnZ2URFRZGVlVVj0rbCwkLS0tJITk4mJCTETSWUpqB/axER71JX/V2dWlBERETE4yhAEREREY+jAEVEREQ8jgIUERER8TgKUERERMTj+GyA4oWDk8RB+jcWEfFdPhegBAYGApCfn+/mkoirlf8bl/+bi4iI7/C5qe79/f2Jjo7m6NGjAISFhVUssie+wTAM8vPzOXr0KNHR0Z61CraIiDiFzwUoAAkJCQAVQYr4pujo6Ip/axER8S0+GaBYLBYSExNp3bp1nSv8ivcKDAxUy4mIiA/zyQClnL+/vyoxERERL+RzSbIiIiI+L2MtrBgFC9uZzxlr3V0ip/PpFhQRERGfk7EWlg0FDDDKoDAd0pfB8JUQN9jNhXMetaCIiIh4k62PURGcwKln49R236EARURExJtkbjkdnJQzysztPkQBioiIiDeJ7gWWagNALP7mdh+iAEVERMSbpEwFLKeDFIu/+TrlYXeWyukUoIiIiHiTuMFmQmzCCAhtaz4PXwVxg9xdMqfSKB4RERFvEzcYhi12dylcSi0oIiIi4nEUoIiIiIjHUYAiIiIiHkcBioiIiHgcBSgiIiLicRSgiIiIiMdRgCIiIiIeRwGKiIiIeBwFKCIiIuJxFKCIiIiIx1GAIiIiIh5HAYqIiIh4HAUoIiIi4nEcDlBWr17N6NGjadOmDRaLhU8++aTivZKSEu677z569epFeHg4bdq04cYbb+TQoUNVPmPo0KFYLJYqj2uvvbbRX0ZERER8g8MBSl5eHn369OH555+v8V5+fj4bN27k4YcfZuPGjXz88cfs3LmTMWPG1Nh34sSJHD58uOLxyiuvNOwbiIiINJWMtbBiFCxsZz5nrLW9TRotwNEDRo0axahRo2y+FxUVxdKlS6tse+655zjnnHPYt28f7du3r9geFhZGQkKCo6cXERFxj4y1sGwoYIBRBoXpcHgpWE69X74tfRkMXwlxg91XVh/g8hyUrKwsLBYL0dHRVbbPmzeP2NhYevbsyZQpU8jJyan1M4qKisjOzq7yEBERaVJbH6MiOIFTz2Xmc5Vtxql9pTEcbkFxRGFhIffffz/XXXcdkZGRFdv/+Mc/kpycTEJCAlu3buWBBx7gxx9/rNH6Um7mzJnMmDHDlUUVERGpW+aW04FIXYwyc19pFIthGEaDD7ZYWLhwIWPHjq3xXklJCVdffTX79u1j5cqVVQKU6jZs2EBqaiobNmygX79+Nd4vKiqiqKio4nV2djZJSUlkZWXV+bkiIiJOs2IUpC+tP0ix+EPCCBi2uGnK5UWys7OJioqyq/52SRdPSUkJ11xzDWlpaSxdurTeQvTr14/AwEB27dpl8/3g4GAiIyOrPERERJpUylTAYgYgcOrZ33yuss0CKQ+7qZC+w+kBSnlwsmvXLpYtW0arVq3qPebnn3+mpKSExMREZxdHRETEOeIGm8mvCSMgtK35PGI1DF9VddvwVRA3yN2l9XoO56Dk5uby66+/VrxOS0tj8+bNxMTE0KZNG6666io2btzI//73P8rKykhPTwcgJiaGoKAgfvvtN+bNm8fFF19MbGws27Zt4+677+ass85i8GBlPIuIiAeLG2y760bdOU7ncA7KypUrGTZsWI3t48ePZ/r06SQnJ9s8bsWKFQwdOpT9+/dz/fXXs3XrVnJzc0lKSuKSSy5h2rRpxMTE2FUGR/qwRERExDM4Un83KknWXRSgiIiIeB+3J8mKiIiINIYCFBEREfE4ClBERETE4yhAEREREY+jAEVEREQ8jgIUERER8TgKUERERMTjKEARERFxtYy15mKDC9uZzxlr3V0ij+fwVPciIiLigIy1sGwoYJgrIRemQ/oyc12fOC3xUhu1oIiIiLjS1seoCE7g1LNxarvURgGKiIiIK2VuOR2clDPKzO1SKwUoIiIirhTdCyz+VbdZ/M3tUisFKCIiIq6UMhWwnA5SLP7m65SH3Vkqj6cARURExJXiBpsJsQkjILSt+Tx8FcQNcnfJPJpG8YiIiLha3GAYttjdpfAqakERERERj6MARURERDyOAhQRERHxOApQRERExOMoQBERERGPowBFREREPI4CFBEREWdwZMVirW5cL82DIiIi0liOrFis1Y3tohYUERGRxnJkxWKtbmwXBSgiIiKN5ciKxVrd2C4KUERERBrLkRWLtbqxXRSgiIiINJYjKxZ7+OrGhmHw4MItbNh7wq3lUIAiIiLSWI6sWOzhqxt/svkg736/jxtf/4HswhK3lUOjeERERJzBkRWLPXR147yiUmYt3gHAbcPOIDIk0G1lUQuKiIiIJ3LDXCkvrPiVI9lFtI8J4+bfJbv8fHVRC4qIiIinccNcKXuP5/HamjQApl5yJiGB/vUc4VpqQREREfE0bpgr5dH/baO4zMp5XWIZ0SPeZeexlwIUERERT9PEc6Us336EZduPEuBnYdroHlgsFpecxxEKUERERDxNE86VUlhSxoz/bgPg5t8lc0brCKefoyEUoIiIiHiaJpwr5ZVVu9l3Ip/4yGAmXdDF6Z/fUApQREREPE0TzZWy/0Q+L678FYCpl/SgRbDnjJ3xnJKIiIjIaU0wV8qM/26jqNTKoM6tuLR3okvP5Si1oIiIiDRDK3YcZdn2IwT4WZgxpqdHJMZW5nCAsnr1akaPHk2bNm2wWCx88sknVd43DIPp06fTpk0bQkNDGTp0KD///HOVfYqKipg0aRKxsbGEh4czZswYDhw40KgvIiIiIvYpLClj+n/NuvmmwR3pEu8ZibGVORyg5OXl0adPH55//nmb78+ePZunn36a559/nnXr1pGQkMCIESPIycmp2OfOO+9k4cKFzJ8/n6+//prc3FwuvfRSysrKbH6miIiIOM+rq3ez93g+rSOCmTy8q7uLY5PFMAyjwQdbLCxcuJCxY8cCZutJmzZtuPPOO7nvvvsAs7UkPj6ef/zjH9xyyy1kZWURFxfH22+/zbhx4wA4dOgQSUlJfP7551x44YX1njc7O5uoqCiysrKIjIxsaPFFRESanf0n8hn+9CqKSq08c21fLuvbtsnO7Uj97dQclLS0NNLT0xk5cmTFtuDgYIYMGcI333wDwIYNGygpKamyT5s2bUhJSanYp7qioiKys7OrPERERKQOtazl8+j/zMTYAckxjOnTxs2FrJ1TR/Gkp6cDEB9fdYrc+Ph49u7dW7FPUFAQLVu2rLFP+fHVzZw5kxkzZjizqCIiIr6rlrV8VnRaypfb8vD3s/DIZSkelxhbmUtG8VT/woZh1HsR6trngQceICsrq+Kxf/9+p5VVRETEqdywCnENNtbyyS8LYuriwwDcNKgj3RI8LzG2Mqe2oCQkJABmK0li4unx1EePHq1oVUlISKC4uJiTJ09WaUU5evQogwbZnoAmODiY4OBgZxZVRETE+dywCrFNNtbyeebINRwsjKRNVAh/G+GZibGVObUFJTk5mYSEBJYuXVqxrbi4mFWrVlUEH/379ycwMLDKPocPH2br1q21BigiIiJewQ2rENtUbS2fHQUdeD1jLACPXJZCuAfNGFsbh0uYm5vLr7/+WvE6LS2NzZs3ExMTQ/v27bnzzjt54okn6NKlC126dOGJJ54gLCyM6667DoCoqChuvvlm7r77blq1akVMTAxTpkyhV69eDB8+3HnfTEREpKk18SrEZKw1g5/MLWZQkjLVbKlJmWq23Fj8sVqtPHBwEqUEcOEZgQzvEV//53oAhwOU9evXM2zYsIrXd911FwDjx49n7ty53HvvvRQUFHDbbbdx8uRJBgwYwJdffklExOm+rn/9618EBARwzTXXUFBQwAUXXMDcuXPx9/evcT4RERGvEd3L7NapHKS4aBXieruThq+ErY/x7i8t2ZTfnfBAmH71ec4vh4s0ah4Ud9E8KCIi4pGqBw3lqxC7YKE/VoyC9KU1g6GEERVr+BzNKeSCp1aRU1jKtNE9uGlwsnPL4CC3zYMiIiLSrDXRKsSAXd1Jj/5vOzmFpfRqG8WN53Z0fhlcyPOzZERERLxJE6xCDNTbnbRqZwb//fEQfhaYeUUv/P08d84TW9SCIiIi4o1SpgKW06N1yruTUh6moLiMqZ+YLSkTBiWT0jbKsc8+ftypRW0IBSgiIiLeqI7upOe+2sX+EwUkRoVw10gH5zxJT4d+/WDSJCgtdUnR7aEuHhER8S21Db31RTa6k7YfzuY/q3cDMH1MT1o4MudJfj5cdhns2wdffgm5uRAd7cQC208BioiI+A5PmcnVTUrLrNz74U+UWg1G9ojnwp4J9h9stcL48fDDDxATA5995rbgBNTFIyIivsRTZnJ1k9e/TmPLwSwiQwJ4bGyKYwc/9BB8+CEEBsInn8AZZ7ikjPZSgCIiIr6jqWdy9SC7M3J5eulOAKZe2oPWkSH2H/zGGzBrlvnz66/Dee6f0E0BioiI+I5qa9AArpvJ1YNYrQb3f7yFolIr53WJ5er+7ew/eMUKuOUW8+eHH4YbbnBNIR2kAEVERHxHHUNvfdm8H/bxQ9oJwoL8eeLyXlgsds558vPPcPnl5midceNgxgzXFtQBClBERMR3NOVMrh7iYGYBsz7fDsA9F3YjKSbMvgMPH4aLL4asLBg0CObMAXsDmyagUTwiIuJbmmomVw9gGAYPLdxCXnEZ/Tu0ZLy909nn5MAll5jDibt0gU8/hdBQl5bVUWpBERER8VKfbD7Iyl8yCPL34x9X9sbPnunsS0vhmmtg0yaIi4PFiyE21vWFdZACFBERES+UkVPEjP9uA2Dy8C6c0bpF/QcZBvzlL/DFF2aLyf/+B507u7ikDaMARURExAtNX/Qzmfkl9EiM5P9+38m+g554Al57Dfz8YP58OOcc1xayERSgiIiIeJn//niIz7Ycxt/PwuyrehPob0d1/vbbMHWq+fOzz8KYMa4tZCMpQBEREWkqGWthxShY2M58zljr8EcczS7k4U+3AvDXYWfYt1Lx8uXwpz+ZP99zD9x+u8PnbWoaxSMiItIUnLBOkGEYPPDxFjLzS+jZJpK/nm/HdPRbt8IVV5xOji2fMdbDqQVFRESkKThhnaAPNhxg+Y6jBPn78fQ1fevv2jl4EEaNguxsc/r6N98080+8gHeUUkRExNs1cp2gAyfzeeTUqJ27RnalW0JEPefLNCdiO3AAunUzFwAMcWB9HjdTgCIiItIUGrFOkNVqcO+HP5FbVEq/9tFMPK+eUTsFBWYS7E8/QXy8OddJTEwjCt/0FKCIiIg0hUasE/TO93v55rfjhAT68dQ1ffGva0K20lL4wx9gzRqIjIQlSyA52SlfoSkpQBEREWkKDVwnKO1YHjM/3wHAA6POJDk2vPadDcNcmfjTTyE4GBYtgj59nPglmo5G8YiIiDQVB9cJKrMaTPngRwpKyhjUuRU3DOxQ9wEPPghvvHF6IrYhQxpZYPdRC4qIiIiHenXNbjbsPUmL4ABmX1XPWjv/+tfpIcT/+Q+MHdskZXQVBSgiIiIeaOvBLJ768hcAHr70TNq1DKt953fegbvuMn+eORNuvrkJSuhaClBEREQ8TEFxGZPnb6KkzGBkj3iuSU2qfefFi+Gmm8yf77wT7rvP/hM5YWZbV1EOioiIiId5/PNt/JaRR+uIYGZd2RuLpZaunW+/hSuvNEfu/PGP8NRTUNu+1TlhZltXUguKiIiIB1m+/QjvfLcPgKeu6UNMeJDtHbdtg0suMec8GTUK5sxxbJZYJ8xs60oKUERERDzE0ZxC7v3wJwD+/LtkzusSZ3vHtDQYORJOnoSBA+GDDyAw0LGTNXJmW1dTgCIiIuIBDMPgng9+4nheMd0TIrjnom62dzx4EC64wHzu0QP+9z8Ir2NuFFsy1oK1qOZ2O2e2bQrKQREREfEAb36zh1U7MwgO8OPZP5xFcIB/zZ2OHoXhw80WlM6dYdkyaNXKsROV554Y1mpv+GHvzLZNQS0oIiLStDx45Ii7/JKewxOLzdliH7z4TLrG21gI8ORJs1tnxw5ISoLlyyEx0fGTleeeUC1ACY6xa2bbpqIWFBERaToePnLEHQpLzCHFxaVWhnWL48ZzbcwWm5Njrkz844/m4n/Ll0OHemaVrY2t3BMAv2CPCU5ALSgiItKUPHzkiDvMWryDHek5tAoPYvZVfWoOKS5fmfi778wViZcuhS5dGn7CRqyq3JQUoIiISNPx8JEjTe2LrenM/WYPAE9e3Zu4iOCqOxQXm/OcrFwJERHmysS9GhlINGJV5aakAEVERJqOl9y9N4X9J/K598MfAfi/33fi/O7xVXcon3xt8WIIDYXPPoPU1MafuIGrKjc1pwcoHTt2xGKx1HjcfvvtAEyYMKHGewMHDnR2MURExBN5yd27q5WUWZn03iayC0vpmxTNlJHVhhRbreZ6Oh9+CEFB8MkncN55zitA+arKlx8wnz0sOAEXJMmuW7eOsrLTzXdbt25lxIgRXH311RXbLrroIubMmVPxOiiollnyRETEt5TfvW99zOzWie5lBiceWEG60j+X/MLm/ZlEhATw3B/OIiigUnuBYcBf/wpvvQX+/vD+++bonWbG6QFKXFzVWe9mzZpF586dGTJkSMW24OBgEhISnH1qERHxBuV37/bIWFstmJnq9aN9Vuw4yiurdwPw5FV9SIqptEqxYcAdd8BLL5lr6rz1Flx2mZtK6l4uzUEpLi7mnXfe4U9/+lOVrOSVK1fSunVrunbtysSJEzl69Gidn1NUVER2dnaVh4iI+LjyIcnpS6HgoPm8bKhXz5tyOKuAu97fDMCEQR25KKXSzbphmKsRP/+8GZy8/jpcd51byukJXBqgfPLJJ2RmZjJhwoSKbaNGjWLevHl89dVXPPXUU6xbt47zzz+foiIbU+6eMnPmTKKioioeSUl1LDstIiK+wceGJJeWWZn83mZO5peQ0jaSBy7ufvpNw4C//Q2efdZ8/dprcNNN7imoh7AYhmG46sMvvPBCgoKC+O9//1vrPocPH6ZDhw7Mnz+fK664wuY+RUVFVQKY7OxskpKSyMrKIjIy0unlFhERD7CwndlyUl1oWzO508s8/eUvPPvVr7QIDuB/k35Hx9hT6+cYBtx9N/zrX+brV1+FP//ZfQV1oezsbKKiouyqv102k+zevXtZtmwZH3/8cZ37JSYm0qFDB3bt2lXrPsHBwQQHB9f6voiI+KDoXuZMs5XnTfHSIcmrd2bw3IpfAXjiil5Vg5N77jkdnLzyis8GJ45yWRfPnDlzaN26NZdcckmd+x0/fpz9+/eT2JD1BERExHf5yJDkAyfzmTx/E4YBfzinPWP6tDHfMAy47z546inz9csvw//9n/sK6mFcEqBYrVbmzJnD+PHjCQg43UiTm5vLlClT+Pbbb9mzZw8rV65k9OjRxMbGcvnll7uiKCIi4q28ZEKxuhSVlnH7vI2czC+hV9sopo3uYb5hGHD//fDkk+brF1+EW25xX0E9kEu6eJYtW8a+ffv405/+VGW7v78/W7Zs4a233iIzM5PExESGDRvGggULiIiwsXKjiIg0b44MSfZAM/67jR8PZBEdFshL1/cjJNDfDE4efBBmzzZ3ev55+Mtf3FtQD+SSAGXkyJHYyr0NDQ1lyZIlrjiliIiIR/lg/X7e/X4fFgs8c+1ZtGsZZgYnU6fCrFnmTs89B6dmWpeqXJYkKyIi0lz9fCiLqZ9sBeDOC7oypGucGZzcey/885/mTs88Y84YKzZpsUAREZH6ZKyFFaPMoc8rRtU5WVxWfgm3vrOBolIrw7rFMen8M8y1dSZNOh2cPPusOWOs1EotKCIi4j3cMfV9+Yy25ZPGFaZD+jIzgbfaua1Wg7+9v5n9JwpIignl3+POws+wmgmwr79uzhD7yiswcaJry+wD1IIiIiLewV1T3zswo+3zK37lqx1HCQ7w46U/9icqyALjx5vBiZ8fvPmmghM7KUARERHv4K6p7zO3VJ0srvzcmVuqbFq+/Qj/WrYTgEfHppASFwrXXgvz5kFAAMyfDzfc4Nqy+hAFKCIi4h3sDBScLrrX6cniylWb0fbXozlMnr8Zw4DrBrTnmpQ4uPJK+OgjCAoyn6++2rXl9DEKUERExDvYESi4RD0z2mbllzDxrQ3kFpVyTscYpl+QDGPGwP/+ByEhsGiR+VocogBFRES8gzumvi9Pyg2MhqCWEBxbZUbbMqvBpPmbSDuWR9voUF66rAtBoy+BpUshPBwWL4YLL3Rd+XyYAhQREfEOTT31feWk3OJjUHwSijNPjRwyzzlr8XZW78wgJNCP10d3otUVo2H1aoiMhC+/hKFDXVM2V3BgKHVT0DBjERHxHk059b2tpFyLv7l92GI+3niAV9ekAfDckHi6Xzsatm6Fli3N4CQ1tWnK6QwODKVuKmpBERER1/Gwu3KH1JGUu3l/Jvd/bCbnTu0WyIiJV5rBSWKi2YLiTcEJuG+EVB3UgiIiIq7hgXflDonuZZa5cpBi8edo6ABueXs9xaVWbgrL5Ob774KjR+GMM8yWk+Rk95W5odw1QqoOakERERHX8MC7cofYSMottAYzccdEjmQXcUXOb/z9qduwHD0KffvC1197Z3AC7hshVQcFKCIi4hoeeFfukGpJudb4EdxVtJAf08sYs28D/3zjPizZ2fD738PKlRAf7+4SN5w7RkjVQwGKiIi4hgfelTusPCn38gM8WfwvPt9ZwlXbVvDM+4/gV1gIo0fDF19AVJS7S9o4TT1Cyg7KQREREddImWrmnFj8T4+AcfNdeUO9v24/L638jZvWf8q05a+aG2+8EV57DQID3Vs4Z2nKEVJ2UAuKiIi4hgfelTfE2l+P8eDHP3HX6rdPByd33glz5vhOcOKB1IIiIiKu42F35Y769WgOf33ze5747N9cs2WZufHxx+GBB8BicW/hfJwCFBERERuO5RZx2yur+Pe8aQxJ24jh54flpZfg//7P3UVrFhSgiIiIVFNYUsZ9z33B0y/cTcqR3zDCwrAsWACXXuruojUbClBEREQqKbMazP7XJ8yYdRvtso9S2iqWgMWfw9lnu7tozYoCFBERqV/5qr6ZW8xhwilTze3Vt3nDDLF1MAyDubPe4o5H/0p0YS4FHTsRuuxL6NzZ3UVrdhSgiIhI3WxNWX94KZTniHrjNPa1+HLG81z/2N0El5Vwonc/YpYvgdjYpi2ErWDQi69pQ2mYsYiI1M3mlPVl5rO3TmNvw+a7pjFixmSCy0rYe95IYr5d457gZNlQSF8KBQfN52VDvWuRRSdRgCIiInWzNWW9Ld40jX1lZWXsn3ALff/1CH4YrB99HR1WfA5hYU1fFm9fv8iJFKCIiEjdbE1Zb4u3TWMPkJtL1kWXkvTmfwBY9Me/0W/h2+Bvx/d1BW9fv8iJFKCIiEjdbC4k528+e9Dicg7bt4+igYOIWvYFRf6BvHDLY4x685/4+buxavSF9YucRAGKiIjUzdaU9SNWm9PWe+s09j/8QNnZ5xD88xYywqOZOvk5JjxzH4HuDE7AI1cVdheLYRiGuwvhqOzsbKKiosjKyiIyMtLdxREREW/y/vsY48djKSxke1xHpv15Ji8+eDmxLYLdXTJTjVE8D3tP4FcPR+pvDTMWEZHmwTDgscfg73/HAizrfDaP/3Eqb94x3HOCE/D69YucRQGKiIj4vsJCuPlmePddAF49eyyvXHIL7906mPat3DBaR+qlAEVERHzbkSNw+eXw7beU+vszdfhf+GzApbz354F0iY9wd+mkFgpQRETE8zhrNtUff4TLLoO9e8kPi+DmMfez+Yx+vH3T2aS0jXJ+ucVpFKCIiIhnsTW1fkOm0V+wAG66CQoKyEhIYtylD3GgdXtev7E/qR1jXFR4cRYNMxYREc/S2NlUy8rgvvvg2muhoIBf+w5i+DWz2RuXxHPXncV5XeJcVXJxIrWgiIiIZ2nMbKonTsAf/gBffgnAN1f9meuTR2P4+/P01b25sGeCCwosrqAARUREPEt0L7Nbp3KQYs9sqlu2wNixsHs3RlgYn0x6lL/RDYDHx6Zw+VntXFdmcTqnd/FMnz4di8VS5ZGQcDpiNQyD6dOn06ZNG0JDQxk6dCg///yzs4shIiLeqiGzqX74IZx7rhmcdOzIG/94pyI4eWxsCn8c0MHlxa4hYy2sGAUL25nPzXBF4sZwSQ5Kz549OXz4cMVjy5bTzXKzZ8/m6aef5vnnn2fdunUkJCQwYsQIcnJyXFEUERHxNram1q9tGv2yMnjoIbj6asjLw7jgAp6Z9S6PHggC4NGxKVw/0E3BybKhkL4UCg6az8uGKkhxgEu6eAICAqq0mpQzDIN///vfPPTQQ1xxxRUAvPnmm8THx/Puu+9yyy23uKI4IiLSVJw1PNie2VRPnoTrr4fPPwfAuOsuZg+7iZe+3gvAo5f15AZ3BCdgO9HX4m9u1yyxdnFJC8quXbto06YNycnJXHvttezevRuAtLQ00tPTGTlyZMW+wcHBDBkyhG+++cYVRRERkabSlK0GGzZAv35mcBISgvHOO8weMbEiOHnksp7ccG7H+svrqi4YRxJ91RVkk9MDlAEDBvDWW2+xZMkSXn31VdLT0xk0aBDHjx8nPT0dgPj4+CrHxMfHV7xnS1FREdnZ2VUeIiLiYRo7PNgehgGvvAKDBsGePZCcjLF2LU+26s9LK38DzODkRnuCE1cGU9G9TufQlLOV6KuuoFo5PUAZNWoUV155Jb169WL48OF89tlngNmVU85isVQ5xjCMGtsqmzlzJlFRURWPpKQkZxdbREQaqzHDg+2Rlwc33gi33grFxXDZZRgbNvDowRBePBWczBhjR3ACrg+m7E30bYqgzku5fKK28PBwevXqxa5duyryUqq3lhw9erRGq0plDzzwAFlZWRWP/fv3u7TMIiLSAPa2GjTEjh0wYAC88w74+8Ps2ZR99DEPfLWfN9amAWbLyfhBHe37PFcHU/Ym+rq6HF7M5QFKUVER27dvJzExkeTkZBISEli6dGnF+8XFxaxatYpBg2xkZ58SHBxMZGRklYeIiHiYhgwPtsf8+XD22fDzz5CYCF99Rcldd3PXBz8yf91+/Czw5FW97Ws5KefKYKpceaLv5QfMZ1ujkJqiHI7ykJwYpwcoU6ZMYdWqVaSlpfH9999z1VVXkZ2dzfjx47FYLNx555088cQTLFy4kK1btzJhwgTCwsK47rrrnF0UERFpSo4MD7ZHURFMmmTODJubC8OGwcaNFA0azG3zNvLp5kME+Fl47g/9uDrVwa5/VwVTjvKUcpTzoJwYpw8zPnDgAH/4wx84duwYcXFxDBw4kO+++44OHcyhXvfeey8FBQXcdtttnDx5kgEDBvDll18SEaElr0VEvJ49w4PtsWcPjBsHP/xgvn7wQZgxgwKrhf97cz1rdh0jKMCPl6/vx/nda08RqLOcw1dWGxL9cMODqYbylHKU86Dh0RbDMIwmPaMTZGdnExUVRVZWlrp7RETs5aw5Slztgw9g4kTIyoKWLeHtt+GSS8gpLOHmuev5Yc8JwoL8ee3GVAadEevu0vqWhe3MlpPqQtuaXVWN5Ej9rbV4RESag/Km+/K748J0SF9m3r17SpCSlwd33gmvvWa+HjgQ3nsPOnbkWG4RN81Zx5aDWUSEBDD3prPp3yHGrcX1SQ1dB8kFXJ4kKyIiTtaQJEZPH87600+QmmoGJxaL2aWzejV07Mje43lc+dI3bDmYRUx4EO9NHKjgxFU8KCdGAYqIiDdpaBKjpw5nNQx44QU45xxzKHFiIixbBo8/DoGBbD2YxZUvfcPe4/m0axnKh7eeS0rbqIafz0NGqHgsZyc6N4K6eEREvElDkxg9qOm+wvHj8Kc/waJF5utLL4U5cyDWzCtZ++sxbnl7A7lFpZyZGMmbN51N68iQhp/PG7q5PIGzEp0bSS0oIiLepKEtIR7UdA/AqlXQp48ZnAQFwTPPmD+fCk4W/XiICXN+ILeolHM7tWLBLQMbF5yA53dzSRUKUEREvElDJ/bylKb74mIzv+T88+HgQejaFb77Du64w8w9Ad74Oo073ttESZnBJb0Tmfuns4kMCWz8uT21m0tsUhePiIg3SZlqdktY/E9379jbElJb031TDT/euhVuuAE2bzZf33QTPPsstGgBgNVqMOuLHfxn9W4AJgzqyN8v7YGfX+1rtTnEE7u5pFZqQRER8SbObglpiplDrVZ4+mlzlM7mzdCqFXz4IbzxRkVwUlBcxl/mbagITu65sBvTRjsxOAHP6+aSOmmiNhGR5mzFKDMoqd6qkDDCOYmSe/fChAmwcqX5+uKL4fXX4dTisQBHswv581vr+elAFkH+fjx5dW8u69u28ee2pUZrkRtnbW2GNFGbiIjYx1V5GYZhzgA7aRJkZ0N4uNmKMnFiRa4JwLZD2dz85joOZxUSEx7Ef27oT2pHF85x4iEjVKR+ClBERJozV+RlHDsGt9wCH39svj73XHjrLTjjjCq7rdhxlL++u5G84jI6x4XzxoSz6dAqvOHnFZ+iHBQRkeYqYy0Un6wZnDQmL2PRIkhJMYOTgABzwrXVq2sEJ3PXpnHzm+vIKy5jUOdWfPyXwe4LTjR5m0dSC4qISHNUedKyymJSod/TjudlHDtmDhV+7z3zdY8e8M47cNZZVXYrLrUy478/M+/7fQCMS03isctTCPSv537ZVSONNHmbx1ILiohIc1R90jIwW0+CWjoWnBgGvP++GZC89x74+cF998GGDTWCk6M5hVz36nfM+34fFgvcd1F3Zl3Zy77gxFUjjXxp8jYfawlSC4qISHPkjOTY9HS47TZYuNB8nZJiTlWfmlpj1x/3Z3LL2xtIzy4kIiSAZ689i2HdW9t3noZO728PX5m8zQdbgtSCIiLSHDV0Rlo4PUKnRw8zOAkIgGnTzFYTG8HJRxsOcPUr35KeXUjnuHA+vX2w/cEJuDaIaMx18CS+1BJ0ilpQRESao4bOSHvggDlC5/PPzddnnWW2mvTpU2PXkjIrT3y+nTlr9wAw/Mx4/jWuDxGOTlvvyhlgGzMzryfxlZagStSCIiJiL1/q43d0RlqrFV5+GXr2NIOToCB44gn4/nubwcmx3CJufP2HiuBk8gVd+M8N/R0PTsC1M8B6yhpFjeUrLUGVaCZZERF7VO/jL68kvbiP324//WS2mnz3nfl64EBzmvozz7S5+w9pJ/jruxs5mlNEeJA/T4/ry4U9E2zua7e6ZoBtqrWEPFmtv5+eFWw5Un8rQBERgforOVdPCe+J8vJgxgxzBtiyMoiIgMceg9tvB3//GrtbrQb/WbObJ5f8QpnV4IzWLXjpj/3oEh/hujI258CxOi+Yxl9T3YuI2CtjLWy8G45/f3qbrREQ9fXx+9pd/P/+B3/9q7mWDsCVV8Izz0Bb22vkZOYXc/f7P7J8x1EALj+rLY9fnkJYkIurGVeO8PE2PjaNvwIUEWm+yu++jdKq221VcnUlavrSEM+DB2HyZPjoI/N1+/bwwgtw6aW1HrJ5fya3z9vIwcwCggL8mDGmJ9eenYTF4sSViGvjg8mhYlKSrIg0X+V337ZUr+TqStT0hSGeZWXw3HNmXslHH5ldOPfcA9u21RqcGIbBnLVpXP3yNxzMLKBDqzAW3jaIP5zTvmmCE/DJ5FAxqQVFRJovW3ff5apXcuWjPWz18Xv7Xfzateaqw5s2ma8HDIBXXrE5Oqfcsdwi7v3wJ7461aUzKiWBf1zVm8iGjNJpDF8ZJiw1KEARkebLVrdNBRuVXG19/K6cp8OVDh+Ge+8118wBiIqCWbPg//7PnLK+Fit/OcqUD37iWG4RQQF+PDiqO+MHdWy6VpPK6gocK/O1HKFmQKN4RKT5qp47Uq7VAMcWzPOSIZ4ViovNhNdHHoHcXLBY4OabzXlN4uJqPaywpIx/fLGjYm6TrvEtePYPZ9E9wcP/Dmukj8fQKB4REXvYe/fdVJ/TFJYsMZNgf/nFfD1ggJl7cvbZdR72S3oOk+dvYkd6DgDjz+3AAxefSUhgzeHGHkcjfbySAhQRad6cNTTT04d47t4Nf/sbLFpkvm7dGv7xD7jxxjq7c6xWg7e+3cPMxTsoKrXSKjyIJ6/uzfnd45uo4E7g7TlClTWjrioFKCIinqyxFVJ2thmIPPUUFBWZC/tNmmQu7hcVVeeh+0/kc8+HP/Ld7hMADOkax5NX96Z1REhjvlHT89Ycoep8aTi7HRSgiIg0hivvaBtTIZWWwmuvmYHIUXOkDRdcAM8+a65CXAer1WDeD/uY+fl28ovLCA305/5R3blhYAf8/NyQCNtYvjLSp5l1VSlAERFpKFff0TakQjIMczG/e+6B7dvNbV27mq0ol11mJsTW4cDJfO776CfW/nocgHM6xvDk1b3p0Cq88d/HXbwpR6guvtRVZQcFKCIiDeXqO1pHK6TNm2HKFFi+3HzdqhVMn24u9BdY9/wkhmEwf91+Hv9sO7lFpYQE+nHfRd0Zf25H72w1qc6RHCFPzfPwla4qOylAEZHmw9kVjyvvaDPWgrWo5nZbFdLBgzB1Krz5ptmCEhRkjtR58EGIjq73VGnH8pj6yZaKVpPUDi158uo+JMd6catJQ3lynoevdFXZSQGKiDQPrqh4XHVHW7FGkLXaG35UqZAyM+Gf/zRXGy4oMLddey3MnAkdO9Z7muJSK6+u2c0zy3dRXGolOMCPey7sxk2Dk/H3hVaThvDkPA9f6aqykwIUEWkeXFHxuOqOtmKNoGoBSnAM/P5TCO9r5pT84x9w8qT53uDB5kidAQOqHlNLq9GGvSd44OMt7DySC8B5XWJ5bGxKzVwTT+3ucBVPz/Pw9OHsTqQARUSaB1dUPK66o61tjaBiAx6fCG/ugMxTwUuPHvD447YTYG20GmUd/JbZ/h8w78diAGLCg/j7pT24rG+bmlPVe3J3hy3OCKaaWZ6HJ1OAIiLNg6sqHlfc0VYvqxVYa4GPjkPG8VPnBa7yg7+/BAm/t/05lVqNDAMWnfwdjx++maOlZnBydf92PHjxmbQMD6r3eMCzujuqc1Yw1czyPDyZAhQRaR68qeIpLyt+sN4KHwAHTi2bFg2MBYYBgRbYPrP2AOVUS8zPBclMP3gr6/J7AtApJJ3HbxjLuZ1b1V0OT+/uqMxZwVQzy/PwZLXPb9xAM2fO5OyzzyYiIoLWrVszduxYfilf8+GUCRMmYLFYqjwGDhzo7KKIiJxWXvEkjIDQtuazpy7mFzsIyh6DR1rAv4ADQAsLXAs8BYzAvL2sJ1jIDEtl6sHbGL3r36zL70mopZApCe/w+e8W1h+cgFk5W6qttWOr1SljLawYBQvbmc8Zax36uk7hzGCqvFXs8gPmsyf+jjQDTm9BWbVqFbfffjtnn302paWlPPTQQ4wcOZJt27YRHn46+eqiiy5izpw5Fa+DgmppYhQRcRZPTzA0DPj0U3OV4U2bzG1hYeYaOgO+g9yVdnVRlVkN3vthH//89v/ILDRbXi6NWs2Dbd6kTdBx6LPKvvLY0+rkKXkqyh3xOU4PUL744osqr+fMmUPr1q3ZsGEDv//96WbI4OBgEhISnH16ERHXc/bIFqsVPvnEDEx+/NHcFh4Of/0r3H03xMWdDgQqBwsGUHzSbLk4VY5vsrrx+Ofb+flQNgDdYv2YnvwR5/p9AdFnOdZdYU93h6fkqXhTF57YxeU5KFlZWQDExMRU2b5y5Upat25NdHQ0Q4YM4fHHH6d169Y2P6OoqIiiotMTFmVnZ7uuwCIidamvxcCR4MVqhY8+gkcfhS2nuiIiIszF/P72N4iNPb1v9WAhrB2cWG8+jDJ2ZgYy85tlrMjJBCAyJIC7RnTl+oEdCPAf1fDvW1+rk6fkqSh3xOdYDMMwXPXhhmFw2WWXcfLkSdasWVOxfcGCBbRo0YIOHTqQlpbGww8/TGlpKRs2bCA4OLjG50yfPp0ZM2bU2J6VlUVkZKSrii8iUtOKUZC+tGZXQsIIMxipHLyU38VX7+4oLYUPPoDHHoNt28xtkZHm7K933gnVbujqKsfR4kiePnI9758YjhV/AixlXH9uZyadfwatWtT8e+p0dV0PT+5OE7fIzs4mKirKrvrbpQHK7bffzmeffcbXX39Nu3btat3v8OHDdOjQgfnz53PFFVfUeN9WC0pSUpICFBFf4i0Tgi1sBwUHa24PbWuWu67KOj8f5swxJ1RLSzPfj442g5I77oCWLe0uRt6HnXll30BezbiCAiMEgFFRa7m34xck/2Fjw7+fo6q3KFUEZR6agCxu5UiA4rIunkmTJrFo0SJWr15dZ3ACkJiYSIcOHdi1a5fN94ODg222rIiIj/CUREt71JWMWVt3x29fwZKJ8PoncOyYuT0uzgxKJk2CqCi7T19YUsY73+3l5Z9mcaw4DIB+Ydt5KPF1+rfYZQZDTUldK+IiTg9QDMNg0qRJLFy4kJUrV5KcnFzvMcePH2f//v0kJiY6uzgi4g08JdHSHnUlY259tGrwchz4HFhRDEWvmduSk80Vh2+6CUJD7T5tUWkZ76/bz/MrfuVIdhEQRsegQ9yb+DajItdg8XNjUqinj44Sr+T0AOX222/n3Xff5dNPPyUiIoL09HQAoqKiCA0NJTc3l+nTp3PllVeSmJjInj17ePDBB4mNjeXyyy93dnFExNNlrIUjKzwj0dIedbUYlAcv+4HPgG+A8q/VAbihD0xbDwH2/+ktKbPy0YYDPPfVrxzMNBcEbBsdyqTzz+DK9lEEbg+HzLZquRCf4/QA5aWXXgJg6NChVbbPmTOHCRMm4O/vz5YtW3jrrbfIzMwkMTGRYcOGsWDBAiIiIpxdHBHxVBlrYePdcPx72+978hwWtloMrFb4/iS83BdWrz+9vQcwGugFhB2zOzgpKbPy6eZDPPfVLvYezwegdUQwfz3/DMadnURwgD/QHhLUciG+ySVdPHUJDQ1lyZIlzj6tiHiT8pwTo7SOnbxkDoucHHjzTXj2WSjPo/MDUoFLgc6n9rMz4CosKeP99ft5ZdXuihaT2BZB3DqkM9cP7EBIoH89nyDiG7QWj4g0vfKck9r4BcMFX7muu8IZI4bS0uD55+G116B8bqaoKJg4Ef4wEH65lhojW+oIuHKLSnnnu728tiaNY7nmqMXYFsH8+bxkbhjYgfBg/bmW5kW/8SLS9GyNdiln8Yf4YY4HJ/YGHY0ZMWQYsGqV2Vry6admtw5A167miJzx46FFC3Nb0kq7RracyCtm7jd7mLs2jexCs0WpbXQotw7pxNWpSc2rxcRbhppLk1CAIiJNz9ZQ3QoN6NpxJOhoyIihzEx46y14+WXYvv309pEjzcnVLroI/KqtvVrPyJZdR3J4Y20aH288SFGpGeh0igvntqFncFnfNgT6O30tV8/mTUPNQcFUE1CAIiJNr/pQ3XKtBkC/p2tvPamtUnAk6HBkavZ168yg5L33oMDMByEsDK6/3mwx6dnToa9tGAZrdh3j9a/TWLUzo2J77/A9/OWM7Yw8/1r84+ueN6pe3lpxetNQc28LpryUAhQRaXr2Tu5VubItX3sGalYKjgQd9a16m5cH8+fDSy/Bhg2n9+nZE/7yFzM4cWBiNYCC4jIW/XiQ179OY+eRXPOUwMiob/lz7Kekhm3Fgj989UrjKjlvrjg9ZU0fe3hTMOXFFKCIiHvUN7lX9cq2+vTylSuF+oKOymqbaM0YZ87q+vbbcGqRU4KC4Oqr4dZbYfBgsFgc+oq/ZeQy77t9fLhhf0V+SXiQP1enJnGT/yN0yP7IuZWcN1ecjvwbups3BVNeTAGKiHim6pWtLeWVwu8W1D67a3WVW2/2b4Z10bCyDLbedHqfzp3hllvM2V4rryhsh5IyK1/+fIR3vtvLt7uPV2xv1zKUG8/twLiz2xMVGggL1zq/kvPmirOuGXo9jTcFU15MAYqIeKa6RvqUK68UHFkPpqwM1mfDnAj49AQUm7NdExQEY8fCzTfD8OE1k17rse94Ph9s2M/8dfvJyDGHCVsscH631lw/sAO/7xqHv1+lFhhXVHLeXHF605o+3hRMeTGXrmbsKo6shigiDeAJiZYrRtVcGbgyR1fN3bUL5s41J1U7WKm7qF8/s6XkuusgJsahIuYVlfL5lsN8sOEAP6SdqNge2yKYa89O4tpzkmjXMsz2wa5YBVgrCzeOI7/3Nfb10GDKwzhSfytAEZGqaq3kVjZtkGKrHAbQKhXyD9hXKRw5AgsWwLx58MMPp7e3agV//KMZmPTt61CxDMNg3Z6TfLB+P59vOUxesRlAWSzwuzNiGXd2EiN7JBAUYEcLjCsqOVWcDeMpv/c+TgGKiDScrZYLiz8kjGj6RMuGVLY5OfDJJ2ZQsmyZ2aUD4GeBYQPg1rth9GgIDnaoKDuP5LBo8yEW/XiIfSfyK7Z3bBXGVf3bcUW/drSJtn91YvEwnvR778Mcqb+VgyIiVXlSomV9I33KFRfDkiXw7rvmDK/lc5aAuRbOIGCQBaLWw5BEu4OT/Sfy+e9Ph1i0+RA70nMqtocH+XNJ70SuTk0itUNLLA6O7hEP5Em/9wIoQBGR6q0UYe28I9Hy4Ep4Zwos2QrriiG3UmNwly4wyIDeuyHh1HT0WAFLvUNuD2YWsGRrOv/76RAb92VWbA/0tzCka2vG9G3D8DNbExakP59O4wk5T96cYOyj9D9MpDmzNbGXgTmLmCeOUCguhqVL4Z0XYdHnkF/pvSjgXGCwP/zfG7D2WiiwVj2+ljviX4/msOTnI3yxNZ0tB7MqtlssMKhzK8b0acNFPROJCgt0yddq1jxlcjmNzPE4ClBEmrPaJvaKSYWglp6RaFlYaAYlH3wAixadnkQNzKDkbOAcoDtwqk7h58frvCMusxr8eCCT5dvNoOS3jLyKXfwscHbHGC5KSeCSXom0jgxp/HcobyE4vt4sH5jX2FumoXclT5lczpuGOTcTSpIVac4Wtqs5QyuAXzBcsLzuytOVle6JE/D552ZA8sUXZuJruVbBcI4F+hdCN8DWYJnQtubkbZXuzLPKIlmV04+VLR5k5V5zFeFygf4WBp8Ry0U9ExjeI57YFo4l0NapvIXAsGJ2M5XzA4tf8x4lkrEWll8A1qKa74W2hcsPNH2ZxKWUJCsi9qltVWFrkVmp1lZ51lbpHv6y4c3zu3ebAcmnn8KaNadH3wC0xAxKzjGgWwlYrJiRibXm55xqJbG2GsS2XstY8/2XrEiPY0NuZ8oMP8AMTCKCAzivaywX9kxgWPfWRIbU0X3TmByJ8haCGmW1LyfGZ1X8DpXWfE+5H4ICFJHmp/oCfLUybFeeGWth9VjbFYsjlW5ZGaxffzoo+fnnqu+npMCYMdD2K4j64VRQUn4OP7N8lYIUw4C04nasze3LN/mT+HbNUjLzSzCH8JjOaN2C87u3Zli31qR2bEmgv51zlTQmR6KuGXFt5cR4QsJoU5SjInCzpZnmfnjKv72HUIAi0pzUmhQbCEZJ1X1rqzxru+ut67hyR47Al1+a3TZLlsDx02vV4O8Pv/+9GZSMGQOdOpnbF7armeyKFYJiOdri96zdW8LanB58k92DQ8WtTr1vfpcWwQEMSI5hSLc4hnVrTVJMLbO61qWxORK1tVJB1ZaCjLWw8W44/v3p992VMNoUiau1BW5+wXDBV80v98NTkoU9iAIUEU/m7Duq2irboCgoPln/EMs673ptHFdaCt99ZwYkX3wBGzZU3TcyEi66CC67DEaNgpYta37eqQrearXya1ES6/POZH1+TzYU9mNvQXSVXYP8/TirfTS/OyOWQWfE0rtdlNlKkrEWfvxLw65jY+fHKB8dUqNLyo+KloLaAr/GJIw6o1vKlYmrtSUxxw9rfsEJeE6ysAdRgCLiqWq7o0p9Fg4sqrviqa1yqq2yNQAs9Q+xrG8BP8MC6cDBXvDi1ebom8qjbsBc++aii8zHwIEQaDv3o7CkjB/3Z7I+bwrrdw9kY343ssoiquxjsUBKmygGndGKwZ1jObtjDKFB/vZdR3vvTBs7P0bl0SE1EopPjRJZMYpaA7+GTBbmim4pZ09apmG9VWmiuBoUoIh4Klt3VPjButvN0R+2Kp76uglqq2xbnRp9U98QS1vHnwR+9ocdAfCzBY4WAk+efj8mBkaONFtIRo6EhIQaX7W41MrOIzn8dCCLLb/+wpa9B/glJ4YSo/xPVCoAoX5F9I3OILXrGfQ/sxdntW9JVGg9c5M4emdaPbhrN6bxFWn1GXHLz/H1NeY5Tqyve1FERxNGXdEtVb07qrEtexrWW5UmiqtBw4xFPFVtQ4CrK18vJGVq3aMiKu/T0NVuM9bCx0NghwFbrbANOFRtn6AgSO0BXXOhWxak9oMOl1W0+hRF9uHXhHvZkpfMloNZbDmYxY7DORSX1RyR0zrgBKnh20ntN5zUnv04MzGy/sTW6pXnifVQdKzmfraGsda2YFyNVqtGVKQ2F0E8FXzaHJUU4PhqxLX97tg7dLeuVZExtKieKzSTlag1zFjEF9SVXFlZeTNwXfkh5fs05K51715z2O/q1ebzjmrlsVigf3+44AI4/3zo5g/fXITVgANFrfhlVxa/bFnJjsLe/FI4mrSitpSSC1Rtuo4KDaR32G/08v+eXqG76BW6i7aBGVj8/CFoE7Sz487fZhKwjcq/tjvT2loeDixyXh5AbS1jGJWClVNaDYB+TzteQTmzW6r670l5d5RyJZxLLUo1KEAR8QS2msyr99HXM+9HnfkhlSunuhbgs1ph+3YzECl/7N9fc7+ePWHYMLjgAkp+dx4HCGF3Ri5px/L4ddGH7Dj5D3YVJpFntT1qJtI/l5Sok/TqNYTebaPp3S6Kdi1DsXzyp5p3/o70w9tT+dfVRdMUeQA2/53MUUm0SnVO5eSM/I7afk+UK+E69i6O2UwoQBFxJXv66utKaKycXFl8HDPDsnIrSaWRIFsfraPFpZbK6cQJ+P57c6TNd9+ZP1dPag0IwOjfn/xzzuVASn9+Tu7FjpIgdmfksfu3XPb98D2l1spl6lnxU5ClhM7B++kesoduIXvpFrKH7iF7SAg8jiWsLYy6teq5Gnvn39jKvynyAOrKA2pM5VT9d82Z3VL2lL8Z50qIayhAEXEGW4EI2DeSor6ExmGLzWb19KU1K9/gGPj9p2bFU6PF5ZTyboLos2HTptPByHffwc6dNb5KWUgI6T3O4pcufVmX0J5VEbH8WhpLsREIu4HdNXMYQgL9SI5tQae4cDrnfkrXspV0D95Nx+BDBFjqaPWprrF3/o2t/JtiZIkrztGUc2ho9I00ESXJijSWzaRHILAFlFRrjShPVq1cWdqT0Ghv0mN5oHT0JzjZAXJ/h7Ezk7ING/HbugW/4uIaH7E/LomNid1Yl9CVTW268UtsB0r9a967+FFGm6BjJCe2pXPbdnSKC6dTbAuS48JJjAzBz89i+3pUdE2deq4v+a9GsOfAnb8zEg0bc357OfsctgJYW79rztIU10h8kiP1twIUkcaqrXWjNtWDCnsqFxv7FBihHIu+lGOtbqZ46Sv4bdtH2P5SYg7k0PrAXvzLapYnKziczW26salNNzYndmNzm65khp7+PxTbIoh2LcNoHxNGUs4ikoq/IynwMElB6SQGHSPQD/sqvRpDdS+DA582TYXWHCvPxo7a8WWaPt6jKEARcSV7h7HaYuOu1jj6NQVfXkRmWQtOloaRWRZNZlkEJ7tMJ9OvHZn5JZw8eYDsvWsIzigm+nAOCenH6Xj0EN0z9pB88hD+Rs1ulBOhkWyN78zWhM5siT+Dg8lnUtaxI4nRoSREhZAYFUpCZAiJUSEknHqEBVVqOXFGpWdrTpH6JpkTxzV1C4q3qLVFbaV+79xEAYqIM1VfXO/EenP7qcqgzPAjtyyUbGs4uWVh5FjDySkLI6csnBxrqPlcFk6ONYzcsnByYkaQY40gq6CEk/nFZBaUUFxaKcAwDOJzj9MtYy9dj+2l+6nnLsf2E1pqY1l64ESLCPa3TSCjbTQ57VtQktKN0Aum0jrSDERaRwYTEuhv89haNbbSs7urZ6Uqi8ZqJnNoOEyBm8fRPCgidiizGuQWlZJbVEre4XXk7JhDXuYBckO6kRt/BblByeSc2E3urvnklHUlp6wP2WXh5FqvrhSAhJFvDXXsxJklwAmCS4vpePIQ/Y8foNOJg3Q+eZAuJ/bS8cQhIgoLbJc5JITCM7phTUkhsE9vgvNmY0k4TkzLHGLIOb1j6E7o+1LDLw40PhmyevJvxRDpU8+aP8N5vGEODXd0tWhItFdTgCJexTAM8orLyCsqJafwVHBR7efyoCO3sObPeUWl5Jx6XVBSPUfjqko/F2BOkwow1q6yBVuKiPAvICKwjAhOEOGfT6SRQ1LuUdqdPEJbOpFwIouYg3uJ2reb0MMHsNTWgOkHJABJQMcwuOghGHw1/p06Ee5fqSVkxQrbd4jOGPLZ2EqvvnV7QJWFM3nyHBruWqlXQ6K9mgIUaXIlZVayCkrILigxnwtLq74uKCG7sPznU+8Vnn7P6uROyUBLGS388mjhn08Lv3xa+BXQwr+A8PBIIsqOEGEcJcI/nxb++UT45RHhn0+Efx4RfubryMJcWhwrICijDE6EQVYM7DsCR8rgmNXm3GoVoqOhWzfzUfoJxGZDImZwElS+Uz5YpkH0EPDvcvrYjLW2VyB25pDPxlR69syEq8rC8zirpaPy51iLwLDi9Naz+sqqIdFeTTko0iiGYZBTVMrJvGKO5xVzIreYE/nFnMgrPr2t2iO3yMZaMQ7ys0CL4AAiQgIJD/Y3g4ri3bQwjtEiNJTw+L5ERLenRekBwnc/TQu/fCL8cgn3L6KFfyER571GeOIAWuSsI3jVcPMPaI2TBEOL3rB7gxloHAdOYD4fB44BR4HCegobHARJCRC13ww8Eg1o4weJFrhiJbT+nblfXaOBqveb18jvOKWhU6O7QmOHG0vTc1ZSaW2/n9U1ZpSRvWVtjqO6PJhyUKTRyqwGx/OKOJpdxNGcQo5kmz8fySnkaHYhR3PM1yfyim0u8maPiIAiIv1yiAw2iGoRQWTZQaLKDhIZkE9UQD6RYWFEBRQSWXaAqOgEIs+8iai25xAREkBooD8WS+V5N0ZT5Y9hKWAMAH+g1fqarQz7nwDrHbBoDJwsgywgk6oByIkiyFpX6/I2VUQDras94oB4P+g+zIyo0g9Wy8fwgzWXm4FQ5VVzbaneFVIjv+PU9wpqWfWPb113mK7OCbDVRdSUw43FcY1dBbm2z7Glsa1n9pbVk7u+pE4KUJohwzDILihl/8l8DmYWcPBkQcXzoawCjmYXkZFbRJkDfSmhgf7EhAcRE1xMTNluWhkHaGnJICYgm1b+mbQMzKWVfxYxse1pWbSNiLIDBFgMqtxR15jG/ZRAoMgfNr8DsSshslolWv6HqqwM8oFcIBvI+t4MOrKAk6ees4DMMshaAmVL7PtyAUArP4ixQgzQqvxhgXZREB8G8b1rGW5sheyt5o+2pmAv37+8Tz71Wfjp7zU/p/ofc3uS/+rq9wfn5wTUFvBUrxy63Gr7eGk6tf1bOSuptL78I2d0tSgB1ue5NUB58cUXefLJJzl8+DA9e/bk3//+N+edd547i+Qz8otL2XMsnz3H89i3bxsH9/zAwRw4WNqWg8WtyK05oWgNFqzEBhXQOiKQeL9DtGY/rSODaZ08hPhwP1ofmUOrvO9pFZhDqCXPPKj6zKnVFfxc/uGVlLfAGKefCjGDjQIgB8gtg1wLfDYScv2gKAqMjpBjwN4fILvMDEwc7bBsAURhtoBEcjoAqRyIRAB+tlqJDAgNP91EXduQxvLAoq58jMqr5v7+E9tN15X/mNuT/FfXHWZ5+Z21Iq27kiBdyVcn+Krr38pZSaU284/8zKUZylsMG9t6pgRYn+e2AGXBggXceeedvPjiiwwePJhXXnmFUaNGsW3bNtq3b++eQpX/QTq+3qxArSXgF2i+16Kz+ZzzW9X37NmnscfXsk+hEci+gpbsLm7HnoI49hS1Ia0onj1FbThSXL1vr3eNrxsbkEXbwCO0DTpK28CjtA06SpvADBICjxMfeIJWAZm211E5Wv6DBSyG2Z1iBYpqeRRWei4POvIr/ZxnY5vNQMM4tQOY0YiNScQAQjCDiuhTj6haniMxW2caqvofwzoT8oxT3Te1rEgMp+/+7Bk9Y0/yX213mEdWQGCEY3ef9VXWzuoa8BS+GHCVq+vfyllJpbV9Tvm6Uc6gBFif57Yk2QEDBtCvXz9eeun0XA1nnnkmY8eOZebMmXUe65Ik2fI/SJUzzT1EkTWA3UXt2FnYnl1F7dmV357dBW05WBiHnxX8DCsB1jL8rWXms2HF31pGS7JoH5BOkt9REjlGguUYrTlJnHGSVmQRVFpqBhclpx6l1Z6r/1xCzaCj/FHigi/uD4RitnJEnHqu/HNELdsbHHbXETyUq/7HsHqCZ10JeRlrYfXY2meddXQCqfqS/+qdgr/a963t/PYkI/raVOu+PMFXff9Wzkoq9cY1jcTlPD5Jtri4mA0bNnD//fdX2T5y5Ei++eabGvsXFRVRVHR6lEV2drbzC7X1MXOkxktW80a9PGyr6+f63q/+cz37GYY5K2lpmT9lZf4YZRYMK1isBsnWQ5xh3Y+/dQ1+DvdjNCELEFzLI/TUI+zUo76fg6jWFeRKfpA40kzi/Olh2zkgMalmEmpdfwzrSsiLG2w2b9fKwbu/+pL/yu8wbfIDDPvuPu1pHfG15nZfzm+o79/KWUmlTZGcqgRYn+aWAOXYsWOUlZURHx9fZXt8fDzp6ek19p85cyYzZsxwbaEyt0CRFba79jR1sQABWAnASoOaJCyYrQ7+mPVP5edAzH/t8uegaq8DbewTWG17ELUHHyGnngNxQlBhgeBWZnfWiY1gOHotbCXbnqqQbQV31e+Mo3vZbjFwxvDd2uYGCY51bvM3nO4qWn6BjWHUVgiKhVap9d992lNZ+1pzu68FXJX52r+V+Cy3JslWDBM9xTCMGtsAHnjgAe66666K19nZ2SQlJTm3MNG9IOYw/NVq1m/lxaj+s61tdvycZQ1nZ2F7dha1Z2dRB3YXtyPfCMHAAhYwsGBYLFiw0jY0g46hB+kYcogOoel0DDtMbFCm+XekPOioHoD44YTAwMlaDTCfT6y3XSG36FzzPTtW8a1TeUvHiQ3UCDBSn4Pdc+H491X3r/7H2ZXThjdF33xlcYMhfpjt7opWqfbdfdpTWXvDVOuO8OVK3Nf+rcRnuSUHpbi4mLCwMD744AMuv/zyiu2TJ09m8+bNrFq1qs7jPT0HpdTwY0dBMhvzu1c89hUn1tgvyFLMmSF76Bn6Gz1DfyMl9De6hewhxM8VCR2V1TacN8pMxm3RGUpyIHtbzX0qnMpfKD+mciJvTOrpP3h1LWKGUf8CZ/ZO+AQ1P7uuXBB3/nFu6vM3diG55roQnbt/T0R8kFesZjxgwAD69+/Piy++WLGtR48eXHbZZe5JkoUGj+IpIpRNuZ35rmgQ32V24MfsRAqsNXMNuoRl0C9sG/1a/Ebv0J2cEZZBIIUuHelT0apSHjSUV9zl37Hye9X/+Fb/A93QSbbqSxytrxKoqxxh7cx98g+oEqlLYytbVdYi4gReEaAsWLCAG264gZdffplzzz2X//znP7z66qv8/PPPdOjQoc5j3T3VfXGplZ8OZPLtb8f5dvdxNuw9SVFp1VaXiJAAzmrfkrOSounXoSV9k6KJCm3MmFYRERHv5vGjeADGjRvH8ePHeeSRRzh8+DApKSl8/vnn9QYn7mC1Gmw7nM3qXRl8+9tx1u85WWMl3NgWwQzsFMO5nVtxTscYOse1wM/P05JCREREvIMWC6zFybxi1vx6jJW/HGX1zmMcy606CiImPMgMSDq14tzOregc18Jmgq+IiIiYvKIFxRMdyizg/fX7WflLBj8eyKRy6BYW5M+gzq343RmxnNs5li6t1UIiIiLiKgpQKjmZX8y/l+2qeN09IYIhXeMY0i2O1A4xBAX4ubF0IiIizYcClEp6JEZyTWo7+ndoyZCurUmICnF3kURERJolBSiVWCwWZl/Vx93FEBERafbUZyEiIiIeRwGKiIiIeBwFKCIiIuJxFKCIiIiIx1GAIiIiIh5HAYqIiIh4HAUoIiIi4nEUoIiIiIjHUYAiIiIiHkcBioiIiHgcBSgiIiLicRSgiIiIiMdRgCIiIiIexytXMzYMA4Ds7Gw3l0RERETsVV5vl9fjdfHKACUnJweApKQkN5dEREREHJWTk0NUVFSd+1gMe8IYD2O1Wjl06BARERFYLBa7jsnOziYpKYn9+/cTGRnp4hJKOV1399B1dw9dd/fQdXePhlx3wzDIycmhTZs2+PnVnWXilS0ofn5+tGvXrkHHRkZG6hfYDXTd3UPX3T103d1D1909HL3u9bWclFOSrIiIiHgcBSgiIiLicZpNgBIcHMy0adMIDg52d1GaFV1399B1dw9dd/fQdXcPV193r0ySFREREd/WbFpQRERExHsoQBERERGPowBFREREPI4CFBEREfE4PhWgvPjiiyQnJxMSEkL//v1Zs2ZNnfuvWrWK/v37ExISQqdOnXj55ZebqKS+xZHr/vHHHzNixAji4uKIjIzk3HPPZcmSJU1YWt/h6O97ubVr1xIQEEDfvn1dW0Af5eh1Lyoq4qGHHqJDhw4EBwfTuXNn3njjjSYqre9w9LrPmzePPn36EBYWRmJiIjfddBPHjx9votL6htWrVzN69GjatGmDxWLhk08+qfcYp9arho+YP3++ERgYaLz66qvGtm3bjMmTJxvh4eHG3r17be6/e/duIywszJg8ebKxbds249VXXzUCAwONDz/8sIlL7t0cve6TJ082/vGPfxg//PCDsXPnTuOBBx4wAgMDjY0bNzZxyb2bo9e9XGZmptGpUydj5MiRRp8+fZqmsD6kIdd9zJgxxoABA4ylS5caaWlpxvfff2+sXbu2CUvt/Ry97mvWrDH8/PyMZ555xti9e7exZs0ao2fPnsbYsWObuOTe7fPPPzceeugh46OPPjIAY+HChXXu7+x61WcClHPOOce49dZbq2zr3r27cf/999vc/9577zW6d+9eZdstt9xiDBw40GVl9EWOXndbevToYcyYMcPZRfNpDb3u48aNM6ZOnWpMmzZNAUoDOHrdFy9ebERFRRnHjx9viuL5LEev+5NPPml06tSpyrZnn33WaNeuncvK6OvsCVCcXa/6RBdPcXExGzZsYOTIkVW2jxw5km+++cbmMd9++22N/S+88ELWr19PSUmJy8rqSxpy3auzWq3k5OQQExPjiiL6pIZe9zlz5vDbb78xbdo0VxfRJzXkui9atIjU1FRmz55N27Zt6dq1K1OmTKGgoKApiuwTGnLdBw0axIEDB/j8888xDIMjR47w4YcfcskllzRFkZstZ9erXrlYYHXHjh2jrKyM+Pj4Ktvj4+NJT0+3eUx6errN/UtLSzl27BiJiYkuK6+vaMh1r+6pp54iLy+Pa665xhVF9EkNue67du3i/vvvZ82aNQQE+MR/+ybXkOu+e/duvv76a0JCQli4cCHHjh3jtttu48SJE8pDsVNDrvugQYOYN28e48aNo7CwkNLSUsaMGcNzzz3XFEVutpxdr/pEC0o5i8VS5bVhGDW21be/re1SN0eve7n33nuP6dOns2DBAlq3bu2q4vkse697WVkZ1113HTNmzKBr165NVTyf5cjvu9VqxWKxMG/ePM455xwuvvhinn76aebOnatWFAc5ct23bdvGHXfcwd///nc2bNjAF198QVpaGrfeemtTFLVZc2a96hO3UrGxsfj7+9eIpo8ePVojmiuXkJBgc/+AgABatWrlsrL6koZc93ILFizg5ptv5oMPPmD48OGuLKbPcfS65+TksH79ejZt2sRf//pXwKw4DcMgICCAL7/8kvPPP79Jyu7NGvL7npiYSNu2bassL3/mmWdiGAYHDhygS5cuLi2zL2jIdZ85cyaDBw/mnnvuAaB3796Eh4dz3nnn8dhjj6mF3EWcXa/6RAtKUFAQ/fv3Z+nSpVW2L126lEGDBtk85txzz62x/5dffklqaiqBgYEuK6svach1B7PlZMKECbz77rvqE24AR697ZGQkW7ZsYfPmzRWPW2+9lW7durF582YGDBjQVEX3ag35fR88eDCHDh0iNze3YtvOnTvx8/OjXbt2Li2vr2jIdc/Pz8fPr2r15u/vD5y+oxfnc3q92qDUWg9UPgzt9ddfN7Zt22bceeedRnh4uLFnzx7DMAzj/vvvN2644YaK/cuHQ/3tb38ztm3bZrz++usaZtwAjl73d9991wgICDBeeOEF4/DhwxWPzMxMd30Fr+Toda9Oo3gaxtHrnpOTY7Rr18646qqrjJ9//tlYtWqV0aVLF+PPf/6zu76CV3L0us+ZM8cICAgwXnzxReO3334zvv76ayM1NdU455xz3PUVvFJOTo6xadMmY9OmTQZgPP3008amTZsqhne7ul71mQDFMAzjhRdeMDp06GAEBQUZ/fr1M1atWlXx3vjx440hQ4ZU2X/lypXGWWedZQQFBRkdO3Y0XnrppSYusW9w5LoPGTLEAGo8xo8f3/QF93KO/r5XpgCl4Ry97tu3bzeGDx9uhIaGGu3atTPuuusuIz8/v4lL7f0cve7PPvus0aNHDyM0NNRITEw0/vjHPxoHDhxo4lJ7txUrVtT599rV9arFMNTeJSIiIp7FJ3JQRERExLcoQBERERGPowBFREREPI4CFBEREfE4ClBERETE4yhAEREREY+jAEVEREQ8jgIUERER8TgKUERERMTjKEARERERj6MARURERDyOAhQRERHxOP8P7fAZlG+ZY4oAAAAASUVORK5CYII=\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -838,7 +838,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.004999999999999994\n"
+      "0.005000000000000001\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
index d7dd1acac..2ae901d83 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
@@ -1077,7 +1077,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1655,7 +1655,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1673,7 +1673,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1691,7 +1691,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1709,7 +1709,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1727,7 +1727,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1745,21 +1745,340 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31323/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
     {
-     "ename": "KeyboardInterrupt",
-     "evalue": "",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [8]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j, lmbd \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(lmbd_vals):\n\u001b[1;32m      9\u001b[0m     dnn \u001b[38;5;241m=\u001b[39m NeuralNetwork(X_train, Y_train_onehot, eta\u001b[38;5;241m=\u001b[39meta, lmbd\u001b[38;5;241m=\u001b[39mlmbd, epochs\u001b[38;5;241m=\u001b[39mepochs, batch_size\u001b[38;5;241m=\u001b[39mbatch_size,\n\u001b[1;32m     10\u001b[0m                         n_hidden_neurons\u001b[38;5;241m=\u001b[39mn_hidden_neurons, n_categories\u001b[38;5;241m=\u001b[39mn_categories)\n\u001b[0;32m---> 11\u001b[0m     \u001b[43mdnn\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtrain\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     13\u001b[0m     DNN_numpy[i][j] \u001b[38;5;241m=\u001b[39m dnn\n\u001b[1;32m     15\u001b[0m     test_predict \u001b[38;5;241m=\u001b[39m dnn\u001b[38;5;241m.\u001b[39mpredict(X_test)\n",
-      "Input \u001b[0;32mIn [6]\u001b[0m, in \u001b[0;36mNeuralNetwork.train\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     95\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mX_data \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mX_data_full[chosen_datapoints]\n\u001b[1;32m     96\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mY_data \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mY_data_full[chosen_datapoints]\n\u001b[0;32m---> 98\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfeed_forward\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     99\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbackpropagation()\n",
-      "Input \u001b[0;32mIn [6]\u001b[0m, in \u001b[0;36mNeuralNetwork.feed_forward\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     36\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfeed_forward\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m     37\u001b[0m     \u001b[38;5;66;03m# feed-forward for training\u001b[39;00m\n\u001b[0;32m---> 38\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mz_h \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmatmul\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mX_data\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mhidden_weights\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;241m+\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mhidden_bias\n\u001b[1;32m     39\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39ma_h \u001b[38;5;241m=\u001b[39m sigmoid(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mz_h)\n\u001b[1;32m     41\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mz_o \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mmatmul(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39ma_h, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moutput_weights) \u001b[38;5;241m+\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moutput_bias\n",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09166666666666666\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
      ]
     }
    ],
@@ -1804,7 +2123,52 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31563/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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Xq3K10jp9Kk0/zlujudOXFbh9QIC/ut93rbrc0kilo4vp2NFk/fbTJs2dvlzZ2dbc7dp2qqu7+rdVxaqllJaSqfWr9mjau0t06mSqEV/rqsIqWO5BAmKAui1q6qU5Q/Tn/FX6fOx81W9dW/1G3ymTn0lzJvxwwX2r1a+kMV8PVUBg3j+qrg901KCJ92nu2z9q/W9bVadZdT306t0KDjVr7luuJTdFQd2m1fTi9IH68/v1mjH+R9VrXl39RnSVn59Jc977+YL7VqtbXi9//rACAv3zvFeqXHG9tXCoDu5O1BtPfC5zcKD6De+qV2c9pkc7vy5LRpanvlKhU7dFDb00Z7BjDL8yX/Vb11K/F+6Uyc/PtTH81ZMFjOHrNOjt+zR34iLnMRwW5FtjuFl1vTjjUf357VrNeP071WtZU/1G3eYYw+/83wX3rRZbQS9/+Vi+Y7h46QhFlSmmKaO/1vY1e53eS05Kcet3KOyIsWfVbVpVL057UH/+sF4zxi9ynIeH3Sw/k0lz3r/wxaBqdcvr5U8fyhPfpMTTGnr7xDzb39Kvrdrf0kQ/z13h1u9Q2MU2qqSX3umtPxZv1ecf/Kp6jSur/+PXy89k0uxpf+a7zyPDblSXWxvry0/+0L9bD6lmTHn1feQ6lSlXXBNf/laS1K5zrJ4ff7d+nLdan33wq0qUDNN9j16vNz/ur8fvmaIsS7aRXxM+ggTEAH1G3a49m/dr/EOfSJLW/rJF/gH+umvozZr//uJ8f5ENCPTXbQ931n3P31HgL7p3Db1Zf3yzSp++NE+StOGPbapYM1q3P9zZp355u3fojdoTd0gThnwhSVr7+zYFBPqr5+OdNf+T3wqO7/3t1XdY1wLj2/fpm5WekqFne72vzJxtjh44oRenP6RaDStp66o9nvtShUyfkTlj+OGpkqS1S7fIP9Bfdz3pwhh+rlvBY/jJm/XH/PPGcI2yuv2hTr41hp/pqj1bD2rCE59Jktb+FqeAAD/1HHSD5n+0tOD4PnCd+o64TZYMS76fW6N+JUnS3z9uyDO752uIsWfd+2TOefjJLyVJa//Y7jgPP9ZJ8z/5XZbMAuLbv536PnNzvvHPsli1fX28U1uthpXU/pYm+vzNH7V19d48+xRl9z50nfbsOKLxL8yXJK35e5cCAvx11/1t9c3Mv2XJdE4UIiJD1LVHM0179xfNm/GXJGnDKkfMBg79n6ZPWqLTSWm6Z2AHrVz2rya9+t/FpAN7j+u9Lx9Wy/a1tfyXOIO+IXwJ94B4WKA5QA3a1tFf3611al/+7RqFRoSo/rW1892v+f8a6t6Rt2vOhB80ffTX+W7z/J1va9ror5zasizZCgzynbwy0Byghq1r6a+fNjq1L/9xg0LDg1W/RY1892t+fazuHXqT5k76WdNf+y7fba69qaEWz1mRm3xI0s5NB9Sn2Qs+lXzkjuHv1zm1O8Zw8IXH8IjbNOetHzX9xQLGcPeJmnbe+M7KsvreGL62lv76cb1T+/If1jvGcMua+e7XvHN93ftMV8199ydNH7sw322q16+oM6fSfPoXY4kYe1qg2V8NW9XUX/+3yan9v/Nw9Xz3a94xVvc+eaPmvrdE08d979KxHh/bQwd2HdWCqb9fabevKoGB/mrYrKqW/7rNqX3ZL1sVGhak+k2q5NknNDxIP85boxV/bHdqP7T/uCQpukIJmUwmrV+5Rz/NX+O0zcGcUtnyFaPc+TWKBKtMhfLnakMC4mHRVUvLHBSoQ7uOOrUf3uN4XaFmdL77/btur/o1GKY5E36Q9Zw6zXMd+DdBiQccJ4nwEmG68b726ty7jb7/5Fc3foPCLbpySQUGBejQnkSn9sP7jkmSKlQvne9+/27cr36tX9Kc937ON75lK0UpvFiojh48qcfG9tTczeP07a639NKnD6l0+RLu/yKF2H9j+IhT++GcmFeoUTbf/f5dt1f9Gg7PGcO2fLfJO4bbqXOva/X9J7+58RsUbtFVSikwKFCHdp83hvfmjOEaZfLd79/1+9Sv2fOa887/FXiOqFG/klJOp+n56Q9p3s63NX/PRI2c8oBKlIl075co5IixZ0VXLpVzHj7m1H443vGL7gXPw9eO0Zz3lxR4jjjXdbdfozqNq+ijlxbI5mNroUZXLCGzOUCH4p3voTuccz9SxSol8+xz9PApvT/uRx08b58218cqKytbh+JPyG636+O3F+uf33c4bdP2+rqSpH3n/e4CuIvXLzNmZ2fr559/1po1a3T48GFZLBaFhIQoOjpazZo1U5cuXRQQ4PVuXrbw4qGSpLQz6U7taWcyJEmhEcH57nci4ZTLx4htWVNvL3lOkuOXPl+6gTcsMkTSf/E8Ky0lU5IUGl5AfI+cvuDnFisZLkkaMOo27dgQrzce/1zFSoXr/pG36o2vBunRLq8rMz3/koyiJrzY2TF8XozPjuGcP4PzXfIY/vlZSY5f+r6d4kNjuFjOGE45fwyfPUcUEN+LjGFJql6vokqVK67/m7lcC6b8qsq1o9Vn+C16c+FTeqLza8pM840xTIw9K/c8nCe+FzkPH714fM/V/aGO2rp6jzav2HUZvby6hef8rpCWmunUnpYzvkLDglz6nLad6qpT14ZaOGulUs47p59VvnKUHnzyf9oZd1ir//K9WMMYXv3Nfv/+/Ro4cKCOHj2q2NhYlSlTRsWKFVNmZqa2bdumb775Ru+9956mTp2q8uXLe7Orl81kckyL2e35X62xu+EqzpH44xp20+sqWb6E+j7bTe/98aIGXzdGp3xg9RU/v5xpxwLCaCsg7hcTmHPD9KnjZzR24LTcP7+Efcc18bundP2dzfTTl39f1mdfbUx+Bo3hm19XyXI5Y/j30Rrc8RXfGMOms2M4/zjabBe/MlyQt5+coayMLO3eclCStHXlLsVvP6y3fhimzj1b6cfP879xtaghxp7133m4gPhe5nn4XLHNqqlmg0p6+YGpV/xZV6OL/S7hSozbdo7ViFe7a/PaeE2flP/CAJWqldK4D+9TVpZVrwybW+DxfJnNfvWVOxVGXk1AXn75ZVWsWFHz5s1TREREnveTk5M1dOhQjRkzRh999JEXenjlUk+nScp7he3szEdqcnqefS7VySOndPLIKUnSjjW7NW3967qxX/uLrk5UFKTkxO/8maTQcMfVoLTk/K/wXMzZK3mrf4tzOgFvX7dPZ06lqUa9ipf1uVeji4/htCs+htMYXrtH09aN870xHH7+GM654nmZY1hSnlWZJClu9R6lnE5TtXoVLvtzrzbE2LMKju+VnYfP1fbmRjpzKlWrf/PNG6JTz844nzfTERpqlvTfbFNB7uzTWg8++T9tWrNPLw2draysvCWFjZpV1Qtv9VJ6aqZGPvq5jh4+5Z7OA/nw6j0ga9eu1fDhw/NNPiQpMjJSw4YN0+rVqw3umfsc3psoa7ZV5as71xiXr+6om9+//fBlfW5IeLA63tVK5c773IS9x5RyKk2lK/jGjWMJ8cdlzbaqXNVSTu3lqzpqjvfvPJLfbq59rtWmQHPeHD0g0N/pxvSiruAx7Hh9RWO454XGsG/ca5Ow75hjDFc7L77VcsbwvwmX9blhkSH6X+/Wqlw7731mAYEBSvah9f2JsWcVeB6u4nh9uefhc7XoVE//LN7i0r0iRdHhg0mO83Al53s9yldy/Fsff959kOd6bMTNevjpG7X8lzi9MGimMvIpH+54YwO9OrmvTiQma2j/aXnuGwHczasJSGRkpBITC/5LI0mHDx9WcHD+9aNXg6zMbG3+61+1ua2pU3vb25vpTFKqdqy9vNWUbFabhr4/QD2H3OTUXvuaaoqMCteeLQcuu89Xk6zMbG1euVttbmrk1N62a2OdOZWmHRviC9jzwjLSLNq6yvG55yYhjdvUVkhYkLau2n1F/b6aZGVma/Pf/6rNrdc4tbe9vZnOnErVjrWXtxSmYwzfn88Yrup7Y3jFLrXp2tipve0tTRxjeP2+y/rc7KxsPf56b/UcdINTe+ubGik41KxNf/97mT2++hBjz8o9D9+Yz3n4dJp2bNh/RZ8fXixUFaqV1tY1vrP64PmyLNnavC5ebTrVdWpv17meziSna8eWQ/nud/+gzrq9V0t9M/NvvTby63xnPpq3raVhr9yhuI0HNPT+aTqeWPRLX6+Et1e7KiqrYHm1BKtHjx4aNWqUBg8erJYtW6pcuXIym82yWCw6evSoVq1apQkTJqhHjx7e7OYVmz3+e4377hk99/ljWjxzmWJb1lSPITdq+uivZcnIUmhEsCrHlFfCnmM6feKMS5+ZmW7RV+8s0j3Db9WZk6la//tWVagZrT6jbtfuTfv188yCn4xa1Mx5d7Fem/O4nv3ofv08d4XqNq2m7o9cr+mvfeeIb3iwKteOVsK+4zp90vUHg3067nu9+fVgjZnxsL6Z8quKl4rQgGdv0/Z1+7Ti580e/EaFz+zx32vct8/ouc8f1eIvljvG8OAbNf3Fef+N4TrllbD3csdwitb/HqcKNcuqz8izY3i5h79V4TFn4k967evBevaTB/Xz7H9Ut3l1dX+8i6a/svC/MVynnBL2HdPpE66N4cz0LM374Gfd83RXnTp2Rmt/26qqsRXU55lbtHLJZm34c/vFP6QIIcaeNee9JXpt1qN69sP++nnuStVtWlXdH+6o6eO+lyUzS6HhQapcK1oJ8cd1+hJnhqrFlJMk7d/p2ysyzZr6p17/6D499+ZdWvztOsU2qqwe/a7VtHd/kSUzW6FhQapcvbQSDp7U6aQ0Va8drbv6t9GOrYf0589bFdPAuXR4/55jysqyaujo25SWZtGcqX+qcjXnFcuOH00mIYFHeDUBGTRokPz8/PTGG28oLS1vHXlYWJjuvfdeDRkyxAu9c5+Nf27T2D4fqO+z3TR61iCdOJykqc9/pfnvL5Yk1WxURW8uGqm3HpmqJbP+cvlzvxz3rZKOntYtD16vbo910ZmkVP25YLU+f2W+sjJ958mlG//eqVcfmq4+T9+k0VMH6viRU5o29lvN/9ixlGuNBhX15teD9dbQmfrl61Uuf+72dfs04q731G/ELXru4weUmW7RP4s3a+orC31uCciNf27X2L6T1XfU7Ro96wmdSDilqS987TyGfxyhtx6ddmlj+PXvlJR4Wrc8cL26PXrOGB67wLfG8PIdenXAx+oz/BaN/uxhHT9yWtNenq/5Hy2VJNVoWElvLnhKbw3+XL9cwtOfZ47/UUnHzqhr//a6dUAHnUlK1aIZyzRzfNG/t+Z8xNizNv69U68+/Kn6PHWTRn/ygI4fPaVpr36n+Z/8LsmxXPGbXz2ht56apV/muX4elhxPm5eklNNXfr/Z1Wzj6r165Zm56vtIR734dm+dSEzW1HeW6JsvHAui1Iwpp/FT79eE0Qu05PsNatuprvz8/FSnXgW9O2Ngns8b9uCnMvmZVLK0Y8nocR/1y7PNFx/9pplTfvfo94JvMtkLwRIHWVlZ2rZtm44ePar09HQFBwcrOjpaMTExMpvNbjvOjZH3u+2zkJcpMv97eeA+9jOuz+Dg0pmCXVvKEijUghjHnmQrWczbXSjyFq9/2dtdKNDq/VW93YV8Na+8z9tduCSF4gEbgYGBatiwobe7AQAAAMDDeBI6AAAAAMMUihkQAAAAoLDjQYTuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAuuxof+FUbMgAAAAAAwDAkIAAAAAMNQggUAAAC4wGrn2r07EEUAAAAAhiEBAQAAAGAYSrAAAAAAF9i4du8WRBEAAACAYUhAAAAAABiGEiwAAADABTyI0D2YAQEAAABgGBIQAAAAAIahBAsAAABwAQ8idA+iCAAAAPgom82mSZMmqV27dmrUqJEGDBig+Pj4Arc/cOCAHnnkEbVo0UJt2rTR2LFjlZ6efknHJAEBAAAAfNTkyZM1Z84cjR07VnPnzpXJZNLAgQNlsVjybHvmzBn17t1bp0+f1tSpU/XRRx9py5Ytevzxxy/pmCQgAAAAgAtsMhXKn8tlsVg0ffp0DRo0SB06dFBMTIwmTpyoo0ePasmSJXm2X7BggVJSUvTBBx+oYcOGatCggSZOnKi///5ba9ascfm4JCAAAACAD9q+fbtSU1PVqlWr3LbIyEjFxsZq9erVebbfu3evqlevrqioqNy2cuXKqUSJElq1apXLx+UmdAAAAOAq1qlTpwu+v3Tp0nzbjxw5IsmRRJyrTJkySkhIyLN96dKldezYMVmtVvn7+0uSUlJSdPr0aZ04ccLl/jIDAgAAALjAKr9C+XO5zt48bjabndqDgoKUmZmZZ/uuXbvq9OnTeu2115Samqrk5GS9+OKLMplM+d4zUhBmQAAAAICrWEEzHBcTHBwsyXEvyNn/l6TMzEyFhITk2b5KlSp67733NHr0aH355ZcKDg5W3759Vb9+fYWHh7t8XBIQAAAAwAedLb1KTExU5cqVc9sTExMVExOT7z4dOnTQH3/8oWPHjikiIkLBwcG69tprdeedd7p8XEqwAAAAABdY7X6F8udyxcTEKDw8XCtXrsxtS05OVlxcnJo1a5Zn+7Vr16pPnz6yWCwqXbq0goODtWrVKiUlJenaa691+bjMgAAAAAA+yGw2q0+fPpowYYKioqJUoUIFjR8/XtHR0erSpYusVqtOnjyZO9NRo0YN7dy5U6+99poeeOABHThwQMOHD1evXr1UqVIll49LAgIAAAD4qMGDBys7O1vPP/+8MjIy1Lx5c02bNk1ms1kHDx5Up06dNG7cON15550qXry4Pv74Y40bN0633nqrSpQooV69eunRRx+9pGOa7Ha73UPfp9C5MfJ+b3ehSDNFRni7C0We/UyKt7tQpJmCg7zdBeDKBTGOPclWspi3u1DkLV7/sre7UKBv9zT2dhfydXv1Dd7uwiXhHhAAAAAAhiEBAQAAAGAY7gEBAAAAXGC1m7zdhSKBGRAAAAAAhiEBAQAAAGAYSrAAAAAAF1i5du8WRBEAAACAYUhAAAAAABiGBAQAAACAYbgHBAAAAHCBzc61e3cgigAAAAAMQwICAAAAwDCUYAEAAAAuYBle9yCKAAAAAAxDAgIAAADAMJRgAQAAAC6w2k3e7kKRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAtsXLt3C59KQLa/H+PtLhRp5jCLt7tQ5FlSKni7C0VaVOkz3u5CkZeZ5VP/7HhF6qkQb3ehSHu4+R/e7gJw1SONAwAAAGAYLkUBAAAALrDauXbvDkQRAAAAgGFIQAAAAAAYhhIsAAAAwAU28SBCd2AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFrILlHkQRAAAAgGFIQAAAAAAYhhIsAAAAwAVWrt27BVEEAAAAYBgSEAAAAACGoQQLAAAAcIHNzoMI3YEZEAAAAACGIQEBAAAAYBhKsAAAAAAXsAqWexBFAAAAAIYhAQEAAABgGEqwAAAAABfY7Fy7dweiCAAAAMAwJCAAAAAADEMJFgAAAOACq3gQoTswAwIAAADAMCQgAAAAAAxDCRYAAADgAlbBcg+iCAAAAMAwJCAAAAAADEMJFgAAAOACVsFyD2ZAAAAAABiGBAQAAACAYSjBAgAAAFzAKljuQRQBAAAAGIYEBAAAAIBhKMECAAAAXGClBMstiCIAAAAAw5CAAAAAADAMJVgAAACAC2w8iNAtmAEBAAAAYBgSEAAAAACGoQQLAAAAcAGrYLkHUQQAAABgGBIQAAAAAIahBAsAAABwgc3OKljuwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAusXLt3CxIQg3QoX01PN26nWsVL6URGmmb9u0GTt6y44D4dK1TXkEZtFFO8tJIyM/R/+3fozfV/Kj07K8+24YFm/d+tA/TOxuWat3uLp75GodWubA09We861YworZOZqZqzd52m7PjrgvtcF11TT9Rtr9rFyuhUZroWH96mt7f8pnTrf/H9q+tQlQ4Oz7PvtT+8reOZqW7/HoVZh/LV9HSTc8bwDhfHcONzxnD8RcbwbQP0zgbfHMPXlqqlx+p0VrXw0jplSdO8/av06e4/L7hP29K19VCt61UzoqxOW9K09MhWvf/vEmWcM4ZvrdBEfau3VaXQKB3PTNGPh9Zr6q7flW23eforFTpty9TUoLrXq0Z4aSVZUjV33xpN3bn8gvu0L1tLj9W5TrUiy+iUJV1LDsfp3W1LlW7NUvmQ4lryvycL3HfB/vV6fv23bv4WhRfnCM87uC5N62ed1KkDFgUX81edGyLV4M7iMpnyvy/BZrVry8JT2rn0jNJPZiuiXKAadi+ham3z/rt21qrpxxX3/Wn1X1DDU18DIAExwjWlK+iTjt31w75temvDMjUrU1HPNGkvk8mkDzb/k+8+nSrW0MfX3an5e7bqjXV/qFaxUhrWpL2igkM1ZNn3TtsWMwdr6vXdVTG8mBFfp9BpElVRH157t346sFXvbP1dTUtW0tB6HWWSSR/tyP+Xi47lamly67u0MH6TJmz5VTUjS+mpetcryhymp1cvkCSVDApT6eBwvbbxZ60/edBp/1OWdI9/r8LkmtIV9Mn1OWN4/TI1K1tRz1zjwhjumDOG1/6hWsUZwwVpWLySJja7Vz8nbNHkHb+ocVQVPV67s/xk0rTdf+S7T/sydfRW03v146ENem/Hz6oeXlqP1+6iEkFhem7D15Kk3lVba1hsVy1J2KJ3tv+fSgSG6eHa16tmRLSeWTfLyK/odY1LVNL7LXvrp0Nb9N62X3VNVGUNqdtJfiaTPv53Wb77XFe2tia17KXvDmzUxLhfVCOitIbU7aSooDANX/uNjmWeUe8/p+bZr3e15rqpQn3Nj1/v6a9VaHCO8LzE7Rn6dVyCqrYJV5N7opS4LV3rvjwpu01q1LNEvvtsmHNSm+efUqO7SqhMTLDi/0nVH28dlclPqnpt3iTkyNZ0bfvxtKe/CkACYoQnG7VRXNJRPfXXj5KkPw7vVaCfnx6t31JT41Yr05qdZ5/RzTvpp/3/atjfiyRJ/xzZL3+TSf3rNlWwf4AycvbpUqmmXmzeWWGBZuO+UCHzRGx7bT91RMPWOK40Lju6WwF+/nqozrX6dOcKZdryxve5hv/T4kPbNWqt4x+5Fcf2yc/kp/tqNM+Nb2zxaEnSz4e363Cab5+Qc8fw8nPGsMlPjza4wBhukTOG/3JhDLforLAA3x3DD9e6XjuSj+iFjfMkSX8f36kAk5/612ivmXv/yncMP123q5Ye2aqXNs2XJK0+sUd+Jj/1qtJawX6Bstiy9VDNjvrn2C6NWD8nd7+45EP6pv0QtSxVQyuP7zbmCxYCj8V00PbTRzRqneMCw/LEXQrw89ODtdrq813/5BvjEQ1u1JLD23JnMVYe3ys/k0n3Vm+pYP9AZViztCnJ+eJEveLldVOF+nonbqnWndzv+S9WSHCO8LwNc08qqmqQ2j9ZVpJU8ZpQ2azS5vlJqndbMQUE5S0N2rn0jKq1C1fju6MkSeUbherE3kxt/+l0ngQkK8Omv95LVEgJf6WdsHr+C12lWAXLPShk8zCzn79alq2kxfv/dWpfFL9D4YFBalGmYp596kWVUZWIEvp8+1qn9k+3r1WHBR/nnpQjA4P0UYc7tPLoft33y1ee+xKFWKCfv1qWqqKfD213al98KE7hgUFqVqpynn3qFotW5fAozdy1yql9xq5V6rz4g9z41i1WVqct6T6ffJj9/NUyupIWxxcwhsteYAxvO28Mb1urDvPPG8PX3aGVR3x7DDeNqqZfj8Q5tf9yZKvCAoLUJKpqnn3qRJZTpbAozd3nXN4ye98/uv2Pt5Vhy1JUULiKmUP1Z6Lz3429KceUlJmqdqXruP27FFaBfv5qXrKqfknY5tT+8+E4hQUEqWnJKnn2iSkWrcphUfpyz0qn9pl7VuqmXyY5lbmd64WGXbXnzDHN2J3/Vf+iiHOE51mz7DqyJV2VW4U5tVdtHabsDLuObsvIdz9bll3mEOdf9YIj/JV5Jm8J5prPTiikRIBqXR/pvo4DBWAGxMMqRRRXkH+A9iQnObXvO+N4XS0ySssS9jm9F1vCcXUjw5qtadd3V5voKsq0WrVg71aNW/ObMm2OKxPp1ix1+W6a9iSfVMUw3zxhVA4rIbN/gPalnHRqj0/JiW9ElP5K3OP0Xt3i/8V3yrV3q3WZasq0Zuu7/Zv1xuZfZMmJb93i0UrOytD7rXqqdZmq8jP56feEnXpt0886lpFiwLcrHFwaw4f3Ob0XG3XeGC6XM4b35DOGv/XtMVwxJEpm/wDtTz3u1H4g9YQkqUpYSa04vsvpvTqR5SRJGbYsvdusj5qXrCGLLVuLDm3QO9sXy2LLVkpWhrJsVpUPKe60b0RAsCICg1UhNP+SjaKoUujZ88QJp/b9qY7zRtXwkvr7mPNsUEwxxwxopi1bH7S8R61KO84TPxzcpAlbl8iSz4xJ1woN1KBEBfVf/plssnvo2xQ+nCM878yRLNmypWLlA53aI8o5XicfzlKFxnn3i72tuDbPT1LF5mEqExOsA6tTdWh9mpr2iXLa7vCGNO3+/Yxufaui9izznX/f4D0kIB5WLDBIkpSSlenUnpplkeS4qe58UcEhkqQp192h7/bGaerW1WpYKlpDG7VVqeBQPfHnd5KkLJtNe5JP5tnfl0ScjW/2efHNeR0eEJRnn6igUEnSB6176vsDWzV95wo1KFFeg2M7qGRQmJ5c5ShpqVu8rMqGROqrvev12c4VqhFZSoNjr9PM9vep29JPnG5WL8qKmS9jDAfljOGOd+i7PXGaGrdaDUtGa2hjxvD5IgKDJeUdw2lWR3zDAoLz7FPC7BjDb11zr/7v8EZ9secv1SteQQ/X6qQoc7hGbpirDFuWliRs1t1VWmlPSqJ+PRKnqKBwDYu9Wdl2m0L8faecpaAYp2afjXE+5wmz40rzuy3u1qKDm/X57r9Vv3gFPR5znaKCwvTMmnl59ulf81qtO7Ffq0/sc/M3KNw4R3ieJdUxYxEY6jybEZgzu5GVlv+iEnW7FtPRben65ZWE3LZanSJU/47/LkBYUq3664Njatw7SsUq+M554XLZKB5yCxIQDzu7MoW9gIth9nyukgX6+UuSFu//V6+vc9yA+s/R/fIzmTTimuv09oblnJBz+OXGN/8A2/JpPxvfJYd3aMKWpZKklcfi5SeTnmnQSe/G/aG9KSc0cs13yrRate30EUnSmhMHtDP5mOZcd7+6VWmo2XvW5vnsosiki4zh/GLsn88YPpIzhpsyhs/13+o1ro/hAJPj1P3b0ThN2vGzJGnNyb0yyU+DY/6nD3cuVXzqcb265TtZbFa90KCbXmx4p9KzLfp8zzIF+5uVnpPg+IKLnScudB5emrBdb8f9IkladXyf/EwmDY3trPe3/+Y0o9IkqpJii5fTEytnu7v7hR7nCM/LjWFBtx/k027Nsuun5w4pPcmq1o+UUrEKZh3dlqFN85IUEOynlg+WkiStmn5CoSX9Ve9W373B39fZbDa9//77+vrrr5WcnKymTZvqxRdfVJUqectTJenYsWMaN26c/vrLsdpoq1atNGrUKEVHR7t8TNI4D0u2OK4IRZx3BejsTeNnLJl59jl71ejXg84lAX8c2itJio0q4/Z+Xq3Oxjc80PkK5tkrmmey84lvzlXP3xJ2OrUvO+qI99kSrQ0nD+UmH2etO3FQyZYMxRQr64beXx2Sc65qRpgLGMNZjOErcSbLUbt9/lX40JwZipTsvLXdaVZHzJcl7nBq//uYowa/TqTjH4F0q0VjNi9Qu5/Hqsefk9Rp6Th9vOs3lQsprtNZvrOSW3JOjPOeJ86O4bwxPjuL+scR5/salh91lMPFRDr/Q/u/8rE6bUnXsqPO5xVfwDnC88xhjoTt/JmOrHRbzvt5f52L/ydFSfssaj+0jOrcUEzR9UPUqGcJNetXUtt+PK2k+EwdWJ2qvctTdO1jZWS3O5btVc4hbFa77DbfKSX0ZZMnT9acOXM0duxYzZ07VyaTSQMHDpTFkv+FqqFDhyohIUGffvqpPv30Ux05ckSPPfbYJR3T6zMgffv2LXD96vPNmDHDw71xv/1nkpRts6lKpHO9ddUIx+udp0/k2WdvTt2sOecK0VkBfo4TTEZ23tpjX7U/9aSybTZVDneuZ60S7ojvruRjefaJz7lfpMD4WrMVERik/5WP0YaTh7T7jHNtfqCfv5Iy09z2HQq7/ck5YziigDF8Kp8xnFMLbvYrOMZwOJh2Utk2qyqFlnRqrxTmeL0nJTHPPvtz7g/JG1/H67PxbVemjpKz0rUxaX/u55Qwh6lscKS2nz7s3i9SiB1IdYzhymHO54mzr3efucB5ooAxfP6qWR3K1tbShO0++XwVzhGeFxEdIJOfdCbBufT37OviFfOWTqUcc8SwTIxzGWd0PcfrUweydHBdmqwWu74dciDP/jN67FGNjhFqN5hk8FzWIrYKlsVi0fTp0zVs2DB16NBBkjRx4kS1a9dOS5YsUdeuXZ22T05O1urVq/Xhhx8qNjZWkvTQQw/pscceU1JSkkqUcO3+Qq/PgLRu3VqrV6/WiRMnVKFChQv+XI0ybVatOnpAN1au7dR+c5U6Op2ZoQ3HE/Lss+roAaVmWXRbtVin9s6VainLZtW6Y4c82uericVm1erj8fpf+Rin9hsqOK5GbjqZ95es1cfilZpt0S0V6zu1X1+ujrJsVq0/cVBZNqteanKzHq7TxmmbzuXrKCQgUKuOx7v/yxRSHhnDiYzhsyy2bK0/Ga/ro8+LVXQ9JWela+upg3n2WXdyn9KyM3VD+YZO7R3KxCjLZtWmU47lX3tUbq6hMTc6bXNv1WtltdvzzJ4UZRZbttaeiFfncnWd2s/OWmxOyjse156IV1q2RTdXbODU3jHacZ7YcPK/X9iKBYaoSnhJrfehZXfPxTnC8wLMfiobG6z4FalOJW37/kmVOcxPpWrlvY+pWAXHDernr5CVuD1nRrBMgBr3KqFbxldw+qndJUKSdMv4Cmrcy3cWq/BV27dvV2pqqlq1apXbFhkZqdjYWK1evTrP9kFBQQoNDdXChQuVkpKilJQUffvtt6pataqKFXO9jM/rMyCPPfaYQkNDNWnSJE2ZMkUVK+Zdru9q997mv/Vll176oP3t+nrXZl1TpoIeqtdSr6/7XZnWbIUHmlWrWCnFn0nSycx0pWVn6e0Ny/VC8+t1OjND/7f/XzUtXUGP1GupT7et1clM3ymdcMWH25frs3Z99G7L7vpm3wY1KVlJD9ZurfFblirTlq2wALNqRpbW/pQkJVnSlGbN0qS43zWq4f+UnJWunw9tV5OSlTSwzrWasWuVkiyO2Y1P/v1bT9Rtr+OZKVp2ZLfqFCurQbHt9VvCv/o7ca+Xv7Wx3tv0t778Xy990CFnDJeuoIfqt9Tra10Yw5YM/V/8v2papoIeqc8Yzs/U3b/rwxb99UaTXvr24Fo1Kl5Z91Vvq0nbf84Zw0GqHl5aB9JO6pQlTelWiz7cuVRP171ZZ7LS9euRODUsUVn9a7TT7H3/6FTOGJ69b4Umt+ivZ+rerD8St6t5yeoaULODpu/+Q4fSky7Sq6Jlyr9/auq19+ntZj01f/96NYmqpPtrttHbcUtyY1wjorQOpJ7MOU9Y9P723zS8/g1KzkrXksPb1CSqkh6o1VYz96zMPU9IUq1IxxXi/GZSfAXnCM9r1LOEFr+UoN/HH1WtThFK3JGpLQtPqVnfKAUE+cmSZtOpAxZFRgcquJi/KjUPU6naQVo28WjuDebH/nXcA1KpeahK13bMhESUcV5Z68Aax9guVTPvAhgoeo4ccZSalytXzqm9TJkySkjIe/EgKChIr776qsaMGaNmzZrJZDKpdOnSmjlzpvz8XJ/XMNkLuivPYA8++KCKFy+uCRMmeOwYVWe84bHPvpgbKtXSk43bqnpklI6mpWjGjnWaGufILFuVraQ5N9yjZ/76UfN2b8ndp2eNBnowtrmqRpZQYlqKZu/cqA+3rMj3VtWKYZFa3v3RPJ9hJHOY925q7VK+jgbFdlD18JI6mnFGX+5eo+k7Hc9IaFGqimZ2uE8j1nyrBfGbcve5s0ojDajVSlXDo3Q044y+2rteH+/4Kze+Jkn3VG+m3tWbqnJ4CZ3KTNf3B7ZoUtwf+T60zAiWFO+tUHJD5Vp6slFbVS+WM4a3nzeGb7xHzyw/bwzXPG8M/3uRMdzj0TyfYaSo0me8clxJ6li2rh6p1UlVwkopMTNZX8Wv1My9jhv8mkZV0yetHtCLG7/R94f+e7r2bRWvUZ9qbVQ5tKSOZZ7R/AOr9dnuZU43Vd9QrqEerNlB5UNL6Ej6KX0Vv0pz41fkOb5RMrO8d92rU7kYPV6no6rlnCdm712lz3Oe19G8ZFV91ra/nlu3UAsPbMjdp1vlxupf41pVCYtSYsYZfR2/VtN2/uUc4/L19Hbznrpl6fvam3L8/MMaLvVUiFeO6wvnCEl6uPkfXjt2/IoUbZiTpNOHLAotGaCYm4qp/u3FJUkJW9K1+IXDajOodO6zPCxpNq378oTi/0lVZopNEWUDVOO6CNW7rbj8A/MvJVo/56Q2zk1S/wU1jPpaeYyKXeS1Y1/MkPW9vd2FfG15Jm+57rmWLl2ab/u3336r4cOHa9u2bU4JxPDhw5WYmKjPPvvMaXu73a533nlH//77rx588EFZrVZNnDhRKSkpmj17tsLDw+WKQpOAHD16VHFxcerYsaPHjuHNBMQXeDMB8RXeTEB8gTcTEF/hzQTEV3grAfEV3kxAfAUJyKW73ARk8eLFGjx4sDZu3Kjg4P9mvYYMGSKLxaIPP/zQafsffvhBL7/8sn777bfcZOP06dPq2LGjhgwZon79+rnU30LzL0HZsmVVtqzvrCwEAAAAuENBCcbFnC29SkxMVOXKlXPbExMTFRMTk2f7tWvXqlq1ak4zHcWKFVO1atW0b98+l4/r9ZvQAQAAgKuBze5XKH8uV0xMjMLDw7Vy5crctuTkZMXFxalZs2Z5ti9Xrpzi4+OVmfnf8trp6ek6ePBggc8NyQ8JCAAAAOCDzGaz+vTpowkTJmjp0qXavn27hg4dqujoaHXp0kVWq1XHjh1TRoZj9bRu3bpJkp588klt3749d3uz2aw777zT5eOSgAAAAAA+avDgwerRo4eef/559e7dW/7+/po2bZrMZrMSEhLUtm1bLVrkuC+nTJkymjVrlux2u/r166f7779fgYGBmj17tiIjI10+ZqG5BwQAAAAozKwqWg8ilCR/f38NGzZMw4YNy/NexYoVtWOH83OjatSooY8++uiKjskMCAAAAADDkIAAAAAAMAwlWAAAAIALbPaiV4LlDcyAAAAAADAMCQgAAAAAw1CCBQAAALjgSh76h/8QRQAAAACGIQEBAAAAYBhKsAAAAAAX2Irggwi9gRkQAAAAAIYhAQEAAABgGEqwAAAAABdYeRChWzADAgAAAMAwJCAAAAAADEMJFgAAAOACHkToHkQRAAAAgGFIQAAAAAAYhhIsAAAAwAU2VsFyC2ZAAAAAABiGBAQAAACAYSjBAgAAAFxgEyVY7sAMCAAAAADDkIAAAAAAMAwlWAAAAIALWAXLPZgBAQAAAGAYEhAAAAAAhqEECwAAAHCBzc61e3cgigAAAAAMQwICAAAAwDCUYAEAAAAuYBUs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFNlGC5Q7MgAAAAAAwDAkIAAAAAMNQggUAAAC4gFWw3IMZEAAAAACGIQEBAAAAYBhKsAAAAAAXUILlHsyAAAAAADAMCQgAAAAAw1CCBQAAALiAEiz3YAYEAAAAgGFIQAAAAAAYxqdKsJZ1esfbXSjSrHZv9wC4Mlliat3T/MWJwtPK+Qd7uwtF2kFrpre7AC+iBMs9mAEBAAAAYBgSEAAAAACG8akSLAAAAOBy2SjVdQtmQAAAAAAYhgQEAAAAgGEowQIAAABcwCpY7sEMCAAAAADDkIAAAAAAMAwlWAAAAIALKMFyD2ZAAAAAABiGBAQAAACAYSjBAgAAAFxACZZ7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4AJKsNyDGRAAAAAAhiEBAQAAAGAYSrAAAAAAF9gpwXILZkAAAAAAGIYEBAAAAIBhKMECAAAAXGATJVjuwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAt4EKF7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4AIeROgezIAAAAAAMAwJCAAAAADDUIIFAAAAuKAoroJls9n0/vvv6+uvv1ZycrKaNm2qF198UVWqVMmz7Xvvvaf3338/38+58847NW7cOJeOyQwIAAAA4KMmT56sOXPmaOzYsZo7d65MJpMGDhwoi8WSZ9sBAwZo+fLlTj9PPvmkgoOD1a9fP5ePSQICAAAA+CCLxaLp06dr0KBB6tChg2JiYjRx4kQdPXpUS5YsybN9WFiYSpcunfuTnp6uKVOmaOTIkYqJiXH5uCQgAAAAgAvsdlOh/Llc27dvV2pqqlq1apXbFhkZqdjYWK1evfqi+7/++uuqVauW7r777ks6LveAAAAAAD7oyJEjkqRy5co5tZcpU0YJCQkX3Hfz5s1aunSpPv/8c/n5XdqcBgkIAAAAcBXr1KnTBd9funRpvu3p6emSJLPZ7NQeFBSk06dPX/AzP/vsMzVq1Mhp9sRVJCAAAACAC4raKljBwcGSHPeCnP1/ScrMzFRISEiB+6WlpWnJkiV68cUXL+u4JCAAAADAVaygGY6LOVt6lZiYqMqVK+e2JyYmXvCm8mXLlslms6lLly6XdVxuQgcAAAB8UExMjMLDw7Vy5crctuTkZMXFxalZs2YF7rd27VrVq1dPkZGRl3VcZkAAAAAAF9jt3u6Be5nNZvXp00cTJkxQVFSUKlSooPHjxys6OlpdunSR1WrVyZMnFRER4VSitX37dtWuXfuyj8sMCAAAAOCjBg8erB49euj5559X79695e/vr2nTpslsNishIUFt27bVokWLnPY5fvy4ihcvftnHNNntRS2XK9iBQ+UuvhEum9VnRhKKqiwVrZsLCyN/caLwtHL+wRffCJftoDXT210o8mpVPOztLhSo+U/PersL+Vp902ve7sIloQQLAAAAcIGNC1VuQQkWAAAAAMOQgAAAAAAwDCVYAAAAgAvsRexBhN7CDAgAAAAAw5CAAAAAADAMJVgGWbXKX59ND1Z8vJ+KFbPrltss6t3bIlMBM3kWizTj8yAt/SVQp0+bVKmyTXfdlalOnbOdttu/30+fTAnSxo0B8g+wq2EDqx5+NEPly/vWUperV/nr80+DtT8nvl1vtejui8R35gxHfJNz4tujZ6auPy++vXqEKykpb54+++sziooixu6I8f79fpr2cZA2bQyQv79dDRpa9dAjGSrnY2N47Sp/ffFpkA7E+ymymF033ZqlnheIb5ZF+nKGWb/nxLdiZZvu6GlRx/Pi26dHmE7lM4a/+DpFJXxsDK9Z5a8Z54zhm2+16K6LjOEvZwTp13Ni3D2fMXxPAeeJL33sPPHXSpM+mOavPfEmlSgu9bjNqgH32C4Y348+89ePS/x06rRUtbJd991tU9cuNqftfl1m0idf+GvffpNKRUld/2fVA/faFBjo+e9U2HCe8D4bJVhuQQJigK1b/DX6+VBdd12W+g/I0JbNAfp0WpDsNunePpZ893n1lRCtWBGgnndZ1OSabO3a6a+Jb4fo9OlM3dndsU9ioklDBoeqUkWbnn0uXZmZ0qfTgzRyeJg+mZaioCAjv6X3bN3qr5deCFWH67LU7/4Mbd0SoM+mB8lml+65N//4jhsbopUrAtTjLosaN8nW7l3+eneiI7535MQ36aRJSUl+evjRDNWNtTrtHxnpWydkT8U4MdGkpwaHqmIlm0Y8my6LRfp8epBGjQjTlKm+M4a3bfXTKy+EqN112ep7f6bitvjri+lm2e3S3QXE942xwVq9IkB33GVR4yZW7d7lpw8mBiv5dKZu754lyTGGTyX56cFHMxRz3hiO8LExHLfVXy+/EKr212Xpvpwx/HnOGO5dQIxfHxuiVSsC1P2cMfzexBAln85Ut/POEw/lE2NfOk9s2GLSkOcCdENHmx5/wKr1m/30/lR/2WzSwL62fPcZMSZAy/4x6b67bWpxjU3bd5k09i1/nTot3dvDsc8/a0x6erTjcwc/ZNWuPSa994m/kk6ZNOpJa76fW1RxnkBRQgJigBkzglSjhk0jn82QJLVoYZXVKs2ZHaQePS15fsnaudNPf/0VqAEPZOT+cte0qVXBIXZ9MiVY/7vBovBw6fPPghQaIr05IU3BOc+dii5n0+jnQ/XvDn81aOgbJ+cvZwSpeg2bho9yxLd5C6uys6WvZgepe4+88d21009//xWo/gMycn/xuKapVcHBdk39OFhdcuK7a5fjalCbdlkqW9a3T8KeivEXnwcpNFR6ffw5Yzjaphdf8K0xPGtGkKrVsOnpnPg2zYnvvNlmdcsnvrt3+mnFX4G6b0Cm7sqJb+OmVgUHS59+HKRON2QpPFzakzOGr22XrTKMYVWvYdOwnBg3y4nx17ODdGcBY/ifvwLVb0CGeuXEuEnOGJ72cbA654zh3bkx9u3zxJTP/VWnpl2vPuf4O9umpVXZVunTWf7qe5dNwefFd/tOk35b7qcnHszWg30cyUarZnaFBEvvfOSvW2+wKTJC+vYnP0WXkV59zip/f6l1M7tOJpk0c56fnnnCqkAf+i2G8wSKEu4B8TCLRdq00V9t22U5tbdrn6X0dJM2b/LPs8/+/Y4/llatnadIGzW0KiPDpA3rA2S3S8uXBeqmmy25v7hJUp06Ns39OsVnfnG7WHy3bHY9vg0aOeK7cYPjX7Q9u/0VHm736V8qJM/F2G6X/loWqBtuch7DtevYNPsr3xnDWRZp80Z/XdvOOVZt2mcrPd2krfnE90BOfFucF9/6OfHddM4YDgu3+/wvFWfHcJvzxnDbC4zhszFuyXnioiwWac0Gkzq1c57p6NzBprR0k9Ztyluysife0dbhWue4NW1kV3qGSWs2ON7PyjIpJMQu/3P+iIoXsysry6S0NDd/kUKM80ThYbcXzp+rDQmIhyUk+Ckry6SKFZ1PzBUqOF4fPJj3j6B4McdIOnrE+b3Dhx2vjxzx05EjJqWmmlS2rF2T3g3WHd3CddMNEXr+2RAdPeo79YlHcuJb4bz4lr9AfIsVEN+Es/FNcPx39y5/hUfYNebFEN1xW4Ru7xqh114J0YkTvhNfyXMxPnp2DEfb9f67werRLVy33Bih0c+FKNHHxnD2BeJ76ILxdY7TkcOO10cTHP/ds8tP4RF2vfpisO66LVw9uobrjVeCddIHx/Dlxzj/MXz0vPPEKy+GqPttEbqja4TGvRLiUzE+mOBIFKpUcv4tqHIFx+v9B/LGokRxx3uHj5z3WYcd/z2UM4Z73WHV/oMmfTbHT8lnpE1bTfpynr/atrKpWKSbv0ghxnkCRY3XE5C9e/fqvffe09ixY/XHH3/keT8lJUWjRo3yQs/cIzXF8Rc4NMz5xBwa6vhvWlrev+ANG1lVrpxNH7wfrHXr/JWaKm3e5K+pnwTJz8+ujAzp9CnHflM/CdLx4yY991y6nn4mQ7t3++uZp8KUnu7Z71VYpJyNb2gB8U0tOL6TPwjW+nPiO+2c+ErS7t1+On7MpNp1rBozNk0PP5qhTRv9NWxoqDJ8JL6S52J86rRjv2k5Y3jU8+ka+rRjDA9/OsxnYpyS4vjv+fENyYlvej7xrd/IquhyNn38QbA2rPNXWqq0ZZO/Ps2Nr2Ofvbv9dOKYSbXq2DR6bLoefDRTmzf6a6SPjeHUyxjDDXJi/NE5Y3jLJn9NP+88seec88TLY9M08NEMbd7or+E+FOMzOfENC3VuDw1x/Dcln5mKZo3sqljerjcmBWjlWpNSUqV1m0x6d0qA/PzsSs+Jb7PGdvXvZdM7HwWo/a1m3fd4oKJK2DXu+ey8H1qEcZ5AUePV6sm1a9fqgQceUNmyZWW32/Xll1+qc+fOeuutt2Q2myVJGRkZWrhwocaNG+fNrl42W865oqAVKvJrDwyUXn8zVRPeDNHwZ8IkSSVL2vT4Exka+0qIgoOlrGzHjsVL2PXSy+ny85Mkq8pXsGnwE2Fa+kugbrk1K++HFzH2i8TXL58UOzBQevWNVL09PkQjhzniG1XSpscez9BrY0Nyy4GeHpYhs9mumrUcV5gaNLSqSlWbnhoSpiVLAnXrbUU/vpLnYpyd5fjAEiXsGn3eGH5ykGMMd/WJMZwT2ILOEQXEd8wbaXp3fLCeH+b4DSSqpE0PPZ6pN8cGKzjY8Yc2ZFiGzGapRs4Yrt/QqspVbRo+JFS/LgnUzT4yhs+ehwuK8YXG8MTxIXr2nDH8yOMZev2c88RTwzIUeM55on7OeeKZIWH6ZUmgbvGBGNtyLsoXeI4o4N+5yW9m6aU3A/Tw047lrEqXtGv4oGyNGBOgkJz4jn3bX9/+5KeBfa1qcY1Nh46Y9NGn/np8eICmvJ2du11Rx3mi8OBBhO7h1QTkrbfeUo8ePfT8889Lkn766Sc999xzeuSRRzRlyhQFFoE19sJzZj7Ov8J2tnY1LCz/wr0KFeya+G6akpJMSk52lHAlJppks5kUEWHPvQrSokW20z+esbFWhYfbtWuXv6Sif9IIC8+Jb1r+8T1/5umsChXseuudNJ3KiW+FijYdOye+khRbL+89CPXqWxUWZtee3b4RX8lzMQ7JGcPNmjuP4bo5Y3i3j8S4oPimX+QcUb6CXW+8k65TSSadSTapfD5juG69vKsPxeaOYa9PgBsm/DLHcPkKdo2/yHmi7gXOE3t9ZAxHhDv+m3reTEdaztXz8PD896tcUZo+KVsnk6RTyVLlCtLRY5LNZlJkhOP/5//gpwfudaysJUnNZVf9Onb1GBCobxf5qded+a+wVdRwnkBR49WRtWPHDvXp0yf39U033aRPPvlE69ev1/Dhw73YM/cpX8EmPz+7Dh1yDvXZ11Wq5v2Ln5kp/bIkUAkJJpUoYVeVKjb5+0s7/3XcZFarllXlyzs+Nyuff9uys6WgoKvwjqTLcDYOh8+L79nXVarkH9+lSwJ1JMGk4iXsqnxefGvWsiolRVr8U6Di9zl/rt3uiO/Z2lpf4KkYX3QMm30jxuVy4pBwyPkXi7PxrVRAfH9bEpAb30o58d2VE98atWxKSZF+/ilA+xnD58Q4/zFcuYAY/3qF54lIH4lxpfJ2+fvZtf+8MXz2dfUqeeOQkSn9+LOfDiVIUSWk6lWkgAApbodjn7q17TqSaJLdblLjBs5/PjWr21U80q7d+3znSjTnCRQ1Xk1AwsPDlZSU5NTWtGlTjR8/XosXL75qy67OZTZLDRtatXx5gNMqBcv+DFR4uF0xMXmvngUESO9NCtaPP5hz26xWaeECsypUsKpqNZtCQqT6DaxavixQlnOW/163zl8ZGSY1aOAbKwiZzY7SqL+W5R/fOgXE94P3grXoR+f4frvQrPI58Q0IkN57N1hz55id9v3nrwBlZprUsJHv1B97KsZnx/Bfy53H8PqcMVzfR1bBMpsdJQ9/Lwt0iu9ffwYoLNyu2gXE96P3gvV/P/43S2y1Sj8sDFS5CjZVyRnDH74brK/PG8MrcsZwg0a+EV+p4DG8/CJjePJ7wfrpvDH8Xc4YPhvjD/KJsa+dJ4KCpGsa2fXrn35O8f3lDz9FhNtVv27eX2IDA6Rx7/rrm+//W73JapXmLPBXpQp21axmV6UKjsRm3SbnX1X27ZdOJZtUvpzv/HLMeaLwsNtNhfLnauPVEqwOHTpozJgxeumllxQbG5tbctW5c2c9++yzGjt2rBISErzZRbe4t0+mhg8L1Ssvh+jGm7K0dau/vppr1oMDMxUUJKWmSvHx/ipf3qbixR3LDd52u0XzvzGrVCmbKlex6dsFZm3Z4q8xY9Nzy1UefDBTTz8VqudGharnXRYlJZn0ySdBiqmbrdbX+sY/fJJ0T59MjRwWqlfHhOiGG7MUF+eveV+Z9cA58d0f769y58T3ltssWjjfrJKlbKpc2abvFpq1dYu/XnrFEd/gYKnn3RbNmhmkEiXsatY8W3v3+OuLGUFq0TJL1zT1rZOyJ2IsSfc/kKnhT4fqhWdD1aOnYwxPyxnD5y/hW5Td3cei54eF6PUxwepyY5a2xflr/ldm9c+Jb1qqtD/eT+XK21UsJ74332bRd/PNKlnKrkqVbfphYaDitvjrhXPGcPe7LZqTM4avaZ6tfXv8NGtGkJq3zFZjHxvDvfpk6tlhoXptTIj+lxPjb74ya4CLY7hSZZu+X2hW3BZ/vXhOjHvcbdHsmUEqXsKups2ztW+Pv2bmnCea+FCMB/a16uGnAzTspQB1u9mqjVv89PkcPw152KrgICklVdqzz6SKFeyKKi75+0t3dbNp1jw/lSllV7Uqds1Z4K8Nm02a+KqjLDOquOOBhDPmOE4YrZvZdPiISVM+91e5snZ1v8U3yq/O4jyBosRkt3tv9eDTp09r6NCh+ueffzRlyhS1b9/e6f1Zs2bptddek9Vq1bZt2674eAcOlbviz7hcy5cF6PPPg3TwgJ9KlrLr9tst6nmX47Lvhg2OlauGDU/XDTc66lGys6UZnwdpyZJAnUk2qUZNq/r2zVSz5s4ng61b/DV9epC2b/NXUJBdbdpm6+FHMgqsufUkqxcvRv21PEBffBakgwcd8b31Not65MR34wbHqkpPD0vX/86J78wZQfrlnPje2zdTTZv9F1+bTfrhu0D98L1ZCYf9FBlpV8frs9S3f6bPPKH7XJ6IseR4yvpn04K0Y7tjDF/bJlsDvTSGswq6w9MAfy8P0KzPzLnx7XqbRXfe5Yjlpg3+evbpUD05LF2db3QkZtnZ0uwZZv2aE9/qNa3q1deia84bw4u+C9Si7wN15LCfIiLt6nB9tu714hj2l/dOFH8tD9DMnDFcqpRdt9xmUfecMbxpg79GPB2mp4alq8s5Y/jLGUFaek6M78nnPPHjd4H6Mec8EZFznujjxRiX8/fOndm/LjPpw0/9te+ASWVKSXd3s+q+ux1Jwur1Jg0cGqiXR2Tr9pscbVnZ0pTP/PXDz346nSzVqWnXQ/2surb5f2PEbpe+nOened/569ARqVSU1Lq5TU88aFVUcW98S+mgNdM7B5bvnCdqVTzsnQO7oMF3L3q7C/nafNvL3u7CJfFqAnLW/v37VaJECUVEROR5b+/evfr555/18MMPX/FxvJmA+AJvJiCAO3gzAfEV3kxAfIW3EhBf4c0ExFcU5gSk3rcvebsL+dp6+0ve7sIl8WoJ1lmVK1cu8L1q1aq5JfkAAAAA4H2srwYAAADAMIViBgQAAAAo7Lx/40LRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAuuxof+FUbMgAAAAAAwDAkIAAAAAMNQggUAAAC4gBIs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFPIfQPZgBAQAAAGAYEhAAAAAAhqEECwAAAHABq2C5BzMgAAAAAAxDAgIAAADAMJRgAQAAAK5gGSy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAWsguUezIAAAAAAMAwJCAAAAADDUIIFAAAAuMDOKlhuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAtYBcs9mAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC3gQoXswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAX2HkQoVswAwIAAADAMCQgAAAAAAxDCRYAAADgClbBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcwCpY7sEMCAAAAADDkIAAAAAAMAwlWAAAAIArWAXLLZgBAQAAAGAYn5oBqeAf4e0uAADgUWOO1/V2F4q0Ffc08HYXirz/2+TtHsDTfCoBAQAAAC4fq2C5AyVYAAAAAAxDAgIAAADAMJRgAQAAAK5gFSy3YAYEAAAAgGFIQAAAAAAfZbPZNGnSJLVr106NGjXSgAEDFB8fX+D2WVlZeuutt9SuXTs1btxYffr00bZt2y7pmCQgAAAAgCvshfTnCkyePFlz5szR2LFjNXfuXJlMJg0cOFAWiyXf7V966SXNmzdPr7zyir755hsVL15cAwcO1JkzZ1w+JgkIAAAA4IMsFoumT5+uQYMGqUOHDoqJidHEiRN19OhRLVmyJM/2Bw4c0Lx58zRu3Dhdd911qlGjhl577TWZzWZt2bLF5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fn2X758uWKjIxU+/btnbb/9ddf1bp1a5ePyypYAAAAgCvshfNBhJ06dbrg+0uXLs23/ciRI5KkcuXKObWXKVNGCQkJebbft2+fKlWqpJ9//lkff/yxjh49qtjYWI0cOVI1atRwub/MgAAAAAA+KD09XZJkNpud2oOCgpSZmZln+5SUFO3fv1+TJ0/WU089pQ8//FABAQG65557dOLECZePywwIAAAAcBUraIbjYoKDgyU57gU5+/+SlJmZqZCQkDzbBwYG6syZM5o4cWLujMfEiRPVoUMHLViwQA8++KBLx2UGBAAAAHCB3V44fy7X2dKrxMREp/bExERFR0fn2T46OloBAQFO5VbBwcGqVKmSDh486PJxSUAAAAAAHxQTE6Pw8HCtXLkyty05OVlxcXFq1qxZnu2bNWum7Oxsbd68ObctIyNDBw4cUJUqVVw+LiVYAAAAgA8ym83q06ePJkyYoKioKFWoUEHjx49XdHS0unTpIqvVqpMnTyoiIkLBwcFq1qyZrr32Wo0YMUJjxoxR8eLFNWnSJPn7++v22293+bjMgAAAAACu8PYDBz3wIMLBgwerR48eev7559W7d2/5+/tr2rRpMpvNSkhIUNu2bbVo0aLc7d977z21aNFCTzzxhHr06KGUlBTNmDFDUVFRLh/TZLdfSeXY1cV2pLa3uwAAgEeNOV7X210o0lbc08DbXSjy/m/TWG93oUBVpr3p7S7kK/6B4d7uwiVhBgQAAACAYbgHBAAAAHBFIX0Q4dWGGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5h8Zukmz2IGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAK7gQYRuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgCtYBcstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAKyjBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcYTd5uwdFAjMgAAAAAAxDAgIAAADAMJRgAQAAAC4wsQqWWzADAgAAAMAwJCAAAAAADEMJFgAAAOAKSrDcghkQAAAAAIYhASnEEhKlFl2lVeu93ZOiixh7FvH1PGLsecTYNYfXp2jx8H36qvcOffvwLm2df0J2e8GXi21Wu+Lmn9D3j+/WV/fs0E9P71X8X8l5tjvwT7IWj9inr/v8q28f2qUV7x1W+qlsT36VQqtpm1qaNPtRLVw5Wp//3zO6+4H2F9w+IMBfdz/QXp98O0QLV47W1O+G6J6HOyogwD/f7UPDgvT5T0+ry21NPNF9IBclWIXUoSPSwGHSmRSTmO/zDGLsWcTX84ix5xFj1xzbnqZlrx9U5Wsj1aB3KR3flq5Ns45JNrvq9SiV7z5b5h5X3IITqtezlErXCdGBFWf099uHZfKTKreOlCTt/ztZf711WDX/V1wNe5dWxqlsbZ57XL++uF83jq8qf7PvXEet26iSXpp0r/78vy36/P1fVL9JFfUb1FkmP5PmfPJHvvs8POJmdbmtiWZN+V3/bj2omnXLq8+j16tsueKa+NICp23DI0P08qQ+KluhhBFfBz6OBKSQsdmkhf8nvfmht3tSdBFjzyK+nkeMPY8YX5otX51Q8arBaj2kvCSpfJNwxwzHgpOqc2uUAoLyJgp7fj2tKm0j1eAuR4IS3ShMSXsztPOnU7kJyJavT6j8NWFq/nB07n6RFc36eUS8Dq1Nyd3OF/R55Hrt2X5E45+bJ0la+9dO+Qf46a4B7TV/xl+yZDrPCoVHhqhrz+aa/s7PmvfZcknShpV7JEkPPnWjpr+7WKeT0iRJra6L0aMjb1FIqNnAbwRfdkmXDo4dO6aXXnpJDzzwgEaMGKHPPvtMa9asUXp6uqf653N27JZenih1u0F64zlv96ZoIsaeRXw9jxh7HjF2nTXLpsStaarUMsKpvVLrCGVn2HRsW/6/I1izbAoMdf41JCjSX5lnrJIku82u6EahqtGluNM2EeUcvySnHMly0zco/AID/dWgeTX9tTTOqX35kq0KDQtS/Wuq5tknLCJYP369Wit+3+7UfnDfcUlSdMWo3O1emHiPNq3Zq+ce+cwj/QfOd0kzIM8++6yWL1+uWrVq6eDBg/r+++9lt9vl5+en6tWrq379+mrQoIEaNGigmJgYBQYGeqrfRVa5stLiL6XoMtQbewox9izi63nE2POIsetSjmbJlm1XRHnnq+cR0Y7XZw5bVK5xWJ79Ym6NUtyCkyrfLFyl64To0JoUJaxPVaN7S0uSTH4mXdO/bJ79Dq48I0kqVjnI3V+l0IquGCWzOUCH4o87tR/ef0KSVKFKSa37Z5fTe0cPJemDV7/P81ltOtdTVla2DuUkIpnpWXr4jkk6uO+4ypYv7pkvUITwIEL3uKQEZP369Ro2bJgGDBggSUpLS9PWrVu1efNmbd68WatXr9aCBY6aQrPZrE2bNl30MzMzM7Vz507VrFlTwcHB2rZtm2bOnKmjR4+qVq1a6tevn6Kjoy/6OUVF8UhJvjOj7BXE2LOIr+cRY88jxq7LSrVJkgJDnGczAnJeZ6Vb892v9s0llLgtXX+MPZjbVv36YqrbrWSBxzpz2KL1M46pRPUglW+SN6kpqsIjgiVJaSmZTu1paRZJUmh4sEuf06ZzrDrd0kgLv/xHKWcyJEnZ2dbcWRHAKJeUgAQFBSk2Njb3dWhoqJo3b67mzZvntp06dUqbNm3Sli1bLvp5u3fvVv/+/XXs2DGVL19eY8eO1WOPPaaKFSuqRo0a+uWXXzR//nzNmjVLNWrUuJSuAgAAA+SudGXK/32TKe8b1iybfnl+v9JPZav5w2UVWSFIx7alaes3JxQQ7KemD+Sd+Th9MFO/vXxA/oEmtX2mgkx+BRywCDr7Xe0FLIRgt138snzbLvU0fFxPbV6zT5++87Nb+wdcqku6B6Rz586Ki4u74DbFixdX+/bt9dhjj13089588001adJECxcuVNOmTfXoo4/q1ltv1ffff693331XP/30k9q0aaNx48ZdSjcBAIBBzKGOJV2z0m1O7dk5r8+/z0OSDqw4o1Pxmbp2SHnV/F8JlakXqno9SqnxfWX076IknYrPcNr+6OZULXk2XiY/6fqXKim8rG/dLJ2aM1sRGuZcdhaac9N4akpGnn3OdWffazXqzbu1dX28Xhw0U1lZ+c9KwQV2U+H8ucpcUgLSvXt3/fTTT9q1a9fFN3bBqlWr9OSTTyomJkYjRoxQZmamevfunXu1JCAgQI888ojWrl3rluMBAAD3Co8OlMlPSkmwOLWfOeJ4XaxS3ns1Uo85VmwqFRPi1F6mXqgk6fTB/z5r37LT+n3sAYVGBajLa1UUWcF37v046/CBk7JmW1W+snN52tnX+3cnFrjvoyO76qFhN2v5kq0a/dgMZaRbCtwWMMolJSB33XWXtmzZop49e2rUqFFatGiR4uPjL/vgwcHByshwZO2lSpXSXXfdpaAg5xNLcnKyIiIi8tsdAAB4mb/ZT6VjQ3Vg5RmnBw8e+OeMAsP8FFUz7/0JkRUcV+7PXyHr+HbHsrDhZRyL2Bxem6IVkxJUqk6IOr9aRaElfXNxmyxLtjavi1ebTrFO7W271NOZ5HTt2HIw3/3uH9xFt9/TWvNn/KVxw+cy84FC45LuARk7dqy2bdumrVu36qefftKCBQtkMpkUFham2NhY1a9fX8OHD3f589q2batXXnlFY8eOVY0aNTRmzJjc9+x2u1atWqWXX35ZnTt3vpRuAgAAA9XrUVK/vXxAf711WNWvL6bjO9K17duTatyntAKC/JSVZtXpgxaFlw1UcLEAVWgWrpK1gvXPu4fV4O5Siqxg1omdGdr6zfGc90Jktdi06sMjCgjxU2z3Uko+5HzlPrRkgE8lJLM//l3jPu6v5yb00uKFaxXbqLJ69G+r6e/8LEtmtkLDglS5RmklHDip00lpql4nWj0HtNO/Ww7qz583K6ZhRafP27/7mNJSMws4GgrEKlhucUkJSI8ePXL/32azaffu3dq6dau2bNmiuLg4zZkz55ISkFGjRumRRx7R5MmT9dZbbzm9t2jRIj399NNq166dnnrqqUvpJgAAMFB0gzC1HVZBm+cc17I3DikkKkCN7yuturc5SoRO7snQry8eUMvHo1X9+uLy8zep4+hK2jjrmLbOO6HMFKvCywaqXvdSqnOr4/kUx3akKz3JUar1+5gDeY5Z/66SanB3aeO+pJdtXLVHY5+arb6PddLod+7VicRkTX17sebP+EuSVLNueb05/QG99fw3WvLderXpVE9+fn6qXb+i3pn5SJ7PGz5gmjat2Wv01wAkSSb7ufOlV8hut+e72sXFnDp1SsWLF3dqO3nypBITExUTE+Om3km2I7Xd9lkAABRGY47X9XYXirQV9zTwdheKvP/bNNbbXShQ9Xfe9nYX8rXnyavrYv0lzYBczOUkH5LyJB+SFBUVpaioqCvsEQAAAOAmlGC5xSXdhA4AAAAAV4IEBAAAAIBh3FqCBQAAABRVJkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAABXUILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAU8iNA9mAEBAAAAYBgSEAAAAACGoQQLAAAAcIXd5O0eFAnMgAAAAAAwDAkIAAAAAMNQggUAAAC4glWw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAX8CBC92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAC5gFSz3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFMyAAAACAj7LZbJo0aZLatWunRo0aacCAAYqPjy9w+wULFqhOnTp5fi60z/mYAQEAAAB81OTJkzVnzhyNGzdOZcuW1fjx4zVw4ED98MMPMpvNebbfsWOHWrRoobffftupPSoqyuVjMgMCAAAAuMJeSH8uk8Vi0fTp0zVo0CB16NBBMTExmjhxoo4ePaolS5bku8+///6rmJgYlS5d2unH39/f5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fnu8+OHTtUs2bNKzouJVgAAADAVaxTp04XfH/p0qX5th85ckSSVK5cOaf2MmXKKCEhIc/2J0+e1PHjx7V69Wp98cUXOnXqlBo1aqRnnnlG1apVc7m/zIAAAAAALjDZC+fP5UpPT5ekPPd6BAUFKTMzM8/2//77ryTJ399fb7zxhiZOnKi0tDTdc889On78uMvHZQYEAAAAuIoVNMNxMcHBwZIc94Kc/X9JyszMVEhISJ7tW7VqpVWrVqlYsWK5bR988IE6duyo+fPn66GHHnLpuMyAAAAAAD7obOlVYmKiU3tiYqKio6Pz3efc5EOSQkNDVbFiRR09etTl45KAAAAAAD4oJiZG4eHhWrlyZW5bcnKy4uLi1KxZszzbz5o1Sy1btlRGRkZuW0pKivbt23dJN6aTgAAAAAA+yGw2q0+fPpowYYKWLl2q7du3a+jQoYqOjlaXLl1ktVp17Nix3ISjY8eOstvtGj58uHbu3KnNmzdr0KBBioqK0h133OHycUlAAAAAAB81ePBg9ejRQ88//7x69+4tf39/TZs2TWazWQkJCWrbtq0WLVokyVGy9fnnnys1NVW9e/dW//79FRERoRkzZjjdQ3IxJrvdfgX3zl9dbEdqe7sLAAB41Jjjdb3dhSJtxT0NvN2FIu//No31dhcKVGfMRG93IV87Rg/1dhcuCTMgAAAAAAxDAgIAAADAMDwHBAAAAHDBlTz0D/9hBgQAAACAYUhAAAAAABiGEiwAAADAFZRguYVPJSA3lG/k7S4AKMxMTAp7nN3m7R4UfYxjz7Lv8HYPgKseZykAAAAAhvGpGRAAAADgslGC5RbMgAAAAAAwDAkIAAAAAMNQggUAAAC4gAcRugczIAAAAAAMQwICAAAAwDCUYAEAAACuoATLLZgBAQAAAGAYEhAAAAAAhqEECwAAAHABq2C5BzMgAAAAAAxDAgIAAADAMJRgAQAAAK6gBMstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC3gQoXswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAABXUILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiABxG6BzMgAAAAAAxDAgIAAADAMJRgAQAAAK6gBMstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAGrYLkHMyAAAAAADEMCAgAAAMAwlGABAAAArqAEyy2YAQEAAABgGBIQAAAAAIYhAQEAAABgGO4BAQAAAFzBPSBuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAtM3u5AEcEMCAAAAADDkIAAAAAAMAwJiJc0u6GxPlj1ur5PmamZeyer18huLu9b65rq+ilztspWKe25DhYBxNiziK/nNbuhkT5Y+Zq+PzNDM/e8r14jurm8b61rqumnjC+J8UUwjj2LMex5jGGD2Qvpz1WGBMQLYlvX1phvR2j/tkN6ufsE/TLzT90/trfuefbOi+5bvWEVjf1hlAICuX3nQoixZxFfz4ttXVtjFg7X/u2H9HKPt/TLzGW6f+zdumfUHRfdt3rDKhr7/UhifBGMY89iDHseYxhXK0adF/Qd3VO7N+zTG/3ekyStWbxBAYH+untEN817+wdZMix59gkIDFC3QTeq35hesqTnfR/OiLFnEV/P6zu6R06MP5AkrVm8MSfGt2vexB9kycjKs09AoL+6PXGT+o25ixi7gHHsWYxhz2MM42rFDIjBAs0BanhdPS1fsNKp/c95KxQaEaIG7WLy3a/FzU3UZ3RPzX5tvqaOnGlEV69axNiziK/nBZoD1LBDrJYvWOXU/uc3K3NiXDff/Rwx7q7Zry3Q1FGzjOjqVYtx7FmMYc9jDHuHyV44f642JCAGK1e9rMxBgTr072Gn9sO7jkiSKtYun+9+O1bvVt9qj2vWa/NlzbZ5vJ9XM2LsWcTX83JjvDPBqT03xrXK5bvfjtW71bf6E5o1boGs2VaP9/Nqxjj2LMaw5zGGcTUrtAnIrbfeqoSEhItveJUJKx4mSUpNTndqTzvjeB0aGZLvficOn9SZpBTPdq6IIMaeRXw9L6x4qKTLiXGSziSlerZzRQTj2LMYw57HGMbVzKv3gCxcuLDA9+Lj4/XTTz8pKipKktStWzdjOuVhfn45j7Cx5z9fZrNdhfNohQwx9izi63l+fjnXhoixxzCOPYsx7HmMYS8hrG7h1QTk5ZdfVkZGhiTJns9foDfffFOSZDKZikwCknLKcWUnNDLUqT00wnGlIvV0muF9KmqIsWcRX8/7L8bOVzBzY5xMjK8U49izGMOexxjG1cyrCcj8+fP1zDPPKCIiQm+88YbKli2b+16TJk303XffqVKlSl7sofsd3n1U1myryteMdmo/+3p/3EFvdKtIIcaeRXw9LzfGNYixpzCOPYsx7HmMYVzNvHoPSLVq1TR37lw1bNhQt99+uxYtWuTN7hgiKzNLm/7cprZ3tHRqb9+jlc4kpWj7ql1e6lnRQYw9i/h63n8xbuHU3r57S2LsJoxjz2IMex5j2Eu8/cBBHkToHgEBAXrqqaf03nvvacKECXr66ad15swZb3fLo2a9+o1iWtbUC3OfUvMbG6vfmLvV85nbNHvcAlkyLAqNCFHdlrVUrFSkt7t61SLGnkV8PW/Wa/NzYjzUEeOX71LPZ27V7HELZcnIOifGEd7u6lWLcexZjGHPYwzjauX1BOSs5s2b596UfssttygrK+8DioqKDb9t0Zgeb6linfJ6acFwdbqnnT4Z/oW+nvCdJKnmNdU06Z/X1LLrNV7u6dWLGHsW8fW8Db9t1Zieb6ti7XJ6af4z6nRPW30y/Et9/db3knJi/PdYYnwFGMeexRj2PMYwrlYme353f3vZwoULNX/+fE2YMEFlypRx2+d28evpts8CUASZCs01maLLznMHPI5x7FmMYY9bYvva210oUONBE73dhXxteG+ot7twSbx6E3pBunXrVmRWvQIAAADwHy6TAAAAADBMoZwBAQAAAAqdQnfjwtWJGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5gowXILZkAAAAAAH2Wz2TRp0iS1a9dOjRo10oABAxQfH+/Svt9//73q1KmjgwcPXtIxSUAAAAAAHzV58mTNmTNHY8eO1dy5c2UymTRw4EBZLJYL7nfo0CG9/PLLl3VMEhAAAADAFfZC+nOZLBaLpk+frkGDBqlDhw6KiYnRxIkTdfToUS1ZsqTA/Ww2m4YNG6Z69epd1nFJQAAAAAAftH37dqWmpqpVq1a5bZGRkYqNjdXq1asL3O+jjz5SVlaWHn744cs6LjehAwAAAD7oyJEjkqRy5co5tZcpU0YJCQn57rNp0yZNnz5d8+bN09GjRy/ruCQgAAAAgAsK6ypYnTp1uuD7S5cuzbc9PT1dkmQ2m53ag4KCdPr06Tzbp6Wl6ZlnntEzzzyjqlWrXnYCQgkWAAAA4IOCg4MlKc8N55mZmQoJCcmz/dixY1W1alX16tXrio7LDAgAAABwFStohuNizpZeJSYmqnLlyrntiYmJiomJybP9N998I7PZrCZNmkiSrFarJOmWW27RbbfdpjFjxrh0XBIQAAAAwBWFtATrcsXExCg8PFwrV67MTUCSk5MVFxenPn365Nn+559/dnq9ceNGDRs2TB9//LFq1Kjh8nFJQAAAAAAfZDab1adPH02YMEFRUVGqUKGCxo8fr+joaHXp0kVWq1UnT55URESEgoODVaVKFaf9z97EXr58eZUsWdLl43IPCAAAAOCjBg8erB49euj5559X79695e/vr2nTpslsNishIUFt27bVokWL3HpMk91uL2KTSQXr4tfT210AUJiZuCbjcXabt3tQ9DGOPYsx7HFLbF97uwsFuubhid7uQr7WTRnq7S5cEs5SAAAAAAxDAgIAAADAMNyEDgAAALigsD6I8GrDDAgAAAAAw5CAAAAAADAMJVgAAACAKyjBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcYPKd53d7FDMgAAAAAAxDAgIAAADAMJRgAQAAAK6gAsstmAEBAAAAYBgSEAAAAACGoQQLAAAAcIGJEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFMyAAAAAADEMCAgAAAMAwlGABAAAALmAVLPdgBgQAAACAYUhAAAAAABiGEiwAAADAFZRguQUzIAAAAAAMQwICAAAAwDCUYAEAAAAuYBUs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAzjWzMgJvItAPAqzsOeZ7d5uwdFG2MYuGK+lYAAAAAAl4lVsNyDNB4AAACAYUhAAAAAABiGEiwAAADAFXZqsNyBGRAAAAAAhiEBAQAAAGAYSrAAAAAAF7AKlnswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAXmGze7kHRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgCtYBcstmAEBAAAAYBgSEAAAAACGoQQLAAAAcIGJEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBV2arDcgRkQAAAAAIYhAQEAAABgGEqwAAAAABewCpZ7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4ApKsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAF7AKlnswAwIAAADAMCQgAAAAAAxDCRYAAADgCjs1WO7ADAgAAAAAw5CAAAAAADAMJVgAAACAC1gFyz2YAQEAAABgGBIQAAAAAIahBAsAAABwBSVYbsEMCAAAAADDkIAAAAAAMAwJCAAAAOACk71w/lwJm82mSZMmqV27dmrUqJEGDBig+Pj4ArffsmWL+vXrpyZNmqhVq1YaPXq0kpOTL+mYJCAAAACAj5o8ebLmzJmjsWPHau7cuTKZTBo4cKAsFkuebRMTE3X//fercuXKWrBggSZPnqx169ZpxIgRl3RMEhAAAADAB1ksFk2fPl2DBg1Shw4dFBMTo4kTJ+ro0aNasmRJnu0PHTqkdu3a6cUXX1TVqlV1zTXXqGfPnvrnn38u6bisggUAAAC4wla0lsHavn27UlNT1apVq9y2yMhIxcbGavXq1eratavT9k2aNFGTJk1yX+/atUsLFixQmzZtLum4JCAAAADAVaxTp04XfH/p0qX5th85ckSSVK5cOaf2MmXKKCEh4YKfecMNN2jfvn2qUKGCJk+efAm9pQTLa5rd0EgfrHxN35+ZoZl73levEd1c3rfWNdX0U8aXKlultOc6WAQQY88ivp5HjD2PGHtWsxsa64NVr+v7lJmauXeyeo3s5vK+ta6prp8yZxPfi2AM40qkp6dLksxms1N7UFCQMjMzL7jvhAkTNHPmTJUuXVr33XefUlNTXT4uMyBeENu6tsYsHK4/vvpbn46eq/ptYnT/2Lvl52fSrHELLrhv9YZVNPb7kQoI5I/uQoixZxFfzyPGnkeMPSu2dW2N+XaE/pj7tz59YY7qt43R/WN7y8/PT7Nem3/Bfas3rKKxP4wivhfBGPaCQlqBVdAMx8UEBwdLctwLcvb/JSkzM1MhISEX3LdBgwaSpPfee08dOnTQkiVL1K1bN5eOy6jzgr6je2j3hn16o98HkqQ1izcqINBfd4+4XfMm/iBLRlaefQIC/dXtiZvUb8xdsqTnXZUAzoixZxFfzyPGnkeMPavv6J458X1PkrRm8Yac+HbTvLd/kCUjb/wCAgPUbdCN6jemF/F1AWMYV+ps6VViYqIqV66c256YmKiYmJg82+/evVsHDx5Uhw4dctvKlCmjYsWK6ejRoy4flxIsgwWaA9SwQ6yWL1jl1P7nNysVGhGiBu3q5rtfi5ubqM/o7pr92gJNHTXLiK5etYixZxFfzyPGnkeMPSvQHKCG19XT8gUrndr/nLciJ755f7GRzsa3p2a/Nl9TR840oqtXLcYw3CEmJkbh4eFaufK/v6vJycmKi4tTs2bN8my/bNkyDRkyRCkpKblt+/fvV1JSkmrUqOHycUlADFauelmZgwJ1aKfzjT2HdzluAqpYq1x+u2nH6t3qW/0JzRq3QNZsq8f7eTUjxp5FfD2PGHseMfas3Pj+e9ipPTe+tcvnu9+O1bvVt9rjmvXafFmzbR7v59WMMewd3n7goLsfRGg2m9WnTx9NmDBBS5cu1fbt2zV06FBFR0erS5cuslqtOnbsmDIyMiRJt99+uyIiIjRs2DDt3LlTa9as0eDBg9WwYUN17NjR5eN6NQGZN29enoecrFixQg899JBuu+02Pf3009q1a5eXeucZYcVDJUmpyelO7WlnHK9DI/OvtztxOElnkly/uceXEWPPIr6eR4w9jxh7VljxMEmXE9+TOpOUku97cMYYhrsMHjxYPXr00PPPP6/evXvL399f06ZNk9lsVkJCgtq2batFixZJkkqUKKEZM2bIZrOpd+/eevzxxxUbG6tp06bJ39/f5WN69R6QF154QR07dlTJkiUlScuXL9fAgQPVpk0btW3bVlu2bFH37t316aef6pprrvFmV93Gzy8n57Pnn67aitj60t5AjD2L+HoeMfY8YuxZfn4mx/8QX49hDMNd/P39NWzYMA0bNizPexUrVtSOHTuc2qpVq6YpU6Zc0TG9moDYz/tLM3nyZN13330aNWpUbtu4ceM0YcIEzZpVNOoUU045rjqcf2UiNMLxOjU5zfA+FTXE2LOIr+cRY88jxp71X3xDndpz43ua+F4pxrCXFJDw4dIUqntA4uPjdfvttzu13X333YqLi/NSj9zv8O6jsmZbVb5GtFN7+ZqO1/vjDnqjW0UKMfYs4ut5xNjziLFn5ca3JvH1FMYwrmZeTUBMJpPT66pVqyotzTljT0pKUkREhJHd8qiszCxt+nOb2t7Rwqm9ffeWOpOUou2ritY9L95AjD2L+HoeMfY8YuxZ/8W3pVN7+x6tiK+bMIZxNfNqAmK329WpUyfdcccdeuaZZ2Q2mzV+/HhlZTnWrV63bp1efvllp7WGi4JZr81XTMuaemHuUDW/sbH6vXyXej5zq2aPWyhLRpZCI0JUt2UtFStVdBIvoxFjzyK+nkeMPY8Ye9asV7/Jie9TjviOuVs9n7lNs8ctkCXDck58I73d1asWY9h43l7tyt2rYHmLVxOQX3/9VRMnTtSNN94om82mY8eOaevWrbJaHcvCPfDAAwoNDdXTTz/tzW663YbftmpMz7dVsXY5vTT/GXW6p60+Gf6lvn7re0lSzWuqadLfY9Wya9G48d4biLFnEV/PI8aeR4w9a8NvWzSmx1uqWKe8XlowXJ3uaadPhn+hryd8Jyknvv+8RnyvAGMYVyuT/fw7wb0sKytLgYGBkqQdO3aodu3aeUq1LlcX/7vd8jkAABRadp6f4VGmQnX7bJG0xDrX210oUMcb3vB2F/L12+IR3u7CJfHqKlj5OZt8SFKdOnW82BMAAADgHIXqsv3VizQeAAAAgGFIQAAAAAAYptCVYAEAAACFkalw3Tp91WIGBAAAAIBhSEAAAAAAGIYSLAAAAMAVrHLtFsyAAAAAADAMCQgAAAAAw1CCBQAAALiAVbDcgxkQAAAAAIYhAQEAAABgGEqwAAAAAFdQgeUWzIAAAAAAMAwJCAAAAADDUIIFAAAAuIJVsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5iowHILZkAAAAAAGIYEBAAAAIBhKMECAAAAXMEqWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC0w2b/egaGAGBAAAAIBhSEAAAAAAGIYSLAAAAMAVrILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiCCiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAUmVsFyC2ZAAAAAABiGBAQAAACAYSjBAgAAAFxBCZZbMAMCAAAAwDAkIAAAAAAMQwkWAAAA4AqbtztQNDADAgAAAMAwJCAAAAAADEMJFgAAAOACHkToHsyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFCQgAAEWJieIGAIUbZykAAAAAhmEGBAAAAHCFzdsdKBqYAQEAAABgGBIQAAAAAIahBAsAAABwgYlVsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAV1CC5RbMgAAAAAAwDAkIAAAAAMNQggUAAAC4ghIst2AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAK6websDRQMzIAAAAAAMQwICAAAA+CibzaZJkyapXbt2atSokQYMGKD4+PgCt9+5c6ceeughtWzZUq1bt9bgwYN1+PDhSzomCQgAAADgApPdXih/rsTkyZM1Z84cjR07VnPnzpXJZNLAgQNlsVjybJuUlKT7779fYWFhmjlzpj755BMlJSXpwQcfVGZmpsvHJAEBAAAAfJDFYtH06dM1aNAgdejQQTExMZo4caKOHj2qJUuW5Nn+l19+UXp6ul5//XXVqlVL9evX1/jx47V7926tW7fO5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fn2b5169b64IMPFBQUlOe906dPu3xcVsECAAAAXFFIH0TYqVOnC76/dOnSfNuPHDkiSSpXrpxTe5kyZZSQkJBn+4oVK6pixYpObVOmTFFQUJCaN2/ucn+ZAQEAAAB8UHp6uiTJbDY7tQcFBbl0T8eMGTM0a9YsPfXUUypZsqTLx2UGBAAAALiKFTTDcTHBwcGSHPeCnP1/ScrMzFRISEiB+9ntdr377rv68MMP9fDDD6t///6XdFwSEAAAAMAVtsJZgnW5zpZeJSYmqnLlyrntiYmJiomJyXefrKwsjRo1Sj/88IOGDx+uBx544JKPSwkWAAAA4INiYmIUHh6ulStX5rYlJycrLi5OzZo1y3ef4cOH6//+7//01ltvXVbyITEDAgAAAPgks9msPn36aMKECYqKilKFChU0fvx4RUdHq0uXLrJarTp58qQiIiIUHBys+fPna9GiRRo+fLhatGihY8eO5X7W2W1cwQwIAAAA4Aq7vXD+XIHBgwerR48eev7559W7d2/5+/tr2rRpMpvNSkhIUNu2bbVo0SJJ0g8//CBJevPNN9W2bVunn7PbuMJktxfS9cQ8oIv/3d7uAgAAAC5giXWut7tQoJtqj/B2F/L1079veLsLl4QZEAAAAACG4R4QAAAAwBW+UzjkUcyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAD+v717D6qy3vc4/sHL4qLg0Y6CaTqCF1yphINbK5WdDtPeXjo6u709mA0mool5OWaXbRqZpF1IC2+NHtTOmImXoqS0ocYp9ZRiJk0SWireUigqES+Ass4fHWkYabfS9Tw/1uP7NbNmWj94Wp/5DKN++f3WswDAGzUcwfIFdkAAAAAA2IYBBAAAAIBtOIIFAAAAeMNTYzqBI7ADAgAAAMA2DCAAAAAAbMMRLAAAAMAbfBChT7ADAgAAAMA2DCAAAAAAbMMRLAAAAMAbfBChT7ADYkjcvTFaunu+tpz7H609skT/+cQIr6/t0ruTtl56Q+EdW1sX0AHo2Fr0az06th4dW4t+rUfH8EcMIAa47+yqZ3Me1/GiU5p7/8v6cO0OPZQ+SqP/OfJ3r43s1VHpW55Uk6ZsXv0rdGwt+rUeHVuPjq1Fv9ajY/grfuoMePDp+3V4f7FeSFoqSdr7QYGaNG2sUU/8hzYtylXVpeprrmnStLFGPPJXJT37D1VdrLI7st+hY2vRr/Xo2Hp0bC36tR4dG8BdsHyCHRCbNXU1Ua94t3a+vafO+iebdyskNFg9B3Sv97o/DYnVmKf/pjfnv63//uc6O6L6LTq2Fv1aj46tR8fWol/r0TH8GQOIzdpGhssV2FSnvjldZ/27b89Iktp3aVvvdQfzD+vByEe0bsHbunL5iuU5/RkdW4t+rUfH1qNja9Gv9egY/sz4EayCggLt3r1bEyZMkCR99tlnWrNmjU6ePKkOHTpo3LhxiouLM5zSd5r9W4gk6Xz5xTrrF8798jwkLLje68q++8naYA5Cx9aiX+vRsfXo2Fr0az06NoQjWD5hdAdk27ZtSkxM1J49v2wfbt++XQ899JA8Ho/i4+NVXV2tpKQkbd++3WRMn2rU6P8r/40f4Bpu73bD6Nha9Gs9OrYeHVuLfq1Hx/BnRndAlixZokceeUSpqamSpOXLl+vhhx/WtGnTar9n+fLlyszM1D333GMqpk9V/Hxe0rW/mQgJ/eX5+fILtmdyGjq2Fv1aj46tR8fWol/r0TH8mdEdkOPHj2v48OG1z0+ePKl77723zvcMGzZMhw8ftjuaZb47XKIrl6/o1qiIOuu3dv7l+fHCkyZiOQodW4t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+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png"
+      }
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "# visual representation of grid search\n",
     "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
@@ -1871,7 +2235,602 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.18333333333333332\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.18611111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.13055555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.24444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.23333333333333334\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.12777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.1527777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9111111111111111\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.8888888888888888\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.8305555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.8888888888888888\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.8805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.8944444444444445\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.975\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.9777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.9805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.9805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.9777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.9444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.9722222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.9527777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9027777777777778\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.8583333333333333\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9055555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.8805555555555555\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.8666666666666667\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.08611111111111111\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.17777777777777778\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.08333333333333333\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.17222222222222222\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.11666666666666667\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.1388888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.11388888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09444444444444444\n",
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
     "# store models for later use\n",
@@ -1909,7 +2868,36 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png"
+      }
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "# optional\n",
     "# visual representation of grid search\n",
@@ -1999,7 +2987,16 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (2259440937.py, line 1)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  Input \u001b[0;32mIn [12]\u001b[0;36m\u001b[0m\n\u001b[0;31m    conda create -n tf tensorflow\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+     ]
+    }
+   ],
    "source": [
     "conda create -n tf tensorflow\n",
     "conda activate tf"
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
index 3214d648b..d7106d882 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
@@ -3021,28 +3021,12 @@
       "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m    140\u001b[0m num_iter \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m250\u001b[39m\n\u001b[1;32m    141\u001b[0m lmb \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.01\u001b[39m\n\u001b[0;32m--> 143\u001b[0m P \u001b[38;5;241m=\u001b[39m \u001b[43msolve_pde_deep_neural_network\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_hidden_neurons\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_iter\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlmb\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    145\u001b[0m \u001b[38;5;66;03m## Store the results\u001b[39;00m\n\u001b[1;32m    146\u001b[0m g_dnn_ag \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((Nx, Nt))\n",
