talks/supervised_learning_ising.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inferring Hamiltonians from experimental data with supervised learning\n",
    "\n",
    "Preamble: Run the cells below to import the necessary Python packages\n",
    "\n",
    "+ This notebook is modified from notebooks originally developed and used in [Pankaj Mehta's ML for physics course](http://physics.bu.edu/~pankajm/PY580.html) at Boston University. Please check out those notebooks and associated textbooks for additional details and exercises."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Preamble / required packages\n",
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "# Import local plotting functions and in-notebook display functions\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image, display\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "# Comment this out to activate warnings\n",
    "warnings.filterwarnings('ignore')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised learning\n",
    "\n",
    "+ Given an input $X$, construct a function that assigns it a label $\\hat{y}$. \n",
    "\n",
    "+ **Regression:** $\\hat{y}$ is a continuous variable. For example, given a picture of a person, predict their age. In physics, a common example is to predict the energy of a particle given its momentum, or forecast the next step in a time series.\n",
    "\n",
    "+ **Classification:** $\\hat{y}$ is a discrete variable. For example, given a picture of an animal, predict whether it is a cat or a dog. In physics, a common example is to predict whether a phase is ordered or disordered, or to detect whether a signal point is a background, signal, or anomaly.\n",
    "\n",
    "The function $\\hat{y} = f_\\theta(X)$ is learned from many instances of labelled data comprising $X \\in \\mathbb{N_\\text{data} \\times N_\\text{features}}$ and known $y \\in \\mathbb{N_\\text{data}}$ pairs. The \"weights\" or parameters $\\theta$ are adjusted during *training*.\n",
    "\n",
    "\n",
    "<img src=\"../resources/supervised_learning.gif\" alt=\"supervised_learning\" style=\"width: 750px;\"/>\n",
    "\n",
    "\n",
    "*Image from [source](https://github.com/ReiCHU31/Cat-Dog-Classification-Flask-App)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised learning as inferring a generator\n",
    "\n",
    "+ We can see supervised learning as the process of learning a *generator* for a dataset: given a set of points, can we approximate the underlying process that produced those points?\n",
    "+ + Forecasting: given some past values, predict future values\n",
    "+ + Regression: Given a known generator with unknonw parameters (like a quadratic Hamiltonian with unknown amplitudes), infer those amplitudes\n",
    "+ + Classification (most famous example in ML): Given examples of labelled images, states, etc, predict the class of unlabelled data. We can think of the learned decision boundary as defining a generator of new examples belonging to that class (see conditional GANs, etc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spin glasses\n",
    "\n",
    "+ A spin glass has a Hamiltonian of the form\n",
    "\n",
    "  $$\n",
    "  H(\\mathbf{s}^{(i)}) = - \\sum_{jk} J_{jk} s_{j}^{(i)} \\, s_{k}^{(i)}.\n",
    "  $$\n",
    "  where $s_{j}^{(i)} \\in \\{-1, 1\\}$ is the spin of the $j^{th}$ spin in the $i^{th}$ experimental sample $\\mathbf{s}^{(i)}$, and $J_{jk}$ is the interaction strength between the $j^{th}$ and $k^{th}$ spins. We assume that there are $L$ spins, and that the sum is over all $L(L-1)/2$ pairs of spins. \n",
    "\n",
    "+ In general, the coupling matrix is not symmetric $J_{jk} \\neq J_{kj}$, and the diagonal elements are zero $J_{jj} = 0$ (no self-interactions)\n",
    "\n",
    "+ Depending on the coupling matrix $J_{j,k}$, the system can be ferromagnetic, anti-ferromagnetic, or a spin glass. In a ferromagnet, all spins prefer to be aligned. In an anti-ferromagnet, all spins prefer to be anti-aligned. In a spin glass, there is no global preference for alignment or anti-alignment. Instead, the system is frustrated, and the spins cannot simultaneously minimize their energy.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Lod experimental measurements of an unknown spin glass\n",
    "\n",
    "+ Suppose we have a spin glass with $L$ spins. \n",
    "\n",
    "+ Our data consists of $N_\\text{data}$ measurements of microstates $\\mathbf{s}^{(i)}$, and their respective energies $E^{(i)} = H(\\mathbf{s}^{(i)})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Microstates shape:  (10000, 40)\n",
      "Energies shape:  (10000,)\n"
     ]
    }
   ],
   "source": [
    "microstates = np.load('../resources/spin_microstates.npy', allow_pickle=True)\n",
    "energies = np.load('../resources/spin_energies.npy', allow_pickle=True)\n",
    "\n",
    "print(\"Microstates shape: \", microstates.shape)\n",
    "print(\"Energies shape: \", energies.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of microstates')"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.imshow(\n",
    "    microstates[np.argsort(energies)].T, \n",
    "    interpolation='nearest', aspect='auto', cmap='binary'\n",
    ")\n",
    "plt.ylabel(\"Spin position\")\n",
    "plt.xlabel(\"Microstate\")\n",
    "plt.title(\"Spin configurations sorted by energy\")\n",
    "## aspect ratio\n",
    "# plt.gca().set_aspect('auto')\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.hist(energies, bins=100)\n",
    "plt.xlabel(\"Energy\")\n",
    "plt.ylabel(\"Number of microstates\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Can we infer the unknown $J_{jk}$, given only the samples and their energies?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model class is defined as our known energy function for each sample,\n",
    "\n",
    "$$\n",
    "H(\\mathbf{s}^{(i)}) = - \\sum_{jk} J_{jk} s_{j}^{(i)} \\, s_{k}^{(i)}.\n",
    "$$\n",
    "\n",
    "We can define the vector $\\mathbf{X}^i$ with components\n",
    "\n",
    "$$\n",
    "\\mathbf{X}^{(i)}_{jk} = s_j^{(i)} s_k^{(i)}.\n",
    "$$\n",
    "\n",
    "or, in vector notation,\n",
    "\n",
    "$$\n",
    "\\mathbf{X}^{(i)} = \\mathbf{s}^{(i)} \\otimes \\mathbf{s}^{(i)}.\n",
    "$$\n",
    "\n",
    "Then the energy of each sample is\n",
    "\n",
    "$$\n",
    "E^{(i)} = - \\sum_{jk} J_{jk} \\mathbf{X}^{(i)}_{jk}.\n",
    "$$\n",
    "\n",
    "Notice that we've exploited our prior knowledge of the physics of this problem in order to put the problem into a linear form. This represents a sort of *feature engineering* where we've used an *inductive bias* to make the problem easier to solve.\n",
    "\n",
    "\n",
    "### A note on flattening\n",
    "\n",
    "Notice that our Hamiltonian contains a double sum, which indexes into two matrices. Rather than keeping track of two indices, we can flatten the matrices into vectors, and use a single index. \n",
    "\n",
    "Flattening over features space is a common technique in machine learning, which we previously used in order to apply PCA to image data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_all shape:  (10000, 40, 40)\n",
      "X_all shape after flattening into data matrix:  (10000, 1600)\n",
      "y_all shape:  (10000,)\n"
     ]
    }
   ],
   "source": [
    "X_all = microstates[:, :, None] * microstates[:, None, :] # outer product creates neighbor matrix\n",
    "print(\"X_all shape: \", X_all.shape)\n",
    "\n",
    "# Data matrix / design matrix always has shape (n_samples, n_features)\n",
    "X_all = np.reshape(X_all, (X_all.shape[0], -1)) \n",
    "print(\"X_all shape after flattening into data matrix: \", X_all.shape)\n",
    "\n",
    "# Match our label shape\n",
    "y_all = energies\n",
    "print(\"y_all shape: \", y_all.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training and testing data\n",
    "\n",
    "+ Rather than fitting our Hamiltonian model to all of the data, we will split the data into a training set and a test set. \n",
    "\n",
    "+ We will fit the model to the training set, and then evaluate the trained model on the test set. \n",
    "\n",
    "+ This is a common technique in machine learning, and is used to avoid overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train shape:  (400, 1600)\n",
      "y_train shape:  (400,) \n",
      "\n",
      "X_test shape:  (200, 1600)\n",
      "y_test shape:  (200,)\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# define subset of samples\n",
    "n_samples = 400\n",
    "\n",
    "# define train and test data sets\n",
    "X_train, X_test = X_all[:n_samples], X_all[n_samples : 3 * n_samples // 2]\n",
    "y_train, y_test = y_all[:n_samples], y_all[n_samples : 3 * n_samples // 2]\n",
    "\n",
    "print(\"X_train shape: \", X_train.shape)\n",
    "print(\"y_train shape: \", y_train.shape, \"\\n\")\n",
    "\n",
    "print(\"X_test shape: \", X_test.shape)\n",
    "print(\"y_test shape: \", y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting a linear model with least squares\n",
    "\n",
    "+ Because our Hamiltonian is linear with respect to the *outer product* state matrices, we expect that linear regression is a good way to infer the coupling matrix $J_{jk}$.\n",
    "\n",
    "+ Recall that the linear model is defined as\n",
    "\n",
    "  $$\n",
    "  \\hat{y} = A \\cdot \\mathbf{x}\n",
    "  $$\n",
    "  where $A$ is a matrix, then $\\mathbf{x}$ is a vector of features, and $\\hat{y}$ is a vector of predictions.\n",
    "\n",
    "+ In our case, the features are the outer product state matrices $\\mathbf{X}^{(i)}$, and the predictions are the energies $E^{(i)}$. We can directly solve for the matrix $A$ using the least squares method:\n",
    "  $$\n",
    "  A = \\left( \\mathbf{X}^T \\mathbf{X} \\right)^{-1} \\mathbf{X}^T \\mathbf{y}\n",
    "  $$\n",
    "\n",
    "  Recall that we need to use the Moore-Penrose pseudoinverse because the matrix $\\mathbf{X}^T \\mathbf{X}$ is not square, and the pseudoinverse is the closest thing to an inverse that we can get.\n",
    "\n",
    "### `scikit-learn` \n",
    "\n",
    "+ Rather than using numpy, we will use the Python machine learning library `scikit-learn` to perform the linear regression. \n",
    "\n",
    "+ `scikit-learn` uses a consistent API for both simple models, like linear regression, and more complex models, like neural networks.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "model = LinearRegression()\n",
    "\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "y_pred_train = model.predict(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(y_train, y_pred_train, \".k\")\n",
    "plt.xlabel(\"True energy (Training Data)\")\n",
    "plt.ylabel(\"Predicted energy (Training Data)\")\n",
    "plt.title(\"Linear regression on training data\")\n",
    "plt.gca().set_aspect('auto')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about experiments that the model hasn't seen before?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_test = model.predict(X_test)\n",
    "# y_pred_test = model.predict(X_test)\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.plot(y_test, y_pred_test, \".k\")\n",
    "plt.xlabel(\"True energy (Test Data)\")\n",
    "plt.ylabel(\"Predicted energy (Test Data)\")\n",
    "plt.title(\"Linear regression on test data\")\n",
    "plt.gca().set_aspect('auto')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overfitting\n",
    "+ High train accuracy just tells us that our model class is capable of expressing patterns found the training data\n",
    "\n",
    "+ For all datasets, there exists a way to get 100% train accuracy as long as I have access to memory equal to the size of the training dataset (1-nearest-neighbor lookup table)\n",
    "\n",
    "+ We therefore need to either regularize (training data can't be perfectly fit) or use a test dataset to see how good our model actually is\n",
    "\n",
    "+ A reasonable heuristic when choosing model complexity is to find one that can just barely overfit train (suggests sufficient power)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scoring a trained regression model\n",
    "\n",
    "We can summarize the performance of a regression model by computing the coefficient of determination, $R^2$. This is a measure of how much of the variance in the data is explained by the model. It is defined as\n",