       "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36msolve_pde_deep_neural_network\u001b[0;34m(x, t, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m    118\u001b[0m \u001b[38;5;66;03m# Let the update be done num_iter times\u001b[39;00m\n\u001b[1;32m    119\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_iter):\n\u001b[0;32m--> 120\u001b[0m     cost_grad \u001b[38;5;241m=\u001b[39m  \u001b[43mcost_function_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mP\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    122\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m l \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(N_hidden\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m    123\u001b[0m         P[l] \u001b[38;5;241m=\u001b[39m P[l] \u001b[38;5;241m-\u001b[39m lmb \u001b[38;5;241m*\u001b[39m cost_grad[l]\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m     20\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     21\u001b[0m \u001b[38;5;124;03m    Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m     22\u001b[0m \u001b[38;5;124;03m    positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;124;03m    arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m     24\u001b[0m \u001b[38;5;124;03m    should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 25\u001b[0m     vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     26\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m     27\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     28\u001b[0m                         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m      9\u001b[0m     start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m     end_value, end_node \u001b[38;5;241m=\u001b[39m  \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m      9\u001b[0m     start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m     end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f..unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     14\u001b[0m     subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36mcost_function\u001b[0;34m(P, x, t)\u001b[0m\n\u001b[1;32m     78\u001b[0m g_t \u001b[38;5;241m=\u001b[39m g_trial(point,P)\n\u001b[1;32m     79\u001b[0m g_t_jacobian \u001b[38;5;241m=\u001b[39m g_t_jacobian_func(point,P)\n\u001b[0;32m---> 80\u001b[0m g_t_hessian \u001b[38;5;241m=\u001b[39m \u001b[43mg_t_hessian_func\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpoint\u001b[49m\u001b[43m,\u001b[49m\u001b[43mP\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     82\u001b[0m g_t_dt \u001b[38;5;241m=\u001b[39m g_t_jacobian[\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m     83\u001b[0m g_t_d2x \u001b[38;5;241m=\u001b[39m g_t_hessian[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m0\u001b[39m]\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:78\u001b[0m, in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     75\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m     76\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhessian\u001b[39m(fun, x):\n\u001b[1;32m     77\u001b[0m     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mReturns a function that computes the exact Hessian.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m---> 78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:61\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     59\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m     60\u001b[0m grads \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(vjp, ans_vspace\u001b[38;5;241m.\u001b[39mstandard_basis())\n\u001b[0;32m---> 61\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mreshape(\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgrads\u001b[49m\u001b[43m)\u001b[49m, jacobian_shape)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m     84\u001b[0m     \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m     85\u001b[0m     \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m     86\u001b[0m     \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m     arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m     89\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m     90\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m     84\u001b[0m     \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m     85\u001b[0m     \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m     86\u001b[0m     \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m     arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m     89\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m     90\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:29\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m     27\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     28\u001b[0m                     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m---> 29\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvspace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mones\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
       "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp..vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m     20\u001b[0m     outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m     ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     22\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m     23\u001b[0m         outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     65\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     66\u001b[0m     vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m     68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m     69\u001b[0m     argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423\u001b[0m, in \u001b[0;36mmatmul_vjp_1..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m    421\u001b[0m A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[1;32m    422\u001b[0m B_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(B)\n\u001b[0;32m--> 423\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43mmatmul_adjoint_1\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mA_ndim\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mB_meta\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:410\u001b[0m, in \u001b[0;36mmatmul_adjoint_1\u001b[0;34m(A, G, A_ndim, B_meta)\u001b[0m\n\u001b[1;32m    408\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# We need to swap the last two axes of A\u001b[39;00m\n\u001b[1;32m    409\u001b[0m     A \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mswapaxes(A, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m2\u001b[39m, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n\u001b[0;32m--> 410\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmatmul\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mG\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    411\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m B_is_vec:\n\u001b[1;32m    412\u001b[0m     result \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msqueeze(result, anp\u001b[38;5;241m.\u001b[39mndim(G) \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45\u001b[0m, in \u001b[0;36mprimitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     43\u001b[0m     argnums \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(argnum    \u001b[38;5;28;01mfor\u001b[39;00m argnum, _   \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[1;32m     44\u001b[0m     ans \u001b[38;5;241m=\u001b[39m f_wrapped(\u001b[38;5;241m*\u001b[39margvals, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 45\u001b[0m     node \u001b[38;5;241m=\u001b[39m \u001b[43mnode_constructor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf_wrapped\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mparents\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     46\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m     47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36\u001b[0m, in \u001b[0;36mVJPNode.__init__\u001b[0;34m(self, value, fun, args, kwargs, parent_argnums, parents)\u001b[0m\n\u001b[1;32m     33\u001b[0m     fun_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(fun, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m__name__\u001b[39m\u001b[38;5;124m'\u001b[39m, fun)\n\u001b[1;32m     34\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     35\u001b[0m                               \u001b[38;5;241m.\u001b[39mformat(fun_name, parent_argnums))\n\u001b[0;32m---> 36\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvjp \u001b[38;5;241m=\u001b[39m \u001b[43mvjpmaker\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparent_argnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:77\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m     74\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     75\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums 0, 1 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     76\u001b[0m     vjp_0 \u001b[38;5;241m=\u001b[39m vjp_0_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 77\u001b[0m     vjp_1 \u001b[38;5;241m=\u001b[39m \u001b[43mvjp_1_fun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (vjp_0(g), vjp_1(g))\n\u001b[1;32m     79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:422\u001b[0m, in \u001b[0;36mmatmul_vjp_1\u001b[0;34m(ans, A, B)\u001b[0m\n\u001b[1;32m    420\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmatmul_vjp_1\u001b[39m(ans, A, B):\n\u001b[1;32m    421\u001b[0m     A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[0;32m--> 422\u001b[0m     B_meta \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmetadata\u001b[49m\u001b[43m(\u001b[49m\u001b[43mB\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    423\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: matmul_adjoint_1(A, g, A_ndim, B_meta)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:61\u001b[0m, in \u001b[0;36mnotrace_primitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     58\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(f_raw)\n\u001b[1;32m     59\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf_wrapped\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m     60\u001b[0m     argvals \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(getval, args)\n\u001b[0;32m---> 61\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:148\u001b[0m, in \u001b[0;36mmetadata\u001b[0;34m(A)\u001b[0m\n\u001b[1;32m    146\u001b[0m \u001b[38;5;129m@notrace_primitive\u001b[39m\n\u001b[1;32m    147\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmetadata\u001b[39m(A):\n\u001b[0;32m--> 148\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m _np\u001b[38;5;241m.\u001b[39mshape(A), _np\u001b[38;5;241m.\u001b[39mndim(A), _np\u001b[38;5;241m.\u001b[39mresult_type(A), _np\u001b[38;5;241m.\u001b[39miscomplexobj(A)\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:23\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m     21\u001b[0m     ingrads \u001b[38;5;241m=\u001b[39m node\u001b[38;5;241m.\u001b[39mvjp(outgrad[\u001b[38;5;241m0\u001b[39m])\n\u001b[1;32m     22\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[0;32m---> 23\u001b[0m         outgrads[parent] \u001b[38;5;241m=\u001b[39m \u001b[43madd_outgrads\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrads\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparent\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mingrad\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     24\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m outgrad[\u001b[38;5;241m0\u001b[39m]\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:165\u001b[0m, in \u001b[0;36madd_outgrads\u001b[0;34m(prev_g_flagged, g)\u001b[0m\n\u001b[1;32m    163\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m mutable:\n\u001b[1;32m    164\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m sparse:\n\u001b[0;32m--> 165\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43msparse_add\u001b[49m\u001b[43m(\u001b[49m\u001b[43mvs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mprev_g\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m, \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m    166\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    167\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m vs\u001b[38;5;241m.\u001b[39mmut_add(prev_g, g), \u001b[38;5;28;01mTrue\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48\u001b[0m, in \u001b[0;36mprimitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     46\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m     47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 48\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
+      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:186\u001b[0m, in \u001b[0;36msparse_add\u001b[0;34m(vs, x_prev, x_new)\u001b[0m\n\u001b[1;32m    183\u001b[0m \u001b[38;5;129m@primitive\u001b[39m\n\u001b[1;32m    184\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21msparse_add\u001b[39m(vs, x_prev, x_new):\n\u001b[1;32m    185\u001b[0m     x_prev \u001b[38;5;241m=\u001b[39m x_prev \u001b[38;5;28;01mif\u001b[39;00m x_prev \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01melse\u001b[39;00m vs\u001b[38;5;241m.\u001b[39mzeros()\n\u001b[0;32m--> 186\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mx_new\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmut_add\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx_prev\u001b[49m\u001b[43m)\u001b[49m\n",
       "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
      ]
     }
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
index a138dc08a..9a859e0d1 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
@@ -1382,7 +1382,7 @@
      "text": [
       "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/keras/optimizer_v2/gradient_descent.py:102: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n",
       "  super(SGD, self).__init__(name, **kwargs)\n",
-      "2023-10-02 06:54:12.770204: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
+      "2023-10-15 21:48:58.909327: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
      ]
     },
     {
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
index 1bf5d0cea..7d8805c35 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
@@ -61,7 +61,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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xY7B4cXI7f5nxVYjmevnpiyuZj6k6Kde8NEiWCyCHXe8iiiIe/2gb/rVqj345E8MH6xFqWpaT9dpmSMIfDJ3+WSwySKstyM1G+rmEiORAazjY9mMVxvxlSVywgBskTHgRRRFTpkzBeeedh759+2qWKygowMsvv4y5c+di3rx56NmzJ8aMGYNly5aplq+trUVVVZXsz29YmTEbZdCUUlWjI7yQ5sWzbNh7BLNX7sFjH27TL2iiHVWerMe8jfKQWrWWUB+Oj1RS2UT4jJr6MJ75NOJPaN3nxdjsRPgDrdHgYHUtvjt4HHe+uT6h9VEjYWsb3Xvvvfj666+xYsUK3XI9e/ZEz549Y9+HDRuG0tJSzJgxQ9XUNH36dDzxxBO219fr8PrJAJGFGTfsPYKBnVtFvkvNRqR58SzHatk0HGbGiP9s+EGWD0SrGSgj3ABzbZDwHtHnqCV8sC4PoAW1Ev/hh+EgIZqX++67Dx999BEWL16MDh06cB9/zjnnYPfu3ar7pk2bhsrKythfaWmp1eomHDNjgNpgwsKGvU3e4lLNC3Uw3kUqWL63rsTRa2nZutVWJP9ixwF8VXrU0foQzmM0UMkWZjRYgkL6P+FftPoBL+Go8CKKIu69917MmzcPX3zxBYqKikydZ9OmTSgoKFDdl5GRgZycHNmf3zAzgzUb6CG9lDTjLuUI8S5S4eXXc7dolnPyETaoZGd+d11pXEQb4T+iofEs7UdvyQGj40sPn4hpERfvOICLnl2KLT9UMteTSBx+0Lw4aja655578Pbbb+PDDz9EdnY2ysvLAQC5ubnIysoCENGc7Nu3D2+++SYAYObMmejSpQv69OmDuro6zJkzB3PnzsXcuXOdrKqrmIo2Mim9SI+SLmFPJgDvwuqOxOqwGwoIcUtHSFHruMxq+gjvE33cjj1hEfju4DGM+ctSZGeEsOWJcbh19joAwG1vrMO6Ry906sqESVJeeHnppZcAAKNGjZJtf/3113HLLbcAAMrKylBS0qQKr6urw0MPPYR9+/YhKysLffr0wSeffIIJEyY4WdWE8cWO/fiqtBIPXNhdMuMxo3kxKbyIkdVmP9t+APe8vVFyPlOnIxIAaxg7a5MI6ggvWp1WPTWQpMVKPyRF7/jluw4CAKoV/lvHGf25iETjfenFUeGF5WWYPXu27PvUqVMxdepUh2rkPrfNjnhpn1GYg3F98gGYm/E0mhVeIGL6/B2YvXKPfDuNTZ6F1Zma9RGGAgJqjYvJaFTxeSGSA73WxdMvaBUVdXSC3h8iUxOWLmdHeRV65bvnpkFrG7lEuXQ14AQlF4se9+/18U7NZDbyLkHFW6qZyZTxGYaUJ2Tgy+8qsHUf+Sd4neKK4/ju4DGuY6KKPSe7AK1z01IU3oTlqdz4z7WO10OPhIVKE3KkA80THxvk71ChMSxiUwn/AmhWBz4i8Sg7+NqGMDLTgnHleDQveqg1hWnzIo7Ce565hPEqRKKpawhj9IwlAIAdv7+Y+biY2cii14tetBH1Lv6CRaasOMarv7UX0ry4hPRlXr67gvv4sCjiSo7surHravQiWtsPVNXgvXUlOMmRDI+wF2X249p6a9nhQkHtnkmA/kBD6xl5F+naZay5gYDIM99ZXo0d5dWWrm8mSZ2yJe49dBzvri2RRUISiccPodKkefEpZrObaqcAV99+1ayVKD18Elv3VeH3V2hnRiacQ+nzcuREHQJq0w5GuSKkenATeibEOhpUPMnB6lrc/sa62Pc0DtNgXWMY42aqZzDnQXNiBB3NrmKMHPnnJQAi2cD/3/ndLNeJ0ObhuV+jurYBz183IE676wdrHmlefArPzEoKSwpwKaWHTwIAPvvG/bUsUhVlRzJqxhKc+fjCuHKsan+jpSD0ZsokvHiTxz/ehq9N5kypqbdHq2pGJ6fVEtd8f1hjD2EHdQ1hvLuuFJ98XYa315Zg6n++ko0pPpBdSPPiFlZdTKSZcnnQUsca+bz4oTEnK6xthSdU2uBMmnvqG0h48SJlR0/KN3D1L/a83eQ25x8aJKr7aOLBVs3TMW18b7eqxA1pXmzk/9aX4rcfbk2IX4DhIn0aPL/4WxxX8V+hfsd9vj1wDNe+vAorv5P7QLFqVFgHDz3ZRRAE0rwkATzOt06bCPQmRlJzxfLdB52tCBGjviH+mfx4tCkC1g9RYCS82MjU/3yNN1ftxdJdxi+h14QFo1BpPzRmv3PXnA1Y/f1hXP/KGtl2Zs0L43WMfV6096l1eoT3sG/+xHMiUfKvfKt2qHTk/4pjtZj4qruht6mE2iREOqnxQ3dPwosDVEm8/rXwWmgyBZG4T3lVjep2ux+NUcZevVl7XSNFnfkBnrxNeq2BR9FmpkuLXtvtsNtUQ819gDUZplcgnxcH8FsjAOI7u8qT9XhDkYWXcBhOZ+q4w1mT1Flx2CXNiy/gEV70+qs6Dh8nvStqCcRaGl0fdqG+Qu25StsBhUqnKH4UXpR9y2MfbMVHX/0Y++7Hn5Qs2G020tO8CIL+ecjnxZsonxlPKgU9TRtPvhXtBJgsxzJfhrABdc1L02c/9PdkNnIA1lWAvYRyprZuD4UqJhrt/jtxDruR8/ANZl4zgaYiykfAo3mxy0HbzlBpwlnUfV6kmhfvQ8KLA7CsAuy1/l7p86LUHvlBEvc7Vmaup0oylTIMlNY1G6kJL0yXJRKIXWuVcZmNdC559IS6H2C0X4nvX6jDcZJ6lYVWpX78fujvyWzkAMp07gDwVelR/HtD04KIVtcRsRtlx+OHxpsqbCo5ylTuxSXfMZUzMmvqOuyqCS9MVyUSidkM3ErsStOv3Ta12iK1Kicxctj1Q3QpCS82Ic3topYE7CcvfJnI6nCjnKnFaV5oJuQ4at31iboGPDX/G6bjWTOs6vVLAvTzvNSqal5E0EzZW3CZjXT28WleRNn/LPhgjExK1JJN+s1Xk8xGNtEoeWFZ2oDXVO3KDueEIpGdz9q1L1FrE1UnzS0DoYfRrEovbH57WVXcNo81ZQLy/sgKbvm8fPbNAfx10S7yp3IIozwvfliAlYQXm2iUPGwWCdZrTUPaVjeVHKG8Cx7BLt8FKVYcdp/7fDfTNf5vfSme/Hg7DT4JIj7aKPE+L2Y6Nb2u8m+f78aGvUf4T0oYoubzIp3U+OGtJbORTTQYmI28jtTPYeZn8QOU/36R/1DzNXGjE+G9ppp8MvU/XwMARvVsh/N7tLNeKYILHtnF3WgjQbcOh4/XmTgrYYSRz4sf5hykebGJRokk60ezkbSzs8tJj+BDrU0kWn0rCOAehfQcfI+eNM42TdiAovG4E21kf1v1g+OoH1FPUtf02QmNr92Q8GITUhuzWrSREu9FGzXVR014UXYiy3cfRMmhE47XKxnZe+g47pqzAf9c/r2hcOJEH2LkfM3bcfmgn0s6auob8eHmfZqaiUY3zEYmINnEHVR9XnxmMSCzkU002BWbaIGczBCqasw5eEqrb9Rhrd9zOLaI2p5nLjF1vVTmqpdWouJYHT7dWo6t+yox89oBANQVHm4IuXZekXxe7ONAVQ3aZWdAEAT8acFOvPZlMXq2z8b/Hjw/rizfbdcurBZdZnQWnkv7a7hMHtQnqE2fSfOSQkhnOsrHrjYLcqJtWPG1kQ6SdWrOXJLPrHlHCHUqjjXNlj/Y/KNOSftm0FKMZru8bdMH/Zzvef3LYgx5+nP89ZQ/2idbIu1m5/5q1fI80Ua8SQnNnEeLqEZXq02ScOMMRqHSfninSXixiQbJgK+UWk/U2R/uqoYV4cXQ54V6EedR83lxwmyk8yzXFB/CI+9v4Trfh5v3ae7zQyfoB574eDsA7WivuGgjN/K8OKAlJLOS/eyvqsGy3RVx24OyaCPvv7hkNrIJWWeheO7KnClOYSXJkLT+Ttu5CXXUOwwHBgQdSXTrvvg8LkY8PG8Lrh3SyUqVCE6MZBMec52edo8r2kgEnvh4G17/cg/zMUTiOWf656rtR+6wm7j6mIU0LzbRoGM2qq3X7gBKD9vn9GpFeBENNC80AXIHvwd+KQUyURTJDyYB8LQbPS1NbQP7xKsxLHILLtEui5pE4tC61wKZjVITmc+L4sGrdQ6iKGLrvkqM+NNi2+pgyefFINqIcB61DsMJnxe3EEUR17y8Gte+vJoEGIfhaTfLVUwIUXi0sA0m2qrRfIvMRolDPvn1/vtJZiObkPq8xM02NY75+Ct9Z01erLzo0n5HrcP67uBxHDpWizYtMsxfhNBFrZ044fWfyAFBWv2jJ+qxtvgwAODgsVrkZWcmriJJjrKZ2CUc8kQbsSKtm1HYPq2pljiCElWGB4JnDSHNiwk27D2CP/9vh0ylKh1kWDoSUbR/Vm3NYTdSF1EUNcOt/7hgh+nzE+ZIJs1LMNjUPsmvylnsajZOCC/3vr3J9nMS1hHIYTf5ueqllQCAZukh3DP6dAD6Pi9abph2LZ4WxZLPy6n/l+w8qFkmmhDLDw3bj6gJuXa3ESCxWUtlfuwG2j2Cnfg+xv0Mu6x8sqUs9pnMQt5BOn74Yc5EmhcLfHfwWOxzo0TPpuw4tFS4ds+qrSRIjNZxz6HjNtWG4EXaGqLZi/2wuqseosYXnigWQs4/l3+P2np9R1q7hF4nNC9SDLssEm4ShnT88INLGgkvFpDaY6U+L8ppkVpDEEVzDm56WAqVPtVHtW6erlnGDw06WTj/zxFHbrvbCJDY8UAquFM4vj384ZNvZKZdtXtp36rSzqZ5oLWLvEPAZ2YjEl4sIH3vpDMdFoddEaLts2o78ryEAtpNQq221TX1eG9dCY6eoNVfreKFhRntYMsPlarbpb/E6Rl9KvH4x9vitnnZ50UKiS7eQSDNSxPTp0/H4MGDkZ2djby8PFxxxRXYuXOn4XFLly7FwIEDkZmZia5du2LWrFlOVtM00hdPL1RaqyHYbjaytDxAhLpG45mW9Pc8PHcLfj13C/7fmxtMX5vQxgmfF6e57PkVsc/S2ks1L3q5jwg+3l5TErfNyz4vMoxCpZ29OiFBvjyA9/sdR4WXpUuX4p577sHq1auxaNEiNDQ0YOzYsTh+XNuvori4GBMmTMCIESOwadMmPPLII5g8eTLmzp3rZFVNIZVUGzSEl9qGRny+Y3/csaJo/8AUtPA0o41Vr7NSa9BR57u1ew6bvzihiRtrGzmFtPnUGPhsEHzE5Zayy2zksG+SUVMks1Li8FuGXUejjRYsWCD7/vrrryMvLw8bNmzA+efHr4QKALNmzUKnTp0wc+ZMAEDv3r2xfv16zJgxA1dddZWT1eVG6vMS1og2mj5/B2av3KN6vO2h0pbMRpH/yRfBOzQ0hvHZN/GCr1USOhzIoo2avtQ47EuRasQnxrTnvE5ryKLCiQ8m+kmBXsZkqebeD48joT4vlZURW3jr1q01y6xatQpjx46VbRs3bhzWr1+P+vr6uPK1tbWoqqqS/bmBVPMiVdm+tWavankR9jtjWpmlROustqJ0FD806GTileXFmLM63iRglYSGSkNdqK8hs5Gj2KXVTZTmxQ8Oon6nqqYeZz2xSHO/qDHR8CoJE15EUcSUKVNw3nnnoW/fvprlysvL0b59e9m29u3bo6GhARUV8Wmsp0+fjtzc3Nhfx44dba+7FjKHXR2fF1VE+x12rS0PEPmfNC/ewe4MzG4gfRekQj2ZjZzFrr4lUUkSfTBW+p7FOw7gpM57t7n0KD7bHtH0+uF5JEx4uffee/H111/jnXfeMSyrnBlGpUC1GeO0adNQWVkZ+ystLbWnwgxo+bxI55h6jcBLeV7CTD4v5s9PEEqfF1EUseWHSq7F/wg2nFhWwgkM1zZKTDVSgnodrToAvL9pH+54cz2KK477QhOWkAy79913Hz766CMsW7YMHTp00C2bn5+P8vJy2bYDBw4gFAqhTZs2ceUzMjKQkeHWejtNr5Y0SR1LvyHC/g7GjlWl9aKNvN+cCRYSmudF8lkWbdQQxuyVe/DEx9txQa88vHbL4ATWKvnxg8Ml0OQ3qL3ScQIrk+Q0MJoASw+foLWNRFHEvffei3nz5uGLL75AUVGR4THDhg3DokVyu9zChQsxaNAgpKWlOVVVU0hfrPoGddu+Vh9iNkldfo72YnZ25Hkxks4J/+OFaKP6xnDMkf2LHQfcqZDH2VlejR+OnGAqq3xr/ZIfiISTxFHP2CZE+MMHyVHh5Z577sGcOXPw9ttvIzs7G+Xl5SgvL8fJkydjZaZNm4abbrop9n3SpEnYu3cvpkyZgm+++QavvfYaXn31VTz00ENOVtUy9RqaFy3Hp7AomjIb6ZmGdPLLGUI+L97Due7D/bWNRNGaj1ayU3GsFuNmLsN5f1xs6ngnzUZ/vaa/7ef0w2Dpd1g1L/9eX+oLFwFHhZeXXnoJlZWVGDVqFAoKCmJ/7733XqxMWVkZSkqaIiqKioowf/58LFmyBGeddRZ+//vf47nnnvNcmDQgHwLqG7TXNlIjLJrzedGLFLFD86KXUdMPHujJhJ/u99Z9lbju5dXYVHJEtl06KMlWXoe10P5kp+Rwk8aFpR0cOlYr++5kckPBAeFX02xEXi+20cCoVf/v12U4VttgXNBlHPV5YXnpZs+eHbdt5MiR2LhxowM1sh9RFPHYh1uxbFdTJBSb2cik5kVH3LTF54U0L0mPEzLDDf9cg8qT9bjyxZWy7aIY0SK0bZGhWKRRJM2LDumSjJP1jSIEQd+X7kC1XHhx0mokCDCsD/u5Tvm8WD8VYUA9hyMLSzRgyOX3l9Y24mSxxD4fEASs+u4Q5qwu4Z4phUXRlGpXT0CxFCqNqM+L+Wgjv9jZCfupPBmfgwkAfvvhVgz6w2dYsLU8TvMSCpLwokVGqKlrNhON5bTWzspESUr0LGuLD6nvpyZiidqGRnxTVoWSQyeYNS8Am/D7+S9HWqiZdRISbZQslB4+gVtnr4t9F4RI4h8zmHXY1es0rHQoUS2QFc1LQ1hEOs2mbcNHViNNok18xsKdmHXjwNj2iM8LzZ20SAtKhRf+d9LJ/CyCYJ8xJ9plPT1/h/p+m66Tqlz5wkpsL4skbr20XwHzcX7oeqj34OCHIyfjtqn1EVpOisrjjDqYy/sX4vwe7WTb9OQTS2sbnfpfT/NixPcVx3DcB7bSVMeNASEjFJBpA0SIrqud/YIZ4cVRsxHs1Yj4ybfLb0QFFwBYuvMg+4E+eCYkvHCgfMkEqD9jFs95lmijszu1xJu3DYm7phZ2+LzoaYOMftfFM5dj9IwlputAyHEqAsMNVXx6KCD3BRPJYVcP+VIKjdwCp5MCgSDY50hrl+8MYQzPUg9+8AAg4YUDteepNsAwJaljEF7UIot0zUaWfF4i6NWJ5XcpHQcJ8zjVqbsRwZERCsRHG5HmRROp8GFmcURHzUYQbFPfCRB8kw3Y7/Bo1Vnaj9uRYCS8cKB8xwRBUJVQWfoNFrORmpzilM9L9Mclai0TIrVIDwXjzKnksKuN9C2sbWjkXkzT8WgjG89FXU5i4LnPfhgHSHjhQKllmb1yj2qEDWu0kZlcDLo+L5bWNor8z1In7zfr5MCp++yGtSZe80Kh0npIX0NzPi/Opji0sw3p1ZX6GjbWFh/G1n2Vtp3PyTxBdkHRRhyoCaMPvLc5bhvLYw+LxgV5+wdLPi8w1rxE27MP2nVSkEyOjOmhgLzdiO7nifA2ErNRQ5i7L3A22shOnxdBtz9JolfAMQ5U1+Dn/1gFANjzzCW2nJMl7UWr5u4u10OaFw6YBxNGnxdDVIQRPfUxr2pZXp/I/7rCC82DkgI3NC//21oucwYnnxd9lCtw8+KsH4lgWxsSYKR5oT7HiP2Vcj/DrfsqcdnfV2DF7gqNI4wxSuMx7+7hyM50V3ghzQsH7LILm9nIqJRa/6DXZ1gKlT5VGd2OhPoRR7jkueXo1q5F3HbHzEYuONo1hEW8vWZv7LsoighRnhdN5D4vHguVFmxMUidQn2M3d7yxHuVVNbjx1TWmz2GkuevfoaXpc9sF9R4csM4Cfj13i6H90Wznotdn2LG2EU8WRsIetv1YhY+++tHtaliCRYmy8rumLKq0MKM+Mp8XM5oXhx0ubXPYBaCXtZ56I2Puf3eT7PvhE3WWz2kkvHjh1SXhhQOeWcA1p2yQWrCoddVkEV3hxYYWRWGLHsI51YvtsAjOsmgjkPCih3SiVNMQ5jbTOO2wa2cboj7HPI1hEd9XHJdtsyN/kp7DbiggWHJRsAsSXjjgeceO1+nPlphcXlR6CD2Vv5VGy5akjkgkfrrfvE2PNC/6SPsHM1oUR1eVtnV5AP08L8nktO4EDQq1lWjTgqd6bc4r7y0JLxzY+RqZ1bzoYcfCjLodJfUjCcWpjtuJrodlOKPlAYxZvOMA/vDf7TLzrZnIISfH/EiotH0LM1KXYx5l27j07ytwzIYlWvQmsWlWnCtthBx2ObBzMAmLxudTddjV6TNsyFGnO2Nbu+cwrRxNqMLS9qRNR6l5ufm1tTirY0s8eFEPB2rnH6ILv0qzob66ohj1nL5oTr6ngmBfxFpkeQB+6eVfq/bg46/K8M9bBiHH5agXN1EKGdt+rNIoyQdpXpIMO/uDapOrUetGG6kuJ8B2XlaH3Y+/9rdjKWHfrFl+TuMySod3qeZl6a6D+Nvnu+2ulm/ZX9UU/rrvaPyCsEY4azayV3unr3lR3/nYh9uwds9hvLLsextr4j+cCrAw8nnxAiS8cGFfQ9lUctRQGFIdEDjWNgoGBOTnZDLVJ1oVI3NWscI5jHAOH/nrMpqNpJ9FBClUWpMF28otHe+o5gX2OWzyrm20v6oGr39ZHPt+wsC3MNlR+rzYd17va17IbMSBnZOZypP1hsmn1B12tbG2tlHkP8P1llxejCuVSDZfRUWCXVrbyEEcte7aqXnhzPPy83+swt5DJ6SHpzROZVLWE35J8+JD7G4mRlkM1d5M/Twv5usSrYmZxSIJZ3Aqu6gTz5DJbKTwebEr0RkRj/NrG9nosKuX50XxM6SCC+Gc2UhvbAp5xGHXG7XwCXZ3CMZaDrZtUayo86K/zchWTsNN4kg6zQtDtFGqhcbur6pxZPbsbIZd+5YHAGhhRrOEwyK+/Nb8EgBmIc2LD/FCv6pXhXQLEnEs2shAkqfJsv9x6xFKW9axmgY8v/jbuDK8UTV+ZuV3FRj69Oe4441IhJGt0YyO+rzY14aCAX2fl99+uFW/LincH32weR8enrcl4dclnxcfkuhMkGqqWb0qZKRZEF7AqHlJ5d4iSXDrGUrfnw82q0et1TeGkR5KjTnVayv2AAAW7zyIVd8dsnUgdjzayMZQaT05q6yyBgeqapCnEXiQyv3Rp1utOXWbhYQXwhDeJpIRCpq+Fsuq0oRzDO/WBifqGrG59Ghsmxc0fXbC8nuk+U2SHamm5bpXVtt6bmd9XgQux/0rzirUFFYBY41TvU6f5I1h1B2y0sz391bwiqN9akxxbCLRg4napEKvChkWZqyswksKT3SYqKqpx7R5W7Dm+0PGhSUEAwJm/Ky/Q7WS45rZiOEFSiWzkZPaEUcz7HJqXsb1ydfcJ4oW/XNSuD9yS3jxSooDb9TCJzgV/WEXSnU7z3stMjrs1jWEsZpzYE4l/rxgJ95ZW4JrXuabSQcDQly0mFvOq7++uBe++OVIrmNYNHYsvyaVNC9OKjmd1KDy+rzoCToR4UW/rqnmxM1KVro7wksamY38hxc0L3oozUY8x4uIOPkZ/caZn1EWVD32HDKXxC8oxCf+cqy5GbSLZulBtG6eznVKlneDzEZynHSqddQ/T+DzNTEqa6WuqZx3yi3hxSs+L6R54SDhwovai6lTCSuOjqJonxo7lWdK0p/+/95cz3wvggHvdMNZ6UHuQYGl7bCZjVJDeKlrCDuqHXHc54Wjeejl8xFhPGHS25/KZuxU93khzQsHiY824itvRXgJi6Jtnakopm6nIjUtLty+H8UVx9G1XQvD4yJmI4XmxaHmZiSYNEsPQuBsSvaZjZJf8D1R14ChT3+O6hrrq/9qwfouRxZG5Ds3r8+L3kRdFK2ZuFK0mwFAPi/eqIVP8Hq3aslhF/bZyRMt5HkJ5U9nvafBQPxs1q0Mu83Sg7qDwmOXnmHqumQ2irC2+LCjggvA7k/TpU1z7nNHfF7YxAZBMNK8AH/9bBd3HaTnT1UyXTIbecRqRMILFx4Yk3WT1HnEbETR1k2w3gtV4cWl+5iVFtL1UzArJLMIY6kgvCQijw2LiS4zLYDnrh3AfW6eDLuGWlgRWLLzIHcdCPccZ4MekRhJeOEgERqFi85oH/vMnaTOUqco2uZASJqXJqT3Yuu+Smz5oVL1uIjw4ozDbv8OuSjIbUryZdT1ZKYFHFkAlE3zkvxtx0ombFZYNH7/vGkwOrVpxn1uI22KlICh5oXFV0qnLiltOHIHryQGdPQtWrZsGS677DIUFhZCEAR88MEHuuWXLFlySqqX/+3YscPJajLjdLf69eNjcdOwzrHv/EnqrPi8MCwUyUgKyy5xnXF0EKmpb8Slf1+By55foXpcUIjvhu26j7ynUdMCSREEoEUGv7scmY0ipCVAeGF5lQMCkGbC+VIA+/o2ASHel0vKuj1HDM+hJ+B4ZBx1Bbe6WY+sy+is8HL8+HH0798fzz//PNdxO3fuRFlZWeyve/fuDtWQD6cH5ZzMNJlKTj1JnXYlrGXYJc2LHSh/evT7ibpG3eNCQf1O3s46KS/TqXUzjJVo/AKCfgbVgAB8cM9w7nqwtAsSXuyB5V4LgmAq7FUQ2H+DnUsJqJ7fuVN7Hre6Wa+sBu9otNH48eMxfvx47uPy8vLQsmVL+ytkkUQkqQtIOhNelaglnxfY6fOSusKLkui9aDAYlAMMfgQBg3VgtFC2W2W7EiFiUJdWWLh9P1NdBEHA6XnZJuphTF1D8redRISaLt9tvNpwQABCpiJHBKQx9jW8YdVq6HYnHhlI3cCtpKleEV48ogCSM2DAABQUFGDMmDFYvHixbtna2lpUVVXJ/pwiEY6oVpYbt7o8QINN/gap7LCr/OlR4aW2QV94CanmeZGfzSlfE1GUCzRGZiPz9TBuGA3h5Ne8eIWASlZnLe4a1S32WRCAdEYBjMc/RguaDKmTiNvyuUqmbY/ILt4SXgoKCvDyyy9j7ty5mDdvHnr27IkxY8Zg2bJlmsdMnz4dubm5sb+OHTs6V8EEtBaZ5oUhR92FvZvU/WqaF1bnqrAo2tZJpHKSOqX0EhXkjISXgJrDrhhfxgxKYVItqkm6LSDoa/3M9l1seV6SX3jxyusR4MiUmybTCPOZjawLL5H/1foVj4yjrpCIZqTmXO4VzYunktT17NkTPXv2jH0fNmwYSktLMWPGDJx//vmqx0ybNg1TpkyJfa+qqnJMgElEY5H5vDCUb5TMVNUaGrMgIQJ7Dp1gK2tAamte5D9ejGleDHxeVPO8yDGrlDNqA8r9ASPNi8kpj11LCPgd76yRxt6gpInJBEFgF17Art3RIto+X/tyT/z5vTGOukMCXha1+0t5Xhg555xzsHu39no6GRkZyMnJkf05hZNrkUQJGmhelEgjhKysOSEC+PybiM9Dj/bGGWH1IDVvE9FoIybNi2Lb4eN18jI29dTGQlJ8XbrntZDtd4pUEHy98nrwdBdSPx1ezYvV0Nro7frjp/FRp6kaKv3Gyj0JyY+j9q57RfPieeFl06ZNKCgocLsaABLTsRoJIMqOr12LjNhnK52EKIo4VhvJ+nnu6W1NnweICC+VJ+px6+tr8dKS7yydy2/E53mJ/F/H4POSqGgj5Yw7YjaS+LwoFon8xciueODCHk1HO9h56WmJRFHEP5d/jw17Dzt2/UTgHeEl8hynXNQD4/vm65YNKSZVrP51kVBp83UEgP9tLUd9YxitmqfF7fPIOJpQNpcexe8+2obPdxxw/Fpq45FX8rw4ajY6duwYvv3229j34uJibN68Ga1bt0anTp0wbdo07Nu3D2+++SYAYObMmejSpQv69OmDuro6zJkzB3PnzsXcuXOdrCYzidAoyBuLkQsnkJ+bidm3DkZOVvyLzUNY4rBrNQOoKAK/nvs1Fu88iMU7D8qc/ZId5fNpMhvpCy9Bjqyl/HVSRBvFaV5EWUsTBHnLa5Eekg1ATnZdohjRcH5fcQzd2rWQdZTvb9qHP3zyDQBgzzOXOFgLZ/GK2SgqvEweE0lF0eXhTzTLhiSaFgECc34YO3xe/rJoF0QALbPSsb+q1tK5koHyypqEXcvLZiNHhZf169dj9OjRse9R35Sbb74Zs2fPRllZGUpKSmL76+rq8NBDD2Hfvn3IyspCnz598Mknn2DChAlOVpOZRAgv0hed9Z0f1TPP8nVFNC3MmGZx4a2wKGJHuXNRX15GqTkIixEn1A827dM9LhgIOKYCF0X92b7SYVcZbSRCvt9MYjNWRIh4ev43+OeKYkwe0x1TLuqBf63agx+OnETlyXrHrpuK8MgU0mfOleeF8zpafPzVj2jVPN36iZKARCo+vGw2clR4GTVqlK4aePbs2bLvU6dOxdSpU52skiUSbTaKfvr9T/rgsQ+3AXAukkcUmyI9rCbRCovGZpJUISyKeHnZ93jfUHiB4UrOZh+9kdCt6vOi6KCk383lBmEjLAL/XFEMAHju892YclGPWNvPy87QO9Q3eM1sxILSfMCc58Ugwy4rjaKIjq2aYW2x3GTojWE0sSRSeFBbx8gji0p73+fFSyRC8yK3LUc+TxzWxfT5WO2TIpqcf9NCFkMbwyLqUiDkVQ1lC2kURXy6tczwODWHXbtQ1kl5nUieF2ld4s8h3e9kkjW9V+xANZkM7IRL8yKLNmJfn8muDLvhsIjmGfEZxD2iBEgoiUzPryYopYTPS7KRiBmT2VweVhFFsUl4sShaiymseYlfHkBkajdZaUHHOgXj64uyays7LKVDr5MLC3rFH8RJ/Kh5UQqszD4vnNfRYs+hE9izam/8+T0ykCaSRP5mNW2wV3xeSPPCQUJCpTnzvCi59dwupq4bybAbNRtZDW0UU2J1YDXiMuyG2cyNOZlphp2C2YFdaWpU9n2NYVFWRqkqFiHK6hZyUHhR3quV3xqnufcbXhHQeAYhuTmbPc+L0cKMBD+JvJte9nkh4YUDu9b+0UOq9DDTRn53WR/Zd1YfGRFN0UZSe/bonu2467B010GcrG9Kyna8tgEPz/0aF89c5ktH3o0lRzD5nU0oqzzJfWxYFJmeQXZmyDmHXcV35XUawqJMaFBXFTd9dnRtHsW9+t1H25y7lkt4RfPCM4MPKcxG7HlerIdKE3Jc93kh4cV/JGZtI75HYleVImajU5oXSR3MnP+3H8oHnCc+3oZ315ViR3k17pqz0Uo1XeGnL67ER1/9iIf+/ZVxYZVoIxayM9OcC5U2WB6gMSxfGkLV50VykFWzoh7K+5WIFZhTFdNJ6gT2dAp2JKkzOr8Woiiiqib5ItQSKTyoXcojsgsJLzzwRvpsLDnCfQ2ppNuoMvI5NWsLi/Y57Cr5+Ksmh9WKY/51utxTYbx8glqeFxZH75yskGGnIMq0I4anjGF0/QZFO1PVvEg+O+uwK6+Lk2HZieaVZd/jxn+uQU29/lIRiYLL5yXObMTu8+IketrKSXM2oN/jC7H9R/9pe/VIpCaLzEZJAm+00T1v8WsZpJNatVm7k/byqJ+KdLZrh7AknaU1T09uH3Hl/WoURWafFx6zUctm7DkvlHXKVSQ0VGpelGGxoijvsJwUKJT3ykn/mkTz1PxvsOLbCry3vtTtqgDgm0ErF4zlWR5AbRJmF3q/4X/bIsudzF5Z7Nj13SCRDrtqGXa9YgZMnp4hAfC+g2YibqSNxY7QbJ6G3mBTnhcl0lTizVTCHf0Cy63cXiaf5YVFtueYnRli6hSeuLwPLu9faJjOXYlU6P3FyG4Y2aPJl6lR4fOitvaRzOfFQbOR8k4lk+Ylih81L8pAAh6H3YawNyIPk2W1+8RqXtS2eeOdJOGFA15hwkyuEyPhxcn3r96maCMlqaJ5Wb/ncNwsUxRFJsehFhkhpk7h5uFd8Nx1A7gETGWn3SIjhDduGyLbJtO8qJqNJEnqHDYbSdtfMvq8eGUxQZ4xSLlgbLN0tkmIAIc1L4zlPvrqRwx5+nNs2MtvyvcaiUynoTb59Up4evL1DA7CGypdb0Z4MfB5UXJayyzNfbydpJrZyA5kwouPNS9KPvm6DJP+tQHVp5wCv1BZKC0sshn6QsEA12DCU5bl+nJ/Gn1VsZMChSjKB8qQV3TUSYjyOX82ZSR+Na4nQ1mBXXgRhDifKjtheQ8ECJj8ziYcrK7F7W+sw4HqxK0N5ASJeiW0Fgn2yitJwgsHvO+gmVwn0gbDomW5dnBH7mtoUadiNrKj25EmNfOz5kXZUd7z9kYs2FaOv38RWXxU7WVvDLNr7IxmNNKz8AimLNcXZdFG8eeWnoFHoBjWtQ1z2ch1RJlZKpl8XryGUng5Pa8F7hl9ukbZps+CAGQxvseCAHRr18J0HQ3PzzlBO3qiHkOe+tznTryJkR60XnMyG/kQXrORGXWpYKB5kbabEd3bGnbuPHZeu5LUSQkFBIXPi4+FF41O48ejkfwvasJHOMyWYZe7LjyaF4br6zZVUZS1RdZ1bQDg8rMKmctG6yHtNJ3M5usWa4oPuV0FAFaS1AHNmTUvEQfxtY+O4awdG2bH0Q8266815mXs0nwM7NxKd7/WZIo0Lz4k0f5easJSa8nKqnbXJ+pgbKdZIBgQZB1fMjpg1p66b2ovdaMoOhIhxnMXWa5uJJhLEzTy5HnhbaOiKNe2OJoQzyUqjtW5XQUAfL4L8mgjAVmMwkt0lp6XnclXORvxcq4St+jfIRc3DeusW0bN9w0gnxdfkmivebWOvyBX28fFKk75vDSXaFva+HhZe613Nho9oqZObQyLsK3ZSP1SOKY/LAKEXhkRQKPEBOqkQBEWRZlZysnIplSHy2FXUGpemt7p/BxtwSRRw9x/v/4RE19dg0MqeaTeXRcfmu4Vp2kz2DIVYnj4WkXIbORDausTK7yoLUfQXqejUINHSq4Pq/i8WFTviDDnuOwnopoXNZ8X1uUBtLjjvCLV7Xz9B5/PixrStui0E20oyTV1XoErVFon2ujtO4fK9klxepYebZb3vr0Jy3dXYOAfPsOJugbc/dYG/eM8sr6UGkaBIXZo3AUYP5sTdeoh/V6x5HqkGv7ATOizlJbN0jCmV57mgKREzeelT2GOpTroEX0pbB0wRLnjsp9TLRyoqsWtr6/FYkVUUVR4UesLlDlUeLnxnM4YdMo2feWA02LbeWaOVn1eRFHeFp0ckMJhEUFJ+9OKeCCsw6NBC8g0L3KzkbRfVJoanJ6kqwkhV7+0CvO3lOse94+l3+OkxuDsJu+sLUG/JxZiw97DsW0LtpZj/Z7DklJ25P8yrxUjs5EPsap5ubx/IV69ZXBchlMtpLPhl244G5NGdsMlZxYwX69ru+bcdQTsNRuFRVGWrM/HsgtO1jdi8c6DuHX2Olm0Qq2O2eiJj7ejvEo/NPPPV/fT3BcQBLx6y2D8/boBePzypkU3efoPFkdz3iUEnEKEfABMxjwvXoFHgxaveWkyG0ln6EpzptMmBrVmq0wUqcXC7foCjhtMm7cFx2obcN/bmwAAew8dx6Q5G3D1rFWxMnZMAAOCYFqwJLORD6ltsCapRx85q7+CdLwYf2YBHh7fKy5Ntxr/ve88/OSsQrw8cZCpeto5YIiQZxr2s+ZFyoTnlsc+R31etBzc9PjtpWfgZ4O0w92j0RqX9S+UzXbtdtg1KtNo0nGHVz0vivJ2T3lenINHq6XsErRSOiifl9NPz0p34hUNghrR37XvKP9K9iwIMO/345VX0r9xqy5QayLdv5Toy8LaaZhdHqDvabn427UDTB0L2Gs2EkVR5vPiZVuzWfTMRkZkpOkLitqJouw2GxloXkzkLFIjOyOE6toG3XrIsv2Sz4tjsDpDXzngNNlAH/34wIXd8f3B4zi7U8vYvoSbjZKvOwEg+V2q69tZJ7Lat7ljvaJ5IeGFAzNrFUmJPnPWGbodabXVHDHvHFGEV5ZrL1Zmt+alNgk1L1KaQqXtf6m1zskz+9Fyxg0FJNlPDZ6LHetsAcYdpgj9mTxhH6y39rFLz0DVyfrY96gg88CFPeLPGad5cfb5WWmXXm5ZepM8exx2zT8Zj8guZDbiwbLm5VRzYTcbOTPSF+osKQDY6yQpiskfbRQzGzkw0GpOjnk0Lxrbz+rYEkBkrSO9tiZCxIjukYUc2+dkMF9XDaN7JCo0L2aoqW/EH/67HWu+90YyOK/CajYJCPFJ6rRQPl+vDHR+Qzd1gU3hRn7XvJDwwoFln5eY5oWtvB0+ko9c0hsAMKSodVM9DI6x20lSGo2QLCu7StFLUmcVrY7Cjkjp568/GzcN64wP7hluGG1U2DIL6x69EEt/NZrnynEYCy9Avw65se9m3oGXl32Pf64oxjUvr+Y/2CH83O4FQWDytQPUhBenHXb9e1/10E14bcP5Bcm/vHhFGUrCCwdWNS/Rh846Q2eNStLj0n6F2PjYRfj9T/rGthl1KNLq2dE31CdJtJEWUfOeEx21dpZL9nOERRFDiiJrDEnTuufnZuLJn/TF6XnZTM+5XXYGMtP4FtZUntfoHoVF0XBldSOKK45zH+M0CQrWcoRgQFAkqdN+hsr26vRAZ6V/8ogCQRV9zYv18+v5vFzWX39Jj0Suaq0H+bxwYN3nhc1s9Jef9ceX31bgqrM7WLpelNbN03H0RFNKcqOXVjrA2OFgK01w5pQpzAuYUade3Cff1Dm58rwA+MMVfXF6uxb4icZaQ4l6Lkb+XkqfFzPV8kbXKsfP7T4gyM2XfJoXhyp1CkvRRp5sKREqjtXi75/vxoBOrRw5v57PS76BadgrUVqkeeHAquYlquI06sCvGtgBz15zFtI5FsAzQnquRDe9sMXBKFGIoog9FcdNqaLDYZFrlpmVFsSO31+MNi30Owotnxeeaw3v1ga5WWm4/8Lu6NJWPfeP3m+285EZ1TuSkVhybS83GA78LbwIzEEGccKLRm8zrk97y/UCklfzAgB/WbQLH0oWkIy+C3ZMKPV+u5F21SOKFxJeeIgmI7OKG2o32eq8CX5rpemuvdyFv7D4W4yasQRPffIN97Fjnl2qupyDFgHBuJOIlNOINmJoQ1ed3QG/vKgH/nx1f8OyiTJrGNZblHfOpny9PdK5SknwsmiWiMvVIsjboV4zZ9G8XNKvAJPHdLdUx1hdPN2jWKfk8InYZ73waV7O6thSU4MyvFtb3WPJYdeHWNe8RP43k8zMKlLNS6Jns9JZp5cnoDMW7gIA/HOFdhi5FsUVx2VZd41gVb1aiWDq2DoL943pjlYMi2E6HZoZxajjU5qN/KyxkHL0pDdWkmZBKWAGFQ67em1F2Vy12rldJpskaR6aSN+XcEzzYo1fjeuJyWO6az6BYd3a4F+3D8GKX6s755PmxWc0hkXbUqS7sV6LVHjh8d2xo3OQ37bk7W14ZFLWolrnZLkWzwCRKM2LUdsPh+VDox2CdnHFcby2ojgW0u4G4/66zLVr86LUvAQEQeFErX1svNkoHgH2KX+t+bx4H6nZOKZ4sfhK3DP6dGSmBXWfwYju7dChVTPVfV7xeSGHXUasOusCTS+sG2YjafhzotapUSPZZ0rMMDYBKw67diSyA6yp5pVHMliNZHUxc2XlvRk9YwkA4PDxOjw0rqeJM5rn+4PH8M8Vxaiq0c4q7DWkmuHFD41CQBFtpLfqsbK9aj1v28a/JO9Q1DUviUkYqQWZjXxGZloAG35zoaVzuGk2ks6m6m0QxMxipa9ZvvsgXjNh0vEirC1Aq62wCCZc4dQJahJGHZ/SYddOs9E62cq8iWHiq2vx9pqShF/XCtIlGYpOOXhLH5veI1GuVK02SxcEK/ld5VjSvHhjDNZl+e6K2Ge75TTWZzD3ruGy72Q28hmCIBhGhrBiVw64HI48MNJOpL4xjEcm9AIAPPPTM+2pDCNmZw3llTWY+OpaPPnf7di9v9rmWiUeVtWrVjGW2Q+PejdRjo8sSeqkNTGjJLRyz+xkw94jji2s5yRqArPMYVenrcStbaRRzjazUXIrXmREf6ttv5nxGQzs3Aqzbjw79j0lNC/Lli3DZZddhsLCQgiCgA8++MDwmKVLl2LgwIHIzMxE165dMWvWLCeraDv/mTRMc1/MbGTx4f/t2rMwqHMrPHbJGaaOrw+L+H/nd8NXvxuLa4d00i1rd+dg1mK1fm/TrPlEnXu+C3bB2gQ0HR7t1rw4NAgoQ2KNBCpRFGVmIz0ThRrVNfWay1EwrkNoG7/414bEXtAm1Mza6aEAJpyZjxHd26JTa3VfCCBeONXq6+wwwwNWhW5vDMKs2OWwG4Xv1zeV9ojs4qzwcvz4cfTv3x/PP/88U/ni4mJMmDABI0aMwKZNm/DII49g8uTJmDt3rpPVtBWtmWWn1s1imQuVqlVefnLWafjPXcORn5tp6vio2ciODL68mBWGGn0Sbs1KIt5/PoddvZSe5uuQl52J31/RlN3ZSOsoQql5Yb/4sdoGnPn4Qny4+UfV/YlOSlZncTkRt9AyVb54w0D86/ahugJoXP+nUlSA9aVWovgpz0vliXqctDDxanLYtcvnhf0GSIt6RfPiqMPu+PHjMX78eObys2bNQqdOnTBz5kwAQO/evbF+/XrMmDEDV111lUO1tBe1B9suOwPLpo7WLZNIXHXYtUH0SIbEZVY99lmO57mEQ7ILACA7o6mbMfL3ik9Sx34do1B1K7d8+qffoLqmAU9fqW1mPVbbgBaS3+qVqAxerERDKn+z1plq6+3SvCSO+sYwXltRjMy0IG4e3oXr2KqaevR/ciEy0wLY8fv4MfFAVQ0OHqvVPYebmhdpWbfHryieijZatWoVxo4dK9s2btw4vPrqq6ivr0daWrymoLa2FrW1TQ+9qoo914YTqD1XZYftRqi0lDo3V3kWgU++LsPm0iOYNr43c+SVbEBzqGqJxGoLYHLY5ThfZppzSljZrM1Bn5c0A42mWWGiMSziH0u/BwBMOr8bOrWJN5t8sWM/bpu9Hv/v/K7Yuq/yVBIwU5dznWbpfOtXSVFLcKdazibHv31HTnKbFqPwPp5315Vi+qc7AESyoEsFVSN2lEX89GokQtvK7yoQCgQwpKg1hjz9ueE57ExSB1iJNrLn+lbxlMNueXk52reX28jbt2+PhoYGVFRUqB4zffp05Obmxv46duyYiKpqoiaVKh+2G9FGUniijayauJSIAO55eyNeWV6M/1tfynycXxLdsWK1CbA57LKf78GLeqB3QQ5+/5M+FmqlVY+mirAlqZM+a/aHbbQautlOV2qyrGtUV/v/7qNtACIrWq/87hBeXPKdbdqFRPO3awfgtJZZ+Os1xpmZlbD6vAzu0gpXD7S+dttHX/2IRz/YYurYe97eyNW+KiXrw1mN2Kyqqcf1r6zBz/+xitn/x26NM48ZVfoOe0Wj6CnhBYi/MdEHpnXDpk2bhsrKythfaSn7gJgolLNNt1fl5DEbTTizAGd3aokR3fVTRrMifQEfnrcF1TX1jMepn8O/WDUbGZfhUe/mZWfi0/tHYOKwLszHtMtmi76T1sJwYUbFs+XxeTEWXszdc2kdeCb5J11MimeFMwpz8OXDF+DKAdaFC808RYKAGT/rjzG98ixf45215vr8+kYRew+dMC54CivaX2W7PnysSRBibeOxaCMX8rzIzUa2XN4ynhJe8vPzUV5eLtt24MABhEIhtGnTRvWYjIwM5OTkyP7cRNVspEy37SOzUXowgHl3n4tHJvS25drK124XQ9hzdU09fvnvrzTP4UesTl6khxdqOG6P6W3X4nfqd/yT+85jOl46gBlF/IiicnkApksAMNYSSl+7Y7UNMo2KHjJn8WRofA6ivD9q7byzitmNFbtTO/CsRybF6gTKjOk+5vNil9mIp2yqOezyMmzYMHz88ceybQsXLsSgQYNU/V28iLrZSFuVGhASl5o9SoOJF8euBqt88Roa1X98Q2MYi7bvx5Ci1vj3hh90z+EkPPZ0nnpZvpuS57HkV6Oxa381Lv37CgDA0l+NQmZaEO1zzEWjKdH6XXmM5+fp+MKiKJtZ8mhejNtoZP/B6loMfuoz9CnMwSeTRxiet1E0rg8JNRH0ntfbdw7F/7aW4+5Rp5s+f16OPbm2zCBqfGZBaTmQmoqYNS/R/13w2JX7rdl0fYs4KrwcO3YM3377bex7cXExNm/ejNatW6NTp06YNm0a9u3bhzfffBMAMGnSJDz//POYMmUK7rzzTqxatQqvvvoq3nnnHSeraStq/Wecz4tkQ1owYHnBR154BrXoe2JXYj3li6o1+5219DvMWLgLvfKzMeHMAnmdEjhS8AyePGWt+7w0fU4PBWRtKi87E1kWnC7tRlpXpiR1JqONjNpF9NKLdxwAAGxjXEhTKsAqn3FZ5Uks312hmVsm1ejQKkv2veupDL1AZLVioxWLjUh0uLsUO7M9S/t81tPaHW3Eg/S+p4TmZf369Rg9uilEeMqUKQCAm2++GbNnz0ZZWRlKSppSZxcVFWH+/Pl48MEH8cILL6CwsBDPPfecb8KkAfWXS/mwpXb/RAovb942BO9v2odfXsS/vottmhfFdy3/m3fXRezYO8qrMb6vXHhJpKaKR6285nv29PNWO2Hl8dLIB7sjh1h9W7Rhd/YLx5mNODRfBvtjbZjz1jfomI2ufmmVL7Po2s3rtw7Gou378dtLz8DJ+jB276/GoC6t7F9LKgHjZnVNPfYeOoG+p+XKtpsVqpWIoijLc8N8Kpv7PbN9UEoIL6NGjdKdDc2ePTtu28iRI7Fx40YHa2U/LTJCOFYbWXhNbWIZ54Ef0N7nJOf3aIfze7QzdaxtDVbRHLQ0L0eONzm0KR3UEpXKHuBb8+f7iuPMZe3UvABAx9bN8Oer+6FtdoZt0QCzbhyIz7/Zz53TQolM82JQNRFysxGf5kV/P4vsIopi3P2Tal6igkz41CrzJLhEGN0zD6N7Rpxv/37dAMeuk4iB88Jnl2J/VS3evG2IrL+ULxgqb2wvL/sOnVo3w8V9CyCKIv7wyTfIzgzhgQt7xB0bFiPOwmrn1SPaDO1LUsdTuOljSggvqUJuVlpMeFE3GykTN0k1L95oCEbYJWQpX3otdftxvUyUjO9uY1jEXxbuxNCubTDSpNBmp6pYitW7qdbOfjbI3jQBF/fNx8V98y2fR+7jxWc24rv/RmajyLW1hLvnv9iNd9aWYq4ie7VU+9Z4Spq95uVV2FHu/zW2/EYiesv9VZG8YZ9uLZcLL9JCki9f/3AUT8+P5H/Z88wl2FhyFK+eWkA2KrzIDhVFhc8LW72ifacLLi8yAT4r3RtOL96ohc9p2azJmVitY1Q6OEmLGIV3egW7wruVYxFLxIfyGOURx2obsGBrWVzq7Xkbf8CLS77Dza+tNVHTU/VzSnhJQIbdRNKqmbZDvVTwNU5SJxdvbRUeT11aqwozFu7CvqMnMfOzXbLt0jYanTGv23ME1TUN9tXNAWbdOFBzn18mTUrsbvbGWYeakOWakmyvUGTGXSFbCTq+/YZF+fII/JoXpuIyfnYqp84DF3aPbePpQ6Tvbb8OLfkr4ACkebGBCWcWYNuPVcjJVL+dytwW0tmn3UngnMIu61ZctBGL8KL4rhzQ7n9nEz7fcQBXnFWImdc2qax/OGJdpW82e6fTeK3VdG+fjbXF6j4/0o7PqB1FfF7M5VUx6tSbNC/65ZQCtdR0yBpe7QXUtGY922djVM92tmvpEoWbJgstnxdlu3t1xfeyfcoq/2v1Xvz+v9tj31nbVNN7wd8Gf39FX0wZ2wP5kmANnls5sns7TB7THcO7tfHMhNsbtfA5Q4pa4/27h2PxQ6NUO1DlbFOmefFK3JkBdmUFVpqNjF7crLRgXO+gvMefn4oe+UCxIJ8dw4xTg5XlPC8e0bz0LojkVbrt3CLNMtK2Y2R+/OirH7Fuz5HYdx77vrHDrrnzSLVvfo8qatU8DdMm9MbpeS3croop7G71PO+RtF08fiqjshpVEo1c9BjpdaSCC8CeNDSWpM5kl1SQmyXPlMtxbCAgYMpFPXBOV/V8a25AmhcbEAAM6NQKAHBEkkI6SrzPSxNekWKNsGuw5NW8iCruueze+dYFD6cm2lZvZxcLib7s5J07h+LbA8cwqEtrzTJS+Zx35myn5iV6ZWkd1Bx09UybWnmJ3KJru+b4/iC7o7jX4H4PEiizK9uBVOO7YFs5WIgI34KuEM4rvJhB7T57ZP5jGhJebEDaCNQamFJrIf3qF7ORXQ67yve00SCcR+nAGTkH48uus6+uIYzahkZkZ+onP3Qqp4zVUOlBXVpj+k/PRJEkj4YbtGyWriu4APL2zy+8qN9/VaHDQKxV29sYFuPeQeV5pHVwc0V2NfzRe9iHq5EuJh49yyGNjAKx/Xle/N16SHixAWknqta3Kd83Qebz4m3NS6fWkRm+XWajbT9Wyr4ba15UBiVW73ydcmOeXYLSwyex+bcXoWWzdM1yXtW8AMB1QzpZP0kCkAq+vEKw1jNU8yUwkjM/3PwjurZtgaJ2TQJfQ1hESJnPT0/zwhM7nwC8Yj5MFG7+WjPZlVnmPqxBATGPFxN9ktpkye9Nx9sjp08wagPKDlv6TbmEvFf4v18Mw/SfnokhRZFZtWBTSymrrJF9N/QpUdnNmudFr1zp4Ygz7xoNJ9MoXg2V9hNSny/eDlNzwFDbxvCo/vrZLtm9Z/FpkpZpDIu+Xhg0PU5S8xeJFNbiohwZHruybbD0VazLtTRpXvjbn6rZiPss3oKEFxuQvlBqDStOeJGUd1vtr8WQotaymb1dmhcl9QwqUzOdCGs5o4HIMeFF437+yu6MpB5AKqDztiOt+19y+AS27quUL5rI2KlLTQ9qmr84h11FqLTHLEdMXHV2BxS1bY4nL+/jdlUskUhtQbz50MQ5GI5h93kRmc+pRO22+V1rR8KLDUibgJpWWdlIWjdvMlM8OqE3rh7YAW/fMdSh2tmDU5mADX1eVIYk9qROxkx+Z7OuAOPUJDtdw1x4z2jzi9Z5FZ4kdUq0nvXoGUtw6d9X4KlPvoltY31W0iqohcIr24NUrX/0RB1uf2Md24UMaNM8HXkWl15gvZvXDemIxQ+NQhePTpZYcVNRzSIcm+kv2EOlo/Xgx++CihokvNiAzGFXTfOiaDe5WWn4z6Rh+PCec9GqeTpm/Kw/hp9ubcEyp3Gq7RtpTNUcdo20JZUn6zH7y2JUVNfqlgMiS9NHM2pqXd8JWmjkBEpGeJLUKTF61q99WWyqTlFYZr1SAeeFxd9iyc6Dlq7pFP+97zy3q5AAvGc2EjU+6x0jhVXzYkXjl3yiCzns2oLUGUo1z4vKyG8UoZFI1j16IQY/9ZluGafMRkb2XjWHXaN3+Jf/txmffXOAuQ56piGnzEbShRSTnSBHkjolTpholD4sSvTMRkdO1NtWD7t/mnIhwWTE1WAjhr7ASZ+X2PIAPva5shPSvNiA9IXqpJJ/Iz3k7dvMsmqwUyGK9UbRRqIY18sr312l0zOP4ALod4iOCS8Mmhct05LfkLYd/mgj9vvPWlQe+hw/cMTleXFwsEhCbT4nTTcgGtmoRyJDpeO0KMrvKu1CS/Oi180xa14sBLqp3Ta/C0HJ0Tt6iJzMNCyfOlq2LTPN3x7+gH1rGymJZiytqqnX7AyMOg2ruXL0cq449Xq3SDcWXvy6/owSueaF7zfx5IRjddiVCi8smhePRUfLYL2dhS2znK2IDZQcPmFYxkuh0kwBAbH/tQsz+7zENC9MxWWQzwuhirJddGzdDG0kTrkZHte8sMIyax7Rnc93p6ExjLXFh9Hv8YWaKbfjVbFyQg4useDU7IRF85KWLO3GgsOuI5oXzrWKnNS8mKVbu+b4/U+MI4c+mXwe3r5zqC+EFxbsHoP12td/NvyAj7/6UVJWcazKObT88/SaEPfyAI5NqfxFcvSOLqOeAKhpWzJoXgA2fwXefr6+UcQfF0SWk39j1V7V8xk5zlmNhNLrDJwKi2XxefHL0hFGBINSsxHfsTxmO9aSjUaaF8U1nVqc04pg/PkvR2HisC6G5foU5mJ4N28HA0TpzrDekt1mI6MncN87m2Kflc1AXVOsPtHSa8fMPi+i/P9UJzl6R5dRm/hLx9OMtOS4zdKO49WbB9l23qqTTU6Q/15fGrc/3vasMBtZFF4O6kQluemwmyw+L9Y0L8Zljhyvw9Z9lczCgLQcS54Xry0JIMXqMhNuM6BTy9jn124ZjF752Qm9Pt/rbRw4oDXRskPzUl1bj1IG01qqkBy9o8uodSBHJVEJGT7PahlFOvAUtsxCz/bWOxpRFFFV03SvfvWfr1XKyL8r33WrmpfLn/8SCzUWWnMzVLpHe3+u/KtEtjAj57Ni6dcH/H4RLv37CmzYeyRun5pA02hkNlI67HpYePE7d47oit9c0huLHjwfHVs3w12juumWt9tstOr7Q3jsg604UddgWFbp+8STBFNvEsTavq5/ZQ1G/GmxrxfitJPUidd0ELUXqk7SQ2YmieYlqEjzrvZC8tpjRQBVJ/U7jjhVrNJh14YIlhkLd6qWdUPzMu/u4XhrdQl+PT45su1KNS+8Yw+PyUYt/4ra4Y2GmheF2cjDenq/+2GmhwK4Y0TX2Hc9x9JbhnexXdP02AdbAQDN0oOYNqG3btl4kxBL6LT8fzV4NXvLdnszz1CiSY5R1WWMXic/aF5+d9kZAIDJF2hneJXKCAIEXD2wAwCgfwfz+SVEEThZ32hYRo8gZ1SO2vnKFWsusV7bLHrCy9mdWuEvP++PvOxMZy6eYKxoxngEB7WyqgK2gc+LEic1L343+9iN1t346rdj8fjlfVRN9Hbwj2XfG5od1UxC4bCIbT9WaZeJ/a+nefFwOJuHIeHFBoxmP37QvNx6bhHWPDIGD17UQ7OM1IFUEIA7RnTF23cOxVt3nhPbzjvYm5nVKo/hjTZSu2JVjbr2x85Z9wvXnx37nEoZdq2E2fPcfbVHpSZ4GCWpU+JlzYuSqJ9UZ5V8U34mmivLSWFv0fb9qtvDYRGvrSjG1z9Uxu2b+dku/O3z3bHvWlpiPfmkgScfABEjdXpQR9F/oby6crSS9jn6M32Z8ILIjNpqJIOZ19ZqtBFXBIuN/UpBy6b725whz0uyYCU7M1+0kZqWRe2cTZ+ZktQ5FW3kwDnfv2c4Xlz8HR7y6QKfWk0lut1JM9meQ+q+JB9s3ocn/7s9brsoAs998W3cNtl3xf9q8LYvf4wmzpM6PaiDGL1QdUkiWaeF5D4vavAO9qaWmVccw+/zwl7Wzlm3tJ7ZKaR5kQqXvHeT71mpbVMxJRktD+Ajh12lj0ifwly8cMPZGqW9j5ZmJfoznZwHaqUm2Lm/WnW7qrCs/H5qg14/YpRlPA6/OzrZhPftGT7AqCnVGvh0+AX5y63+q3kddmsbjO9NfKi0HCc1L3aOW9LLpuraRryyoJpmRAs15161BHPGGXb947CbbGiNy9FIRyczxZ6oU++LtML71ZqFcqK1+vtDqtulNDLmeYlCokuE1OlBHcTohaptSA6HrHSFz4sdVByrMywTHyptLdqIBzsz7Eodk5unkvAiSDUvfPez9PBJ5rJqQkajitbTOEmdonxyvL6+JtqCnFogFgD+/L+dqu+7Vvei1pKVsvZ972zCZf0LbY02cpLrh3ZyuwrMkObFBozGzglnFiSmIg6j9HmRclbHlgCAawZ35DqnXoK4KHEDngi8v+kHXPHClyivrDGRO4THj8I+pAOl1xfrtBPp88lwMPGe2higGgotGuxXfLcaDZKVJBm2E4HWmxydIFrN6WTEjIW74rZpCUxqgs51r6xWLasnn6gJ0EOLWmsf4CBPXdHXleuaIXWmfw6i5wHfPD2IorbNE1gb55AuFKjUNr37/87BtweOoU9hDh587yvmcx49wa95ESHiwfciyez+8Em8Ix3v+fSwMzX8wM6tMLSoNXrYkNzPr+RkpTl2bvWEdNajjaz4vGSEAshICximAzBLspkQtM1Gp/53IfhBS7Ou1iq2l1WpbNXXOKoJ0HrviZMuL35awJGEFxvQe975ucmRqwMAQpJZs7IPyUwLou9p/Ple6hmcmd9aUyL7Lh2jjtU2MHXg6/ccxvG6Rozs0c41n5e0YADv/WKYfSf0OF1UwnWdXOdLXfMSrzWRPn8jzQzAt7K1kpysNE3hh1xp2IkOqm5EbtqxnpJeP6IWKu2keSxZIOHFYZxc8TjRyHxebJrzmcvz0vR5yc6D6H/KZAUAG0uOqB5z9axVAIC1j47hShpop89LqnRHuVlpmHXjQJxRmBO3z8nxWj2ySKWcpAGpP1+Fw64FCTYnMyRbKkQJjVFK9G+I3QszsqBl6eTpGnQddlUaqZ55jJpMBBJebEDvfXLaRptI5GYje87JuqKqFKUK9qvSo7HPP31xpe6xFdV1OK1lFvO17NS8pMpAJQjAsG5tVPfZKQwqYde8SOtjfF4rDpXZmWmoNFj+wgrJ1qaMfo8b/ammKYVLeNHep9a+9MxjTph2Hp3QW/Od9SrJoxZwET2HvBBn6novo5UHwQpmBgYr45/Wmkya17JRV+Ane7JT2OlDpITZ50VSTn35APn3OgvRgtmZIUdzkyQb0lt15YDT4va7YU7RDJXm6Bv0+hy1PjDR5rE7z+9qyuzvJiS82EAznWypSaV5CdkfKm1KeLF4TZ7jPRTFmBSIAC7uk+/MuRmjjcIy4UXlPIrvLLmItAgFBEe1IyEHo7fcRq3vdMMKrxkqbZfmRcXnhcc8dvt5RewVSSIS0hRefPFFFBUVITMzEwMHDsTy5cs1yy5ZsgSCIMT97dixIxFVNUWGTtirX5YGYEGe58UmnxdTmhfzEgWv5oUSlLFzw6kcEQ+N1U5NHxaB568fgCUPjbL9+qp5XtSEl7C+5kW5SKeVPE2CIOgORFbfohYZyRWGLe1X1PpONyaDWtfkmwRpl1bbpyeTKmvTtV1yRLPy4rjPy3vvvYcHHngAL774Is4991z84x//wPjx47F9+3Z06qSdEGfnzp3IyWly+GvXrp3TVTWNnn0yqTQvUp8Xm86ZaLMR6/FvrdmL/h1aOuqjkWz84Yq+uGtUN3Ropb0ooCiKCAUDjiwcyCq8/PfrMll9lGwvq8KeiuPocirFQY2FMOeAoJeh1bpRMtnWyJLeKVXNiwtmI81QaZvWSFMXXpJn3HAKxzUvzz77LG6//Xbccccd6N27N2bOnImOHTvipZde0j0uLy8P+fn5sb9g0J8zjGSKNlKuKu0WljQvEJiOf/T9rbj07ysonJUDQRB0BRegqRN3wv+H1WxUJtGsaMnOn24tj322liHbWbNRMi8zEY0ibJ+TEdvmJU02T9egJ6aqCdg8QpqTK217GUdH1rq6OmzYsAFjx46VbR87dixWrtSPChkwYAAKCgowZswYLF68WLNcbW0tqqqqZH9eIpkk6DQHQqXNYNUPhed48nmxFzsdoJWoO9/qX09LnV9V0xTebEV4CQj6gr5014IHRnCfP9mWmZDeq+yMELY9MQ7Lp14Q2+ZGf6rVhqwuGqq3T09IU7anVI0DcFR4qaioQGNjI9q3by/b3r59e5SXl6seU1BQgJdffhlz587FvHnz0LNnT4wZMwbLli1TLT99+nTk5ubG/jp25EtP7zRemilYxYlQaTNYd9glnxe3cFIYVDu3UXZcrd1VJyXCiwWzkaBjNlLSKz8HQzjTwiez8CIIAppnhGRLabgRsafVB/D0I3rdiOp6Srp5XgTFd3O0bp5u8khvkJCWr2xwoihqNsKePXuiZ88mh79hw4ahtLQUM2bMwPnnnx9Xftq0aZgyZUrse1VVlScEmJzMEKpqGjCmd3vjwj4hGcxGAN8ASj4v9uLkmi2qPi8Gz0/r+VbVNOVmsaZ50XbYtaNlJZ3DrmQo9sq8TzMVFZfmhc9sxBMSbrYddW7THE9d2RdtfCrEOCq8tG3bFsFgME7LcuDAgThtjB7nnHMO5syZo7ovIyMDGRkZqvvc5LMpI7Gp9CguTFbhxad2VkGwz9GOYGftI2NQeuQkBnRq5dg11J6V0fPTinarlGherDjsCoLOzNiGtpVsmhcpbjjnqqGV54fL50VPeOHUvCg1Plb6qBuGdjZ/sMs4ajZKT0/HwIEDsWjRItn2RYsWYfjw4czn2bRpEwoK/LUyc15OJsb1yU8qnxfpujRu9itWTTl22aoJdvJyMjGws3OCC8CepE6K1u5jNvm8CLrSi3UzSL8O/kosZojMbOReNaT89bP4laYB9n6kpr4Rh49rLxGhdh69cUPZpp30I/MyjovtU6ZMwcSJEzFo0CAMGzYML7/8MkpKSjBp0iQAEbPPvn378OabbwIAZs6ciS5duqBPnz6oq6vDnDlzMHfuXMydO9fpqpqiV37qrBDcIrOpubjZr1jKsMt5PPm8+Ac1QcTo+bE8X0vCi+kj2RjYuTWev34AOrdOjlwf2RJNklc0L1qwCg3X/GMVvvqhUnO/aqi0zm9XtvNUnWA5Lrxcc801OHToEJ588kmUlZWhb9++mD9/Pjp3jqirysrKUFLStGpwXV0dHnroIezbtw9ZWVno06cPPvnkE0yYMMHpqnLRtW1zPHbZGTi7o7OzSS8hta+7mere6rtKSeqSE5ZU/6z7pQOnlQy7gqBvYO2Vn419R0+aPj8AXNqv0NLxXqJlsyb/C4/LLsyTID3BBVAXPvQ0L8riqeqXlxCD6d133427775bdd/s2bNl36dOnYqpU6cmoFbWCAYEjO6Z53Y1EkqLjLTYZ99qXjgz7BL+wVy0kfp+6cBZW++c5uWZq/rhb5/vwnVD1BN2PjKhF56e793s4nYjjYDx+mtqV/XU/K7SdbK2K8t7/T45RfJkUEswXp8VOIE0IZavfV4SeC0icajNQI3NRurbpfoSa0nq9LWU7bIz8IcrzkSfQnXflVbN0jHloh6Wru8ncrOaJkhSp2ketj0xzq7q6GKXxkNNwNZbckbZplNV80LCi0m6tWvhdhUSTrbM58U56cXpl5Hn/GFr4xaRQNQEFTt8XhotNAI9f12WVhgM+DWuzxxSc8nRE3WmzpGoCCy7uim1NigNjlAS77CbmiRvnJ1DzLt7ON5dW4KpF/dyuyoJR9YpONijGvspmH9deQ8lzYt/UDcb6R+j2ZYk7dvI9OQkAcHZ5QW8TLMkDgOXota89MxGyiabql1UarQOGzm7Uyuc7WCuCi8jNRs1GI0KFjB6F628rCLn8SnaL/gSc5oX9e1SecGK8GJV7tDL95GsvHD92Vi++yCuOOs0t6uii5OaFz2zUVyeF8nnDq2yUNsQxsHqWnsq52FIeCGYadM8HT3bZ0MQIrZ4pzBej8bKuXnTepP44hfUHpVZs5F0s1GWXiOsaE6CguBqZJ8bXNKvAJf0835eL7vyq6gLLxxmI1HER/eei7dWl+CX43qgXYsMFE2bb0vdvAwJLwQzgYCAT+8fARH8M8JIZlu2soaaFwudhgiRy48lVXMo+BE7NS9SgcWK35NVwSOoMgFPMVnGs9g1r1F12E3jMxv169AS/a5uaU+FfAI57BJcBAKCqazBXGt1mMzNwXpuJ/O8dG7TjLdKhE2orm1k0udFOqBY1rxYMB6p+bx4PXlbqmCXP9zy3RVx2zL1NC/KaKMUNW6T8EIkBJ7+dvnug7r7rZhytDqcti3U18fivdS/bhvKWyXCJsyYjWYt/Q7fHzwW16aix4miaNnnRavtq7Xj7nnyKMaAIMQJPzwTgWTn7E4tXbu2k1pZ3TwvcaHSztXDy5DwQiQEntnn7W+s191v5V3V0ryENLRJvIJSgN4o11BfmFH/+dU3irjgL0vjjo0KLIk2G/56vDyKMRiI17yQ7BJhZI92mHf3ua5d30l/ON08LwptYorKLiS8EImhzsboJKt9Bs9CaLyDF6n03UPNvMPa7JRHRoUXy2HSnM0hJzMNv5QkpQsEhLg6nNO1jbU6JQluD9pOCraZuj4vpHkBSHghfMjzi781fayW5kWagE8Kr107mVYR9xuqPi+Mz0/LbKT1/G89twtf5TiQyr9BQUCdJMPv7ecV4dmf93fs2n7C7UhAJ3NA6UUbxS/MmJrSCwkvREohari3aaVn5+0XSPHiHqo+L4zTY17NC6uGzYyzrjRCKRCQay0fmdAbbTT8s1INt8dsZ4UX7aE5zmHX7RvhEiS8ECmFKMa/7M3SgzijMEe1PLfmhaQXT8H6/JTFojKLluaGVcEmCPzh0lLtXUAQUC/RvJBmrwm3o2yclBn0NC9kNopAwguRUoiQq13PPb0N5t41HDkaZiPejoF8XrwFq1+CUsiJaV4arWleAP61jdIlyV2CAcFWf7Fkwu11x5wUGkJB7fZVcUy+5lOKyi4kvBCphSiKsU6na7vmeOuOc9C7IAdZ6eozHV7NSyqmc/cyrGYjJTHhRUvzwviczbSGNInJIKDweSGaiGpe/nR1P1eu76TZiEc4Js0LQaQAEc1L5G2Xdg/NNISXAyprhHRt21zz/CS7eAvzZqNTDruaPi+WqqVLBmlemIg+s58P6ogbz+mU8Os7KbzwKHDdNp+5BQkvREoR8XmJfJbObrSWoH91RXHcNr0sumQ28hasihflAGCoeWF12BX4nbjTZZoXkOZFQdd2kcnDZf0LY9usZDE2i9M5gB6/7AymcqR5IYgU4G+f78aCrWUA5JEkWRrCixp6DpjkUGkfCx883/I5zGpejKKNeJxweYWXtKDcbFRLwouM9+8+F2/fMRTXD0m8tkWK05qXnw/uyFQ2RWUXWpiRSC2W7TqIZac+f19xPLZdy+dFDb2xiBQv9tEiw3r3xJpkLi5UWjQKlWa7vhmNgFTzEgwIqCezkYzcrDQMP72t29Uw7U/FQkAQwPrUjUKl1z16ofUKeRDSvBCOopevwEvwaV6091GotH3YMTQwCy9a0UYax/M8Zy0BRmvMUQovZDbyJk6ajQREJlSTLzgdd43qplvWSAHULjs58wKR5oVwlGbpQV+ovXmEFz3dC5mN7MOOmS2raj8ua2lsbSOL0UYmmkOaJEyWoo28i5PJ4aJmySljewIAXlrynXY9UtRwRMIL4ShZaUEcQb3b1TAkk8dspDMgqflCdGydhWsHu2ufT1WY1yZS+rzEzEbqxe1QsGkNOhkKh10yG3kTpzUvrJDDLkHYxCs3DUJOZgiv3TJI5kvy/87v6mKt9OEyG3Gee/nUC3DP6NM5j0ptmqcHkZ+bafk8zGsbKQSJaAI0q8sDACaijYJNbTEYENDcBt8fwn68EyqdmpDwQtjORWe0x1e/G4sLerVHt3YtYtsfmdAbY89o72LNtJFGeBjB07E4uYBfMnHbuUWxzw9e2AMbf3sR1zPRgnltI03Ni/U8L7zCblpIbjaa/tMzcVbHlph140DOMxFO4qzwwt5qaGFGgrCR6Mv31JVnYnzffMy5fajLNTKmY+sspnI8ESS/u6yP2eqkDE9feSZ+c0nv2PdQUNBd24UHVouL5sKMNuR5CXEKYcrlATq3aY4P7jkXF/fN5zoPEWH6T8905LyekRm8Uo8EQ8IL4SjtsjPw0o0DcV5390MbjXj252cxlaOAInv4733n4fnrB+D6oZ1kDrB2OkI2Mi6Ao3bNhsawLXleQhpqGpZoI0p6aA1BAK4b0gmXSxLa2YVXNB569Ujm5kPCC0GcgvU9T+YOIZH0PS0Xl/aLH1TsHBNYfV7UZJRL/77CBrORIBNGWJBqXgLUQ9vCJf0KbD+n0xl2WdFr4lqCczJArwbhOhf3ycfAzq0AAC2bpblWD1ahxI1U5KmEnWMCu9ko/qo7yqtx6Fj82lYAn0aEdwCxw9eHiBB9Tk68sV7RvIzs2S5u26wbz0bbFul48zbvm+vNQm8JkVDU+vxgQMAfrugLAAi5OtVkll70d5Ns4xmYc8VoFCuvqlHdzpxh14TPS1CS54U51JtQJXonecx8rDiZ54WFXvnZ+M+kYRjRPV54ubhvAdY9eiGGdWvjQs0SAwkvREJR01rIF69zr0PQ6t/6d8iVRUkZdYPkp2ANN8xGWqXKKzWEFw5tijTpHAvNJGH7uVnuaSKTgeir6IzmxYGTctC6eToGdWmtud8Jgc1LkPBCuE4wIMSEGq2x5n8PWF+kzwitV71ls3SEJAOQUaeQxGbmhGBnxlCzodJRyrSEF9ZoI/BrE0PBAD7/5UgsfPB8NEunHC9WcNLE67bZyO3ru01ChJcXX3wRRUVFyMzMxMCBA7F8+XLd8kuXLsXAgQORmZmJrl27YtasWYmoJuESAUGIDfhaL2Sr5mnoU5jjaD20hJK0YEA2WBl1h+QTYw1pE7A6eeRNUqf0T7FqNgLkPizSZIh6NevWrgV6tM9mvwihTlTzYsMr2Stf/jzc1ry4fX23cVx4ee+99/DAAw/g0UcfxaZNmzBixAiMHz8eJSUlquWLi4sxYcIEjBgxAps2bcIjjzyCyZMnY+7cuU5XlXCJgCDEOhet9zEoCK7Z/zNCAdmaRYYdIckutmHVBMe+MKP69Y4cr1Mtz6qSFwS52WjL42OZjiPsocnnxfq5ChQZn932eXFyVWs/4Ljw8uyzz+L222/HHXfcgd69e2PmzJno2LEjXnrpJdXys2bNQqdOnTBz5kz07t0bd9xxB2677TbMmDHD6aoSLhGRC/TNRoIgOK4m1erf0kMB2SrCxj4vtlUpJZE+Zau3klV4ibUtxQWPnFAXXnhWlZaaHHmddwlrNPm8WH8p4xbvdFl4YdUqJiuOvkl1dXXYsGEDxo6VzzbGjh2LlStXqh6zatWquPLjxo3D+vXrUV8fv8BfbW0tqqqqZH+EvwgGjM1GApyPvNAaj0IBQaF50e8IyWxkEUkbsGw24ta8yLcfOaG+qCirG4sAweUIutQmYKPHrjKNA2P+Q8dIccWLs8JLRUUFGhsb0b69fD2b9u3bo7y8XPWY8vJy1fINDQ2oqKiIKz99+nTk5ubG/jp27GjfDyASgiAITQKBzgvpuPCi0cOFgoLcYdfgPKR5sYZc82LtZvLOjgUIeOWmQbHvdizMyBttRNiHnXf+UckSFoD7mhe3zVZuk5ApgXKmKoqi7uxVrbzadgCYNm0aKisrY3+lpaU21JhIJMFAUyej9zo6nbxLW/Mid9g1zvNCg5UVbHXY5dS8CEJkYdF/TNRfBJHP54U0L24RfU5W38jXbxmMvGylz4vFk1rEbeHJbRx9q9q2bYtgMBinZTlw4ECcdiVKfn6+avlQKIQ2beIT7mRkZCAnJ0f2R/gLmcOuxguZlR7EX685K3GVkhAMCLhrVDdkpQVx67ldDLUBJLtYQxoqbT3aiO+a0ctlZ+qHKPNo1zT9XFJ77EkItiWpUzncbeHBbbOV2zgqvKSnp2PgwIFYtGiRbPuiRYswfPhw1WOGDRsWV37hwoUYNGgQ0tIoYZPfUetDIqHSkR3KifInk8/D/MkjkJkWRN/TcnGZjQusPfvz/oZ1AyI+Lx1aNcOWx8fid5f1MRxQSXYxx+l5LQBAtt6RVFCcdePZ3OfkzfMSHeRyMvX7Gp48L2lkR3ScoNY9tsnlRe14t31O3Bae3MbxDEhTpkzBxIkTMWjQIAwbNgwvv/wySkpKMGnSJAARs8++ffvw5ptvAgAmTZqE559/HlOmTMGdd96JVatW4dVXX8U777zjdFUJl5AOBMoEZX0Kc2Xf7VpoLCMUwE/P7sBUNpquPTqDNoyUJtWLKT6ZfB6OHK9HviQkVfq4L+7Lv7jemuJDTOWirS56ucw0+bwuGJCH6nOtbaTQvFzYOw+ffXMANw/vzHwOQp+7R3XDwm3l+Nkguc+jXW+i2jvttvDg9vXdxnHh5ZprrsGhQ4fw5JNPoqysDH379sX8+fPRuXPkxS0rK5PlfCkqKsL8+fPx4IMP4oUXXkBhYSGee+45XHXVVU5XlXCJYAASs5F+WbtS76sJQVrmoDRFtIhRFWiibY6MUBD5uUHZNqvPu57RbhSO+dXh1P/y68YLL2zXFwQhzmH3+evPxsa9RzC4SDu1O8FHXk4mvnz4grjnFl3GwWq3ofa83RYdUn3dq4Tknr777rtx9913q+6bPXt23LaRI0di48aNDteK8ApSs5GR8GKX76Pa2jRaHZxSJW3k8/LXa87CLa+vw2OXnmG6fsQpEiQIKs1GSqEpLSBAmvGFR6jq0CpL9j0zLYjhp7c1VU9CGzXtSMznxWJDUjve7WifFFe8JEZ4IQg9AgFphl39N1LTts2JquZFx+eFpVyUUT3zsOsP45EeoigTq2jd6q5tm+P7iuM2XkmueVEmoVO2O57ULWPPyMfdo7qhf8eWVipImCAWbWSi2xjQqSU2lRzVPN7tDLdkNiIIlwkITTMbIzW/XWYjNSFIa3YWDPIJLwBIcLEJLf+hgpaZtgovygS7yssq/VZ4QqUDAQFTL+5lsYaEGcz2FunBANIlz9wph938nEzN9bOMSHGrEa0qTbhPULIwo2FZmzQvqsKLxqmVPi8UT5Q4tJ6J3VmMYw67UbNRwEDzQk7ZvsB0gl1B0fYcCpW20p+lus8LCS+E6wiCwNy72KZ54ThPnM8LjVsJQ+t52/0MlJoXZftQmg6ZHXZJ0HUZc9KLAPmzU/d5sVCtU1hZOcJtnxu3IeGFcJ1gQGDu5O0KlVaaggDt/i2kNBvZUgOCBa17fU7X+ISVVhAVPi/KZqZsA6R58QdmF2aMmPvizyPFDs2LlXaU4ooXEl4I9wkI7DNZ28xGapEJrNFGNG4lDOW9Xj51NF664Wxc2o8/54se0WylTQ6eSs0LX7g84Q2ir66Z5yXXvMRjVXho2yLdovCS2tILCS9EQlHNsBsQmB0g1UKczaAuBLHleaFVghOJ/Jl0bN0M488scMDnRb48gLJ5KNsLj9mRcA+z7USAIOurnEhS99/7RlgSgkl4IQiXCQXYuxi7EsDxOOwqy9pluiKM0cz67pTPSzRU2uCZswrRJOO4i1mHXeVzU3uOVnxO0oIC8nMzLWleyGGXIFwmMy3I/BLbFyod3/RZfV40F9ojbEcz2sghoSAqRqtl2JVC8qs/aAp95/R5gbyvUXveVmSHaDuz0o5SXHYh4YVwn4xQgHlqZNe6QWryh9a5lQOXMt074RxaOjnps7LjeSg1L/EOuybzvFitGGEJs0nqBEFQHGO/2QiwNhm7f0x3y9f3MyS8EK6TmRZk7lzsMxuxN32ljwv5vCQO7TwvTTw8vrfl6yh9XozMRuTzktwIkLcx9Wgj69fZub/a9LG3ntvFegV8DPXChOtkhFwwG6mcRtNspBzISPOSMLSet3R7XnaG5euEY5qXqDrfyGxEPi9+IDrP4H4Mgly7pna8HXlWzJ6ia7vmKb96PQkvhOtkpgUS7rCrpj3RdNhVCCvpGj4vLTJotY1EIX1WdggvYtyq0vL9vOtbEd6gyYeJ9zh5X+NEtJEVauvDrl3bK5DwQrhORojdbGTXbEPN8qPlX8GqeZl393DL9SLksJiN2tkhvCiuZ5/mhaQcN2m6/ZwOu4LccOREnhcr1DaQ8ELCC+E6mWmBhJuNeDQvcT4vKpqX3156Bnq0z7albkQTWs+kRjLztEV4iS0PELmg0qclTfHMye3JHzQ9xSZJg6ULEQR5Odsz7OrU4SyG1cdrGxrNXztJID034TqZaUHmsnaZjXiS3Sk1LWkUJ5swtITVDq2yMLhLK7Runo7m6XZ0Y/pmI9OaF8v1IqwQ1XxJtSRBQUCDgeAR57Cr8iSraxpsqGET944+HZlpAfx8cEfDsqR5IeGFSDBqnQBftJFdmpf48zAnqVPRvJB1wBm0bmsgIODfk+wz0zWeGgui7SsaKhsd4+IXZqQH7geiT0kqq0SenYHwIgiyZ6z2uN9eU2K5XlLycjJw07AuTMfXkfBCZiPCfTJC7GYju8YMnsFHOXBRnpfEkSifkfpT0ouWM7bpJHXUVNzl1P2XRgYxmY0Yy9kJNRU+SHghXCczLcgRbeSk5kX93CwmA+p4nCFR9zU6k00PNXWJ0tk6aV78SUDFbMTy7A4dr5MJL4l43nqCek/yp4uDhBfCdXg0L46ubaRRVumToyq80GDmCIm6rXWnNC9aWjVlUkN2nxdqF27SZDZqkl5Y+xDBwGxkN3rX+PDec/HFL0c6XwkfQcIL4TqZaUFmB1ppuasHdjB9TZ6FGbPihBeVMunsTscEO2ZmvEO6tOY+Rk3zIkUp1JCs6g+iz0nq4WLG2TohwouOoJuZFkTXdi3QsXUWAKB183TnK+RxyGGXcI3/TBqG9FBAVZDQQjobsrK6s7rmRf18SuFFWodfXtQDG0qO4IqzTjNdF0IbM4NG39Ny0RAOY2PJUeZj6mOaF0afF8a2N7hLK+Y6EPYTfaelYc3sK4JL87wkwmxkXObN24Zi5me7cPeo0x2vj9ch4YVwjUEmZsjSfodH6FHCpXlJ19a8/GJkN83ZOmEdM4OGIBjFksQT1bxkaDxLZXsxqtXyqaOxo7waF/TK46wJYScxzYukQZzdqSUW7zxofKzKeZyE5RJFbZvjb9cOcLwufoB6XcJXBOzSvHA43SoHNGkdrAhQhDHZmebmV7zZT+sMNC/Kp2w0mHVs3QwXndGefKE8glTzMuNn/ZmOkS0PYHeFVKCmwgcJL4SvCMoEB/PNV7lekR7KAUh6WZJdnOVPV/dDr/xsPHed/mzzqSv7xj4LAPeKd1HNi5bwUq+QhsgR1x9E311pc2jTgi0js5MOu2rnc3GpJF9CwgvhK6QvvZXVndU0L+x1EFQ/E/bTtV0LLHjgfFzev1C3XGFuVuyzmUdSa+Cw29AoTwpGj93b/OaS3shMC+CZn54JABC5DYlKbYszD/xPV/eLfSbZhQ8SXoiEYnXlZbtMNlaOpRwf3kO+Do3APRDU1kfWitHSvCgzmlIL8DZ3jOiKbU9cjP6n1gkypdWQtSlbqhXHhDMLYp8b3Vzp0YeQwy6RUB4a1xO7DlTjusGdTB0vNdnYHW3E2nWQqch7yFK5g3/RvFoDh906heaFpBfvI33HzcgFyjblBNI+TCS7ERckvBAJpV12Bt6/+1zTx9uleVETfNT6DrV08X0Kc01fl3AGmTZM4J9p1zboJ6mra5CfkLRv/sLMCtDSJ+zU85aelxQvfJDZiPAVUh8TLRU/C6y5HtRm4q2bp2P1tDH46ndjTV+fsBd5ZIhgQniJmI20fF7qlT4vfKcnXMaMUkOwaDZ6dEJvzfYU9bmTTsDIbMQHCS+Er5AOUlbMRqqaFxXDUUaa+iuSn5uJ3Kw009cn7EUqjJrJ81Jbz5ekjhy1/YUZk4w0osxMdNmd53dFTqZ6HxHVuEiblRntUCrjqPBy5MgRTJw4Ebm5ucjNzcXEiRNx9OhR3WNuueWWU8vRN/2dc845TlaT8BGyPC9WNC8qg49a3xGyEI5NJA6lfwLvYGUUbXTruV1k30l08RdmxALpq29WVtWaX0XPR0KweRztma+//nps3rwZCxYswIIFC7B582ZMnDjR8LiLL74YZWVlsb/58+c7WU3CRzireYmHktD5A+VjMuvzoubjdHpeizgtm3TMmTSyG/oU5vBdkEgo53Vvi/RgAAM78yzXYP3d1/KVUetXyGzEh2MOu9988w0WLFiA1atXY+jQoQCAV155BcOGDcPOnTvRs2dPzWMzMjKQn5/vVNUIHyPY5LCr5vOiNlsn4cUfKBOK8eb10PN5UWsCUjPCred2wcPje6HLw59wXZNIHDmZadjyxFikcWhSrfq8ANqaFzWhhmQXPhzTvKxatQq5ubkxwQUAzjnnHOTm5mLlypW6xy5ZsgR5eXno0aMH7rzzThw4cECzbG1tLaqqqmR/RPJiV7SRWmekXIARsKbdIRKH0mGXd8XxaB4X1gU7pcIRtRB/kBFiX70eUK5tZO4pax2ntp18XvhwTHgpLy9HXl78omR5eXkoLy/XPG78+PF466238MUXX+Avf/kL1q1bhwsuuAC1tbWq5adPnx7zqcnNzUXHjh1t+w2E97BrYUZl0jEgkjb88cvOkG0jzYs/kAq1AQG4/byu+PkgdgGm4dS0V01YNUzlTk0k6RjcpRVznpfObZpp7tPqP9Tc9cKkeuGCW3h5/PHH4xxqlX/r168HoC5diqKoK8Vec801uOSSS9C3b19cdtll+PTTT7Fr1y588om6SnbatGmorKyM/ZWWlvL+JMJH2LUwY62K8AIAt5xbJPtOwos/kD6nUDCAYEDAed3bMR8fTf+vtl5WQNAPvaZ1jpKPt+88h9lspBd1SGYj5+D2ebn33ntx7bXX6pbp0qULvv76a+zfvz9u38GDB9G+fXvm6xUUFKBz587YvXu36v6MjAxkZLAttEX4H8FBzYsaJLz4A7U1r3jWr4pqXtRmxKqaF67aEV5jaFFrrCk+rLk/LRhQTVJ39cAO+M+GH2Rl9VqZ1kRdXXihVsUDt/DStm1btG3b1rDcsGHDUFlZibVr12LIkCEAgDVr1qCyshLDhw9nvt6hQ4dQWlqKgoIC48JE0mOXz0vUQdMI8nnxB9J2EY0Y4mkfuw8cizuP2rmjSJ27KdrVf/xj4kBc9dJKfHfwuGYZQcVs9PSVZ8YJL3oNQGuXuimShBceHPN56d27Ny6++GLceeedWL16NVavXo0777wTl156qSzSqFevXnj//fcBAMeOHcNDDz2EVatWYc+ePViyZAkuu+wytG3bFldeeaVTVSV8hEx4sTBqkOYluVAzJ/I8u2h7UMvro3aa5pIFRpun0yorfqNls3TcMLSzbhlZ93Lqc3oogNNaZsnL6ZxDq48is5F1HH3r3nrrLUyePBljx0bSqF9++eV4/vnnZWV27tyJyspKAEAwGMSWLVvw5ptv4ujRoygoKMDo0aPx3nvvITs728mqEj7BLoddLZ8XJSS8+APpY0oLRTUv/OdRNxvFt4HMtCD+M2kYACArPT5KjfA+aq/2lQNOw0/OKgSgnWH3jduG4MJnlzbt0+kiuPK8kOaFC0eFl9atW2POnDm6ZaSqsqysLPzvf/9zskqEz7Erz0s0HbwRtACfP5CGwEZzeag53xqhdowgqA9Qg7q05j4/4R3U+o+fDeqA4d0ibhFaDrun57XAlIt64NlFuwDo9xE8ZiPyeeGD9J2EJ7lndDeM6hkfam+X5uW87sZ+W0CT8yfhbaQDSFqI32E3iprmhQTY5EQ9GlayH+qfAXnfo9c6tNoO6/IkhDa0cAvhSX41rhcGq8xsZSGxJtcdevGGs3HdkE5MZc3M3onEI182IvLMzDw6dYddtmOn//RMAIjLFUR4k1E9I6H0hbmZsW3SFP1yzYu8EbCGUWu1QbU2RXle+CDNC+ErpJ2IWbliwpnskWsUbeQPZJqXU+oTM8Kt2jEC9PO8RLluSCdc2q8A2RorCRPeokOrZlj36IXIzgyh12MLAABnaKxRFad5kUUiafcRPJoXkl34IOGF8BVqM2wnIYddfyAdC9KieV7MaF408rywtgMSXPxFu+xIjrCvHx+LE7WNaNtCPWeYUtaQtQedpsGT56Vfh1z9yhIySHghfIU8z4vz17MSjk0kDjXNixlfFfVQaYFWjU5ycjLTkKMQPAMBbe0K69IBmhl2Jc1s0YPnY1PpUVzev5C5vgT5vBA+Qy68JEDzQg67vkC+PAB/npem8zR9vvXcLgCAh8b1hCAIeOrKvpbqSPiLDEljEBRdjcxh10SotHR79/bZ+PmgjlyLRhKkeSF8hmx5gARoRcjnxR9Im4KZDLtRpALx7y7rg6njelEelxQlPSQRXhT79LQysnJamhfS6FqGNC+Er7BreQBWyGzkD2QZdq0IL4rnLRVcTm/XwmTtCD8iE14EpdkIkn3a57h5eBfV7TQnsg5pXghfIbUUJSIHCzns+gPV5QFMCJ56lsihXdvgr9f0RzcSYlKCjFCT4KobbaTTzC7tV4iits1xyXMrZNtJ82IdEl4IXyF96c10AEVtm3OVJ+HFH6glLzTz7Iwi2K4c0IH7nIQ/kWte5PtYzUYA0KcwF5PHdEdtQyP+sfT7yPEkvFiGzEaEZ3jgwu4AgIfH99IsIw+V5usAbj+vCG/eNoTrGBJe/IHashFWHXaJ1CZD5vMib0usmpcoUy7qgWnje3MdQ+hDmhfCM9w/pjuuGdwRBblZmmWsrG302KX8mU/JYdcfSNtCdFZrZnZLGZWJKHqaF6uTGpoUWYfeVMIzCIKgK7gAiXHYjaYNB4B+HVo6cg3CXtQ0cmZ8oshBm4gi9XlRIjMbmfGtonZmGdK8EL7CroUZ9fjnTYOweOdBHKiuwZUDTnPkGoS9SNX6QQsOu5TXh4ii6/PClmBXE5JdrEPCC+Er1AYpuwkFA7jojPaOnJtwBulg0Dwj0q1JZ8d/v24AKk/W4zcfbNU9D2leiCh2+rwoIbORdUh4IXwL+aMQUTLTgvjT1f3Q0CiidfP0uP1Du7ZGXnamofBCLi9EFKnmRdnVyKON+CGzkXVIeCF8RViyvG8gIEAQwLTiL5H8/HxQR9n35ulN3VurZvECjRqJWOyT8AfpQe0kdZlpQc19LNC8yzokvBC+QiqnhAICgoKABpJeCBWy0oNY9OD5CASE2GKNRpDZiIiSndk0PCpbRfN07QR2LJgReAg5NM0gfIVM8yIIMtvxAxd2j+WKIQggsuidVkbc568fELeNHHaJKJ3bNMctw7vgvgtOj1s0sZlEq2dGDiHNi3VIeCF8hVTJEgoohZce5GhL6PLmbUNwWssszLl9KC7tVxi3nzQvhJTHL++DX47tGbe9mWyxTgqVdgMSXghf0apZWuxzMCBg2qlsvDcN6wwAzOYBIjU5v0c7fPnwBTive1vV/RQFQrDQLEPq88J/PAkv1iGfF8JXtGmRgdduGYTMtCAEQcDEYV0wskceOrSKJLejwYewArUfggWpM3htQ5j7eKUZiuCHhBfCd1zQS24a6tSmWexzGkWLEBwEAwIaw1I/KhcrQ/iGLEm0Ub0J4YVcq6xDPT2RVJDDJcHDtYPl4dUUBUKwINWctG7RFIbfqlkahhS1xhsaC8Ce1bElgPiwfoIf0rwQSUUaTZ0JDh679Ay8tabE7WoQPqZdi4zY585tmuP/fjFMs+z//WIY9lfVoGPrZpplCDZI80IkFeSzQPCQmRbEkKLWbleD8DG98rOZy6aHAiS42AQJL0RSEaJoI4KTfUdOul0Fwof8/boBuPGcTrh6YAf85KxI2P29o093uVapA5mNiKQijXxeCE72HSXhheDnsv6FuKx/RGiZec1ZePSS3sjLznS5VqkDTVOJpILMRgQvvxrXU/Y/QfAiCAIJLgmGNC9EUkGh0gQvd43shov75qOoTXO3q0IQBCPU0xNJhTL508PjeyE9FCBbNKFJICCgW7sWlDiMIHyEo8LLU089heHDh6NZs2Zo2bIl0zGiKOLxxx9HYWEhsrKyMGrUKGzbts3JahJJzKDOrbD18XF4iEwCBEEQSYOjwktdXR1+9rOf4a677mI+5k9/+hOeffZZPP/881i3bh3y8/Nx0UUXobq62sGaEslKi8wQ0kOkYCQIgkgmHO3Vn3jiCTz44IM488wzmcqLooiZM2fi0UcfxU9/+lP07dsXb7zxBk6cOIG3337byaoSScTbdw6Nfc7OTNMpSRAEQfgRT01Ji4uLUV5ejrFjx8a2ZWRkYOTIkVi5cqXqMbW1taiqqpL9EalN/w4tY5+lq1ATBEEQyYGnoo3Ky8sBAO3byxfea9++Pfbu3at6zPTp0/HEE084XjfCPzTPCOH1WwYjEBDQLN1TTZwgCIKwAW7Ny+OPPw5BEHT/1q9fb6lSysXRRFHUXDBt2rRpqKysjP2VlpZaujaRHIzulYeRPdq5XQ2CIAjCAbinpffeey+uvfZa3TJdunQxVZn8/HwAEQ1MQUFBbPuBAwfitDFRMjIykJGRobqPIAiCIIjkg1t4adu2Ldq2betEXVBUVIT8/HwsWrQIAwYMABCJWFq6dCn++Mc/OnJNgiAIgiD8haMOuyUlJdi8eTNKSkrQ2NiIzZs3Y/PmzTh27FisTK9evfD+++8DiJiLHnjgATz99NN4//33sXXrVtxyyy1o1qwZrr/+eierShAEQRCET3DUm/G3v/0t3njjjdj3qDZl8eLFGDVqFABg586dqKysjJWZOnUqTp48ibvvvhtHjhzB0KFDsXDhQmRnsy87ThAEQRBE8iKIoii6XQk7qaqqQm5uLiorK5GTk+N2dQiCIAiCYIBn/PZUnheCIAiCIAgjSHghCIIgCMJXkPBCEARBEISvIOGFIAiCIAhfQcILQRAEQRC+goQXgiAIgiB8BQkvBEEQBEH4ChJeCIIgCILwFY5m2HWDaM69qqoql2tCEARBEAQr0XGbJXdu0gkv1dXVAICOHTu6XBOCIAiCIHiprq5Gbm6ubpmkWx4gHA7jxx9/RHZ2NgRBsPXcVVVV6NixI0pLS2npAQeh+5w46F4nBrrPiYHuc2Jw6j6Loojq6moUFhYiEND3akk6zUsgEECHDh0cvUZOTg69GAmA7nPioHudGOg+Jwa6z4nBiftspHGJQg67BEEQBEH4ChJeCIIgCILwFSS8cJCRkYHf/e53yMjIcLsqSQ3d58RB9zox0H1ODHSfE4MX7nPSOewSBEEQBJHckOaFIAiCIAhfQcILQRAEQRC+goQXgiAIgiB8BQkvBEEQBEH4ChJeGHnxxRdRVFSEzMxMDBw4EMuXL3e7Sr5i+vTpGDx4MLKzs5GXl4crrrgCO3fulJURRRGPP/44CgsLkZWVhVGjRmHbtm2yMrW1tbjvvvvQtm1bNG/eHJdffjl++OGHRP4UXzF9+nQIgoAHHnggto3us33s27cPN954I9q0aYNmzZrhrLPOwoYNG2L76V5bp6GhAb/5zW9QVFSErKwsdO3aFU8++STC4XCsDN1nfpYtW4bLLrsMhYWFEAQBH3zwgWy/Xff0yJEjmDhxInJzc5Gbm4uJEyfi6NGj1n+ASBjy7rvvimlpaeIrr7wibt++Xbz//vvF5s2bi3v37nW7ar5h3Lhx4uuvvy5u3bpV3Lx5s3jJJZeInTp1Eo8dOxYr88wzz4jZ2dni3LlzxS1btojXXHONWFBQIFZVVcXKTJo0STzttNPERYsWiRs3bhRHjx4t9u/fX2xoaHDjZ3matWvXil26dBH79esn3n///bHtdJ/t4fDhw2Lnzp3FW265RVyzZo1YXFwsfvbZZ+K3334bK0P32jp/+MMfxDZt2oj//e9/xeLiYvHf//632KJFC3HmzJmxMnSf+Zk/f7746KOPinPnzhUBiO+//75sv1339OKLLxb79u0rrly5Uly5cqXYt29f8dJLL7VcfxJeGBgyZIg4adIk2bZevXqJDz/8sEs18j8HDhwQAYhLly4VRVEUw+GwmJ+fLz7zzDOxMjU1NWJubq44a9YsURRF8ejRo2JaWpr47rvvxsrs27dPDAQC4oIFCxL7AzxOdXW12L17d3HRokXiyJEjY8IL3Wf7+PWvfy2ed955mvvpXtvDJZdcIt52222ybT/96U/FG2+8URRFus92oBRe7Lqn27dvFwGIq1evjpVZtWqVCEDcsWOHpTqT2ciAuro6bNiwAWPHjpVtHzt2LFauXOlSrfxPZWUlAKB169YAgOLiYpSXl8vuc0ZGBkaOHBm7zxs2bEB9fb2sTGFhIfr27UvPQsE999yDSy65BBdeeKFsO91n+/joo48waNAg/OxnP0NeXh4GDBiAV155Jbaf7rU9nHfeefj888+xa9cuAMBXX32FFStWYMKECQDoPjuBXfd01apVyM3NxdChQ2NlzjnnHOTm5lq+70m3MKPdVFRUoLGxEe3bt5dtb9++PcrLy12qlb8RRRFTpkzBeeedh759+wJA7F6q3ee9e/fGyqSnp6NVq1ZxZehZNPHuu+9i48aNWLduXdw+us/28f333+Oll17ClClT8Mgjj2Dt2rWYPHkyMjIycNNNN9G9tolf//rXqKysRK9evRAMBtHY2IinnnoK1113HQBq005g1z0tLy9HXl5e3Pnz8vIs33cSXhgRBEH2XRTFuG0EG/feey++/vprrFixIm6fmftMz6KJ0tJS3H///Vi4cCEyMzM1y9F9tk44HMagQYPw9NNPAwAGDBiAbdu24aWXXsJNN90UK0f32hrvvfce5syZg7fffht9+vTB5s2b8cADD6CwsBA333xzrBzdZ/ux456qlbfjvpPZyIC2bdsiGAzGSYkHDhyIk0oJY+677z589NFHWLx4MTp06BDbnp+fDwC69zk/Px91dXU4cuSIZplUZ8OGDThw4AAGDhyIUCiEUCiEpUuX4rnnnkMoFIrdJ7rP1ikoKMAZZ5wh29a7d2+UlJQAoDZtF7/61a/w8MMP49prr8WZZ56JiRMn4sEHH8T06dMB0H12ArvuaX5+Pvbv3x93/oMHD1q+7yS8GJCeno6BAwdi0aJFsu2LFi3C8OHDXaqV/xBFEffeey/mzZuHL774AkVFRbL9RUVFyM/Pl93nuro6LF26NHafBw4ciLS0NFmZsrIybN26lZ7FKcaMGYMtW7Zg8+bNsb9BgwbhhhtuwObNm9G1a1e6zzZx7rnnxoX779q1C507dwZAbdouTpw4gUBAPlQFg8FYqDTdZ/ux654OGzYMlZWVWLt2bazMmjVrUFlZaf2+W3L3TRGiodKvvvqquH37dvGBBx4QmzdvLu7Zs8ftqvmGu+66S8zNzRWXLFkilpWVxf5OnDgRK/PMM8+Iubm54rx588QtW7aI1113nWpoXocOHcTPPvtM3Lhxo3jBBRekdLgjC9JoI1Gk+2wXa9euFUOhkPjUU0+Ju3fvFt966y2xWbNm4pw5c2Jl6F5b5+abbxZPO+20WKj0vHnzxLZt24pTp06NlaH7zE91dbW4adMmcdOmTSIA8dlnnxU3bdoUSwFi1z29+OKLxX79+omrVq0SV61aJZ555pkUKp1IXnjhBbFz585ienq6ePbZZ8dCfAk2AKj+vf7667Ey4XBY/N3vfifm5+eLGRkZ4vnnny9u2bJFdp6TJ0+K9957r9i6dWsxKytLvPTSS8WSkpIE/xp/oRRe6D7bx8cffyz27dtXzMjIEHv16iW+/PLLsv10r61TVVUl3n///WKnTp3EzMxMsWvXruKjjz4q1tbWxsrQfeZn8eLFqn3yzTffLIqifff00KFD4g033CBmZ2eL2dnZ4g033CAeOXLEcv0FURRFa7obgiAIgiCIxEE+LwRBEARB+AoSXgiCIAiC8BUkvBAEQRAE4StIeCEIgiAIwleQ8EIQBEEQhK8g4YUgCIIgCF9BwgtBEARBEL6ChBeCIAiCIHwFCS8EQRAEQfgKEl4IgiAIgvAVJLwQBEEQBOErSHghCIIgCMJX/H9UhkB8Zzg4bwAAAABJRU5ErkJggg==\n",
+      "image/png": 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\n",
       "text/plain": [
        "
    "
       ]
@@ -196,14 +196,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "2023-10-02 06:54:48.552042: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
+      "2023-10-15 21:49:35.228942: W tensorflow/core/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 4s - loss: 1.7644 - 4s/epoch - 84ms/step\n"
+      "50/50 - 3s - loss: 0.5276 - 3s/epoch - 66ms/step\n"
      ]
     },
     {
@@ -217,7 +217,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.4353 - 499ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.4234 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -231,7 +231,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.4066 - 479ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.4043 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -245,7 +245,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.4033 - 740ms/epoch - 15ms/step\n"
+      "50/50 - 0s - loss: 0.4010 - 460ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -259,7 +259,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.4014 - 596ms/epoch - 12ms/step\n"
+      "50/50 - 0s - loss: 0.3979 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -273,7 +273,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3999 - 561ms/epoch - 11ms/step\n"
+      "50/50 - 0s - loss: 0.3967 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -287,7 +287,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3996 - 515ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3962 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -301,7 +301,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3975 - 495ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3957 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -315,7 +315,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3970 - 473ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3929 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -329,7 +329,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3944 - 687ms/epoch - 14ms/step\n"
+      "50/50 - 0s - loss: 0.3920 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -343,7 +343,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3948 - 500ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3918 - 454ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -357,7 +357,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3932 - 501ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3898 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -371,7 +371,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3923 - 499ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3921 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -385,7 +385,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3919 - 484ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3911 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -399,7 +399,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3928 - 556ms/epoch - 11ms/step\n"
+      "50/50 - 0s - loss: 0.3888 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -413,7 +413,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3901 - 497ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3871 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -427,7 +427,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3907 - 456ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3894 - 458ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -441,7 +441,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3893 - 456ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3873 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -455,7 +455,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3878 - 458ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3855 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -469,7 +469,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3877 - 455ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3871 - 453ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -483,7 +483,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3873 - 462ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3802 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -497,7 +497,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3865 - 468ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3856 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -511,7 +511,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3856 - 487ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3804 - 453ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -525,7 +525,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3853 - 473ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3842 - 453ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -539,7 +539,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3838 - 492ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3815 - 452ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -553,7 +553,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3840 - 477ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3782 - 454ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -567,7 +567,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3836 - 643ms/epoch - 13ms/step\n"
+      "50/50 - 0s - loss: 0.3798 - 454ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -581,7 +581,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3834 - 484ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3804 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -595,7 +595,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3838 - 483ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3812 - 452ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -609,7 +609,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3837 - 468ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3780 - 454ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -623,7 +623,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3821 - 671ms/epoch - 13ms/step\n"
+      "50/50 - 0s - loss: 0.3800 - 453ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -637,7 +637,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3816 - 832ms/epoch - 17ms/step\n"
+      "50/50 - 0s - loss: 0.3767 - 467ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -651,7 +651,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3812 - 581ms/epoch - 12ms/step\n"
+      "50/50 - 0s - loss: 0.3787 - 493ms/epoch - 10ms/step\n"
      ]
     },
     {
@@ -665,7 +665,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3770 - 515ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3758 - 464ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -679,7 +679,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3814 - 654ms/epoch - 13ms/step\n"
+      "50/50 - 0s - loss: 0.3784 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -693,7 +693,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3789 - 522ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3766 - 461ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -707,7 +707,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3799 - 488ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3733 - 456ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -721,7 +721,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3795 - 450ms/epoch - 9ms/step\n"
+      "50/50 - 0s - loss: 0.3749 - 455ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -735,7 +735,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3786 - 692ms/epoch - 14ms/step\n"
+      "50/50 - 0s - loss: 0.3756 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -749,7 +749,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3773 - 741ms/epoch - 15ms/step\n"
+      "50/50 - 0s - loss: 0.3737 - 458ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -763,7 +763,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3765 - 555ms/epoch - 11ms/step\n"
+      "50/50 - 0s - loss: 0.3743 - 459ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -777,7 +777,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 0s - loss: 0.3799 - 485ms/epoch - 10ms/step\n"
+      "50/50 - 0s - loss: 0.3730 - 460ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -791,7 +791,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "50/50 - 1s - loss: 0.3786 - 665ms/epoch - 13ms/step\n"
+      "50/50 - 0s - loss: 0.3706 - 457ms/epoch - 9ms/step\n"
      ]
     },
     {
@@ -801,6 +801,132 @@
       "Epoch 44/100\n"
      ]
     },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3724 - 459ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 45/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3716 - 456ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 46/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3713 - 459ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 47/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3705 - 458ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 48/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3703 - 460ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 49/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3701 - 459ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 50/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3676 - 470ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 51/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3679 - 464ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 52/100\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "50/50 - 0s - loss: 0.3689 - 460ms/epoch - 9ms/step\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Epoch 53/100\n"
+     ]
+    },
     {
      "ename": "KeyboardInterrupt",
      "evalue": "",
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index 3958a79c4..778935197 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
index e61d72b37..83fefb15f 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
@@ -1798,10 +1798,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.033790755027115954\n",
-      "3.888577549915147\n",
-      "[[ 1.2697447   3.97644118]\n",
-      " [ 3.97644118 13.38465596]]\n"
+      "0.12765651865754318\n",
+      "4.348676117830458\n",
+      "[[0.98073929 2.88442538]\n",
+      " [2.88442538 9.24128917]]\n"
      ]
     }
    ],
@@ -1845,10 +1845,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.08238863600759742\n",
-      "1.795225339396409\n",
-      "[[1.         0.64391062]\n",
-      " [0.64391062 1.        ]]\n"
+      "0.08652153831327969\n",
+      "1.7893215781870513\n",
+      "[[1.         0.70344416]\n",
+      " [0.70344416 1.        ]]\n"
      ]
     }
    ],
@@ -1905,30 +1905,30 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 1.29135778  4.3399612 ]\n",
-      " [ 0.08815506 -1.48140137]\n",
-      " [ 0.34149655  1.18571316]\n",
-      " [-1.00375475 -2.69226802]\n",
-      " [ 0.42198678  2.56858701]\n",
-      " [ 0.53278871  2.8969113 ]\n",
-      " [-1.38020451 -4.26263837]\n",
-      " [-0.64969451 -2.00778523]\n",
-      " [-0.32632463 -1.7413913 ]\n",
-      " [ 0.68419351  1.19431161]]\n",
+      "[[ 1.71727268  5.22388434]\n",
+      " [ 0.31027702  0.17469167]\n",
+      " [-0.26149831 -0.93082933]\n",
+      " [ 0.04107874  1.47244548]\n",
+      " [-2.10812381 -5.28818554]\n",
+      " [-1.62910047 -4.07706814]\n",
+      " [ 0.92136836  2.27309401]\n",
+      " [-0.3175938  -1.42457498]\n",
+      " [ 0.68037392  0.16481217]\n",
+      " [ 0.64594566  2.41173033]]\n",
       "          0         1\n",
-      "0  1.291358  4.339961\n",
-      "1  0.088155 -1.481401\n",
-      "2  0.341497  1.185713\n",
-      "3 -1.003755 -2.692268\n",
-      "4  0.421987  2.568587\n",
-      "5  0.532789  2.896911\n",
-      "6 -1.380205 -4.262638\n",
-      "7 -0.649695 -2.007785\n",
-      "8 -0.326325 -1.741391\n",
-      "9  0.684194  1.194312\n",
+      "0  1.717273  5.223884\n",
+      "1  0.310277  0.174692\n",
+      "2 -0.261498 -0.930829\n",
+      "3  0.041079  1.472445\n",
+      "4 -2.108124 -5.288186\n",
+      "5 -1.629100 -4.077068\n",
+      "6  0.921368  2.273094\n",
+      "7 -0.317594 -1.424575\n",
+      "8  0.680374  0.164812\n",
+      "9  0.645946  2.411730\n",
       "          0         1\n",
-      "0  1.000000  0.943439\n",
-      "1  0.943439  1.000000\n"
+      "0  1.000000  0.962653\n",
+      "1  0.962653  1.000000\n"
      ]
     }
    ],
@@ -1974,44 +1974,37 @@
      "text": [
       "     0         1         2         3         4         5         6         7   \\\n",
       "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.089710  0.084075  0.088697  0.086518  0.084247  0.079455  0.077756   \n",
-      "2   0.0  0.084075  0.079226  0.082189  0.080406  0.078545  0.073008  0.071611   \n",
-      "3   0.0  0.088697  0.082189  0.093408  0.090365  0.087247  0.087250  0.084843   \n",
-      "4   0.0  0.086518  0.080406  0.090365  0.087603  0.084764  0.083853  0.081680   \n",
-      "5   0.0  0.084247  0.078545  0.087247  0.084764  0.082205  0.080411  0.078467   \n",
-      "6   0.0  0.079455  0.073008  0.087250  0.083853  0.080411  0.083988  0.081246   \n",
-      "7   0.0  0.077756  0.071611  0.084843  0.081680  0.078467  0.081246  0.078707   \n",
-      "8   0.0  0.076125  0.070275  0.082517  0.079581  0.076592  0.078593  0.076249   \n",
-      "9   0.0  0.074545  0.068987  0.080256  0.077542  0.074772  0.076012  0.073858   \n",
-      "10  0.0  0.070597  0.064412  0.079882  0.076354  0.072805  0.078656  0.075758   \n",
-      "11  0.0  0.068974  0.063055  0.077650  0.074330  0.070986  0.076136  0.073422   \n",
-      "12  0.0  0.067437  0.061775  0.075523  0.072404  0.069257  0.073728  0.071191   \n",
-      "13  0.0  0.065982  0.060567  0.073494  0.070569  0.067611  0.071423  0.069055   \n",
-      "14  0.0  0.064602  0.059427  0.071554  0.068816  0.066042  0.069213  0.067009   \n",
+      "1   0.0  0.082246  0.081621  0.082225  0.081617  0.081120  0.073421  0.072973   \n",
+      "2   0.0  0.081621  0.081679  0.081960  0.081804  0.081742  0.073498  0.073387   \n",
+      "3   0.0  0.082225  0.081960  0.087271  0.086900  0.086636  0.081057  0.080755   \n",
+      "4   0.0  0.081617  0.081804  0.086900  0.086868  0.086932  0.080935  0.080903   \n",
+      "5   0.0  0.081120  0.081742  0.086636  0.086932  0.087311  0.080906  0.081136   \n",
+      "6   0.0  0.073421  0.073498  0.081057  0.080935  0.080906  0.077455  0.077330   \n",
+      "7   0.0  0.072973  0.073387  0.080755  0.080903  0.081136  0.077330  0.077429   \n",
+      "8   0.0  0.072637  0.073376  0.080571  0.080980  0.081466  0.077313  0.077630   \n",
+      "9   0.0  0.072410  0.073465  0.080502  0.081164  0.081896  0.077403  0.077931   \n",
+      "10  0.0  0.064640  0.064948  0.073406  0.073471  0.073618  0.071662  0.071685   \n",
+      "11  0.0  0.064320  0.064896  0.073187  0.073476  0.073840  0.071579  0.071792   \n",
+      "12  0.0  0.064101  0.064938  0.073080  0.073586  0.074161  0.071601  0.072000   \n",
+      "13  0.0  0.063980  0.065069  0.073079  0.073797  0.074577  0.071726  0.072305   \n",
+      "14  0.0  0.063953  0.065289  0.073184  0.074108  0.075089  0.071951  0.072707   \n",
       "\n",
       "          8         9         10        11        12        13        14  \n",
       "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.076125  0.074545  0.070597  0.068974  0.067437  0.065982  0.064602  \n",
-      "2   0.070275  0.068987  0.064412  0.063055  0.061775  0.060567  0.059427  \n",
-      "3   0.082517  0.080256  0.079882  0.077650  0.075523  0.073494  0.071554  \n",
-      "4   0.079581  0.077542  0.076354  0.074330  0.072404  0.070569  0.068816  \n",
-      "5   0.076592  0.074772  0.072805  0.070986  0.069257  0.067611  0.066042  \n",
-      "6   0.078593  0.076012  0.078656  0.076136  0.073728  0.071423  0.069213  \n",
-      "7   0.076249  0.073858  0.075758  0.073422  0.071191  0.069055  0.067009  \n",
-      "8   0.073980  0.071773  0.072953  0.070795  0.068734  0.066762  0.064874  \n",
-      "9   0.071773  0.069746  0.070228  0.068241  0.066344  0.064532  0.062797  \n",
-      "10  0.072953  0.070228  0.074969  0.072310  0.069766  0.067328  0.064987  \n",
-      "11  0.070795  0.068241  0.072310  0.069822  0.067440  0.065158  0.062967  \n",
-      "12  0.068734  0.066344  0.069766  0.067440  0.065214  0.063081  0.061034  \n",
-      "13  0.066762  0.064532  0.067328  0.065158  0.063081  0.061092  0.059182  \n",
-      "14  0.064874  0.062797  0.064987  0.062967  0.061034  0.059182  0.057406  "
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n"
+      "1   0.072637  0.072410  0.064640  0.064320  0.064101  0.063980  0.063953  \n",
+      "2   0.073376  0.073465  0.064948  0.064896  0.064938  0.065069  0.065289  \n",
+      "3   0.080571  0.080502  0.073406  0.073187  0.073080  0.073079  0.073184  \n",
+      "4   0.080980  0.081164  0.073471  0.073476  0.073586  0.073797  0.074108  \n",
+      "5   0.081466  0.081896  0.073618  0.073840  0.074161  0.074577  0.075089  \n",
+      "6   0.077313  0.077403  0.071662  0.071579  0.071601  0.071726  0.071951  \n",
+      "7   0.077630  0.077931  0.071685  0.071792  0.072000  0.072305  0.072707  \n",
+      "8   0.078041  0.078548  0.071805  0.072098  0.072486  0.072967  0.073541  \n",
+      "9   0.078548  0.079255  0.072022  0.072495  0.073059  0.073712  0.074455  \n",
+      "10  0.071805  0.072022  0.067420  0.067457  0.067591  0.067820  0.068141  \n",
+      "11  0.072098  0.072495  0.067457  0.067660  0.067955  0.068340  0.068815  \n",
+      "12  0.072486  0.073059  0.067591  0.067955  0.068407  0.068945  0.069570  \n",
+      "13  0.072967  0.073712  0.067820  0.068340  0.068945  0.069634  0.070406  \n",
+      "14  0.073541  0.074455  0.068141  0.068815  0.069570  0.070406  0.071323  \n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
index ca85740e2..3a4f67502 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
@@ -489,10 +489,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Runtime: 0.179404 sec\n",
+      "Runtime: 0.136236 sec\n",
       "Jackknife Statistics :\n",
       "original           bias      std. error\n",
-      " 100.039        100.029        0.150726\n"
+      "  99.979         99.969         0.14845\n"
      ]
     }
    ],
@@ -917,7 +917,7 @@
      "text": [
       "Bootstrap Statistics :\n",
       "original           bias      std. error\n",
-      " 100.092  14.9578        100.093        0.149299\n"
+      " 99.8342  14.8306        99.8351         0.14857\n"
      ]
     }
    ],
@@ -975,7 +975,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -1292,18 +1292,18 @@
       "Error: 0.06844519414009445\n",
       "Bias^2: 0.06453579006728322\n",
       "Var: 0.003909404072811221\n",
-      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n"
+      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n",
+      "Polynomial degree: 5\n",
+      "Error: 0.05227921801205679\n",
+      "Bias^2: 0.04818727730430286\n",
+      "Var: 0.004091940707753925\n",
+      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Polynomial degree: 5\n",
-      "Error: 0.05227921801205679\n",
-      "Bias^2: 0.04818727730430286\n",
-      "Var: 0.004091940707753925\n",
-      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
       "Polynomial degree: 6\n",
       "Error: 0.03781367141738902\n",
       "Bias^2: 0.03365768507152769\n",
@@ -1607,16 +1607,16 @@
       "Mean squared error on test data: 5.98822371\n",
       "Degree of polynomial:   6\n",
       "Mean squared error on training data: 3.66204648\n",
-      "Mean squared error on test data: 8.14812206\n"
+      "Mean squared error on test data: 8.14812206\n",
+      "Degree of polynomial:   7\n",
+      "Mean squared error on training data: 0.47075725\n",
+      "Mean squared error on test data: 2.00607783\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Degree of polynomial:   7\n",
-      "Mean squared error on training data: 0.47075725\n",
-      "Mean squared error on test data: 2.00607783\n",
       "Degree of polynomial:   8\n",
       "Mean squared error on training data: 0.04912436\n",
       "Mean squared error on test data: 0.21596432\n",
@@ -1631,19 +1631,19 @@
       "Mean squared error on test data: 1.35533773\n",
       "Degree of polynomial:  12\n",
       "Mean squared error on training data: 0.00813803\n",
-      "Mean squared error on test data: 0.17446471\n"
+      "Mean squared error on test data: 0.17446471\n",
+      "Degree of polynomial:  13\n",
+      "Mean squared error on training data: 0.00759119\n",
+      "Mean squared error on test data: 1.08131003\n",
+      "Degree of polynomial:  14\n",
+      "Mean squared error on training data: 0.00472199\n",
+      "Mean squared error on test data: 0.81333804\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Degree of polynomial:  13\n",
-      "Mean squared error on training data: 0.00759119\n",
-      "Mean squared error on test data: 1.08131003\n",
-      "Degree of polynomial:  14\n",
-      "Mean squared error on training data: 0.00472199\n",
-      "Mean squared error on test data: 0.81333804\n",
       "Degree of polynomial:  15\n",
       "Mean squared error on training data: 0.00410478\n",
       "Mean squared error on test data: 92.09172409\n",
@@ -1655,13 +1655,7 @@
       "Mean squared error on test data: 1271.35771826\n",
       "Degree of polynomial:  18\n",
       "Mean squared error on training data: 0.00228742\n",
-      "Mean squared error on test data: 108.27092910\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "Mean squared error on test data: 108.27092910\n",
       "Degree of polynomial:  19\n",
       "Mean squared error on training data: 0.00156376\n",
       "Mean squared error on test data: 1371.99051150\n",
@@ -1670,7 +1664,13 @@
       "Mean squared error on test data: 1887.86252988\n",