    "$$\n",
    "R^2 = 1 - \\frac{\\sum_i (y_i - \\hat{y}_i)^2}{\\sum_i (y_i - \\langle y \\rangle)^2}\n",
    "$$\n",
    "where $y_i$ is the true value of the $i^{th}$ sample, $\\hat{y}_i$ is the predicted value of the $i^{th}$ sample, and $\\langle y \\rangle$ is the mean of the true values. An $R^2$ of 1 indicates that the model perfectly predicts the data, while an $R^2$ of 0 indicates that the model is no better than predicting the mean of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train error was: 1.0\n",
      "Test error was: 0.4943462162181823\n"
     ]
    }
   ],
   "source": [
    "print(\"Train error was:\", model.score(X_train, y_train))\n",
    "print(\"Test error was:\", model.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## But raw score doesn't tell the whole story\n",
    "\n",
    "+ We can get a great fit, but our model might have a lot of free parameters\n",
    "+ There might be multiple valid coupling matrices $J$ that explain the observed data\n",
    "+ Our model might be predictive but not interpretable, or physical\n",
    "+ We either need more data, better data (sample rarer states), or a better model\n",
    "\n",
    "\n",
    "## Let's look at the learned coupling matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x16bd20a90>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Because we flattened the data, we need to reshape the coefficients to get the couplings\n",
    "L = microstates.shape[1]\n",
    "couplings_estimated = np.array(model.coef_).reshape((L, L))\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.imshow(couplings_estimated, cmap='RdBu_r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's try repeating the model fitting several times on different subsets of our experimental data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x900 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.figure(figsize=(9, 9))\n",
    "## Plot 3 x 3 subplots\n",
    "\n",
    "n_samples = 200\n",
    "for i in range(9):\n",
    "\n",
    "    ## Pick random training data set\n",
    "    selection_inds = np.random.choice(range(X_all.shape[0]), size=n_samples, replace=False)\n",
    "    X_train, y_train = X_all[selection_inds], y_all[selection_inds]\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_all[selection_inds], y_all[selection_inds])\n",
    "    couplings_estimated = np.array(model.coef_).reshape((L, L))\n",
    "    \n",
    "    ## Plot learned coupling matrix\n",
    "    plt.subplot(3, 3, i + 1)\n",
    "    plt.imshow(couplings_estimated, cmap='RdBu_r')\n",
    "    plt.axis('off')\n",
    "\n",
    "# spacing between subplots\n",
    "plt.subplots_adjust(wspace=0.1, hspace=0.1)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Narrowing the model class with regularization\n",
    "\n",
    "+ We constrain the model's allowed space of valid representations in order to select for more parsimonious models\n",
    "\n",
    "+ Operationally, regularizers/constraints reduce the \"effective\" number of parameters, and thus complexity, of our model\n",
    "\n",
    "+ Imposing preferred basis functions or symmetries can be forms of regularization\n",
    "\n",
    "\n",
    "### Ridge regression and Lasso:\n",
    "\n",
    "+ We can think of our least-squares problem as choosing the optimal $J$ that minimizes the following objective function, the mean squared error between the model energies and true energies\n",
    "$$\n",
    "\\mathcal{L} = \\sum_{i=1}^{N_{data}} (\\mathbf{X}^{(i)} \\cdot \\mathbf{J}- E^{(i)})^2\n",
    "$$ \n",
    "+ where $i$ indicates different training examples, which have predicted energies given by $\\mathbf{X}^i \\cdot \\mathbf{J}$ and observed energies of $H^i$\n",
    "\n",
    "+ Common regularizers associated loss with the trainable parameters of the model. \n",
    "\n",
    "+ **Ridge regression** is also known as $L2$ regularization, and it discourages any particular weight in the coefficient matrix from becoming too large. Ridge imposes a degree of smoothness or regularity across how a model treats its various inputs. Models that take continuous data as inputs (such as time series, or images), may benefit from the ridge term.\n",
    "\n",
    "+ + If $\\mathbf{J}$ is our trainable linear regression weight matrix (and, in this context, our best estimate for the spin-spin interaction matrix), then we can modify the the losses as follows:\n",
    "$$\n",
    "\\mathcal{L}_{Lasso} = \\sum_{i=1}^{N_{data}} (\\mathbf{X}^{(i)} \\cdot \\mathbf{J}- E^{(i)})^2 + \\lambda \\sum_{jk} | J_{jk} |\n",
    "$$\n",
    "\n",
    "\n",
    "\n",
    "+ **Lasso** is also known as $L1$ regularization, and it encourages *sparsity* in weight space: it incentivizes models were most coefficients go to zero, thereby reducing the models dependencies on features. Lasso is often used in feature selection, where we want to identify the most important features in a dataset.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}_{Ridge} = \\sum_{i=1}^{N_{data}} (\\mathbf{X}^{(i)} \\cdot \\mathbf{J}- E^{(i)})^2 + \\lambda \\sum_{jk} J_{jk}^2\n",
    "$$\n",
    "where the hyperparameter $\\lambda$ determines the \"strength\" of the penalty terms.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try re-fitting the model with these different regularizers. We will vary $\\lambda$, the strength of the regularization, and see how the learned coupling matrix changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rrysA6rnnnmvx+xNPPFGVl5e32q9d+XvT2J1t05YtW9LmU/phspT6v8d9iMjY+PHj8cYbb2D16tVtfi7d+vXr0bNnT4wZM6b51fgnnngCF110ESorK5s/86g9DjzwQHz99dd8JZ+I6EckmUxiyJAh6Nq1K956661sN4eIiLKo6X7h7rvvRu/evVuV+3w+nHLKKbj77rsxZcqUVuVbt25Ft27dMGbMGLz44osYPHgwunXrhpNOOgkDBw6E4zj49NNP8cc//hF1dXVYvHgxBg0aBADtir3vvvtwzTXXYMSIEbjqqqtQUVGBtWvX4oEHHsCHH36Ie++9Fz//+c+1+3rSSSdh2bJl+PTTT1s8eX7MMcdg3bp1WL58+a4cStHxxx+Pjz76CHfffTf69u2LZ599FjNnzsRTTz2Fc889tzlu0aJFOPbYY3HLLbfglltuaffftye2PXXOmzcPDQ0NqKurw8SJE3HmmWfiJz/5CQBg7NixCIVCu+Ow0Z6Q7VVCoh+inXkFyeRJunSvYNXV1ani4mLVp0+fzOwAERFlxcSJE9Wzzz6rFi5cqJ577jl11FFHKcuy1D/+8Y9sN42IiLKs6X4h3c+ECROUz+dT3333Xdo6zjrrLOXxeNSmTZvU3//+d3XOOeeofv36qXA4rLxer6qoqFDnnXee+vLLL1v8XXtildr+hN0ZZ5yhOnfurDwej+rUqZM67bTT1OLFi8X93Bue/DZ9wjrdk9+742nu9tTJJ79/vPgkHdFOau8rSNIrY2PHjsWUKVPw/vvv46c//SmGDBmCYDCIVatW4f7778e///1vPPbYY7jooov25G4SEVEG/eQnP8HixYuxZcsWeL1eDB06FL/97W9x4oknZrtpRERERJRlXKQj2gUffPAB/vjHP+Ldd9/Ftm3bUFRUhMMOOwy//vWvceihh7aIbVqkS2fVqlXYvHkz/va3v+G9997DunXrUFtbi6KiIgwbNgxXX301xowZs7t3iYiIiIiIiIiygIt0REREREREREREWebKdgOIiIiIiIiIiIg6Oi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHYCjjjoKlmWJP9OmTdul7SxcuBCWZWHhwoUZabepe++9F6eddhp69eoFy7Jw1FFHtevvk8kkbr31VvTs2RN+vx8DBw7Efffdt1NtufDCC42O9YUXXrhT9X/fM888g3vvvTcjde3ovvvuw8CBA+H3+9GrVy/ceuutSCaT7a7n7bffbt7nrVu3tip/+umnceCBByIQCKCkpATnnHMO1q1bp61z8+bNKC4uhmVZmDNnTouyTz/9FOPGjUNFRQWCwSCKiopw6KGH4qmnntLWqZTCEUccAcuycNVVV7UZs2bNGkycOBHl5eXw+/3o2rUrTj311BYxL7zwAs4++2z07dsXwWAQPXv2xLnnnovly5e3qu/VV1/F+eefj0GDBsHr9cKyLG0bly5dijPPPBOlpaXw+/3o2bMnrrjiihYxs2bNwoQJE9CzZ08Eg0H07dsXl19+OTZu3Niqvr/+9a8466yzMGDAALhcLvTs2TPttj/55BNMmDAB5eXlCIVCGDhwIG677TY0Nja2iHvvvfcwefJkDBs2DH6/H5ZlYfXq1W3WuWnTJlx11VXo3bs3gsEgevTogUmTJmHt2rUt4tpzTG+88UYceOCBKCoqQiAQQO/evXHJJZdgzZo1afeNaFeZjPmZzI1PPPGE9tra0+rq6jBlyhQcf/zxKC0t3an5RH19Pa655hqUl5cjEAhgyJAheO6553Y6rr2xkj19jpssXrwY06ZNQ01NTUbrTSeTx2zWrFmwLAvhcLjNctO88q9//QsnnHACcnNzEQ6HcfTRR+P999/fqTYRdTTMT8xPHT0/zZ8/HxMnTsTAgQORk5ODrl274pRTTsG///3vXYo1zWGUhiL1xRdfqCVLljT/3HTTTQqAevzxx1v8ft26dbu0ndraWrVkyRJVW1uboZabGTBggBo6dKiaOHGiKi0tVUceeWS7/n7y5MnK7/er6dOnqwULFqjf/OY3yrIs9bvf/a7dbVmxYkWLY/rAAw8oAOr3v/99i9+vWLGi3XW3Zdy4capHjx4ZqavJHXfcoSzLUjfccINasGCBmj59uvL5fOriiy9uVz11dXWqZ8+eqry8XAFQW7ZsaVH+5z//WQFQkydPVm+88YaaNWuWKisrUz169FBVVVVp6z399NOb65w9e3aLsgULFqhLL71U/e1vf1Pz589Xc+fOVWeddZYCoG6//fa0dd53332qrKxMAVBXXnllq/LPP/9cFRcXq+HDh6unn35aLVq0SD333HPqoosuahE3YsQIdfLJJ6vHHntMLVy4UP3tb39T++yzjwqHw2rp0qUtYidOnKj69eunfvKTn6hhw4Yp3XA1f/58FQwG1fHHH6/mzJmjFi5cqP7617+qX/7yly3iysvL1bnnnquefvpptXDhQvXwww+rbt26qbKyMrVp06YWsccdd5zaf//91c9+9jPVt2/ftP3oiy++UIFAQB1wwAHq73//u3rnnXfU1KlTldvtVieffHKL2GnTpqkePXqoCRMmqKOOOkoBUKtWrWpVZywWU/369VMlJSXqgQceUAsWLFB/+ctfVOfOnVXXrl1VJBLZqWN6xRVXqLvvvlu98sorasGCBeqBBx5QZWVlqnPnzmrr1q1pjy/RrthxbF+yZIkaO3asCgaDrX6fqdz43XffqSVLlqhYLJaR+nbVqlWrVH5+vjriiCPU5MmTFQA1derUdtUxevRoVVBQoP7yl7+o+fPnN9fz9NNP71Rce2Mle/ocN7nnnnvSjqO7Q6aO2fr161V+fr4qLy9XOTk5rcpN88q//vUv5ff71eGHH65efPFF9cILL6hDDjlE+f1+tXjx4l3eX6IfO+Yn5qeOnp/OOOMMdfTRR6sHH3xQLVy4UM2ePVsdcsghyuPxqHfeeWenYttzb0Rt4yJdGx5//HEFQFVWVmrjGhoa9lCLdo1t283/v99++7VrkW7p0qXKsiz1+9//vsXvL774YhUMBtW2bdt2qW0LFixoczEpUzK9SLd161YVCATUJZdc0uL3v/vd75RlWeqLL74wruvKK69UBx54YPOi8I6LdLFYTOXn56uTTjqpxd8sXrxYAVC//e1v26xzzpw5KhwOqyeffLJdx/Xggw9W3bt3b7Ns1apVKhwOqxdeeKHNRTrHcdSQIUPUkCFDxEnH5s2bW/3u22+/VV6vV02aNKnF73fst1deeWXaRbqGhgZVVlamxo0bpxzHaff2Kysr21yk3HH7un504403KgCtFpYvueQSBaDFguqOdeqS9z/+8Q8FQM2aNavF75955hkFQL3wwgvafUp3TNvy+uuvKwDq0UcfFWOJMuGCCy5oc2EinR9Krk3HcZzmsWnLli3tvgl67bXXFAD1zDPPtPj96NGjVXl5uUqlUu2Ka2/szmjvOd5Ze/ImKJPHbPz48eqkk05Ke5xM88oJJ5ygOnfu3OIaiUQiqqSkRI0cObI9u0dEivmJ+Slzfij5qa37iLq6OtW5c2d17LHH7lRse+6NqG18u6uhadOmwbIsfPzxxzjjjDNQWFiIPn36AAA++ugjnHXWWc1voevZsyfOPvvsVm8ha+vtrhdeeCHC4TBWrFiBsWPHIhwOo3v37vjVr36FeDyekba7XDt/ml966SUopXDRRRe1+P1FF12EaDSKN954Y1eb16a3334bxx57LPLy8hAKhTBq1Ci88847LWK2bNmCSy65BN27d4ff70dpaSlGjRqFt99+G8D2tzG/9tprWLNmTYvHmXfFG2+8gVgs1ubxUErhpZdeMqrn3XffxSOPPIJZs2bB7Xa3Kl+6dClqa2sxduzYFr8/9NBDUVRUhOeff77V31RVVeHKK6/E7373O1RUVJjvFICSkhJ4PJ42yy655BKMHj261VtXm/zzn//Ep59+imuuuQZ+v1+7nU6dOrX6XXl5Obp169bqbbym/Xb27NnYuHEjrrvuOvH8trX9YcOGwe127/T2vV4vACA/P7/F7wsKCuByueDz+TJaJwAEAoHm37XnmLaltLQUANKef6I9SZdrV6xYgYsuugj9+vVDKBRC165dcdJJJ+Hzzz9vUUdbbydqqveLL77A2Wefjfz8fHTu3BkTJ05EbW3tbt2nXc09L774IsLhMM4888wWv7/ooouwYcMGfPjhh+2Ka2/s7rB8+XKcc8456NSpE/x+P/bZZx888MADLWKkHD9t2jRcd911AND8cR678yNFMnXMnnrqKSxatAgPPvhg2hjTvPL+++/jqKOOQigUao7Jzc3FEUccgcWLF7f5UQ5EtHOYn1pjfvrh56e27iPC4TD23XffVvcRprHtuTeitnGRrp1OO+009O3bF7Nnz8Zf/vIXAMDq1asxYMAA3HvvvXjzzTdx9913Y+PGjRg+fHibnzP2fclkEieffDKOPfZYvPzyy5g4cSL+9Kc/4e67724RZ9s2UqmU+OM4Tsb2d+nSpSgtLUWXLl1a/H7w4MHN5Zn21FNP4fjjj0deXh6efPJJ/M///A+KiopwwgkntFioO++88/DSSy/hlltuwVtvvYVZs2bhuOOOw7Zt2wAADz74IEaNGoUuXbpgyZIlzT9NduZ4Nu3voEGDWrS5rKwMJSUlRscjGo1i0qRJuOaaazB06NA2YxKJBAC0uejl9/uxfPlyxGKxFr+/+uqr0atXr7SfGbcjx3GQSqWwZcsWPPjgg3jzzTdx/fXXt4qbNWsW/vWvf+H+++9PW9c///lPANtvDMaOHYtAIIBwOIzx48dj2bJlYltWrlyJNWvWYL/99hNjddu3bRuHHXYYfD4fCgsLcfbZZ2PDhg3i3y9atAi2be/09i+44AIUFBTg8ssvx8qVK1FXV4dXX30VDz/8MK688krk5OS0u85Ro0Zh2LBhmDZtGiorK1FfX4+PP/4Yv/3tbzF06FAcd9xx2r+XjmkqlUI0GsUnn3yCa665Bv3798dpp53W7nYS7S5t5doNGzaguLgYd911F9544w088MAD8Hg8OPjgg/H1118b1Xv66aejf//+eP755/Gb3/wGzzzzDH75y1+2GauUMsoRqVQqY/vdlqVLl2KfffZptZD+/TxsGtfe2Ez78ssvMXz4cCxduhR//OMf8eqrr2LcuHG4+uqrceuttzbHSTl+8uTJ+PnPfw5g+2dzNuX4tvJqJs5lJo7Zd999h2uuuQZ33XUXunXrljbONK8kEom08wQArRYIiGjXMT/9F/PTjyc/7ai2thYff/yx0b1RW7G7496ow8nmY3x7q7be7jp16lQFQN1yyy3i36dSKVVfX69ycnLUjBkzmn/f9NbOBQsWNP/uggsuUADU//zP/7SoY+zYsWrAgAEtftejRw8FQPzRPabc3re7jh49ulU7mvh8vlZv+2yv77/dtaGhQRUVFbV6m6dt2+qAAw5QI0aMaP5dOBxW11xzjbZ+3dsUd+Z4Xnzxxcrv97dZX//+/dXxxx8v7vOvfvUr1bt3b9XY2KiU+m/f2vHtrtu2bVMul6vV2xVXrFjR3K4NGzY0//7VV19VXq9Xff7550op+W3El156aXM9Pp9PPfjgg61imj4z5+GHH27+Hdp4u2tTXXl5eWrSpEnq7bffVn/7299Ujx49VElJSYt2fl8ymVRHHXWUysvLU2vXrk0bp3u76wknnKAAqIKCAjVlyhQ1f/589Ze//EUVFxervn37at+KEIlE1D777KO6d++u6urq0sZJb5v+6quv1MCBA1v0m6uvvlr79lvpMfhIJKJOOumkFnUeddRR4lvMpWO6cePGFnUefPDB6ttvv9XWSZRJureatDfXJhIJ1a9fvxafP9mUw3e8tprqnT59eos6rrjiChUIBNq8VpvGUZMf07ez7Mzbifr166dOOOGEVr/fsGFD82e6tieuvbE7Q3eOTzjhBNWtW7dWn/9z1VVXqUAg0Pw2GJMcb/p2okycy0wcs9NPP12NHDmyub/pjpNJXhkyZIjq379/i49SSCaTqnfv3m2+9YmI9JifmJ86an7a0bnnnqs8Ho/66KOPdjp2Z+6N6L/4/qZ2Ov3001v9rr6+Hrfffjuef/55rF69GrZtN5d99dVXYp2WZeGkk05q8bvBgwdj/vz5LX43d+5co7fAlpeXizHtoXsMelffPvp9ixcvRlVVFS644IJWrxiceOKJmD59OhoaGpCTk4MRI0bgiSeeQHFxMY477jgMGzas+fFaEzt7PHflePzrX//CvffeizfeeAPBYDBtXFFREc4991z89a9/xfDhw3HmmWdi/fr1uOSSS+B2u2HbdvNbJ2tra3HppZfi+uuvx/777y/uDwD89re/xeTJk/Hdd99h7ty5uOqqq9DQ0IBf//rXzTGXXXYZDjjgAFx88cXaupqeNDz00EMxa9as5t/vv//+OPDAA/HAAw/gjjvuaPV3SilMmjQJ7777Lp5//nl0797dqO3ptv/Tn/60+enTo48+Gl26dMGECRPwzDPPYPLkya3+LhaL4bTTTsOaNWswf/78tN+wJ1m9ejVOOukkdO7cGXPmzEFpaSk+/PBD3HHHHaivr8ejjz7a7jqTySR++tOfYunSpZg5cyYGDBiAVatW4Y477sDo0aMxf/78Vo+QA2bHtKSkBJWVlYjH4/jqq68wffp0HH300Vi4cCHKysp26hgQZVpbuTaVSmH