       "Degree of polynomial:  21\n",
       "Mean squared error on training data: 0.00118508\n",
-      "Mean squared error on test data: 14859.69908626\n",
+      "Mean squared error on test data: 14859.69908626\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "Degree of polynomial:  22\n",
       "Mean squared error on training data: 0.00092647\n",
       "Mean squared error on test data: 876.51191552\n",
@@ -1679,13 +1679,7 @@
       "Mean squared error on test data: 5594.60815105\n",
       "Degree of polynomial:  24\n",
       "Mean squared error on training data: 0.00084705\n",
-      "Mean squared error on test data: 1277.61702282\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "Mean squared error on test data: 1277.61702282\n",
       "Degree of polynomial:  25\n",
       "Mean squared error on training data: 0.00079129\n",
       "Mean squared error on test data: 128664.31650694\n",
@@ -1694,7 +1688,13 @@
       "Mean squared error on test data: 19003.94822514\n",
       "Degree of polynomial:  27\n",
       "Mean squared error on training data: 0.00068946\n",
-      "Mean squared error on test data: 2379.66219404\n",
+      "Mean squared error on test data: 2379.66219404\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "Degree of polynomial:  28\n",
       "Mean squared error on training data: 0.00062595\n",
       "Mean squared error on test data: 4082.19983530\n",
@@ -1707,9 +1707,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
      ]
     },
@@ -2051,7 +2051,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19176/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
      ]
     },
@@ -3720,7 +3720,32 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "  cb = fig.colorbar(im)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_154_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "im = plt.imshow(J, **cmap_args)\n",
@@ -4007,7 +4032,32 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "  cb = fig.colorbar(im)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_172_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "im = plt.imshow(J_sk, **cmap_args)\n",
@@ -4061,7 +4111,32 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "  cb = fig.colorbar(im)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_175_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "_lambda = 0.1\n",
     "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n",
@@ -4123,7 +4198,32 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "  cb = fig.colorbar(im)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
+      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_179_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
     "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
@@ -4160,7 +4260,127 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\r",
+      "  0%|                                                                                                                          | 0/10 [00:00"
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_181_13.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "lambdas = np.logspace(-4, 5, 10)\n",
     "\n",
@@ -4228,7 +4448,22 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_183_0.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "\n",
@@ -4352,7 +4587,32 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
+      "  ax = fig.gca(projection='3d')\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31624/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
+      "  fig.colorbar(surf, shrink=0.5, aspect=5)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_188_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from mpl_toolkits.mplot3d import Axes3D\n",
     "import matplotlib.pyplot as plt\n",
@@ -4718,7 +4978,19 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'scipy' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mscipy\u001b[49m\u001b[38;5;241m.\u001b[39mmisc\u001b[38;5;241m.\u001b[39mimread\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'scipy' is not defined"
+     ]
+    }
+   ],
    "source": [
     "scipy.misc.imread"
    ]
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png
index 313192a04..be484dc60 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png and b/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
index e29087a59..1c1376439 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
@@ -1341,7 +1341,11 @@
      "text": [
       "(426, 30)\n",
       "(143, 30)\n",
-      "Test set accuracy with Logistic Regression: 0.94\n"
+      "Test set accuracy with Logistic Regression: 0.94\n",
+      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
+      "[1.         1.         1.         1.         1.         1.\n",
+      " 1.         1.         0.92857143 0.92857143]\n",
+      "Test set accuracy with Logistic Regression  and scaled data: 0.96\n"
      ]
     },
     {
@@ -1358,16 +1362,6 @@
       "  n_iter_i = _check_optimize_result(\n"
      ]
     },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
-      "[1.         1.         1.         1.         1.         1.\n",
-      " 1.         1.         0.92857143 0.92857143]\n",
-      "Test set accuracy with Logistic Regression  and scaled data: 0.96\n"
-     ]
-    },
     {
      "data": {
       "image/png": 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\n",
@@ -1377,7 +1371,7 @@
      },
      "metadata": {
       "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png"
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_2.png"
       }
      },
      "output_type": "display_data"
@@ -1391,7 +1385,7 @@
      },
      "metadata": {
       "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png"
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png"
       }
      },
      "output_type": "display_data"
@@ -1405,7 +1399,7 @@
      },
      "metadata": {
       "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_5.png"
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png"
       }
      },
      "output_type": "display_data"
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png b/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png
index 3ee8451f5..d77131072 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png and b/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png b/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png
index d77131072..d281ad632 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png and b/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
index 97fa5693c..b675d75e1 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
@@ -86,14 +86,14 @@
      "output_type": "stream",
      "text": [
       "2nd degree coefficients:\n",
-      "zero power:  -1.3439564710454786\n",
-      "first power:  0.020404272938413143\n",
-      "second power:  0.0001539814498783133\n"
+      "zero power:  -0.2774877574815404\n",
+      "first power:  0.11112589053037751\n",
+      "second power:  -0.00033136014047192484\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -107,7 +107,7 @@
     },
     {
      "data": {
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\n",
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\n",
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
index 35cbb7873..cdece0b6f 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
@@ -295,10 +295,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.026250840755899812\n",
-      "3.9783319210079595\n",
-      "[[ 1.06075426  3.40216748]\n",
-      " [ 3.40216748 11.8635085 ]]\n"
+      "-0.10776220958055382\n",
+      "3.743189104728408\n",
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@@ -340,10 +340,10 @@
      "name": "stdout",
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      "text": [
-      "0.08076969085177746\n",
-      "1.9295763474254684\n",
-      "[[1.        0.7135487]\n",
-      " [0.7135487 1.       ]]\n"
+      "0.0704374681593734\n",
+      "1.3273472571412799\n",
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@@ -397,30 +397,30 @@
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-      "[[ 1.52944573  4.65218729]\n",
-      " [ 0.12050822  0.97069774]\n",
-      " [ 0.40413036  1.80861057]\n",
-      " [-0.07004211  0.30763135]\n",
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-      " [-0.41506637 -1.52573941]\n",
-      " [ 1.75627883  5.73410729]\n",
-      " [-0.47187428 -1.10927588]\n",
-      " [-1.42874148 -5.13410999]]\n",
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       "          0         1\n",
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       "          0         1\n",
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@@ -461,37 +461,37 @@
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       "     0         1         2         3         4         5         6         7   \\\n",
       "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
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-      "3   0.0  0.077705  0.081976  0.085023  0.085454  0.085391  0.081955  0.081126   \n",
-      "4   0.0  0.077226  0.082506  0.085454  0.086441  0.086843  0.082760  0.082255   \n",
-      "5   0.0  0.076504  0.082577  0.085391  0.086843  0.087642  0.083000  0.082781   \n",
-      "6   0.0  0.071258  0.076127  0.081955  0.082760  0.083000  0.081584  0.080933   \n",
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-      "8   0.0  0.069033  0.074780  0.080163  0.081570  0.082347  0.080105  0.079878   \n",
-      "9   0.0  0.067915  0.073984  0.079124  0.080773  0.081772  0.079165  0.079121   \n",
-      "10  0.0  0.064634  0.069384  0.076833  0.077710  0.078029  0.078187  0.077613   \n",
-      "11  0.0  0.063407  0.068403  0.075582  0.076662  0.077171  0.076996  0.076587   \n",
-      "12  0.0  0.062221  0.067419  0.074327  0.075587  0.076266  0.075779  0.075521   \n",
-      "13  0.0  0.061084  0.066453  0.073088  0.074509  0.075342  0.074560  0.074439   \n",
-      "14  0.0  0.060001  0.065517  0.071879  0.073445  0.074419  0.073354  0.073362   \n",
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       "\n",
       "          8         9         10        11        12        13        14  \n",
       "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
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-      "3   0.080163  0.079124  0.076833  0.075582  0.074327  0.073088  0.071879  \n",
-      "4   0.081570  0.080773  0.077710  0.076662  0.075587  0.074509  0.073445  \n",
-      "5   0.082347  0.081772  0.078029  0.077171  0.076266  0.075342  0.074419  \n",
-      "6   0.080105  0.079165  0.078187  0.076996  0.075779  0.074560  0.073354  \n",
-      "7   0.079878  0.079121  0.077613  0.076587  0.075521  0.074439  0.073362  \n",
-      "8   0.079434  0.078845  0.076857  0.075984  0.075058  0.074108  0.073152  \n",
-      "9   0.078845  0.078412  0.075980  0.075249  0.074457  0.073630  0.072790  \n",
-      "10  0.076857  0.075980  0.076105  0.074970  0.073802  0.072624  0.071452  \n",
-      "11  0.075984  0.075249  0.074970  0.073972  0.072931  0.071872  0.070811  \n",
-      "12  0.075058  0.074457  0.073802  0.072931  0.072009  0.071062  0.070107  \n",
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-      "14  0.073152  0.072790  0.071452  0.070811  0.070107  0.069365  0.068606  \n"
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+      "6   0.068406  0.068551  0.061869  0.061826  0.061813  0.061833  0.061888  \n",
+      "7   0.068997  0.069320  0.062273  0.062390  0.062523  0.062675  0.062852  \n",
+      "8   0.069522  0.070009  0.062631  0.062894  0.063159  0.063434  0.063723  \n",
+      "9   0.070009  0.070645  0.062963  0.063359  0.063747  0.064134  0.064527  \n",
+      "10  0.062631  0.062963  0.057231  0.057361  0.057502  0.057657  0.057831  \n",
+      "11  0.062894  0.063359  0.057361  0.057613  0.057864  0.058121  0.058388  \n",
+      "12  0.063159  0.063747  0.057502  0.057864  0.058216  0.058567  0.058921  \n",
+      "13  0.063434  0.064134  0.057657  0.058121  0.058567  0.059004  0.059439  \n",
+      "14  0.063723  0.064527  0.057831  0.058388  0.058921  0.059439  0.059949  \n"
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@@ -916,10 +916,10 @@
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       "          0         1\n",
-      "0  3.942604  1.984308\n",
-      "1  1.984308  1.984182\n",
-      "[[3.94260358 1.98430782]\n",
-      " [1.98430782 1.98418221]]\n"
+      "0  3.949162  1.987722\n",
+      "1  1.987722  2.004480\n",
+      "[[3.94916237 1.98772232]\n",
+      " [1.98772232 2.00447992]]\n"
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@@ -949,13 +949,13 @@
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      "text": [
       "Centered covariance using own code\n",
-      "[[3.94260358 1.98430782]\n",
-      " [1.98430782 1.98418221]]\n"
+      "[[3.94916237 1.98772232]\n",
+      " [1.98772232 2.00447992]]\n"
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     {
      "data": {
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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -1044,12 +1044,12 @@
      "output_type": "stream",
      "text": [
       "Eigenvalues of Covariance matrix\n",
-      "5.17615838052499\n",
-      "0.7506274061293645\n",
+      "5.189621963782685\n",
+      "0.7640203256838339\n",
       "First eigenvector\n",
-      "[0.84927263 0.52795454]\n",
+      "[0.84835621 0.52942586]\n",
       "Second eigenvector\n",
-      "[-0.52795454  0.84927263]\n"
+      "[-0.52942586  0.84835621]\n"
      ]
     },
     {
@@ -1057,7 +1057,7 @@
      "output_type": "stream",
      "text": [
       "Eigenvector of largest eigenvalue\n",
-      "[0.84927263 0.52795454]\n"
+      "[0.84835621 0.52942586]\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png
index ebd583089..a44444ca6 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png and b/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
index 2c12a3933..31f5150cc 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
@@ -924,14 +924,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19294/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31672/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
       "  ax = fig.gca(projection=\"3d\")\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       ""
+       ""
       ]
      },
      "execution_count": 1,
@@ -1101,7 +1101,7 @@
     {
      "data": {
       "text/plain": [
-       "[]"
+       "[]"
       ]
      },
      "execution_count": 5,
@@ -1802,16 +1802,16 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.31022577 4.45255977]\n",
-      "[[3.8942133 ]\n",
-      " [3.04191629]]\n",
-      "[[3.8942133 ]\n",
-      " [3.04191629]]\n"
+      "[0.29633889 4.15119514]\n",
+      "[[3.90793019]\n",
+      " [3.18761375]]\n",
+      "[[3.90793019]\n",
+      " [3.18761375]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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/xYYNG9CnTx+88MILiI2Nxc2bN3HixAmsXbsWS5YsQUREBDZs2ID09HS89tpr+qEZ0tPT8dJLLyE5ORljx44FoA1Xy5cvR1xcHDp27IgdO3bgH//4R53BpKFCQkIwcOBAvPbaa/D398fixYtx6NAhk93rly5dihEjRmDYsGGYPHkyWrVqhUuXLuHgwYPYuXMnvv76a7uUl8gqTm7ATSRJu3fvFlOmTBFRUVFCqVQKX19f0a5dO/HYY4+Jn376yWDdSZMmCX9/f6P7OXDggBgyZIgICAgQzZo1Ew888IA4deqUACBef/11g3Wzs7NFx44dhY+Pj2jdurV46623xOuvv26yN5kQQly7dk38+c9/FrGxscLHx0cEBgaKDh06iJkzZxr0BAIgpk2bVqucxvY5Z84cER4eLjw8PGr1FDLm448/FjExMcLHx0fcfffd4pNPPhGTJk0y6E0mhLZL/DvvvCM6deokfH19RePGjUVcXJyYOnWqOHr0qBBC2wts7Nixok2bNkKpVIrg4GAxYMAAkZ2dbbCvGzduiL/85S/64wYHB4uBAweKrVu3Gqz3ySefiJ49ewp/f3/h5+cnoqOjxWOPPSa2b9+uX2fAgAEiISGh1nkZO4fMzEwRFxcnvL29jX6WNZ0/f1688MILIioqSnh7e4ugoCDRrVs38eqrr4pr166JM2fOiNDQUDFw4ECDXlYajUaoVCrRtGlTfc++y5cviyeeeEKEhoaKRo0aiX79+onNmzeLAQMGiAEDBui31fXwqt4FXoiqYRBq9j7U/a6dP39ev0z3+7J48WIRHR0tvL29RVxcnPjiiy8MtjXWm0wIIX7//Xfx4IMPitDQUOHt7S1atGghBg4cKJYsWVLv9SJyNIUQQjgriBERkXQpFApMmzYNixYtcnZRiOyKvcmIiIhI1hiGiIiISNbYgJqIiIxiKwqSCz4ZIiIiIlljGCIiIiJZYxgiIiIiWZNFmyGNRoMzZ84gICDA6LQJREREJD1CCFy9etXkPIQNJYswdObMGURGRjq7GERERGSFwsJCu42yDsgkDOmmECgsLDRrGgUiIiJyvrKyMkRGRhqdCsiWZBGGdFVjTZo0YRgiIiJyMfZu4sIG1ERERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQka04PQ5s2bYJKpUJ4eDgUCgW++eabOtedOnUqFAoFFi5c6LDyERERkXtzehgqLy9Hp06dsGjRonrX++abb/Dbb78hPDzcQSUjIiIiOfBydgFGjBiBESNG1LtOUVERpk+fjh9++AEjR450UMmIiIhIDpz+ZMgUjUaDiRMn4uWXX0ZCQoKzi0NERERuxulPhkx5++234eXlhRdeeMHsbSoqKlBRUaH/uayszB5FIyIiIjcg6SdDO3bswPvvv4/ly5dDoVCYvV16ejoCAwP1r8jISDuWkoiIiFyZpMPQ5s2bce7cObRu3RpeXl7w8vLCyZMn8eKLL6Jt27Z1bjdnzhyUlpbqX4WFhY4rNBEREbkUSVeTTZw4EYMHDzZYNmzYMEycOBFTpkypczulUgmlUmnv4hEREZEbcHoYunbtGo4dO6b/uaCgALt370ZQUBBat26N4OBgg/W9vb3RokULxMbGOrqoRERE5IacHoa2b9+OlJQU/c+zZs0CAEyaNAnLly93UqmIiIhILpwehpKTkyGEMHv9EydO2K8wREREJDuSbkBNREREZG8MQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQkawxDREREJGsMQ0RERCRrDENEREQka04PQ5s2bYJKpUJ4eDgUCgW++eYb/Xu3b9/GK6+8gg4dOsDf3x/h4eF47LHHcObMGecVmIiIiNyK08NQeXk5OnXqhEWLFtV67/r169i5cydee+017Ny5E6tWrcKRI0eQmprqhJISERGRO1IIIYSzC6GjUCiwevVqjBkzps518vPzcc899+DkyZNo3bq1WfstKytDYGAgSktL0aRJExuVloiIiOzJUd/fXnbbs52UlpZCoVCgadOmda5TUVGBiooK/c9lZWUOKBkRERG5IqdXk1ni5s2bmD17Nh5++OF6E2J6ejoCAwP1r8jISAeWkoiIiFyJy4Sh27dvY/z48dBoNFi8eHG9686ZMwelpaX6V2FhoYNKSURERK7GJarJbt++jQcffBAFBQX4+eefTdYbKpVKKJVKB5WOiIiIXJnkw5AuCB09ehS5ubkIDg52dpGIiIjIjTg9DF27dg3Hjh3T/1xQUIDdu3cjKCgI4eHhuP/++7Fz506sWbMGarUaJSUlAICgoCD4+Pg4q9hERETkJpzetT4vLw8pKSm1lk+aNAlz585FVFSU0e1yc3ORnJxs1jHYtZ6IiMj1yKZrfXJyMurLYxIaBomIiIjckMv0JiMiIiKyB4YhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjUvZxeAiIiIyIBaDWzeDBw/7pDDMQwRERGRdKxaBcyYAZw+7bBDMgwRERGRNKxaBdx/PyCEQw/LNkNERETkfGq19omQg4MQwDBEREREUrB5s0OrxqpjGCIiIiLnKy522qEZhoiIiMj5WrZ02qEZhoiIiMj5kpKAiAhAoXD4odmbjIiISC504/cUF2ufxCQlAZ6e0jiupyfw/vva3mQKhUMbUvPJEBERkRysWgW0bQukpAAPP6z9t21b7XKpHHfcOGDlSqBVK/uWqQaFEE7ow+ZgZWVlCAwMRGlpKZo0aeLs4hARETlWXeP36KqkVq7UBhGpHPfOk6Sy48cR+OSTdv/+ZhgiIiJyZ2q19klMXd3WFQptW52CAttWmdnguI76/mY1GRERkTszNX6PEEBhoXY9dziuFRiGiIiI3Jm54/fYepwfZx3XCgxDRERE7szc8XtsPc6Ps45rBYYhIiIid2Zq/B6FAoiM1K7nDse1AsMQERGRO9ON3wPUDia6nxcutP14Q846rhUYhoiIiNxdXeP3RETYr1u9M49rIXatJyIikgspj0BthKO+vzkdBxERkVx4egLJyfI5rpkYhoiIiOzFWU9iyCIMQ0RERPawahUwY4bhwIMREdpGxRJpK0NabEBNRERka7o5uWqOwFxUpF1u78lRySIMQ0RE5H7UaiAvD8jM1P6rVjv22DNm1J6cFKhalpbm2DJRvZwehjZt2gSVSoXw8HAoFAp88803Bu8LITB37lyEh4fDz88PycnJ2L9/v3MKS0RE0rdqlXaC0JQU4OGHtf+2beu4pzEuNCcXaTk9DJWXl6NTp05YtGiR0ff//ve/Y8GCBVi0aBHy8/PRokULDBkyBFevXnVwSYmISPKkUD3lQnNykZbTG1CPGDECI0aMMPqeEAILFy7Eq6++inF3Gpt99tlnCAsLQ0ZGBqZOnerIohIRkZSZqp5SKLTVU6NH27dHlwvNyUVaTn8yVJ+CggKUlJRg6NCh+mVKpRIDBgzA1q1b69yuoqICZWVlBi8iInJzUqmecqE5uaTu4tFLDjmOpMNQSUkJACAsLMxgeVhYmP49Y9LT0xEYGKh/RUZG2rWcREQkAVKpnnKhObmkRmgEDq45jrdH5KFfkz2I7h7okONKOgzpKGr8Mgkhai2rbs6cOSgtLdW/CgsL7V1EIiJyNilVT9lqTi5n9opzkNvXbyN3wS7M7LoRMcpTiFdFY/a6ZPxytSMEHBMYnd5mqD4tWrQAoH1C1LLaL++5c+dqPS2qTqlUQqlU2r18REQkIbrqqaIi4+2GFArt+46qnho3Tts+ydoRqN140MbLBVewbsEB5OQIfH8qAVdEF/17PqjAwJA9UA26jgFPhiFxiP3LI+kwFBUVhRYtWmDDhg3o0kV7oW7duoWNGzfi7bffdnLpiIhIUnTVU/ffrw0+1QORs6qnrJ2TS9crrmao0/WKk9CM7+Y69tNJ5PyrADkbA7HpSgeo0Uf/XnPFeYyMPgTVWG8MSUtAQHgPAHBYm1+nh6Fr167h2LFj+p8LCgqwe/duBAUFoXXr1khLS8P8+fMRExODmJgYzJ8/H40aNcLDDz/sxFITEZEk6aqnjD1RWbjQNQKEFHrF2WBONfUtNX79935kL7+EnN2ROHgrGkAb/fvxymNI7XIaqsnB6DklHp4+zmtQrhDC2NV2nLy8PKSkpNRaPmnSJCxfvhxCCMybNw9Lly7F5cuX0bNnT3zwwQdITEw0+xhlZWUIDAxEaWkpmjRpYsviExE5FycCNc7UdZHydcvL0w4UaUpurn1mgm9A9dzVM1ex/r19yF6lxtqCOFwQIfr3vHAb/ZvtRWryVaheiMJdya1NFsVR399OD0OOwDBERG7JjduU2JXUr1tmpnbkbFMyMoAJE2x77Lqq53TVjEaq505tK0LOe8eQ/bM/8i52wC1UtdltqriCe1vvR+poBYbNSkDTNpb1DmMYsiGGISJyO1Z8aRFc47o568mQWq2dtqSusZruNEDXHD2O7RlHkPPJeeRsb4nfb8YarNbO+wRSO56A6tGm6Pt0ArwbeVtdJIYhG2IYIiK3YuaXFgoKpFP1IwWuct105TTVK656OW1R7WdmCBunyMJqURUYPaBG3yb7oOp3GapprRE7PAoKj7qHv7GEo76/nd6AmoiILGTJSMv2aFPiqlzlulnaK85W1X5mDkapFBUIQBmGtdqP1FFqjJjZHiGxnYyvLOW2WdW4xKCLRERUjVRGWnY1rnTd6hq0MSREG3yCgrRBw4YT04qwFmat9+JTZbhw1Rdfn+6NiUv6ISQ22PiKq1Zpn3ClpGjbQKWkaH92xGS5FmIYIiJyNVIaadmV2OO62XOE6HHjgBMntG2D0tKA5s2B8+e1T4V0weLpp+vugg9ot6unTBVlFVj3t+2Y1mEjooZEoxAR0MB4FZe4M6da9w+fhE9jn/rLbsOQ5ghsM0RE5GqsaVNCtr9ujuqVVlejb3PVaGh9/uAFfPfuIeR874X1ZxJwDQH698YjExnQ9mQziESWNDC3YdssR31/88kQEZGr4USg1rHldXPUk4/6BmA0kyg6gwPZx/DW8Dz0bbIHYfFBmPLvflh1pheuIQDhHsWY2n4T1ryej08ujoEiKwuKiAjDnVgyp5olbbMkgg2oiYhckTuMtOwMtrhujhwh2lSwMMMjj3kgU9MOQDv9si5+B6HqcRapT4Wh68NxUHhUqxps6JxqrtQ26w6GISIiV9XQLy25auh1c2SvtAYEBg0UOI0IrNA8ACVuYmDzvVANuoFRae0Q2bM9gPZ1b2ztnGqAS7ZpYxgiInJlDfnSkrOGXDdHPvkwMzBoYNjuRdcIOrvl01g5MR9DZiaicYseDS+POZKStE/aTLXN6tNH2+hcAkGeYYiIiMgSjnzyYSJYaKDARQThJnwRiSL98tvNwuC15F+Y/uD9DS+DpcwZJ2n8eCA6WjJTorA3GRFRQ7nIwHJkIw7uzXf9o8/h9/RECBh/+vNX/78jeGhX3Nf/PMLDNNL5HTTW2y4yUhuE3nnHrClROB2HDTEMEZHdSH3ST7IPXW8ywPiTjwbOcXbyl9PIWXgc2T83Rt6lDhiFNXgfMxCJqt+z8sahwDvvwH/qxPp35sywXvPYffrUfiJUXY0gyTBkQwxDRGQXrjDpJ9lPXU8+rOjNp6nUIP+zA8j59AKyd4Rj7827Dd6P8S7A6A5/4JHeBejQwxeebSKqQk19YUdqYd3CSWg5NxkRkZQ5sns1SVMDe6WVnyvHjwv3ISfrFtYci8VZTaL+Pd3kp6lJl6F6phViGxcBxeeAlu3MDzuA8bCuGwvJGWFdot3uGYaIyDi2g6mfq0z66e6c/XtqYa+0ou3FWPPeUeT86IufznXATfTUvxeAMgyP2I/UURqMmNUewTGdtGHn2YmWh5377gOCg6UX1iXa7Z5hiIhqk9qjdSmS6F+4suICv6dCI7B7xWFkLytBzv9CseN6PICqL/q2XoVQxf+B1EcC0P+5RPg07l21cV3VsOaEHQC4eLGegjkprJvb7T4pyXFlAsMQEdVU3/+AnfVoXYok+heuUznyKY2poKB76uGEJ5o3r9xE7j/3IuerG8g51A6n1XEA4gAACmjQs/F+qHpfhGpqOBLHxkAhwrXXLSer6roB9VfDAvWHHXM5Oqyb0+3eGVPJCBkoLS0VAERpaamzi0IkbZWVQkRECKH9X1Ttl0IhRGSkdj25010rhYLXSgghsrJq/+5ERGiX25qp31NHlKGGs/vOiU+mbBJjW24T/rhqUIRGuCbGtNwm/j15kyjZe85ww7qu27x55p1fQ1+5uXa/NkYZO+/IyFqflaO+v9mbjIiqWNjTQ/bs3L3aZTi6V525v6d2LIPQCBzIOY7sxaeRszUYv15LgKg2ClC4RzFUsUeR+pAfUp5PhF+QX+2d1Hfd7P3VbOOxkKxixpNE9iYjIsdjOxjLSGGyVGc3IHZGrzpLfv9sWIZb125h84f7kP3FVeTsj0JBpeHkp139DkJ1j3by0y4Takx+WpOp69ZQCgUQFARculR7n86sjqpOQlPJMAwRURW2g7GcMydLlUIDYkf3qlOrgbNnLdumAWW4dPwyvn/3ALLXKLCuMAFl6Kp/T4mbGNR8L1KH3MComTFo1f3O5KdqNbBpY/2/Dw2djd6csLNsmfZfZ4Z1F8EwRERVJNrTQ/Kc8ReuVBq6O/JporHwZwkzy3DkhwLkLDqJnM1NsaU0EWr01b8XqjiPUe0OQXWfD4bMTIR/aI3JT80NqJZcj7oaGpsbdpwV1l0IwxARVZFqTw8yJKUBHx31NLGu8GeJOspQebMSWz/aj5z/XEbOntY4fOsuAFH69zv4HoGq6xmopoTgnsnx8PCq8ceArqry22+190dNxgKquddj3jzgo48aFnYkVB0lVWxATUS12XCaAbIDKTV0d8SkpbpjWPtEyEgZyk6X4YcF+5H9jRprT8TjkgjSr+6NWxgQtBepKdegSotG234Rde/b3KdVNctgyXUD7PNkx9ntzczABtRE5DzObAdDpkmpobsjniY2pH1NtTKc2Fasnfw0tzE2XuqA26ga4DBIcQn3tj2A1DGeGDYrAU0iupnetyVPq2q2W7L0utk61EqhvZmEMAwRkXF8tC5dUmvobu9edQ0IdRVNw7Ay9Fm89XAH7KuIAFD1lCfW5w+oOp5C6qRm6P1kArx8+5m/4/qqKutT/Vyc1RtRKu3NJITVZERErsYRVVPWlsseTxMtGVeomj/jDaRjDjTQlsETlegXuA+qpCtQTW+Du4dFmdiD7ctktOrSkdVVpqocpTD+UDWsJiMiIuOk2tDdXk8TTfVyrMNxRKMxruHeiD14vOtu9E7xQ+PO7WwTNqx5WlVXT0xHPoXlBMNGeZhehYiIJEdXxdKqleHyiAj3q+bQhT8LvTT1Ki58/gMy8TCGZL+AxjOf0j7NadtWW1XUENZUQT71lPOftkipvZmEMAwREbmqceOAEye0VS8ZGdp/CwrcKwjdcXPgvdjxwFu45hFg3gbBweg2OAjeE8fXfhKiaxvTkECke1qlexJnjpgY649nK1JrbyYRDENERK5MV8UyYUJVLyU3cXbfeXwyZTPGtPwNwc3U6P7Vn5CqWW3extOnAzNn1j/dRVqatg2NNax5WiWFgGEqxCkU2mE0ZDawKsMQERFJgtAI7M06gvlD89A7YC9adgjGE8uT8G1JT1yHP1p5FKN9vAduNAmFqO+JTHCw9svc3LYx1tJVVUbUMw4RIK2AUT3E1byGMh5YlWGIiIic5ta1W9jw1g680Gkj7lKeRsf778arG5Lx67UOEPBAt0YHMC8lDzszDqHwdgt8sD8Ffp9+CAVQ99ONZcuAc+fMK0BD28boqirnzTP+vhQDhpzam5mJXeuJiMihLh69hO8XHET2Gg/8cDoeZQjUv+eLGxgUuheqwTfvTH5aR9WSqVHSnTFKt6uN3M4RqPUYhoiI5MxBX4iHv/8DOR+cQvbmZvilLFE/9g8AhHmcw6h2h6G6zweD0xLhH+rf8LI7aywmFwgYroTjDBERkX3ZcUqGypuV+GXpPuT89wqy97TB0dt3AbhL/34H3yNI7aad/LTHpHh4eIVWbWxuoKhvfB5njcXEkdtdEp8MERHJUV1TMuiCghVtR0pPlWLdu/uRky2w9mQ8Lotm+ve8cQvJQXuROvAaRs2oMflp9fBz9Ki2zU9RUdX7DQlorlZ1RQZYTXZHZWUl5s6diy+++AIlJSVo2bIlJk+ejD//+c/w8DCv/TfDEBFRNTackuGPvFPI+WcBcvICsPFyB1TCW/9esOIi7o06iNQxnhg6MwFNIoz8/9ecWd8bENAAsOrKhbGa7I63334bS5YswWeffYaEhARs374dU6ZMQWBgIGbMmOHs4hERuZ4GTMmgvqXG/5YfQM7yi8je2Qr7K2IAtNa/H+dzHKpOhVA9Zsbkp+bO+i6ENhClpQGjR1seZFh1RSZIPgxt27YNo0ePxsiRIwEAbdu2RWZmJrZv3+7kkhERuSgLp2S4VnING97bh5zVt7HmWBzOiw76VTxRiaSme6HqXwrV9LaIGRININr0vi2d9V2mc2aRY0g+DPXr1w9LlizBkSNHcPfdd+P333/Hli1bsHDhQmcXjYjINatgzBwJ+duPzmHpjHz8fL4DKtBLvzwQpRgeuR+pKoHhs+IRFN3F8jKYejpVF5nNmUWOIfkw9Morr6C0tBRxcXHw9PSEWq3Gm2++iQkTJtS5TUVFBSoqKvQ/l5WVOaKoRCQ3duyNZVcmZoHXQIHTiMC43On6LvB3eZ2EKvEEUh9tgqRnE+HdqE/DymBtqJHClBbkdiQfhlasWIHPP/8cGRkZSEhIwO7du5GWlobw8HBMmjTJ6Dbp6emYV9dooEREtlBXexfdJKBSHsn3Trdzcf/9AIDq4zhr7vw0EwvQK2A/VH0uIfW5CLQfFQ2FRxvblcHSUKNr1C2FKS3I7Ui+N1lkZCRmz56NadOm6Zf97W9/w+eff45Dhw4Z3cbYk6HIyEj2JiMi27C2N5YEqtRK9pzDdwsOI/sHHzQqOY6/4xVEouo8LniEYk/KC0h8/2mEJjS3X0FMDYpYXUN7k5HLYm+yO65fv16rC72npyc0Gk2d2yiVSiiVSnsXjYjkypreWE6qUhMagb2rjiJn6RlkbwvB/8oTAegGOOyJrR5JmNk6Cyk9ytH+sR4IGTEIAx0R0OobFLGmVq2Ap54CKiq002y4QrsscimSD0MqlQpvvvkmWrdujYSEBOzatQsLFizA448/7uyiEZFcWdgby9FVahVlFdj4wT7kZF5DzoFonFTfDeBu/fvdGx2Aquc5pE5tiU4P3A2FR5rNjm3A1JMw3YShxkLiU08BMTHaQRg/+gh4/XXD96XeLotciuSrya5evYrXXnsNq1evxrlz5xAeHo4JEybgL3/5C3x8fMzaBwddJCKbsmQS0KQkmw1wWJ8Lhy9i7bsHkbPWEz8UJeAqqv5f54sbGBy6F6ohNzFq1t0I79rC6uOYzZInYXWFJjuMku32JFAVa0scgdqGGIaIyKYsmQR082a7zJ4uNAKH1xVoJz/d0gxba0x+2sLjLEbFHIbqPiUGz+yARiGNzN53g1kbYqp/kYeGApMn2z1EuhVX7d1YD7YZIiLX42Z/ldbJkklALa1Sq0flzUpsWbIPOZ9fQfaetjhWY/LTTr6HoepeDNXjzdF9Ynt4eIWZf062Ut9givWNJG3OtBw198VBGKu4cu9GCWAYIiLbcOW/Sq0JcfW1d6k+Cai5XcjrWO/KyWqTn55KwBXRWf+eN25hYPAeqAaWY9SMaLTpGwsg1rzj2Yu1jcvNmZbDGA7CaH0AJT2LwlBhYSEiIyPtVRYiclWu/FdpQ0LcuHHaL5j6gpSJAQ6NjZ9z/OeTyPnXCeRsDMCmyx1QiaoBDoMVFzEy6iBSx3li6MxEBIR3t/bM7cPSJ2GWTstREwdhbNBcc6RlURiKi4vDrFmzMHv2bPj7+9urTETkSlz5r1JbhDhTk4CaUaWmfmcBfvv4ALI/vYic3RE4UNEOQNUAh+19jkPVuRCpk4PQ64kEePrUM/mps6sqLX0SZu20HByEsYoNq2LlysP0KlU2bNiA9evXIyYmBp9++qm9ykRErsSSv0qlxFSIA7QhTq1u+LF0VWqtWhksvt64ORaF/RUtxiej7zMd8PZvyThQ0Q6eqERK011YMDoPR388iQMV0Xj7t2T0fbYjPH3qCTarVmkbdqekAA8/rP23bVvtckfRPQnTtZ2qSaEAIiOrQow1X9A122XJnbkB9MABbU9IW/xOuxthhc8++0xERESIzp07i9zcXGt24VClpaUCgCgtLXV2UYjcT0aGENr4UP8rI8PZJTWUm2teuW34/7hTv5wSq1PeE+kBb4jB+EF4oFJ/mEBcERPabBEZ038Rl/64bPnOs7KEUChql1+h0L6ysmx2HmaXpWZ5jJXF3M+h+isy0rHnI3WVlUJERBj//I29IiJc5vo56vvbqjAkhBDXr18Xr732mmjUqJEYM2aMOHr0qC3LZVMMQ0R25IRQYRMOCHHq22qR/9l+8VpSrujsd7DWrqO9ToiZXXPFz+/uFLfKb1l/Lrovw7rOQaHQBojKSuuPYamsrNplMhZiTH2RKxTa93/8UftZ5OY69jxcRV0BtK5r6uiAbCVHfX9bPc7Q9evXsXPnTmRlZeGf//wnvL29MW3aNMydOxcBAQG2fHjVYBxniMiOLBlzR0pVGpYMnGhBo9Mbl27gp4V7kf31Taw5cjeKNVUDHHpAjd4B+6Hqewmp0yIRd+9dUHjUUZ1kCTudS4OZ235J13YLMD5MgZQb4EuJJcMTSPW+rEGSgy4uWbIE+fn5yM/Px8GDB+Hp6YmOHTuiV69e6Ny5M7744gscOXIEq1evRvfu0unhwDBEZGeu+GVmwxBXsucc1ryrnfz0x7MdcANVAxw2xlUMa7UPqhFq3DsrDs3bh5gul6UNoDMztW2ETMnIACZMML2eMxj7Io+MNBymgEzT/f789BPwt7+ZXt/RAdlCkhx08c0330SvXr0wadIk9OrVC927dzeYEPXxxx/H/PnzMXnyZOzbt8/mhSUiK9m6h1HN/Y0ebd6YO45Us4x9+gBbtxpeA3MHTqxBaAT2rDyCnGXFyP61OfLLE1A1+SkQ6VmE1PhjUD3kj+TnO0DZpLd5Zba2m38DxzKymD16rJkzTAGZpuvdyB5mlrF1vVtJSYnw8PCw9W4bhG2GSNaMtd1oSAPK+vZXWalt0+Hsth3GyujhYbzMZrZtuVl6U6z7W76Y1iFPtPYsrNUMo4f/PvHGoFyxe8UhoVFrrCuztQ2gzWl3Y6s2Q7b+fSL7cNW2fDVIvgF1XTQajcjLy7P1bhuEYYhky9Y9jKTUY8nSMtZX5jpC3PlDF8TyJzeL+1ptFY1RZrC5H8qFKuxX8dFjm8SZXSUNK7MtGkBb0oPLWq7w+ZOWIwOyHUm+AbUrYZshkiVdmxhbTXRp6/3Zg6ky1lSjzEIjcGjtH8hZXIjsLUHYdjXBYPLTlh4lGHX3Eaju98WgGYm2m/zUVg2g7dnuxhU+fzLkim35apBkmyEiciG2HqLfFYb8t3Q04ztl3vX8J/jvbzHI3hOF45XRAKL1q3T2OwRV9xKonghFt0fi4OHVou79WctW7Tvs2e7GFT5/MmTu/HnEMETktmzdgNIVGmRaeey/f9gYXyIZAOCDCqQE70Xq4HKMmtEOrXvHAYizXRmNsWUDaFPTg1jLFT5/qo0N083CMETkiszpzWPrHkaO6LHU0F5KVh77OhphUvQWpI7zwpC0BMdPfmrFZK4O5+gea2Q79grIboRthohcjbndr209GKK9B1dsyOzx1cvYogVw4YJZqwsAt5q1gFfRSXj6+VheZnOZE/Kk3r7DVQfXJJfmqO9viyZqJSIn031h1my7oZtlvfqEnLrZ0oHak2ZaM9GlrfdXnSXnVY+rZ69jW+80CGiDjikKhQLKjz+wbxAyd/LUOiZzRUSE84MQYN/Pn8jZ7NpXTSLYtZ7cgrXdr82dI8pctt5fA7uVn9x6Wix6IE8MDc4XPrgpACHewstCY6prvSMm+7SmK7pUxmqqi60/f6J6sGu9DbGazEz2GFWWbKch3a/tPQJ1Q/Zn4XlpKjXY/t+DyPnkPHK2t8TvN2MNVmvnfQKqDifweId8JHz3dyiqV5k1bw488oi2Qam9f79t1RVdivelFMtEbold68mxbNFeg+yrIb15bN2A0pb7M/O8dizcjCXPeGDN0ViUaBL0yz2gRp8m+6Dqexmp01sjdngUFB5tASQD6lnO+9K2RVd0qd6XbJBLboZhiKraa9R8SKhrryGF9grkvr15zCzvi98mYSP6A9BOfjq81T6o7lXj3hfbIyS2k/GNnPml3dCu6LwviRyGYUju1GrtX57GakuF0D7KT0vTVivwMbhzuUL3a0voqlqKioDmzSEuXIDCyHlpoMBpROCkRxSmJ2yEakJjDJiWaHryU2dX5TQkvPK+JHIohiG546iyrkPXm8eKWdYlx1j1DwANDLu4aqCAAgKal/6EP95uDYVHG+v37+jqpYaEV96XRA7FrvVyx1FlXYvUu1+bofSfyyHuuw+ixpe9AFCjwzY8IiOgyMpC239Mh8JDoX1ikpcHZGZq/1Wrax/ARt30G6whXdF5XxI5FMOQ3LlrOxR3Nm4ccOKEtndVRob234ICyQYhoRE4kH0Mbw3PQ1LALpTNeM148NH9R/PmwOef1z4vc8brMVW9BGirl4yFKHuwNrzyviRyKHatlzuOKkt2cPv6bWz+cB9yvihD9t62+KNSW701AHnIgxXDA9TVmLjm6Mw//QQMHmz5/u3N0vZLvC+JALBrPTmKVNqhOLuxKzXY5YIr+P6d/chZo8D3pxJQii7693xQgUHN92Bmu5+BbWbsrHr1j7mNidVq4JlnzCuso6uXLO3VJpX7kkgmWE1Gzm+HYu50BSQ5RzecwILReUhptgvN72qMRxb3xZen+qAUgWiuOI8pMZux6k+/4mLxbaw91wND5g80b8fVq3/MbUz84IPApUuW71+qnH1fEskIq8moijOezphb/WFPUnkqJZVy1EN9S41tH+9H9vJLyPk9EoduRRu8n6A8ClWXIqROCcY9k+Ph6VOj/NZU/2RmakOyLbhi9ZIL/F4Q2Yujvr8Zhsh5bDVdQUNIoQu2lMphRNnpMqx/bz+yv1FjbUF7XBTB+ve8cBsDmu2FKvkqVC9E4a7k1qZ3aOns7OZO12EOhYJPVYhcCMOQDTEMSVRD5tqyBSk8lZJSOao5+ctp5Cw8juyfGyPvUgfchg88oEYSNqMdjiEq7AZiHuiMYS93RGDrQMsPYCz8RUZq28HUPFdTT5PMFRQEfPQRgxCRC2EYsiGGIYkyt/ojIwOYMMG2x5bCUylblqOBVSmaSg3yPzuAnE8vIHtHOPbevNvg/WmeH+JvHq+j6e3zVQsb+uTKkjLX9zTJ3P+F/fgjMGiQdWUlIqdgbzJyf84cS0UqI/w6cTLP8nPl+HHhPuRk3cKaY7E4q0nUv+cBNfo22YfUpMuY0PkgWs2fBqhtPEeWJT2sdI2JjZ3nggXAzJmm2yFxpGYiqgPDEDmPM+faksoIvw6ezLNoezHWvHcUOT/64qdzHXATPfXvBaAMwyP2QzVSjXtfjEdwTKc7T64mSmOOrHHjgFGjgMWLgePHgeho4LnnAB8fwMOD3dCJyGoMQ+Q8zhxLRSoj/Np5Mk+RlobdN2KR/fF55PwvFDuuxwOo2ldbr0Ko4v/QTn46vQN8GteY/FQqT9AA40/A3n236glYXU+OjLVDIiKqhmGInMtZX2JSmQHezpN5KgoLMfPR89iIZO3uoME9/geQ2ucCVFPDkTg2BgqPyLr3IZUnaOY+ARs9mt3QichiDEPkfPb6Equvga5URvhtSDnMDCD3YSWatvBD6vBbGPliHMISE01vpCOFJ2jmjkCtq6pj2yAishB7k5F7MrdR8cqV2nYn56v1kqqri7c9WdLVHNrJT0/Mz0DUa4+a3LUmJAQeJSXWBTspzJHl7CEYiMhpHPX97RLTcRQVFeHRRx9FcHAwGjVqhM6dO2PHjh3OLhZJla5KpWYVkq5KRTfNx6pV2l5I1YNQSIi2HYqj25iYMRP9rWu38NM/dmJG542IVhai3WvjcQ7NTe7a48IF7RMya+ieXAFVT6p0HPUETSpVdUTktiRfTXb58mX07dsXKSkp+P777xEaGorjx4+jadOmzi6aaRxG3/EsmdTzoYdqr3fxona5p6fjA5GRKp5Lxy/j+3cPIHuNAusKE1CGrvr3lLiJX3wHYezNL03vuyFBwdmNk6VQVUdEbk3y1WSzZ8/GL7/8gs3W/mULJ1WTSXh6BbdmbpVKSAhw4YLx9xw9f1WN0HzkegRyPjyNnM1NsaU0Eepqf7OEKs5jZLtDSL3PB4NnJKDxoe2Oq0KyJtzb4g8CKVTVEZFTOOz7W0hc+/btRVpamrj//vtF8+bNRefOncWyZcvq3ebmzZuitLRU/yosLBQARGlpqWMKnZUlhEIhhPZ/3VUvhUL7yspyTDnkKCOj9nW39pWba//yZmUJTasIg+OeQoQYiyz9okTlETGnd67Y9tFeob6tNty+slKIiIi6z0GhECIyUrueo2Vl1S5bRIR1v/+6e6rmfcV7isitlZaWOuT7W/JhSKlUCqVSKebMmSN27twplixZInx9fcVnn31W5zavv/66AFDr5ZAwJOUvJznIzbVdGMrIsFsxSwtLxS+j5gsNINQ1jquGQmgAsabnX8UfG0+Z3pkUg4I9/iAwFq4iIxmEiNyYo8KQ5KvJfHx80L17d2zdulW/7IUXXkB+fj62bdtmdJuKigpUVFTofy4rK0NkZKRjqsnY88W5zKlSCQkxbDRdFxt/Rie23Jn8NLcxNl+Kx1HcjVY4bbwXg6VVPxb2RrMre877xnZ4RLLCucnuaNmyJeLj4w2WtW/fHllZWXVuo1QqoVQq7V0049jzxbnMGbdn8WLz5rJq4ICLmkoN/rdcN/lpK+yriAEQAQBIwU+IhA1HdpbSgIP2HLWa4wgRkR1IPgz17dsXhw8fNlh25MgRtGnTxkklMoE9X5zPnN5PdprLqvxcOTa8p5389LvjtSc/7Re4F7OiszHq6ALgqhk7tCQ0SyUo8A8CInIxkg9DM2fORJ8+fTB//nw8+OCD+N///odly5Zh2bJlzi6acVKZ5kHuTD0psWF38dP5uslP/fDT+Q6oqDb5aROUYnjkfqhGCoyY1R7Be/8A7p9r/HfDGEtCs1SqkPgHARG5GMm3GQKANWvWYM6cOTh69CiioqIwa9YsPPXUU2Zv7/Cu9bpB/wDjTx1qzCROZrLHl70V+xQagV2Zh5D90Vnk/C8MO2+0N3i/rVchUhP+gOrhAPR/LhE+jX2qjlVfW5rqbNFmyFlDObArPBHZiKO+v10iDDWUZMYZclaDVldVPagcPQosW6b9gtVx4Jf9zSs38fP7e5G94gbWHI5BkabqqYYCGvRsvB+pfS5C9UwrJIxuB4WHovZOzG1cD2gDg7mhua5JTJ0ZvvkHARHZAMOQDTltbjKpVFu4ImNhsiY7f7Ge3Xce3717CNnrfLChJBHX4a9/rxHKMbTlXqQOv417Z8UhLNH0tBjIzAQeftj0ekFBwEcfmXdO9uy51VD8g4CIGohhyIY4UauLqetJhzE2/LIXGoF9q48iZ+kZ5GwLxm/XEiCqdXxv5VEMVdxRqB70w8AZHeDb1NeyA5j7ZOjHH4FBg2y7T2cN5cA/CIioAdi1Xi74ZWGovrnFjDGnm3Y91/jWtVvYuGgvcjKvIefAXThReTeAu/Wbdmt0AKp7zkH1ZBi6TIiDwqMBjX7NbVxvSWiRes8tqfRwIyKqB8OQM0mp0atUmBqjpi51fdkbucbqFuHY0nEaPjiQgh9Ox6MM3fTvKXETg5rvReqQGxg1MwatuscDiDeyYyuYMwaSpV362XOLiKjBjA5+Sw6gqwqq+cVfVKRdvmqVc8rlbNY+wTD2ZV/HNVaUFCNp/Z9ReboYZQhEqOI8Ho/ZjG/m/IaLZ9X47lwPTP2iP1p1t0OA0HXpb9XKcHlEhHVtn3RPmxRGGmwD2uWRkRzKgYioHmwz5AxSbvTqbJb0uALqvFaV5RWojGgD5ZWzMBYTNFCgzCcEhxdtQI8pHeDh5eC/C2xZPcqeW0Tkphz1/c0nQ85gyXQFcmPqSUd1NaqWSk+VYsWMrXg06heMbbwevnUEIQDwgEDTW+fRM+ay44MQUNWWZsIE7b8NCb22ftpERCQzbDPkDFJv9GprljwFqa9dTU0RESh58lWs+DwYOU/uxMbLHVCJPgCA8cg0r2zuco2lNDcZEZGLYRiqyRG9u+TU6NWaRuL1TJWhfvwJHC/yw8ZtSvzr2HDsfT3OYNNYnz+Q2ukUHu1dDvzTjPK5wzXWYc8tIiKrsM1QdY7q3SWX6QoaOjLynWB682AB8jfdwPLt8cg5noDzomqAQ09Uol/gPqQOuALV9LaIGdK2als5XGMiIjfGQRdtyKyL6egpDdy90WsDG4mfzi9GzoKjyPnJDz+f74AKVA1w2ASlGBG5H6kqgeGz4hEU3cz4Mdz9GhMRuTmGIRsyeTGd1bvLnacrsHBkZKER2JlxZ/LT/DDsqjH5aZTXKaQmFkD1cACSnq02+akp7nyNiYjcHEegdiRLenfZsk2GOzd6NbNh8q5/bcGSZz2w5kgMzmjaA9CGIAU06B2wD6o+l6B6NgLxqmgoPFpbXg53vsZERGQTDEOAc3t3uWujVzMbJs9c1Q8b0R8A4I9rGNpyH1LvrcS9M2MRmtDRNmVx12tMREQ2wTAEyKt3l6PcGS9IFBVBYaQmVgMFTiMCBR7ReLb9JqSOb4Tk6YnwbdrLCYUlIiI5YxgCzJ9A0xWnNHDCRLAVZRXY+ME+nPJ4Go+L1yGggAeqrqsGCiggoJ71Mk78IwIKj0i7loeIiKg+DEOAfSbQlIL6hgqwcTuaC4cvYu27B5Gz1hM/FCXgKroB6Ia1SMA/8QIiUKRf1yMyAli4EFFswExERBLA3mTVuVPPo/qGChACCA4GLl6sWm7heEpCI3B4XQFyPjiF7C3NsLUsERpUhakwj3NQxRyC6j4lBr8Qj0YHd7ABMxERWYRd623IoovphGolmzM1VIAxZoy9U3mzEluW7EPO51eQvactjt1ua/B+R9/DUHUrRuoTzdF9YnvnzPlFRERug2HIhiQ3a729WTrzu46R8ZSunCzFunf3IydbYO2pBFwRTfWre+MWUoL3QJVSDlVaNNr0jbBN+YmIiMBxhqghrB0C4M54SkXvf42vN7dEzsYAbKo2+SkABCsuYmTUQajGeGLozAQ0iehuo0ITERE5B8OQO2rgEAAvvSjwJQbof47zOY7UzoVQTQpC7ycT4OnTr6ElJCIikgyGIXdkaqgAE84hFMlNdyF1QClUz0eh3aBoANG2LycREZEEMAy5o3qGCtD9l8LIZgKAUHhg5cEOaBYb6oiSEhEROR27+7irceOgWfEVbjU1DDUKGA9Cuvc8hAbNig/Yu3RERESSwSdDbubGpRv4aeFeZH99E2uO9MNZTRGSsBktUYx47MNrmG96J/aYg60+7jCcARERuSyGITdQsucc1rx7GNk/+ODHsx1wA/fAA2okYTOG4XtEBt9Au9EJSO3fCJhsxg4dOQdbfaNku9pAl0RE5JIYhlyQ0AjsWXkEOcuKkf1rc+SXJwCoqg57yuMjvO3xKppVntcuuAhgfQQwfIG05mCra5TsoiLt8noGgCQiIrIV+Q266O/vklUyFWUVyPvXXuSsKEfOgWicUhsOcNjDfz9UPc/j0c570fa9GbVniteNMP3SS8A772j/29gcbI4KIKZGyTYyACQREckLB120h+xsYM4cl6mSuXD4Ir575yByvvfED0WJuIaqAQ59cQNDwvZANbQCI9PuRnjXhDsBY6Lxpz5CaAPGl18CX30FzJxZ+zqYmoPNlm17Nm+uf7qQOwNAYvNmIDnZumMQERGZQV5haOLE2sskVCUjNAKH1v6BnMWFyN4ShG1XE6BB1QCHLTzOYlTMYaQ+4ItBMxLRKKSn4Q7MDRghIcCJE5YFG1u37TG3kbajG3MTEZHsyCsMGaN7YpKWBowe7fAqmdvXb2snP/2iFNl7onC80nCAw06+h6HqXozUJ0PR7ZE4eHiF1b0zSwKGp6f5T1zs0bbH3EbajmzMTUREssQwBNRfJWNt1VA9210uuIJ1Cw4gJ0fg+1MJuCK66DfzQQVSgvdCNbAco2ZEo03fWACx5p2HPQKGWq19IlRf1Zs1QdLUKNmObsxNRESyxTBUXc0nK9ZWDRnZ7nZIS6yLegbvHVVh05UOUFeb/DREcQEj7zoE1VhPDJ2ZiIBwKyc/tTRgmBP07NW2p55RsvWNuRcuZONpe+L4TkREWkIGSktLBQBRqv3KrfuVm1u1UVaWEApF7XUUCu0rK8v4we5sp6mxnRoKoYZCjEWWAISIVx4Vr/TMFVsW/y4qKyptd7K6ctcse81yZ2UJERFhuE5ERO3zysio/5rpXhkZ1pe3ZjkiI+u+vo5SWan9fcjI0P5bacPPSArM/fyJiJxI//1dWmrX4zAM6YJCZGTVF15lZe0vivrWv6Ps1GVR3ji0VhCqHojK/ELFsfXH7XvCpgKGJUEvN9e8MFQ9SFpKasHD3YOCtUGfiMjBHBWG5DXOEIAmdVXJVG8EnJcHpKSY3nFuLk4pY5Dz3jFk/+wPzcVL2IBhZm1n9+7idVWBWDq+j259U1Vv7jIeUF2NxR09DpO9cHwnInIhjhpnSF4Ttf73v0CrVobLIiJqf8GZ2Str9tAdaNOnFaZ/PQDrL3ZHCC6aVw5HdBfX9RabMEH7r+6LzZI2QLr9vP++9r91gUDH3dr2mGosDmgbi6vVDi2WTVn6+RMRyYDLhaH09HQoFAqkpaVZvnFqqnZ8ndxcICND+29BQe2/9M3sbfXr7W7wgBr9mvyOt0fk4a35GvPKYWz/arX2iVRmpvZfe33hWjO+z7hx2sBoTpB0ZXIIChzfiYioFpfqTZafn49ly5ahY8eO1u/EnPF1kpKgDmsJj7PFUBh5WwMFLnk2xxOTFVj58hWExHbSvqFWA4tnW95d3JGTlVrb/X7cOG33eXfufSSHoMDxnYiIanGZJ0PXrl3DI488go8++gjNmjWz+f6FRmD3isN4Y1AeejQ5jAfOLoKAApoacUhAm2lCvvoQEz8egJDY4Ko3ralS0rVRqflEQjeg4apVtji9Krru9zXLV72ckZHGx/epq+rNXcghKDTk8yciclMuE4amTZuGkSNHYvDgwSbXraioQFlZmcHL6HplFVj3t+2Y1mEj2vicQZfxsfjLz8nYfj0eqzEOc5QLcE0ZYrCNIjISivqqhiypUnJGGxU5tQGylByCAj9/IqJaXKKa7Msvv8TOnTuRn59v1vrp6emYN2+e0ffOH7yA7949hJzvvbD+TILB5Kd+uI4hLfZCNfQWRs68Gy07pwHq5y2vGjK3SslZk5XqApuxqjlTk7W6M7kMBMnPn4jIgOS71hcWFqJ79+5Yv349OnXSts1JTk5G586dsXDhQqPbVFRUoKKiQv9zWVkZIiMjcU/jX5B/rRdEtQdiLT1KoLr7CFQP+GJQWgf4BfnZ9XwMZGYCDz9ser2MDG3VlK1xBGLjjLXhiox0v6DAz5+IJM5RXeslH4a++eYbjB07Fp7V/ietVquhUCjg4eGBiooKg/eM0V1MaEcaQme/Q0jtUQLVE6Ho+nAcPLycVFtowXhGdh+XiAwxKBAROR3D0B1Xr17FyZMnDZZNmTIFcXFxeOWVV5CYmGhyH7qL+c647/DAS53Quncrk9s4hNwGNCQiIrKAo8KQ5NsMBQQE1Ao8/v7+CA4ONisIVffUp/3sejEtJpc2KkRERBLmMr3J3JZcBjQkIiKSKMlXk9mCox6zNQjbqBARERlgNZncmDMyNhEREdkcw5At8ekOERGRy2EYshVL5xdjcCIiIpIENqC2BUvnF1u1StulPiVFO+hiSor2Z1vPQ0ZEREQmMQw1lKXzizl6YlYiIiKqF8NQQ1kyv5gzJmYlIiKiejEMNVRxsfnrWRKciIiIyCEYhhqqZUvz17MkOBEREZFDMAw1VFKStteYbvqMmhQK7YznSUmWBSciIiJyCIahmtRq7WzymZnaf02139HNLwbUDkQ15xezJDgRERGRQzAMVWdtl3dz5xezJDgRERGRQ3BuMh1dl/eal0MXUsyZNNXcgRSNDdAYGakNQpyYlYiICIDj5iZjGAK0IaZt27p7eikU2qc8BQW2e2rDEaiJiIjqxYlaHcmSLu+2mkyVE7MSERFJAtsMAezyTkREJGMMQwC7vBMREckYwxBQ1eW9LuzyTkRE5LYYhgBt+50JE+pfh13eiYiI3BLDEKDt6v7OO3W//9JL7PJORETkphiG6ptJHtBWkX35pbxmkrd0FG4iIiIXxjDEmeQNWTsKNxERkYtiGGK3+iq6UbhrhsOiIu1yBiIiInJDDEPsVq9VX3WhbllaGqvMiIjI7TAMcSZ5LVYXEhGRTDEMcSZ5LXOrAYuK2LiaiIjcCsMQoO02v3Il0KqV4fKICPNmq3cH5lYDzpzJxtVERORWOGt9dXKeSV6t1gaboqK6hxkwRvf0TC6hkYiIHMZRs9YzDFEVXW8ywPJAFBEBFBTIJzwSEZHdOer7m9VkVKWu6sLmzevfjo2riYjIhXk5uwAkMePGAaNHG1YXFhUBjz5qels5jMVERERuh2GIavP0BJKTq37OyzNvO3cfi4mIiNwSq8nINI7FREREboxhiEzjWExEROTGGIbIPByLiYiI3BTbDJH5jDWultNYTERE5JYYhsgyNRtXExERuThWkxEREZGsMQwRERGRrEk+DKWnp6NHjx4ICAhAaGgoxowZg8OHDzu7WEREROQmJB+GNm7ciGnTpuHXX3/Fhg0bUFlZiaFDh6K8vNzZRSMiIiI34HITtZ4/fx6hoaHYuHEj+vfvb9Y2nKiViIjI9Tjq+9vlepOVlpYCAIKCgupcp6KiAhUVFfqfy8rK7F4uIiIick2SryarTgiBWbNmoV+/fkhMTKxzvfT0dAQGBupfkZGRDiwlERERuRKXqiabNm0avvvuO2zZsgURERF1rmfsyVBkZCSryYiIiFwIq8lqeP7555GdnY1NmzbVG4QAQKlUQqlUOqhkRERE5MokH4aEEHj++eexevVq5OXlISoqytlFIiIiIjci+TA0bdo0ZGRk4Ntvv0VAQABKSkoAAIGBgfDz83Ny6YiIiMjVSb7NkEKhMLr8008/xeTJk83aB7vWExERuR62GbpD4lmNiIiIXJxLda0nIiIisjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1lwlDixcvRlRUFHx9fdGtWzds3rzZ2UUiIiIiN+ASYWjFihVIS0vDq6++il27diEpKQkjRozAqVOnnF00IiIicnEKIYRwdiFM6dmzJ7p27YoPP/xQv6x9+/YYM2YM0tPTTW5fVlaGwMBAlJaWokmTJvYsKhEREdmIo76/Jf9k6NatW9ixYweGDh1qsHzo0KHYunWrk0pFRERE7sLL2QUw5cKFC1Cr1QgLCzNYHhYWhpKSEqPbVFRUoKKiQv9zaWkpAG3CJCIiIteg+962dyWW5MOQjkKhMPhZCFFrmU56ejrmzZtXa3lkZKRdykZERET2c/HiRQQGBtpt/5IPQyEhIfD09Kz1FOjcuXO1nhbpzJkzB7NmzdL/fOXKFbRp0wanTp2y68WUmrKyMkRGRqKwsFBWbaV43jxvOeB587zloLS0FK1bt0ZQUJBdjyP5MOTj44Nu3bphw4YNGDt2rH75hg0bMHr0aKPbKJVKKJXKWssDAwNl9Uuk06RJE563jPC85YXnLS9yPW8PD/s2cZZ8GAKAWbNmYeLEiejevTt69+6NZcuW4dSpU3jmmWecXTQiIiJycS4Rhh566CFcvHgRf/3rX1FcXIzExESsXbsWbdq0cXbRiIiIyMW5RBgCgOeeew7PPfecVdsqlUq8/vrrRqvO3BnPm+ctBzxvnrcc8Lzte94uMegiERERkb1IftBFIiIiIntiGCIiIiJZYxgiIiIiWWMYIiIiIllzyTC0ePFiREVFwdfXF926dcPmzZvrXX/jxo3o1q0bfH19cdddd2HJkiW11snKykJ8fDyUSiXi4+OxevVqexXfapac96pVqzBkyBA0b94cTZo0Qe/evfHDDz8YrLN8+XIoFIpar5s3b9r7VCxiyXnn5eUZPadDhw4ZrOdun/fkyZONnndCQoJ+HVf4vDdt2gSVSoXw8HAoFAp88803Jrdxh/vb0vN2l/vb0vN2l/vb0vN2l/s7PT0dPXr0QEBAAEJDQzFmzBgcPnzY5HaOuMddLgytWLECaWlpePXVV7Fr1y4kJSVhxIgROHXqlNH1CwoKcO+99yIpKQm7du3C//3f/+GFF15AVlaWfp1t27bhoYcewsSJE/H7779j4sSJePDBB/Hbb7856rRMsvS8N23ahCFDhmDt2rXYsWMHUlJSoFKpsGvXLoP1mjRpguLiYoOXr6+vI07JLJaet87hw4cNzikmJkb/njt+3u+//77B+RYWFiIoKAgPPPCAwXpS/7zLy8vRqVMnLFq0yKz13eX+tvS83eX+tvS8dVz9/rb0vN3l/t64cSOmTZuGX3/9FRs2bEBlZSWGDh2K8vLyOrdx2D0uXMw999wjnnnmGYNlcXFxYvbs2UbX/9Of/iTi4uIMlk2dOlX06tVL//ODDz4ohg8fbrDOsGHDxPjx421U6oaz9LyNiY+PF/PmzdP//Omnn4rAwEBbFdEuLD3v3NxcAUBcvny5zn3K4fNevXq1UCgU4sSJE/plrvB5VwdArF69ut513OX+rs6c8zbGFe/v6sw5b3e5v6uz5vN2h/tbCCHOnTsnAIiNGzfWuY6j7nGXejJ069Yt7NixA0OHDjVYPnToUGzdutXoNtu2bau1/rBhw7B9+3bcvn273nXq2qejWXPeNWk0Gly9erXWZHfXrl1DmzZtEBERgVGjRtX6y9KZGnLeXbp0QcuWLTFo0CDk5uYavCeHz/vf//43Bg8eXGuUdil/3tZwh/vbFlzx/m4IV76/bcFd7u/S0lIAqHcSVkfd4y4Vhi5cuAC1Wl1rtvqwsLBas9rrlJSUGF2/srISFy5cqHeduvbpaNacd03vvvsuysvL8eCDD+qXxcXFYfny5cjOzkZmZiZ8fX3Rt29fHD161Kblt5Y1592yZUssW7YMWVlZWLVqFWJjYzFo0CBs2rRJv467f97FxcX4/vvv8eSTTxosl/rnbQ13uL9twRXvb2u4w/3dUO5yfwshMGvWLPTr1w+JiYl1rueoe9xlpuOoTqFQGPwshKi1zNT6NZdbuk9nsLaMmZmZmDt3Lr799luEhobql/fq1Qu9evXS/9y3b1907doV//rXv/DPf/7TdgVvIEvOOzY2FrGxsfqfe/fujcLCQrzzzjvo37+/Vft0FmvLuHz5cjRt2hRjxowxWO4qn7el3OX+tpar39+WcKf721rucn9Pnz4de/bswZYtW0yu64h73KWeDIWEhMDT07NW2jt37lytVKjTokULo+t7eXkhODi43nXq2qejWXPeOitWrMATTzyBr776CoMHD653XQ8PD/To0UMyf0k05Lyr69Wrl8E5ufPnLYTAJ598gokTJ8LHx6fedaX2eVvDHe7vhnDl+9tWXO3+bgh3ub+ff/55ZGdnIzc3FxEREfWu66h73KXCkI+PD7p164YNGzYYLN+wYQP69OljdJvevXvXWn/9+vXo3r07vL29612nrn06mjXnDWj/Ypw8eTIyMjIwcuRIk8cRQmD37t1o2bJlg8tsC9aed027du0yOCd3/bwBbW+NY8eO4YknnjB5HKl93tZwh/vbWq5+f9uKq93fDeHq97cQAtOnT8eqVavw888/IyoqyuQ2DrvHzW5qLRFffvml8Pb2Fv/+97/FgQMHRFpamvD399e3qp89e7aYOHGifv0//vhDNGrUSMycOVMcOHBA/Pvf/xbe3t5i5cqV+nV++eUX4enpKd566y1x8OBB8dZbbwkvLy/x66+/Ovz86mLpeWdkZAgvLy/xwQcfiOLiYv3rypUr+nXmzp0r1q1bJ44fPy527dolpkyZIry8vMRvv/3m8POri6Xn/d5774nVq1eLI0eOiH379onZs2cLACIrK0u/jjt+3jqPPvqo6Nmzp9F9usLnffXqVbFr1y6xa9cuAUAsWLBA7Nq1S5w8eVII4b73t6Xn7S73t6Xn7S73t6XnrePq9/ezzz4rAgMDRV5ensHv7fXr1/XrOOsed7kwJIQQH3zwgWjTpo3w8fERXbt2NeiWN2nSJDFgwACD9fPy8kSXLl2Ej4+PaNu2rfjwww9r7fPrr78WsbGxwtvbW8TFxRncXFJhyXkPGDBAAKj1mjRpkn6dtLQ00bp1a+Hj4yOaN28uhg4dKrZu3erAMzKPJef99ttvi+joaOHr6yuaNWsm+vXrJ7777rta+3S3z1sIIa5cuSL8/PzEsmXLjO7PFT5vXdfpun5v3fX+tvS83eX+tvS83eX+tub33B3ub2PnDEB8+umn+nWcdY8r7hSQiIiISJZcqs0QERERka0xDBEREZGsMQwRERGRrDEMERERkawxDBEREZGsMQwRERGRrDEMERERkawxDBEREZGsMQwRERGRrDEMERERkawxDBGRS8rMzISvry+Kior0y5588kl07NgRpaWlTiwZEbkazk1GRC5JCIHOnTsjKSkJixYtwrx58/Dxxx/j119/RatWrZxdPCJyIV7OLgARkTUUCgXefPNN3H///QgPD8f777+PzZs3MwgRkcX4ZIiIXFrXrl2xf/9+rF+/HgMGDHB2cYjIBbHNEBG5rB9++AGHDh2CWq1GWFiYs4tDRC6KT4aIyCXt3LkTycnJ+OCDD/Dll1+iUaNG+Prrr51dLCJyQWwzREQu58SJExg5ciRmz56NiRMnIj4+Hj169MCOHTvQrVs3ZxePiFwMnwwRkUu5dOkS+vbti/79+2Pp0qX65aNHj0ZFRQXWrVvnxNIRkStiGCIiIiJZYwNqIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKSNYYhIiIikjWGISIiIpI1hiEiIiKStf8HUKxiSDrd3iUAAAAASUVORK5CYII=\n",
+      "image/png": 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\n",
       "text/plain": [
        "
    "
       ]
@@ -1896,9 +1896,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[4.13542726]\n",
-      " [2.97804446]]\n",
-      "[4.07929472] [2.96841776]\n"
+      "[[3.96783837]\n",
+      " [3.23305112]]\n",
+      "[3.95982273] [3.21682143]\n"
      ]
     }
    ],
@@ -2002,15 +2002,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[3.9208878 ]\n",
-      " [3.21055226]]\n",
-      "[[3.84859258]\n",
-      " [3.26931499]]\n"
+      "[[3.91619855]\n",
+      " [3.20101684]]\n",
+      "[[3.85813693]\n",
+      " [3.24679418]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -2389,20 +2389,20 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.87533278]\n",
-      " [2.94854992]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31803769 4.15962297]\n",
+      "[[3.70224083]\n",
+      " [3.16389131]]\n",
+      "Eigenvalues of Hessian Matrix:[0.29022057 4.66510547]\n",
       "theta from own gd\n",
-      "[[3.87533278]\n",
-      " [2.94854992]]\n",
+      "[[3.70224083]\n",
+      " [3.16389131]]\n",
       "theta from own sdg\n",
-      "[[3.90803422]\n",
-      " [2.93820524]]\n"
+      "[[3.67541155]\n",
+      " [3.1532465 ]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "
    "
       ]
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png
index 6cba933bb..5d43021c4 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png
index 11eac25c0..02725ea3d 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png
index cc836188d..e6704c45f 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
index 4a84c43ea..29309e4fe 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41.ipynb
@@ -116,20 +116,20 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.83505053]\n",
-      " [3.09726322]]\n",
-      "Eigenvalues of Hessian Matrix:[0.27717261 4.34154132]\n",
+      "[[3.89481038]\n",
+      " [3.13155259]]\n",
+      "Eigenvalues of Hessian Matrix:[0.28194659 4.81122914]\n",
       "theta from own gd\n",
-      "[[3.83505053]\n",
-      " [3.09726322]]\n",
+      "[[3.89481038]\n",
+      " [3.13155259]]\n",
       "theta from own sdg\n",
-      "[[3.77589027]\n",
-      " [3.07286416]]\n"
+      "[[3.88291866]\n",
+      " [3.19123037]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -374,9 +374,9 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.81651921]\n",
-      " [3.10399758]]\n",
-      "Eigenvalues of Hessian Matrix:[0.30971881 4.52950417]\n"
+      "[[4.23636536]\n",
+      " [2.77184871]]\n",
+      "Eigenvalues of Hessian Matrix:[0.30125775 4.66878535]\n"
      ]
     },
     {
@@ -384,13 +384,13 @@
      "output_type": "stream",
      "text": [
       "theta from own gd\n",
-      "[[3.81651921]\n",
-      " [3.10399758]]\n"
+      "[[4.23636536]\n",
+      " [2.77184871]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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Gl156Ce3bt0e9evUQGxuLhx9+GGfPnpWvwERERORVZA+GioqK0LFjRyxatKjGuhs3bmDXrl34+9//jl27diE9PR1HjhzBqFGjZCgpEREReSONEELIXQgjjUaDVatWYfTo0Va32bFjB2699VacPHkSTZs2tWu/hYWFCAsLQ0FBARo0aOCi0hIREZE7SXX/9nPbnt2koKAAGo0GDRs2tLpNSUkJSkpKTM8LCwslKBkRERF5ItmbyRxRXFyMGTNm4IEHHqg1Qpw7dy7CwsJMj4SEBAlLSURERJ7EY4KhsrIy3H///aioqMBHH31U67YzZ85EQUGB6ZGbmytRKYmIiMjTeEQzWVlZGcaOHYucnBxs2LDBZrthYGAgAgMDJSodEREReTLFB0PGQOjo0aPIzMxE48aN5S4SEREReRHZg6Hr16/j2LFjpuc5OTnYs2cPwsPDERsbizFjxmDXrl1Ys2YN9Ho98vLyAADh4eEICAiQq9hERETkJWQfWp+VlYWBAwfWWP7II49g1qxZSExMtPi6zMxMDBgwwK734NB6IiIiz6OaofUDBgxAbfGYgtIgERERkRfymNFkRERERO7AYIiIiIhUjcEQERERqRqDISIiIlI1BkNERESkagyGiIiISNUYDBEREZGqyZ5niIiIiLyQXg9s3gycOwfExAB9+wK+vnKXyiIGQ0RERORa6enA888Dp09XLouPBxYuBFJT5SuXFWwmIyIiItdJTwfGjDEPhADgzBnD8vR0ecpVCwZDRERE5Bp6vaFGyNJUWsZlU6YYtlMQBkNERETkGps316wRqkoIIDfXsJ2CMBgiIiIi1zh3zrXbSYQdqImIiKTkQaOsHBYT49rtJMKaISIiIqmkpwPNmwMDBwIPPGD4t3lzRXYqdkrfvoZRYxqN5fUaDZCQYNhOQRgMERERScEDR1k5zNfXMHweqBkQGZ8vWKC4mjAGQ0RERO7moaOsnJKaCnzzDRAXZ748Pt6wXIF5hthniIiIyN0cGWU1YIBkxXKb1FRAq/WYvlEMhoiIiNzNQ0dZ1Ymvr8cEdmwmIyIicjcPHWWlFqwZIiIicjfjKKszZyz3G9JoDOsVNsrKIR6cMoA1Q0RERO7moaOs7ObhKQMYDBEREUnBA0dZ2eXrr4F77vHolAEaISzV13mXwsJChIWFoaCgAA0aNJC7OEREpGYe3JxUwzffAPffbz0lgLH5LyfHqWOU6v7NPkNERETuYi3w8ZBRVrVKTwfuvbf2bTwkZQCDISIiIndITzckWqzafBQfb+g75KlNYkbGJJL2UnjKAPYZIiIicjVvn3rDVhLJ6hSeMoDBEBERkSupYeoNR2p6FDgxa3UMhoiIiFzJkak3PJUjNT0ekDKAwRAREZErqWHqDWMSyeo5k6ry9QW++soj+kcxGCIiInIlNUy9UVsSSaMVK2yPNjPS64GsLGD5csO/EjchMhgiIiKqq6o3c72+9loTjcYj+tHYZC2JZEICsHKloaO4PRSQvZpD64mIiOrC0hD6xo0NfYM0GvOO1N4w9UZVqamAVut8EknjqLvqnc2No+4+/9z1ZbaAGaiJiIicZe1mbgyCGjcGLl2qXJ6QYAiEPKAfjdvp9YYaIGudzTUaFMbGIuzMGWagJiIiUiRbQ+g1GiA4GPjpJyA/3/On3nCWtSzc9oy6O3NGkiIyGCIiInKGPTfz06cNN/5x46Qrl5LUloW7pES+clXDDtRERETOUMMQ+rqwlYX76FF5ymUBgyEiIiJnqGEIvbPsycL92We2R91VH6nmJrIHQ5s2bcLIkSMRGxsLjUaD1atXm60XQmDWrFmIjY1FcHAwBgwYgP3798tTWCIiIiNbiQe9ZQi9M+xtQnzyScPz6p+h8fk//+me8lUjezBUVFSEjh07YtGiRRbXz5s3D++++y4WLVqEHTt2IDo6GoMHD8a1a9ckLikREVEVtSUelHMIvcwJDAHY3zTYqpXlXEXx8Yblo0a5vmwWyN6BetiwYRg2bJjFdUIILFiwAC+//DJS/xyG+J///AdRUVFIS0vDU089JWVRiYiIzBkTD1rqJCzHEPraOixLWRZHmhAHDLCYq6hCaLDz0x1uLaaRovIMaTQarFq1CqNHjwYAHD9+HC1btsSuXbvQuXNn03ZarRYNGzbEf/7zH4v7KSkpQUmVXuqFhYVISEhgniEiInIPa8PHpVRbziPAELRJFRAZcwidOWO535BGYwjScnLMPqfiq8XYsDAbuhU38e2R1jhXEQLA/XkCZa8Zqk1eXh4AICoqymx5VFQUTp48afV1c+fOxezZs91aNiIiIhNfX0MNh9SMQdiZM8CUKbXnPJoyxVADI0WQZmxCHDPGZhbuy39cwdq390O3xhc/nEnBdXQ3bVofp3Hd/aWVv8+QPTTV2mKFEDWWVTVz5kwUFBSYHrm5ue4uIhERkbSqzun10EPAxYvWtxUCyM01BE5SsTZ3WXw8zr/+CRZ80RgDG+1G5C2hePhffbDyTC9cRyjifM7hmeRNWPfGThzPDZSkqIquGYqOjgZgqCGKqdL+mJ+fX6O2qKrAwEAEBkrzARIREUnOWpOYLVLnPPpz7jKxcRNyvt6JzC3++ODoUPz+9ySzzdoHHYG221lon4xE14eSoPEx3PMLCwslKaaig6HExERER0dj/fr1pj5DpaWl2LhxI9566y2ZS0dERCSD2nL42CJhzqOSwhJkfZAN3fIbyDjYFmcqBprW+aIcfRtmQzugEKOeT0SLAa0BtJasbNXJHgxdv34dx44dMz3PycnBnj17EB4ejqZNm2LKlCl488030apVK7Rq1QpvvvkmQkJC8MADD8hYaiIiIpnYyuFjibHDsptzHl3JuYrv3t4P3bc+WHc6GdfQzbSuHq7jzrhsaEfoMfzFZIS37FzLnqQlezC0c+dODBxYGS1OnToVAPDII49g6dKl+Otf/4qbN29i4sSJuHLlCnr06IEff/wRoaGhchWZiIhIPo42dbk559HJX05D9+4f0GWGYtOV9ihHb9O6aJ/zGNX6MLT3B+P259sjqGEvl7+/KyhqaL27FBYWIizM/UPziIiI3C4ry9Bp2l4JCS7NeSQqBHYvPwTdp+eh+18Mfi9uY7Y+OfAoRnU5A+3jEej+SDv4+Dk/Vkuq+7fsNUNERETkAOM0ILXl8ImIAN57zzCSywU5j0qvl2Ljomzo0q4j48AtyNUnATB0gvaBHn3CsqHtfxWjnkvELXe0AtDK8EJjNmw58y/ZgcEQERGRJ7Enh88nn9S5JqjgVAG+f2c/dDrgu1PJKERX07oQFGFoTDa0w8sxfHoSItp0qrkDpWTDtgObyYiIqO6UkIFZbSwFG3VsEsv99Swy5h+F7uf6yLrcHmUIMK2L8snHyFaHoB0bhDumtEdweHDtZXNBNmyp7t8MhoiIyDp7ghxnawAYQNVdHT9DUSHw+9dHoPvkHDJ+jcKum+b5f9oG/AFt51xoH2uMHo8l29f/xzgVh7URb1am4rCEwZALMRgiInKCPUGOszUAHtSE4m3KbpRh04fZ0C27hoz9LXFSH29ap0EFbgvdB23fy9A+1wythyY6/gb2dvDOzLQ5hQk7UBMRkXysBTlnzhiWf/ONYZ4ra8n/apsPy559KyUg8pLaq8LThVg3fx90qwS+O5WMq6KLaV0wbmBIdDa0w0ox4sUkNEnqULc3s3fov9TZsGvBYIiIiMzVluG4apATFlZ78r+q82EZawDs3bc7JxS1N8Dx8NqrMzvPGfr/rA9B5qX2KMVtpnVNNBcw8pZD0N4bgEEvtEdIRA/XvbG9Wa4lzIZtC4MhIiIyZyvDsTHIycqyb39VawDs3XfVAMqV7A1wPKn26k+iQmDfqqPQfXwWum2R2HmjHYDKgKO1fw60nU5COyEcPR9Phm+Am7JR2zP0X4Js2I5gMEREROZc3XxRtQZAziYUewMcJdRe2am8uBybP8pGxrJC6LITkVNeOceXBhXoWX8/tH0uQTu5Kdre1QKAE32AHGXP0H83ZcN2FoMhIiIyZ2/zxYABwNKljtUAyNWE4kiAI3ftlQ3Xzl7DD/P3QbdKj7UnknFFVM7xFYSbGBSZDe2dJRj5YltEpbSXvHwADEHlN99YroVzYTZsV2EwRESkdtX70Nx2m33NHAMGOF4DIFcTiiMBjgI7AJ/bcx4Zbx+Gbn0wfr7QAaWonOOrseYSRrQ4CO09fhgypR3qHb5hKNtFPaC30B/KkU7hznQgN76mpMQQLANAfr5z7yUVoQIFBQUCgCgoKJC7KEREyrJypRDx8UIYwgHDIz5eiBdfFEKjMTyqrjMuW7my9n0kJJhvU/097d23q6Slmb+XtUdamhCZmfZtm5np+nL+qUJfIfatPirmDM4Ut9bLrvHWt/jniGldM8WmD/aI8pJyw4usfZe2vqvq2zizbV1eU8vrCr74QpL7N4MhIiK1MgYl1e+0xqDkxRftD3LKyw3BgTGYKC+3/d6OBFB15UiAU15uKJulz8b4+SQk2D5GB5XdLBMb398jpnbNFC39TtR42x71ssWbQzLFft1RUaGvMH+xre9y5Ur7tnFkf9U58xobrysAJLl/M+kiEZEa2Zsl+NgxYOtW9+TZkTKHj/F4bTXPGbMiGztbA5ab/1w0mqwovwg/zs+GbmU51hxPwiXR2LQuEMW4o0k2tENuYuT0NojpFFX7sdX2XcbFGY7jzBnr2xiPH3A8g7SzWadtvK4QQBjApItEROQG9vah2brVfZ2EfX2l64Ds6AgnN3YAPr/vAr59+xB06wLxU357FKOnaV245jKGJx6ANtUXQ6e1R/3o7rZ3aM93Wdt64zbGPlOA4x3Ine10but1EmEwRESkRgrsJOx2jgY4qamVo8vqWHt16Lvj0H1wCrotjbH9ejIEKjsHJ/qdgrZ9DrQPh6HP0ynwC+rj2M5d+R05sq+q2zp7Pink/GIwRESkRh6YJdglbAU4lprunKi90pfqse3/9kO35DIyfm+GI2UtALQwre8WcgDaXvnQPhOLlLtbQePT1PljcuV35Mi+qm7r7PmkkPOLfYaIiNTI0T40alDH6TduXLyB9e9mQ/dNKdYca4sLoolpXQBKcHvEXowadBOjprVCXDcXBgH2fJfGPkNnz9r+vgHHzw1nzycbr5Oqz5CP2/ZMRETKZexDA1T2mTFSaJZgtzJ2mK7ef8WYnTo93eLL8vdfwL8nbIY25ldENAFGz+2BJUf74pIIx3CswaKIWcgc8yEunLiB7y90xzPL+7k2EALs+y4XLgTef7/2bYzftzPnhrPnkz2vk4Jbx6opBIfWExFZIfUQdyUyDqW3Nty+2lD6w+uOi3l3ZYreob8LDfRmmzbzzRX/1+x1cTMs0vFcO3Vlz3fpyPftzLnh7Plk5XVS5RliMxkRUV1JOUTcHTy9/HWVlQUMHGhzs0+T3sN7f4zEodKWZsu7BB+Etud5aJ+OQQeffdCMvbdmk4+Lh+RbZc93KVUGakfPJwuvKywqkuT+zWCIiKgu6tjPhBRg+XLggQdsbjYOaViBcfBHKQaEZ0N7x3WMmtYKCT1iDRs4m2uHrJLq/s3RZEREzrJ3FnRSNjtHNCVFXsLy+7Zi2PRkhDXtWnMDe3PtZGUZgiG11sQpEIMhIiJnODILOm90inXs55PIeE+PhzRRiBD58EHN71MAQFw8Xj35TO3fpb05c8aOBS5frnzOmkTZcTQZEZEzHMm4qzZ6vaH2Y/lyw796vdwlMqkor8Cvi/fhb7dlITnoGFoNaoZpa+/A0+Ijw3rUHNGk0WigeX+h7aDW3pw5VQMhwOaINXI/1gwRETlDjRmc7aHAPlTFV4uxYWE2dCtu4tsjrXGuIsW0zg9l6N8oGwNvb4yLXf6FyI9fd376jb59Ddtby7VjDWsSZcdgiIjIGWrN4FwbBfWhuvzHFax9ez90a3yx7kx7FKFyjq9QFGJYwj5oRwoMm56MRold/lzTH3jpMedH1tU2/5kt1ubuIklwNBkRkTPkyOCs5CHwChhJdTzrFHQLjkOX1RBbClKgr/J7P87nHEYlHYV2XAgGTG6PwAaBbikDAMu1Y40bA5cu2X5tWhowbpxj76fk86KOOJqMiEjJHJ0Fva7c1fzkqhups7OW10FFeQV+++8h6D7Lh25nHPaVtAJQOcdX+6Aj0HY7C+2Tkej6UBI0Pm6opbP0+Vma/0yvBwYNsr0/R2sSFdgs6ZHcmtJRIZiBmojcRooMzitXGrIgW8qMrNE4/16Wyu5spuS0NOsZnKs+0tKcK+ufiguKxff/2CGebrdRxPqcNdu1L8rEgIa7xHujs8Txjafq9D52ceTzM2a5tvQ9Wshybff7u+O8UBCp7t9sJiMi7yZFE4I738NdzU/W+vc4mynZzizOyMx0uGboSs5VfPf2fui+9cG608koQj30xWbE4ByuIgwNYhtg5CgN7preDuEtGzm0b6c58/kZXwNYrkl05DNXQLOkFCS7f7s11FII1gwRqZQraz7kkplpX41LZqb9+3RwLi6H9umimo8TW3LFwtQscXuj34QfSk27uRsrxRnEyPud1uXzc1VNojvOCwWS6v7NPENE5J2cnIVccdwxhN8dOZKcnbXc+JYVArv+exCv9c9Cp+DDaN4nHs+n98eGK11QDn8kBx7FsjavYyXGIAbVjlXq77Qun19qKnDihKGGLC3N8G9OjuP9e5jawaXYgZqIvI83ZYd2xxB+d91IU1MNTT2WOvRayNVTer0UGxdlQ5d2HRkHbkGuPglAEgDAB3r0CcvG6H6XMLbfecRd2Q988AFgIUO05N9pXT8/X9+6dyJnageXYjBERN5HhpFNbmMrkZ+xb0jfvvbv0503Uksjqar0oSo4VWDo/6MDvs9NRiEq5/gKQRGGxmRDO7wcw6cnIWL/ceAvfwG+tWNIupTfqRICEXecFyrGYIiIvI83NSG4Ywi/u2+k1Wo+cn89C907R6HbUB9ZlzugHLeZ1kX55GNkq0PQjg3CHVPaIzi8p2FFejpwzz2Ov7cU36kSAhGpUzt4OfYZIiLvo4Rf7q5kbH6KizNfHh/vXFbnOvbvsUVUCOz58jBmD8xCl5CDaNozFpO/6Y+fLndFOfyRFPAHZvTMwrbP9uFsSQQ+O9QPI16/FcHhwYYdGJs5nSHFd+rmz89urj4vVIxD64nI+8iRHVoKrh7CbylhX0KC/XNxVVF2owybPsyGbtk1ZOxviZP6eNM6DSrQu0E2tH2vQPt8c7Qa3Lz2ndk7TL8qOb5TF35+dcIM1HWm+GCovLwcs2bNwn//+1/k5eUhJiYGjz76KF555RX4+NhXscVgiEiFXJnTxZvV4UZaeLoQ6+bvg26VwHenknFVNDStC8YNDInOhnZYKUa8mIQmSRH2l2n5cuCBB+zfXs7v1IsDESXgdBx/euutt/DJJ5/gP//5D5KTk7Fz505MmDABYWFheN7ZalQi8n4OjmxSLQdHNp3ecQ4Z848g46d62HCpA8qq9P9pormAkbccgvbeAAx6oT1CIno4VyZHm7rk/E5dMTKMZKf4mqERI0YgKioKixcvNi275557EBISgi+++MKufbBmiEjFlPzLXcll+5OoEMhOPwrdx2eh2x6J3260M1vf2j8H2k4noZ0Qjp6PJ8M3wAXlt5Vd2Sg8HPjqK0MworDPjVyDNUN/6tOnDz755BMcOXIErVu3xu+//44tW7ZgwYIFcheNiDyBUn+5K3iCzfLicmz+KBu6LwqRsS8ROeWtAbQGYOj/0yt0H7R9LkM7uSnaDGsBING1BTB2ULY1muyzz4A77nDte5MqKT4Yeumll1BQUIC2bdvC19cXer0ec+bMwbhx46y+pqSkBCUlJabnhYWFUhSViMg+1ua1MmZSttX3xQ01StfOXsMP8/dBt0qPtSeScUV0Nq0Lwk0MjtoL7Z2lGDG9LaJSOtTpveySmgqsXGnIM3SpWp6hxo2BTz+VPWgk76H4YOjLL7/EsmXLkJaWhuTkZOzZswdTpkxBbGwsHnnkEYuvmTt3LmbPni1xSYmI7GArOzYAPPkkEBZmufnHhTVK5/acR8bbh6FbH4yfL3RAKXqZ1kVoLmJEy4PQjgnA4BdSUC/Syf4/dWFM4JiVZXgAhs+EzWLkYorvM5SQkIAZM2Zg0qRJpmVvvPEGli1bhkOHDll8jaWaoYSEBPYZIiL5OTJsvHqQU8eZ5kWFwIFv/4Duw9PQbY3A/4pSzNbf4n8C2g4noH20EW77S4pr+v8Q1QH7DP3pxo0bNYbQ+/r6oqKiwuprAgMDERgY6O6iERE5zpEMyVWbzbRap+ZbKy8ux9bP9kP3nyvQ/Z6IP8pvAXCLaX2Pevug7X0R2knxSBrREhqf5k4fGpGnUnwwNHLkSMyZMwdNmzZFcnIydu/ejXfffRePPfaY3EUjInKcI8PGqwY5YWF2z7dW1K47fngnG7qV5Vibk4RLoqNps0AU444m2dAOuYmR09sgplOK9X0SqYTig6EPPvgAf//73zFx4kTk5+cjNjYWTz31FF599VW5i0bkfTxgqLfHszWvVXXGIMfYZ8aGedrNeLWwJ0rQ07QsXHMZwxMPQJvqi6HT2qN+dHcnC0/knRQfDIWGhmLBggUcSk/kbgoe6u1Vaptg0wW+K+yLEgShhd9JaDvkYNT4hujzdAr8gvq49H3oT/wB4RU4USsRVXbMrd4MY+yzkp4uT7m8lbUJNmszYABEXDwENBZXV0CDPE00htyhR3b6URwraYp3fxuAAVM6wS9I8b97PVN6uiE55MCBhulDBg40PFf69aLXG2oaly83/KvXy10i2Sl+NJkrMAM1US1sZftV4qSm3vJr3HhTGjsWuHzZ4iZCo8HN+pGYHLUCFcdysBiPAwB8UPmn2/A/DTQrOd+ay1k71+o4sk82HlYDLNn9Wzjg1KlTjmyuGAUFBQKAKCgokLsoRPYrLxciM1OItDTDv+Xl7nmfzEwhDH/Sa39kZrrn/R21cqUQ8fHmZYuPNyz3VCtXCqHRGB5VjksPCD004m6sNC1+CJ+Li75NzI8/IcHx45fq/PJk1s61r76qubzqQ6MxfCdK+0yN55ml8mo0iryGpLp/OxQMhYSEiFdeeUVcv37dXeVxCwZD5HGkvOGnpdkXDKWluf69HeWBf8ztdfrlj0RBkHmQcxIJ4m6sFM18c8VzHbPEz+/sEqVFpXUPZLwxoHS12s41e64XJf2AEMJwjnhgACfV/duhZrKtW7fihRdeQG5uLubMmYMJEya4q8LKpdhMRh5F6up3e5MAZmbKO8eXJzbn1aKivALbF++H7t+XoNvTFIdLW8AHevTFZsTgHBoEliC+VwJGPROPDmNaQ+Njua+Qwzy1eUdK9k4Ua0taGlDL1FGS8pTrvBqp7t9O9Rn6/PPP8fLLLyMiIgLvvfceBijog7OEwRB5DDlu+Mb3tDbUWylBhpx/zF3UR+nm5Zv46b1s6L4qwbdH2yJfNDGt80cpBjbeC+2gIoya1hrx3R3IR2QvLwso3caRLOG1UVJgsXy5oZO3LUoK4CDd/dup0WQPP/wwjhw5gpEjR2L48OG4++67cezYMVeXjUh9Nm+2O7GeyxiHegOVtQNGxucLFsh/c7Q3c7MjGZ7tUccRQxcPX8LSJ7bg7tjtiGhcgVFv3IrFR/oiXzRBGAowrtkvWPHcVlw4eRM/XOyGiSv6uycQAuQ5vzxRXc8hjQZISDAEzUphb7JPR5KCehGnx1sKITBkyBBcu3YN77//Pr7//ntMmjQJs2bNQmhoqCvLSOQanjACSa4bvnGot6VRJgsWKKPZRI4/5k7OLn/s55PQLciBblMj/FKYggpU5vhJ8D0Dbbtj0D4Uin4TUxBQv7frymuLXOeXp3HkHKqeK0pJPyCqspXs01grqKQATkqOdDD6+OOPxWOPPSbat28v/Pz8RGBgoOjevbuYPHmyWLx4sbj99ttFfHy82LFjhxu6NzmPHahJ0g6jdencKvfILiWPMDJ2ALXWgdXVHUAd6HCqL9OLbZ9lixk9M0W7wKM1Nu0UfFC81j9T7Eo7KCr0Fa4pnzPkPr88hb3n2tdf1zxHnBnZJxUroxaVPABBkaPJ4uPjxZgxY8Q777wjtmzZIoqLi2tsM2fOHJGcnOyyAroCgyGVk3IEUl2DLqlv+I6SO1iS8o+5nYHD2wkLRLRPntliP5SKOxr9Jt6/J0uc2JLrujLVldLPLyWx91yT+5pwlKW/UQoO4BQZDNkjLy9P+Pj4uHq3dcJgSMWkHE7qqqBLqb/elDIcW6o/5namHLgfaQIQIhQFYmzCL+K/E7eIKyeuurYsrqTU80uJPCxwsJsHBXCKHFpvZ7MbNm3ahP79+7tyt3XC0WQqJtUIJFeP0rGUJTYhQb7+O+4Yjl2XPlxS9P+y89xZ0Pw9tPtLX/SflILABoGuLYO7KO38UjJP6GvoxRQ9tN7TMBhSMamGk7oj6FLKH2F3DMdW8JQAFeUV+O2/h5Dx6TlM2voQInHebOoLIwENkBAPjacOQ1fK+UVUC6nu35y9j7ybVCOQ3DFKx9dXGTlKHBmObU95nRyh5U4lhSXIfD8buuU3kHGoFc5WtAPQDvvxIb7BGFRAYx4QaTSG6VKVNmLIEa48vxhYkYdjMETeTarhpN6cw+PMGfu3y8qq/Yao1xtqhCx9F0IYvo8pUwCt1u030ys5V/Hd2/uh+9YH604n4xq6mdbVxzXcGbcP2pFRKGq/FKFzX1ZuygG5KbiWj8hebCYj72esiQDMb8KunH7AU7I4Oyo9HXj6aeDCBdvbRkQAFy9WPrd0Q5R5SoATW04j470/oMsMxcYrHaCv8nswxicPo9ocgfb+YNw+pYN5/x/WfFjGqT3IzdhMRuQqUiQUNGZxHjPGc5Kw2WLtRmdN1UAIsNzsJXHSP1EhsCvtEHSfnoduRwz2FrcBEG9anxx4FNquZ6B9ogm6jU+Cj1+05R0ppclSSRRUy0dUV6wZIvWQ4te9t4zScdVEldVrxCSoGSq9XoqsD7KhS7uOjIOtcFofa1rnAz36hmVDO+AqRj2XiJa3N3PqPRRFrlorD534kzwLa4aIXE2KX/epqYZfwp7epGKr07RRWBhQUGB9ffXO1W7qw3X1ZAG+f2c/dDrg+9xkFKKraV09XMfQ2H3QDi/H8BfboXGrTg7tW9Hk7K/DqT3IizAYInI1b2hSsfcG9uCDwEcf2b8/FzYnntp2BhnvHoNuQ31kXe6ActxmWhflk49RrQ9Be18w7pjSHkENe9a+M0/sEyT3qDxvHjRAqsNgiJzjiTcPsp+9N7BWrRzfn5N9uESFwO9fH4Huk3PQ/RqF3TeTAMSZ1icF/AFtl1xoH4/ArY+2g49fP/vK5omjoZTQX4cTf5IXYZ8hcpwn3jzIMfaOjjt2DGjZ0rlRdHYE1GU3yrBxUTZ0y64h40BLnNIbOj/7QI/+yEK/4B1I6hiELq+NRKs7Wzp+nJ46Gkop/XWkGKlJqibZ/dutk30oBOcmcyEpJz0ledk7h5WL57oqyC0QK577RYxrtkWE4arZLoNRJP7ZcK64HtKk7nOkSTlvnavZOW+aSEtzf1m8df4uUgSPnZtMiVgz5CL2TMsQEQG89x4QF8emM29g7+i4Oo6iO73jHDLmH4Hup3rIvNQBZQgwrYvUXMDIVoegHRuIIbf8gcAJD7qmJkcptSvOUFrZ9XpDmbKyDM8HDDA8eP1THXFuMhdiMOQi9v4BNmLTmXewt3+YA/3IRIVA9teHsOetH3B4fxl+Ke2OzeiLChi2bxNwHNpOp6B9rDF6TGgH3wBf18+RJtW8de6gtCSfbDonN+HQelIeR4fIyjjXFLmQvaPjbGxXXlyOzR9lQ/dFIYr3HsbLFf/Aw6i8eZ7XRGFrp4loN+chtBnWAkAL8x24eo40Tx4NJUeST2vBrtyj2ohcwEfuApAHcfSmYPzjOGWK4Q8pqc61s9fwzbRtGN9iCyJDruH2aZ1xas8lfFTxNOJgHthEIR9375mFNjf3WN6Zq/PaGEdDGYOH6jQaQ1OfUkdDGUflxcWZL4+Pd30Akp5uqIkaONBQmzZwoOG5cVSgtVFtAK9/8ghsJiP72aqar40r+y5wWL+ind2Vh2/nH4FufTB+vtABpaic4ysS53HQtz0a6S/AYghSW/OOO/rJeMNoKHdfD7WNuLP374AS+12RR2AzGSlPbVXztrgqCy37JiiOqBDYrzsG3UdnkLEtAv8rSgFQOcfXLf4noO1wAtpHG+G2NhfhO6SWSV9ra+pyR14bKeatcxVrQY87k3zaymdkL2ahJoVjMESOsXbzsMUV/S7YN0ExyovL8cu/9kH3+VXo9ibieHkrAJUJGHvU2wdt74vQTopH0oiW0Pg0N6xYvty+N7B083RXPxlPmEJFrh8B9k7LYosS+10RVcFmMnKO8VfqmTOGPgHVZyw3ctWoFlePJCKHXc+7jh/f3QfdynKszUnCJdHYtC4QxRgUuRfaocUYOb0tojtEWt6JK5q6vGUyXHvJmRjS3hF31vC6pDpiMxkpW9Wq+eBgy/0ujM+feKLu7+fqkURkl7y9+fj2nUPQ/RCEn/I7oASVc3yFay5jROIBaO/xw5CpKagffavtHbqiqcsTanJcRe5pNxyp0ZFqVBuRG3A0GdWdtVEtRq+9ZqjVSU93/j04Q7YkRIXAwTV/4J93ZqFXaDZiO0bgL1/0w9r8W1GCILTwO4kXumQha8EenL/RAP/5ow9S5/VE/ej69r2BsakLqDmKy5GbpzEYHzfOu5P7OfIjwB3sHXH31VfSjGojchPWDJFrGH+tz5ljCH6qq2u/Hk/OCaNw+lI9tn66Dxn/uQLd781wtKwlgMp5vrrX2w9trwvQToxDsvYWaHya1e0NPanTstzk/hFgbz+t1FTDQw21deSV2GeIXMed/XqUlnHXw924eAM/zs+G7ptSrPkjCRdFhGldAEpwe8ReaAffxKjprRHbJbqWPdUBUyTYppRpN9TWT4sUg9NxuFCdP0z+0baPu/9we0NOGFdy8LzM338B3759CLp1AVh/vgOKEWxa10hzBcOb74f2bl8MnZaC0NhQKY7A+7j6b4WSfgTw7yDJgB2olYJ5bezn7ip9a80rERHAgw8C4eGGP9hq+ANt53l5+Pvj0H1wCrot4dh2LQUClR2Tm/vlQptyHNrxDdDn6RT4h/SR8gi8jzv+Vsgx7UZtZeHgBPJSrBkCHJ9zR601EbZIVaVv/L50OmDZMvNh/d4SqNb2K7yW81IAOPyX+ViyuzN0e5ricKn5/F5dQw5A2zMf2mdi0T61FTQ+VjrGkmPc/beCzVSkUmwmc6FaP0xrv+beew944QXmtXGElFX63hyo1lbDoNXW2i+rAhqcRjwSkYMK+MIfpRjYeC+0g4owalprxHdXUQdzqZp1pMqBxWYqUiHJ+vwKD3D69Gnx4IMPivDwcBEcHCw6duwodu7caffrCwoKBABRUFBgvmLlSiE0GiEMt9TKh6Vl1h6Zma49WE9n/Eyrf4bGZStX1v09ysuFiI+3/p1oNEIkJBi28zS1nZMajRCzZ9t1Xr4e9b5Y8dwv4urJq3IfkTxWrqx5jsTHu+b8qy4zk38riNzE6v3bxRSfZ+jKlSvo3bs3/P398f333+PAgQOYP38+GjZsWLcdc84d95BiJm25c6+4i41zUgjg5hvz7drV39+LwH0Lb0NY0zAXF9IDGGsNq58jxvQOdcl3ZYncw9+JqM4U34H6rbfeQkJCApYsWWJa1rx587rvmHPuuI+7MwR7683HxjmpgUBwWaF9+1LreSlHxmbmwCLyeIqvGcrIyEC3bt1w7733IjIyEp07d8Znn31W62tKSkpQWFho9qihrjdKY+ZVR2bIVhN3Zgj21puPnefkTf9QCNjICKzW89LeWsMPPjDMu5WVZQig6sLeLM1q/U6IPIDig6Hjx4/j448/RqtWrfDDDz/g6aefxnPPPYfPP//c6mvmzp2LsLAw0yMhIaHmRo7OuWPpOefckYeX3XwuHb2Mz/+yBa9OvmLX9sGvTDccOs/Lmuz9kfPCC4YJSAcOrPtUMa6aYoSI5OPWHkku4O/vL3r16mW2bPLkyaJnz55WX1NcXCwKCgpMj9zc3JodsIydcK11ljZ2wv3qq5odMRMS3NMR05uVlxs6kKalGf6ta+dmKTpqu9EfmSfFu9pM0T9st/BFmQCE8EG5OIV4oUctHfibNBGipMRyB2Gel/Z3ZnbHOcPvhMjlpOpArfg+QzExMWjXrp3ZsqSkJKxcudLqawIDAxEYGFj7jjnnjnTckYzOw+a3qiivwG//PQTdZ/nQ7YzDvpJWAJqa1ncIOgxt93Mo7fwiNB9MAVDtnDS6cAFo2dLw2Z04wfOy+nDz224znAPW0jtY4qq+RO7uK0dEbqP4PEMPPPAAcnNzsbnKyKAXXngBv/76K7Zu3WrXPhzOM8RkZq7j7nxACs69UlJYgg0L9iLjy5vIONQKZysqm2Z9UY5+DbOhHViIUVNaILFflaZcS+dkVZ6US8md34+1IHvcOOCddwzPHf3z5u45vojIIcwz9Kf//e9/ws/PT8yZM0ccPXpU/Pe//xUhISFi2bJldu/DZjWbq5twyMCb8wFZcfn4FfHF01vEmLitoj4KzQ63PgrFmLit4ount4hLxy7XvqOSEiEiIjz7s3Nnrh9b+ZhefLH2c8/aIy2t7mUjIpeRqplM8TVDALBmzRrMnDkTR48eRWJiIqZOnYonn3zS7tdz1nqZKGXGbTc7seU0dO/+AV1mA2y62h76KhkrYn3OYVTbo9COC8HA59ojsIGN5lsjT//s3FkjaG/G52PHgK1bDbVS588bOk3botTPk0ilOFFrFSNGjMCIESPkLgY5ykvzAYkKgV1ph6D79Dx0O2Kwt7gNgHjT+pTAo9B2OwPtk5Ho+mBb+Pg5McTfkz87d+f6sXf4/NatlYGNXg/Mn297qhgPGYFIRK7lEcEQeSgvygdUer0UWR9kQ5d2HRkHW+G0PglAEgDAB3r0DcuGdsBVjHouES1vbwWgVd3e0JM/O0cyhDtTC+NMoKik2d+JSHEYDJH7GPMBeeiv8asnC/D9O/uh0wHf5yajEF1N6+rhOobG7oN2eDmGv9gOjVt1cu2be/Jn5+5aLWcDRQ8bgUhE0mEwRO7j6l/jEowcO7XtDHTzj0G3IRQbr7RHOW4zrYv2OY+RrQ9De18w7pjSHkENe7r0vc14ck2Gu2u16hIocvg7EVngER2o64odqGshxdB0V6QvcEeuIhj6/+z58jB0/8qD7n/R2HOzrdn6doHHoO1yGtrHI9D9kXbw8ZM4absnpn4wdnC2Fazk5Dh/rhk7aAOWA0VPSDtARDZJdf9mMKRmbgowLKpL0OXikUllN8qwcVE2dMuuIeNAS5zSV3Z+9oEevRvsg7bfFYx6rjlaDW5u937dRsG5lKySIljxxECRiBzCYMiFGAxZ8PXXwNixNZcr7Ze1vcOobdQyFJ4uxPdv74NOJ/DdyRQUIMy0Lhg3MDRmL7R3lWP4tLZokhTh4oNQKSmCFU8MFInIbgyGXEiRwZCcf8S/+Qa4/37rs3W7ohnDVeqQb+f0jnPImH8Eup/qIfNSB5QhwLQuUnMBI1sdgnZsIAa90B7B4cGuLTcZMFghojpgniFvJmXzlKX3vvfe2rep69BnV3JgZJKoEMhOPwrdx2eh2x6J3260A1DZSbdNwHFoO52C9rHG6DGhHXwDZBiJpbbgwNdX/nOIiMgGBkNSs9b/5cwZw3J3Nk8Zk+HZSwkJ/ewccbTo7+cx/+HTOFHeGkBrAIAGFegVug/aPpehndwUbYa1ANDCfWU1shbwuCoIVltARUTkZmwmk5KL+r84zd4mJyMlTE1gY2RSBTQ4jXgkIgcV8EUQbmJw1F5o7yzFiOltEZXSRNry2po8tK6dwOWsVSQikhj7DLmQYoIhueebWr4ceOAB+7ZNSFBGnyEASE+HuGcMAAFNlcUVfz57DP+G5paW0I4JwOAXUlAvsp4sxbRa62eLvUGwO+f7IiJSIPYZ8kZyzzflSJI7mRP6iQqB/bpj0H10BrptbRCPb7AQzyMBlTUiBf4RyHt0BhYvGg/fAJmDttrm47LFnj5a7p7vi4hIxRgMSUnu+aZsZe4FDDfS5ctlqWEoLy7HL//aB93nV6Hbm4jj5ZVzfO1EEs7Xa4FJ7bLQvz8QO6wjGvXvh0ZKufHbmo/LHrUFwe6e74uISMUYDElJ7vmmapviwWjFispkeRK4nncdP767D7qV5ViT0w6XRSfTukAUY1DkXmiHFmPk9LaI7tAJQCcre5KZK2rzaguC5a5VJCLyYgyGpKSE+aasTVYpYebevL35yJh3CBnrg/BTfgeUoHKOr3DNZYxIPADtPX4YMjUF9aNvdXt5XKIutXn2BMFy1yoSEXkxdqCWgxKmEZBweLaoEDi45g/oPjwN3S8R+LUoxWx9C7+T0HbIgfbhhuj9VAr8gjwwRrc1H5eRtSDYVudnKeb7IiJSGI4mcyHFBUOA1+eK0ZfqsfXTfdAtvQLd3uY4VtbcbP2t9fZBe9tFaCfFo93IltD4aCzvyJPYmo9r+nRDfyxng2BOTkpEKsNgyIUUGQx5oRsXb+DH+dnQfVOKNX8k4aKonOMrACW4o8leaAffxMhprRHbJVrGkrqRrVq/ugbB7qxV9PIAnYg8D4MhF2Iw5D7n913AmncOQbcuAOvPd0AxKuf4aqS5guHN90N7ty+GTktBaGyojCWVkLuDCnfsn8kciUiBGAy5kMcFQwr/hX7ou+PIWHQKui3h2HYtBQI+pnXN/XKhTTkO7fgG6PN0CvxD/GUsKdmFyRyJSKEYDLmQRwVDCvyFri/VY/vi/dAtuQzdnmY4UpZotr5ryAFoe+ZD+0ws2qe28o7+P2oh9xQxRES1YAZqNZJzEtdqbl6+ifXz90L3dSnWHGuLfNHBtM4fpbi98V6MGlSEUdNaI757OwDtJCkXuRiTORIRMRhSDAVMt3Dh4EWsefsgdN8H4Me89riJHqZ1YSjA8Gb7oL1bgzunpaBBfDe3lIEkxmSOREQMhhRDpl/oR9efgG7hCeg2N8LWwhRUoDLxX1Pf09Am/wHtQ6HoN6k9/EN6u+x97aLwvlNegckciYgYDCmGRL/QK8or8L+lB6BbfBG6XQk4WNoSQHPT+s7BB6HtcR7ap2PQ8d7W0PjE1+n9nKbAvlNeSe4pYoiIFIDBkFK48Rd68dVi/LwgG7ovb+LbI22QV1GZAdoPZRgQvhfa269j1NRb0LRXEoAkh9/DpRTUd8rrKWGKGCIimXE0mVKUlgIhIYamIWt8fYEbN4CAAJu7u3T0Mta+fQC6tX744WwKilDftK4BCjAsYT+0WmDY9GQ0bBbmiiNwDY5ukocSpoghIqqGo8nUZuvW2gMhwLB+61arfYb+2HASuoU50G1siC0F7VGBPqZ18b5nMSrpKLQP1MeAye0RUP82FxbehTi6SR6pqYbO+eyjRUQqxGBIKeztC3TmDJCVBZw7h4rIKOw8EQHdvy9D91sc9pe0AtDMtGnHoMMY1f0ctH+JQpcH2kLjE+uWorsURzfJx9eXASYRqRKDIaWwsy+QeH4KNJcuAgB8AMQgHgexEPsxAL4oR/9Ge6EdeA2jXmiJ5n3aAGjjvjK7A0c3ERGRxNhnSCmMfWWsjOoRVf71qbK8AhpoILB56By0/3giGiU2dH9Z3cnG58A+Q0RE6iHV/dvH9iYkCeOoHqByFM+fKmB4Xj0QAgAfCGg0GvQ78AkaNfWCiVBr+Rw4uomIiNyBwZBCiAqBndfbYnmbWcgTUWbrLiACGtTyZVXtVOwNUlMNw+fj4syXx8dzWD0REbkc+wzJqPR6KTIX7oVu+Q1kHGyFMxXtALwKH7yM/sjCgOD/IalLMPr11wBvTrG9Q2/qVMzRTUREJBEGQxK7erIA383bB923Gnyfm4JrqJzjqx6u4864bGhH6HHXtM5o3OoOw4qsLOBNO3Ze107FSpv+gqObiIhIAgyGJHBq2xno5h+DbkMoNl5pj3JUzvEV7XMeo1ofhvb+YNz+fHsENexVcwdSTJnA6S+IiEilGAy5gagQ2PPlYej+lQfd/6Kx52ZbAJX9X9oFHoO2y2loH49A90fawccvyvrOAPdPmcDpL4iISMU4tN5Fym6UYeOibOiWXUPGgZY4pa+c4NQHevRusA/aflegnZKIW+5oVsueauGOKRM4/QURESkUp+OwYu7cufjb3/6G559/HgsWLJC1LAWnCrBu/n7odALfnUxBAbqY1oWgCENisqG9qxzDp7VFk6SOdX9DV3cq1uuBDz7g9BdERKRqHhUM7dixA59++ik6dOggWxlyfz2LjPlHofu5PrIut0cZKuf4itRcwMhWh6AdG4hBL7RHcHhP1xfAVZ2KLdUy1cabRqoRERFV4THB0PXr1/Hggw/is88+wxtvvCHZ+4oKgb3fHIHuk3PQbY/CrptJACrn+GoTcBzaTqegfawxekxoB9+AOnRiloq1PkK14fQXRETkpTwmGJo0aRKGDx+OQYMG2QyGSkpKUFJSYnpeWFjo0HuV3SjD5o/3QfdFITL2t8CJ8so5vjSowG2h+6Dtexmjnm2KNsNaAGjh6OHIR6831AjZGwi5YqQaERGRgnlEMLRixQrs2rULO3bssGv7uXPnYvbs2Q69x7Wz17DunX3QrarA2pPJuCo6m9YF4wYGR2dDe2cpRkxvi8hk+Zrp6mzzZvubxtw1/YXS8hkREZGqKT4Yys3NxfPPP48ff/wRQUFBdr1m5syZmDp1qul5YWEhEhISamx3dlceMt45At36YGy42AGlqMzxE6G5iJG3HIR2TAAGT22PkIgedT8YJXCk7098fN1GqlnCfEZERKQwih9av3r1atx9993wrVJzoNfrodFo4OPjg5KSErN1lhiH5l29chW5mfnQfXQGum1NsKMo2Wy7Vv450HY8Ce2EcPR6Ihm+AV5YW5GVBQwcaHu7994DJk92bY2Ntb5Kxhoo5jMiIqIqpBpar/hg6Nq1azh58qTZsgkTJqBt27Z46aWXkJKSYnMfxg+zuW82Tugrt9egAj3q74e29yVon01A27taQOOjqWVPXsCYV8hWNmtX5xViPiMiInIQ8wz9KTQ0tEbAU69ePTRu3NiuQKiqE/qmCEQxBkfuxaihxRg5vS2iO7R3ZXGVz93ZrK2x1VeJ+YyIiEgmPnIXQErLnt+BS+f1+Pb8rXjy836I7hApd5HkkZpqaJKKizNfHh/vvqYqe/sqMZ8RERFJTPHNZK4gVTWbiaeMlpKynPb2VcrMZM0QEREBYDOZ5/Kk0VKuymZtj759DZ+Drb5KzGdEREQSU1UzmdsZR0tV7xtjnP09PV2ecimBsa8SUNk3yaiufZX0ekPN0/Llhn/1+joUlIiI1IbBkKvUltnZuGzKFHXfqN3RVyk93TBKbeBA4IEHDP82b67uwJOIiBzCPkOuwj4x9rOnr5I92zBvERGRV2OfIU/D0VL2s9VXyZ5+V7Zq4jQaQ02cVqvMzutERKQYbCZzFXtndefs77Wzt9+VI3mLiIiIasFgyFWMo6Wqdw420miAhASOlqqNI/2uWBNHREQuwmDIVdw5WsrI20dNOVLbw5o4IiJyEQZDruTOzM5qGDXlSG0Pa+KIiMhFGAy5WmoqcOKEYdRYWprh35ycugdCashf5EhtjxQ1cUREpAocWi83W0PI1TTbu/FYbWWprnqslkaeJSQYAiEOqyci8mhS3b9ZMyQne5q+1DRqypnaHnfUxBERkaowGJKLvU1fahs15Uy/K2PeonHjDP96eg0ZERFJikkXpWRsEjtzBnjhBfsSBqpx1FRqquHYbWWgJiIicgEGQ1Kx1LfFmqpNX2qd7d1WlmoiIiIXYTOZFKw1idly7pw8o6a8PZ8RERFRFQyG3K22rMq2GJu+3Jm/qDo15DMiIiKqgkPr3c3e2eyrsjZc3p6Z3OuCs8ATEZGCcNZ6Kbg7uAAcH+VVW9OXO/vRcBZ4IiJSKfU2k0nVHOToKC93NH3ZQ035jIiIiKpQZzAk5fQWtubQAoAmTYBly+RNGKi2fEZERER/Ul8wZKs5CDA0B7lqBJWt0WAaDfDJJ8CDD8qbMFCN+YyIiIigxmBIjuYgKUeDOYuzwBMRkUqprwO1XM1B1rIqA4YRZ3JnWjbWYI0ZYwh8qtaccRZ4IiLyYuoLhuRsDqo+GsxSVur4eENQIkdtkbEGy1KZOAs8ERF5KfXlGapXzzBqzNb0FtVz/LiaknP6SJFygIiIyAap8gypLxhq0KAyEAEsNwe5OxDR6w0BmbW+S1IFZERERAomVTCkvg7UgPwdmpnTh4iISDHU12fIyFqHZilqYpjTh4iISDHUGwwB7p3eojbM6UNERKQY6mwmkxtz+hARESkGgyE52MpKDTCnDxERkUQYDMlF7k7cREREBEDtfYbkJmcnbiIiIgLAYEh+cnXiJiIiIgBsJiMiIiKVYzBEREREqsZgiIiIiFRN8cHQ3Llz0b17d4SGhiIyMhKjR4/G4cOH5S4WEREReQnFB0MbN27EpEmTsH37dqxfvx7l5eUYMmQIioqK5C4aEREReQGPm7X+woULiIyMxMaNG9GvXz+7XiPVrLdERETkOlLdvz1uaH1BQQEAIDw83Oo2JSUlKCkpMT0vLCx0e7mIiIjIMym+mawqIQSmTp2KPn36ICUlxep2c+fORVhYmOmRkJAgYSmJiIjIk3hUM9mkSZOwdu1abNmyBfHx8Va3s1QzlJCQwGYyIiIiD8JmsmomT56MjIwMbNq0qdZACAACAwMRGBgoUcmIiIjIkyk+GBJCYPLkyVi1ahWysrKQmJgod5GIiIjIiyg+GJo0aRLS0tKg0+kQGhqKvLw8AEBYWBiCg4NlLh0RERF5OsX3GdJoNBaXL1myBI8++qhd++DQeiIiIs/DPkN/UnisRkRERB7Oo4bWExEREbkagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlXzmGDoo48+QmJiIoKCgtC1a1ds3rxZ7iIRERGRF/CIYOjLL7/ElClT8PLLL2P37t3o27cvhg0bhlOnTsldNCIiIvJwGiGEkLsQtvTo0QNdunTBxx9/bFqWlJSE0aNHY+7cuTZfX1hYiLCwMBQUFKBBgwbuLCoRERG5iFT3b8XXDJWWluK3337DkCFDzJYPGTIEW7dulalURERE5C385C6ALRcvXoRer0dUVJTZ8qioKOTl5Vl8TUlJCUpKSkzPCwoKABgiTCIiIvIMxvu2uxuxFB8MGWk0GrPnQogay4zmzp2L2bNn11iekJDglrIRERGR+1y6dAlhYWFu27/ig6GIiAj4+vrWqAXKz8+vUVtkNHPmTEydOtX0/OrVq2jWrBlOnTrl1g9TaQoLC5GQkIDc3FxV9ZXicfO41YDHzeNWg4KCAjRt2hTh4eFufR/FB0MBAQHo2rUr1q9fj7vvvtu0fP369dBqtRZfExgYiMDAwBrLw8LCVHUSGTVo0IDHrSI8bnXhcauLWo/bx8e9XZwVHwwBwNSpUzF+/Hh069YNvXr1wqeffopTp07h6aeflrtoRERE5OE8Ihi67777cOnSJbz++us4d+4cUlJS8N1336FZs2ZyF42IiIg8nEcEQwAwceJETJw40anXBgYG4rXXXrPYdObNeNw8bjXgcfO41YDH7d7j9oiki0RERETuoviki0RERETuxGCIiIiIVI3BEBEREakagyEiIiJSNY8Mhj766CMkJiYiKCgIXbt2xebNm2vdfuPGjejatSuCgoLQokULfPLJJzW2WblyJdq1a4fAwEC0a9cOq1atclfxnebIcaenp2Pw4MFo0qQJGjRogF69euGHH34w22bp0qXQaDQ1HsXFxe4+FIc4ctxZWVkWj+nQoUNm23nb9/3oo49aPO7k5GTTNp7wfW/atAkjR45EbGwsNBoNVq9ebfM13nB9O3rc3nJ9O3rc3nJ9O3rc3nJ9z507F927d0doaCgiIyMxevRoHD582ObrpLjGPS4Y+vLLLzFlyhS8/PLL2L17N/r27Ythw4bh1KlTFrfPycnBXXfdhb59+2L37t3429/+hueeew4rV640bbNt2zbcd999GD9+PH7//XeMHz8eY8eOxa+//irVYdnk6HFv2rQJgwcPxnfffYfffvsNAwcOxMiRI7F7926z7Ro0aIBz586ZPYKCgqQ4JLs4etxGhw8fNjumVq1amdZ54/e9cOFCs+PNzc1FeHg47r33XrPtlP59FxUVoWPHjli0aJFd23vL9e3ocXvL9e3ocRt5+vXt6HF7y/W9ceNGTJo0Cdu3b8f69etRXl6OIUOGoKioyOprJLvGhYe59dZbxdNPP222rG3btmLGjBkWt//rX/8q2rZta7bsqaeeEj179jQ9Hzt2rLjzzjvNthk6dKi4//77XVTqunP0uC1p166dmD17tun5kiVLRFhYmKuK6BaOHndmZqYAIK5cuWJ1n2r4vletWiU0Go04ceKEaZknfN9VARCrVq2qdRtvub6rsue4LfHE67sqe47bW67vqpz5vr3h+hZCiPz8fAFAbNy40eo2Ul3jHlUzVFpait9++w1DhgwxWz5kyBBs3brV4mu2bdtWY/uhQ4di586dKCsrq3Uba/uUmjPHXV1FRQWuXbtWY7K769evo1mzZoiPj8eIESNq/LKUU12Ou3PnzoiJicEdd9yBzMxMs3Vq+L4XL16MQYMG1cjSruTv2xnecH27gide33Xhyde3K3jL9V1QUAAAtU7CKtU17lHB0MWLF6HX62vMVh8VFVVjVnujvLw8i9uXl5fj4sWLtW5jbZ9Sc+a4q5s/fz6KioowduxY07K2bdti6dKlyMjIwPLlyxEUFITevXvj6NGjLi2/s5w57piYGHz66adYuXIl0tPT0aZNG9xxxx3YtGmTaRtv/77PnTuH77//Hk888YTZcqV/387whuvbFTzx+naGN1zfdeUt17cQAlOnTkWfPn2QkpJidTuprnGPmY6jKo1GY/ZcCFFjma3tqy93dJ9ycLaMy5cvx6xZs6DT6RAZGWla3rNnT/Ts2dP0vHfv3ujSpQs++OADvP/++64reB05ctxt2rRBmzZtTM979eqF3NxcvPPOO+jXr59T+5SLs2VcunQpGjZsiNGjR5st95Tv21Hecn07y9Ovb0d40/XtLG+5vp999lns3bsXW7ZssbmtFNe4R9UMRUREwNfXt0a0l5+fXyMqNIqOjra4vZ+fHxo3blzrNtb2KTVnjtvoyy+/xOOPP46vvvoKgwYNqnVbHx8fdO/eXTG/JOpy3FX17NnT7Ji8+fsWQuDf//43xo8fj4CAgFq3Vdr37QxvuL7rwpOvb1fxtOu7Lrzl+p48eTIyMjKQmZmJ+Pj4WreV6hr3qGAoICAAXbt2xfr1682Wr1+/HrfddpvF1/Tq1avG9j/++CO6desGf3//Wrextk+pOXPcgOEX46OPPoq0tDQMHz7c5vsIIbBnzx7ExMTUucyu4OxxV7d7926zY/LW7xswjNY4duwYHn/8cZvvo7Tv2xnecH07y9Ovb1fxtOu7Ljz9+hZC4Nlnn0V6ejo2bNiAxMREm6+R7Bq3u6u1QqxYsUL4+/uLxYsXiwMHDogpU6aIevXqmXrVz5gxQ4wfP960/fHjx0VISIh44YUXxIEDB8TixYuFv7+/+Oabb0zb/PLLL8LX11f885//FAcPHhT//Oc/hZ+fn9i+fbvkx2eNo8edlpYm/Pz8xIcffijOnTtnely9etW0zaxZs8S6devEH3/8IXbv3i0mTJgg/Pz8xK+//ir58Vnj6HG/9957YtWqVeLIkSNi3759YsaMGQKAWLlypWkbb/y+jR566CHRo0cPi/v0hO/72rVrYvfu3WL37t0CgHj33XfF7t27xcmTJ4UQ3nt9O3rc3nJ9O3rc3nJ9O3rcRp5+fT/zzDMiLCxMZGVlmZ23N27cMG0j1zXuccGQEEJ8+OGHolmzZiIgIEB06dLFbFjeI488Ivr372+2fVZWlujcubMICAgQzZs3Fx9//HGNfX799deiTZs2wt/fX7Rt29bs4lIKR467f//+AkCNxyOPPGLaZsqUKaJp06YiICBANGnSRAwZMkRs3bpVwiOyjyPH/dZbb4mWLVuKoKAg0ahRI9GnTx+xdu3aGvv0tu9bCCGuXr0qgoODxaeffmpxf57wfRuHTls7b731+nb0uL3l+nb0uL3l+nbmPPeG69vSMQMQS5YsMW0j1zWu+bOARERERKrkUX2GiIiIiFyNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIiIiFSNwRARERGpGoMhIvJIy5cvR1BQEM6cOWNa9sQTT6BDhw4oKCiQsWRE5Gk4NxkReSQhBDp16oS+ffti0aJFmD17Nv7v//4P27dvR1xcnNzFIyIP4id3AYiInKHRaDBnzhyMGTMGsbGxWLhwITZv3sxAiIgcxpohIvJoXbp0wf79+/Hjjz+if//+cheHiDwQ+wwRkcf64YcfcOjQIej1ekRFRcldHCLyUKwZIiKPtGvXLgwYMAAffvghVqxYgZCQEHz99ddyF4uIPBD7DBGRxzlx4gSGDx+OGTNmYPz48WjXrh26d++O3377DV27dpW7eETkYVgzREQe5fLly+jduzf69euHf/3rX6blWq0WJSUlWLdunYylIyJPxGCIiIiIVI0dqImIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESq9v8x1BIQwAc54QAAAABJRU5ErkJggg==\n",
+      "image/png": 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u3DgkJSVBo9Fg3bp11n21tbV45plncMMNN6BFixZISkrC/fffj9OnTwevwURERBRSgh4MVVRUoFevXli8eHGTfZWVldi1axf++Mc/YteuXcjLy8PBgwfxy1/+MggtJSIiolCkEUKIYDfCQqPRYO3atZgwYYLDY3bs2IEBAwbg+PHj6Nixo1vnLSsrQ2xsLEpLSxETE+On1hIREZGUAvX5HSHZmSVSWloKjUaD1q1bOzymuroa1dXV1u/LysoC0DIiIiJSoqAPk3miqqoKc+bMwb333us0Qly4cCFiY2OtX6mpqQFsJRERESmJYoKh2tpa3HPPPaivr8cbb7zh9Ni5c+eitLTU+lVUVBSgVhIREZHSKGKYrLa2FnfddReOHj2KjRs3uhw31Gq10Gq1AWodERERKZnsgyFLIHTo0CHk5+cjPj4+2E0iIiKiEBL0YKi8vByHDx+2fn/06FHs3r0bcXFxSEpKwsSJE7Fr1y58+umnMJlMKC4uBgDExcUhKioqWM0mIiKiEBH0qfUFBQUYOXJkk+1TpkzBvHnzkJ6ebvdx+fn5GDFihFvPwan1REREyqOaqfUjRoyAs3hMRmWQiIiIKAQpZjYZERERkRQYDBEREZGqMRgiIiIiVWMwRERERKrGYIiIiIhUjcEQERERqRqDISIiIlI1BkNERESkagyGiIiISNUYDBEREZGqMRgiIiIiVWMwRERERKrGYIiIiIhUjcEQERERqRqDISIiIlI1BkNERESkagyGiIiISNUigt0AIiIikgmTCdiyBThzBkhMBLKzgfDwYLdKcgyGiIiICMjLA554Ajh58tq2lBTgtdeAnJzgtSsAOExGRESkdnl5wMSJtoEQAJw6Zd6elxecdgUIgyEiIiI1M5nMPUJCNN1n2TZrlvm4EMVgiIiISM22bGnaI9SQEEBRkfm4EMVgiIiISM3OnPHvcQrEYIiIiEjNEhP9e5wCMRgiIiJSs+xs86wxjcb+fo0GSE01HxeiGAwRERGpWXi4efo80DQgsnz/6qshXW+IwRAREZHa5eQAq1cDycm221NSzNsb1hkymYCCAmDFCvO/ITDLjEUXiYiIyBzwjB/vvAJ1iBZm1Ahhr7BAaCkrK0NsbCxKS0sRExMT7OYQEREpj6UwY+OwwTKU1rgHyQ8C9fnNYTIiIiJyLsQLMzIYIiIiIudCvDAjc4aIiIjUzJ2V6kO8MCODISIiUi53PsjJMXcTokO8MCOHyYiISJny8oC0NGDkSODee83/pqWF/ArrfuPJSvUhXpiRwRARESmPJx/k1JSnCdFSFmaUQd0iBkNERKQsIT6zKSC8SYj2pDCju2TSu8ecISIiUhZPPshHjAhYs2TLXl6VtwnR7hRmdJejukWW3r3Vq4FRozw/rxcYDBERkbKE+Mwmv3KUIP3ww+493l5CdHi470Gmq949jcbcu/f99749j5uCPky2efNmjBs3DklJSdBoNFi3bp3NfiEE5s2bh6SkJDRr1gwjRozAnj17gtNYIiIKvhCf2eQ3zvKq5s0D4uODlxDtbu/e119L8/yNBD0YqqioQK9evbB48WK7+xctWoSXX34Zixcvxo4dO9ChQweMHj0aV65cCXBLiYhIFuQ4s8nXJGB/JxG7k1dl+X8wVqp3t9euuFia528k6MHQbbfdhhdeeAE5dhKvhBB49dVX8eyzzyInJwc9evTAP//5T1RWViI3NzcIrSUioqDzZWaTFDOXfE0CliKJ2J2elwsXgPnzmyZEt21rDqTi4qRLQne3165DB2mev5GgB0POHD16FMXFxdDpdNZtWq0Ww4cPx9dOus6qq6tRVlZm80VERCHEm5lNUgQdvk7xl6pEgLs9L126AMeOAfn55hydtm2Bc+fMwaSUM7vc7d0bMsT/z22HrIOh4p+7xxISEmy2JyQkWPfZs3DhQsTGxlq/UlNTJW0nEZEqyKAejI2cnGsf5Lm55n+PHnUcCPk76PB1ir+UJQI8yasKDwcuXjT3tp0/b7tfqrpNUtYt8oKsgyELTaMXSgjRZFtDc+fORWlpqfWrqKhI6iYSEYU2mdSDacIys2nSJPO/jobGpAg6fF28VMrFT131vADmBGqTCaipCU7dJinqFnlJ1sFQh5/HChv3ApWUlDTpLWpIq9UiJibG5ouIiLyk9GrPUgUdvk7xl7JEQMOeF0cuXDDX8UlJCd6K9J707klI1sFQeno6OnTogPXr11u31dTUYNOmTRgSoHFEIiJVC4Vqz1IFHb5O8Ze6REBODvC737keajp3zr3zSVW3yZ3ePYkFPRgqLy/H7t27sXv3bgDmpOndu3fjxIkT0Gg0mDVrFv7yl79g7dq1+PHHHzF16lQ0b94c9957b3AbTkSkBlIO5QSKVEGHr1P8pS4RkJcHvPSS/wLVANdtqq+rx+6VBwLyXEGvQP3dd99h5MiR1u9nz54NAJgyZQqWL1+Op59+GlevXsX06dNx6dIlDBw4EEajEa1atQpWk4mI1CMUqj1bgo5Tp+z3cGk05v2eBh2WoaiJE83naHhud5KAfX28M8569Dzl7evjhdO7irH+zcMwrNdg/YkMnBcZkj8nAGiE8McrJW9lZWWIjY1FaWkp84eIiDxRUGBOlnYlP//aEg321sIKwtCHDUveE2A/6PAlYdfekhepqeZAxp1z+vp4e9x931zxx+vjRNXlKmxZugeG1Vdg3JOE/1V1tdnfAqdQgRTJP78ZDBERkWMmk3nWmKtelaNHzQGPo7WwXnst4EmxTUgRdFj4GgD6O4BcscI8689TbdvaTq/31+vzM1EvsPeTIzC8dxLGrS2x6UJ3VKGZdb8G9ejXYh90vc9Bf08bZE1MQdvEtgyG/IHBEBGRD9ztVXG0CrnEvQsekWOvlRQ87RmyBLWHD5vXA/Pj63Ph0EWsf30/jF+YYDxyPU7V2+YeJYWdgb7zYehvC8ct0zPQNiPeui9Qn98MhoiIyDVXvSqWHiRHydaNe5BIWq569Bryc7BaW1mLbe/uhXHlJRgK22NnZTeIBvO1onEVw+P3QD+sHLoHUpA1rjM0YfaTyBkM+RGDISIKuFDsgXB2Td7kFpG0HPXoNeaHobDDG47D+PYxGDZFI784E1dg+1l7Q/RB6Huchu6OVsie1h3RraPdOm+gPr+DPpuMiCjkyDlvxheWejD2hMKss1BjqfBs72fx4YfN65J5GaiXnihF/pv7Yfi4GsaDnfBTXScAnaz722rOQ9fxAHSjBUY/ej2SbuwKoKvD8wUbgyEiIn9ylDdjqdYsh7wZKbhbg+bsWXMPk9J7yZQiJwcYP97nXkpTjQk7/70fhg/OwfhdG2wr6w4TBlr3R6IGQ1vvgW5AKfT3J6D33RkIixjq76uRDIfJiIj8Rc15M57kqIRCL5kKnNxxBoYlh2HcGI4vT3bDRRFns79r5FHoup2AfkIzDJ+WiVZJ/q//x2EyIiKl8aRac6jlzTgrINhYqPeSKVTl+UpsemMPjOsqYdiTgn01nQFc6/GLRSluSdoH/cgajH6wI9I1x6/1NiU0D17D/YDBEBGRv6g9b8ZRjkpjQpgDplmzzEM4odZLphCiXuCH1Qdh/OcZGLbFYMul7qhBf+v+MJgwoOVe6PtegG5SPAZMyURE9CDzUPD9vwqpnDgGQ0RE/iL1wptKYMlRef114Le/dXxcKPeSyVjJnnNYv+QgjAYB47EuKK7PAHBtyYuO4Seh7/ITdL+IxC2PZaJN+g22JwjRnDgGQ0RE/uJqDSwgYGs8BVV4OJCQ4N6xodpLFiguSjjUlNdg61t7YPhPKYw/JKDwaiaAdtb9zVGBEe32Qp9dCf1DqeiqT4cmLMXxczla70zhvX0MhoiIXHG3ZpA7eTNXrwIffaTIv549wl4y6dkp4SBSUnB6yu+Rtz8Lhi3NUFCShQr0sXlYn2b7oOt5Fro7YzH04SxoY/o3PrN9gcyJs9xzR474dh43MRgiInLG05pBlryZ3/wGuHCh6f6LFxU9nOA2qVaKJzMHw1Xi5CkkLpiBfKzGZzD/fCWElUCXdhB6vQajpndFQo9MAJmeP2egcuLs3XMS49R6IiJHvF1rS81T7BuScqV4FaurqIYppROiLp+FvUUs6qHBeU17/OvWf2P01BT0nNjV4XIXHglElfFG91wZgFiAy3H4A4MhIvKYLwENl6a4RsqV4lXk2FcnYVz6Ewz5Uag+fR6fYpzrB/n758tVLSlfg3w791yggiEOkxER2eNLfoTap9g35KcKyGpTXlyOgjf2wrDuKoz7O+JgbToAc2LzPVjh3kn8/fPlLCfO0tv36qvev7eu7jkJMRgiIrLHl4CGycO2nK1ppiZOEvHr6+qxe+UBGN8/C8M3sdh6uTtqMcD60HDUYXDMHuj6XcIdN1YBL7nxfFL8fDlb78zX3r4g/nHAYIiIyB5fAhomD1NjdoYLTQmJ2HLDDLx9aATWn+iKc8I2sTk94gT0XY9BNzYKN8/IRGzHXj8/MBv48Lng/XxJ1dsXxD8OmDNERGSPr/kRTB4mi59/FoQQNgnP9T9/NxGrsRY5aIkruLnDXuiyq6B/JA2dR3Z0nPgcij9fdu65QOUMhUl2ZiIiJbPkRwDXPmAs3MmPsAwnJCfbbk9JUeYHFXlM1AvsyTuAK7+a1iQQAoAwmD/w34uahk2v7sLFimh8dGYgZvxnOK6/pZPzGWCh+PPV8J4LMPYMEdE17hYXVBNfZ0PxNVWVC4cu4svF+2H43ATjketxff0BFEDCmYWh9vOVl2dTo4uzyYgosDwtLqgWvuZHMHlY/nwIKGora7H9vb0wrrwEQ2E7fFeRCYEh1v23wOheG7xNHg6lny9Hdb0CgMEQEYXs4ot+E0ofOGTLiz8Cjmw8DuPbx2Eo0GJjcSauoJfN/h7aQ9D3OAX9xFa4KasDMN6NdqhlZqEjztY9CwAOkxGpHaslk1q5WWG87GQZ8t/YB8PH1TAe6IQjdZ1sDm+rOY/RHQ9AN0pAN/16JN3Y4dpOqQsVhgoHhUo5TEZEgRHIxReJ5MLFCuwCGpTdOw3jo9Kw9coNqMNA6+4I1GJo7B7oBlyG/v4E9LknA2ERQ+0/j9SFCl1RSk5RkAuQMhgiUjtWSyY1cvFHgAYCsdXngOoy1CESXSKPQtftBPTjm2HEo5loldTb/eeSslChM0rKAwzyMCGDISK1Y7VkUqHqg8egdeO4PwzZiGULOyP9pnQA6d4/obeJ+N727CgtD9BVoVKJMWeISGpy76ZmToPv5P4eq9nP7404dRo/HTZh3bdJ+GJ7a2guXoARetePD+Ziut727AQrD9DX+8BOIclA5QxBqEBpaakAIEpLS4PdFFKbNWuESEkRwnxrm79SUszb5WTNGiE0GvNXw7ZatsmtvXKilPfYV3V1QuTnC5Gba/63ri7YLXLp8ivvifIW7WzemxNIEbdjjbgDq0Qdwmzft8Y/+6mpwbtOyz1pr12u7sn8fMfX1fArP9+/7fXHfdDoPKVAQD6/GQwRScWXX2bBYO+XWWqq/NopJ0p7j72lkICv+kq1yH+lUMwZlC+ejHpNmKARpkbvjQkQ9Q2+nAZDwbq+urqmr7cngVpurnvBUG6uf9rr7/ugQeBd+umnAfn85jAZkRSUOl2dwz3uk9N7LOX75ub084C3C+blLg6tPwbD2ydg3NIM+SVZqEBLhMGEY0hDMk56t+ZUeDiwYgVw551+a6tHHEwzb8LREJ6vj/eExPdBoD6/mUBNJAWlTldncUH3yeU9lnLGkIvp59BogFmzzInBjT/oJGrX5eOl2LB4L4yf1sJw6DocN9kmNrfXnMPMhA+RWuzkvXHFZALatfP+8b7ydYanq2Rkf65qL5f7wEcMhoikwOnqoU8O77HUM4a8/aDzY7vqquqw41/7YFxxAYbv4vFNeRbqMdi6PwrVGNZmD/SDyqCbkoied3RB2Kq2wL0eXKc9wbw3fZ3hGcjaRnK4D/yAwRCRFDhdPfQF+z32pdfGXd580PmhXce3noTxHz/BsDESG05n4rK4wWZ/t6gj0GedhG5Ccwx/NAst2t9oewJ/vOaBujftDSX6o2cnULWNgn0f+AlzhoikwOnqoS/Y73Eg8kK8eQ4vHlNeXI5NS/fBsLYSxv2pOFBznc2hbTSXMCp5P3Q310E37Tp0HJzs/Nyu3htnAnlvrloFTJ8OnD9/bZtlKBFoMs3c2j7A/d41qfMAJb4PmDNEpGTBLsFP0gv2exyI4QlveijcfL5ja3biw78Cxm9i8dXl7qhFf+u+cNRhUKu90PW7CP2v2qLf5EyERw12crZGXL03lu+DeW8+/TTwf//XdPvJk9eGEv3RsyN1HmCw7wN/kXSumkxwaj0FDaerh75gvceBqiXjaQ0qN9s1HPk2m9IiTohHMjeJvKe3iUvHLvvW5oZtd/TeBPPeXLXK9WtkmTqvlPpOEr2egfr85jAZkdQ4XT30BeM9DuQwnb2ZYamp9nsofm6XOHUKGjvtqocGJ5GCG/ADhiccgP6mKuge7oTrb+kETZjGt3ba4+y9Cdb7lpgInDvn+thgVr/2hgSvZ6A+v2UfDNXV1WHevHn497//jeLiYiQmJmLq1Kn4wx/+gLAw9ypIMBgiopBkZ/kCAJ7nlbjDxQedqBfY9+kRGJedwpUN3+DZK3MAAGG41q56aKCBwN4HXkKXvz+OqJZR/mmbkribUwUAubnApEmSNkfumDP0sxdffBFLly7FP//5T3Tv3h3fffcdHnjgAcTGxuKJJ54IdvOIiIInkKuh28k9uXDoIja8sR+Gz0ww/tQZJ03XA7gewHAU4nosxmNIwrUcorBUc7u6y2mB0EDzJIdL5jOwQonsg6Ft27Zh/PjxGDNmDAAgLS0NK1aswHfffRfklhGR5DjE6Jq3q6F7obayFt8s3wfDioswFrbFjoosCAyx7o/GVdwUvwe6weXQ//oGJI49AWz9iu9fQ+4GOO3a+acoIrlF9sHQsGHDsHTpUhw8eBBdu3bF999/j6+++gqvvvpqsJtGRFKSsrJyqJFwxtBPBSdg+McxGDdFYeOZTJShp83+HtpD0PU4Bf0drZD9SBaaxfWzPYGScl4CwTJDz1kxSwBYsoSBYwDJPhh65plnUFpaim7duiE8PBwmkwkLFizAJCfjqNXV1aiurrZ+X1ZWFoimEpG/SF1ZmRwqO1mG/Df2wfhJFQz703CkrhOAjtb98ZoLGJ16APrR9Rg9rTOS+3UB0CVo7VWchlPRHaXsPvVU8NZFUynZB0MrV67EBx98gNzcXHTv3h27d+/GrFmzkJSUhClTpth9zMKFCzF//vwAt5SI/CIQlZXJylRjwq4VB2D8oASGb9tgW1kW6jDQuj8CtRgSuwf6AZehu689bry3G8Iihjg5I7nkKNerXTvgjTeuJcVTwMh+NllqairmzJmDGTNmWLe98MIL+OCDD7B//367j7HXM5SamsrZZERKEMgVt1Xq5I4zWP/mYRi+DMeXJzNwQcTb7L8+8hj03Y5DNy4aI2dkoVVSqyC11AtKyjNTUluDhLPJflZZWdlkCn14eDjq6+sdPkar1UKr1UrdNCLP8ZefayGy8KOcXL14FZvf3ANDXjmMe5Kxp7oLgGuJvDEoxS2J+6AbUQPdb9Jw3Yg0AGlBaq0PlJZnJnV1aHKb7IOhcePGYcGCBejYsSO6d++OwsJCvPzyy/j1r38d7KYReUZpv6iDJUQWfgwmUS/w49pDMCw7DeO2Vth8sTuqcS2xOQwm9G+xD7obz0M/KQ4DpmQisvmgILbYD5hnRj6Q/TDZlStX8Mc//hFr165FSUkJkpKSMGnSJDz33HOIinKvYBeLLlLQOfpFLUVxPKUL9gKoCnVu33msX3wARoOA8ej1OFPfwWZ/Svhp6DsfgX5MBG6Z0Q1xndsEqaUSsPzMOJqhxZ8ZxWIFaj9iMERBxV/UngtkZWWFqimvwdfv7IXxP5dh2J2AXVczbfY3QyVGtNsD/bBK6H6dgm6/uE6a5S7kgHlmIYs5Q0ShYssW5zVFhACKiszH8Re1WSArKyuEqBc4tP4YjO+cgGFzM+SXZKECvW2O6RV9APqeZ6CbGINhj3SHNqa//ZNJLdC5cVLlmYVKjl+oXIeEGAwRSY0Jwd4JYGVlubp8vBQbl+yD4ZMaGA+n41hdOoB06/72mnPQpR2ATgeMnt4VHXpmAMgIWnsBBCc3Too8s0BcRyCCFOYqusWjYbKioiKkpqZK2R5JcJiMgioUu/D5l6YkTDUm7PjXPhj+fR7GnXH45koWTA3+Zo1CNYa12QPdwDLopyai5x1dEBbh3oLVARGs3Dh/55kF4joCEaSEQK6iLHOGWrRogdmzZ2POnDlo0aKFZI3yNwZDFFShlhDMvzT96sS2UzAuOYgiw16cOq/FYVyPLchGPcw/C92ijkCXeRL625tj+KNZaNFepr97g50b5yjPzGLVKveKGQbiOgIRpAT7/fCTgH1+Cw9s3bpVDBgwQCQmJor33nvPk4cGVWlpqQAgSktLg90UUqs1a4TQaMxf5l+B5i/LtjVrgt1C91iuo+E1KPE6gqj8bLn49PlvxcxeBSIj6oi4HWvECaTYvJ7nwtqL9cP/LI59VRTs5rovP7/pz4W9r/x86dqwZo0QKSn2nzclxb2fT6mvo67OcRst91Jqqvk4X8jh/fCDQH1+e9S/OmTIEHzzzTf461//iueeew59+vRBQUGBJEEaUUixJAQnJ9tuT0lRRFc1ANfLZADmZTJMpoA2S+7q6+pRuGI/XrytADe3KUSbhEiMnd8ff/9+OLJqdmM1JiIZtn+9txXnMGrzc+h09lvPn9BkMg/Nrlhh/jdQ74cccuNycoCXX7a/z1JvKC/P+Tmkvg5PJlT4Qg7vh4J4Ndh8//334+DBgxg3bhzGjBmD22+/HYcPH/Z324hCS04OcOyYOTcoN9f879GjygiEgMD9Eg8BxT+U4P1pX+G+9K1IjLqAG+/thjlfjED+5T6oRRTSIoowrVs+Pmj5KDQQTX8Rextc5uWZh0ZGjgTuvdf8b1qa6wDAH+RQLNNkAmbPtr/P3ddU6usIVJAih/dDSbztUqqoqBBbtmwRs2bNEmFhYUKr1YrZs2eLsrIyf/Zc+QWHyYj8IDfXvW733NxgtzTgrl66Kr5ctFM81T9f9Ire3+QlaYErYlzCdvH6xAJx0HhU1Jvq/T+MEewhTMvwj702+HP4xxl/vKZSX0eghq/k8H74QaA+vz2aWr906VLs2LEDO3bswL59+xAeHo6ePXtixowZ6N27N/79738jKysLa9euRb9+/VyfkIiUg39pWol6gf3//QnGd47jdMFBFJdG4zjSbBKf+zbfC12vEujvbo3BD2YhquVA25P4s4fA1RCmRmPuERk/Xrpk2fBwcxL9xInm57NXLPPVV+Vfb0jq68jONg+Pu5pQkZ3t3fkt5PB+KIknkVNKSoqYOHGieOmll8RXX30lqqqqmhyzYMEC0b17d79Fa/7AniEiPwiRvzS9deHwRbFy1lbxYNfNIjX8pN3E5wvh7cTm2xaIkr3nXJ/Qnz0EckqWtZfEnJoamOR6f74OUl6HowkVlq9Vq3x/jobPFaz3ww8C9fnt9+U4zp49i6SkJJhklETJqfVEfqKiZTJqK2vxzfJ9MH54EYZdbbGjIsua3XM78rAaE6GBgM0CF568Dv4subBihTlHyJXcXGDSJNfH+SpYdaj8XcZCyuuwV6LCQonFHSUiyzpD7hBCYPPmzRg+fLg/T+sTBkNEfmTvl3hqqnyXyfDgg+CnghMwvnUMhoIobDyTiTLE2uzvrj2EW7ufwAuH74W2rMQ2ELLw5APXX8Glvwp71tQAb7wBHDkCdO4MTJ8OuLkgtmwoKWBftQq4666m2+XY1iCRZZ0hpeIwGZGf1dWZhxpyc83/ynVozN4QQYN6M2WnysRHv98upvcoENdHHm0yWhGvOS/u6bhVvPfAZnFyx2nzOaVIfPZ1GMMfQ5hPPSVEeLjt48LDzduVRglDQ4GqN6Rwih0mkyP2DBGpkIMqv+aBLYE/Nn8JL1bORB0irfsiUIshsXug638Z+snt0eeeDIRHNerdkWJIyh/DGL70iDz9NPB//+f43E89BSxa5Fl7gk3uQ0OhuEyPBBQ7TCZHqgmG5H7zk7oF8ufTxVIE9dDgJFKQjqO4LrIIuozj0P8yGiMezURMiovfEXL+ELM3hBkfD8ycCTz7rP3Xu6YGaN7cee2d8HCgslJ5Q2ZyJrc8L5kK1Oe3jFb4I58Es9gaKZ/UVYsD+PN59eJVfPubd5wWiAyDQEcUoeiV1ThUk4Yl/xuOXy4Y6DoQAq5NjdbYzRgyb09N9X1qtDcshT3nzwfi4szbLlwAnn/e8ev9xhuu32+TyXwc+Q9LVcgKg6FQYOkeb/zL393y86RuUgcqEv98inqB/605iL+NK4AufifaxGvwynvu/QWZlFDv+RNa6rcATQMiqeu3uBO0fvQRMG8ecPGi7XZHr/eRI+49t7vHkXvkHFSrkaQZSTIR0gnUTMIjX0hdtViin8+SvedE7mNbxZTOW0Ri2Jkmp50Ytkr6ujuBTtJ1kQwuhPDu9X7lFfdeq1dekea61CxUFnCWEBOo/Sikc4bknL9A8uYir8bjmiz2+Onns6a8Btve3QvDysswft8euyq72azo1QyVGNFuD3RDK6F/MAXd9J2guS7df/VmHAlUHpSDZPAmydHevN7MGQoupZWqCLBAfX57tBwHyRBXJlYWOSW5e7LwqreBtJc/n6Je4PCG4zC8dRzGLdHIP5uFcvS2OaZX9AHobjgD/Z0xGPpwFqJb97c9ZyCWIggPl/6PDE+W2vDm9Y6KMi9u6mw22ezZDISkkpNjfu/k8ntBpRgMKR2T8JTD3l+A/q4064lABNIe/HyWnijFhsX7YPy0BoZD6ThWlwYgzXpIO8056DodhF4vMGpaFyT2zgCQ4ficOTnmHhN7r7mS/ur2JGj19veBZdr8yy/b9hCFh5sDIaVNq1eaQATV5BSHyZTO3+XnSRruDnMEUiCGWF0MwQgAAmEY2eIbbK3oDVODv88iUYNhrfdAP6gUuvs7oNedXREW4WTOh6NeNzn1xnnDkynYd93l2++DUKhATSGFw2TkHq5MLH9yWFHcHndWz05ONrd/xQrvAomvv3aai6IBoEE9NBXlMCECGVE/QZ9ZBN2E5hg+LRMtO/Rx73lc9bop+a9uT3p7fP19EBVl/lkkUhtJ07NlIqRnk1koofy8mjRcrsLd2TqBWFG8MWezWQAh4uOdz15y4eqb77l17RuG/VEc+6rIt2vwZUaco+VF5LDsiDdLbfD3AYUIzibzo5AeJmtI6cMBocLZatTOBKvSrKOqxRcuND3WxbBefV09flhzCIblZ2D8JgZhl85jPfSu2+DtUJw/ZsQ56lWaNMncIyaHHC93l9po+DugfXvzvpIS/j4gxeJyHH6kmmCIgs9RbpA7gln+oPGH6JQp5uEzexoFGGd/PAfj4gNYbzCh/PhFaEUVziARW2AuFleEVCTijO8rvNvja96Tp+9XMHO8XE3BlluCPpEfMGeISGmc5QY5YwkIgllptuFsloICx4EQYJ299I8er2Pp8Vux+2o33I4teA1PIBXXPoivNGuHK0/OR2Kv16G5685rj218roce8r7dvsyI8+b9CmaOl7Mp2I6COkvV6WAEb0QKwuU4iPzF1RRoe+SY5O5mgFGwP+HnQCgPqzERKbC99lZV55G0YAY0YRrzh3Fysv0TOVs3yxVfSkt4834BtlPZA80StE6aZP7XMlvOWYI+YA7e/L3eHFEIYTBE5C/e1ONJSZHfX+1uBhi9ks4jd9pmrEp4HGEQTYfBGn4Qjx9/bQFRe7xdp8yX9Z18LUQql0KmntQhIiK7GAwR+Yu7vRSvvGJOls7PN+fKyCAQqquqw9Y3f8BzNxVgyJg2KEIK6u1n+UBAA5GaijknpmPS3fUIP3va8YkbfxC//bbj4wDPezB8WTTV10Kkvj7enUVX3cEq9EQ+Y84Qkb+4U7cnJQV4/HFZDIkd3VwEw9KjMBZEYcOZTJShp3XfE3gNqzERArANiTQa8/eWAMOTD2Kplv/wttK0q/fLEX/kePkz2ZlV6Il8xmCIyF9kXgDzyukryF+yF8ZPqmDc3xGHatMBpFr3x2kuYnTKfuhHmTD60cEIK3IjwPDkg9jXZGdnZSO8Wd/J2fvliD/eR38nO7sbhAczQZ9I7iStYiQTqii6SPIhk4J3plqT+O79vWLB6HxxU2yhiECNTZMiUCOyY3aLP9+SL75dvkfUVdspKOiq6KAnBQHz870rPmnv9fSw+KNTjt6vp57y//toeb0cXbu9AoruXoOj4pnuFp4kkiEWXfQj1hmigAtSAczTu4phfOMwjF9qsP5EBs6Ltjb7O0cch77bMejGRWPk9EzEpPjhfvCkIKCn62YFak23QK1rJuV6cK7qEBEpEIsu+hGDIQpVVy9exZZ/7IVxzRUYfkzGj9VdbPa3Qhlu7rAP+hHV0D3cCZ1v7iRNQ9z9IHY3cAL8U11abjxZdNWbauSsQk8hhkUXiagJUS+w56PDMC4/BcPWlth8oTuq0Ne6X4N69GuxD/o+56C7uw0G/ToLkc0HOj+pPz5A3c3Z8STZWaqE62CSOtm5YfFMInIbgyEimTt/4ALWLz4A4xcmGH+6HqfruwC41gOUHHYG+s6HoR8Tjlumd0N8l+7un9yfs5rc/SB2N3AKxSnjTHYmkiUGQ0QyU1Neg+3L9sHw4SUYdrfHrspuEBhi3d8MlRjedg/0wyqheyAZmWM7QxPmRU9CMJdwcCdwCsUp4zKfcUikVswZChSO5ZMDol7g8IbjML59HMYt0dhYnIVytLI5pmf0AehvOAPdxBgM+00WoltH+/akSsjH8SbhWimY7EzkFuYMNXDq1Ck888wz+Pzzz3H16lV07doV7777Lvr27ev6wXLA1aSpkdITpdi4ZB8Mn9TAeCgNR+vSAKRZ97fTnMPojgeh1wmMnt4Fib0zAGT4rwFKyMcJ5V4Ub+oiEZFkZB8MXbp0CUOHDsXIkSPx+eefo3379jhy5Ahat24d7Ka5h6tJEwBTjQnfvb8PxtzzMOyIw/YrWTBhkHV/JGowrPUe6AaWQjc5Ab3vzkBYxFDpGuRuns2aNeZ/g/VB7W11aSVgsjORbMh+mGzOnDnYunUrtviwyGDQhsmUMBRBkin65jSMbx6BYUMEvjzVDZdEG5v9XSOPQp95ArrxzTBiehZadmgZuMa5W+/GItg9mRxmJlIl1hn6WVZWFvR6PU6ePIlNmzYhOTkZ06dPx8MPP+zwMdXV1aiurrZ+X1ZWhtTU1MAHQ1IWWCPZqSipwOale2FYWwnj3hTsq+lss78NLuLxtitwU8ZZdL/7BnSYniPffJzG/F3kkIjIDcwZ+tlPP/2EN998E7Nnz8bvf/97fPvtt5g5cya0Wi3uv/9+u49ZuHAh5s+fH+CW2iG3qcH869qvRL3A96sOwvjPMzBuj8GWS91Rg/7W/WEwYWDLvdD3u4B7MgrR9dOXoTl1EjgPYCuARUHsbfF0XS4hzMfNmmXOdeHPDRGFENn3DEVFRaFfv374+uuvrdtmzpyJHTt2YNu2bXYfw54hO5jE7RdnfzyH9UsOwmAQWH+8K87Wt7fZ3zH8JPRdfoJ+bCRueSwLrTvFBm5JCW/Y+7lwhT2ZRBQg7Bn6WWJiIrKysmy2ZWZmYo0lsdMOrVYLrVYrddNck0uBtdWrgTvvbLqdSdwuVZdVY+vbe2FcVQrDDx2w+2o3AO2s+1ugHCPb74Uu+yp0D6aiqz4dmrCUaycwmczBhr33P1C9Lc56BBvOalqzBli82PX5lFTkkIjIDbIPhoYOHYoDBw7YbDt48CA6dZJojSV/ksPU4FWrHK9xxKGPJkS9wIEvjsL4bhEMW5qj4FwWKtHH5pg+zfZB3+ssdHfGYshDWdDGDDDvMJmAzZtsg45gT2F3p0ew4awmd4IhJRU5JCJyh+8L30vr22+/FREREWLBggXi0KFD4t///rdo3ry5+OCDD9w+R2lpqQAgSktLJWypE2vWCJGSIoT5o8/8lZpq3i718zZ8Tmdf+fnStkXGLv50Saya/bV4KGOT6Bhe1OSl6RBWLO6/bov44NGvxNkfS+yfxN57nJIixKxZ7r3+ubn+v7A1a4TQaJo+l0Zj/mr881dXZ26zvcdYHpeaaj6OiCgAAvX5LfucIQD49NNPMXfuXBw6dAjp6emYPXu209lkjamyArWraf2NebtKtgLVVdXh23/ugyH3Aoy74vFteRbqce290KIK2XF7oBt0BfoHknBDThdowjSOT+gsJ8jd28vfeTjelnXwZFV5IiKJcWq9H8kiGAo0T+vIhHhS7LGvTsLw5k8wFkRhw+lMlCLWZn+W9jB0Waegz2mBm6ZloXnb5u6d2J2gIyzMfJyj/VLUmvIleZ9LRRCRTDCBmnzjSZJramrIrZJdXlyO/CV7YfzoKgz7O+JQbTqAa4nNcZqLGJWyH/pbTBg9rTNSB14P4HrPn8idnCBLIBTIvDFfyjoodakIlo4gIi8xGFIyZ7/8PUlyVer6Tg3U19Wj8MMDML5/FoZvWuPr0izUYoB1fzjqMDhmD/T9L0H3q3bo+6tuCI8a4uSMbnI36Jg1yzzEFKglJXxd8V1pS0WwdAQR+YDDZErl6pe/OxWGw8OBDz+8liOiMKd3FWP9m4dhWK/B+hMZOC/a2uy/LuI49BnHoRunxc0zMhGT4uS997ZXwZPhKMvsskD0XITyiu+NybmOExH5hDlDfhRywZC7v/wdJcNa/Oc/9usPydTVi1fx1Vt7YVh9BcY9SfhfVVeb/a1Qhps77INueBX0v0lD55vdLL/gS6+CnIMONSRDc/0/opDGYMiPQioY8vSXv4KTYUW9wN5PjsDw3kkYt7bEpgvdUYVm1v0a1KNfi33Q9T4H/T1tMOjXWYhsHnntBO709vijV0HOQYeC33+3yKnKOxH5HYMhPwqpYMibX/4KSiw9f+ACvlxyAMYvTDAeuR6n6m1zWpLDzkDX+TD0t4XjlukZaJsRb/9E7vT2+LNXQc5Bh4Lef4+tWAHce6/r41RUOoIolHA2GdnnzSwhGSfD1lbWYtu7e2FceQmGwvbYWdkNAtcSm6NxFcPj90A/rBy6B1KQNa4zNGEukoMd9fY0Xn7En9Wh5TwDS8bvv898TRQnIgKDIeWR+y9/N3ohDm84DuPbx2DYFI2NxVkoRy+b/TdEH4S+x2no7miF7GndEd26n2fP72wtMACYNg0YO9b9wPLUKfeOC+WgQ67ksv4fESkagyGlkfMvfwdDUxV/+AvWH+sKw8fVMB7shJ/qOgG4ltzcVnMeuo4HoBstMPrR65F0Y1cAXZuc3i2uensA4Nw5IDkZePxx9875298CzZoFf7iLmpLD+n9EpHjMGVIiOSbsOhiaqoe5TROxGmthblMkajC09R7oBpRCf38Cet+dgbCIMP+0w90cEov4eODiRefLZsghEZqck3POFhF5jQnUfhS0YEjKxFU5/fI3mVCXlIrwkjOwt4JXPTQoRgf8tccH0N3eEiOmZ6Flh5bStMWTZUg0GiAuznUwZDmWU7TlLZQTxYlUisGQHwUlGApERdwg/vKvPF+JTW/sgXFdJS7+7yT+WXef6wcFYnqzO8UmG5s/H3j9deD8edfHcoo2EVHAcDaZkrk7m8lXAUzYFfUCP6w+COM/z8CwLQZbLnVHDfoDAO7BCvdO4sl6ad5qmEPiri5dzD1q97kR0AXiGoiIKKAYDPmbq9lMGo15narx42XfhV+y5xzWLzkIg0Fg/bEuKK7PAJBh3d8x/CT0XX7Cr264CKxy44SBmuGWk2MOOKdNMydLu+JJuzhFm4go5HCYzN8UXBG3uqwaX7+zF4b/lML4QwIKr2ba7G+OCoxsvwe6YVehfygVXfXp0IRp5LskRU2NedaYo+Gvhu0C5HkNREQqxmEypfKmKGKQiHqBg4ajMLxTBONXzVBQkoUK9LE5pk+zfdD1PAv9XbEY8lAWtDEDmp5IrtObo6KAf/zD+cy7hu2S4zUQEZHkGAz5m8yLIl46ehkbFu+D8b+1MBy6DidM1wG4zro/IawEurSD0Os1GDW9KxJ6ZALIdHg+K8vQlL2k8WBOb/akXXK9BiIikhSHyfxNZkNGdVV1+Paf+2BccQGGnfH4tjwLAJCNLUjEGZxHPDSt22D0kAropiSi58Su5qEvb8l1erMn7ZLrNRARqQyHyZRKBkNGx746CePSn2DIj8KG05koxQ3WfbcjD0swA4kovvaAlinAg68BOSN8f3K5LknhSbvkeg1ERCQJ9gxJJRBFEX/uwajadxSF26qwojADhgPpOFibbnNYG80ljE7Zh4c7b8QtBc9Bg0ZvOSssExGRDLHooh+FWgXq+rp6HPvdYrRd+gJiqq9NHS9CCp7Aa/gYv8TgmD3Q9bsE/X3t0PdX3cxPm5bmeN2uUJ0txSEvIiLF4jBZKPDjcMuZ3WdhXHIIxvUaRB0/iHcxC2jUw5OCk1iDO1C59F9o8chk2xMUFDhfwFQIoKjIHDiEyhBRIKqAExGR4jEYkqmqy1XYsnQPjGuuwPBjEv5X1RVAAsJgwjHcA0Cg8dKmGgDQaNBiwbPAQ/fa9oAoaMq/XwSqCjgRESkegyGpuTlMI+oF9n5yBMZlJ2H4qiU2XeiOKvS17tegHn2b78e064xI/dGLHh6ZT/n3qxCqAk5ERNJjMCQlF8M0Fw5dxJeL98PwuQnGI9fjVP31AK63HpoUdgb6zoehuzUco2ZkoG1GFrDie+BeN567cQ9Pdrb5uV1N+c/O9upSZWXLFvUNCRIRkdcYDEnFwTCNOHkKuOMOPKN9BS9Vz4TAEOu+aFzF8Pg90A0th/7XKcga1xmasEY9Nd728Mhgyn/AqG1IkIiIfNI47YT8wckwjQYCAho8Vv0yNBC4IfognuxbAOPCnbh4AfjifD/M/mgEuo+/3n7xQ0sPj8ZBYUSNxjyF314Pj6XCcnKy7faUlNDKoVHTkCAREfmMU+t91SgnqCy9F36YuwLDVsxw+dDz/1iDtr/xIgCx9DoB9nt4XAU2oT7dXGZVwImIyDucWq8EeXkQM5+A5tS1/JRSpOBbTMQwNx7etlW1d8/r6xpaoV5hWU1DgkRE5DP2DHnh5I4zOPDMu7g5/48QsB1rrIcG9qa925Wf71tQEuo9PL4KRBVwIiKSDCtQ+5GvL2bl+UpsXroXhrwKGPcmY391Oo4hDck46TjoCQ8H6us5TBNsDBiJiBSLw2RBJOoF/pd3CIZlp2Hc3gpbLnZHNfpZ94/EBqTCydRtwPwhDARumKbhh3779uZtJSUMAEJ9SJCIiHzGYOhnJXvOYf2SgzAaBIzHuqC4viuArtb9qeGnoL/+CPRjInFr6lHgt26cdNYsc26PN3k9nrA3HNQQl6AgIiJySLXBUE15Dba+tQfGVaUwfJ+AwquZANpZ9zdHBUa02wt9diV0D6Yi49Z0aMJ+npJe4Gbi8/jxwEsvSTtM42jZiYa4BAUREZFDqsoZ+m71bny94jIMW5qhoCQLFWhpc1zvZvuh71kM3Z2xGPpwFrQxWvsnDPTUbUd5L5Z2OKu2LFWbiIiIJMacIQn0m5gO4NqLmRBWAl3aQeh0Goye0RUJPboB6Ob6RIGcuu1sSY+4OPcCIYBLUBARETmgqmAoEtW4qc0u6AaVQT81ETfkdEFYRHvvTuZrrR93uFp5/YknPD8nl6AgIiKyoaphstOHTyOxs5+XYJBq6rarITCNBmjbFjh3zrPz+lrbiIiIKEACNUymuLXJFi5cCI1Gg1mzZnn82BbtWvi/QZap25Mmmf/1Vz6OOyuvnztnDogcrVPWkLM1y4iIiFRMUcHQjh078NZbb6Fnz57Bbor03B3Ouu8+87/OAiIuQUFEROSQYoKh8vJy/OpXv8Lbb7+NNm3aBLs50nN3RfU2beyvRN9QqK1KT0RE5EeKSaCeMWMGxowZg1GjRuGFF15wemx1dTWqq6/VAiorK5O6ef6XnW0OYlzNFnv7beDYMXNNI1agJiIi8pgigqEPP/wQu3btwo4dO9w6fuHChZg/f77ErZJYeDjw8MPA8887P+7kyWvT5ZkYTURE5DHZD5MVFRXhiSeewAcffIDo6Gi3HjN37lyUlpZav4qKiq7tNJmAggJgxQrzv5Y1xOSoSxf3juN0eSIiIq/Jvmdo586dKCkpQd++fa3bTCYTNm/ejMWLF6O6uhrhjYaAtFottFo71aM//hiYO9d+AUM55tO4mzfk7nFERETUhOzrDF25cgXHjx+32fbAAw+gW7dueOaZZ9CjRw+X57DWKUDD+tM/s8y0kmOCcaCX/SAiIpIRLsfxs1atWjUJeFq0aIH4+Hi3AiGXhDAHFbNmmZOQLUGFVMUUPRHIZT+IiIhUSvY5QwHRcN0uwLwMRloaMHIkcO+95n/T0szb7ZEyD8my7EfjqfOcLk9EROQXsh8m8wenw2QN5eYCWq399cAcDac5W0jVn4GKHHqqiIiIAihQw2QMhhr68ktg6lTn64E1zNFxtJCqnPOQiIiIFIJrkwWSZd0uwPV6YJbhNJPJ3CNkL5a0bJs1S95T94mIiEiFwVDjNbwaJiKXlLh3jjNn3FtItWEeEhEREcmSuoKh9993nojsSV0fdwsdsiAiERGRrMl+ar1f/fKXwKRJjhORLeuBuarrk53tfo8PCyISERHJmrqCIcAc+Dhaw8uTuj6eBE5EREQkW+oaJnPH+PHAvHlAmza22xvX9bEEToDzPCROfyciIpI1BkMNWYotPv88cPGieVtcHDB/vnk6feNp8iyISEREpHjqqjPkrE6BLzWDWBCRiIjI71h00Y9cvpiWBVHdLbZIREREkmPRxUBizSAiIiLVYjAEsGYQERGRijEYAjwrtkhEREQhhcEQcK1mUOMp8haWtctYM4iIiCjkMBgCWDOIiIhIxRgMWbBmEBERkSqpbzkOZ3JyzBWoWTOIiIhINRgMNeZs7TIiIiIKORwmIyIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNc4m8weTidPxiYiIFIrBkK/y8oAnnrBd9T4lxVzRmoUaiYiIZI/DZL7IywMmTrQNhADg1Cnz9ry84LSLiIiI3MZgyFsmk7lHSIim+yzbZs0yH0dERESyxWDIW1u2NO0RakgIoKjIfBwRERHJFoMhb50549/jiIiIKCgYDHkrMdG/xxEREVFQMBjyVna2edaYRmN/v0YDpKaajyMiIiLZYjDkrfBw8/R5oGlAZPn+1VdZb4iIiEjmGAz5IicHWL0aSE623Z6SYt7OOkNERESyx6KLvsrJAcaPZwVqIiIihWIw5A/h4cCIEcFuBREREXmBw2RERESkagyGiIiISNUYDBEREZGqyT4YWrhwIfr3749WrVqhffv2mDBhAg4cOBDsZhEREVGIkH0wtGnTJsyYMQPbt2/H+vXrUVdXB51Oh4qKimA3jYiIiEKARgh7y67L17lz59C+fXts2rQJN910k1uPKSsrQ2xsLEpLSxETEyNxC4mIiMgfAvX5rbip9aWlpQCAuLg4h8dUV1ejurra+n1ZWZnk7SIiIiJlkv0wWUNCCMyePRvDhg1Djx49HB63cOFCxMbGWr9SU1MD2EoiIiJSEkUNk82YMQOfffYZvvrqK6SkpDg8zl7PUGpqKofJiIiIFITDZI08/vjj+Pjjj7F582angRAAaLVaaLXaALWMiIiIlEz2wZAQAo8//jjWrl2LgoICpKenB7tJREREFEJkHwzNmDEDubm5+Oijj9CqVSsUFxcDAGJjY9GsWbMgt46IiIiUTvY5QxqNxu72ZcuWYerUqW6dg1PriYiIlIc5Qz+TeaxGRERECqeoqfVERERE/sZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RQTDL3xxhtIT09HdHQ0+vbtiy1btgS7SURERBQCFBEMrVy5ErNmzcKzzz6LwsJCZGdn47bbbsOJEyeC3TQiIiJSOI0QQgS7Ea4MHDgQN954I958803rtszMTEyYMAELFy50+fiysjLExsaitLQUMTExUjaViIiI/CRQn9+y7xmqqanBzp07odPpbLbrdDp8/fXXQWoVERERhYqIYDfAlfPnz8NkMiEhIcFme0JCAoqLi+0+prq6GtXV1dbvS0tLAZgjTCIiIlIGy+e21INYsg+GLDQajc33Qogm2ywWLlyI+fPnN9mempoqSduIiIhIOhcuXEBsbKxk55d9MNS2bVuEh4c36QUqKSlp0ltkMXfuXMyePdv6/eXLl9GpUyecOHFC0hdTbsrKypCamoqioiJV5UrxunndasDr5nWrQWlpKTp27Ii4uDhJn0f2wVBUVBT69u2L9evX4/bbb7duX79+PcaPH2/3MVqtFlqttsn22NhYVf0QWcTExPC6VYTXrS68bnVR63WHhUmb4iz7YAgAZs+ejcmTJ6Nfv34YPHgw3nrrLZw4cQLTpk0LdtOIiIhI4RQRDN199924cOEC/vSnP+HMmTPo0aMH/vvf/6JTp07BbhoREREpnCKCIQCYPn06pk+f7tVjtVotnn/+ebtDZ6GM183rVgNeN69bDXjd0l63IoouEhEREUlF9kUXiYiIiKTEYIiIiIhUjcEQERERqRqDISIiIlI1RQZDb7zxBtLT0xEdHY2+fftiy5YtTo/ftGkT+vbti+joaFx33XVYunRpk2PWrFmDrKwsaLVaZGVlYe3atVI132ueXHdeXh5Gjx6Ndu3aISYmBoMHD4bBYLA5Zvny5dBoNE2+qqqqpL4Uj3hy3QUFBXavaf/+/TbHhdr7PXXqVLvX3b17d+sxSni/N2/ejHHjxiEpKQkajQbr1q1z+ZhQuL89ve5Qub89ve5Qub89ve5Qub8XLlyI/v37o1WrVmjfvj0mTJiAAwcOuHxcIO5xxQVDK1euxKxZs/Dss8+isLAQ2dnZuO2223DixAm7xx89ehS/+MUvkJ2djcLCQvz+97/HzJkzsWbNGusx27Ztw913343Jkyfj+++/x+TJk3HXXXfhm2++CdRlueTpdW/evBmjR4/Gf//7X+zcuRMjR47EuHHjUFhYaHNcTEwMzpw5Y/MVHR0diEtyi6fXbXHgwAGba+rSpYt1Xyi+36+99prN9RYVFSEuLg533nmnzXFyf78rKirQq1cvLF682K3jQ+X+9vS6Q+X+9vS6LZR+f3t63aFyf2/atAkzZszA9u3bsX79etTV1UGn06GiosLhYwJ2jwuFGTBggJg2bZrNtm7duok5c+bYPf7pp58W3bp1s9n2yCOPiEGDBlm/v+uuu8Stt95qc4xerxf33HOPn1rtO0+v256srCwxf/586/fLli0TsbGx/mqiJDy97vz8fAFAXLp0yeE51fB+r127Vmg0GnHs2DHrNiW83w0BEGvXrnV6TKjc3w25c932KPH+bsid6w6V+7shb97vULi/hRCipKREABCbNm1yeEyg7nFF9QzV1NRg586d0Ol0Ntt1Oh2+/vpru4/Ztm1bk+P1ej2+++471NbWOj3G0TkDzZvrbqy+vh5XrlxpsthdeXk5OnXqhJSUFIwdO7bJX5bB5Mt19+nTB4mJibjllluQn59vs08N7/e7776LUaNGNanSLuf32xuhcH/7gxLvb18o+f72h1C5v0tLSwHA6SKsgbrHFRUMnT9/HiaTqclq9QkJCU1WtbcoLi62e3xdXR3Onz/v9BhH5ww0b667sb/97W+oqKjAXXfdZd3WrVs3LF++HB9//DFWrFiB6OhoDB06FIcOHfJr+73lzXUnJibirbfewpo1a5CXl4eMjAzccsst2Lx5s/WYUH+/z5w5g88//xwPPfSQzXa5v9/eCIX72x+UeH97IxTub1+Fyv0thMDs2bMxbNgw9OjRw+FxgbrHFbMcR0MajcbmeyFEk22ujm+83dNzBoO3bVyxYgXmzZuHjz76CO3bt7duHzRoEAYNGmT9fujQobjxxhvx+uuv4+9//7v/Gu4jT647IyMDGRkZ1u8HDx6MoqIivPTSS7jpppu8OmeweNvG5cuXo3Xr1pgwYYLNdqW8354KlfvbW0q/vz0RSve3t0Ll/n7sscfwww8/4KuvvnJ5bCDucUX1DLVt2xbh4eFNor2SkpImUaFFhw4d7B4fERGB+Ph4p8c4OmegeXPdFitXrsSDDz6I//znPxg1apTTY8PCwtC/f3/Z/CXhy3U3NGjQIJtrCuX3WwiB9957D5MnT0ZUVJTTY+X2fnsjFO5vXyj5/vYXpd3fvgiV+/vxxx/Hxx9/jPz8fKSkpDg9NlD3uKKCoaioKPTt2xfr16+32b5+/XoMGTLE7mMGDx7c5Hij0Yh+/fohMjLS6TGOzhlo3lw3YP6LcerUqcjNzcWYMWNcPo8QArt370ZiYqLPbfYHb6+7scLCQptrCtX3GzDP1jh8+DAefPBBl88jt/fbG6Fwf3tL6fe3vyjt/vaF0u9vIQQee+wx5OXlYePGjUhPT3f5mIDd426nWsvEhx9+KCIjI8W7774r9u7dK2bNmiVatGhhzaqfM2eOmDx5svX4n376STRv3lz89re/FXv37hXvvvuuiIyMFKtXr7Yes3XrVhEeHi7++te/in379om//vWvIiIiQmzfvj3g1+eIp9edm5srIiIixJIlS8SZM2esX5cvX7YeM2/ePPHFF1+II0eOiMLCQvHAAw+IiIgI8c033wT8+hzx9LpfeeUVsXbtWnHw4EHx448/ijlz5ggAYs2aNdZjQvH9trjvvvvEwIED7Z5TCe/3lStXRGFhoSgsLBQAxMsvvywKCwvF8ePHhRChe397et2hcn97et2hcn97et0WSr+/H330UREbGysKCgpsfm4rKyutxwTrHldcMCSEEEuWLBGdOnUSUVFR4sYbb7SZljdlyhQxfPhwm+MLCgpEnz59RFRUlEhLSxNvvvlmk3OuWrVKZGRkiMjISNGtWzebm0suPLnu4cOHCwBNvqZMmWI9ZtasWaJjx44iKipKtGvXTuh0OvH1118H8Irc48l1v/jii6Jz584iOjpatGnTRgwbNkx89tlnTc4Zau+3EEJcvnxZNGvWTLz11lt2z6eE99syddrRz22o3t+eXneo3N+eXneo3N/e/JyHwv1t75oBiGXLllmPCdY9rvm5gURERESqpKicISIiIiJ/YzBEREREqsZgiIiIiFSNwRARERGpGoMhIiIiUjUGQ0RERKRqDIaIiIhI1RgMERERkaoxGCIiIiJVYzBEREREqsZgiIgUacWKFYiOjsapU6es2x566CH07NkTpaWlQWwZESkN1yYjIkUSQqB3797Izs7G4sWLMX/+fLzzzjvYvn07kpOTg908IlKQiGA3gIjIGxqNBgsWLMDEiRORlJSE1157DVu2bGEgREQeY88QESnajTfeiD179sBoNGL48OHBbg4RKRBzhohIsQwGA/bv3w+TyYSEhIRgN4eIFIo9Q0SkSLt27cKIESOwZMkSfPjhh2jevDlWrVoV7GYRkQIxZ4iIFOfYsWMYM2YM5syZg8mTJyMrKwv9+/fHzp070bdv32A3j4gUhj1DRKQoFy9exNChQ3HTTTfhH//4h3X7+PHjUV1djS+++CKIrSMiJWIwRERERKrGBGoiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqjEYIiIiIlVjMERERESqxmCIiIiIVI3BEBEREakagyEiIiJSNQZDREREpGoMhoiIiEjVGAwRERGRqv0/Jx4UF4ulq+AAAAAASUVORK5CYII=\n",
       "text/plain": [
        "
    "
       ]
@@ -481,73 +481,73 @@
       "Own inversion\n",
       "[[4.]\n",
       " [3.]]\n",
-      "Eigenvalues of Hessian Matrix:[0.28641189 4.39287528]\n",
-      "0 [-15.65565751] [-18.44347438]\n",
-      "1 [-0.02618169] [0.02215597]\n",
-      "2 [-0.02447466] [0.02071142]\n",
-      "3 [-0.02287894] [0.01936105]\n",
-      "4 [-0.02138725] [0.01809873]\n",
-      "5 [-0.01999282] [0.01691871]\n",
-      "6 [-0.0186893] [0.01581562]\n",
-      "7 [-0.01747077] [0.01478446]\n",
-      "8 [-0.01633169] [0.01382052]\n",
-      "9 [-0.01526688] [0.01291943]\n",
-      "10 [-0.01427149] [0.0120771]\n",
-      "11 [-0.013341] [0.01128968]\n",
-      "12 [-0.01247118] [0.0105536]\n",
-      "13 [-0.01165807] [0.00986552]\n",
-      "14 [-0.01089797] [0.00922229]\n",
-      "15 [-0.01018743] [0.00862101]\n",
-      "16 [-0.00952322] [0.00805892]\n",
-      "17 [-0.00890232] [0.00753349]\n",
-      "18 [-0.00832189] [0.00704231]\n",
-      "19 [-0.00777931] [0.00658316]\n",
-      "20 [-0.00727211] [0.00615394]\n",
-      "21 [-0.00679797] [0.00575271]\n",
-      "22 [-0.00635475] [0.00537764]\n",
-      "23 [-0.00594042] [0.00502702]\n",
-      "24 [-0.00555311] [0.00469926]\n",
-      "25 [-0.00519105] [0.00439287]\n",
-      "26 [-0.0048526] [0.00410646]\n",
-      "27 [-0.00453622] [0.00383872]\n",
-      "28 [-0.00424046] [0.00358844]\n",
-      "29 [-0.00396398] [0.00335448]\n",
+      "Eigenvalues of Hessian Matrix:[0.35058127 4.29679459]\n",
+      "0 [-8.31895514] [-8.15055258]\n",
+      "1 [-0.75472506] [0.63957747]\n",
+      "2 [-0.69314603] [0.58739348]\n",
+      "3 [-0.63659131] [0.53946725]\n",
+      "4 [-0.58465096] [0.49545139]\n",
+      "5 [-0.5369485] [0.45502684]\n",
+      "6 [-0.49313815] [0.41790059]\n",
+      "7 [-0.45290234] [0.38380352]\n",
+      "8 [-0.41594943] [0.35248847]\n",
+      "9 [-0.38201155] [0.32372846]\n",
+      "10 [-0.35084272] [0.29731502]\n",
+      "11 [-0.32221699] [0.27305669]\n",
+      "12 [-0.29592687] [0.25077762]\n",
+      "13 [-0.2717818] [0.23031634]\n",
+      "14 [-0.24960675] [0.21152452]\n",
+      "15 [-0.229241] [0.19426595]\n",
+      "16 [-0.21053692] [0.17841553]\n",
+      "17 [-0.19335893] [0.16385836]\n",
+      "18 [-0.17758251] [0.15048894]\n",
+      "19 [-0.16309331] [0.13821034]\n",
+      "20 [-0.14978631] [0.12693357]\n",
+      "21 [-0.13756504] [0.11657689]\n",
+      "22 [-0.12634093] [0.10706523]\n",
+      "23 [-0.1160326] [0.09832963]\n",
+      "24 [-0.10656534] [0.09030678]\n",
+      "25 [-0.09787053] [0.08293853]\n",
+      "26 [-0.08988514] [0.07617146]\n",
+      "27 [-0.08255129] [0.06995653]\n",
+      "28 [-0.07581582] [0.06424868]\n",
+      "29 [-0.06962991] [0.05900655]\n",
       "theta from own gd\n",
-      "[[3.98706221]\n",
-      " [3.01094846]]\n",
-      "0 [-0.00370554] [0.00313577]\n",
-      "1 [-0.00346394] [0.00293132]\n",
-      "2 [-0.00316561] [0.00267887]\n",
-      "3 [-0.00286972] [0.00242847]\n",
-      "4 [-0.00259385] [0.00219502]\n",
-      "5 [-0.00234197] [0.00198187]\n",
-      "6 [-0.00211371] [0.00178871]\n",
-      "7 [-0.00190742] [0.00161414]\n",
-      "8 [-0.00172117] [0.00145652]\n",
-      "9 [-0.00155308] [0.00131428]\n",
-      "10 [-0.00140139] [0.00118591]\n",
-      "11 [-0.00126452] [0.00107008]\n",
-      "12 [-0.00114101] [0.00096557]\n",
-      "13 [-0.00102956] [0.00087126]\n",
-      "14 [-0.000929] [0.00078616]\n",
-      "15 [-0.00083826] [0.00070937]\n",
-      "16 [-0.00075639] [0.00064009]\n",
-      "17 [-0.00068251] [0.00057757]\n",
-      "18 [-0.00061585] [0.00052115]\n",
-      "19 [-0.0005557] [0.00047025]\n",
-      "20 [-0.00050142] [0.00042432]\n",
-      "21 [-0.00045244] [0.00038288]\n",
-      "22 [-0.00040825] [0.00034548]\n",
-      "23 [-0.00036838] [0.00031174]\n",
-      "24 [-0.0003324] [0.00028129]\n",
-      "25 [-0.00029993] [0.00025381]\n",
-      "26 [-0.00027064] [0.00022902]\n",
-      "27 [-0.0002442] [0.00020665]\n",
-      "28 [-0.00022035] [0.00018647]\n",
-      "29 [-0.00019883] [0.00016826]\n",
+      "[[3.81759234]\n",
+      " [3.15457792]]\n",
+      "0 [-0.06394871] [0.05419212]\n",
+      "1 [-0.05873105] [0.04977051]\n",
+      "2 [-0.0523738] [0.04438319]\n",
+      "3 [-0.04619338] [0.03914571]\n",
+      "4 [-0.04057027] [0.03438051]\n",
+      "5 [-0.03557316] [0.0301458]\n",
+      "6 [-0.03117156] [0.02641575]\n",
+      "7 [-0.02730775] [0.02314144]\n",
+      "8 [-0.02392053] [0.020271]\n",
+      "9 [-0.02095266] [0.01775594]\n",
+      "10 [-0.01835274] [0.01555268]\n",
+      "11 [-0.01607534] [0.01362274]\n",
+      "12 [-0.01408051] [0.01193226]\n",
+      "13 [-0.01233322] [0.01045155]\n",
+      "14 [-0.01080274] [0.00915458]\n",
+      "15 [-0.00946219] [0.00801855]\n",
+      "16 [-0.00828799] [0.0070235]\n",
+      "17 [-0.0072595] [0.00615193]\n",
+      "18 [-0.00635865] [0.00538851]\n",
+      "19 [-0.00556958] [0.00471983]\n",
+      "20 [-0.00487843] [0.00413413]\n",
+      "21 [-0.00427304] [0.00362111]\n",
+      "22 [-0.00374279] [0.00317175]\n",
+      "23 [-0.00327833] [0.00277816]\n",
+      "24 [-0.00287151] [0.00243341]\n",
+      "25 [-0.00251517] [0.00213144]\n",
+      "26 [-0.00220306] [0.00186694]\n",
+      "27 [-0.00192967] [0.00163526]\n",
+      "28 [-0.00169021] [0.00143234]\n",
+      "29 [-0.00148047] [0.00125459]\n",
       "theta from own gd wth momentum\n",
-      "[[3.9993736 ]\n",
-      " [3.00053008]]\n"
+      "[[3.99630114]\n",
+      " [3.00313452]]\n"
      ]
     }
    ],
@@ -631,17 +631,17 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.92351924]\n",
-      " [3.025027  ]]\n",
-      "Eigenvalues of Hessian Matrix:[0.33104875 3.95055425]\n",
-      "0 [-11.75315452] [-11.48461009]\n",
-      "1 [3.84783351e-15] [-1.7484672e-15]\n",
-      "2 [-4.8897518e-16] [-4.48356153e-16]\n",
-      "3 [4.61653285e-16] [3.79106945e-16]\n",
-      "4 [-4.8897518e-16] [-4.48356153e-16]\n",
+      "[[4.08185019]\n",
+      " [2.82781715]]\n",
+      "Eigenvalues of Hessian Matrix:[0.32244056 3.90871918]\n",
+      "0 [-14.19393543] [-14.29174301]\n",
+      "1 [-6.35255737e-15] [-1.10851799e-14]\n",
+      "2 [-5.89805982e-17] [-2.66490332e-16]\n",
+      "3 [9.81853487e-16] [1.10741066e-15]\n",
+      "4 [-5.89805982e-17] [-2.66490332e-16]\n",
       "beta from own Newton code\n",
-      "[[3.92351924]\n",
-      " [3.025027  ]]\n"
+      "[[4.08185019]\n",
+      " [2.82781715]]\n"
      ]
     }
    ],
@@ -711,9 +711,9 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.08928088]\n",
-      " [2.79578306]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31588332 4.45642521]\n"
+      "[[3.41716708]\n",
+      " [3.50046106]]\n",
+      "Eigenvalues of Hessian Matrix:[0.24252405 4.30774404]\n"
      ]
     },
     {
@@ -721,13 +721,13 @@
      "output_type": "stream",
      "text": [
       "theta from own gd\n",
-      "[[4.08928088]\n",
-      " [2.79578306]]\n"
+      "[[3.41716708]\n",
+      " [3.50046106]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -744,8 +744,8 @@
      "output_type": "stream",
      "text": [
       "theta from own sdg\n",
-      "[[4.10188623]\n",
-      " [2.87242312]]\n"
+      "[[3.38135654]\n",
+      " [3.49216685]]\n"
      ]
     }
    ],
@@ -849,15 +849,15 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.84094234]\n",
-      " [3.01300561]]\n",
-      "Eigenvalues of Hessian Matrix:[0.26776828 4.97262227]\n",
+      "[[4.12427537]\n",
+      " [2.85355539]]\n",
+      "Eigenvalues of Hessian Matrix:[0.33486875 3.91080327]\n",
       "theta from own gd\n",
-      "[[3.83774539]\n",
-      " [3.01544605]]\n",
+      "[[4.12417157]\n",
+      " [2.85365229]]\n",
       "theta from own sdg with momentum\n",
-      "[[3.8186717 ]\n",
-      " [3.06511966]]\n"
+      "[[4.25050227]\n",
+      " [2.8249367 ]]\n"
      ]
     }
    ],
@@ -981,9 +981,9 @@
      "output_type": "stream",
      "text": [
       "theta from own AdaGrad\n",
-      "[[2.00019432]\n",
-      " [2.99888222]\n",
-      " [4.00105497]]\n"
+      "[[1.99999773]\n",
+      " [3.0000164 ]\n",
+      " [3.99998703]]\n"
      ]
     }
    ],
@@ -1098,9 +1098,9 @@
      "output_type": "stream",
      "text": [
       "theta from own RMSprop\n",
-      "[[1.9996357 ]\n",
-      " [3.00788598]\n",
-      " [3.99589367]]\n"
+      "[[2.01023308]\n",
+      " [2.95235306]\n",
+      " [4.04597076]]\n"
      ]
     }
    ],
@@ -1211,9 +1211,9 @@
      "output_type": "stream",
      "text": [
       "theta from own ADAM\n",
-      "[[2.0001042 ]\n",
-      " [2.99949077]\n",
-      " [4.00048049]]\n"
+      "[[1.99998193]\n",
+      " [3.0000747 ]\n",
+      " [3.99992263]]\n"
      ]
     }
    ],
@@ -1353,7 +1353,7 @@
     {
      "data": {
       "text/plain": [
-       "[]"
+       "[]"
       ]
      },
      "execution_count": 11,
@@ -1442,7 +1442,7 @@
     {
      "data": {
       "text/plain": [
-       ""
+       ""
       ]
      },
      "execution_count": 12,
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_16_2.png b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_16_2.png
index e5435f4eb..87c78de51 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_22_2.png b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_22_2.png
index bcbc69131..811738404 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_5_1.png b/doc/LectureNotes/_build/jupyter_execute/exercisesweek41_5_1.png
index 8c31b59a8..9a45572de 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb
new file mode 100644
index 000000000..c2385ad8c
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb
@@ -0,0 +1,73 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "be117070",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "\n",
+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6f7356c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Exercises week 42\n",
+    "**October 9-13, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday October 22 at midnight**\n",
+    "\n",
+    "You can hand in the exercises from week 41 and week 42 as one exercise and get a total score of two additional points."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aa378ef2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Overarching aims of the exercises this week\n",
+    "\n",
+    "The aim of the exercises this week is to get started with implementing\n",
+    "gradient methods of relevance for project 2. The exercise this week is a simple\n",
+    "continuation from the  previous week with the addition of automatic differentation.\n",
+    "Everything you develop here will be used in project 2. \n",
+    "\n",
+    "In order to get started, we will now replace in our standard ordinary\n",
+    "least squares (OLS) and Ridge regression codes (from project 1) the\n",
+    "matrix inversion algorithm with our own gradient descent (GD) and SGD\n",
+    "codes.  You can use the Franke function or the terrain data from\n",
+    "project 1. **However, we recommend using a simpler function like**\n",
+    "$f(x)=a_0+a_1x+a_2x^2$ or higher-order one-dimensional polynomials.\n",
+    "You can obviously test your final codes against for example the Franke\n",
+    "function. Automatic differentiation will be discussed next week.\n",
+    "\n",
+    "You should include in your analysis of the GD and SGD codes the following elements\n",
+    "1. A plain gradient descent with a fixed learning rate (you will need to tune it) using automatic differentiation. Compare this with the analytical expression of the gradients you obtained last week. Feel free to use **Autograd** as Python package or **JAX**. You can use the examples form last week.\n",
+    "\n",
+    "2. Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate). Compare this with the analytical expression of the gradients you obtained last week.\n",
+    "\n",
+    "3. Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from week 39. Discuss the results as functions of the various parameters (size of batches, number of epochs etc)\n",
+    "\n",
+    "4. Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD using automatic differentiation..\n",
+    "\n",
+    "5. Add RMSprop and Adam to your library of methods for tuning the learning rate. Again using automatic differentiation.\n",
+    "\n",
+    "The lecture notes from weeks 39 and 40 contain more information and code examples. Feel free to use these examples.\n",
+    "\n",
+    "We recommend reading chapter 8 on optimization from the textbook of [Goodfellow, Bengio and Courville](https://www.deeplearningbook.org/). This chapter contains many useful insights and discussions on the optimization part of machine learning."
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.txt b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.txt
new file mode 100644
index 000000000..e69de29bb
diff --git a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
index cf3333aca..065efc24a 100644
--- a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
@@ -225,8 +225,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.31579721  1.74724767 -0.89609007  2.48464841 -0.36051635 -2.41246325\n",
-      "  0.28008933  0.45134965 -0.52204004 -0.48145226]\n"
+      "[-1.0526992  -0.18065292  0.78521833  0.80074264  0.59327016 -1.16492688\n",
+      "  0.85276246 -0.04581197 -0.65825344 -0.87931006]\n"
      ]
     }
    ],
@@ -662,26 +662,26 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[0.69873514 0.39457095 0.31927572 0.01704432 0.11837671 0.15047127\n",
-      "  0.56465688 0.50274255 0.69818111 0.82296251]\n",
-      " [0.45308692 0.37112277 0.77794957 0.43043913 0.95327702 0.89793609\n",
-      "  0.29401213 0.08245909 0.1520039  0.59511582]\n",
-      " [0.98004227 0.101058   0.57572321 0.61394448 0.963198   0.49616116\n",
-      "  0.83488328 0.05432856 0.12814914 0.03856554]\n",
-      " [0.283078   0.19166136 0.29275129 0.39300201 0.59004971 0.29199381\n",
-      "  0.40644745 0.9036573  0.44729805 0.34447052]\n",
-      " [0.57670824 0.6568551  0.84380376 0.86221134 0.28908491 0.25663096\n",
-      "  0.62862896 0.1937079  0.15673992 0.44921888]\n",
-      " [0.25139357 0.11197884 0.26514544 0.11896755 0.13404683 0.21059098\n",
-      "  0.86012593 0.67890723 0.97948913 0.30567713]\n",
-      " [0.51845286 0.76010633 0.71640333 0.75282841 0.47447472 0.78882958\n",
-      "  0.84159521 0.3729492  0.80152684 0.04084872]\n",
-      " [0.38088413 0.63567272 0.82909728 0.13829298 0.26037366 0.92772833\n",
-      "  0.74577867 0.42239354 0.20594513 0.72328506]\n",
-      " [0.38831624 0.44520102 0.17305512 0.0106014  0.94866246 0.84929103\n",
-      "  0.81753152 0.06664867 0.96750421 0.50462474]\n",
-      " [0.32584888 0.58948347 0.22729927 0.01919702 0.74280244 0.73448544\n",
-      "  0.33995567 0.61197218 0.5320148  0.34517495]]\n"
+      "[[0.80207897 0.22885848 0.14526269 0.91022359 0.76135601 0.52687741\n",
+      "  0.68711054 0.01455922 0.70967214 0.47297104]\n",
+      " [0.87431418 0.15724663 0.06301519 0.41894238 0.47364408 0.06406913\n",
+      "  0.31588043 0.87953769 0.74731872 0.10490195]\n",
+      " [0.87533326 0.71038664 0.29726695 0.34011629 0.51741855 0.32185967\n",
+      "  0.58793527 0.0510594  0.81948868 0.5914397 ]\n",
+      " [0.96850702 0.53558374 0.40512793 0.83443463 0.96618584 0.54644868\n",
+      "  0.1871257  0.28585116 0.79035184 0.2171263 ]\n",
+      " [0.46873567 0.91358019 0.28294305 0.03061555 0.86850963 0.19910208\n",
+      "  0.16650509 0.07417526 0.42535003 0.98765625]\n",
+      " [0.29588674 0.70249832 0.5364857  0.1036131  0.56249706 0.15827078\n",
+      "  0.53515878 0.40182469 0.24828523 0.44402322]\n",
+      " [0.95746721 0.33159476 0.86811569 0.89098129 0.67109613 0.96599594\n",
+      "  0.17078905 0.22297358 0.2193546  0.4993133 ]\n",
+      " [0.60675691 0.33800793 0.23780865 0.30914432 0.64695862 0.19717411\n",
+      "  0.94400087 0.07404236 0.20967833 0.74391438]\n",
+      " [0.72651548 0.13310008 0.78220032 0.90556496 0.45014    0.19314584\n",
+      "  0.71977472 0.97866042 0.53700083 0.10479359]\n",
+      " [0.17829104 0.30129931 0.77203046 0.2707158  0.09391542 0.82988221\n",
+      "  0.61480907 0.29282684 0.37667238 0.91086026]]\n"
      ]
     }
    ],
@@ -800,13 +800,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.1388976715362099\n",
-      "4.3703468543933255\n",
-      "0.08844723450419088\n",
-      "[[ 1.06638817  3.39483726  3.28607817]\n",
-      " [ 3.39483726 11.55955126 10.56366546]\n",
-      " [ 3.28607817 10.56366546 16.19343949]]\n",
-      "[25.58818643  0.05982961  3.17136288]\n"
+      "0.016972818397989375\n",
+      "3.9050595316983907\n",
+      "0.11007935789924998\n",
+      "[[ 1.21860973  3.69519297  6.31082439]\n",
+      " [ 3.69519297 12.18993003 19.00431775]\n",
+      " [ 6.31082439 19.00431775 65.3283771 ]]\n",
+      "[72.14421971  0.08339896  6.5092982 ]\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
index bbd74577f..5f4b5d2b2 100644
--- a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
@@ -143,7 +143,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19329/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31707/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
       "  ax = fig.gca(projection='3d')\n"
      ]
     },
diff --git a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
index 4e6375da4..8d2bf7f69 100644
--- a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
@@ -1344,27 +1344,27 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "2.226296567359957\n",
-      "[[17.7651068   3.38511413 15.76004012 10.19888258 11.875794   11.66323494\n",
-      "   6.85548858  6.58948138  5.08030109  4.18726877]\n",
-      " [ 3.38511413  0.64502836  3.00305172  1.94338159  2.26291451  2.22241171\n",
-      "   1.30630294  1.25561567  0.96804366  0.79787771]\n",
-      " [15.76004012  3.00305172 13.98127617  9.04778116 10.53542722 10.34685874\n",
-      "   6.08174081  5.84575663  4.50691065  3.71467081]\n",
-      " [10.19888258  1.94338159  9.04778116  5.85514104  6.81784973  6.69582036\n",
-      "   3.93571082  3.78299706  2.9165822   2.40389562]\n",
-      " [11.875794    2.26291451 10.53542722  6.81784973  7.93884803  7.79675445\n",
-      "   4.5828247   4.40500157  3.39612983  2.79914677]\n",
-      " [11.66323494  2.22241171 10.34685874  6.69582036  7.79675445  7.65720414\n",
-      "   4.50079895  4.32615859  3.33534416  2.7490462 ]\n",
-      " [ 6.85548858  1.30630294  6.08174081  3.93571082  4.5828247   4.50079895\n",
-      "   2.64550753  2.54285633  1.96046928  1.61585143]\n",
-      " [ 6.58948138  1.25561567  5.84575663  3.78299706  4.40500157  4.32615859\n",
-      "   2.54285633  2.44418822  1.884399    1.55315304]\n",
-      " [ 5.08030109  0.96804366  4.50691065  2.9165822   3.39612983  3.33534416\n",
-      "   1.96046928  1.884399    1.45281756  1.19743643]\n",
-      " [ 4.18726877  0.79787771  3.71467081  2.40389562  2.79914677  2.7490462\n",
-      "   1.61585143  1.55315304  1.19743643  0.98694705]]\n"
+      "1.3329671101137754\n",
+      "[[ 5.35146218  5.08271388  8.11911824  8.05880359  2.9797317   2.96911909\n",
+      "   7.59642735  1.24785221  3.14389839  8.36403046]\n",
+      " [ 5.08271388  4.827462    7.71137935  7.65409368  2.83009076  2.82001111\n",
+      "   7.21493779  1.18518557  2.98601306  7.94399217]\n",
+      " [ 8.11911824  7.71137935 12.31814386 12.22663583  4.52078202  4.5046808\n",
+      "  11.52512898  1.89321335  4.76985203 12.68971917]\n",
+      " [ 8.05880359  7.65409368 12.22663583 12.13580759  4.4871984   4.4712168\n",
+      "  11.43951204  1.8791492   4.73441814 12.59545081]\n",
+      " [ 2.9797317   2.83009076  4.52078202  4.4871984   1.65913552  1.65322635\n",
+      "   4.22974406  0.69481287  1.75054469  4.65715086]\n",
+      " [ 2.96911909  2.82001111  4.5046808   4.4712168   1.65322635  1.64733822\n",
+      "   4.21467941  0.69233822  1.74430995  4.64056395]\n",
+      " [ 7.59642735  7.21493779 11.52512898 11.43951204  4.22974406  4.21467941\n",
+      "  10.78316665  1.77133246  4.4627795  11.8727831 ]\n",
+      " [ 1.24785221  1.18518557  1.89321335  1.8791492   0.69481287  0.69233822\n",
+      "   1.77133246  0.29097377  0.7330932   1.9503219 ]\n",
+      " [ 3.14389839  2.98601306  4.76985203  4.73441814  1.75054469  1.74430995\n",
+      "   4.4627795   0.7330932   1.84698999  4.91373404]\n",
+      " [ 8.36403046  7.94399217 12.68971917 12.59545081  4.65715086  4.64056395\n",
+      "  11.8727831   1.9503219   4.91373404 13.07250301]]\n"
      ]
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    ],
@@ -2001,15 +2001,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.09327269724691106\n",
-      "3.904648525660773\n",
-      "-0.17022089147584388\n",
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-      "2.845716766413386 2.3597516959642966 7.019140656913589\n",
-      "[[ 0.94815131  2.84571677  2.3597517 ]\n",
-      " [ 2.84571677  9.56288861  7.01914066]\n",
-      " [ 2.3597517   7.01914066 10.71437568]]\n",
-      "[17.97062694  0.08221578  3.17257288]\n"
+      "-0.02582613386840159\n",
+      "3.8311393813043355\n",
+      "-0.30339081517583943\n",
+      "1.1608179281668718 12.374777250972322 24.97606135399951\n",
+      "3.6353716266230895 4.038211969489939 12.83140314044099\n",
+      "[[ 1.16081793  3.63537163  4.03821197]\n",
+      " [ 3.63537163 12.37477725 12.83140314]\n",
+      " [ 4.03821197 12.83140314 24.97606135]]\n",
+      "[33.84671508  0.08066381  4.58427764]\n"
      ]
     }
    ],
@@ -2638,7 +2638,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -2764,12 +2764,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.0071642501586093735 0.9871776311306221\n"
+      "0.01229732982000352 0.93003138502386\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
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diff --git a/doc/LectureNotes/_build/jupyter_execute/statistics_181_0.png b/doc/LectureNotes/_build/jupyter_execute/statistics_181_0.png
index da2c6c184..88a0af820 100644
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diff --git a/doc/LectureNotes/_build/jupyter_execute/statistics_188_1.png b/doc/LectureNotes/_build/jupyter_execute/statistics_188_1.png
index 30859b967..08cbabfcd 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/statistics_188_1.png and b/doc/LectureNotes/_build/jupyter_execute/statistics_188_1.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/week34.ipynb b/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
index aa00669d5..2ab49b241 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
@@ -985,8 +985,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.5829913  -0.55086461  0.15975618 -0.92729959 -1.95190644  0.60383004\n",
-      " -1.02308518 -1.48134747 -0.38259375 -1.42172457]\n"
+      "[ 0.27919014 -0.36550376 -0.86282204  1.31714002 -1.99484719 -0.63837812\n",
+      "  1.45062284 -0.33079132 -0.58182803 -0.7207467 ]\n"
      ]
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@@ -1424,26 +1424,26 @@
      "name": "stdout",
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-      "  0.28490569 0.09308274 0.65628888 0.30478013]\n",
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-      "  0.6289054  0.31705377 0.22001043 0.99268332]]\n"
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+      "  0.86852099 0.19772911 0.93022647 0.45253585]\n",
+      " [0.5810785  0.94823368 0.73379189 0.09408163 0.14549142 0.8353591\n",
+      "  0.46754435 0.29732036 0.7698352  0.39200159]\n",
+      " [0.77265782 0.37376184 0.43647835 0.38782352 0.97449977 0.02276062\n",
+      "  0.36802977 0.43941514 0.99006712 0.98316168]\n",
+      " [0.89897156 0.04956816 0.52067151 0.52180619 0.21275991 0.86420934\n",
+      "  0.50653545 0.49057373 0.77067609 0.16043757]\n",
+      " [0.22616902 0.70408916 0.43902948 0.68992377 0.5608253  0.84132082\n",
+      "  0.95661705 0.7082333  0.33600213 0.44116407]\n",
+      " [0.96459246 0.32141575 0.95679388 0.44595818 0.1875353  0.47700752\n",
+      "  0.03321947 0.55865092 0.96543101 0.63227278]]\n"
      ]
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@@ -1557,13 +1557,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.042044382097756156\n",
-      "4.034169230664804\n",
-      "0.4600624385659884\n",
-      "[[ 1.22368396  3.61504341  4.56171141]\n",
-      " [ 3.61504341 11.96611032 13.21879159]\n",
-      " [ 4.56171141 13.21879159 31.04223754]]\n",
-      "[38.67554897  0.10440776  5.45207509]\n"
+      "-0.022210866177877393\n",
+      "3.7588118737641243\n",
+      "0.5615739502773949\n",
+      "[[ 1.30150056  3.81953844  7.0377961 ]\n",
+      " [ 3.81953844 12.2361161  19.72546953]\n",
+      " [ 7.0377961  19.72546953 73.31248389]]\n",
+      "[79.90960269  0.08394792  6.85654993]\n"
      ]
     }
    ],
@@ -1916,7 +1916,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19344/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31718/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
       "  data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))\n"
      ]
     },
diff --git a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
index a01dbcb4c..c5399826b 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
@@ -1519,7 +1519,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.9963311287748658\n"
+      "0.995840825550726\n"
      ]
     }
    ],
@@ -1550,7 +1550,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.007891914573161948\n"
+      "0.007607459165915922\n"
      ]
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@@ -1585,23 +1585,23 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.00712321 0.05126901 0.00172452 0.00104613 0.01477821 0.06642248\n",
-      " 0.04547353 0.0207306  0.01552289 0.01492    0.0200568  0.01097423\n",
-      " 0.02400359 0.04111096 0.02126208 0.00799998 0.00976647 0.0447389\n",
-      " 0.0006527  0.02468681 0.03543039 0.00627535 0.04259402 0.02635835\n",
-      " 0.04362755 0.00478655 0.01989299 0.01508632 0.04372783 0.00324969\n",
-      " 0.01508966 0.08185315 0.01214101 0.01130932 0.00186362 0.02809859\n",
-      " 0.00480371 0.08481871 0.01881546 0.04314342 0.11022363 0.01288591\n",
-      " 0.03370315 0.00858536 0.00202679 0.00229911 0.00446979 0.0496375\n",
-      " 0.00426531 0.02593026 0.03063575 0.03119091 0.05459089 0.01916913\n",
-      " 0.00183869 0.00015239 0.01347636 0.01267006 0.02702978 0.02944425\n",
-      " 0.01424197 0.00354492 0.06026294 0.00148709 0.02061026 0.03616508\n",
-      " 0.03543958 0.02079171 0.00595615 0.01765474 0.01268892 0.00225484\n",
-      " 0.01135167 0.03894328 0.04426647 0.03717939 0.01502518 0.03195835\n",
-      " 0.00474485 0.06331463 0.01671556 0.01762067 0.00219624 0.07358383\n",
-      " 0.01038358 0.0002364  0.04669463 0.00048325 0.00012934 0.01529503\n",
-      " 0.0093869  0.00952586 0.0154222  0.01463052 0.0296969  0.01372375\n",
-      " 0.02536494 0.00472549 0.04225015 0.04690007]\n"
+      "[0.00552246 0.00115669 0.02017377 0.01896127 0.01389847 0.01591021\n",
+      " 0.02816083 0.0100949  0.02757522 0.00182747 0.00584432 0.02081274\n",
+      " 0.01365363 0.0191717  0.01068907 0.02763182 0.02950229 0.02485679\n",
+      " 0.01456159 0.00644939 0.0297291  0.08272096 0.01335857 0.00825399\n",
+      " 0.04478101 0.05834444 0.04198166 0.034985   0.00562524 0.01524072\n",
+      " 0.01529708 0.02083512 0.01161357 0.01708691 0.02279888 0.02912421\n",
+      " 0.00076617 0.02329285 0.00626773 0.01054509 0.00460405 0.01476097\n",
+      " 0.0036718  0.00569405 0.07804489 0.03894873 0.02103178 0.00726135\n",
+      " 0.00353575 0.00857028 0.00923278 0.01616709 0.02881357 0.00550379\n",
+      " 0.02942218 0.00946636 0.03982972 0.0149713  0.04103307 0.05526765\n",
+      " 0.00463639 0.00254359 0.00915433 0.02588522 0.00090992 0.00739382\n",
+      " 0.02075115 0.024632   0.00115506 0.01963203 0.00086063 0.01580414\n",
+      " 0.01059601 0.03376827 0.02745507 0.02109939 0.05977068 0.04662395\n",
+      " 0.00283853 0.03903968 0.0001225  0.02385515 0.02089297 0.04214702\n",
+      " 0.01289962 0.00798188 0.04746791 0.04822955 0.02066371 0.01045774\n",
+      " 0.01164198 0.03633213 0.00183398 0.0105301  0.00880924 0.015244\n",
+      " 0.01596986 0.01176096 0.01448147 0.00610607]\n"
      ]
     }
    ],
@@ -1655,15 +1655,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 1.95558642  0.77265448  2.8784267   1.83384573 -0.41219619]\n",
+      "[ 2.04899609 -0.34193915  5.64527549 -0.69997503  0.31290684]\n",
       "Training R2\n",
-      "0.9969332511584248\n",
+      "0.9952222065466447\n",
       "Training MSE\n",
-      "0.006829400694106674\n",
+      "0.008897354602673473\n",
       "Test R2\n",
-      "0.9950597269547777\n",
+      "0.9915165982451293\n",
       "Test MSE\n",
-      "0.011917343246903285\n"
+      "0.009442796383765939\n"
      ]
     }
    ],
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
index c6d8f3978..2b4851ed5 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
@@ -2023,7 +2023,7 @@
      "text": [
       "Bootstrap Statistics :\n",
       "original           bias      std. error\n",
-      " 99.8182  15.0632        99.8197        0.152701\n"
+      " 100.115  15.1213        100.117        0.151517\n"
      ]
     }
    ],
@@ -2089,7 +2089,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
@@ -2442,18 +2442,18 @@
       "Error: 0.06844519414009445\n",
       "Bias^2: 0.06453579006728322\n",
       "Var: 0.003909404072811221\n",
-      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n",
-      "Polynomial degree: 5\n",
-      "Error: 0.05227921801205679\n",
-      "Bias^2: 0.04818727730430286\n",
-      "Var: 0.004091940707753925\n",
-      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n"
+      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Polynomial degree: 5\n",
+      "Error: 0.05227921801205679\n",
+      "Bias^2: 0.04818727730430286\n",
+      "Var: 0.004091940707753925\n",
+      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
       "Polynomial degree: 6\n",
       "Error: 0.03781367141738902\n",
       "Bias^2: 0.03365768507152769\n",
@@ -2468,13 +2468,7 @@
       "Error: 0.017355848195593312\n",
       "Bias^2: 0.010331721306655165\n",
       "Var: 0.007024126888938144\n",
-      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
       "Polynomial degree: 9\n",
       "Error: 0.026605727637184558\n",
       "Bias^2: 0.010018312644139219\n",
@@ -2489,12 +2483,24 @@
       "Error: 0.07160048164232538\n",
       "Bias^2: 0.014436800088896381\n",
       "Var: 0.05716368155342902\n",
-      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
+      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "Polynomial degree: 12\n",
       "Error: 0.11547777218876518\n",
       "Bias^2: 0.016285782696017142\n",
       "Var: 0.09919198949274803\n",
-      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
+      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "Polynomial degree: 13\n",
       "Error: 0.2284246870217162\n",
       "Bias^2: 0.01975416527168255\n",
@@ -2511,7 +2517,7 @@
      },
      "metadata": {
       "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_162_3.png"
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_162_4.png"
       }
      },
      "output_type": "display_data"
@@ -3060,9 +3066,9 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
      ]
     },
@@ -3197,7 +3203,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19367/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31736/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
       "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
      ]
     },
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png b/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png
index 6adf14c0a..736939b6c 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png and b/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37_162_4.png b/doc/LectureNotes/_build/jupyter_execute/week37_162_4.png
new file mode 100644
index 000000000..0a1c6cc0b
Binary files /dev/null and b/doc/LectureNotes/_build/jupyter_execute/week37_162_4.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
index fd37b75b7..b2849e31e 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
@@ -1679,7 +1679,7 @@
      "output_type": "stream",
      "text": [
       "RandomizedSearchCV(estimator=Ridge(), n_iter=100,\n",
-      "                   param_distributions={'alpha': })\n",
+      "                   param_distributions={'alpha': })\n",
       "Best estimated lambda-value: 0.9849967686928113\n",
       "MSE score: 1.0853136633465326\n",
       "R2 score: -0.0002382102844775691\n"
diff --git a/doc/LectureNotes/_build/jupyter_execute/week39.ipynb b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb
index 129be84cb..77072dd0d 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week39.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb
@@ -1160,14 +1160,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_19394/3838917029.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31749/3838917029.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
       "  ax = fig.gca(projection=\"3d\")\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       ""
+       ""
       ]
      },
      "execution_count": 1,
@@ -1337,7 +1337,7 @@
     {
      "data": {
       "text/plain": [
-       "[]"
+       "[]"
       ]
      },
      "execution_count": 5,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week40.ipynb b/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
index b61608683..da63ddffb 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
@@ -485,20 +485,20 @@
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.06481015]\n",
-      " [2.84666445]]\n",
-      "Eigenvalues of Hessian Matrix:[0.28638913 4.44842116]\n",
+      "[[4.42484459]\n",
+      " [2.65626992]]\n",
+      "Eigenvalues of Hessian Matrix:[0.30361418 4.06484621]\n",
       "theta from own gd\n",
-      "[[4.06481015]\n",
-      " [2.84666445]]\n",
+      "[[4.42484459]\n",
+      " [2.65626992]]\n",
       "theta from own sdg\n",
-      "[[4.02231445]\n",
-      " [2.89996783]]\n"
+      "[[4.53049637]\n",
+      " [2.68581655]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "
    "
       ]
diff --git a/doc/LectureNotes/_build/jupyter_execute/week40_25_1.png b/doc/LectureNotes/_build/jupyter_execute/week40_25_1.png
index 464798a94..1adb4c03c 100644
Binary files a/doc/LectureNotes/_build/jupyter_execute/week40_25_1.png and b/doc/LectureNotes/_build/jupyter_execute/week40_25_1.png differ
diff --git a/doc/LectureNotes/_build/jupyter_execute/week41.ipynb b/doc/LectureNotes/_build/jupyter_execute/week41.ipynb
index 19e341be3..cf7d8ff7d 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week41.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week41.ipynb
@@ -3368,7 +3368,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -3956,7 +3956,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -3974,7 +3974,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -3992,7 +3992,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4010,7 +4010,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4028,7 +4028,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4046,7 +4046,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4064,7 +4064,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4082,11 +4082,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4104,11 +4104,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4126,11 +4126,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4148,11 +4148,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4170,11 +4170,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4192,7 +4192,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -4210,11 +4210,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4232,11 +4232,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4254,11 +4254,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4276,11 +4276,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4298,11 +4298,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4320,11 +4320,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4342,11 +4342,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4364,11 +4364,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -4429,15 +4429,15 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_74401/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31761/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -5062,10 +5062,6 @@
       "Learning rate  =  1.0\n",
       "Lambda =  0.1\n",
       "Accuracy score on test set:  0.08333333333333333\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
       "\n"
      ]
     },
@@ -5073,6 +5069,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n",
       "Learning rate  =  1.0\n",
       "Lambda =  10.0\n",
       "Accuracy score on test set:  0.09444444444444444\n",
@@ -5098,13 +5098,7 @@
       "Learning rate  =  10.0\n",
       "Lambda =  0.01\n",
       "Accuracy score on test set:  0.1388888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
+      "\n",
       "Learning rate  =  10.0\n",
       "Lambda =  0.1\n",
       "Accuracy score on test set:  0.11388888888888889\n",
diff --git a/doc/LectureNotes/_build/jupyter_execute/week42.ipynb b/doc/LectureNotes/_build/jupyter_execute/week42.ipynb
new file mode 100644
index 000000000..743a68302
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/week42.ipynb
@@ -0,0 +1,4633 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "50ce4eae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "\n",
+    ""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f46bd6b4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Week 42 Constructing a Neural Network code with introduction to Tensor flow\n",
+    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
+    "\n",
+    "Date: **October 16-20, 2023**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8c0fa4d7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plan for week 42\n",
+    "\n",
+    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "  * Exercise on writing your own stochastic gradient and gradient descent codes. This exercise continues from the previous  week but now with inclusion of automatic differentiation\n",
+    "\n",
+    "  * Discussion of project 2\n",
+    "\n",
+    "  * [See video on automatic differentiation from last year](https://www.youtube.com/watch?v=cWCebuNKrA8). This video will be updated before Tuesday.\n",
+    "\n",
+    "  \n",
+    "\n",
+    "**Material for the lecture on Thursday October 12, 2023.**\n",
+    "\n",
+    "  * Building our own Feed-forward Neural Network and discussion of project 2\n",
+    "\n",
+    "  * Readings and Videos:\n",
+    "\n",
+    "    * These lecture notes\n",
+    "\n",
+    "    * [Aurelien Geron's chapters 10-11](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Textbooks/TensorflowML.pdf)\n",
+    "\n",
+    "    * For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.     \n",
+    "\n",
+    "    * [Neural Networks demystified](https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs)\n",
+    "\n",
+    "    * [Building Neural Networks from scratch](https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex)\n",
+    "\n",
+    "    * [Video on Neural Networks](https://www.youtube.com/watch?v=CqOfi41LfDw)\n",
+    "\n",
+    "    * [Video on the back propagation algorithm](https://www.youtube.com/watch?v=Ilg3gGewQ5U)\n",
+    "\n",
+    "I also  recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at ."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "89b6b637",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Lecture Thursday October 19"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3a32ad82",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Review of the back propagation algorithm\n",
+    "\n",
+    "During the last lecture we discussed in detail the back propagation\n",
+    "algorithm. This algorithm is based on a repeated application of the\n",
+    "chain rule. Let us bring back the basic equation and at the same time\n",
+    "link this with the basic mathematics of automatic differentiation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4f9291ee",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the Back propagation algorithm\n",
+    "\n",
+    "The four equations  derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.\n",
+    "\n",
+    "First, we set up the input data $\\boldsymbol{x}$ and the activations\n",
+    "$\\boldsymbol{z}_1$ of the input layer and compute the activation function and\n",
+    "the pertinent outputs $\\boldsymbol{a}^1$.\n",
+    "\n",
+    "Secondly, we perform then the feed forward till we reach the output\n",
+    "layer and compute all $\\boldsymbol{z}_l$ of the input layer and compute the\n",
+    "activation function and the pertinent outputs $\\boldsymbol{a}^l$ for\n",
+    "$l=2,3,\\dots,L$.\n",
+    "\n",
+    "Thereafter we compute the ouput error $\\boldsymbol{\\delta}^L$ by computing all"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7753981f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta_j^L = f'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b093c71",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,2$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "96ca25bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a156d8bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Finally, we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,2$ and update the weights and biases according to the rules"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f35c8afe",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "w_{jk}^l\\leftarrow  = w_{jk}^l- \\eta \\delta_j^la_k^{l-1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ffa6d322",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7b6e59f6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The parameter $\\eta$ is the learning parameter discussed in connection with the gradient descent methods.\n",
+    "Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e93ff00c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up a Multi-layer perceptron model for classification\n",
+    "\n",
+    "We are now gong to develop an example based on the MNIST data\n",
+    "base. This is a classification problem and we need to use our\n",
+    "cross-entropy function we discussed in connection with logistic\n",
+    "regression. The cross-entropy defines our cost function for the\n",
+    "classificaton problems with neural networks.\n",
+    "\n",
+    "In binary classification with two classes $(0, 1)$ we define the\n",
+    "logistic/sigmoid function as the probability that a particular input\n",
+    "is in class $0$ or $1$.  This is possible because the logistic\n",
+    "function takes any input from the real numbers and inputs a number\n",
+    "between 0 and 1, and can therefore be interpreted as a probability. It\n",
+    "also has other nice properties, such as a derivative that is simple to\n",
+    "calculate.\n",
+    "\n",
+    "For an input $\\boldsymbol{a}$ from the hidden layer, the probability that the input $\\boldsymbol{x}$\n",
+    "is in class 0 or 1 is just. We let $\\theta$ represent the unknown weights and biases to be adjusted by our equations). The variable $x$\n",
+    "represents our activation values $z$. We have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c437395",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3d7b1140",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3df5aec",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "63345646",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
+    "of our network."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6ac465b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Defining the cost function\n",
+    "\n",
+    "Our cost function is given as (see the Logistic regression lectures)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cf06b4a0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
+    "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\boldsymbol{\\theta}) .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "719f761f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
+    "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$.  \n",
+    "The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather\n",
+    "than maximizing a negative number.  \n",
+    "\n",
+    "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  \n",
+    "\n",
+    "$y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n",
+    "\n",
+    "$y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n",
+    "\n",
+    "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$)..  \n",
+    "\n",
+    "If $\\boldsymbol{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n",
+    "output vector $\\boldsymbol{y}_i$.  \n",
+    "The probability of $\\boldsymbol{x}_i$ being in class $c$ will be given by the softmax function:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "342de1d9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
+    "{\\sum_{c'=0}^{C-1} \\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_{c'})}} ,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "211a69ba",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which reduces to the logistic function in the binary case.  \n",
+    "The likelihood of this $C$-class classifier\n",
+    "is now given as:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5f0cd5a2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe018e32",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Again we take the negative log-likelihood to define our cost function:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9d48faca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "897c8b0c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "See the logistic regression lectures for a full definition of the cost function.\n",
+    "\n",
+    "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "68347a7f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Example: binary classification problem\n",
+    "\n",
+    "As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\\beta$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8425d868",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9108d4ac",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we had defined the logistic (sigmoid) function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "77e0ec3b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64ed867c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "51819578",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "db6532a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
+    "\n",
+    "Now we replace $x_i$ with the activation $z_i^l$ for a given layer $l$ and the outputs as $y_i=a_i^l=f(z_i^l)$, with $z_i^l$ now being a function of the weights $w_{ij}^l$ and biases $b_i^l$. \n",
+    "We have then"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24e5e213",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d398c961",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "236d161c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25e3004d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n",
+    "Our cost function at the final layer $l=L$ is now"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9440c725",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "782f5282",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0e8498a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "68398b35",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In case we use another activation function than the logistic one, we need to evaluate other derivatives."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "19887152",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Softmax function\n",
+    "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "80e8dc5d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
+    "\\frac{\\partial f(z_i^l)}{\\partial z_j^l} \\frac{\\partial z_j^l}{\\partial w_{jk}^l}= \\frac{\\partial f(z_i^l)}{\\partial z_j^l}a_k^{l-1}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "68d33776",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "For the Softmax function we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c86943c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "efe53876",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Its derivative with respect to $z_j^l$ gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fce5b9b2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "97210471",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which in case of the simply binary model reduces to  having $i=j$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4f515591",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Developing a code for doing neural networks with back propagation\n",
+    "\n",
+    "One can identify a set of key steps when using neural networks to solve supervised learning problems:  \n",
+    "\n",
+    "1. Collect and pre-process data  \n",
+    "\n",
+    "2. Define model and architecture  \n",
+    "\n",
+    "3. Choose cost function and optimizer  \n",
+    "\n",
+    "4. Train the model  \n",
+    "\n",
+    "5. Evaluate model performance on test data  \n",
+    "\n",
+    "6. Adjust hyperparameters (if necessary, network architecture)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec34f212",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Collect and pre-process data\n",
+    "\n",
+    "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n",
+    "package. You may also find it for example [here](http://yann.lecun.com/exdb/mnist/).  \n",
+    "The *MNIST* (Modified National Institute of Standards and Technology) database is a large database\n",
+    "of handwritten digits that is commonly used for training various image processing systems.  \n",
+    "The MNIST dataset consists of 70 000 images of size $28\\times 28$ pixels, each labeled from 0 to 9.  \n",
+    "The scikit-learn dataset we will use consists of a selection of 1797 images of size $8\\times 8$ collected and processed from this database.  \n",
+    "\n",
+    "To feed data into a feed-forward neural network we need to represent\n",
+    "the inputs as a design/feature matrix $X = (n_{inputs}, n_{features})$.  Each\n",
+    "row represents an *input*, in this case a handwritten digit, and\n",
+    "each column represents a *feature*, in this case a pixel.  The\n",
+    "correct answers, also known as *labels* or *targets* are\n",
+    "represented as a 1D array of integers \n",
+    "$Y = (n_{inputs}) = (5, 3, 1, 8,...)$.\n",
+    "\n",
+    "As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from\n",
+    "measurements of height (in m)  \n",
+    "and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example:  \n",
+    "\n",
+    "$$ X = \\begin{bmatrix}\n",
+    "1.85 & 81\\\\\n",
+    "1.71 & 65\\\\\n",
+    "1.95 & 103\\\\\n",
+    "1.55 & 42\\\\\n",
+    "1.63 & 56\n",
+    "\\end{bmatrix} ,$$  \n",
+    "\n",
+    "and the targets would be:  \n",
+    "\n",
+    "$$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$  \n",
+    "\n",
+    "Since each input image is a 2D matrix, we need to flatten the image\n",
+    "(i.e. \"unravel\" the 2D matrix into a 1D array) to turn the data into a\n",
+    "design/feature matrix. This means we lose all spatial information in the\n",
+    "image, such as locality and translational invariance. More complicated\n",
+    "architectures such as Convolutional Neural Networks can take advantage\n",
+    "of such information, and are most commonly applied when analyzing\n",
+    "images."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "e389e60e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)\n",
+      "labels = (n_inputs) = (1797,)\n",
+      "X = (n_inputs, n_features) = (1797, 64)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_51_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "# import necessary packages\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn import datasets\n",
+    "\n",
+    "\n",
+    "# ensure the same random numbers appear every time\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "# display images in notebook\n",
+    "%matplotlib inline\n",
+    "plt.rcParams['figure.figsize'] = (12,12)\n",
+    "\n",
+    "\n",
+    "# download MNIST dataset\n",
+    "digits = datasets.load_digits()\n",
+    "\n",
+    "# define inputs and labels\n",
+    "inputs = digits.images\n",
+    "labels = digits.target\n",
+    "\n",
+    "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
+    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
+    "\n",
+    "\n",
+    "# flatten the image\n",
+    "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
+    "n_inputs = len(inputs)\n",
+    "inputs = inputs.reshape(n_inputs, -1)\n",
+    "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
+    "\n",
+    "\n",
+    "# choose some random images to display\n",
+    "indices = np.arange(n_inputs)\n",
+    "random_indices = np.random.choice(indices, size=5)\n",
+    "\n",
+    "for i, image in enumerate(digits.images[random_indices]):\n",
+    "    plt.subplot(1, 5, i+1)\n",
+    "    plt.axis('off')\n",
+    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
+    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a264b82",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Train and test datasets\n",
+    "\n",
+    "Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.  \n",
+    "\n",
+    "We will reserve $80 \\%$ of our dataset for training and $20 \\%$ for testing.  \n",
+    "\n",
+    "It is important that the train and test datasets are drawn randomly from our dataset, to ensure\n",
+    "no bias in the sampling.  \n",
+    "Say you are taking measurements of weather data to predict the weather in the coming 5 days.\n",
+    "You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data\n",
+    "collected from 12.00 to 24.00."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "8750ea41",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Number of training images: 1437\n",
+      "Number of test images: 360\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sklearn.model_selection import train_test_split\n",
+    "\n",
+    "# one-liner from scikit-learn library\n",
+    "train_size = 0.8\n",
+    "test_size = 1 - train_size\n",
+    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
+    "                                                    test_size=test_size)\n",
+    "\n",
+    "# equivalently in numpy\n",
+    "def train_test_split_numpy(inputs, labels, train_size, test_size):\n",
+    "    n_inputs = len(inputs)\n",
+    "    inputs_shuffled = inputs.copy()\n",
+    "    labels_shuffled = labels.copy()\n",
+    "    \n",
+    "    np.random.shuffle(inputs_shuffled)\n",
+    "    np.random.shuffle(labels_shuffled)\n",
+    "    \n",
+    "    train_end = int(n_inputs*train_size)\n",
+    "    X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]\n",
+    "    Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]\n",
+    "    \n",
+    "    return X_train, X_test, Y_train, Y_test\n",
+    "\n",
+    "#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)\n",
+    "\n",
+    "print(\"Number of training images: \" + str(len(X_train)))\n",
+    "print(\"Number of test images: \" + str(len(X_test)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3897eca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Define model and architecture\n",
+    "\n",
+    "Our simple feed-forward neural network will consist of an *input* layer, a single *hidden* layer and an *output* layer. The activation $y$ of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have \n",
+    "\n",
+    "$$ z = \\sum_{i=1}^n w_i a_i ,$$\n",
+    "\n",
+    "$$ y = f(z) ,$$\n",
+    "\n",
+    "where $f$ is the activation function, $a_i$ represents input from neuron $i$ in the preceding layer\n",
+    "and $w_i$ is the weight to input $i$.  \n",
+    "The activation of the neurons in the input layer is just the features (e.g. a pixel value).  \n",
+    "\n",
+    "The simplest activation function for a neuron is the *Heaviside* function:\n",
+    "\n",
+    "$$ f(z) = \n",
+    "\\begin{cases}\n",
+    "1,  &  z > 0\\\\\n",
+    "0,  & \\text{otherwise}\n",
+    "\\end{cases}\n",
+    "$$\n",
+    "\n",
+    "A feed-forward neural network with this activation is known as a *perceptron*.  \n",
+    "For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer.  \n",
+    "This activation can be generalized to $k$ classes (using e.g. the *one-against-all* strategy), \n",
+    "and we call these architectures *multiclass perceptrons*.  \n",
+    "\n",
+    "However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and  \n",
+    "Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function.  \n",
+    "\n",
+    "Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU).  \n",
+    "We will be using the sigmoid function $\\sigma(x)$:  \n",
+    "\n",
+    "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n",
+    "\n",
+    "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad593a03",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Layers\n",
+    "\n",
+    "* Input \n",
+    "\n",
+    "Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons.  \n",
+    "\n",
+    "* Hidden layer\n",
+    "\n",
+    "We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer.  \n",
+    "Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer.  \n",
+    "\n",
+    "* Output\n",
+    "\n",
+    "If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,\n",
+    "which could output 0 or 1 according to the Heaviside function. This would be an example of a *hard* classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a *soft* classifier, which outputs the probability of being in class 0 or 1.  \n",
+    "\n",
+    "For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class.  \n",
+    "\n",
+    "Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons $j = 0,1,...,9$. The activation of each output neuron $j$ will be according to the *softmax* function:  \n",
+    "\n",
+    "$$ P(\\text{class $j$} \\mid \\text{input $\\boldsymbol{a}$}) = \\frac{\\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_j)}}\n",
+    "{\\sum_{c=0}^{9} \\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_c)}} ,$$  \n",
+    "\n",
+    "i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\\boldsymbol{a}$, with $\\boldsymbol{w}_j$ the weights of neuron $j$ to the inputs.  \n",
+    "The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  \n",
+    "The exponent is just the weighted sum of inputs as before:  \n",
+    "\n",
+    "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i+b_j.$$  \n",
+    "\n",
+    "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n",
+    "weights to the output layer."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e37b3844",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Weights and biases\n",
+    "\n",
+    "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n",
+    "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless.  \n",
+    "\n",
+    "Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range\n",
+    "of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron $j$, $b_j$:  \n",
+    "\n",
+    "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i + b_j.$$  \n",
+    "\n",
+    "The bias weights $\\boldsymbol{b}$ are often initialized to zero, but a small value like $0.01$ ensures all neurons have some output which can be backpropagated in the first training cycle."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "3d909fc7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# building our neural network\n",
+    "\n",
+    "n_inputs, n_features = X_train.shape\n",
+    "n_hidden_neurons = 50\n",
+    "n_categories = 10\n",
+    "\n",
+    "# we make the weights normally distributed using numpy.random.randn\n",
+    "\n",
+    "# weights and bias in the hidden layer\n",
+    "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n",
+    "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n",
+    "\n",
+    "# weights and bias in the output layer\n",
+    "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n",
+    "output_bias = np.zeros(n_categories) + 0.01"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b89c2d9f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Feed-forward pass\n",
+    "\n",
+    "Denote $F$ the number of features, $H$ the number of hidden neurons and $C$ the number of categories.  \n",
+    "For each input image we calculate a weighted sum of input features (pixel values) to each neuron $j$ in the hidden layer $l$:  \n",
+    "\n",
+    "$$ z_{j}^{l} = \\sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},$$\n",
+    "\n",
+    "this is then passed through our activation function  \n",
+    "\n",
+    "$$ a_{j}^{l} = f(z_{j}^{l}) .$$  \n",
+    "\n",
+    "We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron $j$ in the output layer:  \n",
+    "\n",
+    "$$ z_{j}^{L} = \\sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.$$  \n",
+    "\n",
+    "Finally we calculate the output of neuron $j$ in the output layer using the softmax function:  \n",
+    "\n",
+    "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n",
+    "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "435c0ced",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Matrix multiplications\n",
+    "\n",
+    "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n",
+    "layer have the dimensions  \n",
+    "$W_{hidden} = (n_{features}, n_{hidden})$,\n",
+    "we can easily feed the network all our training data in one go by taking the matrix product  \n",
+    "\n",
+    "$$ X W^{h} = (n_{inputs}, n_{hidden}),$$ \n",
+    "\n",
+    "and obtain a matrix that holds the weighted sum of inputs to the hidden layer\n",
+    "for each input image and each hidden neuron.    \n",
+    "We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$:  \n",
+    "\n",
+    "$$ \\boldsymbol{z}^{l} = \\boldsymbol{X} \\boldsymbol{W}^{l} + \\boldsymbol{b}^{l} ,$$\n",
+    "\n",
+    "meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  \n",
+    "This is then passed through the activation:  \n",
+    "\n",
+    "$$ \\boldsymbol{a}^{l} = f(\\boldsymbol{z}^l) .$$  \n",
+    "\n",
+    "This is fed to the output layer:  \n",
+    "\n",
+    "$$ \\boldsymbol{z}^{L} = \\boldsymbol{a}^{L} \\boldsymbol{W}^{L} + \\boldsymbol{b}^{L} .$$\n",
+    "\n",
+    "Finally we receive our output values for each image and each category by passing it through the softmax function:  \n",
+    "\n",
+    "$$ output = softmax (\\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "3037d7ab",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "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",
+      " 9.84443254e-01 3.11507992e-04]\n",
+      "probabilities sum up to: 1.0\n",
+      "\n",
+      "predictions = (n_inputs) = (1437,)\n",
+      "prediction for image 0: 8\n",
+      "correct label for image 0: 6\n"
+     ]
+    }
+   ],
+   "source": [
+    "# setup the feed-forward pass, subscript h = hidden layer\n",
+    "\n",
+    "def sigmoid(x):\n",
+    "    return 1/(1 + np.exp(-x))\n",
+    "\n",
+    "def feed_forward(X):\n",
+    "    # weighted sum of inputs to the hidden layer\n",
+    "    z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
+    "    # activation in the hidden layer\n",
+    "    a_h = sigmoid(z_h)\n",
+    "    \n",
+    "    # weighted sum of inputs to the output layer\n",
+    "    z_o = np.matmul(a_h, output_weights) + output_bias\n",
+    "    # softmax output\n",
+    "    # axis 0 holds each input and axis 1 the probabilities of each category\n",
+    "    exp_term = np.exp(z_o)\n",
+    "    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
+    "    \n",
+    "    return probabilities\n",
+    "\n",
+    "probabilities = feed_forward(X_train)\n",
+    "print(\"probabilities = (n_inputs, n_categories) = \" + str(probabilities.shape))\n",
+    "print(\"probability that image 0 is in category 0,1,2,...,9 = \\n\" + str(probabilities[0]))\n",
+    "print(\"probabilities sum up to: \" + str(probabilities[0].sum()))\n",
+    "print()\n",
+    "\n",
+    "# we obtain a prediction by taking the class with the highest likelihood\n",
+    "def predict(X):\n",
+    "    probabilities = feed_forward(X)\n",
+    "    return np.argmax(probabilities, axis=1)\n",
+    "\n",
+    "predictions = predict(X_train)\n",
+    "print(\"predictions = (n_inputs) = \" + str(predictions.shape))\n",
+    "print(\"prediction for image 0: \" + str(predictions[0]))\n",
+    "print(\"correct label for image 0: \" + str(Y_train[0]))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61c33a3f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Choose cost function and optimizer\n",
+    "\n",
+    "To measure how well our neural network is doing we need to introduce a cost function.  \n",
+    "We will call the function that gives the error of a single sample output the *loss* function, and the function\n",
+    "that gives the total error of our network across all samples the *cost* function.\n",
+    "A typical choice for multiclass classification is the *cross-entropy* loss, also known as the negative log likelihood.  \n",
+    "\n",
+    "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  \n",
+    "\n",
+    "$$ y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  \n",
+    "\n",
+    "$$ y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  \n",
+    "\n",
+    "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset.  \n",
+    "\n",
+    "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector.  \n",
+    "We define the cost function $\\mathcal{C}$ as a sum over the cross-entropy loss for each point $\\boldsymbol{x}_i$ in the dataset.\n",
+    "\n",
+    "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n",
+    "probability of the correct category $c'$  \n",
+    "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n",
+    "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\boldsymbol{\\theta}$ represents the parameters of our network, i.e. all the weights and biases."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "665f44ff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Optimizing the cost function\n",
+    "\n",
+    "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n",
+    "is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a *local* minimum of the cost function.  \n",
+    "Each parameter $\\theta$ is iteratively adjusted according to the rule  \n",
+    "\n",
+    "$$ \\theta_{i+1} = \\theta_i - \\eta \\nabla \\mathcal{C}(\\theta_i) ,$$\n",
+    "\n",
+    "where $\\eta$ is known as the *learning rate*, which controls how big a step we take towards the minimum.  \n",
+    "This update can be repeated for any number of iterations, or until we are satisfied with the result.  \n",
+    "\n",
+    "A simple and effective improvement is a variant called *Batch Gradient Descent*.  \n",
+    "Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient\n",
+    "on a subset of the data called a *minibatch*.  \n",
+    "If there are $N$ data points and we have a minibatch size of $M$, the total number of batches\n",