69Ol46qmnsGLFihbfqG2SawHg5JNPbvHvwYMHIxaL4bvvvkPnzp1blA0bNgyVlZVG9WY6736fad5pT37ak7m9SSwWwzvvvIPLL78coVCoRZ4fO3Ys7r//fnzwwQcYM2bMLuf4HWXqXO7KMXv++ecxd+5cfPLJJ2KsaV75+c9/jkmTJuGqq67CjTfeCMdxcOuttzZ/3MqufNwJEbWN+akl5qcffn7a0c0334ynn34a9913H4YNG7ZTsbvj3qij4SJdO7V1E3vOOefgnXfewc0334zhw4cjLy8PlmVh7NixiEajYp2hUKjFZ0wB29+q8P23M+67775QSon1ZXJSVlxcjE8//bTV7xsaGpBIJFBUVJSxbQHA5s2bAQBnnHFG2piqqirk5OTg73//O+644w7MmjULN998M8LhME499VRMnz691dtz27Izx7O4uBixWAyNjY0tPgOmqV3SYDZx4kScdtppOOigg5q/krvpPEciEfj9fuTm5gIAHnroISilcMUVV+Cyyy6Dy+XCeeedh86dO+PNN99EcXExAODGG2+E1+vFVVdd1VxnfX09AKCxsRE1NTXIz89vMUBXVFQ0f25d0+fe3XDDDbjgggtQWlqKOXPm4I033sB7773X6vMwEokEampqkJOTA6/X29yOE044oUXckCFDUFZWho8//rjVcVBKYfLkyXjqqafw5JNP4pRTTtEeN5102z/hhBOaPzvk++LxOE499VS89957ePXVV3HwwQfv9PZ/85vfIBKJ4NNPP21+fPuII45ASUkJJk6ciPPPPx9HHnlku+p89NFHMW/ePFRWVuKggw4CABx++OE47LDD0KdPH9x7772YOnVqi78xPaYej6e5zlGjRuHEE09Er169cNddd2HGjBnt3X2i3aKtXHvttdfigQcewPXXX48jjzwShYWFcLlcmDx5slGuBf47XjRpeltgW38fDocxZMgQo3p352c6FhcXN7+FZkdVVVUA0JyHTePaG5tJ27ZtQyqVwn333Yf77ruvzZimjwnZ1Ry/o0ycy105ZvX19bjyyivx85//HOXl5c25uumjLWpqauD1eptziGlemThxIrZs2YI77rgDDz30EIDtL5j9+te/xt13342uXbsa7TMRmWN++i/mpx9+ftrRrbfeijvuuAO/+93vxI9P0sXujnujjoYvsbXT91eia2tr8eqrr2LKlCn4zW9+g2OPPRbDhw/HoEGDmi+MTOnTpw+8Xq/4c9ttt2Vsm4MGDcKWLVuwadOmFr9v+pwT0ye3TJWUlAAA7rvvPlRWVrb50/RqUklJCe69916sXr0aa9aswZ133okXXngBF154odG2duZ4Nn0W3fc/52XTpk3YunWreDy++OILzJ49G4WFhc0/TU9/9enTB4cffnhzbE5ODv72t79h69at+Oyzz7B582Y88cQT+PrrrzFy5MjmgXrp0qVYvXo1unTp0lxn05OZF1xwAQoLC8UPnh0xYgRSqRRWrlzZXGcqlcIhhxzSoq0AMHPmTBQWFuK1114D8N/PO2iLUqrVonHTYtLjjz+OWbNm4Wc/+5m2bRLd9oHWi9bxeBwTJkzAggUL8NJLL+HYY4/dpe1/+umn2HfffVt9vsLw4cMB7NxnZ3z66adwu92tPruid+/eKC4ublXnrhzTbt26oby8HN98802720m0u7T1qu9TTz2F888/H7///e9xwgknYMSIETjooIOMPvt1ZyxatMgoR3i93hYfAp5pgwYNwldffdXq6fLv52HTuPbGZlJhYSHcbjcuvPDCtDm+6YWjXc3xO8rEudyVY7Z161Zs3rwZf/zjH1vk1GeffRYNDQ0oLCzEueee2xzfnrxy/fXXY+vWrfj888+xevVqLF68GNXV1cjJyRFfOCSi9mN++i/mpx9+fmpy6623Ytq0aZg2bRp++9vf7lLs7rg36mj4JN0usiwLSqlWH9w7a9asFm97zYRsvN31lFNOwU033YQnn3yyxRcLPPHEEwgGgzjxxBMzti1g+5M9BQUF+PLLL42+AKFJRUUFrrrqKrzzzjt4//33m3/v9/vTvoK1M8fzxBNPRCAQwBNPPNHi6aumb2uaMGGCtq4FCxa0+t0TTzyBJ598Ei+99FKbr3rvuED2yiuv4Ouvv27xpSL33ntv86vyTT799FP88pe/xLRp03DkkUeKb+VcsGABXC4XevfuDWD7tw4fddRRreKOPvpoTJgwAb/4xS+aB/wxY8YgFAph3rx5LT7g9uOPP8amTZtwyCGHNP9OKYWLL74Yjz/+OB5++OFW35K7M0499VTceOONmDdvXotvoJ03bx6UUi223/QE3fz58/HCCy+0evpuZ5SXl2Pp0qWor69vcZybvqRE9+Hgujpt20ZlZWWLfvbNN99g27ZtLerc1WO6YsUKrF+/vtXbLIj2NpZltcq1r732Gr799lv07ds349vbW95OdOqpp2LmzJl4/vnn8dOf/rT5908++STKy8ubxwjTuPbGZlIoFMLRRx+NTz75BIMHDzb+hjddjgfaftJkR5k4l7tyzLp06dJm/r/rrruwaNEizJs3r/lFyqY2tCev+P3+5py8du1a/P3vf8fFF1+s/VgNIsoc5ifmpx9qfgKA22+/HdOmTcNNN93U6p06OxO7O+6NOhou0u2ivLw8HHHEEbjnnntQUlKCnj17YtGiRXj00UdRUFCQ0W19/xtFTX300UfNK++RSARKKcyZMwfA9hXtHj16AAD++te/YuLEiXjsscdw/vnnAwD2228/TJo0CVOnToXb7cbw4cPx1ltv4ZFHHsEdd9zR4vHZhQsX4uijj8bUqVMxbdq0nWprOBzGfffdhwsuuABVVVU444wz0KlTJ2zZsgWfffYZtmzZgoceegi1tbU4+uijcc4552DgwIHIzc1FZWUl3njjjRbfUjlo0CC88MILeOihhzBs2DC4XK7mt/rtzPEsKirCTTfdhJtvvhlFRUU4/vjjUVlZiWnTpmHy5MnYd999m2PbOp5tLXw1fR33qFGjWkzSn3/+eWzYsAH77LMPYrEYFi5ciBkzZuCyyy5r8VZG3SPS++23X4ttXnLJJcjLy8OIESPQuXNnbN26FbNnz8bf//53XHfddSgtLQUA9OzZEz179myzzq5du7aos6CgALfddht+/etf48ILL8TZZ5+NTZs24eabb0ZFRQWuuOKK5tirr74ajz76KCZOnIhBgwbhgw8+aC7z+/048MADm/+9Zs2a5qT1n//8BwCa+23Pnj2bz+PAgQNx5ZVX4sEHH0Rubi7GjBmDb775BjfddBMOPPBA/OQnP2mu84wzzsC8efNw4403ori4uMX28/LyWpy/L7/8El9++SWA7U9KNjY2Nm9/3333bY695pprMGHCBIwePRq//OUvUVJSgg8++AB33nkn9t13X4wZM6a5zi1btmDRokUA/vvq1rx581BaWorS0tLmR78vuugi/OlPf8Lpp5+Om266CQMGDMDKlSvx+9//Hjk5ObjsssvafUz/93//F7/85S9xxhlnoHfv3nC5XPj888/xpz/9CcXFxS0+j5BobzR+/Hg88cQTGDhwIAYPHox///vfuOeee3bbZC83N7d5nNlV8+bNQ0NDA+rq6gBsH1+axpOxY8ciFAph0aJFOPbYY3HLLbfglltuaf7bMWPGYPTo0bj88ssRiUTQt29fPPvss3jjjTfw1FNPwe12tyuuvbGWZeHII49szlW7asaMGTjssMNw+OGH4/LLL0fPnj1RV1eHFStWYO7cuZg/f367cnxTnRdccAG8Xi8GDBjQ/LERTTJxLttzzL5/LgOBQJv5/4knnoDb7W5VZppXli5diueffx4HHXQQ/H4/PvvsM9x1113o168fbr/99l3aXyIyx/zE/PRDzU9//OMfccstt+DEE0/EuHHjWtxHAGjxsINpbHvujSiNLHxZxV5P9+2uO34DZ5P169er008/XRUWFqrc3Fx14oknqqVLl6oePXqoCy64oDku3be7tvUNM03by4Smb5Bt6+fxxx9vtd87/k4ppRKJhJo6daqqqKhQPp9P9e/fX/35z39utZ25c+cqAOovf/mLcdvSfQvpokWL1Lhx41RRUZHyer2qa9euaty4cc1xsVhMXXbZZWrw4MEqLy9PBYNBNWDAADV16tQW3+ZZVVWlzjjjDFVQUKAsy8rYMZ0xY4bq37+/8vl8qqKiQk2dOlUlEokWMemO5/el61svvviiGjJkiMrJyVHBYFAddNBB6tFHHzX6Vpx0x/Wxxx5Thx9+uCopKVEej0cVFBSoI488Uv3tb38z2m+08e2uTWbOnKn2339/5fP5VHFxsTr33HPVunXrWsTovlH3+9+e2nT82vrZ8bpSavu3aN11112qb9++yuv1qrKyMnX55Zer6urqVu1P9/P9bz1uOi9t/Xz/m6/mz5+vjj/+eNWlSxcVDAZV//791a9+9Su1devWFnG6b3D6/vaXL1+uzjvvPNWzZ0/l9/tVRUWF+ulPf6q++OKLnTqmmzZtUj/72c9Unz59VCgUUj6fT/Xu3Vtddtll2m/WJco0k2/PayvXVldXq0mTJqlOnTqpUCikDjvsMPXuu++qI488ssX1o/v2vO/X21bs7qC7Tpu23TQ+tPXNenV1derqq69WXbp0UT6fTw0ePFg9++yzOx1nGltXV6cAqLPOOqtd+6s7x0optWrVKjVx4kTVtWtX5fV6VWlpqRo5cqS64447lFLmOV4ppW644QZVXl6uXC5XqzlWppkeX9253JHuOJnkla+//lodccQRqqioSPl8PtW3b1910003qfr6+l3aT6KOivmJ+amj5acjjzxSe3+0o/bEmt4bUdsspQw+OZ/IwJQpU/Dss89i+fLlrb4Ig4iIiH5YXn/9dYwfPx6fffbZTj/NT0RElGnMT/Rjxi+OoIxZsGABbr75Zi7QERER/QgsWLAAZ511Fm+AiIhor8L8RD9mfJKOiIiIiIiIiIgoy/gkHRERERERERERUZZxkY6IiIiIiIiIiCjLsrJI9/rrr+O4445DUVERcnJyMHToUNx3331wHCcbzSEiImJuIiKivRLzExFRx7HHP5Purrvuwg033AAA6N27N8LhMJYuXQrHcXDyySfjxRdfhMtltnboOA42bNiA3NxcWJa1O5tNRETfo5RCXV0dysvLjcftvVUmcxPA/ERElC0/ptwE8N6JiOjHwjg/qT1o8eLFyrIs5XK51DPPPNP8+08//VR17txZAVD33HOPcX3r1q1TAPjDH/7whz9Z/Fm3bt3uSBl7TKZzk1LMT/zhD3/4k+2fH3puUor3TvzhD3/482P8kfLTHn2Sbty4cXj99ddxySWX4OGHH25R9swzz+Dcc89FcXExNm7cCK/XK9ZXW1uLgoICLPrkS4Rzc9PGuQxeKXIJIfl+t1hHTnSLGOOEisQYuDxiyKbGlBgjtTnokk99yuAd0Y5BDwrEI3KQgWpXWFue55fbuzVqizFhn1xPwC33K3e0Rlvu+PX7AwCueKMYo9zy9aLcch820aj02wp55OOSMHh3hg9yH48qeZ+CBufJ1VilLXcCeWIdJhpsuV/luOT9dgn9CgBioU7acq/Bi+5vr6rVljc21OOS44ahpqYG+fn5coV7qUznJuC/+WnF8uXI1eSnjzfJ13fXfJ+2vCQg5wx/9VoxJl5YIcYYXE5GY2yOMMaGVFysI+4KiDE+Sx5srHiDHOMkxZg6b4G2POCRL7qqmHzsTOYjJte3O6rPy3ZQHvekHAcAUPI5MBpjDeqR8lPQID9ZBtsxUZuQY/IN5iwu4Tw5Pvk6MBGx5XEkzyMfG3fDVjEmEe6iLZfm5IA+P/1YchOw++6dlgu56aBrXxHruvXyw7XlJ5fJ42bD3MfFmOTp14kxuQbz9nkrqsWYMX0LteXeKjmXpgq7iTEJJbfXZBx3Xn9QjNl85CXa8rIc+dp/f32dGDOqW/r+1OyfT4shnkFHaMstg6WLmpfkfpV/6kQxJlHQXYzxxOVjU+vK0ZYXNm4U60gVdBVjTPxu4Sox5sajeokxm269SlteNvV+sQ7vxi/EmPUFA8QYN+Sk0aVhjRiTLOktxkhG3vKOttxJNGL1ExeL+Um+KjMkEong7bffBgBMmjSpVfmZZ56Jyy+/HNu2bcOCBQtw/PHHi3U2