+    "is $N/M$.  \n",
+    "We denote each minibatch $B_k$, with $k = 1, 2,...,N/M$. The gradient then becomes:  \n",
+    "\n",
+    "$$ \\nabla \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
+    "\\frac{1}{M} \\sum_{i \\in B_k} \\nabla \\mathcal{L}_i(\\theta) ,$$\n",
+    "\n",
+    "i.e. instead of averaging the loss over the entire dataset, we average over a minibatch.  \n",
+    "\n",
+    "This has two important benefits:  \n",
+    "1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima.  \n",
+    "\n",
+    "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient.  \n",
+    "\n",
+    "The various optmization  methods, with codes and algorithms,  are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2d0168d0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Regularization\n",
+    "\n",
+    "It is common to add an extra term to the cost function, proportional\n",
+    "to the size of the weights.  This is equivalent to constraining the\n",
+    "size of the weights, so that they do not grow out of control.\n",
+    "Constraining the size of the weights means that the weights cannot\n",
+    "grow arbitrarily large to fit the training data, and in this way\n",
+    "reduces *overfitting*.\n",
+    "\n",
+    "We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes:  \n",
+    "\n",
+    "$$  \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
+    "\\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\boldsymbol{w} \\rvert \\rvert_2^2 \n",
+    "= \\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}(\\theta) + \\lambda \\sum_{ij} w_{ij}^2,$$  \n",
+    "\n",
+    "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n",
+    "\n",
+    "In order to train the model, we need to calculate the derivative of\n",
+    "the cost function with respect to every bias and weight in the\n",
+    "network.  In total our network has $(64 + 1)\\times 50=3250$ weights in\n",
+    "the hidden layer and $(50 + 1)\\times 10=510$ weights to the output\n",
+    "layer ($+1$ for the bias), and the gradient must be calculated for\n",
+    "every parameter.  We use the *backpropagation* algorithm discussed\n",
+    "above. This is a clever use of the chain rule that allows us to\n",
+    "calculate the gradient efficently."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c0a8db3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Matrix  multiplication\n",
+    "\n",
+    "To more efficently train our network these equations are implemented using matrix operations.  \n",
+    "The error in the output layer is calculated simply as, with $\\boldsymbol{t}$ being our targets,  \n",
+    "\n",
+    "$$ \\delta_L = \\boldsymbol{t} - \\boldsymbol{y} = (n_{inputs}, n_{categories}) .$$  \n",
+    "\n",
+    "The gradient for the output weights is calculated as  \n",
+    "\n",
+    "$$ \\nabla W_{L} = \\boldsymbol{a}^T \\delta_L   = (n_{hidden}, n_{categories}) ,$$\n",
+    "\n",
+    "where $\\boldsymbol{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  \n",
+    "Since we are going backwards we have to transpose the activation matrix.  \n",
+    "\n",
+    "The gradient with respect to the output bias is then  \n",
+    "\n",
+    "$$ \\nabla \\boldsymbol{b}_{L} = \\sum_{i=1}^{n_{inputs}} \\delta_L = (n_{categories}) .$$  \n",
+    "\n",
+    "The error in the hidden layer is  \n",
+    "\n",
+    "$$ \\Delta_h = \\delta_L W_{L}^T \\circ f'(z_{h}) = \\delta_L W_{L}^T \\circ a_{h} \\circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,$$  \n",
+    "\n",
+    "where $f'(a_{h})$ is the derivative of the activation in the hidden layer. The matrix products mean\n",
+    "that we are summing up the products for each neuron in the output layer. The symbol $\\circ$ denotes\n",
+    "the *Hadamard product*, meaning element-wise multiplication.  \n",
+    "\n",
+    "This again gives us the gradients in the hidden layer:  \n",
+    "\n",
+    "$$ \\nabla W_{h} = X^T \\delta_h = (n_{features}, n_{hidden}) ,$$  \n",
+    "\n",
+    "$$ \\nabla b_{h} = \\sum_{i=1}^{n_{inputs}} \\delta_h = (n_{hidden}) .$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "0bf3739e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Old accuracy on training data: 0.1440501043841336\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "New accuracy on training data: 0.09951287404314545\n"
+     ]
+    }
+   ],
+   "source": [
+    "# to categorical turns our integer vector into a onehot representation\n",
+    "from sklearn.metrics import accuracy_score\n",
+    "\n",
+    "# one-hot in numpy\n",
+    "def to_categorical_numpy(integer_vector):\n",
+    "    n_inputs = len(integer_vector)\n",
+    "    n_categories = np.max(integer_vector) + 1\n",
+    "    onehot_vector = np.zeros((n_inputs, n_categories))\n",
+    "    onehot_vector[range(n_inputs), integer_vector] = 1\n",
+    "    \n",
+    "    return onehot_vector\n",
+    "\n",
+    "#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)\n",
+    "Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)\n",
+    "\n",
+    "def feed_forward_train(X):\n",
+    "    # weighted sum of inputs to the hidden layer\n",
+    "    z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
+    "    # activation in the hidden layer\n",
+    "    a_h = sigmoid(z_h)\n",
+    "    \n",
+    "    # weighted sum of inputs to the output layer\n",
+    "    z_o = np.matmul(a_h, output_weights) + output_bias\n",
+    "    # softmax output\n",
+    "    # axis 0 holds each input and axis 1 the probabilities of each category\n",
+    "    exp_term = np.exp(z_o)\n",
+    "    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
+    "    \n",
+    "    # for backpropagation need activations in hidden and output layers\n",
+    "    return a_h, probabilities\n",
+    "\n",
+    "def backpropagation(X, Y):\n",
+    "    a_h, probabilities = feed_forward_train(X)\n",
+    "    \n",
+    "    # error in the output layer\n",
+    "    error_output = probabilities - Y\n",
+    "    # error in the hidden layer\n",
+    "    error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)\n",
+    "    \n",
+    "    # gradients for the output layer\n",
+    "    output_weights_gradient = np.matmul(a_h.T, error_output)\n",
+    "    output_bias_gradient = np.sum(error_output, axis=0)\n",
+    "    \n",
+    "    # gradient for the hidden layer\n",
+    "    hidden_weights_gradient = np.matmul(X.T, error_hidden)\n",
+    "    hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
+    "\n",
+    "    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient\n",
+    "\n",
+    "print(\"Old accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))\n",
+    "\n",
+    "eta = 0.01\n",
+    "lmbd = 0.01\n",
+    "for i in range(1000):\n",
+    "    # calculate gradients\n",
+    "    dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)\n",
+    "    \n",
+    "    # regularization term gradients\n",
+    "    dWo += lmbd * output_weights\n",
+    "    dWh += lmbd * hidden_weights\n",
+    "    \n",
+    "    # update weights and biases\n",
+    "    output_weights -= eta * dWo\n",
+    "    output_bias -= eta * dBo\n",
+    "    hidden_weights -= eta * dWh\n",
+    "    hidden_bias -= eta * dBh\n",
+    "\n",
+    "print(\"New accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "33e198f3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Improving performance\n",
+    "\n",
+    "As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.  \n",
+    "In order to obtain a network that does something useful, we will have to do a bit more work.  \n",
+    "\n",
+    "The choice of *hyperparameters* such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a *grid-search* is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates $\\eta = 10^{-6}, 10^{-5},...,10^{-1}$ with different regularization parameters $\\lambda = 10^{-6},...,10^{-0}$.  \n",
+    "\n",
+    "Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an *iteration*, and a full training period\n",
+    "going through the entire dataset ($n/M$ batches) an *epoch*.\n",
+    "\n",
+    "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers.  \n",
+    "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "932f6c5e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Full object-oriented implementation\n",
+    "\n",
+    "It is very natural to think of the network as an object, with specific instances of the network\n",
+    "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "91e351de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "class NeuralNetwork:\n",
+    "    def __init__(\n",
+    "            self,\n",
+    "            X_data,\n",
+    "            Y_data,\n",
+    "            n_hidden_neurons=50,\n",
+    "            n_categories=10,\n",
+    "            epochs=10,\n",
+    "            batch_size=100,\n",
+    "            eta=0.1,\n",
+    "            lmbd=0.0):\n",
+    "\n",
+    "        self.X_data_full = X_data\n",
+    "        self.Y_data_full = Y_data\n",
+    "\n",
+    "        self.n_inputs = X_data.shape[0]\n",
+    "        self.n_features = X_data.shape[1]\n",
+    "        self.n_hidden_neurons = n_hidden_neurons\n",
+    "        self.n_categories = n_categories\n",
+    "\n",
+    "        self.epochs = epochs\n",
+    "        self.batch_size = batch_size\n",
+    "        self.iterations = self.n_inputs // self.batch_size\n",
+    "        self.eta = eta\n",
+    "        self.lmbd = lmbd\n",
+    "\n",
+    "        self.create_biases_and_weights()\n",
+    "\n",
+    "    def create_biases_and_weights(self):\n",
+    "        self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)\n",
+    "        self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01\n",
+    "\n",
+    "        self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)\n",
+    "        self.output_bias = np.zeros(self.n_categories) + 0.01\n",
+    "\n",
+    "    def feed_forward(self):\n",
+    "        # feed-forward for training\n",
+    "        self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias\n",
+    "        self.a_h = sigmoid(self.z_h)\n",
+    "\n",
+    "        self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias\n",
+    "\n",
+    "        exp_term = np.exp(self.z_o)\n",
+    "        self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
+    "\n",
+    "    def feed_forward_out(self, X):\n",
+    "        # feed-forward for output\n",
+    "        z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias\n",
+    "        a_h = sigmoid(z_h)\n",
+    "\n",
+    "        z_o = np.matmul(a_h, self.output_weights) + self.output_bias\n",
+    "        \n",
+    "        exp_term = np.exp(z_o)\n",
+    "        probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
+    "        return probabilities\n",
+    "\n",
+    "    def backpropagation(self):\n",
+    "        error_output = self.probabilities - self.Y_data\n",
+    "        error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)\n",
+    "\n",
+    "        self.output_weights_gradient = np.matmul(self.a_h.T, error_output)\n",
+    "        self.output_bias_gradient = np.sum(error_output, axis=0)\n",
+    "\n",
+    "        self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)\n",
+    "        self.hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
+    "\n",
+    "        if self.lmbd > 0.0:\n",
+    "            self.output_weights_gradient += self.lmbd * self.output_weights\n",
+    "            self.hidden_weights_gradient += self.lmbd * self.hidden_weights\n",
+    "\n",
+    "        self.output_weights -= self.eta * self.output_weights_gradient\n",
+    "        self.output_bias -= self.eta * self.output_bias_gradient\n",
+    "        self.hidden_weights -= self.eta * self.hidden_weights_gradient\n",
+    "        self.hidden_bias -= self.eta * self.hidden_bias_gradient\n",
+    "\n",
+    "    def predict(self, X):\n",
+    "        probabilities = self.feed_forward_out(X)\n",
+    "        return np.argmax(probabilities, axis=1)\n",
+    "\n",
+    "    def predict_probabilities(self, X):\n",
+    "        probabilities = self.feed_forward_out(X)\n",
+    "        return probabilities\n",
+    "\n",
+    "    def train(self):\n",
+    "        data_indices = np.arange(self.n_inputs)\n",
+    "\n",
+    "        for i in range(self.epochs):\n",
+    "            for j in range(self.iterations):\n",
+    "                # pick datapoints with replacement\n",
+    "                chosen_datapoints = np.random.choice(\n",
+    "                    data_indices, size=self.batch_size, replace=False\n",
+    "                )\n",
+    "\n",
+    "                # minibatch training data\n",
+    "                self.X_data = self.X_data_full[chosen_datapoints]\n",
+    "                self.Y_data = self.Y_data_full[chosen_datapoints]\n",
+    "\n",
+    "                self.feed_forward()\n",
+    "                self.backpropagation()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e8c2feb6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Evaluate model performance on test data\n",
+    "\n",
+    "To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.  \n",
+    "We measure the performance of the network using the *accuracy* score.  \n",
+    "The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of $1$.  \n",
+    "\n",
+    "$$ \\text{Accuracy} = \\frac{\\sum_{i=1}^n I(\\tilde{y}_i = y_i)}{n} ,$$  \n",
+    "\n",
+    "where $I$ is the indicator function, $1$ if $\\tilde{y}_i = y_i$ and $0$ otherwise."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "1534af1b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Accuracy score on test set:  0.9444444444444444\n"
+     ]
+    }
+   ],
+   "source": [
+    "epochs = 100\n",
+    "batch_size = 100\n",
+    "\n",
+    "dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
+    "                    n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
+    "dnn.train()\n",
+    "test_predict = dnn.predict(X_test)\n",
+    "\n",
+    "# accuracy score from scikit library\n",
+    "print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
+    "\n",
+    "# equivalent in numpy\n",
+    "def accuracy_score_numpy(Y_test, Y_pred):\n",
+    "    return np.sum(Y_test == Y_pred) / len(Y_test)\n",
+    "\n",
+    "#print(\"Accuracy score on test set: \", accuracy_score_numpy(Y_test, test_predict))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "85627e28",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Adjust hyperparameters\n",
+    "\n",
+    "We now perform a grid search to find the optimal hyperparameters for the network.  \n",
+    "Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around $98\\%$ ($2\\%$ error rate)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "19382903",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.11666666666666667\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.20833333333333334\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.12222222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.14722222222222223\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.17777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.16111111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.20277777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.5305555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.5944444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.5888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.6111111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.5222222222222223\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.5555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.8055555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.85\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.85\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.875\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.8666666666666667\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.8638888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.9555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.925\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9472222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.9277777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.9472222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9305555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.9555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.7694444444444445\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.19166666666666668\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.08611111111111111\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.08611111111111111\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09166666666666666\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "  exp_term = np.exp(self.z_o)\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
+      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.07777777777777778\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "eta_vals = np.logspace(-5, 1, 7)\n",
+    "lmbd_vals = np.logspace(-5, 1, 7)\n",
+    "# store the models for later use\n",
+    "DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
+    "\n",
+    "# grid search\n",
+    "for i, eta in enumerate(eta_vals):\n",
+    "    for j, lmbd in enumerate(lmbd_vals):\n",
+    "        dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
+    "                            n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
+    "        dnn.train()\n",
+    "        \n",
+    "        DNN_numpy[i][j] = dnn\n",
+    "        \n",
+    "        test_predict = dnn.predict(X_test)\n",
+    "        \n",
+    "        print(\"Learning rate  = \", eta)\n",
+    "        print(\"Lambda = \", lmbd)\n",
+    "        print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
+    "        print()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12bc42df",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Visualization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "ec0dc239",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_31871/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "  return 1/(1 + np.exp(-x))\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_74_1.png"
+      }
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_74_2.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# visual representation of grid search\n",
+    "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
+    "import seaborn as sns\n",
+    "\n",
+    "sns.set()\n",
+    "\n",
+    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "\n",
+    "for i in range(len(eta_vals)):\n",
+    "    for j in range(len(lmbd_vals)):\n",
+    "        dnn = DNN_numpy[i][j]\n",
+    "        \n",
+    "        train_pred = dnn.predict(X_train) \n",
+    "        test_pred = dnn.predict(X_test)\n",
+    "\n",
+    "        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
+    "        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
+    "\n",
+    "        \n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Training Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Test Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4dd39506",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## scikit-learn implementation\n",
+    "\n",
+    "**scikit-learn** focuses more\n",
+    "on traditional machine learning methods, such as regression,\n",
+    "clustering, decision trees, etc. As such, it has only two types of\n",
+    "neural networks: Multi Layer Perceptron outputting continuous values,\n",
+    "*MPLRegressor*, and Multi Layer Perceptron outputting labels,\n",
+    "*MLPClassifier*. We will see how simple it is to use these classes.\n",
+    "\n",
+    "**scikit-learn** implements a few improvements from our neural network,\n",
+    "such as early stopping, a varying learning rate, different\n",
+    "optimization methods, etc. We would therefore expect a better\n",
+    "performance overall."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "d9dbb807",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.18333333333333332\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.18611111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.13055555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.24444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.23333333333333334\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.12777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.1527777777777778\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9111111111111111\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.8888888888888888\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.8305555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.8888888888888888\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.8805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.0001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.8944444444444445\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.975\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.9777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.9805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.9805555555555555\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.9777777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.9444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9861111111111112\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.9888888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.01\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.9722222222222222\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.9527777777777777\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.9027777777777778\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.8583333333333333\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.9055555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.8805555555555555\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.8722222222222222\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  0.1\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.8666666666666667\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.08611111111111111\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.17777777777777778\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.08333333333333333\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.08888888888888889\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09444444444444444\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on test set:  0.17222222222222222\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on test set:  0.11666666666666667\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on test set:  0.1388888888888889\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on test set:  0.11388888888888889\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  10.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on test set:  0.10555555555555556\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on test set:  0.09444444444444444\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sklearn.neural_network import MLPClassifier\n",
+    "# store models for later use\n",
+    "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
+    "\n",
+    "for i, eta in enumerate(eta_vals):\n",
+    "    for j, lmbd in enumerate(lmbd_vals):\n",
+    "        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n",
+    "                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n",
+    "        dnn.fit(X_train, Y_train)\n",
+    "        \n",
+    "        DNN_scikit[i][j] = dnn\n",
+    "        \n",
+    "        print(\"Learning rate  = \", eta)\n",
+    "        print(\"Lambda = \", lmbd)\n",
+    "        print(\"Accuracy score on test set: \", dnn.score(X_test, Y_test))\n",
+    "        print()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "214af3ab",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Visualization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "d57415ac",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_78_0.png"
+      }
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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OHTjp89ykNc+rcPH8Wba5pdEzOnX8TEDanlcwC1ZgkIDYoGaDcvrf+7dq8XcbNf6d+arduLwGPHS1HA5DUz768S+3rVi9pIZ9eLtcYc4szzVsVUXPvNtPi+du1GdvfqcKVUvq9oevVoHCMfpgxFc59Glyn4z4zt2o8e/OV+1GFTTgwU6XEN8B2cb3+v6tdM9T12rJ9xs1+vW5yl8wWv3v66iK1Urq+Qcm5dCnyZ1qNq2k/00YosWzVmv8S7NVu3kVDXjqejkcDk15a+5fbluxdpyGfX5vtjHudntb3ffaLfri3e+07setqt64ogYN66XI6HBNfdu/A5e8oFadOA1/6Sb9uGiLxn76o+rUK6s7BrWX4TA0ecKybLcZcv/V6tS5riaNX6rtWw+rarWSuvWONipRsoDeeOXbLOvXrV9WPXo1zemPkmvVqlNGw1+9WT8t3KLPPv5RdeqX0x2Dr5TDYWjyuOxj/J+HrlanLvU0aexS7dhySFWql9Std7ZV8ZIF9OZL30iSrr2hkR4c2lVTJizT2l92q0btOA2+r5MiI8P1+fjsXzcvqtm0kp6beK8Wz1qtcS/OVp3mVTTg6R4yHA5NeWvOX25bsXYZDZ98f/Z9xB3tdP9r/TT1nbkZfcTdw29UZHSEpr79131PXlOzcQX9b/QgLf56nca/9q1qN62kAY91s77rRs7/y20r1iytYWMHZxvjgkXzqXDx/Ppo2ExtW7Pb57mEU+cC+hmA80hAbNDv3g76fdthvf74F5KkNUt3yOVy6sZB7TVj7FKlprizbOMKc6p7v5a69YFO2T4vSZ1uaKzjh+P12mNT5fWaWrd8pwoWidENA1rr45e/CZmz9P2GXKXftx7W6098KUlas/Q36+zwXe3+Pr73d8z2eYfDUL97r9LaZb/pxYc/z1i+c8shffT1Q2rYsorWrdiZcx8ql+k3tJt+33RAr987VpK0ZtEWax9+4BrN+GCBUpPTsmzjCnOq+11X6tYnuis1OTXb173xgWv006zV+uz5WZKkX5dsV1zlEup+15UhlYDcdnsb7dp5VK+8YJ04WPXL73K6HOrTr6WmTV2p1FTffTRfvkhde30jffrhIn0x5WdJ0rq1eyRJdw/poE8//EHx8YkZ60dGhmnoE9fpxImzKp7NWc5QcOudbbTrtyN6ZfhsSdLqlb/L5XLo5v6tNO3zi8S4R2N9OmqhvpycHuM1eyRJd9/XUaM/WKT404nqc+sV+nHBZo3+4IeMdcqULazrezcJqQSk/9Dr9Pum/XptyBhJ0ppFm+UMc+qmBztrxgfzL95HDLpKtz1x/UX7iJse6KyfZq3SZ8/PlCT9umSbylQuoesHXRVyCUi/hzvr9y0H9fpDEyVJa37cZvXDQzpqxic/XjzGd7TVrf/tmu3zklS5Tpwkafnc9Tp28FTOfQDgT7gGJIeFhTlVr1klLZu/2Wf50u83KTomQnUaV8x2u6Ztq6vfvR009aMfNOaN7DvZsHCXkpNS5f3TlAwJpxIVFu5SVExE4D5ELpYR3wWZ4jvvfHwrZLtd07bV1G/IVZr68Y8a80bWA92CRWKVr0C0Vv64zWf5vl3HFH/ynJq1rxGwz5DbhYW7VK9VNS37dp3P8qVfr1V0bKTqtKiS7XZNO9ZRv6HdNPXtuRqTfvCQ2f/dPFJjhs3wWeZOdSssPHTOjYSFOVWvQXktXey7ry35cZuioyNUt37ZLNvExEbom9lrtXzZDp/lB9LLKkqVLuizfPCQDjp58qy+n7M+sI2/TISFOVWvYXkt/Wm7z/LFP2xVdEyE6jYol2WbmNhIfTNrjVYszRTj/b4xfurhyfpklG85UJrbE1r7cLhLda+opmXfZO4j1qT3EVWz3a5px7rqN/RaTXlrjsYMn5HtOs/c9I5GPzfdZ1laWmj1EZIUFu5UvRZVtWzuBp/lS+est2LcrFK22zW9qpb6PdRZU0fO05gXs6+MqFSrjM6cTiT58JNHRq78d7khAclhJcsWVli4Swf3/uGz/NA+63FchaLZbrdj4wEN6Piqpnz040VHMr6etEKlyxVRr4FtFJMvUjXql1WP267QLz9t09n4pMB+kFwqI757fGuGD+2zHl88vgc1oNNrVnw9WeN77kyy3GkeFY8r6LM8Nn+kYvNHqmRcocB8gMtAyfJFFRYRpoO7jvosP7T7uCQprnKJbLfbsW6vBjR6WlPemnvRfXj/b0cyapFjC0brmv5XqMNNLfT1mB8D9wFyuVKlCyo83JVxYHvewQPWwUCZskWybHPkcLzefeu7LNu0bltdaWken+WNmlRUx2vq6rWXvpFphub8kedjfHBfpn4iI8aFs2xz5PBpjXz9Ox3YlynG7Wr4xHjf3hM6diRekjVq0uW6BurUuZ6+mr46Jz5KrlSyfFGFZ9dH/P53fcQeDWj4pKa8NUced/bXLWbuIzr3b62ON7XU16N/COAnyP1KliuqsAiXDv5+zGf5oT3pMa5YPNvtdqzfpwGthmnKyPnZftdJUuXacTobn6hnPh6oaZtf1oxtr+qJ9weoUIiOlsIeQT+F4Ha7NW/ePK1evVqHDh1SamqqoqKiVLJkSTVp0kSdOnWSyxX0Zv5jMfmjJEmJZ5N9liees4abo2OzH6k4cSzhb197wy+/a9qYxbpraFfdNbSrJGnnloN65b9T/k2TLysx+SIlSYnnAhvflOQ0Lf5ug7rf0lL7dh7T8gWbVaBwrO558lq53V5FRocHoPWXh5gC6fvwmUwxTt+no9N/B5mdOHLa7/eo1ayy3vh2qCRpx6979dWnP156Qy9TMbHn9+EUn+WJSdbjaD/3tTbtqqvj1XU1c9ovOpv+u4mJidB/H++mcWMW62Cmi05Dyfl+4tw53zKfxMT0GPs5Yty6fQ117FxXM7/4RWcz/T3UrltGb390uyRpx9ZDmj0tdC5Cjy0QLSnn+4g35zwuSdrx6x7N/jS0EpCLHkucTd+HLxrj+L997Uq14lS0VEF99/kKzfz0R5WrUkL9H+2qV7+8X/d1fk0pSdmXxwH/RlBHQPbt26du3brpqaee0rZt2xQZGalixYopLCxMW7du1ZNPPqnu3bvr0KFDwWzmv+Iw0ofFLnLi0fsv7mhz/3M91HtgW03+YJEeu+1jvfnUNOUvGKMRnwxURGTYP37dy4nDkXPxHTlsthZ9/aseHH6Dvvz5Wb037T5tXb9POzYdUHJi6HTIDkd6N3GRs+f/JsbnHdn7hx67/g29Mni0YvJH6d35T6pgsXz/+nUvB+f7iIsNTvgzatGmXQ09+X89tOHXvfr0owsHZv+5v5OOHz+j6V+sDEhbL1cX+uGL7MP+xPjKGnryuR7asG6vRn+QdQamI4dP69Eh4/Xi/2YqJjZS74++UwULxfyrdl8uDMf5fTj7OJqB6CP2/aGh3V/Xy4M/VUz+KI1c8HTI9BFSzn7XvfnoZD3c/U198f4Cbf7ld82dvEIvDB6jMpWKq2Pv0J244mK8ppEr/11ugjq0MGzYMJUpU0bTpk1TvnxZO5KEhAQ9/PDDGj58uD788MMgtPDfO3vGKoXKfCY+OsY6q5n5bIa/ihTPr843NtXUj3/UhHet2S82rtqtHZsO6MOvHtLVPZvo68kr/kXLLw/nz0JmPoOZEd8zKVm28VdyYqre/r8Z+vClb1S8dEEdPXhKKUlpurpnY23Y//s/b/Rl5mz6xczR+aJ8lkefP3Of8O/L/U4ejdfJo9aZuu1rd+vTlcPVuX/rv51hKy84P1qRZR+Osh6fO/vX+3Cvm5rp7v900Ppf9+rZp75UWvoU3M1bVtGVHWppyKAxMhyGDElG+oG4w2nI9JoXTXrymovGOPp8jP+6H+7Vp7kG3dtBG9bt1bOPf5ER4z878cdZnfjjrCRp25ZDGjt1iLp2b3DRGbbyknMZfYTvWfjzfcS5MwHoI47E62T62fzta3Zr9C/Pq3P/Nn87w1ZecTa9n80aY2sfTvwXMd6WPoHFn21ZvVtn4xNVsWbcP35d4K8ENQFZs2aNpk6dmm3yIUn58+fX0KFD1a9fP5tbFjiH952Ux+1RqXK+ddyly1nXJuzbdSy7zf5WsdIF5XA4tGXtXp/le387qvhT51S+avb1oHlNRnzLZ46v9fifxleSmrWrrrMJSdqybp/27bRep0DhGBUrWUA7t16+o3KX6vCe41aMKxbzWV46/fG+HYf/0etGxUSoRef62rZ2tw6nX09ivd8fOns6UUVLh8Z1NocOnZLH7VVcpuuK4spYj/fu+SO7zSRJ9z14tXr0aqofF23RKy985XNg3LZ9DUVEhGn0+MFZtpv3w1P6fu56vZY+lWxed+igFePSZXxjfP7xvt0Xj/G9D1+jHjc21Y8LNuvV531jHBUdrpatq2nb5oM69KcLeA8fPKWzZ5JULERq6A+l9xGlK/l+75SulN5HbP+HfURseh+xJnMfcVxnTyeqWAhdi3d47x/p33W+1zWWrpAe49+O/KPXjckfpSu61NO2tXu07zffa3hc4S4lnDr7zxoM/I2glmDlz59fx4799QHioUOHFBmZfW3j5SAt1a2Nq/foik51fJa3vqaOzsQnafuG/f/odQ/vPSGP26PamWZ5iqtQVAUKxejIgdCYzSIjvh1r+yxvfXV6fDf+s/hKUtebm2dcW3Nej9uukNdj6pdMs2PlZWkpbm1c8Zuu6NbQZ3nr6xrpzOlz2p7N2TN/eL1ePfT2rbrxvqt9lldrUF75C8dq9+YD/7TJl5W0VI82bNin1m2r+yxv076GzpxJ0raLJLt33t1ePXo11bSpKzXiuZlZzsqP/2yJhgwa4/Pv26+sWYqGDBqj8Z8tyZkPlAulpXq0Yf0+tc40e13bK2vqTEKStm3JPsYD77lSPW5sqmlTftYLz2aNsdfj1aNPXqub+rf0WV6tZinlLxCtXTt9D+jyqov3EY3T+4jdF9nyr3k9ph5+e4BuvP8an+XVGlp9xO8h0kdI6TFeuUtXdKnns7x11/o6czpR23/d949e153q1r0jbtSNQzr6LG95TV1FRoVrQwhNN++vYM92lVdmwQrqCEjv3r315JNP6oEHHlDz5s1VqlQphYeHKzU1VUePHtUvv/yi119/Xb179w5mM/+1KR8u0otj7tRTb92ieTNWq2bD8uo1sI3GvPGdUlPcio6JULkqxXV430nF+3nTn/hT5zRr/DL1HthWkrRu+U4VL11Q/e7toKOHTum7L3/JyY+Uq0z56Ae9OHqgnnqrr+bNWKOaDcpZ8X3z+wvxrVxch/f7H19J+mricr3w6UANfqKbfv5hq+o3r6w+d7fX1E9+DJkE77wpb87Vi9Mf1FOjB2ne5OWq2bSSet3XSWOGz1RqcpqiYyNVrnopHd5zXPEn/DtjlpKUpi9Hfq++j3ZVwqlz+vWnrYqrXEL9hl6rXZv2a97nF79DdV4zafxSvfpmP/3fsJ76bs561a5TRjf1aalPP1yk1FS3oqPDVb5CUR06eFrx8YmqXKWEbr6llbZvPaSfftiimrVK+7ze3j1/6OiReB3NdAFqi1bWlMk7/uEZ6cvZ5LFL9co7/fR/I3rqu2/Wq1bdMrrxlpb6dNTCCzGuWEyHDp5S/OlEVa5aQjf3t2K8eOFW1aztW4qyd/dxJSamaurE5ep3RxslxCdp3ardiitXWLfd2Va7dhzR99+GzrTHn7/5rV6a/rCeHj1Y309eplpNK6n3fVdrzPAZ/6KPSNUXI7/TLY9205mT57Tup62Kq1JC/Ydep10b92ve5Lxf3vZnU96dpxc/H6KnPrhd86auVM0mFdXrnqs05sWv02McoXJVS+rw3j8Uf9K/77qU5DRN+3Chbnmos07/cUZrftymCjVLq//DnbVywWb9mmkaaiBQDDOI8zKapqn3339fn332mRITE7M8HxMTo379+unBBx+8cCHsv9Cl5pP/+jX+qVYda6n/fR1VpmIx/XE0Qd9MXqEZY5dKkuo2rahXx9+tN578Ugtmrc2ybccejfToSzdqQIdXdOzQaZ/netx2hbre3EwlyxTWyeNntHbZbxr39rxLOtAOGCN4GXirDrXU/74OF+L7+c++8R03SG88Ne3i8X2xtwZ0fDVLfNt1rae+91ypEnGFdOzQaX07ZaW+mhTEa2uOB28mo1ZdG6j/Y9eqTJUS+uPwaX0z5ifN+GCBJKluq2p6dfYjeuP+cVowJWt8OvZpqUdHDtCARk/r2P4LU6EahqGuA9qo2x3tVLpiMZ05najl367TuBdnZ5lRxw5pNbPec8MuV7SprgED26hM2SI68ccZzZ65RtOmWheP129QTm+8e6teffFrzftugwYMbKtbb29z0dd69IEJWp/NGdHb7mij2+5oq45tX8ixz/F3DHfwLjy5om113XZXW5UpV0Qnjp/RVzNWa9rnVozrNSyvN96/Va+N+Erz5mzQgLvaqf/Av4jxvRO0Yd1eGYbUrUcjde/ZRKXLFNKZhCQt/XG7Pvv4xywzm9nFueOfnQ3/t1p1baBbH++uuColdOLwaX095kfNGGVdo1jvimp6dfZ/9cZ9n2l+Nn1Epz4t9eh7d2hAwyd1NHMfcXtbXXtH+/Q+4pyWfXO+jwjOdPNGVNTfr5RDWnWup/6PdFGZSsX1x5HT+mb8Us342Jp4om6LKnr1y/v1xiOTtCCbk5Adb2ymR9/spwEth2VMbSxZMe522xXqdmtrlSpfRGdOJeqHWWs08c25F715YU6bu/+doLyvP9buy3rfoNygUbng/N3/U0FNQM5LS0vT1q1bdfToUSUlJSkyMlIlS5ZUjRo1FB4euOlOg5mAhIQgJiAhI4gJSCgIZgISKoKZgISKYCUgoSKYCUioyM0JyKp9FYLdhGw1Lbcn2E24JLniBhthYWGqV6/e368IAAAA4LLGndABAAAA2CZXjIAAAAAAud3leNO/3IgREAAAAAC2IQEBAAAAYBtKsAAAAAA/XI43/cuNGAEBAAAAYBsSEAAAAAC2oQQLAAAA8IPH5Nx9IBBFAAAAALYhAQEAAABgG0qwAAAAAD94OXcfEEQRAAAAgG1IQAAAAADYhhIsAAAAwA/ciDAwGAEBAAAAYBsSEAAAAAC2oQQLAAAA8AM3IgwMoggAAADANiQgAAAAAGxDCRYAAADgBy+zYAUEIyAAAAAAbEMCAgAAAMA2lGABAAAAfvBw7j4giCIAAAAA25CAAAAAALANJVgAAACAH7gRYWAQRQAAAAC2IQEBAAAAYBtKsAAAAAA/eDl3HxBEEQAAAIBtSEAAAAAA2IYSLAAAAMAPHtMIdhPyBEZAAAAAANiGBAQAAACAbSjBAgAAAPzg4dx9QBBFAAAAALYhAQEAAABgGxIQAAAAALbhGhAAAADAD16Tc/eBQBQBAAAA2IYEBAAAAIBtKMECAAAA/MA0vIFBFAEAAADYhgQEAAAAgG0owQIAAAD84DGNYDchT2AEBAAAAIBtSEAAAAAA2IYSLAAAAMAPXs7dB0RIJSDPfTcl2E3I0054Y4LdhDzvnDci2E3I0/am7g52E/K8WpEHg92EPC/NDKmvdttFGynBbgJw2SONAwAAAGAbTpMAAAAAfvCYnLsPBKIIAAAAwDYkIAAAAABsQwkWAAAA4AevuBFhIDACAgAAAMA2JCAAAAAAbEMJFgAAAOAHZsEKDKIIAAAAwDYkIAAAAABsQwkWAAAA4AcP5+4DgigCAAAAsA0JCAAAAADbUIIFAAAA+MFrciPCQGAEBAAAAIBtSEAAAAAA2IYSLAAAAMAPzIIVGEQRAAAAgG1IQAAAAADYhhIsAAAAwA9ek3P3gUAUAQAAANiGBAQAAACAbSjBAgAAAPzgETciDARGQAAAAADYhgQEAAAAgG0owQIAAAD8wCxYgUEUAQAAANiGBAQAAACAbSjBAgAAAPzALFiBwQgIAAAAANuQgAAAAACwDSVYAAAAgB+YBSswiCIAAAAA25CAAAAAALANJVgAAACAHzyUYAUEUQQAAABgGxIQAAAAALahBAsAAADwg5cbEQYEIyAAAAAAbEMCAgAAAMA2lGABAAAAfmAWrMAgigAAAABsQwICAAAAwDaUYAEAAAB+8JrMghUIjIAAAAAAsA0JCAAAABCivF6v3n33XbVp00b169fXwIEDtXfv3ouuf/z4cT3yyCNq3ry5mjdvrgcffFBHjhy5pPckAQEAAAD84JEjV/77N0aNGqUpU6ZoxIgRmjp1qgzD0KBBg5Samprt+g8//LAOHz6szz77TJ999pmOHDmiIUOGXNJ7cg2ITTasMjRtrFOH9hnKV0C6qptH1/bxyrhIKWFaqjRzglPLFzp0JkEqVdZU195etergzXb9pHPS0/eE6YZbPWpzdfbr5GVbV3s1Z5xXR/eZii0gterqUIebHTIuEmCPx9QP07xa+b1XCSekonFSx5udatjO94/4l3le/TDdoz8OSfkLS006OnR1X4ecrtCrAd2x2q0F41N1fL9X0fkNNesaprY3hf1ljJdOT9PaeWlKOGGqSJxD7W4MU912YZKkU0e9euOOxIu+X8OOLvV6JDJHPktutH9tolZPOq1T+9MUVcChmtfkU/1eBS4aX6/H1IZZ8dq+4KwST3qUv5RLDXoXVOXWMT7rbZt3Rhu/TtCZo27FFnWqVpf8qn1tvou+bl5GP5Gztq/26LvxaTq2z1RMAUMtujp15U2uv4zv4ulu/fK9RwknTBWNM3TlTS41aOd7aLJpuUcLP0/T8QOm8hUy1KiD9bqusNCKryRtWW3q63GmjuyTYgtIrbsauvpm/WWMF06TVnxvKv6EVCxOuvpmQ43b+a7/8zxTC6ebOn5IKlBYatZR6tzXCLl9OBSlpqZqzJgxGjp0qNq1aydJeuutt9SmTRvNnz9f3bp181k/ISFBq1at0gcffKBatWpJku6++24NGTJEp06dUqFChfx6XxIQG/y22dBb/3OpeTuvet/u0Y5NDk0b65RpSt1vyT5ZGPWiS7+uNNSlt1e1Gnq1d6ehz95x6kyCdM0NvtucTZDe+p9LfxwNzY5i9xavRj/nUYO2hroOcGr3JlNzxnllmlKnvs5st/l+glcLvvDq6lscqljL0IZlpsa/5JHhkBq0sQ4ufprl0awPvarf2lD3uxw6Gy99N9Gjw7tNDXw2tP509m3xaNLwZNVp41LH28K1d7NHC8anyjSl9n3Cs91m0cRULf4yTVf2DVe5Wg5tWebW1FdSZDgN1WntUr7Chga/GZVlu5+/TtOmJW41viYspz9WrnF0W7LmvXhMla6IUZN+BXVka4pWTTot05Qa3lgw223WTDmt9dPj1fCmgipZM0K7VyRq0evHZTikSq2sJGTL3AQt++ik6vfMr7j6UTq2I0U/f3ZSacnei75uXkU/kbP2bPFo7LBU1W/rVOfbnNq92avvx7lleqUOfbP/W54/0a0fvnCr4y0uVajl0MalHk1+OU0Oh6F6bazfyY61Hk0Ykap6bZ3qcodTR/Z49d1Yt87Fm+oxJPu+J6/6fYupj54z1aitdN0AQ7s2mfpmnCnTNNS5b/bbzJlgat4XUpdbDFWqJf26zNRnL5lyOKSGbaxjhh9mmZr+oamGraUedxk6Fy99O9HUwd2m7n42NI8rQsm2bdt07tw5tWjRImNZ/vz5VatWLa1atSpLAhIREaHo6GjNmjVLzZo1kyTNnj1bFSpUUIECBfx+39DpHYNo5kSnylc2dc/jHklSvaYeeTzSN1Od6tzLq/AI3/X37DS0ZrlDve9wq3tfK9mo08hURKQ09VOnWnfyKibWWnfNckMTR7mUnGTnJ8pdvp/oVVwlQ/0fs3bnmk0kj0da+IVX7Xo6FB6RtQNdOc+rRu0Nde5vfclVbyQd3GVq2ddeNWjjkNdjat5Er6o1MnT7Mxf+TMpWNfTKYLe2r/WqeqPQqWBcNDlVJSs5dONQa0SiWhOXvB5p8ZepuuKGMIVlE+O1892q186lq/pZBwlVGrp0aFeiVn6TpjqtrbOXZWv4Hvgd3OHRpiVudRoQrgq1sz8ozIvWTDmtIhXDdeXDxSRJZRtFy+s2tX56vOp2zy9XRNZ9bceCs6rcJkaN+xSUJMXVj9KJ31O0Zc4ZVWoVI9M0tX5GvCpdEa1mtxXOWCf+UJo2zzkTcgkI/UTOWjDJrdKVDPUZav29V2/ilNct/fClW217urLtI1bNc6the6c69bMSlKoNnTq0K1nLv3FnJCCr53tUsJihvkPD5HAaqtbIqbOnpSUz3brubjOkztDPmWiqTCVpwGPWPlWriSGPx6v5X5i6qqey3YdXzJOatJe69reeq9HI0IFdXi3+2lTDNoa8HlNzJ5qq0Ui685kL+2rZqtILg01tXWuqZqPQibE/cussWB06dPjL5xcuXJjt8vPXbpQqVcpnefHixXX48OEs60dEROiFF17Q8OHD1aRJExmGoWLFimnixIlyOPzv70KjZwyitFRp2wZDja/wHbVo2sar5CRD2zdm3ZEP7bOWNWxh+iyvUc9USrKhrb9az587K7073KUa9bwa+pI7hz5B7uZONbVzo6m6V/jGsX5rQylJ0u+bzOy3S5Mio323ickvnUuw1j9zWko8K9Vu7rtOyfKGYgpIm1dm/7p5kTvN1O4NHtVq5Xu+onZrl1KTpD2bPRfdLmuMDSUmZB870zT11agUFSvrUKseoTP64UkzdXhTsiq0iPZZXqlVjNKSTR3ZkpL9dm5T4dG+XXhEfqdSzlz4fXR+toSaDSjss47TZcibFjr7r0Q/kdPcqaZ2bfCqzhW+Jw3qtnYqNUnavSn7kX5PmhThu9sruoBvH+FOMxUeKTmcF2Ick1/yuKWUEDrxlpZqaudGqX6mfbhh+j68a1P221n7sO8yax+2/p9w2tqH62Tah0uVNxQbQvtwKEtKsv6QwsN9RxQjIiKUkpL1+8c0TW3fvl0NGzbUpEmTNG7cOMXFxenee+/V2bNn/X5fEpAcduyI5E4zVLKM7x9xidLW4yMHsyYg+QtYz/2RaUKBY+mJ6PEj1jYREdLLn6Rp8GMe5csfmp3EiSPWl1jxON84Fi1tPT5+MPu4tO/p0OqFXm1d7VXyOVNrFnm1bbWpJh2sP4moGMnhlE4d9d0u8YyppDPSySOhE++Th0153FLRON/uokgp6/GJg9kfXFxxQ7jWLUrTjtVuJSea+vWHNP22xqMGV2U/8LrhR7cO7vCq6+Bwn4ONvC7hSJq8bqlAad+kK38pK07xh9Ky3a5u9/z67Yez2r82UamJXu386awOrE1SlfbW8KhhGCpUNlz5irtkmqaSz3i0bf4Z/fbjWdXqki9nP1QuQz+Rs04cuUgf8TfxbXODS2sWerR9tUfJ50ytXeTWjtVeNepwIZFpdZ1Lfxwy9eO0NCWdNbV3q1dLZ7lVo6lD0flCp584ccRKJorH+S4vVtr6eexg9ttd1dPQLwuta0eSzplatcjU1tVSsw5W7KLT9+GTR31/R4lnTCWeyXocgtxr4cKFf/nvYiIjrcqGzBecp6SkKCoqa5n0t99+q8mTJ+u1115T48aN1axZM3344Yc6ePCgpk+f7nd7KcHKYYlnrT/yqExnIM6fkUjK5hrcGvVMFS9lasIol8Ij3apUzdS+3w1N/dQlw2EqJdlazxUmlSqbg42/DCSdtTrNzGfRzj9Ovsg1zm26O/T7JlMfP3PhbHHzqw1ddaP1xRceaahhW0NLvvaqZHlDdVsZOntamvmhR06XlJr9Sek8Kflc9jEO/5sYt+gepr2bPRr/bHLGskZXu9Smd/Z120tnpKlcLYcq1Qutbin1nJXAZR7NCIuyHqcmZp/g1e6WX0e2JOu74ccyllXrEKv6N2StwT26LUVfP2kdSRStHK7a3fIHpO2XC/qJnHW+j8h8pv18fFMSs09Aruju0u7NXo3+vwsHPk2vdqp97wvJeOV6DrXr7dKc0W7NGW2N9JeubKjv46F1/Udi+onli8X4Yvtwu+7W6MioZy78DlpeLXW80To2CY801LitqcVfS6XKm6rfyhrZm/ahGVL78KXw5rFz9+dLr44dO6Zy5cplLD927Jhq1KiRZf01a9aoYsWKio2NzVhWoEABVaxYUXv27PH7fUPrmz4IzPS/+YtNOJPdcleYNPTFNH36hkuvPG51xAULm+o/xK33X3QpInQmBvpb3n8QX3eqqZH/dSvhlHTj/Q4VL2to92ZT86d4FR7lUc//WAcXNz7glCvMo6lvezTlLSk8QrryRodSU5Tlup28zEw//r2kGKeZ+nRoks6cMtX9vggVK+vQ3s0e/TQ1VRGRKep2j28A92726PAur/r9X+jt3ObfnCQ3svmu86SZ+vqpw0o65VHr/xRRwbgwHdmarHVfxissylCru4r4rJ+vhEvXjiipcyfcWjPltGb+95B6vF5a0QVD4zob+omcZf7NxIvZ7cPuVFMfDE3RmVOmet4fpmJlDO3Z7NWiqW6FR6Xq+nusBGPGyDStnu9Rh74uVWng0MkjpuZPdGv0Mym6+6UIhUeGxijIPzmWSEs19fZ/TSWckvrcb6hEWWnXZun7KaYiorzq/R/rF9PnAUOuMFOT3zY1KX0f7nijodQUM2T24VBWo0YNxcbGauXKlRkJSEJCgrZs2aL+/ftnWb9UqVKaM2eOUlJSFBFh7SBJSUk6cOCArrvuOr/flwQkh0Wnz4iZdM53+fmzFdG+M2ZmKBEnPf2m9eV35oxUMk46eUwyvYZiQ+vk5V+KirF63cxnf1ISzz+fdZv1y0wd2i3d86Iz4wLRKvWsdaeP8qpFZ4dKVzQUEWWozyMu3fAfUyePSoVLShGRhn6Zl6Yi9ULjS0+SItNPcqRkinFq+uPImKyx2LzUrSO7vbr9hUhVaWh1MxXrOhUZI33zQaoaX+NSyYoXDn43L3MrKlaq1jQ0Doj/LDwmfaQjyfcoLi0p+5ERSdq9/JxO7klT12ElFFffGiIvVSdS4TEOLf/4pGp0zKfCFS6cIY4p7FJMYev3ULxahKYOOajt80PnQnT6iZwVGWt9zsx9xPnHma+jkaSNy6yZwga9GK6qDa2/+8r1nIqKNTRrVJqaXeNVdD5Dv3zn0ZU3u3TNbWHp60hlqzn05n9StGqeR1d0D43DmPPHCpeyD/+6TDq4W7rvRUM10i8kr5q+D385ylTLzqbi0vfhfo8Y6p1pH14xz1S1ejn4oZArhIeHq3///nr99ddVuHBhxcXF6bXXXlPJkiXVqVMneTwenTx5Uvny5VNkZKR69Oih0aNH66GHHtKDDz4oSXr77bcVHh6unj17+v2+Qf/LvfXWW/2ej378+PE53JrAK17alMNh6ughQ9KFU53WYymufNbTn6kp0qolDlWr7VWxUlL+9CmVd/9mbVO+SmjUFfujaGnJ4ZD+OOQbk/OPS5TLum+dSq91rVjb97nK9RySrHsElK5oaPNKr6JipUq1HSpVwVrnzGlTp49LZaqExoGFJBUu5ZDDIZ045HuAfOKw9bh4uawHyKePWTEuX8s3oahY13p8fJ/XJwHZ/otbNVu6QmpGm/Pyl3TJcEgJh30nkjj/uFDZrKUmZ49bz5Wo4Xt6slRtawTp1IE0xZZwad8viSpWLUIFSl0oaclfKkwRsQ6d/SN0Jq6gn8hZRUoZVnwPeyVd+Ls+kR7f4tnFN72PqFDLt/+oVNd6fHSfV4WKGzLNrOuUrOBQdH7p6N7QuefV+X34+CHf5ecflyyXdZuT6dcmVartu7xqelJxZJ8UV1HauNJUdKxUubaRZR8uGyL78KXw5NJZsP6NBx54QG63W88884ySk5PVtGlTjR49WuHh4Tpw4IA6dOigl156ST179lTx4sUzrgEZMGCAHA6HmjRpos8//1z58/t/hjzohWwtW7bUqlWrdOLECcXFxf3lv8tReLhUva6p1cscPqUWq5Y4FB1rqlL1rMmEyyVNeN+pH+Zc6Mi9Hmn+bKdKlDZVpgIJyHlh4YYq1bXm5zf/FOD1S01FxUrlqmftKIqXtZZlnvlm92bry6xwSevx8m+9+uoT3y+4xTO9MhxSreZB/9OxTVi4ofJ1nNqy3O0T481L3YqMlcpUyxqLYmWtZZlnyNq7xYpnoZIXtkk8Y+rEIVPlaoXe6IckucIdKlk7Unt+TvSJ7+/Lzyk8xqFiVbMmIAXKWAlF5hmyjm6zHucr7pLDIS1+7w9tmBHvs87x31KUcsarIhVCp4aefiJnhYUbqljXoU3LPD7x3bjUkx7frHEoXsZalnmGrD1bzsfXoSLpJz/Ox/y8Ywe8SkyQCpfMeweCFxMWbqhKXes+Hn+O8br0fbh89azblEy/RjTzDFm/b7Z+Fknfh5d+a2rmJ777+Q8zTRkOqU7zQH0C5GZOp1NDhw7VihUrtG7dOn388ccqU6aMJKlMmTLavn27z+hG5cqV9eGHH2rlypVasWKFRo4cmbG+v4I+AjJkyBBFR0fr3Xff1UcffXTJH+BycP0tHr3yhEvvjXCp7TUe/bbFoTlfOnTTnR6FR1jlWQf3GSpeylT+gtaMFB2u8+r7mQ4VKmqqdDlTC2Y79dtmQw8Nc+sSplkOCVf3deiDJz0a94JHza9xaPcW6+7F1w605vZPPmfqyD5TRUsZii1oqE4LQ+VrGJr0qkedbzVVvKyhvdtMzf/cq9rNDZVP/7Jsc71DHz3t0cwPParTwtBvv5paMNWrDjc5VLRU6HzxSVL7PmEa+3SypryUrMadwrRvq0dLp6fp6jvCFRZhKDnR1PF9XhUu5VBMAUM1mjtVprpD015L0VX9TRUrY2j/dq9+mpKa/tyFZOPonouPpISKhjcW0Jz/HdXC146reodYHd2Wog2zEtTstkJyRTiUmujVqf2pyl8yTFEFnCrfNFrFq4Xrh7ePq3GfgipYJkzHdqRo3ZfxKtc0SsWrWSMj9XsW0Nov4hWR36m4epGKP5SmtVNOq3CFMFXrEPs3rcpb6CdyVoc+Ln3yVKomvpiqple7tHerVz9Nd6vLQOseIMnnTB3dZ6pIenxrtXCoXHVDn7+Wqqv7h6lYWauPWPi5WzWbOzKSltY9XPppmjVaV7WhQ6ePmZo/ya2CxQ016xz0QxhbXdPX0HtPmhrzgqkW10i7t1h3Ob9+oKHwCENJ56w7pBctJeUraKhuC6lCDWncq6a63SqVKCvt2SZ997mpOs2lCumJd/vrDb3/tKlpH3pVt4WhHb+amjdV6nSTQmofhr0M0/y7SyDtcdddd6lgwYJ6/fXXc+w9Vu6tmGOv/XdWLzU0c4JThw8YKlRE6tjdoy69rQOvresNvTQ0TIP+61abq61lbrc0a4JTSxc4dO6MVK6yqR79PKrbJPtf1/Ej0qO3hfu8ht1OeC9yQYsNNizz6rsJHh07KBUoIrW+zqEre1kHuTvXe/X+4x71fcSpZldbX2rJ50x9O86rDUu9SjwjFSklNengUPueDrnCLnS4a3/wat7nHp08KhUqLl1xrUNtrw/emfpz3uBdEbhluVsLJ6bqjwNe5S9qqPm1YWrd0zqL/vsGt8Y8kayeD0eoUSfr7HxyoqkF41K1eZlbSWdMFSppqEGHMF1xQ5hPjDcuTtPUl1P04EfRGSMnwbI3tWjQ3nv3z+e09vPTOn0wTTFFXKrVJZ/q9bBmtDq0MUnf/t9Rtbu/iKp1sKbQTU30atXEU9qzIlEpZz3KVyJMVa+MUd3uBeRMj6/pNbX1+zPaMveMEo64FRHrUIUW0Wrar1DGtSd2qxV5kflCbRAq/USaGZwD803LPJo3MU3HD5gqUNRQy2udatfL6g92bfDoo8dTddMjYWrSyWpf8jlT341L08ZlHiWdsUY0Gnd0qs0Nroz4mqappbM8+nmOWyePmMpf2FDVRg51HhCm2ILBOTiONoI3NdT6Zaa+nWBm7MNtrzPUoZcVhx3rTb37uKn+jxhqcbW1LOmcqa/Hmfp1qZR4xkpOmnUwdFVP+ezDq38w9d3npk4clQoXl9pca6j99cFLPjpV3Bq09/47D667yG3ng+ydhp8HuwmXJNckIEePHtWWLVt05ZVX5th7BDMBCQXBTEBCRTATkFAQzAQkVAQzAQkVwUpAQkUwE5BQQQJy6S63BCTX9FIlSpRQiRIlgt0MAAAAADko1yQgAAAAQG7mNUP3esVAIooAAAAAbEMCAgAAAMA2lGABAAAAfvCIqYkDgREQAAAAALYhAQEAAABgG0qwAAAAAD94TUqwAoEREAAAAAC2IQEBAAAAYBtKsAAAAAA/cCPCwCCKAAAAAGxDAgIAAADANpRgAQAAAH7wciPCgGAEBAAAAIBtSEAAAAAA2IYSLAAAAMAPHm5EGBCMgAAAAACwDQkIAAAAANtQggUAAAD4gRsRBgZRBAAAAGAbEhAAAAAAtqEECwAAAPCDl1mwAoIREAAAAAC2IQEBAAAAYBtKsAAAAAA/eEUJViAwAgIAAADANiQgAAAAAGxDCRYAAADgB2bBCgxGQAAAAADYhgQEAAAAgG0owQIAAAD84DU5dx8IRBEAAACAbUhAAAAAANiGEiwAAADAD8yCFRiMgAAAAACwDQkIAAAAANtQggUAAAD4wStKsAKBERAAAAAAtiEBAQAAAGAbSrAAAAAAPzALVmAwAgIAAADANiQgAAAAAGxDCRYAAADgB0qwAoMREAAAAAC2IQEBAAAAYBtKsAAAAAA/UIIVGIyAAAAAALANCQgAAAAA24RUCVa98GC3IK87F+wG5HkOJQa7CXlaWMyZYDchz0sz3cFuQp7nlRnsJuRpRz3JwW4CgogSrMBgBAQAAACAbUhAAAAAANgmpEqwAAAAgH/KK0qwAoEREAAAAAC2IQEBAAAAYBtKsAAAAAA/MAtWYDACAgAAAMA2JCAAAAAAbEMJFgAAAOAHSrACgxEQAAAAALYhAQEAAABgG0qwAAAAAD9QghUYjIAAAAAAsA0JCAAAAADbUIIFAAAA+IESrMBgBAQAAACAbUhAAAAAANiGEiwAAADADyYlWAHBCAgAAAAA25CAAAAAALANJVgAAACAH7yiBCsQGAEBAAAAYBsSEAAAAAC2oQQLAAAA8AM3IgwMRkAAAAAA2IYEBAAAAIBtKMECAAAA/MCNCAODERAAAAAAtiEBAQAAAGAbSrAAAAAAPzALVmAwAgIAAADANiQgAAAAAGxDCRYAAADgB2bBCgxGQAAAAADYhgQEAAAAgG0owQIAAAD8wCxYgcEICAAAAADbkIAAAAAAsA0lWAAAAIAfTDPYLcgbGAEBAAAAYBsSEAAAAAC2oQQLAAAA8INXzIIVCIyAAAAAALANCQgAAAAA21CCBQAAAPjB5EaEAcEICAAAAADbkIAAAAAAsA0lWDZZttLQ+6Od+n2voUIFpd7dPRp4i1fGRUbyUlOlD8c69e18h07HSxXKmbrtZq+6dfJKkg4elrr1Db/o+3Xv7NHwJzw58Elyp0DH97xFSwx9MsGpPfsMFS0sdbvaozv7eRUWlvOfKbdZutLQe6MdGTG+sbtXd/5NjD8Y69A36TGuWE4acLNH3Tr53sVp0RJDH01was8+qWhh6dqrvborBGO8ZKX0zmhp1x6pUEGpT3dpUD/9ZXzfGyt9PU86FS9VKifd0Ue6rpPvejPnSmOmSvsOSsUKS9dfI91zmxQWgr0/+3DOoh/Oeat+cWrcZ5Hat9ehAgVMdbsuVTf3Tf3LGE8cH6GFC8KUEG+obDmvet+Yoqs6ui/6Hh+OitDM6RH6fmFCDn2Ky5uXEqyACMGvIPv9usnQg0+7dM2VXt17p0frNjr03qdOeb3SoFu92W7z+HCXlqwwdNvNXjVr5NW2nYZGvOHU6XipX2+vihWRxr+flmW7qbMc+v4Hh27omv3r5kU5EV9JWrHa0KPPWq/7wN0e7fzd0MhPnDp12tCTD4VOcidZMX7gaac6X2nqvjs9WrfR0MhPHfJ6pbsvEuPHhju1eIWhATd71byRqa07DQ1/w6lT8V71/1OMH37WqWuuNPXQ3V799ruhdz9x6NRp6amHQmcfXrdJuvcpqfOV0oN3Sms2Sm9/KnlN6Z5bs9/mkWHSTyuspKNFI2nrb9Jzb1jJyG29rXXGT5NeGmnomnamht5jPffeZ9L2XdJ7L9j3+XID9uGcRT+c8zZvduq5/4tWu/ZpGnBHsjZvcmnsmAh5TemWfqnZbvPSiCit/Nml3jelqkFDt3btdOqdt6IUH5+iG3pl3WbjBqdmz7z4yU0gUEhAbPDROKeqVzH1wtNWZ3lFc4/cHumzyU7depNXkRG+62/7zdAPSx267y637upvdcItmpiKipTe/tCp667xKn8+qV5t37Nwm7cZ+v4Hh+6/y6OG9Xyfy8tyKr6z5zpUsrj0wtMeOZ1SyyamTp4yNHGaQ/+9zxNSZ5A/HOdQjSqmXkyPcevmptweacxkh27LJsZbf5MWLbX2xUGZYvzWhw51T4/xrLkOlSouveQTY2nCNIeG3ucNmRi/P1aqUUV69RnrcZvmktstfTJJuv0mZYnvlh3SwqWGHrrL1OD0BKVVEykqUnrjI6nHNVJMtDRqrNSqiam3h1/YtnZ16boBhpatMnVFUzs+Xe7APpyz6Idz3qTxEapU2avHnkyWJDVt5pHbLX3xeYR69U5VRKYY7/zNoeXLwnT7wGT1TU9QGjX2KDLS1KcfR6rTNamKjb2wfnKS9MarUSpcxNQfxznLj5zFNSA5LDVVWv2roQ5tfM8AdWznVWKSobUbsv6R/77XWtaulW8S0bi+qaRkQ6t/zbqNaUovvu1UpfKm+t8YOmfdcjK+aWmGoqJMOZ0X1ilYwFRamqHExAB/kFwsNVVa9auhDm1849WpnelHjH1/L03qe5WUbGhVeoxT06SoKGWKsUIqxqmp0i+/Sp3a+i6/pp2UmGRozYas2/y+1/p5ZSvf5U0bWNusXCedOCXFnzGyrFOlglSogKmfVgToA1wG2IdzFv1wzktNlTasd6p1G9/KhzZt05SUZGjTRmeWbfbtsw7xWrT0LbeqW9+j5GRD63/1zd4+/ihShQp7dfU1WasrcIFp5s5/lxsSkBx24LDVgZYv67t3lIuzHu/bn7VjLlTQeu7QkUyvdcj6efBw1m3mLnRo8zaHht7n8emo87qcjG+fGzzad8DQ2CkOJZyRNmw2NGmaU61beFUgf4A/SC72dzHem02MCxe0fh464vvc/kPW4/Mx7nuDV3sPSJ+lx3j9ZuvMZpsQivH+Q+fj67u8XBnr5579WbcpVND6eTDTPrw/Yx+W8sVKLqeZZZ34M1LCWev3GirYh3MW/XDOO3LYobQ0Q3FlfJO80nHW4wMHsh7OFShgxfjoEd/nDh9yZLzmeWtWO7VgfpgeHZosB0eGsEHQBy93796tb775RvHx8WrTpo3atWvn8/zZs2f1wgsv6KWXXgpSC/+dM2etTjQm2nd5dJT182w2Z3Ca1DdVprSpV951KTLCrdo1TO3YZeidj1xyOEwlJWfdZvxUhxrU8appw8swDf4XcjK+TRqYur2PV29/6NLbH1rLalT16qVnLn7xXl50Psax/yDGL7/rVGSER3VqmNq+y9DbHzl9Yty0gak7+nj11odOvfWhlTnXqGrq5WdCp7Y74az1M3N8Y87H91zWbZo2kMqWNvXCu1JkpFS3hrRtp/TGh5LDYSox2SrH6nKVNGmmNerRsa108pT04kjJ5VS2/UhexT6cs+iHc97Z9BhHR/t+x0enxzzxXNYkr159j0qV8mrU+5GKiExSteoe/b7LqdGfRMjhMJWcHuNzZ6W33ojSbQNSVKZs6FRQILiCmueuWbNGN9xwg7755hstXrxY99xzj+6//36lpl64MCo5OVmzZs0KXiP/JW/63/LFZqhwZLM8LEwa9WqaShY3NfjRMLXuFq7Hh7k0ZKDV4UZF+q6/bqOhbb85NKBP6HzhnZeT8R3xplNjpzg06FaPPnkrTc897tbpeEP3PuYKqYO38zHWJcb4w1fdKlnc1N2PutSqW5geG+bUvQOtffR8jJ9/06HPpjh0960ejX7LreGPu3U6XvrPY86QifH5ofOL7sPZ9NLhYdInr0kli0sDHzHUtKuhR4ZJD9xpPR+dHt//PWLNivV/r0ktrjXUa5DUoLZUp0bWfiQvYx/OWfTDOe+f9BNhYdILr5xTsWJePTE0Rj2759eLI6I04PYUSdbJC0n6YFSkihb1qmfv7C9khy/TNHLlv8tNUEdA3njjDfXu3VvPPGNdeTl37lw9/fTTuueee/TRRx8pLA/MsZcv/QKvc5nOACUmWT//fAHYn5UrI415162Tp6TTCVK5OOnoccnrNZQ/n++6C35yKH8+U61bhNboh5Rz8T16XJrxjUN39rNmdJGkpjJVp7qp3gPDNHuOQ316hsaZonyx1n71T2I89l2PTpzyKD49xkfSY1wgn6mjx6Xp3zh0Vz+v7rvTimVTSbWru9VrYJhmzTHVNwRifH4fzjzSce58fGOy3658GWniSOnEKVOn463HGfHNb/3OYqKlFx6XnrpfOnTUVFxJ66z09DlS2dI59IFyIfbhnEU/nPNi0vfhxETfA83z18FEx2T//R8XZ+qNtxN1+pShhASrhOv4MUNer6F8+Uz9vMKln34I08gPzsk0JY/nQkLp8VgJDyVZyAlB3a22b9+u/v37Zzzu0qWLPvnkE61bt06PPfZYEFsWOGVLm3I6TO076NtpnH9cqXzWTiM5Rfp2nkMHD0uFC0mVyksul7Rlu7VNzWq+2yxe4dCVrUNntpU/y6n4HjlmnVFoUNf3y61KJVMF85vatefyO9vwT5Utrb+MceWLxPibeYYOHJaK/G2MfbevWkkqmN/Uzj0583lym3KlJafT1L6Dvsv3HbB+Vq6QdZvkFOmrecqIb+UKVnw3b7eer1XN+vnDcmntRisRqVrRSj5OnJKOHJNqVc2pT5T7sA/nLPrhnFe6tFcOh6lDB30P284/Ll8+ayKWkiItnB+mI4cNFSxkqlx5r5xO6bcdVqlglaoeLV3sUmqqocF3xqrr1fnV9er8mjzRmk6r69X59eZrITRUClsFNQGJjY3VqVOnfJY1btxYr732mr7//vvL9rqPP4uIkBrVN7VoscNnloIFPzmUL9ZUnZpZO+Ywl/TSO05N//rC1eQejzRlplNl40xVqXhhm/gEaf9BQw3qhN7oh5Rz8S0bZ32hrt3g+yeyZ590OsFQ6VKhE+/zMV642PCJ8fyfDD9ifCF+Ho/0+UyHysWZqlJRf4qx70HE7vQYx5XKsY+Uq0RESE3qSfMX+85k8v1PUv5YU/VqZt0mzCWNeEf64usLyzweaeIM68LfqhWtZVO/kl4d5bvt+C8lp0Nqn2l2rLyMfThn0Q/nvPBwqW49j5YtcfnEeMniMMXGmqpeI2sJtsslvT8yUnO+vXBfD49Hmj0rXKXjPKpQ0av+A1I0ctRZn39dulmlWCNHnVX/ASk5/tkuN8EutaIEKwDatWun4cOH67nnnlOtWrUySq46duyop556SiNGjNDhw5f/VC2DbvVo8KMuDX3OpR5dPVq/yaFxUxx6cLBHkRFW6cXvewyViTNVuKA1neNNPbyaPM2h4kVNVSxvaspMp37daOitF9w+w6G//Z5+hqlC6HTEmeVEfAsXtG6ENX6KFeyWTbw6dMTQR+OcKlXCVK9rQ2PY/7y7b/Xq7ked+u9zTvXo6tX6TdasNA8N9mbEeNceQ2UzxXjSNIeKF1V6jB36daOhd17w+MR4XEaMTR0+In2QHuPeIRTje26TBj4iPfw/qWdXad1macwU6dHByojvzj1Wicr5+Pa93rrRYImi1tnjSTOsGxq+98KFkolbe0l3/dfQiyNNXXWF9PNa6eNJhgb1M0OqBEtiH85p9MM575b+KXpiaLReGB6lazqnacsWp6Z9Ea47B6UoIkI6d07at9epUqW9KljQmrr42u6pmjUjXEWKelWunFdfzQrX5k1OPfd8khwOqWRJUyVL+h4/rPzZelytemjFF/YyTDN4swfHx8fr4Ycf1ooVK/TRRx+pbVvfifAnT56sF198UR6PR1u3bv3X75d0uOK/fo1/atESQx985tSe/YaKF5Vu7uHRbTdbf9yr1hka9HCYhj3u1vVdrGVpbumjsU59M8+h+ASpehVTdw/wqFVT31/X9z849Pgwl2aOS1XF8rZ/rFwjJ+JrmtKkaQ5N+8qpg0ekooWllk29uu8uT8YUnXZzXOwqWhssXGJo1GdO7dkvFS8q9enh1YA/xfjOh116/nG3ru9ixTDNLX041qGv02Nco4qpwQO8WWI8cZpDX37l0MEjUrHCUsumpu4PUozDjOCdk5m/2LpL+e79VlJxyw3SHTdbz/2yThrwkKEXnzB1QxdrWZrbuoHhV99bU+vWqCINGaAsNxf8doH0wQRrat7SJaS+PaT+vez8ZL7SzODNXhQK+7AkeRWcr/VQ6YePeoJ39fuypS5NGBuhAwccKlLU1HXdU9X7JmvEYv2vTj32aIweHZqkqztb9/Jwu6WJ4yO0YH6YziQYqlzFo363pqhxk4tPWjNhXIQmjo/Q9wsTbPlM2alQJveefK771f+C3YRsbew+LNhNuCRBTUDO27dvnwoVKqR8+fJleW737t2aN2+eBg8e/K/fJ5gJCBAIwUxAQkEwE5BQEcwEJFQEKwEJFcFMQEJFbk5Aas9+LthNyNbm658LdhMuSa74ti1XrtxFn6tYsWJAkg8AAAAAwcfkagAAAABskytGQAAAAIDcLvgXLuQNjIAAAAAAsA0JCAAAAADbUIIFAAAA+OFyvOlfbsQICAAAAADbkIAAAAAAsA0lWAAAAIAfKMEKDEZAAAAAANiGBAQAAACAbSjBAgAAAPzAfQgDgxEQAAAAALYhAQEAAABgG0qwAAAAAD8wC1ZgMAICAAAAwDYkIAAAAABsQwkWAAAA4A+mwQoIRkAAAAAA2IYEBAAAAIBtKMECAAAA/MAsWIHBCAgAAAAA25CAAAAAALANJVgAAACAH0xmwQoIRkAAAAAA2IYEBAAAAIBtKMECAAAA/MAsWIHBCAgAAAAA25CAAAAAALANJVgAAACAPyjBCghGQAAAAADYhgQEAAAAgG0owQIAAAD8wI0IA4MREAAAAAC2IQEBAAAAYBtKsAAAAAB/UIIVEIyAAAAAALANCQgAAAAA21CCBQAAAPjB5EaEAcEICAAAAADbkIAAAAAAsA0lWAAAAIA/mAUrIBgBAQAAAGAbEhAAAAAAtqEECwAAAPADs2AFBiMgAAAAQIjyer1699131aZNG9WvX18DBw7U3r17L7p+Wlqa3njjDbVp00YNGjRQ//79tXXr1kt6TxIQAAAAIESNGjVKU6ZM0YgRIzR16lQZhqFBgwYpNTU12/Wfe+45TZs2Tc8//7ymT5+uggULatCgQTpz5ozf70kCAgAAAPjDzKX//qHU1FSNGTNG999/v9q1a6caNWrorbfe0tGjRzV//vws6+/fv1/Tpk3TSy+9pPbt26ty5cp68cUXFR4erk2bNvn9viQgAAAAQAjatm2bzp07pxYtWmQsy58/v2rVqqVVq1ZlWX/p0qXKnz+/2rZt67P+okWL1LJlS7/fN6QuQo8wwoLdBAAIaWFGSH3tBEWSmRLsJuRp4QYXISP36dChw18+v3DhwmyXHzlyRJJUqlQpn+XFixfX4cOHs6y/Z88elS1bVvPmzdPHH3+so0ePqlatWnriiSdUuXJlv9vLCAgAAADgFyOX/vtnkpKSJEnh4eE+yyMiIpSSkvVkxtmzZ7Vv3z6NGjVKjzzyiD744AO5XC7dcsstOnHihN/vy6koAAAA4DJ2sRGOvxMZGSnJuhbk/P8lKSUlRVFRUVnWDwsL05kzZ/TWW29ljHi89dZbateunWbOnKm77rrLr/dlBAQAAAAIQedLr44dO+az/NixYypZsmSW9UuWLCmXy+VTbhUZGamyZcvqwIEDfr8vCQgAAADgj2DPdhXgWbBq1Kih2NhYrVy5MmNZQkKCtmzZoiZNmmRZv0mTJnK73dq4cWPGsuTkZO3fv1/ly5f3+30pwQIAAABCUHh4uPr376/XX39dhQsXVlxcnF577TWVLFlSnTp1ksfj0cmTJ5UvXz5FRkaqSZMmatWqlR5//HENHz5cBQsW1Lvvviun06nrr7/e7/dlBAQAAAAIUQ888IB69+6tZ555Rn379pXT6dTo0aMVHh6uw4cPq3Xr1pozZ07G+iNHjlSzZs103333qXfv3jp79qzGjx+vwoUL+/2ehmma/2Lg5vLiPVIt2E0AACBHMQ1vzor3pgW7CXle6bhDwW7CRVUY+0qwm5CtPbc/HuwmXBJGQAAAAADYhgQEAAAAgG24CB0AAADwh/nPb/qHCxgBAQAAAGAbEhAAAAAAtqEECwAAAPBD6Mwdm7MYAQEAAABgGxIQAAAAALahBAsAAADwByVYAcEICAAAAADbkIAAAAAAsA0lWAAAAIA/uBFhQDACAgAAAMA2JCAAAAAAbEMJFgAAAOAHg1mwAoIREAAAAAC2IQEBAAAAYBtKsAAAAAB/UIIVEIyAAAAAALANCQgAAAAA21CCBQAAAPiDGxEGBCMgAAAAAGxDAgIAAADANpRgAQAAAP5gFqyAYAQEAAAAgG1IQAAAAADYhhIsAAAAwB+UYAUEIyAAAAAAbEMCAgAAAMA2lGABAAAA/qAEKyAYAQEAAABgGxIQAAAAALahBAsAAADwh2kEuwV5AiMgAAAAAGxDAgIAAADANpRgAQAAAH4wmAUrIBgBAQAAAGAbEhAAAAAAtqEECwAAAPAHJVgBwQgIAAAAANswAmKTJSuld0ZLu/ZIhQpKfbpLg/pJxkWmk05Nld4bK309TzoVL1UqJ93RR7quk+96M+dKY6ZK+w5KxQpL118j3XObFBZiv1nim/OIcc4ivjmPGOesZSsdGjXapd17DRUsKPXu7tYdt3j+Mr4fjXVpznynTsdLFcqZuvVmt7p28kqSDh02dG3fiIu+33Wd3Rr2hDsHPknu9csvTo0eE6G9ex0qWMDUdd3TdEvf1L+M8bhx4Zq/IEzx8YbKlfPqpptS1amjb9x69orRqVNZz0lPn3ZWhQtzyh+BF2LdY3Cs2yTd+5TU+UrpwTulNRultz+VvKZ0z63Zb/PIMOmnFdaXXYtG0tbfpOfesL4Eb+ttrTN+mvTSSEPXtDM19B7rufc+k7bvkt57wb7PF2zEN+cR45xFfHMeMc5Z6zcZevjpMF19pVdD7nTr140Ovf+pS16vdNetnmy3eXJ4mJascOjWmz1q1sirbTsNvfBGmE7Hu3VLb4+KFjE19v2ULNt9MculeT841KNr9q+bV23a5NDTz0TpyvZu3TkwRRs3OjV6dLhMr9S/f2q22zz/fKRW/OzSzTelqlEjj377zaE334xUfHyKevdKkySdPGno1CmHhvwnWbVr+8Y0f36SD+QMEhAbvD9WqlFFevUZ63Gb5pLbLX0ySbr9Jiky0wmeLTukhUsNPXSXqcHpX4ytmkhRkdIbH0k9rpFioqVRY6VWTUy9PfzCtrWrS9cNMLRslakrmtrx6YKP+OY8YpyziG/OI8Y566NxLlWvYmrE09ZB7RXNvXJ7pLGTXep/kydLfLf9ZuiHpU7de1ea7uxvHfQ2T4/vOx+6dN01HuXLJ9Wr7XsAvGWboXk/OHTfXW41rBdaB8fjxkeoSmWvnnoqWZLUrJlHbo80+fNw3XhjqiIyxfi33xxauixMd96Zov79rASlcWOPIqOkjz6KUOdr0hQbK+3caY18tGnjVsmSoRVTBM8lXQNy/PhxPffcc7rzzjv1+OOPa+zYsVq9erWSkpJyqn2XvdRU6ZdfpU5tfZdf005KTDK0ZkPWbX7fa/28spXv8qYNrG1WrpNOnJLizxhZ1qlSQSpUwNRPKwL0AXI54pvziHHOIr45jxjnrNRUac2vDl3Vxvfsecd2HiUmGVq3Ieuhxu69Vs1Q21Zen+WN63uVlGxo1a9ZtzFN6aW3w1SxvKl+N4bW6EdqqrR+vVNt2viWTrVr61ZSkqENG5xZttm7z4phq5a+29Sv51FysqF166xz0Dt3OhUba5J8wFaXlIA89dRTmjp1qo4fP65ff/1Vr776qm699VY1adJE1113nZ588klNnjxZGzduVFpaWk61+bKy/5CUlmaofFnf5eXKWD/37M+6TaGC1s+DR7K+liQdPCzli5VcTjPLOvFnpISz0oHD/7rplwXim/OIcc4ivjmPGOesA4cNpaUZKlfW9wC2bJz1eO/+rBconI/voSO+zx04ZD0+dDjrNt8tdGjzNoeG3ueWM+vxdp52+LBDaWmGypTxTdji4qzHBw5kPZwrWMCK/5FMMT6UHuPD6ct37nIoXz5Tzz4bqWuvi1WXrrEa/nykTpy4yIUlIc4wc+e/y80llWCtW7dOQ4cO1cCBAyVJiYmJ2rx5szZu3KiNGzdq1apVmjlzpiQpPDxcGzZkc1opk5SUFP3222+qUqWKIiMjtXXrVk2cOFFHjx5V1apVNWDAAJUsWfIffLTcIeGs9TM22nd5TJT18+y5rNs0bSCVLW3qhXelyEipbg1p207pjQ8lh8NUYrI1TN3lKmnSTOtsW8e20slT0osjJZdTSkrOyU+VexDfnEeMcxbxzXnEOGeduUh8o9Pjey4x6zaN63tVprRXr73rUmSEW7VreLVjl6F3PnLJ4TCzjd2EqS41qONVk4berE/mcWfTYxwT43ukGZ0e83OJWZOF+vU9Kl3Kq5HvRSoiMlk1qnu0a5dTH38SIYfDVHJyegKy06Hjxw116+ZV795J2rvPoc8+C9dDD0fr44/OKSoqRz8aQtQlJSARERGqVatWxuPo6Gg1bdpUTZteKHI9ffq0NmzYoE2bNv3t6+3atUu33367jh8/rtKlS2vEiBEaMmSIypQpo8qVK2vBggWaMWOGJk+erMqVK19KU3MNM72vuNgMFY5sxqDCw6RPXpOefkUa+Ii1YbEipp5+wLooMjrSWu9/j0hhYdL/vSY986qhqEhTd/a1vvSiInPgw+RCxDfnEeOcRXxzHjHOWeb5fOBi8c1meViY9N6raRr2apj+82i4JKloEVOP3Z+mJ4aHZYndrxsNbfvNoTdHZH+xdV7nNdODeIkxfvXVRL36aqT++18rUylSxKv770vR8OcjFRlp/WE8/liywsOlqlWtX2S9eh5VqODVAw9Ea968MF1/PRUtCLxLSkA6duyoLVu2qEWLFhddp2DBgmrbtq3atm170XXOe/XVV9WwYUMNGTJEo0eP1n/+8x91795dw4cPl2EYcrvdeuyxx/TSSy/p008/vZSm5hr5Yq2fmc+wnUu/bCY2JvvtypeRJo6UTpwydTreenzkuOT1GiqQPitFTLT0wuPSU/dLh46aiitpnXGaPkcqWzqHPlAuQ3xzHjHOWcQ35xHjnHU+vplHOhLPxzc2++3KlTE1+t1UnTwlnU4wVC7O1NHjhrxeQ/nz+a674Cen8uczdUWL0Bv9kKTY9JGPxHO+mUZieswzj4ycFxdn6p13knTqlKGEBKuE69ix8zG2tqldO2tM69bxKCbG1K7fuV1cFialaYFwSXtWr169NHfuXO3cuTMgb/7LL7/ooYceUo0aNfT4448rJSVFffv2lZF+msrlcumee+7RmjVrAvJ+wVCutOR0mtp30Hf5vgPWz8oVsm6TnCJ9Nc+qHy5SyFrH5ZI2b7eer1XN+vnDcmntRusLsGpF60vvxCnpyDGpVtWc+kS5C/HNecQ4ZxHfnEeMc1aZ0qacDlP7D/oemJ1/XKl81gPc5BTp23kOHTxsqHAhqVJ5Uy6XtHW7tU2Nar7bLFnhUPvWnpC7t8p5cXFeORymDmaK8cGD1mFc+QpZY5ySIs2f79Lhw4YKFTJVvrxXTqe0Y4d1AU3Vql6dPSvNmevSnj2+h4Omac0SV4BpeJFDLikBuemmm7Rp0ybdeOONevLJJzVnzhzt3bv3H795ZGSkkpOtQs+iRYvqpptuUkSmeeQSEhKUL1++7Da/LERESE3qSfMXXygDkKTvf5Lyx5qqVzPrNmEuacQ70hdfX1jm8UgTZ0jl4kxVrWgtm/qV9Ooo323Hfyk5HVL7TLOy5FXEN+cR45xFfHMeMc5ZERFSw/peLVrs9Invgp+cyhdrqnbNrAexYS7plXfCNOPrC1eTezzSlJkulY3zqkrFC9vEJ0j7DzrUoE7oHgyHh1uzVy1ZGuYT458WuxQba6pmjayzgrlc0jvvRuqbb8Iylnk80oyZYYqL86piRa9cLunttyM1+fNwn22XLXMpJcVQgwahNdsY7HNJ5xJGjBihrVu3avPmzZo7d65mzpwpwzAUExOjWrVqqU6dOnrsscf8fr3WrVvr+eef14gRI1S5cmUNH35hInXTNPXLL79o2LBh6tix46U0M9e55zZp4CPSw/+TenaV1m2WxkyRHh1szT1/9py0c49ULk4qXFByOqW+11s3uCpRVKpUXpo0w7qR1nsvXKhXvrWXdNd/Db040tRVV0g/r5U+nmRoUD8zZIb+JeJrB2Kcs4hvziPGOeuuWz36z6Nhevy5MF3f1aP1mxwaP8WpBwa7M+L7+x5DZeNMFSpoxffGHh59Ps2pYkVNVSxv6ouZTq3faOjNF9J8rsvZ+bt11r9iNmf5Q0n//qn679AoDRsWqS5d0rR5s1NTp4br7kEpioiQzp2T9u51qHRpUwULmnI6peuvT9X06eEqWtRUufJezZoZpk2bnBoxIkkOhzXBQp8+qZowIUKFC5lq2syt33c5NG58hFq0cKtxYxKQLEI3Dw4owzTNfxRKr9erXbt2afPmzdq0aZO2bNmibdu2ae3atX6/xsmTJ3XPPfeobNmyeuONN3ye+/bbb/Xoo4+qTZs2euuttxR7sSLSS2nzkWr/+jX+qfmLrbvj7t5vfZndcoN0x83Wc7+skwY8ZOjFJ0zd0MValua2bpz11ffWlI41qkhDBijLTa2+XSB9MMGaErJ0CalvD6l/Lzs/We5AfHMeMc5ZxDfnhUqMk8ysdw+3w6IlDn34mUt79xsqXtTUTT08uvVm6wB29TqH7n44XM89nqbuXaxlaW7p47EufTvPqfgEqXoVU4MGuNWyqW+iMe8Hh54YFq7p41JUsXzwj/7ivcG7KHvJEpfGjgvX/v0OFS1qqsf1qbrpJqs9v/7q1MOPROvxx5LUubN17w+3Wxo3Llzz5ocpIcFQlSoe3XZrqpo2vZBYeL3S7K/C9NVXYTp0yKH8+U116ODWHbenZLm5oV1Kxx0Kzhv7odLbbwa7Cdn6/aFHgt2ES/KPE5DsmKaZcf3GpTh9+rQKFizos+zkyZM6duyYatSoEaDWBTcBAQDADsFKQEJFMBOQUEECcukutwQkoJdz/ZPkQ1KW5EOSChcurMKFC//LFgEAAAABEvxBuDyB+dUAAAAA2IYEBAAAAIBtQnRGbQAAAODSGJRgBQQjIAAAAABsQwICAAAAwDaUYAEAAAD+oAQrIBgBAQAAAGAbEhAAAAAAtqEECwAAAPAHJVgBwQgIAAAAANuQgAAAAACwDSVYAAAAgB+4EWFgMAICAAAAwDYkIAAAAABsQwkWAAAA4A/TCHYL8gRGQAAAAADYhgQEAAAAgG0owQIAAAD8wSxYAcEICAAAAADbkIAAAAAAsA0lWAAAAIAfuBFhYDACAgAAAMA2JCAAAAAAbEMJFgAAAOAPSrACghEQAAAAALYhAQEAAABgG0qwAAAAAD8wC1ZgMAICAAAAwDYkIAAAAABsQwkWAAAA4A9KsAKCERAAAAAAtiEBAQAAAGAbSrAAAAAAf1CCFRCMgAAAAACwDQkIAAAAANtQggUAAAD4gRsRBgYjIAAAAABsQwICAAAAwDYkIAAAAABsQwICAAAAwDYkIAAAAABswyxYAAAAgD+YBSsgGAEBAAAAYBsSEAAAAAC2oQQLAAAA8AM3IgwMRkAAAAAA2IYEBAAAAIBtKMECAAAA/EEJVkCEVAKyJDnYLcjb9qQVDXYT8rxoR0qwm5CnlXTGB7sJed5Jb2ywm5DnpZr5gt2EPC3NDKlDp6C4JdgNQI6jBAsAAACAbUjjAQAAAH9QghUQjIAAAAAAsA0JCAAAAADbUIIFAAAA+IEbEQYGIyAAAAAAbEMCAgAAAMA2lGABAAAA/qAEKyAYAQEAAABgGxIQAAAAALahBAsAAADwA7NgBQYjIAAAAABsQwICAAAAwDaUYAEAAAD+oAQrIBgBAQAAAGAbEhAAAAAAtqEECwAAAPAHJVgBwQgIAAAAANuQgAAAAACwDSVYAAAAgB+4EWFgMAICAAAAwDYkIAAAAABsQwkWAAAA4A9KsAKCERAAAAAAtiEBAQAAAGAbSrAAAAAAf1CCFRCMgAAAAACwDQkIAAAAANtQggUAAAD4gRsRBgYjIAAAAABsQwICAAAAwDaUYAEAAAD+oAQrIBgBAQAAAGAbEhAAAAAAtqEECwAAAPADs2AFBiMgAAAAAGxDAgIAAADANpRgAQAAAP6gBCsgGAEBAAAAYBsSEAAAAAC2IQEBAAAAYBuuAQEAAAD8wTUgAcEICAAAAADbkIAAAAAAsA0lWAAAAIAfjGA3II9gBAQAAACAbUhAAAAAANiGEqwg2bRKmj1OOrRPyldAatdN6nyzZFxkbC8tVfp6orRyoXQ2QSpZVrq6t9T8KnvbnVvtWpOqnyYk6o/9HkXnd6hRl0i1vDFSxkUC6vWY+nlGstbPS9bZk14VKu1UqxujVKtthM96f+z36IfPzmnvRrecLqlsbZc63BWjQiWddnysXGXHarcWjE/V8f1eRec31KxrmNreFHbRGHs8ppZOT9PaeWlKOGGqSJxD7W4MU912YZKkU0e9euOOxIu+X8OOLvV6JDJHPktutGmVNHOcQ4f3SbEFpPbdTHW52fzLPuGriYZ+Xmhk9AnX9DbV4qrsp2hJOic99x+Huvc3dcXVoTmNy/bVHn03Pk3H9pmKKWCoRVenrrzJ9Zf78OLpbv3yvUcJJ0wVjTN05U0uNWjn+9W5ablHCz9P0/EDpvIVMtSog/W6rrDQKtagj8h5O1enadGEZB3f71FMfkONu0ao9Y0Rf/ldt3x6itbNT9WZE14VLu1Q65siVadtuCTp9FGP3hl45qLv16BjuK5/ODpHPstlKzS7z4AjAQmCXZul95+TmrSTrh8g7dwszRoreb1St1uy3+aTl6QNK62ko0YDaf8uaeI70tl4qcMNNjY+FzqwNU1fPn9GtdqEq92t0dq/xa0fJyTKNE1dcXP2HefiyUla8WWSWveJUplaLm1blqpZr56V4ZBqtraSkITjHk14LF6F45y6fmis3KmmfpqQqCn/l6C73iuosIjQObjYt8WjScOTVaeNSx1vC9fezR4tGJ8q05Ta9wnPdptFE1O1+Ms0Xdk3XOVqObRlmVtTX0mR4TRUp7VL+QobGvxmVJbtfv46TZuWuNX4mrCc/li5xs7N0sjnHGraztQNA0z9ttnQzLGGvF7p2luy/7b7+CVHep9gqmYDU/t2GZrwjqGz8VLHG3y3OZsgvfecQyeOGgrVb889WzwaOyxV9ds61fk2p3Zv9ur7cW6ZXqlD3+z3tfkT3frhC7c63uJShVoObVzq0eSX0+RwGKrXxjoJsWOtRxNGpKpeW6e63OHUkT1efTfWrXPxpnoMyf5vIy+ij8h5+7e49fnz51SnTZiuujVS+7a4tWh8skyv1LZP9onYj5OStfTLFLXtG6lyNZ3asjxN019JlMMh1WodrtjCDt35RmyW7VZ9k6JNS9LU8OrQ2YdhLxKQIPh6klS2knTnY9bjOk0lj1v67gupUy8p3PckvPbtlH5dbqjH7aa69rWW1WokRURK0z+VWnaSorP2HyFjyeQklajoVPdH80mSKjcOl9dtasW0JDXrEZVtorBhfrJqtwtXm1usBKVig3Ad/d2jNd8mZyQgiyclKTzK0C0j8iss0nqNgiWc+vL5BB3+za1ydULny2/R5FSVrOTQjUOtL7lqTVzyeqTFX6bqihvCso3x2vlu1Wvn0lX9rC+wKg1dOrQrUSu/SVOd1tbZ4bI1fEeSDu7waNMStzoNCFeF2qEzyvT1JIfKVpLuesxKDuo0NeVxS3O/MHR1LzPbPmHdckM33O5Vt77WNrUamYqIlKZ9aqhVJzOjT1i3XPr8A4dSkuz8RLnPgklula5kqM9Qa3+s3sQpr1v64Uu32vZ0ZbsPr5rnVsP2TnXqZ/2tV23o1KFdyVr+jTsjAVk936OCxQz1HRomh9NQtUZOnT0tLZnp1nV3m3K6QuNEBX1Ezvvp82SVrOTUDf+NkSRVaRImj1taNi1ZLW+IyDbG6+anqm67MLW/xfq9VGoYpiO7PFr1TapqtQ6XK8xQmRq+h4KHfnNr05I0dbgtUuVqc5iInME1IDZLS5V2bJAatvZd3riNlJJk6LdNWbc5vM/6Wa+F7/JqdaWUZEPb1+dMWy8H7jRT+zamqXor3yO0GldEKDVJ2r85LdvtPGlSeLRvZx2d31DSGetgzjRNbV+RqvqdIjKSD0kqVdWlB8YXDqnkw51mavcGj2q18v0iqt3apdQkac9mz0W3i8wU45j8hhITsj8Db5qmvhqVomJlHWrVI3Tim5Yqbd8gNWrtG5fGbcy/6BOsuNZv4btNtbqmUpINbUvvExLPSqOed6h6PVMPv+jNkfZfDtyppnZt8KrOFb4HrHVbO5WaJO3elH1sPGlSRKZB1OgCvvuwO81UeKTkcF7Y12PyWyeVQiXpo4/Iee40U3s2uFWzpe/nrtU6TKlJ0r7N7my3u9h3XeKZ7Pd50zT17agkFSvrUIseEdmuE+oMM3f+u9yQgNjsjyOSO81QiTjf5cVKWz+PHsi6Tb4C1s8TR32XHzt84TVD1ekjHnncUuE43125UGnr8cmD2X/xNesRqU2LUrRrTapSEr3a9EOKdq1JU90rrQ43/qhXKedMFSjh1HcfnNVbfU/qlRtO6IthCYo/lv1r5lUnD1tn44tminGRUtbjEwez/yK74oZwrVuUph2r3UpONPXrD2n6bY1HDa7K/ozahh/dOrjDq66Dw30O5vK64xl9gu83SPGMPiFrLGILWOv+kalPOJ7RJ1jbhEdIz3/s1Z1DTcXmD2y7LycnjlxkHy5txen4wey/vdvc4NKahR5tX+1R8jlTaxe5tWO1V406XEhkWl3n0h+HTP04LU1JZ03t3erV0llu1WjqUHS+0NiP6SNy3qnDXnncUpFMMS78NzFu0SNCGxalaufqNKUkmtrwQ6p2rnGr3lXZl1Zt+ilNh3Z41PnuqJCLMeyVa8fWrrvuOn388ccqVapUsJsSUIlnrZ+Rmc6qnX+cnM31dtXqSUVLmZoyyjqgqFBNOvC7NGO0ZDhMpSTnbJtzs+Sz1oFDRKYzPBFR1uOUpOwPLJpcF6n9m92a+r8LF9/V7xShFr2seuPEeKsz/2HsOZWu5tL1Q2OVGG/qh3GJmvSUdQ1IeGRodM7J587H2Hd5+F/ss5LUonuY9m72aPyzF3bQRle71KZ39l98S2ekqVwthyrVy7XdUo5ISu8Toi7SJyRlE9/q9aRipUxNGeVQRIRXFapJ+3+Xpo12+PQJrjDr4vRQd34fztzvnt+nUxKz7yeu6O7S7s1ejf6/1IxlTa92qn3vC2ehK9dzqF1vl+aMdmvOaOssdOnKhvo+Hjq18/QROe9CjDN916U/vtg+3Lx7hPZtdmvS/85lLGvQKVxX9Mr+mpHlM1JUtpZTFeqF1ggT7BfUv+JZs2Zd9Lm9e/dq7ty5Kly4sCSpR48e9jQqh5npfcTFZrYxshmTcoVJD70gjXtTeusJa8MChU31GSJ9/KJ1LUioMjP63OwDmt3MIO40UxMeS9DZ0151vjdGRco4dWBLmpZ9kaSwSENXD46RJ300O6agQ72eyifDYb1OoVIOjftvgjb9kKJGXUIj8Gb6ibWL7rPZLHenmfp0aJLOnDLV/b4IFSvr0N7NHv00NVURkSnqdo/v0P7ezR4d3uVVv/8LjZj+mfcf9wlejX3ToTeesM7GFyhsqu8Qrz560RHSfUJ2zL+pPssuxu5UUx8MTdGZU6Z63h+mYmUM7dns1aKpboVHper6e6yD5Bkj07R6vkcd+rpUpYFDJ4+Ymj/RrdHPpOjulyJC4kQFfUTOy/iuu8QYf/bYGZ09ZarbfVEqWsapfZvdWvJFssKjpC6DfTPGfVvcOrLLo5ufiQls4/Oay7DcKTcKagIybNgwJSdbZz5MM+tv9NVXX5VkHUTmlQQkOv3vOvMZofOPM58FPa94nDT0DSnhtKlzCdbjU8cl02soJl/o/jVExli9bmqi7xHG+ZGPiJisvfL2Zak6tsejviPyqWID6yCifN0wRcQ4NO/Dc2pwTYTC00dQKjcOz0g+JCmuRpgiYwwd/T37etu8KDL9YuaUTPtsavrjyGxivHmpW0d2e3X7C5Gq0tDqZirWdSoyRvrmg1Q1vsalkhUvlLFsXuZWVKxUrWloXVQqXegTMo90/F2fUCJOevwNrxJOW7NclYiTTtInZCsy9vxZYt/l5x9nvg5BkjYu8+jwblODXgxX1YbWflm5nlNRsYZmjUpTs2u8is5n6JfvPLryZpeuuS0sfR2pbDWH3vxPilbN8+iK7nn/bD19RM47H8PMIx3nH2f3Xbd1WZqO7vbq1hExqtTQ2j8r1HUpMtbQ3A+S1OiaCJWocCGeW5amKTLWUNWmeX+fRfAF9RqQGTNmqFatWmrevLl++uknbdu2LeNfVFSU5s+fr23btmnr1q3BbGZAFSstORymjh3yXX48/XGp8lm3SU2Rfl5oXeuRv6BUqpzkdEp7f7OeL1clR5ucqxUq5ZThsOpj/+zUIetx0bJZv6zij1nPlanpO8Rcro7V6f6xz5Pxuu60rAdyHo+psPC8f1bzvMKlHHI4pBOHfGN8Ij3mxctl7UZOH7PiVr6Wb/wr1rUeH9/n+1rbf3GrZktXyMwY9GfFM/oE389+vo8oXT7rPpiaIq1YaOh4ep9QOkufQALyZ0VKGXI4pD8y9RMnDllxKl4u6353Kn0frlDLd/+uVNd6fHSfV6ePe2WaWdcpWcGh6PzS0b2hceE/fUTOK1zKIcMhncy0D59/XKxc1u+60+nfdWVr+SYUFdK/647v872e8bdVaarRMixkYxzKvF6v3n33XbVp00b169fXwIEDtXfvXr+2/frrr1W9enUdOJDNRcx/IagJSMWKFTV16lTVq1dP119/vebMmRPM5tgiLFyqWldat+zP5UPSmiVSdKypitWzbuNySZ+/Ly3+U3i8HmnRbKl4aVOlK+R4s3MtV7ihcnVc2r481WcUbduyFEXGGCpdLeuZnCJlrN0+8wxZB7ZaoxoFSzgUHmWobC2Xtq9I9UlCdv+aprRk64aEoSIs3FD5Ok5tWe72ifHmpW5FxkplqmXtRoqVtZZlnv1m7xbrC7FQyQvbJJ4xdeKQqXK1QvPMZli4NaPd2mVGpj7B+Ms+YfL7hhbPuXCgYPUJDhUvbSquQs63+3ISFm6oYl2HNi3z+OzDG5d6FBUrlauedR8unt5PZJ4ha0/6Ply4pENF0g+8d2/2XefYAa8SE6TCJUPjQI4+Iue5wg2Vr+PStuVpPjHesjRNkTGG4qpljU3R9H048wxZ+9K/6wqVuBDjpDNenTzkVdmaoRtjv5m59N+/MGrUKE2ZMkUjRozQ1KlTZRiGBg0apNTU1L/c7uDBgxo2bNg/es+gz4Llcrn0yCOPaOTIkXr99df16KOP6syZi9+VMy/odou0e5v00QvSxvQ7os+bJnXpY11knnRO+n2rdOa0tb7DKbW/Vlo4y0o6tq6TPhxh3dDwpnskR9B/i8F1xc3ROrjDrZkvn9Wu1dYd0X+ekaxWN1n3AElJ9OrgtjSdS7+wvGrzcJWu7tJXb5zVmjnJ2rMhTcu/TNLC0edUtVmYSle3RkbaD4jW2RNeTf1fgnatTtWGBcma/foZla7uUtXmoXOBqSS17xOmA9u9mvJSsnascmvB+BQtnZ6mdjeFKyzCUHKiqf3bPDoXb/WCNZo7Vaa6Q9NeS9HKb9P0+3q3fvoiVd99mpL+3IUvuaN7Ln6WNFR0u8Wr3dukD19waOMqadY4Q99PM9S1j5nRJ+zK1Cdcea2phbMMLZptaOs66YMRDu3cLPW5xxvyfUJ2OvRxaf92UxNfTNW2VR59Pz5NP01368qbrXuAJJ+zZrA6ezr9viotHCpX3dDnr6VqxTdu7Vzv0Q9fpOmbT9JUs7lD5ao7FFvQUOseLv00za25Y9O0c71Hq+e7NfqZVBUsbqhZ59A5UUEfkfPa9onQge0eTXspUb+tTtOiCUlaPiNFrW+OSP+uM3Vgmzvju6568zDFVXdqxuuJWvVtinavT9PSL5I179MkVWvmUlz1C/vn+RhnN5KCvC01NVVjxozR/fffr3bt2qlGjRp66623dPToUc2fP/+i23m9Xg0dOlS1a9f+R+9rmNldfBEkCQkJGjZsmFavXq0TJ05o7ty5Kls2cFO4/LSnWsBe699at0z6aoI17W7BIlL766y7nEvS9vXSG48Zuv1RU62utpa53dI3E6UVC6TEM1KZytK1/aTajYP3GTLbk1Y0aO+9fXmKFk9O0skDHuUr4lDjbpFq3tOa0WrvhjRNeipB1z4Uo3odrQsYUxK9+nF8krYvT1HSGVMFSzpV96oINe8RKWfYhbOWB7am6cfxiTq0w62wCEPVWoSrw8BoRcYG54sw2pESlPeVpC3L3Vo4MVV/HPAqf1FDza8NU+ueViL2+wa3xjyRrJ4PR6hRJyuBS040tWBcqjYvcyvpjKlCJQ016BCmK24Ik+tPMd64OE1TX07Rgx9FZ5wVDZaSzvigvffaZdLsCY6MPuHK60xd09vqnretl15/zKk7HvXqiqutZW639PVEQysWGDp3RipbWbqun/eifcIfR6QnBvi+RjCc9Abvrqmblnk0b2Kajh8wVaCooZbXOtWul7W/7trg0UePp+qmR8LUpJN1YJZ8ztR349K0cZlHSWesEY3GHZ1qc4MrYx82TVNLZ3n08xy3Th4xlb+woaqNHOo8IEyxBYMzApJqBucgMhT6CElKM4OXWG5dnqofJyXrxAGv8hVxqOm14WrV0/pe27MhTeOePKfrH4pSg07WRfwpiaYWjkvS1uVp6TF2qP5V4Wp5Q4TPd93mJama9nKi7v0wX7aly3a7pcrKYDfhouo/8Fawm5Ct9e8+/I+227Bhg2688UZ99913qlixYsbyvn37qnr16nruueey3W7UqFH64Ycf9PDDD+uOO+7QwoULVaZMGb/fN1clIOfNmjVLM2bM0Ouvv67ixYsH7HVzUwKSFwUzAQkVwUxAQkEwE5BQEcwEJFQEKwEJFcFMQEJFbk5AGtyfOxOQIlu++cvnFy5cmO3yefPm6f7779f69esVGXlhlrkHH3xQycnJ+uijj7Jss2HDBg0cOFDTpk3T0aNHddttt11yApIr/4p69OiRZ2a9AgAAAHKjpKQkSVJ4uG9peUREhOLjs56US0xM1H//+1/997//VYUKFXT06NEs6/gjVyYgAAAAAPxzsRGOv3N+1CM1NdVnBCQlJUVRUVFZ1h8xYoQqVKigPn36/LOGpiMBAQAAAPyR6y5c+HdKlSolSTp27JjKlSuXsfzYsWOqUaNGlvWnT5+u8PBwNWzYUJLk8Vgz2V177bXq3r27hg8f7tf7koAAAAAAIahGjRqKjY3VypUrMxKQhIQEbdmyRf3798+y/rx583wer1+/XkOHDtXHH3+sypUr+/2+JCAAAABACAoPD1f//v31+uuvq3DhwoqLi9Nrr72mkiVLqlOnTvJ4PDp58qTy5cunyMhIlS/ve8fsI0eOSJJKly6tIkWK+P2+wZ/PDgAAALgMGGbu/PdvPPDAA+rdu7eeeeYZ9e3bV06nU6NHj1Z4eLgOHz6s1q1bB/xm4blyGt6cwjS8OYtpeHMe0/DmLKbhzXlMw5vzmIY3ZzENb87LzdPwNrw3d07Du+79f3YfkGBhBAQAAACAbUjjAQAAAH+ETN1QzmIEBAAAAIBtSEAAAAAA2IYSLAAAAMAP/3bGKVgYAQEAAABgGxIQAAAAALahBAsAAADwByVYAcEICAAAAADbkIAAAAAAsA0lWAAAAIA/KMEKCEZAAAAAANiGBAQAAACAbSjBAgAAAPzAjQgDgxEQAAAAALYhAQEAAABgG0qwAAAAAH9QghUQjIAAAAAAsA0JCAAAAADbUIIFAAAA+MEwqcEKBEZAAAAAANiGBAQAAACAbSjBAgAAAPxBBVZAMAICAAAAwDYkIAAAAABsQwkWAAAA4AeDEqyAYAQEAAAAgG1IQAAAAADYhhIsAAAAwB+UYAUEIyAAAAAAbEMCAgAAAMA2lGABAAAAfmAWrMBgBAQAAACAbUhAAAAAANiGEiwAAADAH5RgBQQjIAAAAABsQwICAAAAwDaUYAEAAAB+YBaswGAEBAAAAIBtSEAAAAAA2IYSLAAAAMAflGAFBCMgAAAAAGwTUiMgIyrVD3YT8jRHVFSwmwD8K464UsFuQp7n3vl7sJuQ9xmcW8xJhtMZ7CbkebekBrsFyGkhlYAAAAAA/xSzYAUGp0kAAAAA2IYEBAAAAIBtKMECAAAA/GFSgxUIjIAAAAAAsA0JCAAAAADbUIIFAAAA+IFZsAKDERAAAAAAtiEBAQAAAGAbSrAAAAAAf1CCFRCMgAAAAACwDQkIAAAAANtQggUAAAD4wfAGuwV5AyMgAAAAAGxDAgIAAADANpRgAQAAAP5gFqyAYAQEAAAAgG1IQAAAAADYhhIsAAAAwA8GJVgBwQgIAAAAANuQgAAAAACwDSVYAAAAgD9MarACgREQAAAAALYhAQEAAABgG0qwAAAAAD8wC1ZgMAICAAAAwDYkIAAAAABsQwkWAAAA4A9KsAKCERAAAAAAtiEBAQAAAGAbSrAAAAAAPzALVmAwAgIAAP6/vfuOr/H8/zj+TiQRYitCjNqkRm1qF9UqSlFfm1qlVq3aatRMEUpUaqc2NWLrMn61a1Ss2iTEDgnZvz9OEj0SdXByTnLyej4e59HmOue6z+f+5HadfO7ruu8DABZDAQIAAADAYliCBQAAAJgimjVY5sAMCAAAAACLoQABAAAAYDEswQIAAABMwF2wzIMZEAAAAAAWQwECAAAAwGJYggUAAACYgiVYZsEMCAAAAACLoQABAAAAYDEswQIAAABMwF2wzIMZEAAAAAAWQwECAAAAwGJYggUAAACYIoo1WObADAgAAAAAi6EASQTl67+r2QcnadNjH/lcmqP/DWny0j512lSX98lp8g3+SQtOe+qjzu/He817n1TQ7EOTtTFoqRadm6W2o5rLwdF4EsslY1r1nt1FK/29tTFoqTz3fat3a5cw164laeXrldSsPWO04ba3lpyeppYDG5rct9C7b2vzgwXKkfet13o+JSC/iatc9SLyXNtbPx8fp0W/DdFn3WuZ3LfQO27adGqCsrtljvdclbrumrmut9b9NVbzdw5S61515eCYyoyRJ03WHIdLVi+uaX+M1YaHS7Tixjz19OyktOnTmGvXkozy9Utr9oEJ2vRoiXwufq//fd3kpX3qtKkm7xMe8n28VAv8pr8gx+U1++BEbXy4WIvOeqrtyObxjtnilQtr6q5R2vRoiVYFzNOgBT2UxTWTmfYsaSj/QSl9/+d4bXywUEvPe+p/gxu/tE+d1lU179gUbXq4SPP/9tCHnWrFe029djU076/J8g1apCVnZ6jdqGZK5fDiMaFKo3LaEbZMpWoUf4O9AYxRgJiZe5UiGrvha109fUNjmnlol89udRrfSq2HffrCPjWaV9bgxb10ZOdxfdN0io799rf6e/fQ+62rxb2mbN1SGr12oG6c89c3n07VJq/tajWkqb6Y1iHuNfb29pqwZbjea1xB3l8v1djmHnp8/7G+3TxU+UvmTdT9tjb3SoX0zaqvdPWsv8a1nqlflu9Tx9HN1WpQo5f2LVAyj8at6x/vjwhTn08JyG/iKl4mn0Z7ddC1i4Ea32upft1wVB2+qq//fVH7pX3zF8upMfM6JVhUlHmvsEZ83043Lt/RuC+XynfZfrXsXktdh5pePCZH1hyHC777tiZuG6HHD4I1trmHFgxbppot3tOo1QMSdZ8tzb1KEY1dP1hXz9zQmObfaZfPHnUa31KthzZ9YZ8azStr8KIvdWTnCX3zqYchx/O6P5fjkhq9ZoBunA/QN808tMlrh1oN+URffNc+7jVFKxSUx6+jlT6zi6Z2mqPvusxVtjxvacbecUqbwTYKPffKhTVm3UBdPXNDYz+brl+W7VXHsZ+p1ZBPXtinerNKGrSgh47uPKFvmk/Tsd/81P+Hbnq/VdW41zTp9aEGzf9CV8/4a0yL6Vo8do3qtq6uEcv7JLjN9FnSqe/szmbfv2QtOok+kpmU+4mfSNqNaqELxy5rcodZkqTD24/JwTGVWn7dRGum+SrsaVi8Ph3HtdKeNfs1t/9iQ58dx5U+czq1/6alfl22V5JUv2NtBV69o0ntZikqKkpHd51QpuwZ9Wm/j+X11SJFRkTq/TbVVLRCQfUoN1iXTl6VJB3/w0/zjnuo3Ael49psUZthTXXxxBVN7fKDJOnwzpNycEylzwY01NpZ2xT2NDxeHwfHVPqkRz21H9lMYU9e/fmUhPwmrja96urimQB5DFopSTqy55wcHFKpRbfaWrdwj8JCI+L1cXBMpcbt3lO7vh8kmH9JqtesnG77P9DUgSsUFRWtv/7vvDJldVHTjtU1b8ImRUZEJep+WYs1x+HmXzXSw9tBGtv8O0WEP/u9DVr4pXIXyaXr5/wtkIHE125U85gcz5YkHd5+PCbHn2jNdN8Ej8mOY1tqz9oDmjtgiaHPjuNKnyWd2o9u8a8c1/pXjqN1dNdJZcqewZDj/ksUGRGp1sOaKvhBsAbWGavHD4IlSUd3ndTC09PVclBjLRy50kJZSDxtRzTTheNXNKWTlyTp8I4TSuWYSi0HNdbaGVsSzu+YFtqz7qDmDvKRJB3ZeULps7io3chm+nX5Ptnb26ntiE91ZOcJjW/lGdfv/NFL+vH4VJWtU0JHf/nbaJu9Z3VSZHhkIu4pUipmQMzI0clBpWq9o70/HzBq371mv9KmT6OS1YvF65MjXzblKZorXp89a/+UWyFXuRXOadh2agc9DQ5VVNSzPxge3gmSU2rHuKn96p9W1ok//IwKjfDQcHUq1ldrvttktv1MahydHFSqejHt3XjEqH3Pz4eUNn0alahaNMF+FeqXVpuhTbViykbNT+AD62XPpxTkN3E5OqZSqUoFtG+H8Qf/3u0nlTZdapUonz/BfhVqFlWbXnW10utXLfDYmvC2nRz09Em4ov510WTQvRA5OjkojUtq8+1EEmLtcXj+sJ80otFEo+IjPCwirr8tcHRyUKma7tr780Gj9t1rD8TkOP5SnWc5Nu6zZ+2B53LsGJPjZ8fswzuPYnLsLEnKW8xNf+87G1d8SIbPurOHLqjSx+XMtp/WYshvce1b/3yuDhryWy2hY/gt5SmSS/vWHzLus+5gTH5dlSlHRmXIkk77Nx81es3V0zf04HaQKjUoa9Res0Vlla1TUt7Dlplpz4BnKEDMKGeBHHJK7agbz53h8v/npiQpd5Fc8frkLe4mSbp+LsCo/UZcH8OgvGH2NrkVzqkWAxvLJWNaFa9UWJ/2/VgHNh/Vo/uPJRmm/i+fuqamfRtoyYXZ2ha2QnMOT1apGu7m3dEkxjV/dkPez980ave/eEuSlLuQa4L9zh25pA7u/bV86iZFRsY/w/Oy51MK8pu4XPNmlaOTg25cvm3U7n/lriTJLX/C18WcO3ldHWpP0oq5v71wJmOTz/8pV76sata5hlzSO6tY6bxq0rGaDv5+Wo8fPjHvjiQR1h6H79y4F3cSyNnFWWXqlNTn37bSid1+NjMLHZfj88b5istxTDHxb6bneLshxwMa/SvHDXRgy1E9um8oOB7efqQc+bIlGJdr/vjtyY1rAcOYe/35MfeCYcx1Syi/xRLOr/+FZ7+T4AchigiPiJe7dJlclD6zi1HuMmXPoF6eneQ1YInuBTx4432yJXbRSfOR3Fj1dMyaNWvUuHFjOTk5xbXt379fCxYs0M2bN1W4cGH16NFDhQoVsmKUpnPJ5CJJCg4y/mAPeWT4OaG1qeli+oQ81+fJo6cxfdJKko7/fkqrpm5Qtynt1G1KO0nS+aMXNaHNs2nUjNkyqEbzynp0P1jeg5cqNCRULb9uoonbhqtPleG6cPyyGfYy6UmX0ZCj2DzHConN4Qsu/rwbcP8/t/uy51MK8pu4XGLO6oY8DjVqDwk2/Jw2nXOC/e7eCnrptk8cuKg1P/6hLl9/rC5ffyxJ+ufUDU3uv+JNQk7SrD0O/9vaOwvklNpRD+8E6YeBS153l5Icl0yGfLxajmPGkaAQo/Ynz/Ux5Hijuk1pq25T2koyLBGa0GZmXJ/ti39X/3nd1WNaB62aulFRUVFq1u9j5S3uJgen5D/LlC5jwsfjf+U39nfy/Dj97BhOo9AnYfpj9X417vmBrvhd174Nh5Upewb1+K69IsIj5Zz22axoP68uOn3gvH75aS8XnyNRWHUGZOTIkXr06FHcz3v37lWnTp0UFRWlatWq6fbt22rWrJmOHj36H1tJOuzt7Qz/E51wKRqVwL2j7WL6RD/Xxy52UzFT/X3ndtNngz6Rz/g1GlB7tDw+n62Mb2XQxK3DlTqNoYBzdHKQSyYXDf1wvPas3a+DW//SiIYTFRz0RC0Hv/jCteTuRTmMFfWCdpiG/Cau1xk3TNV77Kdq3qWmls3+RYPb/qBpQ1YrQ2YXjZ//uVI7O772dpMya4/DsVI5pNKoxpM0/OMJOn/koqbvHqvStd55k11LMuztY/50eKUc2yfYxS4mydExffp6ddVngxrLZ/xaDXh/jDw6eynjW+k1ccuwuBxvnf+r5g5Yoo86v68V1+dqxfW5cs2fXb4/7NTT4Kfm2EWretmYGx0Vf8bTPi6/8RIc08fQ7vnlfP26bK+++qGr1gV6a86Bb3X6wHmdO3xBT0MMJz3qtauuElWLaUbPH82yP0BCrHqq4Pl/KHPmzFH79u01dOjQuLaJEyfKw8NDy5Yl/TWIsetRY8+WxYo9Qxz8MCSBPiExfYzPaDjHnPUMfhiirLmyqEGXOlo+8WctHmVYK3/iDz+dPXRB3ien6cPP39eG2dsU8uiJrp6+oTs37sVt58njp/L7v7Mq+O7b5tnJJCg2r8+fiY9dLxySQN5hOvKbuB4HxZyhfG6mI23MNRqxM02vKmuODPrwswpaOfc3LfXcIUk6efCizp28prmb++uD5uW1yefPN4g8abL2OBwrMiJSR3aekGS4QPrHv6ep1dBPdfz3U+bYTat6luPnx4SYHAcllOOE+xjnOLMadHlfyyeu1+LRqyT9K8cnPPRhp9raMGe7JGntjM1a//025SqYQ0F3H+nhnUcatLCnHt17bMY9tY7gh4Zcubwovwksn3xRftOkSx3Tx/A7eRocqmndvTWn/xLlyPeWbl2+o6choarfoaYC/vBT1lyZ9YVHe80b7KMHgUGyT2Uv+1SG4sY+lb3s7e3e6KSITeCkm1kkqWtArly5ok8+MT5T37JlS/n5+Vkpolfjf+GWIiMileu5NfGxP1/1ux6vz/WzhnXKbs/1if35it91Zc/7luzt7XVq3xmj11w+dU0P7wQp3zt5JEk3zt+UY+r4ZzUdHB0U+iT+XV9shf/FQEPeC+Ywas9VwPDzlTM3rBGWzSC/iSvg6l1FRkQqZ96sRu258hl+vvrPrdfabracmWRvby+/o1eM2q+cv6WH94OVr1COF/RM3qw9DldpVD7eRdgR4RG6eOKKsuUx/h0nV3E5LphIOf6/s0aveZbj3JKkIuUKqFrTioqMiNS1s/56eMewkqJw2QL656/Lb76DVuZ/ITDh/MaMwVdOJ5DfmGs/4veJye9pwzhdqUEZuVcpoqfBobrid0NPQ0KVKVsGZcuTVf/8dVll65RU+swuGuDdXdue+GjbEx9N2T5ckjRl+3AtOjPDrPuKlMuqBUjs1Gust99+WyEhxmdO7t+/r/Tp01syrNcWHhquE7tPq1rTSkbthusyHuvMwX/i9fG/cFP+F26qerMqRu3Vm1XRtbP+Crx6R/7/3FRkRGS8D7XcRXIp41sZdPOS4Q+Ug1uPquC7b8ddjCYZ7uH9TtWi+nuv8YemLQkPDdfJfWdVtXF5o/bqTSvo0f1gnT180UqR2Qbym7jCwyJ08tAlVf3A+AtDq9UvqUcPQ3T2xLXX2m7AFUNh8075t43a3fK/pYyZXXTzum1eg2Ptcbj5gEbq69Ut7qyxZJiNca9SRBePGxeDydWzHFc0aq/RrNJ/5PhWTI6Nfy/Vm1WKn+Pn7vKUu0jOmBwbbtRQqqa7hiztLZeMz2a5ytYtqfwl8sS7c1RyFB4arpN7zqhqkwpG7dWbVTSMuYcuxOtjyO8tVf/U+HdS/dOKunbOkF9J+rhrHXWb3MboNU37fKSoyCjt3/KX9m8+qi8rDzd6eMYsxfLs+aNGfephzl1FCmb1JVh16tRR/vz5VbBgQTk5OWnq1Kny8fGRo6Ojjh49qjFjxqhmzZrWDPOVLPt2rSbvHKmRK/tr28Jf5f5eUbUY2Fg/DvlJYU/DlDZ9GuVzzy3/C7f08I7hItKfxq/VoIVfKujeI/258bCqNC6vWi3f07iW0yQZbvO4znOzWgw0fAvqkZ0nlCNfNrUd1UK3rtzWFu9fJEk/e25R/Y61Nd53qBaOWK4nj5+qzYjmio6O1qqpG6yTEAtZNnmDJvl+reFLe2n70t1yr1RYzfs10PyRqxT2NFxp0zsrbzE3BVwKjDtbBtOR38S1wutXTVjURcM822jH2sMqXiafmnWpoQVTtyosNEJpXVIrb6EcCrh6Vw/vB798g5Ie3g/W+sX71LyzYfz8a995Zc+VWW161dWtG/e1bVXy/0PtRaw5DvuMW6OJ20Zo1OoB8p27Q2kzpFHLr5vK2cVZS76xndtNL5uwTpN3jNDIlV9p28Lf5F6liFoMbKQfhyyLGRNic3wzbkz46dt1GrSgp4LuPtafmw6rSqPyqvXZexr3v+mSDLfbXee5RS0GGr7g9Miuk8qR7y21HdnckOMfDTn+5ac9ajWkiUau+kqrPTYpW56s+sKjvf7eeybu+0SSu2UTf9akbcM0YnlfbV/0uyG//Rtq/rAVcfnNW9xNARdvPcvvhJ81aP4XenT3sf70PaIqDcupVosqGt/62U0SNszerolbhuoLj3ba73tE79Z+R62+/kQrpmzQzUuBkhRvGVuamGVy184F6PLfr3dCxJYkxztOJUV20S+6yskC/P39dfbsWZ07dy7uv5cvX9bhw4fl7OysMmXKqGjRovLy8lLmzJnf+P3q2bcwQ9QvV7VJRbX/5jPlLppLd2/c08Y527Rmmq8kw5mb734bo6mdZmvH4t/j+nzcra5aDGisbHmyKuBioFZM+lm7fHYbbbdp3wZq2P0DuebPrnsB93Vk5wktHL487gNUkt5yy6Iuk9qqwkdl5OjkoL/3ntEPAxfrSgJT4uZmn8a630D7XqNyajeiqXIXzqm7/ve1ad4urZ1pWJNdqnoxTd02TB7d52mnT/wPqHptq2ngD93Uvnh/3Yo5U/Qqz6cEKSG/9m7xb29pKe/Ve0dte9dT7gLZdOfWQ/n+9KfWLdgjSSpZsYCm+HTXd1+v0q6fj8TrW7dpOQ2Y/Jk61J6kwBvGMxtNOlRTg1aV5Jo7i+4FBunovvNaPG27yYWMuUX8Y5kZM2uOw2XeL6G2o1qo4LtvKzoqWsd+O6WFw5fpqqWWK9pZZnFD1SYV1H50i3/leIfWTP9Xjn8dramfz9GOxX/E9fm4W1216N/wWY4nr9cunz1G223ap4Eadq9rnOMRK4xObhQum19feLRXobL59fhBsPauO6hFo1bqyePEvwjdLlWqRH8PSar6SXm1G9VcuYvk1N0b97Vx7g6tnbFFklSqRnF57BqpqZ3naufSZ8fox13eV/OvGipbniwKuBSoFVM26pefjMfkWi2rqPXQpnJ9O5sCr97Rprk7tWHOjhfGEfteA+uO04ndpxNnZ5+zIyzpXvdbu/5ka4eQoN+2f23tEF6JVQuQhISHh8vR0XAdw9mzZ1WkSJF4S7Vel6UKkJTK2gUI8KasWYCkFJYqQFI0CxUgKZWlCpCUjALk1SW3AiTJ3TA7tviQpKJFE/6GZQAAAMDiktRp++SL0yQAAAAALIYCBAAAAIDFJLklWAAAAEBSZJe0Lp1OtpgBAQAAAGAxFCAAAAAALIYlWAAAAIApoqwdgG1gBgQAAACAxVCAAAAAALAYlmABAAAAJuAuWObBDAgAAAAAi6EAAQAAAGAxLMECAAAATMEKLLNgBgQAAACAxVCAAAAAALAYlmABAAAApuAuWGbBDAgAAAAAi6EAAQAAAGAxLMECAAAATGDHCiyzYAYEAAAAgMVQgAAAAACwGJZgAQAAAKbgLlhmwQwIAAAAAIuhAAEAAABgMSzBAgAAAExgF2XtCGwDMyAAAAAALIYCBAAAAIDFsAQLAAAAMAV3wTILZkAAAAAAWAwFCAAAAACLYQkWAAAAYApWYJkFMyAAAAAALIYCBAAAAIDFsAQLAAAAMIEdd8EyC2ZAAAAAAFgMBQgAAAAAi2EJFgAAAGAKlmCZBTMgAAAAACyGAgQAAACAxbAECwAAADBFlLUDsA3MgAAAAACwGAoQAAAAABbDEiwAAADABHwRoXkwAwIAAADAYihAAAAAAFgMS7AAAAAAU7AEyyyYAQEAAABgMRQgAAAAACyGJVgAAACAKViCZRYpqgBxKJjf2iHYtOjAO9YOweZFR0RYOwTbFvTI2hHYvFTp0lk7BJsXHRlp7RBsWnQ44zDwpliCBQAAAMBiUtQMCAAAAPDaoqwdgG1gBgQAAACAxVCAAAAAALAYlmABAAAAJrDjLlhmwQwIAAAAkEJFRUVp5syZql69ukqXLq3PP/9cV65ceeHrz58/r27duqlSpUqqUqWK+vTpI39//1d6TwoQAAAAIIWaM2eOVqxYofHjx2vlypWys7NT165dFRYWFu+19+/fV6dOneTi4iIfHx95e3vr/v376tKli0JDQ01+TwoQAAAAwBTR0Unz8ZrCwsK0YMEC9e7dWzVr1lSxYsU0ffp03bp1Szt37oz3+l27dunJkyeaNGmSChcurBIlSmjq1Km6cOGCjh49avL7UoAAAAAAKdCZM2cUHBysypUrx7VlyJBB7u7uOnToULzXV6lSRbNnz1bq1KnjPffw4UOT35eL0AEAAIBkrE6dOv/5/C+//JJg+82bNyVJOXPmNGrPnj27AgIC4r0+d+7cyp07t1HbDz/8oNSpU6tChQomx0sBAgAAAJjCxu6C9eTJE0mSk5OTUXvq1KlNmtFYsmSJli1bpqFDhypr1qwmvy8FCAAAAJCMvWiG42WcnZ0lGa4Fif1/SQoNDVWaNGle2C86Olqenp7y8vJS9+7d1bFjx1d6X64BAQAAAFKg2KVXgYGBRu2BgYFydXVNsE94eLgGDRqkuXPnavDgwerfv/8rvy8FCAAAAGAKa9/tysx3wSpWrJjSpUunAwcOxLUFBQXJz89P5cuXT7DP4MGDtW3bNn333Xfq3Lnza70vS7AAAACAFMjJyUlt27aVh4eHsmTJIjc3N02dOlWurq6qV6+eIiMjde/ePaVPn17Ozs5at26dtmzZosGDB6tixYq6fft23LZiX2MKZkAAAACAFKpPnz5q3ry5RowYoVatWilVqlSaP3++nJycFBAQoGrVqmnLli2SJF9fX0nSlClTVK1aNaNH7GtMYRcdbWOX8/+HjwoPtnYINi068I61Q7B50RER1g7BptmnT2ftEGxedMgTa4dg86IjI60dgk2LDmccTmw7wpZZO4QX+vCd4dYOIUHbTn1r7RBeCTMgAAAAACyGAgQAAACAxXAROgAAAGACu5Rz5UKiYgYEAAAAgMVQgAAAAACwGJZgAQAAAKZgCZZZMAMCAAAAwGIoQAAAAABYDEuwAAAAAFNEsQTLHJgBAQAAAGAxFCAAAAAALIYlWAAAAIApuAuWWTADAgAAAMBiKEAAAAAAWAxLsAAAAABTsATLLJgBAQAAAGAxFCAAAAAALIYlWAAAAIApWIJlFsyAAAAAALAYChAAAAAAFsMSLAAAAMAUUSzBMgdmQAAAAABYDAUIAAAAAIthCRYAAABgiugoa0dgE5gBAQAAAGAxFCAAAAAALIYlWAAAAIAp+CJCs2AGBAAAAIDFUIAAAAAAsBiWYAEAAACm4IsIzYIZEAspV72IPNf10c8nxmvR70P1WffaJvct9I6bNvlNVHa3zHFt2d0ya+v5KS98fDWpRWLsRpJVrk4Jzfx9lNYHeGnxySlq2b+ByX0LvZtPvnfmKUferPGeq9q4nDx/HaG112Zr6SkPDZjzuTJly2DO0JON8vVKataeMdpw21tLTk9Ty4ENTe5b6N23tfnBAuXI+9ZrPZ8SlKvtLs/tX+vnizO06PA4fda7vsl9C5XKo03XZil7niz/+bpuY5pp6805bxpqslaubsxYcXOuFv89VS37f2xy30Lv5pPvXe8ExwpTnk8JGCfMp/wHpfT9n+O18cFCLT3vqf8NbvzSPnVaV9W8Y1O06eEizf/bQx92qhXvNfXa1dC8vybLN2iRlpydoXajmimVQ6oXbrNKo3LaEbZMpWoUf4O9AYwxA2IBxcvk0+i5HbV7y3Etmb5N75TPrw7968ve3k4rvH79z775i+XUGO/P5eBoPDjcvx2kr1p8H+/1DdtUUY0GpbVj9SGz7kNSVrxiQX2zoo92rzuoxePWqUSVwuow8lPZ2dtrhYfvf/bNXyKPxq7qJwfH+P8Uqjcpr+GLe2rzgt+0ePzPypwtg9oNb6LJmwapV80xCg+NSKxdSnLcKxXSN6u+0h9rD2jx2DV6p0oRdRzdXPZ2dlo+ddN/9i1QMo/GreufYI5NeT4lKF6+gEYv/kK7NxzRkkmb9E7FguowtJFhjPDc9p9987u7aYxPz3hjxPNKVC6kxl1MP/Fhi4pXLKRvVvQ1jBXj16lElSLqMOpT2dnbmTZWrP7qhcfpy55PCRgnzMe9cmGNWTdQf6z+U4tGr1KJqkXVcexnsrO30/JJGxLsU71ZJQ1a0EPrZ23ToR0n9F7j8ur/QzeFPQ3Xr8v3SZKa9PpQPae11+61B+Q9ZJkyvJVe7Uc2V4GSeTWmxfR420yfJZ36zu6cqPuKlCll/Eu2sja96+riaX95DFopSTqy55wcHOzVolttrVuwW2EJ/CHr4JhKjdtVVbt+HyjsaXi858PDInXm2FWjtsIlcqtGg9JaPG2bTh25nCj7khS1HfKJLp68qqndf5QkHfnlb6VyTKXP+jXQuu+3J5g/B8dUaty9rtoPb5Lg85LUelAjHdx+XLO+WhrXdu18gGb+NkqVPiytvRuOJM4OJUFthjXVxRNXNLXLD5KkwztPysExlT4b0FBrZ217YY4/6VFP7Uc2U9iTV38+JWkzoIEunrouj96LJUlHfvOTg2Mqtej9gdb98MuLj+HOtdRucCOFPQ37z+2nTuuk/jPa6d7Nh8r2r5nUlKbt0Jixopu3JOnIrr+VyiGVPvvKhLFiRNPXej4lYZwwn7YjmunC8Sua0slLknR4xwmlckylloMaa+2MLQnmsuOYFtqz7qDmDvKRJB3ZeULps7io3chm+nX5Ptnb26ntiE91ZOcJjW/lGdfv/NFL+vH4VJWtU0JHf/nbaJu9Z3VSZHhkIu5pMsRdsMyCJViJzNEplUpVKqh9O4z/Ue/ddlJp06VWiQr5E+xXoWYxteldVyu9ftWCqVtNeq8vv2miaxcC9fPCPW8cd3Lh6OSgktWKat+mo0btezccVtr0zirxXpEE+1X4oJTafN1YK77brAWjV8d73s7OTkd/89OWRX8YtV//55YkKWf+7Gbag6TP0clBpaoX096NxgXXnp8PKW36NCpRtWiC/SrUL602Q5tqxZSNmj9y5Ss/n1I4Ojmo1HuFtW/zMaP2vb5/KW06Z5WoVCjBfhXqlFCbAQ200nObFoxf/5/v0XX0p7oXGKSdK/80U9TJT9xY8dxxbBgr0vz3WDHkE63w8NWCUfHHipc9n1IwTpiPo5ODStUsrn3rDxq171l7UGnTp1HJasXi9cmR7y3lKZJL+9Ybr37Ys+6g3Aq5yq2wqzLlyKgMWdJp/2bjz8urp2/owe0gVWpQ1qi9ZovKKlunpLyHLTPTngHPUIAkMtc8WeXo5KAbl+8YtftfuStJcns7W4L9zp28pg61JmqF16+KjHz52Ydajd5V0dJ5NXf8RkWloAukXN/OJqfUjrrxz02jdv+LgZIkt4I5Eux37ugldSg1WCs8fBUZERXv+ejoaHmPWKn9W44ZtVdtVE6SdMXvhhmiTx5c82c35Pj88zk2FGO5C7km2O/ckUvq4N5fy6duSvAYftnzKYVrvrfkmNpRN2KO2Vj+l2KP4YSL3XPHLqtDhZFa4blNkZHxj+FYZWoUU50WlTS939IUNTY879lYccuoPfY4dnvRcXz0kjqUHBQzViRwHL/k+ZSCccJ8XAsYcnn9+VxeiDlWC+eM1ydvMTdJ0vVzAc/1MWwjd+GcCn4QoojwCOXIZ/x3R7pMLkqf2UWu+Z+1Z8qeQb08O8lrwBLdC3jwxvsEPM/qS7COHz+uAwcOqFu3bpKk/fv3a9GiRbp+/bry5s2rzz//XOXLl7dylK/PJb2zJCnk8VOj9pDgUElS2nSpE+x391bQK71Ps841derwJZ08ePE1oky+0mVMK0kKefRcfmN+TpshTYL97r7GgJqrQHZ1GddC549d1qGdJ1+5f3L1LMdPjNrjcpz+RTm+/5/bfdnzKYVLzDEaL7+PY8cI5wT73b358KXbTpveWf2mtdXSKb7xCpyUJl2mlx3HL8jzS8aK1xlLbBHjhPmky+giSQoJej6Xhp8T+lxzecHx/eRfn4WhT8L0x+r9atzzA13xu659Gw4rU/YM6vFde0WER8o57bO/R/p5ddHpA+f1y097ufj8eSzBMgurzoBs27ZNrVq10sGDhmnG3377TZ06dVJ0dLRq1qyp8PBwdejQQb/99ps1w3wj9vZ2hv95wfFqjjOS7mXzqdA7blrz4x8vf7GNsYvJb/QLBoRoM53xzVMkpyb7DlZ4aITGt5/zwvezRS/LcVQKykViSMwxovu4FroT8EA///DfN7tICezsLDNWpFSME+bz8s+1+DOe9vb2CfeJPe5jjm/PL+fr12V79dUPXbUu0FtzDnyr0wfO69zhC3oaYjjpUa9ddZWoWkwzev5olv0BEmLVGZDvv/9evXr1Us+ePSVJXl5e+uKLL9S3b9+413h5eWnmzJmqXTt53r3lcVDM2YfnZjrSuhh+fn5m5HVU+7CUHj0I0aE/zrzxtpKb4IchkuKfXYs9mxkcFPLG71GqejGN9PlSTx491dAmHrp15c7LO9mQl+U45OGb5zglexxzlvP5M/CxY8bzZzRNVbFeCdX8pJz6fDhZdvZ2spNdXLFjn8pe0VHRKaqQfvlY8Xp5hgHjhPkEPwyW9Gx2NFZsboMfxj9WHz8w9Hl+diRNzDgS+/t5Ghyqad29Naf/EuXI95ZuXb6jpyGhqt+hpgL+8FPWXJn1hUd7zRvsoweBQbJPZS/7VIbixj6Vvezt7VL0Uk6Yj1ULkKtXr6pRo0ZxP1+/fl316xvf+75hw4by8vKydGhmE3D1riIjIpUzn/F9y3PlM9wn/uo/b74somLt4vpz16kEr2Wwdf6XAhUZEalcBYzXycf+fPWM/xttv1bzShrg1Vk3/rmpEc2m645/ylsO4H8xJsfPXU+Tq4Dh5ytnUs71MIkh4PJtwxiR33hddq6YGx1cPXczoW4vVa1hGaVO46Qf/hgZ77nNN77XzpV/alrfpQn0tE0vHisMx/GbjhUpHeOE+fhfiM2l8XUzsbm9cvp6vD6x137kKuiqC8eu/KuPa0wfQ/4rNSijR/eD5ffnubhrGTNly6BsebLqn78uq2ydkkqf2UUDvLtrgHd3o/eYsn24bl6+rfZF+ipFS0EnbhKTVZdg5cmTR3/88WzZUPHixXXmjPFZ/BMnTihHjoQvJE4OwsMidPLQJVX9oIRRe7UPS+rRwxCdPX71BT1Nky5jGrm9/VaKuu3uv4WHRujk/51T1UbGd++o9kl5PXoQrLNHLr32tivUK6lBP3TR6QP/qH/9iSmy+JCk8NBwndx3VlUbG1+LVb1pBT26H6yzh1PWdUfmFh4aoZP7/1HVBu8atVdrWEaPHoTo7F+XX2u7Ph6b1af+JKPH1qV7JUl96k+Sj8fmN4w8eQkPjdDJfedUtXE5o/Zqn5Q3HMdHOI7fBOOE+YSHhuvknjOq2qSCUXv1ZhUNuTx0IV4f/wu35H/hlqp/WtG4z6cVde2cvwKvGmbuP+5aR90mtzF6TdM+HykqMkr7t/yl/ZuP6svKw40enjFLsTx7/qhRn3qYc1eRgll1BqRr164aPny4bt68qYYNG6pnz54aMmSIQkNDVbhwYR0/flyzZ89Wr169rBnmG1sx5xdNWNxVw2a21Y41h1S8bD4161JTC6ZuVVhohNKmS628hXIo4OpdPbwX/Erbzl/UcDeMq8/d2SUlWT51kyZuGKjhi3to+9K9cq9USM37fKgFo9co7Gm40qZ3Vt6iuRRw6bYe3n1k0jYdUzuo36xOCnn8VMu/81XeIsZ3Hbnjfz9FFSTLJm/QJN+vNXxpL21fulvulQqreb8Gmj9y1bMcF3NTwKVAPbxjWo7xzIrpWzVhdR8N8+6iHcv/T8XLF1CznnW1YPx6Q37TOStvEVcFXLmjh3cfm7TNwGv3FHjtnlFbxXqGC9fPv+GJj+Rq+dRNmrhxoIYv7qntPnsMY0XfD7Vg1Op/Hce5FHDR9LECzzBOmM+yiT9r0rZhGrG8r7Yv+l3uVYqoRf+Gmj9sRUwu0yhvcTcFXLwVl8ufJvysQfO/0KO7j/Wn7xFVaVhOtVpU0fjWz77zY8Ps7Zq4Zai+8Gin/b5H9G7td9Tq60+0YsoG3Yy5896je8ZjTJqYG2FcOxegy39fs1AGYOusOgPSpEkTTZgwQVu3blWTJk3Utm1bXbt2TaNHj1br1q31/fffq3PnzurYsaM1w3xjx/df0Le9lip3/mwa5dVBtRuX0fzJW7Q25qLxgu5umr66lyrUin9v75fJlDWdpGfryFOi47vPaHy7OcpdyFWjlvVS7c8q68eRq7VmpuEbpAuVzqcZv4xQxfqlTN6me6VCypozk9JnctHE9QM145cRRo8P29dIrN1Jko7/cVrjWs9S7iKuGr2ir95vWUU/Dl+hNTO2SJIKvfu2PH8frYoflrZypMnT8X3n9G1nb+UumEOjFnZX7WYVNX/sz1o7Z5ckqWCpPJq+ZbAq1C3xki3hvxzffVrj285W7sKuGrWst2q3qKwfR6x6bqwY+UpjBZ5hnDCfY7/7aVzLGcpdJKdGr+mv9/9XVd5Dlmn1NF9JUqEyb2vm3rGq+FGZuD47l+6WZ88fVbZOSX2zpr9K1SyuyZ3maPeaA3GvObLrpCa0m6WydUtq7PpBqta0omb3W6QFI1LGd6yYRVRU0nwkM3bRSeQqxIsXL+ry5ct6/PixHB0d5erqKnd3d6VOnfBtal/HR4UHm21biC86MGVdnG0N0RER1g7BptmnT2ftEGxedEjKPVliKdEp5PsyrCU6nHE4se0IS7pffvhRzi+tHUKCtgbMtnYIr8Tq3wMSq0CBAipQoIC1wwAAAACQiJJMAQIAAAAkaUlj4VCyZ9VrQAAAAACkLBQgAAAAACyGJVgAAACAKViCZRbMgAAAAACwGAoQAAAAABbDEiwAAADAFFEswTIHZkAAAAAAWAwFCAAAAACLYQkWAAAAYILo6Chrh2ATmAEBAAAAYDEUIAAAAAAshiVYAAAAgCm4C5ZZMAMCAAAAwGIoQAAAAABYDEuwAAAAAFNEswTLHJgBAQAAAGAxFCAAAAAALIYlWAAAAIApovgiQnNgBgQAAACAxVCAAAAAALAYlmABAAAApuAuWGbBDAgAAAAAi6EAAQAAAGAxLMECAAAATBDNXbDMghkQAAAAABZDAQIAAADAYliCBQAAAJiCu2CZBTMgAAAAACyGAgQAAACAxbAECwAAADBFFEuwzIEZEAAAAAAWQwECAAAAwGJYggUAAACYIpovIjQHZkAAAAAAWAwFCAAAAACLYQkWAAAAYIJo7oJlFsyAAAAAALAYChAAAAAAFsMSLAAAAMAU3AXLLJgBAQAAAGAxFCAAAAAALIYlWAAAAIAJuAuWeTADAgAAAMBiKEAAAAAAWAxLsAAAAABTcBcss2AGBAAAAIDFUIAAAAAAsBi76OhoLucHAAAAYBHMgAAAAACwGAoQAAAAABZDAQIAAADAYihAAAAAAFgMBQgAAAAAi6EAAQAAAGAxFCAAAAAALIYCBAAAAIDFUIAAAAAAsBgKEAAAAAAWQwECAAAAwGIoQAAAAABYDAUIAAAAAIuhAElioqKiNHPmTFWvXl2lS5fW559/ritXrlg7LJs1Z84ctWvXztph2JQHDx5o1KhRqlGjhsqWLatWrVrp8OHD1g7Lpty9e1eDBg1S5cqVVaZMGXXr1k3//POPtcOySZcuXVKZMmW0bt06a4diU27cuKGiRYvGe6xevdraodmU9evXq0GDBipZsqQ+/vhjbd261dohAZIoQJKcOXPmaMWKFRo/frxWrlwpOzs7de3aVWFhYdYOzeYsWrRIM2fOtHYYNqd///46fvy4pk2bpjVr1uidd95R586ddeHCBWuHZjN69Oiha9euydvbW2vWrJGzs7M6duyoJ0+eWDs0mxIeHq6BAwcqJCTE2qHYnLNnzyp16tTas2eP9u7dG/do1KiRtUOzGRs2bNCwYcPUsmVL+fr6qkGDBurfv7/++usva4cGUIAkJWFhYVqwYIF69+6tmjVrqlixYpo+fbpu3bqlnTt3Wjs8m3Hr1i116dJFnp6eyp8/v7XDsSlXrlzRvn37NHr0aJUvX14FChTQ8OHDlSNHDvn6+lo7PJtw//595c6dW+PGjVPJkiVVsGBB9ezZU7dv39b58+etHZ5NmTVrllxcXKwdhk06d+6c8ufPr+zZsytbtmxxD2dnZ2uHZhOio6Pl6empDh06qEOHDsqXL5++/PJLvffeezp48KC1wwMoQJKSM2fOKDg4WJUrV45ry5Ahg9zd3XXo0CErRmZbTp06pYwZM2rjxo0qXbq0tcOxKZkzZ9a8efNUokSJuDY7OztFR0fr4cOHVozMdmTOnFnTpk1T4cKFJUl37tzR/Pnz5erqqkKFClk5Ottx6NAhrVy5UpMnT7Z2KDbp7NmzHK+J6OLFi7px40a8GaX58+ere/fuVooKeMbB2gHgmZs3b0qScubMadSePXt2BQQEWCMkm/T+++/r/ffft3YYNilDhgyqWbOmUdvWrVt19epVVatWzUpR2a6RI0dq1apVcnJykpeXl9KmTWvtkGxCUFCQBg8erBEjRsQbj2Ee586dU7Zs2dS6dWtdvnxZ+fLlU8+ePVW9enVrh2YTLl++LEkKCQlR586d5efnp9y5c6tHjx58/iFJYAYkCYldv+3k5GTUnjp1aoWGhlojJOCNHDlyRMOGDVOdOnX40EsEHTp00Nq1a9W4cWN9+eWXOnXqlLVDsgnffPON3n33Xa5HSCRhYWG6fPmyHj9+rH79+mnevHkqWbKkunbtqj///NPa4dmEx48fS5K+/vprNWzYUAsWLFDVqlXVs2dPcowkgRmQJCR27WtYWJjROtjQ0FClSZPGWmEBr2XXrl0aOHCgSpcurWnTplk7HJsUu4Rl3LhxOnbsmHx8fDRx4kQrR5W8rV+/XocPH9amTZusHYrNcnJy0qFDh+Tg4BB3wq1EiRK6cOGC5s+frypVqlg5wuTP0dFRktS5c2c1bdpUklS8eHH5+flp4cKF5BhWxwxIEhI71R8YGGjUHhgYKFdXV2uEBLwWHx8f9e7dWzVq1JC3tzcXlprR3bt35evrq8jIyLg2e3t7FSxYMN7YgVe3du1a3b17V7Vq1VKZMmVUpkwZSdLo0aP18ccfWzk625E2bdp4s/1FihTRrVu3rBSRbYn9m6FIkSJG7YUKFdL169etERJghAIkCSlWrJjSpUunAwcOxLUFBQXJz89P5cuXt2JkgOmWLVumcePGqU2bNpoxY0a8PzLwZgIDAzVgwACjO9mEh4fLz89PBQsWtGJktsHDw0NbtmzR+vXr4x6S1KdPH82bN8+6wdmIM2fOqEyZMvG+H+jvv//mwnQzcXd3l4uLi44fP27Ufu7cOeXNm9dKUQHPsAQrCXFyclLbtm3l4eGhLFmyyM3NTVOnTpWrq6vq1atn7fCAl7p06ZImTJigevXqqXv37rp7927cc87OzkqfPr0Vo7MNxYoVU7Vq1TRmzBiNHz9eGTJk0Ny5cxUUFKSOHTtaO7xkL0eOHAm2Z82aVW5ubhaOxjYVKVJEhQsX1pgxYzR69GhlzpxZq1at0rFjx7RmzRprh2cTnJ2d1aVLF82ePVs5cuRQqVKltHnzZu3bt0+LFi2ydngABUhS06dPH0VERGjEiBF6+vSpKlSooPnz53MWGcnC9u3bFR4erp07d8b77pqmTZtq0qRJVorMdtjZ2WnGjBn67rvv1K9fPz169Ejly5fXTz/9pFy5clk7POCl7O3tNXfuXHl4eKhfv34KCgqSu7u7Fi5cqKJFi1o7PJvRs2dPpUmTJu77xAoWLKhZs2apUqVK1g4NkF10dHS0tYMAAAAAkDJwDQgAAAAAi6EAAQAAAGAxFCAAAAAALIYCBAAAAIDFUIAAAAAAsBgKEAAAAAAWQwECAAAAwGIoQAAAAABYDAUIACQzoaGhcnd3V5kyZTRu3DhrhwMAwCuhAAGAZMbOzk6LFy9WqVKl5OPjo0uXLlk7JAAATEYBAgDJjJOTkypUqKAuXbpIkk6dOmXliAAAMB0FCAAkUwUKFJAknT592sqRAABgOgoQAEimvL29JUlnzpyxciQAAJiOAgQAkqG9e/dq+fLlypgxo/z8/KwdDgAAJqMAAYBkJigoSMOGDVOdOnXUqlUr3bt3T7du3bJ2WAAAmIQCBACSmTFjxigiIkLjx4+Xu7u7JJZhAQCSDwoQAEhGtm3bJl9fX3377bfKkiVLXAHChegAgOSCAgQAkonbt29r9OjRatmypWrXri1JypMnjzJkyMB1IACAZIMCBACSiZEjRypjxowaMmSIUXvx4sVZggUASDYoQAAgGVi9erV2796tKVOmKG3atEbPubu76+rVq3r8+LGVogMAwHR20dHR0dYOAgAAAEDKwAwIAAAAAIuhAAEAAABgMRQgAAAAACyGAgQAAACAxVCAAAAAALAYChAAAAAAFkMBAgAAAMBiKEAAAAAAWAwFCAAAAACLoQABAAAAYDEUIAAAAAAshgIEAAAAgMX8PwvBmW2DvMdFAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_78_1.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# optional\n",