PaYdzs1FODf9BM+dgUW6vIDBIp0nJsY4OQYTUYNFuga3fCMvtXnPLtJlZi045dInAJNFurhHvgnKNajHaJFO2JYTkBOaKy73PbNFusxc7p69aJHOm6lFOrd+IukY3KyacBks0oVNFukM+rBPGGtMJn+hsNnN6g/5LTO7IzcB/z0mubm5yMtLfy5yGuQ+nJvr15bnBQ0W6VLyCwJxTTubmCzSxb27/kLInl2kky8Gy5ZvNuHTH7+gwSJd0uDYmcxHjBbpvPq8bLRIZzAWGS3SmYyxBvVI+WlPLtI5Bot0JnMWl3CeHF/QtElaKlOLdC752k1o5uyA2SKdSX76IecmYPfeO0m5yeULiXWFwsKcPFceN91BfX4DgIRBbsozWKQLhQ3unYRteZNyLk0ZtDdji3QhOQ82CtdbXli+9nPk3RaPHQAgJI9Xnlz9xkwW6eyA3K/yhO0AZn3PIw95cKSHTNzyQp9JvzLhD8n7bXIuG/z6fGtSh7dev3gJALlC/wXM1nryhHMAAMkMHGO3wdgJyPlpj31QwyeffIJEIoFAIIChQ4e2Kvd6vRg+fDgA4MMPP9xTzSIiog6MuYmIiPZGzE9ERB3THlukW758OQCgoqICHk/bK/a9e/duEft98XgckUikxQ8REdHOykRuApifiIgos3jvRETUMe2xRbrq6u2fA1BYmP69/k1lTbHfd+eddyI/P7/5p3t3+X3iRERE6WQiNwHMT0RElFm8dyIi6pj22CJdLLb989p8vvQfgO33b3//eDQabbP8hhtuQG1tbfPPunXrMt9QIiLqMDKRmwDmJyIiyizeOxERdUx77IsjAoHtH2yZSKT/JN14fPsnLwaDbX+opN/vb05GREREuyoTuQlgfiIioszivRMRUce0x56kM3m7kMlj3URERJnC3ERERHsj5icioo5pjz1J169fPwDA2rVrkUql2vwA1JUrV7aINbWyOoZQMv3XAB/TQ/463U83p38bEwCUGXzDfTTUSYyJpeSvjS5w5A91Lfenf/S9iXILp9eWvxrdcsnbSdiO3BaffA5s+dCgwKP/uuJNjfLXq3dNbpbbEiwTYxKO/HXPVkD/9fSuhm1iHU5uZzHG4NAhYXCA/ZYtxuQk9V8THnfJ51oZfH16FG6DesQQuOrk8w23vp+7YvJXoyufPEiEPfL1BPlyggrmizFVMf21UOZJ/8p8k2N7FWjLI5E99jrPbrM7cxMAfLypETkN6fvy8DL56+crNzZoy7sE5fPQWNhTjEmk5M6Xl5KvhU7u9Pm4iXILX1EvD+XwGnS/mrgcE/bLY5bJ+Jkj5KfNBvmpXNWKMY6rWIwxyacul36MdRvkJztHbouJpMG455NTAnISjfrtKKHfAUjYcm73uOQYn1s+CSZzACj9wXHJQzkcg/yU75b7p+XIJ8oJyPmpNq6fa5SoerGO43sXpC37MeQmYPfnJ51lD54mxgy/+W1t+Sm3HyfWETj/FjGmrlGem/qqvhRjTvm/L9nQkXq4s36ZWIcq7inGLNuqv+8EgMElBk9AnnSNGNItqR8XX/+PfL2dpOTja8f2F2OcYy4UY5Qwb3eW/lOsI2/iTWLM+qQ8J7eiJnlbvp8udPS5fUuwXK5DjDBTHJb7Veyvt4kx3c85Sx+w9B9iHU7XgWJMmTsmxnznyDkuVVQhxkh8m+Xr/7PpJ2jLI5EIujwib2uPZbEDDzwQXq8XsVgMH3/8cavyZDKJyspKAMDBBx+8p5pFREQdGHMTERHtjZifiIg6pj22SJeXl4fjjtv+isqjjz7aqnz27NmIRCIoLi7GUUcdtaeaRUREHRhzExER7Y2Yn4iIOqY9+jz4jTfeCMuyMGvWLDz77LPNv//ss89w7bXXAgCmTJmi/RYjIiKiTGJuIiKivRHzExFRx7NHF+lGjRqF22+/HY7j4JxzzkGfPn1wwAEHYOjQodi8eTPGjRuHX/3qV3uySURE1MExNxER0d6I+YmIqOPZ45+seuONN2Lu3Lk45phjsG3bNqxYsQKDBg3Cvffei5dffhlut8EnAxMREWUQcxMREe2NmJ+IiDqWPfbtrjsaP348xo8fn41NExERtYm5iYiI9kbMT0REHceP4zvKiYiIiIiIiIiIfsC4SEdERERERERERJRlWXm7a6btUxJCbm5O2vLF6+vFOg7uGtaWL1oXEes4sru+DgCIpsQQKF9IjHE1Vosxliuqb4u/QKzDr+QGpxx5rTe/fr0Y44QKxZhtqaC2vDQod+ktri5iTJEYASRsR4zxeYX2uOT2WjG578EbEEP8lnye6mw5xuPN1ZbnRLeJdTQE5CMcUnExptHyizHKr28vADjCNecyOAcRJX+zWq7BOYBbrqcuKfe9Mk9MW24yzviUfjs+S25HR9c134fc3PT9tHJjg1jH8LL0+Q0APtgg13FImX7sBAC45f7puPVtAQArqe97AOCq36ItjwZLxDr8Qv8EgKSj5Hoi34ox3qCcn2oS+nE43y9/btSWZIEYUyxGAI0p+djkevRjjeXYYh1ug7mI8sjjtM9gPIrb8rl03Pp+nhOV2xv15osxIcjHxiS/m8QkAvr2+GK1Yh1xeMUYn9sSY+DIc8KoJffzYqUfsxxhnwHAbSfSlznpy2g7R23/Scdl0B0qbz9OWz7o2nliHZ//vzFiTK7fYO5kkA9ckc1ijNtOasvfyDtUrONYMQL48jv53rRs1hQxpvMvbhNjbOH+akwfefxdsG6QGHOES772X1gm3yOclSecp177iXU4whwDAMrDpWLM5pScv+wcOStvqNePnT0jX4t1vNpYLsaMD8r32784ZH8xxh0cIcY4/fTXgvroVbEOtX93Mca3cakYU9RF3qfKTfLc9NDox9ryrd3k45Lz/HRtuR2V2wHwSToiIiIiIiIiIqKs4yIdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLLMUkqpbDdiZ0UiEeTn52PTpk3Iy8tLG2cZ1DV/TURbfkRF+vqbvLOqRow5vCJfjEk68imJp+SYLtDvkwknkCvGRJVbjAm65bNgG/REb7RaW54MFop1xA02FI5XiTH1/iIxxi/sd33SEevI94ohqE3KMS6DCyHokdftPSolVySot+Xt5KXqxBhlyTulvAExxhWt1ZbHQqXydgyGUp/BdVAbl/uEST2SaEreTq5Pf21HIhF0L++C2tpa7RjcETXlpw0b9fnJDfk8fLAxqi0/pDxHrOPNlTVizFE95PxkMk7XJ+R9EvOTkuswyk+QB9BABq4nAHA36vOTHZLzk0FKQKBxixhT7SuW6xH2O2Zwsk3yU9SRj6/JnCbsk/OGtCW3kxDrqHc8YoxRfnLJcyPl8Ykxrph+W9GAPBcx6FZG10GDQQd1m0w2BFGD7eR40/eHSCSCiq5lzE1taMpNm79dqz82brlvZuIGsvuZM8SYf866XIzxu+XxYUVVoxhznGe1ttyp2SrWYe9zlBijLLm9JtebyTnI++h5bXn10NPFOgwOL8Kaa7LJAuF+GwAGFIe05QmD3NR33UIxZlnXI8WYmph8g7Vfqb69AFAds7XlPeu/EetIdNlXjPFUrRFjrFRcjFEevxiz7akHtOX5V08X6zBhOfJ9p3LJeTsTTObAtrCOY5qf+CQdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLPNkuwGZ4K1aC28ynLY8kt9DrOOYivR/DwDzVtaIdYzpnSfGzFtZK8Yc26tAjEnYthij3H59gEteo00YdJGgWwxBVUxub4ldI8Y4OcXacreTEutIOvJ+O4FcMcZgt+FW+vbk+eTj25hSYkzQY4kxOVuWiTG1xQPEGC/0+5R0B8Q6oim5P+SlYmJMY6iTGJMTqxJjlC9HW+6SDy98sRqD7QTFmCI7KsbEvIVye4Ru7nHJPbgqpj/XdXH5euvo/NVr4U+lzy+NhT3FOg4p0/ebNw3y0wm9C8SY+WsiYsxh3eU85zZ4+c/x6q85EymXT4yRI4DauCPGFNly7nb8+n0yGEZQG5fHRr9BfgpY8tb8Ln1u8RmcyLqkfOxCBvkpt3a5GNNQ3E+MCaQatOVJn36uBwDxpHwOYDDXaPTJ14pRfvLo53JugwQViMvXNlLy+c5V8vmOu+X99llCPV65Lbrrti4ht5P05Jkn4AhBJnOndbN/Icbse/WrYsyXfx4vxkTiwn0RgGTxYG25O7BGrENZcv+N2fIR3tIoj0W9lj4vxjijztKWJ6Pydt5ZVSPGnFkh7/eobgViTDC6VVtu55eKdSyMHCLGHF4ozxC8m1eKMSm7mxgTDOtzTyxnX7GOL7bI9wdDhbwOAJ+5KsSYQQF5W4VX3KYtNxmFowb3uG5Lvl/JWbFYjEn2HWnQIr03/lMtxqSEa7uxvs5oW3ySjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHRERERERERERUZZ5st2ATEgWVSCZl5e23G0rsQ5l6dcrR/cuEOt4d32dGDO2R0CMeX1VjRhzTM98MSbi6LcVS8rHJeBxxBi3cOwAoCjgFmMiyUIxJiyUW4lGsQ6fN1eMqXfkSyPHa4kxCaGenE1finXYnfeVYxz5XDpBuc8EPfI+IaHvE1El95nSoNwfHHQWY+ykvC07p1iMcTdWa8tjlnzdegJyv7JSCTHGDsnXgTIY0+DY2mKfwXWb79efJysun8eOLl5YgbgmPyVSch+GW3+ujuohX9vz10TEmGN6pG9nk1dX6K8VABjdq0CMiQqvEdbE9P0XAEJe+djl+eR+XmBQT7UlH+OwS78tT0w+BzkG+SmifGJMyC2P5VFht3O3fSPWEe7UX95OSh6vfP4cMcZvsE9KGKvrhfwFAMVeue8pj9xeEyb5yRPZqC2PukJyHQH52rbi9WKMMqgnZXK+hdQRNDjXbs280pVgbpLUpjxwUunnqPkGh9AlnCaDKRoMTjW+/PN4MabPxL+KMQtnnC3GSN138nz5Orn6yKgYM6g0KMb0r/5UjKka8RMxRrp3KttYKdZxSLeDxJhNkE+m32D++q2tz7eRk8aIdVQ8/YoYYzCThp1XJsY4fukIA+66zdryam+JWMdggz7jROV7iLpqOcfZJXI9W353pbbc86s/i3VI9xmAPM4AQLLvSDnIgDRfGdNHPi5SeyMRs+U3PklHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoyyyllMp2I3ZWJBJBfn4+vlu7Cnl5uekDlSPW5fjD2vKELR8mt8sSY179pkqMmdC/QIx5/utqMeak/sXacp9KiHWkXD4xJhK3xZhiT1KMiVl+MUY6DSGX3BYr0SjGNHg0/en/BD3y+XbXb9GWR/z6cwQAeTF9HQDghArFGOWWz6U7WitvK6A/NlYyJtYBl/z6gGXQFuWXz5Nye8SY7+JubbnPLZ/rAq88zphwxRvEGOX2ijGOL6QtTxo015+IaMsjkTp06tkPtbW1yMvLkyvsQJry0+ZNm7THxmVyzflztOWNjr7/AoDHID+9tVLOK+P7ymPN88u2iTFj+hZpy3MQF+uIuwJiTF3CID/55PxuW/I4Ek3pL6qwW77oXLE6MabBXyDGBA3GLFeD/jw1BPTnCADCtWvFGLuwuxijLDknmOQnO5ivLbdsed5j2Sk5JiX3T+ULijEmNif0473fYC6SL6cMIybzJ+WVr8uUcD05BncmgXj6/hCJ1KG0V3/mpjY05aZNQm4yIfW8VIbuMJMGHSJgMOblj7xSjPls3r3a8p4GF9PWqJx3THJTr3x53i7vNVAV02+rGAbzToPrulEZzE0Nlh3yEvq5iJ0j3zt9d9vlYky3S38hxiRL+4oxcMnzA5O5nsRK1O9yHQCAjcvFEKfvIWLMi//R54ODu8njS5cc+diZ9HHXJ6+JMfaB48QYaZ4hzTEAwC3MrSJ1dSjtva+Yn/gkHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWcZFOiIiIiIiIiIioizzZLsBmVDl+JB0/GnLS1S9WIcrFdOWVyfkQ+V1WWLM8X0KxZjZy7aJMT/pFxZjlmxq0JYfWiK31+OS99vnluuJKJ+8LbkaOEppy+tsg3Vnt3zsfAZtsZyUGKO8QW152OAKVL4cuS223JaEJZ8Dt3LEmEZbf3B83pBYh0cZHLuQfK2kXPI+BapWizG5BT30dRj0cVdDtRgj9QcAiPnzxZhA4xYxZnNKf2yCHvla8XkD2nLlTYh1dHRbozbiXjtteSe3V6zDSurzU70t9yu3wdA4uleBGPO8QX46fWCxGFO5UZ+fRhTL15zXYPzM9bnFmKiQVwDAtuWxUVJvkJ+UV77+5VEPgC1fm04gV1tuMqdRwQIxRuq/AJAyyBvymQQakvrzFPAYzEXccowSxkYAsA1eB/dVrxFjcvMrtOVBk/zUKOcnWHJ7kwG5f3ob5TGiyirQlvsNJoR+K32M0pTRdglbIWGnH/tCX70t1uH0H6Utj2juzZpsi6bPj00KAvLV7/bLMbWLHxBjjvl/72vLF14xSKyjk1tOTiX58phXG5fzzpZGeT7tEcbyWshziFWbo2JMSUg+l0PCcm6yc/RzCGGYBwB0vnGGGJMwGOujKXl+kFv3rRiTyu+qLTcZsTx1m8WYZKf+ckVCWwDAMrgfHNNXf31L/Q4APFVyDnTF68SYxIHjxBh3vXzv9P+WxrXl4wbI10q/fH2edJJm+YlP0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoy7hIR0RERERERERElGVcpCMiIiIiIiIiIsoyT7YbkAk+twWf20pbbnvzxTrcDdu05eUu+VA5vhwxJq7EEJzYt0iM+WhrTIw5pItfW/51rSPW0btAXscNGPSi9Gfnv2rithgT9Ojbk5OqE+twNVaLMU5eZzEmbgXkbfnC2vKqqLzPXZAUY+xQoRjjj0XEmHpfgRgTjldpy6MBuf96DDpEFF4xJmhQj53fRa7Hpb8wrVRcrEN59NcbAMAlX0/+VKMYEw2WiDFdNGMiANgGY5ErFtWXJ+RxqKPL8bkQ9qU/78odEutw1W/RlndxyWOE45XzU9TgdbsxBvmpcmODGDO8TN+eb6oTYh3d3HIn9rrkQcJlyTHRpJwvvcI1l2fJ++Sq059rALAN8lPC8snbEna7Oibnp04Gx87xyX3ca5CfGnx5YkxevEZbHnUViHV4LHm/o8otxgTkEKO5hpSf4MjtVb6g3BgDnkS9GGMyBygVrhXHID9ZmvmTpeRj0tHVJGzYmnl3YODhYh1WXD/WF3vkcbOoUD9PBoB6g/E3YcsxbkvOcfOvHaUt/8PidWId147sLsaYqDW4L1pTo5+nAcCoCv3YmbflK7GO3t99I8aooWPFmG/q5LHIldDnyohBbhru/EeMsQvk8xRY8JQY890xl4kxnarWaMu3hLqJdZT65Xncsm3y/UqfQvl+xWtwvxKq1e9TqqiHWIeTUyzG2Ab1mPDUbhBjzhuyv74t8jADz7ZV+vI6OY8CfJKOiIiIiIiIiIgo67hIR0RERERERERElGVcpCMiIiIiIiIiIsoyLtIRERERERERERFlGRfpiIiIiIiIiIiIsoyLdERERERERERERFnGRToiIiIiIiIiIqIs82S7AZkQthLItRLpAxKOWEe9v0i/jdhWuSEqKIZsblRiTEVIjjmoRF5fXR7R73e/Qp9Yxz/XRsSYYWVhMabO4Bzk+91ijN9tacuVJ0+so96bK8YEhe0AgM9JiTGNtn6fcv3yeUy6CsUYyF0Gjl8+NrG4LcZYAf214nPJx642Ke93gSsuxsSdgBjjc8v93IrX67fjk49dVULuDzkueb/9HoMYpRnv/k/c9urrMOjjdjBfX56U6+joQiqOkNL0ZbnbIBos0ZYHY1XtbFXbamLy9V/ulxs8oljuF99U6/uwSX56d12dGDOkS44YE4nL+akoKOengJSflLxPjXndxBi/Sx7wfUo+TwmlnwIWBuR9jit5bHQb5KekwRgbT8rnyeUv0JabHLuquNx/i7xJMSbhyOd7z+UnMQR5Pvl8uz1+McYP+dg0pvT5KegxyE+h9HMjOyXvS0fXKehBXij9GKCUPBdxcvRzMHfDNrEO5ZfvIeK2fN2WoEGMgZzikBLmyteO7C7Wsc9VL4sx7/9hvBjz8AdrxJiLhleIMdI9jXLJywHO8AlijPe7b8SYviW9xRixPfqpKQAgif3lIAPW2CvFmOUb5L5nFelze2l8k1jHB40FYsxBZfIYnSmuyHfa8qqQPJ9ZXSOPM32L5Ny/uUGe8wzoPECMiUb12+qaq89dANAY6Ksv98prKwCfpCMiIiIiIiIiIso6LtIRERERERERERFlGRfpiIiIiIiIiIiIsoyLdERERERERERERFnGRToiIiIiIiIiIqIs4yIdERERERERERFRlrV7kW7VqlWYOXMmLr74YhxwwAHweDywLAt33HGH+LdLlizBKaecgtLSUgSDQey77764/fbbEYvFdqrxRERETZifiIhob8PcRERE7eFp7x/MmDEDM2bMaPeGnn76aVxwwQWwbRtdu3ZF9+7dsXTpUtxyyy2YO3cuFi5ciFAo1O56iYiIAOYnIiLa+zA3ERFRe7R7ka6kpATjx4/HiBEjMHz4cMyaNQvPP/+89m9Wr16NSZMmwbZtTJ8+Hb/+9a9hWRbWrFmDE044AZWVlZgyZQruv//+ndqJmOWHz/KnLff5LLGOoFCufDliHbbLJ8bk+RwxJmHJDzh63WIIysNKW/7PtRGxjiMr8sSY/90SFWMq8tKfnybh6HdijPLqz9RWyOcp7JWPb9TWHzsACKmUGBNL6fuezy33TeWSY7yJerkef1iMKUluFWPsQGdtueXIxyXHKw89VlTuV95QQIwxeWC40ZurLQ9C3qcyT0KMabCkkQaojdtiTL5fHmtsR9+Hv2uUt1MQ0A80SXk426P2xvwUdwUQd6XvpwbDEfxKf6CdgL7/AkDKID+FvPIJ1e1LE4PLG93c+v757ro6sY7Du8v7/elmeRzpVSjnp5yoPDYqj76e75Scn/L9BvnJ4LoL2fJ4VO/sen4KeOT2epKNYozbJy80BBJbxBjbr89PUHJuz/PLEyxXY40Y480pFmMykp8suUOY5KdGg/wUScjbKgzIYw2EOdbmRjnnFmrOU8JgDrcn7Y25yR2tgduTfh7g+OXxamtCf62UBvPFOlbUyH2zT4HcpxzI9ysmMvE5UF/df4oY89f/3SzGXH9UbzGm4N/6fgQA8Hi1xasHjhOr6J6Qx/Fkp/5yWwxIc0uTeZPJCOCO1ooxjkEfHlkg9+FNjn7ulMrvKtYx1KCLe1d+IMYkex8iV2Qg0XO4trxT9TqxjpLCQjFmZVS+XykJynnb8cjjSFdhWvnlVvkJ5rBP35b6hqRYB7ATi3Q33XRTi38/99xz4t/cc889iMfjOP7443Hdddc1/75Hjx547LHHMGrUKDzyyCO4+eab0bmzMMEiIiJqA/MTERHtbZibiIioPXb7F0copfDiiy8CACZNmtSqfOTIkRg4cCCSySRefvnl3d0cIiIiAMxPRES092FuIiLq2Hb7It3atWuxceNGAMCoUaPajGn6/Ycffri7m0NERASA+YmIiPY+zE1ERB1bu9/u2l7Lly8HAPj9fpSXl7cZ07t37xax6cTjccTj8eZ/RyLyZ6oRERG1hfmJiIj2NsxNREQd225/kq66uhoAUFBQAMtq+0OIC//vQwObYtO58847kZ+f3/zTvXv3zDaWiIg6DOYnIiLa2zA3ERF1bLt9kS4W2/4tGD5f+m/U8Pu3fyNaVPg2xxtuuAG1tbXNP+vWyd8aQkRE1BbmJyIi2tswNxERdWy7/e2ugcD2rxxOJNJ/PXHTY9jBoP7r3/1+f3NSIiIi2hXMT0REtLdhbiIi6th2+5N0TY9j19TUQCnVZkzTo9pNsURERLsb8xMREe1tmJuIiDq23f4kXb9+/QBsf8Vnw4YN6Nq1a6uYlStXtohtL79lw2/Zactr4vJaZNJpOwk2Cfv0r1QBgFeMAAr8clu2xdLvS5Ncn1uM8bnb/hyLJkO6hMU6/neL/jF6ABhcKh+b2V9tFWPOHFgqxsQd/T75hPMIADFbjsn3yecp7gTEmGKrXt8WV45Yhy+q/7wRAHD8cj0m7NzOYkxD0tGWBzzysOLRn8btrMy8hmClYmKMrdK/pQQAbIN9Ul45pj4qX9thg77nT+r7FQAoj75PlKW+E+uwVbG23KfSv8r/Q7An8pPPcuCz0l8zNfG0Rc3k/CRnH30P3y7PoO9VZSg/eV1SfpLHtE83y/lpSOdM5Sf9tQDI+SlokJ+iKf34Cpidp7gVEmOKE/oPkI+788Q6TPKTMpg/yUcGcAzyUzSlr8nvlo+dMHXazpWZ6bNJflLQPwWlDHKl7ZX7Q200Jcbk+w2u7WSjGJN06/tEub1NrEOp/LRlCWUwsO7F9kRucn37JVzh9OPs2rJDxDpy/fqLZU29PJ71KTDJTrKEwdw+YTAGh73668lgM0ZtOX+wPJ6NfbhSjJl36ZlijJS3E3E5r7+xXp7vHddLHmcaDXJcYWSttjxW1FOsw9ewRYyxEvJYhWD6cabJZkvOlaVB/dgp5S4ACFlJMQaOfHxNuBvkMTji079AEM6T+zjc8vX/8Sq5LacZzNF8m5eJMVsK+mvLhyRXiHWk8npryyMJOdcCe+BJuoqKCnTp0gUA8P7777cZ0/T7gw8+eHc3h4iICADzExER7X2Ym4iIOrbdvkhnWRZOPfVUAMCjjz7aqnzx4sVYtmwZvF4vTj755N3dHCIiIgDMT0REtPdhbiIi6th2+yIdAFx33XXw+Xx46623cM899zR/vsKaNWswceJEAMDkyZObXzUiIiLaE5ifiIhob8PcRETUcbV7ke79999HSUlJ889zzz0HALjzzjtb/H7Hr/ju1asXZs6cCZfLhSlTpqB79+4YOnQo+vXrh6+//hrDhg3DPffck7m9IiKiDof5iYiI9jbMTURE1B7t/uTbZDKJbdtaf4BfY2MjGhv/+wGMtt3yQyjPP/989O3bF3feeScWL16ML7/8Er1798bZZ5+N66+/vvnrxomIiHYG8xMREe1tmJuIiKg92r1Id9RRR6X9OnDJyJEjMXfu3J36WyIiIh3mJyIi2tswNxERUXvskc+kIyIiIiIiIiIiovS4SEdERERERERERJRl7X67697ISkRhJdLvSq4/T6zDV7dRW54IlIl11MZtMabYk5RjfPJpaXTkx+Z9bktbXmfQ3oo8vxgz+6utYsyZ+5SIMR9saBBjDi3St9nx5op1hFLyduJOWIzxpxrFmGqEtOUNUfkcdM3JF2OshNyWGLxijB9y/wy79Wv7tsHav5WKiTHVbvlc5itHjFEu+XpKJPTXk9tlcL259NcbAIR98rHJQVyMqbH0/QoA8i1936rPkb8Rzm3p9ylh+cQ6Ojor3gArnv68hw3ykz/yrbY8Fewq1lEbl6+VAq8cU2xwyqMGb+tyCX0rYtDeXoV7Lj9VbpTzxojCXc9PuXZUjEkq+fo3yU81Ln2eq29MiXV0Dcn7ZJKfEpZ8Lv0G43DI0rdZGYxZlp0QY6pc8n4XmOQnt9yemHAteFxusQ5hOggAyPPJ9YSUnJ8ilvw5ablCfmoIdRLr0OWnuEs+hx1dqs8hSOWlzz/BuHy95QlzGqkcAL6tk+ed3XLl+at0z2MaI+VKk3lc0CNvxzZ49/Prlw4XY85/7nMx5m8TemjLo245p4wtrBNjalLyfCbslY/fap9+TrNsda1Yx7G9SsUYT0R/7w8Aq2rl/tk7KMc4wv2gyRht2XJOXpJzgBgzcu3HYkyiYqgY8/bXVdryUwYUiXUY7DaO7VWYkXoaSgeKMflC90yU7S/WERMu7ka33F8APklHRERERERERESUdVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoyzzZbkAmWHYcVsqXtjzqdsQ6PIF8bbnbkttRYteIMVVWoRiT65bXTm0l71N9QmnLi4Ly6Q9HvxNjzhxYKsZ8sKFBjDmkPEeMeX99vbb8sMIqsQ4nJJ+DlK0/dgBgu4NiTCKuP0+lIfkcxB25LZY3LMeIEQDkTSFl6dtcn5D7ptuV/nptD1e0Voxp8BeIMcWo05YrKyTWEXfcYkzISooxsOXjl+9OiTGumP6ak682oMqtHxejSbmtHZ3lJGHZ6