+    "# visual representation of grid search\n",
+    "# uses seaborn heatmap, could probably do this in matplotlib\n",
+    "import seaborn as sns\n",
+    "\n",
+    "sns.set()\n",
+    "\n",
+    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "\n",
+    "for i in range(len(eta_vals)):\n",
+    "    for j in range(len(lmbd_vals)):\n",
+    "        dnn = DNN_scikit[i][j]\n",
+    "        \n",
+    "        train_pred = dnn.predict(X_train) \n",
+    "        test_pred = dnn.predict(X_test)\n",
+    "\n",
+    "        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
+    "        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
+    "\n",
+    "        \n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Training Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Test Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe7af77c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Testing our code for the XOR, OR and AND gates\n",
+    "\n",
+    "Last week we discussed three different types of gates, the so-called\n",
+    "XOR, the OR and the AND gates.  Their inputs and outputs can be\n",
+    "summarized using the following tables, first for the OR gate with\n",
+    "inputs $x_1$ and $x_2$ and outputs $y$:\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            1       
    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e12b1cf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The AND and XOR Gates\n",
+    "\n",
+    "The AND gate is defined as\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            0       
       1            0            0       
       1            1            1       
    \n",
+    "\n",
+    "And finally we have the XOR gate\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            0       
    "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4b5002b4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Representing the Data Sets\n",
+    "\n",
+    "Our design matrix is defined by the input values $x_1$ and $x_2$. Since we have four possible outputs, our design matrix reads"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a44df1a3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{X}=\\begin{bmatrix} 0 & 0 \\\\\n",
+    "                       0 & 1 \\\\\n",
+    "\t\t       1 & 0 \\\\\n",
+    "\t\t       1 & 1 \\end{bmatrix},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "acdb4e08",
+   "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."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0567fd0f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the Neural Network\n",
+    "\n",
+    "We define first our design matrix and the various output vectors for the different gates."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "412401df",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[0.80625657 0.36420967]\n",
+      " [0.90297441 0.30170017]\n",
+      " [0.89823921 0.28566769]\n",
+      " [0.93420126 0.25920793]]\n",
+      "[0 0 0 0]\n"
+     ]
+    }
+   ],
+   "source": [
+    "\"\"\"\n",
+    "Simple code that tests XOR, OR and AND gates with linear regression\n",
+    "\"\"\"\n",
+    "\n",
+    "# import necessary packages\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn import datasets\n",
+    "\n",
+    "def sigmoid(x):\n",
+    "    return 1/(1 + np.exp(-x))\n",
+    "\n",
+    "def feed_forward(X):\n",
+    "    # weighted sum of inputs to the hidden layer\n",
+    "    z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
+    "    # activation in the hidden layer\n",
+    "    a_h = sigmoid(z_h)\n",
+    "    \n",
+    "    # weighted sum of inputs to the output layer\n",
+    "    z_o = np.matmul(a_h, output_weights) + output_bias\n",
+    "    # softmax output\n",
+    "    # axis 0 holds each input and axis 1 the probabilities of each category\n",
+    "    probabilities = sigmoid(z_o)\n",
+    "    return probabilities\n",
+    "\n",
+    "# we obtain a prediction by taking the class with the highest likelihood\n",
+    "def predict(X):\n",
+    "    probabilities = feed_forward(X)\n",
+    "    return np.argmax(probabilities, axis=1)\n",
+    "\n",
+    "# ensure the same random numbers appear every time\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "# Design matrix\n",
+    "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
+    "\n",
+    "# The XOR gate\n",
+    "yXOR = np.array( [ 0, 1 ,1, 0])\n",
+    "# The OR gate\n",
+    "yOR = np.array( [ 0, 1 ,1, 1])\n",
+    "# The AND gate\n",
+    "yAND = np.array( [ 0, 0 ,0, 1])\n",
+    "\n",
+    "# Defining the neural network\n",
+    "n_inputs, n_features = X.shape\n",
+    "n_hidden_neurons = 2\n",
+    "n_categories = 2\n",
+    "n_features = 2\n",
+    "\n",
+    "# we make the weights normally distributed using numpy.random.randn\n",
+    "\n",
+    "# weights and bias in the hidden layer\n",
+    "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n",
+    "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n",
+    "\n",
+    "# weights and bias in the output layer\n",
+    "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n",
+    "output_bias = np.zeros(n_categories) + 0.01\n",
+    "\n",
+    "probabilities = feed_forward(X)\n",
+    "print(probabilities)\n",
+    "\n",
+    "\n",
+    "predictions = predict(X)\n",
+    "print(predictions)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53c52dab",
+   "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": "7d192a02",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Code using Scikit-Learn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "766d5af6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1e-05\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.0001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.001\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.25\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.75\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.75\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.01\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  1.0\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  1.0\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  0.1\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.75\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.75\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.75\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  1.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.001\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  0.01\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate  = "
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n",
+      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      " 10.0\n",
+      "Lambda =  0.1\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  1.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n",
+      "Learning rate  =  10.0\n",
+      "Lambda =  10.0\n",
+      "Accuracy score on data set:  0.5\n",
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "
    "
+      ]
+     },
+     "metadata": {
+      "filenames": {
+       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week42_88_4.png"
+      }
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# import necessary packages\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.neural_network import MLPClassifier\n",
+    "from sklearn.metrics import accuracy_score\n",
+    "import seaborn as sns\n",
+    "\n",
+    "# ensure the same random numbers appear every time\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "# Design matrix\n",
+    "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
+    "\n",
+    "# The XOR gate\n",
+    "yXOR = np.array( [ 0, 1 ,1, 0])\n",
+    "# The OR gate\n",
+    "yOR = np.array( [ 0, 1 ,1, 1])\n",
+    "# The AND gate\n",
+    "yAND = np.array( [ 0, 0 ,0, 1])\n",
+    "\n",
+    "# Defining the neural network\n",
+    "n_inputs, n_features = X.shape\n",
+    "n_hidden_neurons = 2\n",
+    "n_categories = 2\n",
+    "n_features = 2\n",
+    "\n",
+    "eta_vals = np.logspace(-5, 1, 7)\n",
+    "lmbd_vals = np.logspace(-5, 1, 7)\n",
+    "# store models for later use\n",
+    "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
+    "epochs = 100\n",
+    "\n",
+    "for i, eta in enumerate(eta_vals):\n",
+    "    for j, lmbd in enumerate(lmbd_vals):\n",
+    "        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n",
+    "                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n",
+    "        dnn.fit(X, yXOR)\n",
+    "        DNN_scikit[i][j] = dnn\n",
+    "        print(\"Learning rate  = \", eta)\n",
+    "        print(\"Lambda = \", lmbd)\n",
+    "        print(\"Accuracy score on data set: \", dnn.score(X, yXOR))\n",
+    "        print()\n",
+    "\n",
+    "sns.set()\n",
+    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "for i in range(len(eta_vals)):\n",
+    "    for j in range(len(lmbd_vals)):\n",
+    "        dnn = DNN_scikit[i][j]\n",
+    "        test_pred = dnn.predict(X)\n",
+    "        test_accuracy[i][j] = accuracy_score(yXOR, test_pred)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Test Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9b182ae1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Building neural networks in Tensorflow and Keras\n",
+    "\n",
+    "Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n",
+    "and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n",
+    "and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.  \n",
+    "\n",
+    "In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n",
+    "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n",
+    "NumPy arrays."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60683ec5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Tensorflow\n",
+    "\n",
+    "Tensorflow is an open source library machine learning library\n",
+    "developed by the Google Brain team for internal use. It was released\n",
+    "under the Apache 2.0 open source license in November 9, 2015.\n",
+    "\n",
+    "Tensorflow is a computational framework that allows you to construct\n",
+    "machine learning models at different levels of abstraction, from\n",
+    "high-level, object-oriented APIs like Keras, down to the C++ kernels\n",
+    "that Tensorflow is built upon. The higher levels of abstraction are\n",
+    "simpler to use, but less flexible, and our choice of implementation\n",
+    "should reflect the problems we are trying to solve.\n",
+    "\n",
+    "[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n",
+    "in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n",
+    "to represent your model, and then create a Tensorflow *session* to run the graph.\n",
+    "\n",
+    "In this guide we will analyze the same data as we did in our NumPy and\n",
+    "scikit-learn tutorial, gathered from the MNIST database of images. We\n",
+    "will give an introduction to the lower level Python Application\n",
+    "Program Interfaces (APIs), and see how we use them to build our graph.\n",
+    "Then we will build (effectively) the same graph in Keras, to see just\n",
+    "how simple solving a machine learning problem can be.\n",
+    "\n",
+    "To install tensorflow on Unix/Linux systems, use pip as"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "8a0c6901",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (2357089093.py, line 1)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  Input \u001b[0;32mIn [14]\u001b[0;36m\u001b[0m\n\u001b[0;31m    pip3 install tensorflow\u001b[0m\n\u001b[0m         ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+     ]
+    }
+   ],
+   "source": [
+    "pip3 install tensorflow"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b66e0227",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
+    "(current release of CPU-only TensorFlow)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "df994f58",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "conda create -n tf tensorflow\n",
+    "conda activate tf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9005559",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "To install the current release of GPU TensorFlow"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "7287b5eb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "conda create -n tf-gpu tensorflow-gpu\n",
+    "conda activate tf-gpu"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c066b083",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Keras\n",
+    "\n",
+    "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n",
+    "that supports Tensorflow, CTNK and Theano as backends.  \n",
+    "If you have Anaconda installed you may run the following command"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "6582adea",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "conda install keras"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d305596",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "You can look up the [instructions here](https://keras.io/) for more information.\n",
+    "\n",
+    "We will to a large extent use **keras** in this course."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a4508850",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Collect and pre-process data\n",
+    "\n",
+    "Let us look again at the MINST data set."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "5f2256f6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# import necessary packages\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import tensorflow as tf\n",
+    "from sklearn import datasets\n",
+    "\n",
+    "\n",
+    "# ensure the same random numbers appear every time\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "# display images in notebook\n",
+    "%matplotlib inline\n",
+    "plt.rcParams['figure.figsize'] = (12,12)\n",
+    "\n",
+    "\n",
+    "# download MNIST dataset\n",
+    "digits = datasets.load_digits()\n",
+    "\n",
+    "# define inputs and labels\n",
+    "inputs = digits.images\n",
+    "labels = digits.target\n",
+    "\n",
+    "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
+    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
+    "\n",
+    "\n",
+    "# flatten the image\n",
+    "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
+    "n_inputs = len(inputs)\n",
+    "inputs = inputs.reshape(n_inputs, -1)\n",
+    "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
+    "\n",
+    "\n",
+    "# choose some random images to display\n",
+    "indices = np.arange(n_inputs)\n",
+    "random_indices = np.random.choice(indices, size=5)\n",
+    "\n",
+    "for i, image in enumerate(digits.images[random_indices]):\n",
+    "    plt.subplot(1, 5, i+1)\n",
+    "    plt.axis('off')\n",
+    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
+    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "a5dfa0e9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from tensorflow.keras.layers import Input\n",
+    "from tensorflow.keras.models import Sequential      #This allows appending layers to existing models\n",
+    "from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer\n",
+    "from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n",
+    "from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)\n",
+    "from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function\n",
+    "\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "\n",
+    "# one-hot representation of labels\n",
+    "labels = to_categorical(labels)\n",
+    "\n",
+    "# split into train and test data\n",
+    "train_size = 0.8\n",
+    "test_size = 1 - train_size\n",
+    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
+    "                                                    test_size=test_size)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "dd935ce0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "epochs = 100\n",
+    "batch_size = 100\n",
+    "n_neurons_layer1 = 100\n",
+    "n_neurons_layer2 = 50\n",
+    "n_categories = 10\n",
+    "eta_vals = np.logspace(-5, 1, 7)\n",
+    "lmbd_vals = np.logspace(-5, 1, 7)\n",
+    "def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n",
+    "    model = Sequential()\n",
+    "    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
+    "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
+    "    model.add(Dense(n_categories, activation='softmax'))\n",
+    "    \n",
+    "    sgd = optimizers.SGD(lr=eta)\n",
+    "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
+    "    \n",
+    "    return model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "67158cb2",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
+    "        \n",
+    "for i, eta in enumerate(eta_vals):\n",
+    "    for j, lmbd in enumerate(lmbd_vals):\n",
+    "        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n",
+    "                                         eta=eta, lmbd=lmbd)\n",
+    "        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
+    "        scores = DNN.evaluate(X_test, Y_test)\n",
+    "        \n",
+    "        DNN_keras[i][j] = DNN\n",
+    "        \n",
+    "        print(\"Learning rate = \", eta)\n",
+    "        print(\"Lambda = \", lmbd)\n",
+    "        print(\"Test accuracy: %.3f\" % scores[1])\n",
+    "        print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "86d74ee3",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# optional\n",
+    "# visual representation of grid search\n",
+    "# uses seaborn heatmap, could probably do this in matplotlib\n",
+    "import seaborn as sns\n",
+    "\n",
+    "sns.set()\n",
+    "\n",
+    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "\n",
+    "for i in range(len(eta_vals)):\n",
+    "    for j in range(len(lmbd_vals)):\n",
+    "        DNN = DNN_keras[i][j]\n",
+    "\n",
+    "        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n",
+    "        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n",
+    "\n",
+    "        \n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Training Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Test Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "563d3f68",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Breast Cancer Data, now with Keras"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "34e6467a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "import tensorflow as tf\n",
+    "from tensorflow.keras.layers import Input\n",
+    "from tensorflow.keras.models import Sequential      #This allows appending layers to existing models\n",
+    "from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer\n",
+    "from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n",
+    "from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)\n",
+    "from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "from sklearn.model_selection import train_test_split as splitter\n",
+    "from sklearn.datasets import load_breast_cancer\n",
+    "import pickle\n",
+    "import os \n",
+    "\n",
+    "\n",
+    "\"\"\"Load breast cancer dataset\"\"\"\n",
+    "\n",
+    "np.random.seed(0)        #create same seed for random number every time\n",
+    "\n",
+    "cancer=load_breast_cancer()      #Download breast cancer dataset\n",
+    "\n",
+    "inputs=cancer.data                     #Feature matrix of 569 rows (samples) and 30 columns (parameters)\n",
+    "outputs=cancer.target                  #Label array of 569 rows (0 for benign and 1 for malignant)\n",
+    "labels=cancer.feature_names[0:30]\n",
+    "\n",
+    "print('The content of the breast cancer dataset is:')      #Print information about the datasets\n",
+    "print(labels)\n",
+    "print('-------------------------')\n",
+    "print(\"inputs =  \" + str(inputs.shape))\n",
+    "print(\"outputs =  \" + str(outputs.shape))\n",
+    "print(\"labels =  \"+ str(labels.shape))\n",
+    "\n",
+    "x=inputs      #Reassign the Feature and Label matrices to other variables\n",
+    "y=outputs\n",
+    "\n",
+    "#%% \n",
+    "\n",
+    "# Visualisation of dataset (for correlation analysis)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)\n",
+    "plt.xlabel('Mean radius',fontweight='bold')\n",
+    "plt.ylabel('Mean perimeter',fontweight='bold')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)\n",
+    "plt.xlabel('Mean compactness',fontweight='bold')\n",
+    "plt.ylabel('Mean concavity',fontweight='bold')\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)\n",
+    "plt.xlabel('Mean radius',fontweight='bold')\n",
+    "plt.ylabel('Mean texture',fontweight='bold')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)\n",
+    "plt.xlabel('Mean perimeter',fontweight='bold')\n",
+    "plt.ylabel('Mean compactness',fontweight='bold')\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "# Generate training and testing datasets\n",
+    "\n",
+    "#Select features relevant to classification (texture,perimeter,compactness and symmetery) \n",
+    "#and add to input matrix\n",
+    "\n",
+    "temp1=np.reshape(x[:,1],(len(x[:,1]),1))\n",
+    "temp2=np.reshape(x[:,2],(len(x[:,2]),1))\n",
+    "X=np.hstack((temp1,temp2))      \n",
+    "temp=np.reshape(x[:,5],(len(x[:,5]),1))\n",
+    "X=np.hstack((X,temp))       \n",
+    "temp=np.reshape(x[:,8],(len(x[:,8]),1))\n",
+    "X=np.hstack((X,temp))       \n",
+    "\n",
+    "X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1)   #Split datasets into training and testing\n",
+    "\n",
+    "y_train=to_categorical(y_train)     #Convert labels to categorical when using categorical cross entropy\n",
+    "y_test=to_categorical(y_test)\n",
+    "\n",
+    "del temp1,temp2,temp\n",
+    "\n",
+    "# %%\n",
+    "\n",
+    "# Define tunable parameters\"\n",
+    "\n",
+    "eta=np.logspace(-3,-1,3)                    #Define vector of learning rates (parameter to SGD optimiser)\n",
+    "lamda=0.01                                  #Define hyperparameter\n",
+    "n_layers=2                                  #Define number of hidden layers in the model\n",
+    "n_neuron=np.logspace(0,3,4,dtype=int)       #Define number of neurons per layer\n",
+    "epochs=100                                   #Number of reiterations over the input data\n",
+    "batch_size=100                              #Number of samples per gradient update\n",
+    "\n",
+    "# %%\n",
+    "\n",
+    "\"\"\"Define function to return Deep Neural Network model\"\"\"\n",
+    "\n",
+    "def NN_model(inputsize,n_layers,n_neuron,eta,lamda):\n",
+    "    model=Sequential()      \n",
+    "    for i in range(n_layers):       #Run loop to add hidden layers to the model\n",
+    "        if (i==0):                  #First layer requires input dimensions\n",
+    "            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))\n",
+    "        else:                       #Subsequent layers are capable of automatic shape inferencing\n",
+    "            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))\n",
+    "    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)\n",
+    "    sgd=optimizers.SGD(lr=eta)\n",
+    "    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])\n",
+    "    return model\n",
+    "\n",
+    "    \n",
+    "Train_accuracy=np.zeros((len(n_neuron),len(eta)))      #Define matrices to store accuracy scores as a function\n",
+    "Test_accuracy=np.zeros((len(n_neuron),len(eta)))       #of learning rate and number of hidden neurons for \n",
+    "\n",
+    "for i in range(len(n_neuron)):     #run loops over hidden neurons and learning rates to calculate \n",
+    "    for j in range(len(eta)):      #accuracy scores \n",
+    "        DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)\n",
+    "        DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)\n",
+    "        Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]\n",
+    "        Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]\n",
+    "               \n",
+    "\n",
+    "def plot_data(x,y,data,title=None):\n",
+    "\n",
+    "    # plot results\n",
+    "    fontsize=16\n",
+    "\n",
+    "\n",
+    "    fig = plt.figure()\n",
+    "    ax = fig.add_subplot(111)\n",
+    "    cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)\n",
+    "    \n",
+    "    cbar=fig.colorbar(cax)\n",
+    "    cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)\n",
+    "    cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])\n",
+    "    cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])\n",
+    "\n",
+    "    # put text on matrix elements\n",
+    "    for i, x_val in enumerate(np.arange(len(x))):\n",
+    "        for j, y_val in enumerate(np.arange(len(y))):\n",
+    "            c = \"${0:.1f}\\\\%$\".format( 100*data[j,i])  \n",
+    "            ax.text(x_val, y_val, c, va='center', ha='center')\n",
+    "\n",
+    "    # convert axis vaues to to string labels\n",
+    "    x=[str(i) for i in x]\n",
+    "    y=[str(i) for i in y]\n",
+    "\n",
+    "\n",
+    "    ax.set_xticklabels(['']+x)\n",
+    "    ax.set_yticklabels(['']+y)\n",
+    "\n",
+    "    ax.set_xlabel('$\\\\mathrm{learning\\\\ rate}$',fontsize=fontsize)\n",
+    "    ax.set_ylabel('$\\\\mathrm{hidden\\\\ neurons}$',fontsize=fontsize)\n",
+    "    if title is not None:\n",
+    "        ax.set_title(title)\n",
+    "\n",
+    "    plt.tight_layout()\n",
+    "\n",
+    "    plt.show()\n",
+    "    \n",
+    "plot_data(eta,n_neuron,Train_accuracy, 'training')\n",
+    "plot_data(eta,n_neuron,Test_accuracy, 'testing')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "09879108",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Fine-tuning neural network hyperparameters\n",
+    "\n",
+    "The flexibility of neural networks is also one of their main\n",
+    "drawbacks: there are many hyperparameters to tweak. Not only can you\n",
+    "use any imaginable network topology (how neurons/nodes are interconnected),\n",
+    "but even in a simple FFNN you can change the number of layers, the\n",
+    "number of neurons per layer, the type of activation function to use in\n",
+    "each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you\n",
+    "know what combination of hyperparameters is the best for your task?\n",
+    "\n",
+    "* You can use grid search with cross-validation to find the right hyperparameters.\n",
+    "\n",
+    "However,since there are many hyperparameters to tune, and since\n",
+    "training a neural network on a large dataset takes a lot of time, you\n",
+    "will only be able to explore a tiny part of the hyperparameter space.\n",
+    "\n",
+    "* You can use randomized search.\n",
+    "\n",
+    "* Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8ec1769",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Hidden layers\n",
+    "\n",
+    "For many problems you can start with just one or two hidden layers and it will work just fine.\n",
+    "For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a\n",
+    "few hundred neurons.\n",
+    "You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of\n",
+    "neurons, in roughly the same amount of training time. \n",
+    "\n",
+    "For more complex problems, you can gradually\n",
+    "ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such\n",
+    "as large image classification or speech recognition, typically require networks with dozens of layers\n",
+    "and they need a huge amount\n",
+    "of training data. However, you will rarely have to train such networks from scratch: it is much more\n",
+    "common to reuse parts of a pretrained state-of-the-art network that performs a similar task."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "43cc1fe5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Which activation function should I use?\n",
+    "\n",
+    "The Back propagation algorithm we derived above works by going from\n",
+    "the output layer to the input layer, propagating the error gradient on\n",
+    "the way. Once the algorithm has computed the gradient of the cost\n",
+    "function with regards to each parameter in the network, it uses these\n",
+    "gradients to update each parameter with a Gradient Descent (GD) step.\n",
+    "\n",
+    "Unfortunately for us, the gradients often get smaller and smaller as the\n",
+    "algorithm progresses down to the first hidden layers. As a result, the\n",
+    "GD update leaves the lower layer connection weights\n",
+    "virtually unchanged, and training never converges to a good\n",
+    "solution. This is known in the literature as \n",
+    "**the vanishing gradients problem**. \n",
+    "\n",
+    "In other cases, the opposite can happen, namely the the gradients can grow bigger and\n",
+    "bigger. The result is that many of the layers get large updates of the \n",
+    "weights the\n",
+    "algorithm diverges. This is the **exploding gradients problem**, which is\n",
+    "mostly encountered in recurrent neural networks. More generally, deep\n",
+    "neural networks suffer from unstable gradients, different layers may\n",
+    "learn at widely different speeds"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9cbce9f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Is the Logistic activation function (Sigmoid)  our choice?\n",
+    "\n",
+    "Although this unfortunate behavior has been empirically observed for\n",
+    "quite a while (it was one of the reasons why deep neural networks were\n",
+    "mostly abandoned for a long time), it is only around 2010 that\n",
+    "significant progress was made in understanding it.\n",
+    "\n",
+    "A paper titled [Understanding the Difficulty of Training Deep\n",
+    "Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio](http://proceedings.mlr.press/v9/glorot10a.html) found that\n",
+    "the problems with the popular logistic\n",
+    "sigmoid activation function and the weight initialization technique\n",
+    "that was most popular at the time, namely random initialization using\n",
+    "a normal distribution with a mean of 0 and a standard deviation of\n",
+    "1. \n",
+    "\n",
+    "They showed that with this activation function and this\n",
+    "initialization scheme, the variance of the outputs of each layer is\n",
+    "much greater than the variance of its inputs. Going forward in the\n",
+    "network, the variance keeps increasing after each layer until the\n",
+    "activation function saturates at the top layers. This is actually made\n",
+    "worse by the fact that the logistic function has a mean of 0.5, not 0\n",
+    "(the hyperbolic tangent function has a mean of 0 and behaves slightly\n",
+    "better than the logistic function in deep networks)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2dfb3f9a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The derivative of the Logistic funtion\n",
+    "\n",
+    "Looking at the logistic activation function, when inputs become large\n",
+    "(negative or positive), the function saturates at 0 or 1, with a\n",
+    "derivative extremely close to 0. Thus when backpropagation kicks in,\n",
+    "it has virtually no gradient to propagate back through the network,\n",
+    "and what little gradient exists keeps getting diluted as\n",
+    "backpropagation progresses down through the top layers, so there is\n",
+    "really nothing left for the lower layers.\n",
+    "\n",
+    "In their paper, Glorot and Bengio propose a way to significantly\n",
+    "alleviate this problem. We need the signal to flow properly in both\n",
+    "directions: in the forward direction when making predictions, and in\n",
+    "the reverse direction when backpropagating gradients. We don’t want\n",
+    "the signal to die out, nor do we want it to explode and saturate. For\n",
+    "the signal to flow properly, the authors argue that we need the\n",
+    "variance of the outputs of each layer to be equal to the variance of\n",
+    "its inputs, and we also need the gradients to have equal variance\n",
+    "before and after flowing through a layer in the reverse direction.\n",
+    "\n",
+    "One of the insights in the 2010 paper by Glorot and Bengio was that\n",
+    "the vanishing/exploding gradients problems were in part due to a poor\n",
+    "choice of activation function. Until then most people had assumed that\n",
+    "if Nature had chosen to use roughly sigmoid activation functions in\n",
+    "biological neurons, they must be an excellent choice. But it turns out\n",
+    "that other activation functions behave much better in deep neural\n",
+    "networks, in particular the ReLU activation function, mostly because\n",
+    "it does not saturate for positive values (and also because it is quite\n",
+    "fast to compute)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f806c047",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The RELU function family\n",
+    "\n",
+    "The ReLU activation function suffers from a problem known as the dying\n",
+    "ReLUs: during training, some neurons effectively die, meaning they\n",
+    "stop outputting anything other than 0.\n",
+    "\n",
+    "In some cases, you may find that half of your network’s neurons are\n",
+    "dead, especially if you used a large learning rate. During training,\n",
+    "if a neuron’s weights get updated such that the weighted sum of the\n",
+    "neuron’s inputs is negative, it will start outputting 0. When this\n",
+    "happen, the neuron is unlikely to come back to life since the gradient\n",
+    "of the ReLU function is 0 when its input is negative.\n",
+    "\n",
+    "To solve this problem, nowadays practitioners use a  variant of the ReLU\n",
+    "function, such as the leaky ReLU discussed above or the so-called\n",
+    "exponential linear unit (ELU) function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ef9e2a08",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e2750d8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Which activation function should we use?\n",
+    "\n",
+    "In general it seems that the ELU activation function is better than\n",
+    "the leaky ReLU function (and its variants), which is better than\n",
+    "ReLU. ReLU performs better than $\\tanh$ which in turn performs better\n",
+    "than the logistic function. \n",
+    "\n",
+    "If runtime\n",
+    "performance is an issue, then you may opt for the  leaky ReLU function  over the \n",
+    "ELU function If you don’t\n",
+    "want to tweak yet another hyperparameter, you may just use the default\n",
+    "$\\alpha$ of $0.01$ for the leaky ReLU, and $1$ for ELU. If you have\n",
+    "spare time and computing power, you can use cross-validation or\n",
+    "bootstrap to evaluate other activation functions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e566f13",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on activation functions, output layers\n",
+    "\n",
+    "In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).\n",
+    "\n",
+    "It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.\n",
+    "\n",
+    "**For the output layer:**\n",
+    "\n",
+    "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n",
+    "\n",
+    "* For regression tasks, you can simply use no activation function at all."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "03205666",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Batch Normalization\n",
+    "\n",
+    "Batch Normalization\n",
+    "aims to address the vanishing/exploding gradients problems, and more generally the problem that the\n",
+    "distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.\n",
+    "\n",
+    "The technique consists of adding an operation in the model just before the activation function of each\n",
+    "layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new\n",
+    "parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model\n",
+    "learn the optimal scale and mean of the inputs for each layer.\n",
+    "In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and\n",
+    "standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current\n",
+    "mini-batch, from this the name batch normalization."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad7c3e53",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Dropout\n",
+    "\n",
+    "It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but\n",
+    "excluding the output neurons) has a probability $p$ of being temporarily dropped out, meaning it will be\n",
+    "entirely ignored during this training step, but it may be active during the next step.\n",
+    "\n",
+    "The\n",
+    "hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.\n",
+    " It is viewed as one of the most popular regularization techniques."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c3b98a7c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient Clipping\n",
+    "\n",
+    "A popular technique to lessen the exploding gradients problem is to simply clip the gradients during\n",
+    "backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural\n",
+    "networks).\n",
+    "\n",
+    "This technique is called Gradient Clipping.\n",
+    "\n",
+    "In general however, Batch\n",
+    "Normalization is preferred."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e7f21477",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## A very nice website on Neural Networks\n",
+    "\n",
+    "You may find this [website](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.29243&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false) very useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54968291",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## A top-down perspective on Neural networks\n",
+    "\n",
+    "The first thing we would like to do is divide the data into two or three\n",
+    "parts. A training set, a validation or dev (development) set, and a\n",
+    "test set. The test set is the data on which we want to make\n",
+    "predictions. The dev set is a subset of the training data we use to\n",
+    "check how well we are doing out-of-sample, after training the model on\n",
+    "the training dataset. We use the validation error as a proxy for the\n",
+    "test error in order to make tweaks to our model. It is crucial that we\n",
+    "do not use any of the test data to train the algorithm. This is a\n",
+    "cardinal sin in ML. Then:\n",
+    "\n",
+    "* Estimate optimal error rate\n",
+    "\n",
+    "* Minimize underfitting (bias) on training data set.\n",
+    "\n",
+    "* Make sure you are not overfitting.\n",
+    "\n",
+    "If the validation and test sets are drawn from the same distributions,\n",
+    "then a good performance on the validation set should lead to similarly\n",
+    "good performance on the test set. \n",
+    "\n",
+    "However, sometimes\n",
+    "the training data and test data differ in subtle ways because, for\n",
+    "example, they are collected using slightly different methods, or\n",
+    "because it is cheaper to collect data in one way versus another. In\n",
+    "this case, there can be a mismatch between the training and test\n",
+    "data. This can lead to the neural network overfitting these small\n",
+    "differences between the test and training sets, and a poor performance\n",
+    "on the test set despite having a good performance on the validation\n",
+    "set. To rectify this, Andrew Ng suggests making two validation or dev\n",
+    "sets, one constructed from the training data and one constructed from\n",
+    "the test data. The difference between the performance of the algorithm\n",
+    "on these two validation sets quantifies the train-test mismatch. This\n",
+    "can serve as another important diagnostic when using DNNs for\n",
+    "supervised learning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4500b85e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Limitations of supervised learning with deep networks\n",
+    "\n",
+    "Like all statistical methods, supervised learning using neural\n",
+    "networks has important limitations. This is especially important when\n",
+    "one seeks to apply these methods, especially to physics problems. Like\n",
+    "all tools, DNNs are not a universal solution. Often, the same or\n",
+    "better performance on a task can be achieved by using a few\n",
+    "hand-engineered features (or even a collection of random\n",
+    "features). \n",
+    "\n",
+    "Here we list some of the important limitations of supervised neural network based models. \n",
+    "\n",
+    "* **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).\n",
+    "\n",
+    "* **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.\n",
+    "\n",
+    "* **Homogeneous data.** Almost all DNNs deal with homogeneous data of one type. It is very hard to design architectures that mix and match data types (i.e. some continuous variables, some discrete variables, some time series). In applications beyond images, video, and language, this is often what is required. In contrast, ensemble models like random forests or gradient-boosted trees have no difficulty handling mixed data types.\n",
+    "\n",
+    "* **Many problems are not about prediction.** In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a *wrong* model. The model might or might not be useful for understanding the underlying science.\n",
+    "\n",
+    "Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems."
+   ]
+  }
+ ],
+ "metadata": {
+  "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"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/week42.py b/doc/LectureNotes/_build/jupyter_execute/week42.py
new file mode 100644
index 000000000..e0de0fafb
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/week42.py
@@ -0,0 +1,1930 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# 
+# 
+
+# # Week 42 Constructing a Neural Network code with introduction to Tensor flow
+# **Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University
+# 
+# Date: **October 16-20, 2023**
+
+# ## Plan for week 42
+# 
+# **Material for the active learning sessions on Tuesday and Wednesday.**
+# 
+#   * Exercise on writing your own stochastic gradient and gradient descent codes. This exercise continues from the previous  week but now with inclusion of automatic differentiation
+# 
+#   * Discussion of project 2
+# 
+#   * [See video on automatic differentiation from last year](https://www.youtube.com/watch?v=cWCebuNKrA8). This video will be updated before Tuesday.
+# 
+#   
+# 
+# **Material for the lecture on Thursday October 12, 2023.**
+# 
+#   * Building our own Feed-forward Neural Network and discussion of project 2
+# 
+#   * Readings and Videos:
+# 
+#     * These lecture notes
+# 
+#     * [Aurelien Geron's chapters 10-11](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Textbooks/TensorflowML.pdf)
+# 
+#     * For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.     
+# 
+#     * [Neural Networks demystified](https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs)
+# 
+#     * [Building Neural Networks from scratch](https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex)
+# 
+#     * [Video on Neural Networks](https://www.youtube.com/watch?v=CqOfi41LfDw)
+# 
+#     * [Video on the back propagation algorithm](https://www.youtube.com/watch?v=Ilg3gGewQ5U)
+# 
+# I also  recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at .
+
+# ## Lecture Thursday October 19
+
+# ## Review of the back propagation algorithm
+# 
+# During the last lecture we discussed in detail the back propagation
+# algorithm. This algorithm is based on a repeated application of the
+# chain rule. Let us bring back the basic equation and at the same time
+# link this with the basic mathematics of automatic differentiation.
+
+# ## Setting up the Back propagation algorithm
+# 
+# The four equations  derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.
+# 
+# First, we set up the input data $\boldsymbol{x}$ and the activations
+# $\boldsymbol{z}_1$ of the input layer and compute the activation function and
+# the pertinent outputs $\boldsymbol{a}^1$.
+# 
+# Secondly, we perform then the feed forward till we reach the output
+# layer and compute all $\boldsymbol{z}_l$ of the input layer and compute the
+# activation function and the pertinent outputs $\boldsymbol{a}^l$ for
+# $l=2,3,\dots,L$.
+# 
+# Thereafter we compute the ouput error $\boldsymbol{\delta}^L$ by computing all
+
+# $$
+# \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
+# $$
+
+# Then we compute the back propagate error for each $l=L-1,L-2,\dots,2$ as
+
+# $$
+# \delta_j^l = \sum_k \delta_k^{l+1}w_{kj}^{l+1}f'(z_j^l).
+# $$
+
+# Finally, we update the weights and the biases using gradient descent for each $l=L-1,L-2,\dots,2$ and update the weights and biases according to the rules
+
+# $$
+# w_{jk}^l\leftarrow  = w_{jk}^l- \eta \delta_j^la_k^{l-1},
+# $$
+
+# $$
+# b_j^l \leftarrow b_j^l-\eta \frac{\partial {\cal C}}{\partial b_j^l}=b_j^l-\eta \delta_j^l,
+# $$
+
+# The parameter $\eta$ is the learning parameter discussed in connection with the gradient descent methods.
+# Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training.
+
+# ## Setting up a Multi-layer perceptron model for classification
+# 
+# We are now gong to develop an example based on the MNIST data
+# base. This is a classification problem and we need to use our
+# cross-entropy function we discussed in connection with logistic
+# regression. The cross-entropy defines our cost function for the
+# classificaton problems with neural networks.
+# 
+# In binary classification with two classes $(0, 1)$ we define the
+# logistic/sigmoid function as the probability that a particular input
+# is in class $0$ or $1$.  This is possible because the logistic
+# function takes any input from the real numbers and inputs a number
+# between 0 and 1, and can therefore be interpreted as a probability. It
+# also has other nice properties, such as a derivative that is simple to
+# calculate.
+# 
+# For an input $\boldsymbol{a}$ from the hidden layer, the probability that the input $\boldsymbol{x}$
+# is in class 0 or 1 is just. We let $\theta$ represent the unknown weights and biases to be adjusted by our equations). The variable $x$
+# represents our activation values $z$. We have
+
+# $$
+# P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} ,
+# $$
+
+# and
+
+# $$
+# P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) ,
+# $$
+
+# where $y \in \{0, 1\}$  and $\boldsymbol{\theta}$ represents the weights and biases
+# of our network.
+
+# ## Defining the cost function
+# 
+# Our cost function is given as (see the Logistic regression lectures)
+
+# $$
+# \mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n
+# y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) .
+# $$
+
+# This last equality means that we can interpret our *cost* function as a sum over the *loss* function
+# for each point in the dataset $\mathcal{L}_i(\boldsymbol{\theta})$.  
+# The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
+# than maximizing a negative number.  
+# 
+# In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  
+# 
+# $y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and
+# 
+# $y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ 
+# 
+# i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$)..  
+# 
+# If $\boldsymbol{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th
+# output vector $\boldsymbol{y}_i$.  
+# The probability of $\boldsymbol{x}_i$ being in class $c$ will be given by the softmax function:
+
+# $$
+# P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}}
+# {\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} ,
+# $$
+
+# which reduces to the logistic function in the binary case.  
+# The likelihood of this $C$-class classifier
+# is now given as:
+
+# $$
+# P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+# $$
+
+# Again we take the negative log-likelihood to define our cost function:
+
+# $$
+# \mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}.
+# $$
+
+# See the logistic regression lectures for a full definition of the cost function.
+# 
+# The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!
+
+# ## Example: binary classification problem
+# 
+# As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\beta$ as
+
+# $$
+# \mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right),
+# $$
+
+# where we had defined the logistic (sigmoid) function
+
+# $$
+# p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+# $$
+
+# and
+
+# $$
+# p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}).
+# $$
+
+# The parameters $\boldsymbol{\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. 
+# 
+# Now we replace $x_i$ with the activation $z_i^l$ for a given layer $l$ and the outputs as $y_i=a_i^l=f(z_i^l)$, with $z_i^l$ now being a function of the weights $w_{ij}^l$ and biases $b_i^l$. 
+# We have then
+
+# $$
+# a_i^l = y_i = \frac{\exp{(z_i^l)}}{1+\exp{(z_i^l)}},
+# $$
+
+# with
+
+# $$
+# z_i^l = \sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,
+# $$
+
+# where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.
+# Our cost function at the final layer $l=L$ is now
+
+# $$
+# \mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+# $$
+
+# where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get
+
+# $$
+# \frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.
+# $$
+
+# In case we use another activation function than the logistic one, we need to evaluate other derivatives.
+
+# ## The Softmax function
+# In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need
+
+# $$
+# \frac{\partial f(z_i^l)}{\partial w_{jk}^l} =
+# \frac{\partial f(z_i^l)}{\partial z_j^l} \frac{\partial z_j^l}{\partial w_{jk}^l}= \frac{\partial f(z_i^l)}{\partial z_j^l}a_k^{l-1}.
+# $$
+
+# For the Softmax function we have
+
+# $$
+# f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.
+# $$
+
+# Its derivative with respect to $z_j^l$ gives
+
+# $$
+# \frac{\partial f(z_i^l)}{\partial z_j^l}= f(z_i^l)\left(\delta_{ij}-f(z_j^l)\right),
+# $$
+
+# which in case of the simply binary model reduces to  having $i=j$.
+
+# ## Developing a code for doing neural networks with back propagation
+# 
+# One can identify a set of key steps when using neural networks to solve supervised learning problems:  
+# 
+# 1. Collect and pre-process data  
+# 
+# 2. Define model and architecture  
+# 
+# 3. Choose cost function and optimizer  
+# 
+# 4. Train the model  
+# 
+# 5. Evaluate model performance on test data  
+# 
+# 6. Adjust hyperparameters (if necessary, network architecture)
+
+# ## Collect and pre-process data
+# 
+# Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**
+# package. You may also find it for example [here](http://yann.lecun.com/exdb/mnist/).  
+# The *MNIST* (Modified National Institute of Standards and Technology) database is a large database
+# of handwritten digits that is commonly used for training various image processing systems.  
+# The MNIST dataset consists of 70 000 images of size $28\times 28$ pixels, each labeled from 0 to 9.  
+# The scikit-learn dataset we will use consists of a selection of 1797 images of size $8\times 8$ collected and processed from this database.  
+# 
+# To feed data into a feed-forward neural network we need to represent
+# the inputs as a design/feature matrix $X = (n_{inputs}, n_{features})$.  Each
+# row represents an *input*, in this case a handwritten digit, and
+# each column represents a *feature*, in this case a pixel.  The
+# correct answers, also known as *labels* or *targets* are
+# represented as a 1D array of integers 
+# $Y = (n_{inputs}) = (5, 3, 1, 8,...)$.
+# 
+# As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from
+# measurements of height (in m)  
+# and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example:  
+# 
+# $$ X = \begin{bmatrix}
+# 1.85 & 81\\
+# 1.71 & 65\\
+# 1.95 & 103\\
+# 1.55 & 42\\
+# 1.63 & 56
+# \end{bmatrix} ,$$  
+# 
+# and the targets would be:  
+# 
+# $$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$  
+# 
+# Since each input image is a 2D matrix, we need to flatten the image
+# (i.e. "unravel" the 2D matrix into a 1D array) to turn the data into a
+# design/feature matrix. This means we lose all spatial information in the
+# image, such as locality and translational invariance. More complicated
+# architectures such as Convolutional Neural Networks can take advantage
+# of such information, and are most commonly applied when analyzing
+# images.
+
+# In[1]:
+
+
+get_ipython().run_line_magic('matplotlib', 'inline')
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+get_ipython().run_line_magic('matplotlib', 'inline')
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# flatten the image
+# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
+n_inputs = len(inputs)
+inputs = inputs.reshape(n_inputs, -1)
+print("X = (n_inputs, n_features) = " + str(inputs.shape))
+
+
+# choose some random images to display
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
+
+# ## Train and test datasets
+# 
+# Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.  
+# 
+# We will reserve $80 \%$ of our dataset for training and $20 \%$ for testing.  
+# 
+# It is important that the train and test datasets are drawn randomly from our dataset, to ensure
+# no bias in the sampling.  
+# Say you are taking measurements of weather data to predict the weather in the coming 5 days.
+# You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data
+# collected from 12.00 to 24.00.
+
+# In[2]:
+
+
+from sklearn.model_selection import train_test_split
+
+# one-liner from scikit-learn library
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
+# equivalently in numpy
+def train_test_split_numpy(inputs, labels, train_size, test_size):
+    n_inputs = len(inputs)
+    inputs_shuffled = inputs.copy()
+    labels_shuffled = labels.copy()
+    
+    np.random.shuffle(inputs_shuffled)
+    np.random.shuffle(labels_shuffled)
+    
+    train_end = int(n_inputs*train_size)
+    X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]
+    Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]
+    
+    return X_train, X_test, Y_train, Y_test
+
+#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)
+
+print("Number of training images: " + str(len(X_train)))
+print("Number of test images: " + str(len(X_test)))
+
+
+# ## Define model and architecture
+# 
+# Our simple feed-forward neural network will consist of an *input* layer, a single *hidden* layer and an *output* layer. The activation $y$ of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have 
+# 
+# $$ z = \sum_{i=1}^n w_i a_i ,$$
+# 
+# $$ y = f(z) ,$$
+# 
+# where $f$ is the activation function, $a_i$ represents input from neuron $i$ in the preceding layer
+# and $w_i$ is the weight to input $i$.  
+# The activation of the neurons in the input layer is just the features (e.g. a pixel value).  
+# 
+# The simplest activation function for a neuron is the *Heaviside* function:
+# 
+# $$ f(z) = 
+# \begin{cases}
+# 1,  &  z > 0\\
+# 0,  & \text{otherwise}
+# \end{cases}
+# $$
+# 
+# A feed-forward neural network with this activation is known as a *perceptron*.  
+# For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer.  
+# This activation can be generalized to $k$ classes (using e.g. the *one-against-all* strategy), 
+# and we call these architectures *multiclass perceptrons*.  
+# 
+# However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and  
+# Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function.  
+# 
+# Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU).  
+# We will be using the sigmoid function $\sigma(x)$:  
+# 
+# $$ f(x) = \sigma(x) = \frac{1}{1 + e^{-x}} ,$$
+# 
+# which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.
+
+# ## Layers
+# 
+# * Input 
+# 
+# Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons.  
+# 
+# * Hidden layer
+# 
+# We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer.  
+# Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer.  
+# 
+# * Output
+# 
+# If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,
+# which could output 0 or 1 according to the Heaviside function. This would be an example of a *hard* classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a *soft* classifier, which outputs the probability of being in class 0 or 1.  
+# 
+# For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class.  
+# 
+# Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons $j = 0,1,...,9$. The activation of each output neuron $j$ will be according to the *softmax* function:  
+# 
+# $$ P(\text{class $j$} \mid \text{input $\boldsymbol{a}$}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}}
+# {\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,$$  
+# 
+# i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\boldsymbol{a}$, with $\boldsymbol{w}_j$ the weights of neuron $j$ to the inputs.  
+# The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  
+# The exponent is just the weighted sum of inputs as before:  
+# 
+# $$ z_j = \sum_{i=1}^n w_ {ij} a_i+b_j.$$  
+# 
+# Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500
+# weights to the output layer.
+
+# ## Weights and biases
+# 
+# Typically weights are initialized with small values distributed around zero, drawn from a uniform
+# or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless.  
+# 
+# Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range
+# of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron $j$, $b_j$:  
+# 
+# $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$  
+# 
+# The bias weights $\boldsymbol{b}$ are often initialized to zero, but a small value like $0.01$ ensures all neurons have some output which can be backpropagated in the first training cycle.
+
+# In[3]:
+
+
+# building our neural network
+
+n_inputs, n_features = X_train.shape
+n_hidden_neurons = 50
+n_categories = 10
+
+# we make the weights normally distributed using numpy.random.randn
+
+# weights and bias in the hidden layer
+hidden_weights = np.random.randn(n_features, n_hidden_neurons)
+hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+
+# weights and bias in the output layer
+output_weights = np.random.randn(n_hidden_neurons, n_categories)
+output_bias = np.zeros(n_categories) + 0.01
+
+
+# ## Feed-forward pass
+# 
+# Denote $F$ the number of features, $H$ the number of hidden neurons and $C$ the number of categories.  
+# For each input image we calculate a weighted sum of input features (pixel values) to each neuron $j$ in the hidden layer $l$:  
+# 
+# $$ z_{j}^{l} = \sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},$$
+# 
+# this is then passed through our activation function  
+# 
+# $$ a_{j}^{l} = f(z_{j}^{l}) .$$  
+# 
+# We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron $j$ in the output layer:  
+# 
+# $$ z_{j}^{L} = \sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.$$  
+# 
+# Finally we calculate the output of neuron $j$ in the output layer using the softmax function:  
+# 
+# $$ a_{j}^{L} = \frac{\exp{(z_j^{L})}}
+# {\sum_{c=0}^{C-1} \exp{(z_c^{L})}} .$$
+
+# ## Matrix multiplications
+# 
+# Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden
+# layer have the dimensions  
+# $W_{hidden} = (n_{features}, n_{hidden})$,
+# we can easily feed the network all our training data in one go by taking the matrix product  
+# 
+# $$ X W^{h} = (n_{inputs}, n_{hidden}),$$ 
+# 
+# and obtain a matrix that holds the weighted sum of inputs to the hidden layer
+# for each input image and each hidden neuron.    
+# We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$:  
+# 
+# $$ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,$$
+# 
+# meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  
+# This is then passed through the activation:  
+# 
+# $$ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .$$  
+# 
+# This is fed to the output layer:  
+# 
+# $$ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .$$
+# 
+# Finally we receive our output values for each image and each category by passing it through the softmax function:  
+# 
+# $$ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$
+
+# In[4]:
+
+
+# setup the feed-forward pass, subscript h = hidden layer
+
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
+
+def feed_forward(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    exp_term = np.exp(z_o)
+    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+    
+    return probabilities
+
+probabilities = feed_forward(X_train)
+print("probabilities = (n_inputs, n_categories) = " + str(probabilities.shape))
+print("probability that image 0 is in category 0,1,2,...,9 = \n" + str(probabilities[0]))
+print("probabilities sum up to: " + str(probabilities[0].sum()))
+print()
+
+# we obtain a prediction by taking the class with the highest likelihood
+def predict(X):
+    probabilities = feed_forward(X)
+    return np.argmax(probabilities, axis=1)
+
+predictions = predict(X_train)
+print("predictions = (n_inputs) = " + str(predictions.shape))
+print("prediction for image 0: " + str(predictions[0]))
+print("correct label for image 0: " + str(Y_train[0]))
+
+
+# ## Choose cost function and optimizer
+# 
+# To measure how well our neural network is doing we need to introduce a cost function.  
+# We will call the function that gives the error of a single sample output the *loss* function, and the function
+# that gives the total error of our network across all samples the *cost* function.
+# A typical choice for multiclass classification is the *cross-entropy* loss, also known as the negative log likelihood.  
+# 
+# In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  
+# 
+# $$ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
+# 
+# $$ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  
+# 
+# i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset.  
+# 
+# Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector.  
+# We define the cost function $\mathcal{C}$ as a sum over the cross-entropy loss for each point $\boldsymbol{x}_i$ in the dataset.
+# 
+# In the one-hot representation only one of the terms in the loss function is non-zero, namely the
+# probability of the correct category $c'$  
+# (i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong
+# you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\boldsymbol{\theta}$ represents the parameters of our network, i.e. all the weights and biases.
+
+# ## Optimizing the cost function
+# 
+# The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent
+# is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a *local* minimum of the cost function.  
+# Each parameter $\theta$ is iteratively adjusted according to the rule  
+# 
+# $$ \theta_{i+1} = \theta_i - \eta \nabla \mathcal{C}(\theta_i) ,$$
+# 
+# where $\eta$ is known as the *learning rate*, which controls how big a step we take towards the minimum.  
+# This update can be repeated for any number of iterations, or until we are satisfied with the result.  
+# 
+# A simple and effective improvement is a variant called *Batch Gradient Descent*.  
+# Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient
+# on a subset of the data called a *minibatch*.  
+# If there are $N$ data points and we have a minibatch size of $M$, the total number of batches
+# is $N/M$.  
+# We denote each minibatch $B_k$, with $k = 1, 2,...,N/M$. The gradient then becomes:  
+# 
+# $$ \nabla \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \nabla \mathcal{L}_i(\theta) \quad \rightarrow \quad
+# \frac{1}{M} \sum_{i \in B_k} \nabla \mathcal{L}_i(\theta) ,$$
+# 
+# i.e. instead of averaging the loss over the entire dataset, we average over a minibatch.  
+# 
+# This has two important benefits:  
+# 1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima.  
+# 
+# 2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient.  
+# 
+# The various optmization  methods, with codes and algorithms,  are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).
+
+# ## Regularization
+# 
+# It is common to add an extra term to the cost function, proportional
+# to the size of the weights.  This is equivalent to constraining the
+# size of the weights, so that they do not grow out of control.
+# Constraining the size of the weights means that the weights cannot
+# grow arbitrarily large to fit the training data, and in this way
+# reduces *overfitting*.
+# 
+# We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes:  
+# 
+# $$  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
+# \frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 
+# = \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$  
+# 
+# i.e. we sum up all the weights squared. The factor $\lambda$ is known as a regularization parameter.
+# 
+# In order to train the model, we need to calculate the derivative of
+# the cost function with respect to every bias and weight in the
+# network.  In total our network has $(64 + 1)\times 50=3250$ weights in
+# the hidden layer and $(50 + 1)\times 10=510$ weights to the output
+# layer ($+1$ for the bias), and the gradient must be calculated for
+# every parameter.  We use the *backpropagation* algorithm discussed
+# above. This is a clever use of the chain rule that allows us to
+# calculate the gradient efficently.
+
+# ## Matrix  multiplication
+# 
+# To more efficently train our network these equations are implemented using matrix operations.  
+# The error in the output layer is calculated simply as, with $\boldsymbol{t}$ being our targets,  
+# 
+# $$ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .$$  
+# 
+# The gradient for the output weights is calculated as  
+# 
+# $$ \nabla W_{L} = \boldsymbol{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
+# 
+# where $\boldsymbol{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  
+# Since we are going backwards we have to transpose the activation matrix.  
+# 
+# The gradient with respect to the output bias is then  
+# 
+# $$ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$  
+# 
+# The error in the hidden layer is  
+# 
+# $$ \Delta_h = \delta_L W_{L}^T \circ f'(z_{h}) = \delta_L W_{L}^T \circ a_{h} \circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,$$  
+# 
+# where $f'(a_{h})$ is the derivative of the activation in the hidden layer. The matrix products mean
+# that we are summing up the products for each neuron in the output layer. The symbol $\circ$ denotes
+# the *Hadamard product*, meaning element-wise multiplication.  
+# 
+# This again gives us the gradients in the hidden layer:  
+# 
+# $$ \nabla W_{h} = X^T \delta_h = (n_{features}, n_{hidden}) ,$$  
+# 
+# $$ \nabla b_{h} = \sum_{i=1}^{n_{inputs}} \delta_h = (n_{hidden}) .$$
+
+# In[5]:
+
+
+# to categorical turns our integer vector into a onehot representation
+from sklearn.metrics import accuracy_score
+
+# one-hot in numpy
+def to_categorical_numpy(integer_vector):
+    n_inputs = len(integer_vector)
+    n_categories = np.max(integer_vector) + 1
+    onehot_vector = np.zeros((n_inputs, n_categories))
+    onehot_vector[range(n_inputs), integer_vector] = 1
+    
+    return onehot_vector
+
+#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)
+Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)
+
+def feed_forward_train(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    exp_term = np.exp(z_o)
+    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+    
+    # for backpropagation need activations in hidden and output layers
+    return a_h, probabilities
+
+def backpropagation(X, Y):
+    a_h, probabilities = feed_forward_train(X)
+    
+    # error in the output layer
+    error_output = probabilities - Y
+    # error in the hidden layer
+    error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)
+    
+    # gradients for the output layer
+    output_weights_gradient = np.matmul(a_h.T, error_output)
+    output_bias_gradient = np.sum(error_output, axis=0)
+    
+    # gradient for the hidden layer
+    hidden_weights_gradient = np.matmul(X.T, error_hidden)
+    hidden_bias_gradient = np.sum(error_hidden, axis=0)
+
+    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient
+
+print("Old accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))
+
+eta = 0.01
+lmbd = 0.01
+for i in range(1000):
+    # calculate gradients
+    dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)
+    
+    # regularization term gradients
+    dWo += lmbd * output_weights
+    dWh += lmbd * hidden_weights
+    
+    # update weights and biases
+    output_weights -= eta * dWo
+    output_bias -= eta * dBo
+    hidden_weights -= eta * dWh
+    hidden_bias -= eta * dBh
+
+print("New accuracy on training data: " + str(accuracy_score(predict(X_train), Y_train)))
+
+
+# ## Improving performance
+# 
+# As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.  
+# In order to obtain a network that does something useful, we will have to do a bit more work.  
+# 
+# The choice of *hyperparameters* such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a *grid-search* is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates $\eta = 10^{-6}, 10^{-5},...,10^{-1}$ with different regularization parameters $\lambda = 10^{-6},...,10^{-0}$.  
+# 
+# Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an *iteration*, and a full training period
+# going through the entire dataset ($n/M$ batches) an *epoch*.
+# 
+# If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers.  
+# Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/).
+
+# ## Full object-oriented implementation
+# 
+# It is very natural to think of the network as an object, with specific instances of the network
+# being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below.
+
+# In[6]:
+
+
+class NeuralNetwork:
+    def __init__(
+            self,
+            X_data,
+            Y_data,
+            n_hidden_neurons=50,
+            n_categories=10,
+            epochs=10,
+            batch_size=100,
+            eta=0.1,
+            lmbd=0.0):
+
+        self.X_data_full = X_data
+        self.Y_data_full = Y_data
+
+        self.n_inputs = X_data.shape[0]
+        self.n_features = X_data.shape[1]
+        self.n_hidden_neurons = n_hidden_neurons
+        self.n_categories = n_categories
+
+        self.epochs = epochs
+        self.batch_size = batch_size
+        self.iterations = self.n_inputs // self.batch_size
+        self.eta = eta
+        self.lmbd = lmbd
+
+        self.create_biases_and_weights()
+
+    def create_biases_and_weights(self):
+        self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)
+        self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01
+
+        self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)
+        self.output_bias = np.zeros(self.n_categories) + 0.01
+
+    def feed_forward(self):
+        # feed-forward for training
+        self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias
+        self.a_h = sigmoid(self.z_h)
+
+        self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias
+
+        exp_term = np.exp(self.z_o)
+        self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+
+    def feed_forward_out(self, X):
+        # feed-forward for output
+        z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias
+        a_h = sigmoid(z_h)
+
+        z_o = np.matmul(a_h, self.output_weights) + self.output_bias
+        
+        exp_term = np.exp(z_o)
+        probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
+        return probabilities
+
+    def backpropagation(self):
+        error_output = self.probabilities - self.Y_data
+        error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)
+
+        self.output_weights_gradient = np.matmul(self.a_h.T, error_output)
+        self.output_bias_gradient = np.sum(error_output, axis=0)
+
+        self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)
+        self.hidden_bias_gradient = np.sum(error_hidden, axis=0)
+
+        if self.lmbd > 0.0:
+            self.output_weights_gradient += self.lmbd * self.output_weights
+            self.hidden_weights_gradient += self.lmbd * self.hidden_weights
+
+        self.output_weights -= self.eta * self.output_weights_gradient
+        self.output_bias -= self.eta * self.output_bias_gradient
+        self.hidden_weights -= self.eta * self.hidden_weights_gradient
+        self.hidden_bias -= self.eta * self.hidden_bias_gradient
+
+    def predict(self, X):
+        probabilities = self.feed_forward_out(X)
+        return np.argmax(probabilities, axis=1)
+
+    def predict_probabilities(self, X):
+        probabilities = self.feed_forward_out(X)
+        return probabilities
+
+    def train(self):
+        data_indices = np.arange(self.n_inputs)
+
+        for i in range(self.epochs):
+            for j in range(self.iterations):
+                # pick datapoints with replacement
+                chosen_datapoints = np.random.choice(
+                    data_indices, size=self.batch_size, replace=False
+                )
+
+                # minibatch training data
+                self.X_data = self.X_data_full[chosen_datapoints]
+                self.Y_data = self.Y_data_full[chosen_datapoints]
+
+                self.feed_forward()
+                self.backpropagation()
+
+
+# ## Evaluate model performance on test data
+# 
+# To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.  
+# We measure the performance of the network using the *accuracy* score.  
+# The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of $1$.  
+# 
+# $$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$  
+# 
+# where $I$ is the indicator function, $1$ if $\tilde{y}_i = y_i$ and $0$ otherwise.
+
+# In[7]:
+
+
+epochs = 100
+batch_size = 100
+
+dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,
+                    n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)
+dnn.train()
+test_predict = dnn.predict(X_test)
+
+# accuracy score from scikit library
+print("Accuracy score on test set: ", accuracy_score(Y_test, test_predict))
+
+# equivalent in numpy
+def accuracy_score_numpy(Y_test, Y_pred):
+    return np.sum(Y_test == Y_pred) / len(Y_test)
+
+#print("Accuracy score on test set: ", accuracy_score_numpy(Y_test, test_predict))
+
+
+# ## Adjust hyperparameters
+# 
+# We now perform a grid search to find the optimal hyperparameters for the network.  
+# Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around $98\%$ ($2\%$ error rate).
+
+# In[8]:
+
+
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+# store the models for later use
+DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+
+# grid search
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,
+                            n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)
+        dnn.train()
+        
+        DNN_numpy[i][j] = dnn
+        
+        test_predict = dnn.predict(X_test)
+        
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on test set: ", accuracy_score(Y_test, test_predict))
+        print()
+
+
+# ## Visualization
+
+# In[9]:
+
+
+# visual representation of grid search
+# uses seaborn heatmap, you can also do this with matplotlib imshow
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_numpy[i][j]
+        
+        train_pred = dnn.predict(X_train) 
+        test_pred = dnn.predict(X_test)
+
+        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)
+        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+
+# ## scikit-learn implementation
+# 
+# **scikit-learn** focuses more
+# on traditional machine learning methods, such as regression,
+# clustering, decision trees, etc. As such, it has only two types of
+# neural networks: Multi Layer Perceptron outputting continuous values,
+# *MPLRegressor*, and Multi Layer Perceptron outputting labels,
+# *MLPClassifier*. We will see how simple it is to use these classes.
+# 
+# **scikit-learn** implements a few improvements from our neural network,
+# such as early stopping, a varying learning rate, different
+# optimization methods, etc. We would therefore expect a better
+# performance overall.
+
+# In[10]:
+
+
+from sklearn.neural_network import MLPClassifier
+# store models for later use
+DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
+                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
+        dnn.fit(X_train, Y_train)
+        
+        DNN_scikit[i][j] = dnn
+        
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on test set: ", dnn.score(X_test, Y_test))
+        print()
+
+
+# ## Visualization
+
+# In[11]:
+
+
+# optional
+# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_scikit[i][j]
+        
+        train_pred = dnn.predict(X_train) 
+        test_pred = dnn.predict(X_test)
+
+        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)
+        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+
+# ## Testing our code for the XOR, OR and AND gates
+# 
+# Last week we discussed three different types of gates, the so-called
+# XOR, the OR and the AND gates.  Their inputs and outputs can be
+# summarized using the following tables, first for the OR gate with
+# inputs $x_1$ and $x_2$ and outputs $y$:
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            1       
    
+
+# ## The AND and XOR Gates
+# 
+# The AND gate is defined as
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            0       
       1            0            0       
       1            1            1       
    
+# 
+# And finally we have the XOR gate
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
+# 
    $x_1$ $x_2$ $y$ 
       0            0            0       
       0            1            1       
       1            0            1       
       1            1            0       
    
+
+# ## Representing the Data Sets
+# 
+# Our design matrix is defined by the input values $x_1$ and $x_2$. Since we have four possible outputs, our design matrix reads
+
+# $$
+# \boldsymbol{X}=\begin{bmatrix} 0 & 0 \\
+#                        0 & 1 \\
+# 		       1 & 0 \\
+# 		       1 & 1 \end{bmatrix},
+# $$
+
+# 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.
+
+# ## Setting up the Neural Network
+# 
+# We define first our design matrix and the various output vectors for the different gates.
+
+# In[12]:
+
+
+"""
+Simple code that tests XOR, OR and AND gates with linear regression
+"""
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
+
+def feed_forward(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    probabilities = sigmoid(z_o)
+    return probabilities
+
+# we obtain a prediction by taking the class with the highest likelihood
+def predict(X):
+    probabilities = feed_forward(X)
+    return np.argmax(probabilities, axis=1)
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
+
+# Defining the neural network
+n_inputs, n_features = X.shape
+n_hidden_neurons = 2
+n_categories = 2
+n_features = 2
+
+# we make the weights normally distributed using numpy.random.randn
+
+# weights and bias in the hidden layer
+hidden_weights = np.random.randn(n_features, n_hidden_neurons)
+hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+
+# weights and bias in the output layer
+output_weights = np.random.randn(n_hidden_neurons, n_categories)
+output_bias = np.zeros(n_categories) + 0.01
+
+probabilities = feed_forward(X)
+print(probabilities)
+
+
+predictions = predict(X)
+print(predictions)
+
+
+# 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.
+
+# ## The Code using Scikit-Learn
+
+# In[13]:
+
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.neural_network import MLPClassifier
+from sklearn.metrics import accuracy_score
+import seaborn as sns
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
+
+# Defining the neural network
+n_inputs, n_features = X.shape
+n_hidden_neurons = 2
+n_categories = 2
+n_features = 2
+
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+# store models for later use
+DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+epochs = 100
+
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
+                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
+        dnn.fit(X, yXOR)
+        DNN_scikit[i][j] = dnn
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on data set: ", dnn.score(X, yXOR))
+        print()
+
+sns.set()
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_scikit[i][j]
+        test_pred = dnn.predict(X)
+        test_accuracy[i][j] = accuracy_score(yXOR, test_pred)
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+
+# ## Building neural networks in Tensorflow and Keras
+# 
+# Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn
+# and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
+# and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.  
+# 
+# In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
+# clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
+# NumPy arrays.
+
+# ## Tensorflow
+# 
+# Tensorflow is an open source library machine learning library
+# developed by the Google Brain team for internal use. It was released
+# under the Apache 2.0 open source license in November 9, 2015.
+# 
+# Tensorflow is a computational framework that allows you to construct
+# machine learning models at different levels of abstraction, from
+# high-level, object-oriented APIs like Keras, down to the C++ kernels
+# that Tensorflow is built upon. The higher levels of abstraction are
+# simpler to use, but less flexible, and our choice of implementation
+# should reflect the problems we are trying to solve.
+# 
+# [Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation
+# in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*
+# to represent your model, and then create a Tensorflow *session* to run the graph.
+# 
+# In this guide we will analyze the same data as we did in our NumPy and
+# scikit-learn tutorial, gathered from the MNIST database of images. We
+# will give an introduction to the lower level Python Application
+# Program Interfaces (APIs), and see how we use them to build our graph.
+# Then we will build (effectively) the same graph in Keras, to see just
+# how simple solving a machine learning problem can be.
+# 
+# To install tensorflow on Unix/Linux systems, use pip as
+
+# In[14]:
+
+
+pip3 install tensorflow
+
+
+# and/or if you use **anaconda**, just write (or install from the graphical user interface)
+# (current release of CPU-only TensorFlow)
+
+# In[15]:
+
+
+conda create -n tf tensorflow
+conda activate tf
+
+
+# To install the current release of GPU TensorFlow
+
+# In[16]:
+
+
+conda create -n tf-gpu tensorflow-gpu
+conda activate tf-gpu
+
+
+# ## Using Keras
+# 
+# Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)
+# that supports Tensorflow, CTNK and Theano as backends.  
+# If you have Anaconda installed you may run the following command
+
+# In[17]:
+
+
+conda install keras
+
+
+# You can look up the [instructions here](https://keras.io/) for more information.
+# 
+# We will to a large extent use **keras** in this course.
+
+# ## Collect and pre-process data
+# 
+# Let us look again at the MINST data set.
+
+# In[18]:
+
+
+# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+import tensorflow as tf
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+get_ipython().run_line_magic('matplotlib', 'inline')
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# flatten the image
+# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
+n_inputs = len(inputs)
+inputs = inputs.reshape(n_inputs, -1)
+print("X = (n_inputs, n_features) = " + str(inputs.shape))
+
+
+# choose some random images to display
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
+
+# In[19]:
+
+
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+
+from sklearn.model_selection import train_test_split
+
+# one-hot representation of labels
+labels = to_categorical(labels)
+
+# split into train and test data
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
+
+# In[20]:
+
+
+
+epochs = 100
+batch_size = 100
+n_neurons_layer1 = 100
+n_neurons_layer2 = 50
+n_categories = 10
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
+    model = Sequential()
+    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_categories, activation='softmax'))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
+
+
+# In[21]:
+
+
+DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
+                                         eta=eta, lmbd=lmbd)
+        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = DNN.evaluate(X_test, Y_test)
+        
+        DNN_keras[i][j] = DNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
+
+
+# In[22]:
+
+
+# optional
+# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        DNN = DNN_keras[i][j]
+
+        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+
+# ## The Breast Cancer Data, now with Keras
+
+# In[23]:
+
+
+
+import tensorflow as tf
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+from sklearn.model_selection import train_test_split as splitter
+from sklearn.datasets import load_breast_cancer
+import pickle
+import os 
+
+
+"""Load breast cancer dataset"""
+
+np.random.seed(0)        #create same seed for random number every time
+
+cancer=load_breast_cancer()      #Download breast cancer dataset
+
+inputs=cancer.data                     #Feature matrix of 569 rows (samples) and 30 columns (parameters)
+outputs=cancer.target                  #Label array of 569 rows (0 for benign and 1 for malignant)
+labels=cancer.feature_names[0:30]
+
+print('The content of the breast cancer dataset is:')      #Print information about the datasets
+print(labels)
+print('-------------------------')
+print("inputs =  " + str(inputs.shape))
+print("outputs =  " + str(outputs.shape))
+print("labels =  "+ str(labels.shape))
+
+x=inputs      #Reassign the Feature and Label matrices to other variables
+y=outputs
+
+#%% 
+
+# Visualisation of dataset (for correlation analysis)
+
+plt.figure()
+plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean perimeter',fontweight='bold')
+plt.show()
+
+plt.figure()
+plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)
+plt.xlabel('Mean compactness',fontweight='bold')
+plt.ylabel('Mean concavity',fontweight='bold')
+plt.show()
+
+
+plt.figure()
+plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean texture',fontweight='bold')
+plt.show()
+
+plt.figure()
+plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean perimeter',fontweight='bold')
+plt.ylabel('Mean compactness',fontweight='bold')
+plt.show()
+
+
+# Generate training and testing datasets
+
+#Select features relevant to classification (texture,perimeter,compactness and symmetery) 
+#and add to input matrix
+
+temp1=np.reshape(x[:,1],(len(x[:,1]),1))
+temp2=np.reshape(x[:,2],(len(x[:,2]),1))
+X=np.hstack((temp1,temp2))      
+temp=np.reshape(x[:,5],(len(x[:,5]),1))
+X=np.hstack((X,temp))       
+temp=np.reshape(x[:,8],(len(x[:,8]),1))
+X=np.hstack((X,temp))       
+
+X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1)   #Split datasets into training and testing
+
+y_train=to_categorical(y_train)     #Convert labels to categorical when using categorical cross entropy
+y_test=to_categorical(y_test)
+
+del temp1,temp2,temp
+
+# %%
+
+# Define tunable parameters"
+
+eta=np.logspace(-3,-1,3)                    #Define vector of learning rates (parameter to SGD optimiser)
+lamda=0.01                                  #Define hyperparameter
+n_layers=2                                  #Define number of hidden layers in the model
+n_neuron=np.logspace(0,3,4,dtype=int)       #Define number of neurons per layer
+epochs=100                                   #Number of reiterations over the input data
+batch_size=100                              #Number of samples per gradient update
+
+# %%
+
+"""Define function to return Deep Neural Network model"""
+
+def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
+    model=Sequential()      
+    for i in range(n_layers):       #Run loop to add hidden layers to the model
+        if (i==0):                  #First layer requires input dimensions
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))
+        else:                       #Subsequent layers are capable of automatic shape inferencing
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
+    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)
+    sgd=optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
+    return model
+
+    
+Train_accuracy=np.zeros((len(n_neuron),len(eta)))      #Define matrices to store accuracy scores as a function
+Test_accuracy=np.zeros((len(n_neuron),len(eta)))       #of learning rate and number of hidden neurons for 
+
+for i in range(len(n_neuron)):     #run loops over hidden neurons and learning rates to calculate 
+    for j in range(len(eta)):      #accuracy scores 
+        DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)
+        DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)
+        Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]
+        Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]
+               
+
+def plot_data(x,y,data,title=None):
+
+    # plot results
+    fontsize=16
+
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)
+    
+    cbar=fig.colorbar(cax)
+    cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)
+    cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])
+    cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])
+
+    # put text on matrix elements
+    for i, x_val in enumerate(np.arange(len(x))):
+        for j, y_val in enumerate(np.arange(len(y))):
+            c = "${0:.1f}\\%$".format( 100*data[j,i])  
+            ax.text(x_val, y_val, c, va='center', ha='center')
+
+    # convert axis vaues to to string labels
+    x=[str(i) for i in x]
+    y=[str(i) for i in y]
+
+
+    ax.set_xticklabels(['']+x)
+    ax.set_yticklabels(['']+y)
+
+    ax.set_xlabel('$\\mathrm{learning\\ rate}$',fontsize=fontsize)
+    ax.set_ylabel('$\\mathrm{hidden\\ neurons}$',fontsize=fontsize)
+    if title is not None:
+        ax.set_title(title)
+
+    plt.tight_layout()
+
+    plt.show()
+    
+plot_data(eta,n_neuron,Train_accuracy, 'training')
+plot_data(eta,n_neuron,Test_accuracy, 'testing')
+
+
+# ## Fine-tuning neural network hyperparameters
+# 
+# The flexibility of neural networks is also one of their main
+# drawbacks: there are many hyperparameters to tweak. Not only can you
+# use any imaginable network topology (how neurons/nodes are interconnected),
+# but even in a simple FFNN you can change the number of layers, the
+# number of neurons per layer, the type of activation function to use in
+# each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you
+# know what combination of hyperparameters is the best for your task?
+# 
+# * You can use grid search with cross-validation to find the right hyperparameters.
+# 
+# However,since there are many hyperparameters to tune, and since
+# training a neural network on a large dataset takes a lot of time, you
+# will only be able to explore a tiny part of the hyperparameter space.
+# 
+# * You can use randomized search.
+# 
+# * Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly.
+
+# ## Hidden layers
+# 
+# For many problems you can start with just one or two hidden layers and it will work just fine.
+# For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a
+# few hundred neurons.
+# You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of
+# neurons, in roughly the same amount of training time. 
+# 
+# For more complex problems, you can gradually
+# ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such
+# as large image classification or speech recognition, typically require networks with dozens of layers
+# and they need a huge amount
+# of training data. However, you will rarely have to train such networks from scratch: it is much more
+# common to reuse parts of a pretrained state-of-the-art network that performs a similar task.
+
+# ## Which activation function should I use?
+# 
+# The Back propagation algorithm we derived above works by going from
+# the output layer to the input layer, propagating the error gradient on
+# the way. Once the algorithm has computed the gradient of the cost
+# function with regards to each parameter in the network, it uses these
+# gradients to update each parameter with a Gradient Descent (GD) step.
+# 
+# Unfortunately for us, the gradients often get smaller and smaller as the
+# algorithm progresses down to the first hidden layers. As a result, the
+# GD update leaves the lower layer connection weights
+# virtually unchanged, and training never converges to a good
+# solution. This is known in the literature as 
+# **the vanishing gradients problem**. 
+# 
+# In other cases, the opposite can happen, namely the the gradients can grow bigger and
+# bigger. The result is that many of the layers get large updates of the 
+# weights the
+# algorithm diverges. This is the **exploding gradients problem**, which is
+# mostly encountered in recurrent neural networks. More generally, deep
+# neural networks suffer from unstable gradients, different layers may
+# learn at widely different speeds
+
+# ## Is the Logistic activation function (Sigmoid)  our choice?
+# 
+# Although this unfortunate behavior has been empirically observed for
+# quite a while (it was one of the reasons why deep neural networks were
+# mostly abandoned for a long time), it is only around 2010 that
+# significant progress was made in understanding it.
+# 
+# A paper titled [Understanding the Difficulty of Training Deep
+# Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio](http://proceedings.mlr.press/v9/glorot10a.html) found that
+# the problems with the popular logistic
+# sigmoid activation function and the weight initialization technique
+# that was most popular at the time, namely random initialization using
+# a normal distribution with a mean of 0 and a standard deviation of
+# 1. 
+# 
+# They showed that with this activation function and this
+# initialization scheme, the variance of the outputs of each layer is
+# much greater than the variance of its inputs. Going forward in the
+# network, the variance keeps increasing after each layer until the
+# activation function saturates at the top layers. This is actually made
+# worse by the fact that the logistic function has a mean of 0.5, not 0
+# (the hyperbolic tangent function has a mean of 0 and behaves slightly
+# better than the logistic function in deep networks).
+
+# ## The derivative of the Logistic funtion
+# 
+# Looking at the logistic activation function, when inputs become large
+# (negative or positive), the function saturates at 0 or 1, with a
+# derivative extremely close to 0. Thus when backpropagation kicks in,
+# it has virtually no gradient to propagate back through the network,
+# and what little gradient exists keeps getting diluted as
+# backpropagation progresses down through the top layers, so there is
+# really nothing left for the lower layers.
+# 
+# In their paper, Glorot and Bengio propose a way to significantly
+# alleviate this problem. We need the signal to flow properly in both
+# directions: in the forward direction when making predictions, and in
+# the reverse direction when backpropagating gradients. We don’t want
+# the signal to die out, nor do we want it to explode and saturate. For
+# the signal to flow properly, the authors argue that we need the
+# variance of the outputs of each layer to be equal to the variance of
+# its inputs, and we also need the gradients to have equal variance
+# before and after flowing through a layer in the reverse direction.
+# 
+# One of the insights in the 2010 paper by Glorot and Bengio was that
+# the vanishing/exploding gradients problems were in part due to a poor
+# choice of activation function. Until then most people had assumed that
+# if Nature had chosen to use roughly sigmoid activation functions in
+# biological neurons, they must be an excellent choice. But it turns out
+# that other activation functions behave much better in deep neural
+# networks, in particular the ReLU activation function, mostly because
+# it does not saturate for positive values (and also because it is quite
+# fast to compute).
+
+# ## The RELU function family
+# 
+# The ReLU activation function suffers from a problem known as the dying
+# ReLUs: during training, some neurons effectively die, meaning they
+# stop outputting anything other than 0.
+# 
+# In some cases, you may find that half of your network’s neurons are
+# dead, especially if you used a large learning rate. During training,
+# if a neuron’s weights get updated such that the weighted sum of the
+# neuron’s inputs is negative, it will start outputting 0. When this
+# happen, the neuron is unlikely to come back to life since the gradient
+# of the ReLU function is 0 when its input is negative.
+# 
+# To solve this problem, nowadays practitioners use a  variant of the ReLU
+# function, such as the leaky ReLU discussed above or the so-called
+# exponential linear unit (ELU) function
+
+# $$
+# ELU(z) = \left\{\begin{array}{cc} \alpha\left( \exp{(z)}-1\right) & z < 0,\\  z & z \ge 0.\end{array}\right.
+# $$
+
+# ## Which activation function should we use?
+# 
+# In general it seems that the ELU activation function is better than
+# the leaky ReLU function (and its variants), which is better than
+# ReLU. ReLU performs better than $\tanh$ which in turn performs better
+# than the logistic function. 
+# 
+# If runtime
+# performance is an issue, then you may opt for the  leaky ReLU function  over the 
+# ELU function If you don’t
+# want to tweak yet another hyperparameter, you may just use the default
+# $\alpha$ of $0.01$ for the leaky ReLU, and $1$ for ELU. If you have
+# spare time and computing power, you can use cross-validation or
+# bootstrap to evaluate other activation functions.
+
+# ## More on activation functions, output layers
+# 
+# In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).
+# 
+# It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.
+# 
+# **For the output layer:**
+# 
+# * For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).
+# 
+# * For regression tasks, you can simply use no activation function at all.
+
+# ## Batch Normalization
+# 
+# Batch Normalization
+# aims to address the vanishing/exploding gradients problems, and more generally the problem that the
+# distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.
+# 
+# The technique consists of adding an operation in the model just before the activation function of each
+# layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new
+# parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model
+# learn the optimal scale and mean of the inputs for each layer.
+# In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and
+# standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current
+# mini-batch, from this the name batch normalization.
+
+# ## Dropout
+# 
+# It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but
+# excluding the output neurons) has a probability $p$ of being temporarily dropped out, meaning it will be
+# entirely ignored during this training step, but it may be active during the next step.
+# 
+# The
+# hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.
+#  It is viewed as one of the most popular regularization techniques.
+
+# ## Gradient Clipping
+# 
+# A popular technique to lessen the exploding gradients problem is to simply clip the gradients during
+# backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural
+# networks).
+# 
+# This technique is called Gradient Clipping.
+# 
+# In general however, Batch
+# Normalization is preferred.
+
+# ## A very nice website on Neural Networks
+# 
+# You may find this [website](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=circle®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.29243&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false) very useful.
+
+# ## A top-down perspective on Neural networks
+# 
+# The first thing we would like to do is divide the data into two or three
+# parts. A training set, a validation or dev (development) set, and a
+# test set. The test set is the data on which we want to make
+# predictions. The dev set is a subset of the training data we use to
+# check how well we are doing out-of-sample, after training the model on
+# the training dataset. We use the validation error as a proxy for the
+# test error in order to make tweaks to our model. It is crucial that we
+# do not use any of the test data to train the algorithm. This is a
+# cardinal sin in ML. Then:
+# 
+# * Estimate optimal error rate
+# 
+# * Minimize underfitting (bias) on training data set.
+# 
+# * Make sure you are not overfitting.
+# 
+# If the validation and test sets are drawn from the same distributions,
+# then a good performance on the validation set should lead to similarly
+# good performance on the test set. 
+# 
+# However, sometimes
+# the training data and test data differ in subtle ways because, for
+# example, they are collected using slightly different methods, or
+# because it is cheaper to collect data in one way versus another. In
+# this case, there can be a mismatch between the training and test
+# data. This can lead to the neural network overfitting these small
+# differences between the test and training sets, and a poor performance
+# on the test set despite having a good performance on the validation
+# set. To rectify this, Andrew Ng suggests making two validation or dev
+# sets, one constructed from the training data and one constructed from
+# the test data. The difference between the performance of the algorithm
+# on these two validation sets quantifies the train-test mismatch. This
+# can serve as another important diagnostic when using DNNs for
+# supervised learning.
+
+# ## Limitations of supervised learning with deep networks
+# 
+# Like all statistical methods, supervised learning using neural
+# networks has important limitations. This is especially important when
+# one seeks to apply these methods, especially to physics problems. Like
+# all tools, DNNs are not a universal solution. Often, the same or
+# better performance on a task can be achieved by using a few
+# hand-engineered features (or even a collection of random
+# features). 
+# 
+# Here we list some of the important limitations of supervised neural network based models. 
+# 
+# * **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).
+# 
+# * **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.
+# 
+# * **Homogeneous data.** Almost all DNNs deal with homogeneous data of one type. It is very hard to design architectures that mix and match data types (i.e. some continuous variables, some discrete variables, some time series). In applications beyond images, video, and language, this is often what is required. In contrast, ensemble models like random forests or gradient-boosted trees have no difficulty handling mixed data types.
+# 
+# * **Many problems are not about prediction.** In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a *wrong* model. The model might or might not be useful for understanding the underlying science.
+# 
+# Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems.
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--- a/doc/LectureNotes/week42.ipynb
+++ b/doc/LectureNotes/week42.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d2a36f3c",
+   "id": "50ce4eae",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "310c269f",
+   "id": "f46bd6b4",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "427a552f",
+   "id": "8c0fa4d7",
    "metadata": {
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@@ -58,7 +58,7 @@
     "\n",
     "    * [Neural Networks demystified](https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs)\n",
     "\n",
-    "    * \"Building Neural Networks from scratch\":\"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex\n",
+    "    * [Building Neural Networks from scratch](https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex)\n",
     "\n",
     "    * [Video on Neural Networks](https://www.youtube.com/watch?v=CqOfi41LfDw)\n",
     "\n",
@@ -69,7 +69,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b53157af",
+   "id": "89b6b637",
    "metadata": {
     "editable": true
    },
@@ -79,7 +79,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9002bf39",
+   "id": "3a32ad82",
    "metadata": {
     "editable": true
    },
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "228a98c1",
+   "id": "4f9291ee",
    "metadata": {
     "editable": true
    },
@@ -117,7 +117,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c38b5eaf",
+   "id": "7753981f",
    "metadata": {
     "editable": true
    },
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "991e9164",
+   "id": "8b093c71",
    "metadata": {
     "editable": true
    },
@@ -139,7 +139,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5c5f27f",
+   "id": "96ca25bd",
    "metadata": {
     "editable": true
    },
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41dd527c",
+   "id": "a156d8bd",
    "metadata": {
     "editable": true
    },
@@ -161,7 +161,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49fa0a94",
+   "id": "f35c8afe",
    "metadata": {
     "editable": true
    },
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da9bdf96",
+   "id": "ffa6d322",
    "metadata": {
     "editable": true
    },
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e012a3c",
+   "id": "7b6e59f6",
    "metadata": {
     "editable": true
    },
@@ -196,7 +196,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a10b5095",
+   "id": "e93ff00c",
    "metadata": {
     "editable": true
    },
@@ -224,7 +224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dae5d47e",
+   "id": "3c437395",
    "metadata": {
     "editable": true
    },
@@ -236,7 +236,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b98a58c",
+   "id": "3d7b1140",
    "metadata": {
     "editable": true
    },
@@ -246,7 +246,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d44d09a5",
+   "id": "e3df5aec",
    "metadata": {
     "editable": true
    },
@@ -258,7 +258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "deac74cc",
+   "id": "63345646",
    "metadata": {
     "editable": true
    },
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9346792f",
+   "id": "6ac465b3",
    "metadata": {
     "editable": true
    },
@@ -281,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd47740a",
+   "id": "cf06b4a0",
    "metadata": {
     "editable": true
    },
@@ -294,7 +294,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "624d266a",
+   "id": "719f761f",
    "metadata": {
     "editable": true
    },
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab1fdd1f",
+   "id": "342de1d9",
    "metadata": {
     "editable": true
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@@ -332,7 +332,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a005eeef",
+   "id": "211a69ba",
    "metadata": {
     "editable": true
    },
@@ -344,7 +344,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d9e3087",
+   "id": "5f0cd5a2",
    "metadata": {
     "editable": true
    },
@@ -356,7 +356,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "308b820e",
+   "id": "fe018e32",
    "metadata": {
     "editable": true
    },
@@ -366,7 +366,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae243251",
+   "id": "9d48faca",
    "metadata": {
     "editable": true
    },
@@ -378,7 +378,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79055e74",
+   "id": "897c8b0c",
    "metadata": {
     "editable": true
    },
@@ -390,7 +390,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa673507",
+   "id": "68347a7f",
    "metadata": {
     "editable": true
    },
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cc3f2e2",
+   "id": "8425d868",
    "metadata": {
     "editable": true
    },
@@ -414,7 +414,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28883e22",
+   "id": "9108d4ac",
    "metadata": {
     "editable": true
    },
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2563a79",
+   "id": "77e0ec3b",
    "metadata": {
     "editable": true
    },
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f267068b",
+   "id": "64ed867c",
    "metadata": {
     "editable": true
    },
@@ -446,7 +446,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a4a0387",
+   "id": "51819578",
    "metadata": {
     "editable": true
    },
@@ -458,7 +458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19fb027a",
+   "id": "db6532a5",
    "metadata": {
     "editable": true
    },
@@ -471,7 +471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f41bc98e",
+   "id": "24e5e213",
    "metadata": {
     "editable": true
    },
@@ -483,7 +483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23638b6a",
+   "id": "d398c961",
    "metadata": {
     "editable": true
    },
@@ -493,7 +493,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3f6e3e3",
+   "id": "236d161c",
    "metadata": {
     "editable": true
    },
@@ -505,7 +505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61c4f101",
+   "id": "25e3004d",
    "metadata": {
     "editable": true
    },
@@ -516,7 +516,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58ac0397",
+   "id": "9440c725",
    "metadata": {
     "editable": true
    },
@@ -528,7 +528,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "585c0850",
+   "id": "782f5282",
    "metadata": {
     "editable": true
    },
@@ -538,7 +538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6b1c1c8",
+   "id": "0e8498a5",
    "metadata": {
     "editable": true
    },
@@ -550,7 +550,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97ae8668",
+   "id": "68398b35",
    "metadata": {
     "editable": true
    },
@@ -560,7 +560,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28f524e4",
+   "id": "19887152",
    "metadata": {
     "editable": true
    },
@@ -571,7 +571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "233b736f",
+   "id": "80e8dc5d",
    "metadata": {
     "editable": true
    },
@@ -584,7 +584,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0e7c038",
+   "id": "68d33776",
    "metadata": {
     "editable": true
    },
@@ -594,7 +594,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d17816a2",
+   "id": "3c86943c",
    "metadata": {
     "editable": true
    },
@@ -606,7 +606,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a196a75",
+   "id": "efe53876",
    "metadata": {
     "editable": true
    },
@@ -616,7 +616,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2dcca96",
+   "id": "fce5b9b2",
    "metadata": {
     "editable": true
    },
@@ -628,7 +628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f8acea2",
+   "id": "97210471",
    "metadata": {
     "editable": true
    },
@@ -638,7 +638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4adc4dc7",
+   "id": "4f515591",
    "metadata": {
     "editable": true
    },
@@ -662,7 +662,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17f30edb",
+   "id": "ec34f212",
    "metadata": {
     "editable": true
    },
@@ -712,7 +712,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "69ec827f",
+   "id": "e389e60e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -767,7 +767,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "867080d1",
+   "id": "9a264b82",
    "metadata": {
     "editable": true
    },
@@ -788,7 +788,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1659b538",
+   "id": "8750ea41",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -826,7 +826,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "304e16d9",
+   "id": "d3897eca",
    "metadata": {
     "editable": true
    },
@@ -870,7 +870,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73aaf166",
+   "id": "ad593a03",
    "metadata": {
     "editable": true
    },
@@ -910,7 +910,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "302a43c9",
+   "id": "e37b3844",
    "metadata": {
     "editable": true
    },
@@ -931,7 +931,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "20c961e1",
+   "id": "3d909fc7",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -957,7 +957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b63a63bc",
+   "id": "b89c2d9f",
    "metadata": {
     "editable": true
    },
@@ -985,7 +985,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1ee6c2a",
+   "id": "435c0ced",
    "metadata": {
     "editable": true
    },
@@ -1022,7 +1022,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "85e741aa",
+   "id": "3037d7ab",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1068,7 +1068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "618d4858",
+   "id": "61c33a3f",
    "metadata": {
     "editable": true
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@@ -1099,7 +1099,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c098021",
+   "id": "665f44ff",
    "metadata": {
     "editable": true
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@@ -1137,7 +1137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcfe9ca6",
+   "id": "2d0168d0",
    "metadata": {
     "editable": true
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@@ -1171,7 +1171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be9470b3",
+   "id": "9c0a8db3",
    "metadata": {
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@@ -1212,7 +1212,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "3b549560",
+   "id": "0bf3739e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1291,7 +1291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70834cc0",
+   "id": "33e198f3",
    "metadata": {
     "editable": true
    },
@@ -1312,7 +1312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "feb328ab",
+   "id": "932f6c5e",
    "metadata": {
     "editable": true
    },
@@ -1326,7 +1326,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "bd075104",
+   "id": "91e351de",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1436,7 +1436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b719fba",
+   "id": "e8c2feb6",
    "metadata": {
     "editable": true
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@@ -1455,7 +1455,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "78fbbfb2",
+   "id": "1534af1b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1482,7 +1482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcce4264",
+   "id": "85627e28",
    "metadata": {
     "editable": true
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@@ -1496,7 +1496,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "a8928377",
+   "id": "19382903",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1527,7 +1527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d4e3a22",
+   "id": "12bc42df",
    "metadata": {
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@@ -1538,7 +1538,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "ebaa30a1",
+   "id": "ec0dc239",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1582,7 +1582,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4814ac9f",
+   "id": "4dd39506",
    "metadata": {
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@@ -1605,7 +1605,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "6637dc3a",
+   "id": "d9dbb807",
    "metadata": {
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     "editable": true
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a6900f5",
+   "id": "214af3ab",
    "metadata": {
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@@ -1643,7 +1643,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "a0f6228d",
+   "id": "d57415ac",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1688,7 +1688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44c09155",
+   "id": "fe7af77c",
    "metadata": {
     "editable": true
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@@ -1715,7 +1715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77bd71a7",
+   "id": "7e12b1cf",
    "metadata": {
     "editable": true
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@@ -1753,7 +1753,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce2fbb3d",
+   "id": "4b5002b4",
    "metadata": {
     "editable": true
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@@ -1765,7 +1765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "879d5714",
+   "id": "a44df1a3",
    "metadata": {
     "editable": true
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@@ -1780,7 +1780,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7745ce0e",
+   "id": "acdb4e08",
    "metadata": {
     "editable": true
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@@ -1790,7 +1790,7 @@
   },
   {
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-   "id": "8b0d5a8a",
+   "id": "0567fd0f",
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@@ -1803,7 +1803,7 @@
   {
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    "execution_count": 12,
-   "id": "5b55a578",
+   "id": "412401df",
    "metadata": {
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     "editable": true
@@ -1879,7 +1879,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9c53340",
+   "id": "53c52dab",
    "metadata": {
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@@ -1889,7 +1889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bac1dab3",
+   "id": "7d192a02",
    "metadata": {
     "editable": true
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@@ -1900,7 +1900,7 @@
   {
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    "execution_count": 13,
-   "id": "beecbfc5",
+   "id": "766d5af6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1968,7 +1968,7 @@
   },
   {
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-   "id": "621fb11f",
+   "id": "9b182ae1",
    "metadata": {
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@@ -1986,7 +1986,7 @@
   },
   {
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-   "id": "719e5f7f",
+   "id": "60683ec5",
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@@ -2021,7 +2021,7 @@
   {
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-   "id": "543cc574",
+   "id": "8a0c6901",
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     "editable": true
@@ -2033,7 +2033,7 @@
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-   "id": "412729e1",
+   "id": "b66e0227",
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@@ -2045,7 +2045,7 @@
   {
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-   "id": "c5ec8938",
+   "id": "df994f58",
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     "editable": true
@@ -2058,7 +2058,7 @@
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   {
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-   "id": "9c6d6428",
+   "id": "b9005559",
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@@ -2069,7 +2069,7 @@
   {
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-   "id": "54583091",
+   "id": "7287b5eb",
    "metadata": {
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     "editable": true
@@ -2082,7 +2082,7 @@
   },
   {
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-   "id": "a26c5a94",
+   "id": "c066b083",
    "metadata": {
     "editable": true
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@@ -2097,7 +2097,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "258c4979",
+   "id": "6582adea",
    "metadata": {
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     "editable": true
@@ -2109,7 +2109,7 @@
   },
   {
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-   "id": "d5b6d9cd",
+   "id": "7d305596",
    "metadata": {
     "editable": true
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@@ -2121,7 +2121,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "015ceead",
+   "id": "a4508850",
    "metadata": {
     "editable": true
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@@ -2134,7 +2134,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "150d32d9",
+   "id": "5f2256f6",
    "metadata": {
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     "editable": true
@@ -2189,7 +2189,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "65ff5321",
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@@ -2218,7 +2218,7 @@
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@@ -2248,7 +2248,7 @@
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@@ -2275,7 +2275,7 @@
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@@ -2317,7 +2317,7 @@
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@@ -2328,7 +2328,7 @@
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@@ -2505,7 +2505,7 @@
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@@ -2533,7 +2533,7 @@
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@@ -2556,7 +2556,7 @@
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@@ -2587,7 +2587,7 @@
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@@ -2619,7 +2619,7 @@
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@@ -2657,7 +2657,7 @@
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@@ -2682,7 +2682,7 @@
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@@ -2694,7 +2694,7 @@
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@@ -2717,7 +2717,7 @@
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@@ -2737,7 +2737,7 @@
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@@ -2759,7 +2759,7 @@
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@@ -2777,7 +2777,7 @@
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@@ -2796,7 +2796,7 @@
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@@ -2808,7 +2808,7 @@
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@@ -2853,7 +2853,7 @@
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diff --git a/doc/pub/week42/html/._week42-bs001.html b/doc/pub/week42/html/._week42-bs001.html
index 1b3d4ceb5..03786cf02 100644
--- a/doc/pub/week42/html/._week42-bs001.html
+++ b/doc/pub/week42/html/._week42-bs001.html
@@ -299,7 +299,7 @@ MathJax.Hub.Config({
     
  •  Aurelien Geron's chapters 10-11
    • 
     
  •  For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.
    •      
     
  •  Neural Networks demystified
    • 
-    
  •  "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex
    • 
+    
  •  Building Neural Networks from scratch
    • 
     
  •  Video on Neural Networks
    • 
     
  •  Video on the back propagation algorithm
    • 
 
diff --git a/doc/pub/week42/html/week42-reveal.html b/doc/pub/week42/html/week42-reveal.html
index eb63767fb..d92545289 100644
--- a/doc/pub/week42/html/week42-reveal.html
+++ b/doc/pub/week42/html/week42-reveal.html
@@ -229,7 +229,7 @@ MathJax.Hub.Config({
 
 
  •  Neural Networks demystified
    • 
 
-
  •  "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex
    • 
+
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  •  Video on Neural Networks
    • 
 
diff --git a/doc/pub/week42/html/week42-solarized.html b/doc/pub/week42/html/week42-solarized.html
index 35551489d..87bc0bb33 100644
--- a/doc/pub/week42/html/week42-solarized.html
+++ b/doc/pub/week42/html/week42-solarized.html
@@ -271,7 +271,7 @@ MathJax.Hub.Config({
     
  •  Aurelien Geron's chapters 10-11
    • 
     
  •  For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.
    •      
     
  •  Neural Networks demystified
    • 
-    
  •  "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex
    • 
+    
  •  Building Neural Networks from scratch
    • 
     
  •  Video on Neural Networks
    • 
     
  •  Video on the back propagation algorithm
    • 
 
diff --git a/doc/pub/week42/html/week42.html b/doc/pub/week42/html/week42.html
index 5f5ea50f5..a08c937c1 100644
--- a/doc/pub/week42/html/week42.html
+++ b/doc/pub/week42/html/week42.html
@@ -348,7 +348,7 @@ MathJax.Hub.Config({
     
  •  Aurelien Geron's chapters 10-11
    • 
     
  •  For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.
    •      
     
  •  Neural Networks demystified
    • 
-    
  •  "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex
    • 
+    
  •  Building Neural Networks from scratch
    • 
     
  •  Video on Neural Networks
    • 
     
  •  Video on the back propagation algorithm
    • 
 
diff --git a/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz b/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz
index bc0d9d974..aad24838a 100644
Binary files a/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz and b/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz differ
diff --git a/doc/pub/week42/ipynb/week42.ipynb b/doc/pub/week42/ipynb/week42.ipynb
index adc0b59eb..702b9e719 100644
--- a/doc/pub/week42/ipynb/week42.ipynb
+++ b/doc/pub/week42/ipynb/week42.ipynb
@@ -2,7 +2,7 @@
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@@ -14,7 +14,7 @@
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@@ -58,7 +58,7 @@
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@@ -69,7 +69,7 @@
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@@ -79,7 +79,7 @@
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@@ -161,7 +161,7 @@
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@@ -185,7 +185,7 @@
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@@ -196,7 +196,7 @@
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@@ -258,7 +258,7 @@
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@@ -269,7 +269,7 @@
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@@ -281,7 +281,7 @@
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@@ -294,7 +294,7 @@
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@@ -319,7 +319,7 @@
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@@ -332,7 +332,7 @@
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@@ -344,7 +344,7 @@
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@@ -356,7 +356,7 @@
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@@ -366,7 +366,7 @@
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@@ -378,7 +378,7 @@
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@@ -390,7 +390,7 @@
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@@ -402,7 +402,7 @@
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@@ -414,7 +414,7 @@
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@@ -424,7 +424,7 @@
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@@ -436,7 +436,7 @@
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@@ -446,7 +446,7 @@
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@@ -458,7 +458,7 @@
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@@ -471,7 +471,7 @@
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@@ -483,7 +483,7 @@
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@@ -493,7 +493,7 @@
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@@ -505,7 +505,7 @@
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@@ -516,7 +516,7 @@
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@@ -528,7 +528,7 @@
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@@ -538,7 +538,7 @@
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@@ -550,7 +550,7 @@
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@@ -560,7 +560,7 @@
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@@ -571,7 +571,7 @@
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@@ -584,7 +584,7 @@
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@@ -594,7 +594,7 @@
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@@ -606,7 +606,7 @@
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@@ -616,7 +616,7 @@
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@@ -628,7 +628,7 @@
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@@ -638,7 +638,7 @@
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@@ -662,7 +662,7 @@
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@@ -712,7 +712,7 @@
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@@ -767,7 +767,7 @@
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@@ -788,7 +788,7 @@
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@@ -826,7 +826,7 @@
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@@ -870,7 +870,7 @@
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@@ -910,7 +910,7 @@
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@@ -931,7 +931,7 @@
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@@ -957,7 +957,7 @@
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@@ -985,7 +985,7 @@
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@@ -1022,7 +1022,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "85e741aa",
+   "id": "3037d7ab",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1068,7 +1068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "618d4858",
+   "id": "61c33a3f",
    "metadata": {
     "editable": true
    },
@@ -1099,7 +1099,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c098021",
+   "id": "665f44ff",
    "metadata": {
     "editable": true
    },
@@ -1137,7 +1137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcfe9ca6",
+   "id": "2d0168d0",
    "metadata": {
     "editable": true
    },
@@ -1171,7 +1171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be9470b3",
+   "id": "9c0a8db3",
    "metadata": {
     "editable": true
    },
@@ -1212,7 +1212,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "3b549560",
+   "id": "0bf3739e",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1291,7 +1291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70834cc0",
+   "id": "33e198f3",
    "metadata": {
     "editable": true
    },
@@ -1312,7 +1312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "feb328ab",
+   "id": "932f6c5e",
    "metadata": {
     "editable": true
    },
@@ -1326,7 +1326,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "bd075104",
+   "id": "91e351de",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1436,7 +1436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b719fba",
+   "id": "e8c2feb6",
    "metadata": {
     "editable": true
    },
@@ -1455,7 +1455,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "78fbbfb2",
+   "id": "1534af1b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1482,7 +1482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcce4264",
+   "id": "85627e28",
    "metadata": {
     "editable": true
    },
@@ -1496,7 +1496,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "a8928377",
+   "id": "19382903",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1527,7 +1527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d4e3a22",
+   "id": "12bc42df",
    "metadata": {
     "editable": true
    },
@@ -1538,7 +1538,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "ebaa30a1",
+   "id": "ec0dc239",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1582,7 +1582,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4814ac9f",
+   "id": "4dd39506",
    "metadata": {
     "editable": true
    },
@@ -1605,7 +1605,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "6637dc3a",
+   "id": "d9dbb807",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a6900f5",
+   "id": "214af3ab",
    "metadata": {
     "editable": true
    },
@@ -1643,7 +1643,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "a0f6228d",
+   "id": "d57415ac",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1688,7 +1688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44c09155",
+   "id": "fe7af77c",
    "metadata": {
     "editable": true
    },
@@ -1715,7 +1715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77bd71a7",
+   "id": "7e12b1cf",
    "metadata": {
     "editable": true
    },
@@ -1753,7 +1753,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce2fbb3d",
+   "id": "4b5002b4",
    "metadata": {
     "editable": true
    },
@@ -1765,7 +1765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "879d5714",
+   "id": "a44df1a3",
    "metadata": {
     "editable": true
    },
@@ -1780,7 +1780,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7745ce0e",
+   "id": "acdb4e08",
    "metadata": {
     "editable": true
    },
@@ -1790,7 +1790,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b0d5a8a",
+   "id": "0567fd0f",
    "metadata": {
     "editable": true
    },
@@ -1803,7 +1803,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "5b55a578",
+   "id": "412401df",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1879,7 +1879,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9c53340",
+   "id": "53c52dab",
    "metadata": {
     "editable": true
    },
@@ -1889,7 +1889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bac1dab3",
+   "id": "7d192a02",
    "metadata": {
     "editable": true
    },
@@ -1900,7 +1900,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "beecbfc5",
+   "id": "766d5af6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1968,7 +1968,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "621fb11f",
+   "id": "9b182ae1",
    "metadata": {
     "editable": true
    },
@@ -1986,7 +1986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "719e5f7f",
+   "id": "60683ec5",
    "metadata": {
     "editable": true
    },
@@ -2021,7 +2021,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "543cc574",
+   "id": "8a0c6901",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2033,7 +2033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "412729e1",
+   "id": "b66e0227",
    "metadata": {
     "editable": true
    },
@@ -2045,7 +2045,7 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "c5ec8938",
+   "id": "df994f58",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2058,7 +2058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c6d6428",
+   "id": "b9005559",
    "metadata": {
     "editable": true
    },
@@ -2069,7 +2069,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "54583091",
+   "id": "7287b5eb",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2082,7 +2082,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a26c5a94",
+   "id": "c066b083",
    "metadata": {
     "editable": true
    },
@@ -2097,7 +2097,7 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "258c4979",
+   "id": "6582adea",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2109,7 +2109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5b6d9cd",
+   "id": "7d305596",
    "metadata": {
     "editable": true
    },
@@ -2121,7 +2121,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "015ceead",
+   "id": "a4508850",
    "metadata": {
     "editable": true
    },
@@ -2134,7 +2134,7 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "150d32d9",
+   "id": "5f2256f6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2189,7 +2189,7 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "65ff5321",
+   "id": "a5dfa0e9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2218,7 +2218,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "d53f312f",
+   "id": "dd935ce0",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2248,7 +2248,7 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "8ad38cb9",
+   "id": "67158cb2",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2275,7 +2275,7 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "86db69c6",
+   "id": "86d74ee3",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2317,7 +2317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8505aad",
+   "id": "563d3f68",
    "metadata": {
     "editable": true
    },
@@ -2328,7 +2328,7 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "3e92f5a7",
+   "id": "34e6467a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2505,7 +2505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ee81bce",
+   "id": "09879108",
    "metadata": {
     "editable": true
    },
@@ -2533,7 +2533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcbe8f77",
+   "id": "f8ec1769",
    "metadata": {
     "editable": true
    },
@@ -2556,7 +2556,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a96fed60",
+   "id": "43cc1fe5",
    "metadata": {
     "editable": true
    },
@@ -2587,7 +2587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4af9d16",
+   "id": "a9cbce9f",
    "metadata": {
     "editable": true
    },
@@ -2619,7 +2619,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28934494",
+   "id": "2dfb3f9a",
    "metadata": {
     "editable": true
    },
@@ -2657,7 +2657,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4964c0d9",
+   "id": "f806c047",
    "metadata": {
     "editable": true
    },
@@ -2682,7 +2682,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8b4480c",
+   "id": "ef9e2a08",
    "metadata": {
     "editable": true
    },
@@ -2694,7 +2694,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63f6fb19",
+   "id": "2e2750d8",
    "metadata": {
     "editable": true
    },
@@ -2717,7 +2717,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6db7b6af",
+   "id": "4e566f13",
    "metadata": {
     "editable": true
    },
@@ -2737,7 +2737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa471ee5",
+   "id": "03205666",
    "metadata": {
     "editable": true
    },
@@ -2759,7 +2759,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6995145",
+   "id": "ad7c3e53",
    "metadata": {
     "editable": true
    },
@@ -2777,7 +2777,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51f8d2f9",
+   "id": "c3b98a7c",
    "metadata": {
     "editable": true
    },
@@ -2796,7 +2796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d5a8be2",
+   "id": "e7f21477",
    "metadata": {
     "editable": true
    },
@@ -2808,7 +2808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2365782a",
+   "id": "54968291",
    "metadata": {
     "editable": true
    },
@@ -2853,7 +2853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "580cd291",
+   "id": "4500b85e",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week42/week42.do.txt b/doc/src/week42/week42.do.txt
index 30bc8846d..1a0785c82 100644
--- a/doc/src/week42/week42.do.txt
+++ b/doc/src/week42/week42.do.txt
@@ -20,7 +20,7 @@ DATE: October 16-20, 2023
     * "Aurelien Geron's chapters 10-11":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/Textbooks/TensorflowML.pdf"
     * For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7.     
     * "Neural Networks demystified":"https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs"
-    * "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex
+    * "Building Neural Networks from scratch":"https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex"
     * "Video on Neural Networks":"https://www.youtube.com/watch?v=CqOfi41LfDw"
     * "Video on the back propagation algorithm":"https://www.youtube.com/watch?v=Ilg3gGewQ5U"
 I also  recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at URL:"http://neuralnetworksanddeeplearning.com/chap4.html".
diff --git a/doc/web/course.dlog b/doc/web/course.dlog
index a6e450606..6f739ab60 100644
--- a/doc/web/course.dlog
+++ b/doc/web/course.dlog
@@ -240,3 +240,6 @@ output in course.html
 running mako on course.do.txt to make tmp_mako__course.do.txt
 Translating doconce text in tmp_mako__course.do.txt to ipynb
 output in course.ipynb
+running mako on course.do.txt to make tmp_mako__course.do.txt
+Translating doconce text in tmp_mako__course.do.txt to html
+output in course.html
diff --git a/doc/web/course.do.txt b/doc/web/course.do.txt
index 14c7500a0..794b365c8 100644
--- a/doc/web/course.do.txt
+++ b/doc/web/course.do.txt
@@ -11,10 +11,10 @@ chapters = {
  'week37': 'Week 37 September 11-15: Resampling techniques, Cross-validation and the Bootstrap',
  'week38': 'Week 38 September 18-22: Summary of linear regression methods and start Logistic Regression',
  'week39': 'Week 39 September 25-29: Logistic Regression and Gradient methods',
- 'week40': 'Week 40 October 2-6: Stochastic Gradient Descent and Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm',
- 'week41': 'Week 41 October 9-13: Building a multi-layer perceptron code and introduction to Tensorflow',
- 'week42': 'Week 42 October 16-20: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks)',
- 'week43': 'Week 43 October 23-27: Deep learning, Convolutional Neural Networks and Recurrent Neural Networks',
+ 'week40': 'Week 40 October 2-6: Stochastic Gradient Descent', 
+ 'week41': 'Week 41 October 9-13: Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm',
+ 'week42': 'Week 42 October 16-20: Building a multi-layer perceptron code and introduction to Tensorflow', 
+ 'week43': 'Week 43 October 23-27: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks)',
  'week44': 'Week 44 October 30- November 3: Decision Trees and Ensemble models',
  'week45': 'Week 45 November 6-10: Decision Trees, Random Forests and Gradient Boosting',
  'week46': 'Week 46 November 13-17: Support Vector Machines',
diff --git a/doc/web/course.html b/doc/web/course.html
index 702520178..a8a45a874 100644
--- a/doc/web/course.html
+++ b/doc/web/course.html
@@ -148,27 +148,25 @@ div.toc p,a {
                2,
                None,
                'week-39-september-25-29-logistic-regression-and-gradient-methods'),
-              ('Week 40 October 2-6: Stochastic Gradient Descent and Neural '
-               'Networks, starting to build a multi-layer Perceptron model, '
-               'the Back Propagation algoritm',
+              ('Week 40 October 2-6: Stochastic Gradient Descent',
                2,
                None,
-               'week-40-october-2-6-stochastic-gradient-descent-and-neural-networks-starting-to-build-a-multi-layer-perceptron-model-the-back-propagation-algoritm'),
-              ('Week 41 October 9-13: Building a multi-layer perceptron code '
+               'week-40-october-2-6-stochastic-gradient-descent'),
+              ('Week 41 October 9-13: Neural Networks, starting to build a '
+               'multi-layer Perceptron model, the Back Propagation algoritm',
+               2,
+               None,
+               'week-41-october-9-13-neural-networks-starting-to-build-a-multi-layer-perceptron-model-the-back-propagation-algoritm'),
+              ('Week 42 October 16-20: Building a multi-layer perceptron code '
                'and introduction to Tensorflow',
                2,
                None,
-               'week-41-october-9-13-building-a-multi-layer-perceptron-code-and-introduction-to-tensorflow'),
-              ('Week 42 October 16-20: Deep learning, Solving Differential '
+               'week-42-october-16-20-building-a-multi-layer-perceptron-code-and-introduction-to-tensorflow'),
+              ('Week 43 October 23-27: Deep learning, Solving Differential '
                'Equations with NNs and Convolutional Neural Networks)',
                2,
                None,
-               'week-42-october-16-20-deep-learning-solving-differential-equations-with-nns-and-convolutional-neural-networks'),
-              ('Week 43 October 23-27: Deep learning, Convolutional Neural '
-               'Networks and Recurrent Neural Networks',
-               2,
-               None,
-               'week-43-october-23-27-deep-learning-convolutional-neural-networks-and-recurrent-neural-networks'),
+               'week-43-october-23-27-deep-learning-solving-differential-equations-with-nns-and-convolutional-neural-networks'),
               ('Week 44 October 30- November 3: Decision Trees and Ensemble '
                'models',
                2,
@@ -194,18 +192,18 @@ div.toc p,a {
                2,
                None,
                'projects-fall-2023-dates-are-tentative'),
-              ('Project 1, Deadline October 9 (available September 3)',
+              ('Project 1, Deadline October 15 (available September 3)',
                3,
                None,
-               'project-1-deadline-october-9-available-september-3'),
-              ('Project 2, Deadline November 6 (available October 8)',
+               'project-1-deadline-october-15-available-september-3'),
+              ('Project 2, Deadline November 13 (available October 8)',
                3,
                None,
-               'project-2-deadline-november-6-available-october-8'),
-              ('Project 3, Deadline December 11 (available November 5)',
+               'project-2-deadline-november-13-available-october-8'),
+              ('Project 3, Deadline December 11 (available November 12)',
                3,
                None,
-               'project-3-deadline-december-11-available-november-5')]}
+               'project-3-deadline-december-11-available-november-12')]}
 end of tocinfo -->
 
 
@@ -312,7 +310,7 @@ end of tocinfo -->
    
  •  ipynb file
    • 
 
 
-
    Week 40 October 2-6: Stochastic Gradient Descent and Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm 
    
+
    Week 40 October 2-6: Stochastic Gradient Descent 
    
 
 
      
  
    •  HTML:
      • 
@@ -326,7 +324,7 @@ end of tocinfo -->
    
    •  ipynb file
      • 
 
    
 
-
    Week 41 October 9-13: Building a multi-layer perceptron code and introduction to Tensorflow 
    
+
    Week 41 October 9-13: Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm 
    
 
 
      
  
    •  HTML:
      • 
@@ -340,7 +338,7 @@ end of tocinfo -->
    
    •  ipynb file
      • 
 
    
 
-
    Week 42 October 16-20: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks) 
    
+
    Week 42 October 16-20: Building a multi-layer perceptron code and introduction to Tensorflow 
    
 
 
      
  
    •  HTML:
      • 
@@ -354,7 +352,7 @@ end of tocinfo -->
    
    •  ipynb file
      • 
 
    
 
-
    Week 43 October 23-27: Deep learning, Convolutional Neural Networks and Recurrent Neural Networks 
    
+
    Week 43 October 23-27: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks) 
    
 
 
      
  
    •  HTML:
      • 
@@ -434,7 +432,7 @@ end of tocinfo -->
 
    
 
 
    Projects Fall 2023 (dates are tentative) 
    
-
    Project 1, Deadline October 9 (available September 3) 
    
+
    Project 1, Deadline October 15 (available September 3) 
    
 
      
  
    •  LaTeX and PDF:
      • 
 
        
@@ -451,7 +449,7 @@ end of tocinfo -->
    
      •  ipynb file
        • 
 
      
 
    
-
    Project 2, Deadline November 6 (available October 8) 
    
+
    Project 2, Deadline November 13 (available October 8) 
    
 
      
  
    •  LaTeX and PDF:
      • 
 
        
@@ -468,7 +466,7 @@ end of tocinfo -->
    
      •  ipynb file
        • 
 
      
 
    
-
    Project 3, Deadline December 11 (available November 5) 
    
+
    Project 3, Deadline December 11 (available November 12) 
    
 
      
  
    •  LaTeX and PDF:
      • 
 
        
diff --git a/doc/web/tmp_mako__course.do.txt b/doc/web/tmp_mako__course.do.txt
index 0279311f7..ce215cf5e 100644
--- a/doc/web/tmp_mako__course.do.txt
+++ b/doc/web/tmp_mako__course.do.txt
@@ -87,7 +87,7 @@ The teaching material is produced in various formats for running codes (jupyter
    * "ipynb file": "https://compphysics.github.io/MachineLearning/doc/pub/week39/ipynb/week39.ipynb"
 
 
-===== Week 40 October 2-6: Stochastic Gradient Descent and Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm =====
+===== Week 40 October 2-6: Stochastic Gradient Descent =====
 
 
 
@@ -99,7 +99,7 @@ The teaching material is produced in various formats for running codes (jupyter
    * "ipynb file": "https://compphysics.github.io/MachineLearning/doc/pub/week40/ipynb/week40.ipynb"
 
 
-===== Week 41 October 9-13: Building a multi-layer perceptron code and introduction to Tensorflow =====
+===== Week 41 October 9-13: Neural Networks, starting to build a multi-layer Perceptron model, the Back Propagation algoritm =====
 
 
 
@@ -111,7 +111,7 @@ The teaching material is produced in various formats for running codes (jupyter
    * "ipynb file": "https://compphysics.github.io/MachineLearning/doc/pub/week41/ipynb/week41.ipynb"
 
 
-===== Week 42 October 16-20: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks) =====
+===== Week 42 October 16-20: Building a multi-layer perceptron code and introduction to Tensorflow =====
 
 
 
@@ -123,7 +123,7 @@ The teaching material is produced in various formats for running codes (jupyter
    * "ipynb file": "https://compphysics.github.io/MachineLearning/doc/pub/week42/ipynb/week42.ipynb"
 
 
-===== Week 43 October 23-27: Deep learning, Convolutional Neural Networks and Recurrent Neural Networks =====
+===== Week 43 October 23-27: Deep learning, Solving Differential Equations with NNs and Convolutional Neural Networks) =====