c97wmCs8QblMUtSZMvXSrWlP98AEPYa5CeDPiz1naKgfD3lRLeKMWcOLBZjKjfK+Wl42R7KTzlyexMpuc8kTfKTMFYb5SdlkJ98eXKMGAHAkcdPW8gtdUJOBgC3S95vj8FL3JnLT/p+pVRArCMBOedmKj/l7gX5iblJ1mhb8Njpr7yiwJ55jqNbSB5DDKamGeMTbvhM7gdNxjOPQZDBdBpPnjVIjPmfr/S58sz+8hhih7uLMQanEnf+c40Y8/ND9ds6tpc8V9nSaIsxnX3ySNPLL89FlMF9miRpUEfCks9TLCXPZ+ySXkZtkpyZv0lb7lTLbfkuWC7GFAXkc2DF9XkSAHx++V7ZVbdZjJEsrddvp6EualQPn6QjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZZ5sNyATGgLFcAfz0pYHXZZYR3UioC0vjEXEOpQ3KMYU+OR10bqkI8bIewR4hE2FPHItJvsUd+R6Di2yxZj319eLMSO7hbXls5fFxTpOGSCfg4Qtn4MCnxiCkC+pLa9JycfOoPvCbRDjMaio1paHhBzh8BV4UnJj3PLBU3ItiHkK5U0Z1KP8+n6VUHKfsUzOU81GMaYur0KuyODguP0F2vJgQh7TCrz668AllBNQ5y0AfOnzU47BOFwj5afGarEOx58jxoRdcj+PpjJzzr3CoBUwGNSUxy/GmOSnEYV7Jj+98HVCrOOk/mIIYgbnoCggj3wh767nJ5Pc4zZ4OdhrkJ9qknJ+CgupxSg/ueTtKEveqZhbzk9eg+OXifyklJw03LWZyU8m81PXbs5PzE2ykMfS3geYzMHWRvRjSI8cuRZlMB+sisljtMmYZxvsVNLRB4UMerjJsTMRiMm53Q7J48wZ+5Roy8fO/Eis47WLDxJjTO5Xbjiihxwk2NIo94ctjfq+CQClJennZk1WVMt5OyX0GQAYWKwvz/Fm5rmpw7rnijHy0TOjPPq5qeVk5rr1bV4mxtQWDxBj5BUNwMntrC13134r1jGiWH8hREwSP/gkHRERERERERERUdZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWebJdgMyweey4HNZacu/a0yJdRQE3NrylCtPrMMNR4yxYhExJtcXEmPqbXl9NVfFtOXK8Yl1bEWOGONzlBjjeHPFmMMKq8SY2cvi2vLTBxaLdXywoUGMOahM3u9GW97vcCKqLc8LBcQ6XAZ9JumX+6fHSYgxcUseEvw167TliYLuYh1uR74mXQYxfjECqDHo5zUp/bmMppJiHT1DthijvPL5NhGy5PZYtv74OcF8eUO20GeUPOZ1dAGPC0FP+vF6s0F+yvfr85PtKxTrSJ8h/8tjMNaEM5Sf8ix931JKvm6/U/I4HdyD+emFr/X7NGFAkVhHxvKTMKYBcn4KB+XxypOoF2OSnrBcj0F+crsM8lPkW225nd9VrMNkXHOl9PMrIHP5Kb4X5SfLYCAJKf08DQDg6I+xE5CvSejmCMxNoritENfMY//3u0axDpOxSOLbvEyMKeo8cJe3A5jlwXy3kJPlSwlwy9d1Q1LuozkhObebkNLgaxcfJNYx56utYsypA0tMm6TlEU6UZkrVbP+wnFMcyGNeP/n2CrZLHu3djdX6OgzOtUmfCRus7FhxOW87AXnHl3m6acu3Nsq5aVTVGjEmlV8uxgSlTgPAHa0VYxxfUFuufPJ8RgnzZOWT5/0An6QjIiIiIiIiIiLKOi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZZ5sNyATqmM2Uj47bXlXq06sY2syT1vu9rnFOqriSowJesJiTF60WoyxvYVijKthm7a8Pq+bWEfYK4YgZsv7HUo1iDFOSN6nUwbo15U/2CBv55DyHDFmVW1SjOmeJx+ciDdfW54f2SjWsc3fWYwJOvI5cCyfGJPrSogxjUK/SaYcsY6UI78+kO8PiDGWkrcVsCwxpjCpv+aq/HLfTLrl/uDzxMWYnJQ8XqmAfrwCAGXpj3HU4LoNuPV9RgnlBFTFbCS96fNTuaoV69iSLNCWuy05P9XG07ehSY43V4wJx2rEGCWMewDgqtuiLZfGGQDI98vjSNRgPMq1o2KMk1MsxpzUX1+eqfy0slYep3vkyddmrXCeCuoyk59C8lCDhEl+cqfEmPpwubY8lZT7gy2H7FX5aauvQKwjZZCfvCb5KV4jxtgGcznp2EQd+bj4XOn7jK0po+08LgseV/rjvH+nkFiHNI1wy6cR9SUDxBjL4Jr0//slMWbTvuPFmLKgPq8oV2ZunQ2GRbji9XI9Pvk8uYT5oIkz9ikRY77cGhNj9i2Rx87ahP6EF1U+J9axcdhPxZgutpxLYTDPlWdgwOIafT3ltsF9Z648jrtrvxVjUvldxRgT/YL641cSlPtmo6dCjAnVbxBj3PVbxZi6wl7ytpL6e7AqlzxPLhLWX1yN8n0ewCfpiIiIiIiIiIiIso6LdERERERERERERFnGRToiIiIiIiIiIqIs4yIdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZZkn2w3IhDy/G3l+d9pyx8oX6yi09OuV7sZqsQ6/LyjGRJRPjGkIFIkxATECsPM6a8uDLiXWEXUsMSbfJ6/1xp2wGJOy5fYkbEdbflBZjljHqtqkGNMr3yvGvL2qVowZ3d2vLf/WUyrW0TW2UYxZ79GfawAodzeKMcor9yy/ZWvLG2y5z5TYNXJblHwO4JKHsIDS9xkAcAK52vLiyLdyHUoeZ+q9eWKMxyUfP7d8qaA+pb8uw155O66Evs+4ElG5IR1cvt+NvIAmP7mKxTqkCFf9FrEOv9DHAcP85C8QY+Ra5PzkN8pP8nbyDPJTUoXEmERKbk8stev5aWVtQozpnS8f4UVrI2LMUV3042em8tPapJyfunkyk5+CwrBWZZKfVL3clnj6a7qZMK8EgICTEmOk/FRav0muA/L1b5KffG75+Fkm+UmYhpnkJ08yfZ/xJJmbJKtrEwg76cebfoXyOBMX5u2+T18V6/ANO0mMMaEOOlmMKRfmNACgXPr7Fd/aj8U6EhVDxRiTuZ7jle+dMqEhKSfTHK88nu1bIo/RS9bL4+uh3fT7/cU+p4t1DLIaxJhXVsn7fXJZnRhj58jzuIPL9fn/PzVy7veu/ECMSfY+RIwxYRncO7kj+txTUvudvKHCcjEkWdxTrsdA0GCfaoTr32TNw/EV6stTBvMH8Ek6IiIiIiIiIiKirOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWebJdgMywW1t/0lHWfJaZMxW2vKUN1+sw2dpGvF/QrqG/h+DEMBOiCEpl09b7nHkOkLKEWPiTkCM8acaxRjbHRRjCvS7hEbhPAJA9zyvGPP2qlox5rhecp94+ZsqbflJ/YvEOlRjSIzpFJQv5bpUWIzxQu58jnCIS1RErGOru0CMKQq4xRiD0w1vwxYxRnn0HcsJyufaUnJjktLBM+WSz1Nhslpb7njkfWpw6a/JBldSrKOj87q2/6Rj0ocbU/px2PEVi3UE9rL8lLD015xPpcQ6QgbbiVvy+GmSn5IG+UkasxpT8snukSckOQCL1spj7JEVeWLMnGXbtOWnDZSPnUl+6pKh/OQzmMspYRw2yU9bLLktxX45P5mM9u4G/TkAAOXTH2MnYJCfbHmstg1yWMygD7szkZ/cuWIddVb6uWe9JY8NHV2e341cTT826b+WkFeSQ08S62hMyvcZYV0S/T8m93rwy9f2tpitLS8t7iHW4aleJ8YECruLMXtKjsHxNZEwmNAc2k0+ByOmvqMt/9etx8qNaYyKIeP6FooxCYMLQc4G8lxvYGq9WMeyoqFiTB+DtpjwbfhcjEl0PUBbrkr7ZqQttXF5jHi4Uj5+Uw6rEGOKIyu15cmS3mIdtUK6rTO8deKTdERERERERERERFnGRToiIiIiIiIiIqIs4yIdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLLMk+0GZII3FoHXp9KWK8sS6wh5fNryRpdfrMPvlrfTmErfzibhRI0Y4/hzxBipNXF4xToaUo4YU2zVizHVCIkxibi8rZAvqS0PJ6JiHRFvvhgzurt8vl/+pkqMObl/kbZ83n9qxDrG9giKMR47JsaEvQExBko+B+66zdpyO6dYrMPnyNcKnJQYEnfcYkytR38OACDfpa/H9unHBwCojdtijFwLEDW45kpTct+L+PXnwa3kc5CDuLbcFsoJcEcjcHvTj/suoe8BQK6Qn0zGcr9Lzj1RueshJyb3PSeQK8a4hO6XUPL0pN5gHClORMSYGldYjEkkDPKTd9fzU61Bfjqqi3xs5izbJsacPlA/Rry5skas48Rucq40yk9CHwcAKDknuBr1++2Y5CfbID8Z5MqoQT0JT6EYk+/Sv54e98jzwYgjt1czjW5mO3JQSWyLGFMf7KQPMGhLrpU+/ygrIVfQwVkADG6PtHyWvl8pS34WxO/ec8+LGHQrdPnuM215tPtQsQ63wThjoiEpX7dxW96rfL9+nmFw+2okYMs5rs6R70X+deux2vJfvLJMrOPP43qLMa6UnJvgMbh3MuAV8mCyRG5vn4y0xEy86wG7XEe9Qf9dtlXuM+W58jxjymEVYoyn9lsxprFIfx58Bvem+cIUzfIYTLbBJ+mIiIiIiIiIiIiyjot0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoy9q9SKeUwnvvvYfrrrsOhxxyCAoKCuDz+VBeXo7TTz8dCxYs0P79kiVLcMopp6C0tBTBYBD77rsvbr/9dsRiBt+wQkRE1AbmJiIi2hsxPxERUXu0e5Fu/vz5OPzww/GHP/wBlZWV6Ny5M/bff3/U1dXhhRdewDHHHIObb765zb99+umncfjhh+OVV16B3+/HPvvsgxUrVuCWW27BEUccgcbGxl3eISIi6niYm4iIaG/E/ERERO3hae8fKKXQt29fXHvttTjrrLNQWFgIAEgkEpg2bRruvPNO3HHHHTj44IMxfvz45r9bvXo1Jk2aBNu2MX36dPz617+GZVlYs2YNTjjhBFRWVmLKlCm4//77270TdjAPdjAvbbm7YZvJjmmLE26fWEXAbYkxeVXLxZi64n5ijMnqaiRma8vz/W6xDp/BPsVcOWJMQ1TfFgAoDcndsSalb09eKCDWkR/ZKMZ86ykVY07qXyTGzPtPjbZ8TJ8CsY531kTEmONK5eMLOyWGfOcExZhO/lx9gCX3Tv3VZl5PfcIRYwoCcj93Cd18S1Q+dmWehBhTreT+meuT21tlFYsxRclabXnEmy/WkfTo25t0y/u8p+yNuQnITH6yHP31HXPLY6fPLV9Pudu+EWNM8pNXuqAAVAv5qdDgujXJT3F3+mPfpL5Rvr4zkZ/CQfn6L6jLTH46bWBIjHlzZY22/ITeBWIdC9fK+enoEoP85JbPwVYl56cSnzAfMcgrcq8y05CU85PJPMwREmZ1XD6+mcpPeQbtrbLk/lmU1PebiEeYZwBIafJTai/KTcDemZ82NSRQ70p/nEqC8vUWd/RXi8F0Bt697IOXEhVDteUGu2RkXV1SjOlskHdyMnAApTEGkOfJgNkYUuDb9XuEGScPFOuo3Nggxgwvk+9fXQl5EbzBJV8rCVu/jpBMyuN4STAzvW+BwX3lERXy3EmagtUK8zwAGKn+I8YkwoPFGBPbAmViTL7QPVX7l85a1+Eyq6PdV/aIESPw1Vdf4fLLL29OMgDg8/nw+9//HmPGjAEAzJw5s8Xf3XPPPYjH4zj++ONx3XXXwbK2n9kePXrgscceAwA88sgj2Lx5c3ubREREHRxzExER7Y2Yn4iIqD3avUiXl5cHjyf9CuDo0aMBAN98899X5JVSePHFFwEAkyZNavU3I0eOxMCBA5FMJvHyyy+3t0lERNTBMTcREdHeiPmJiIjaI+MPGTd9iGlwh8ek165di40bt7+FY9SoUW3+XdPvP/zww0w3iYiIOjjmJiIi2hsxPxER0Y52/Y21O1BKYfbs2QBaJpTly7d/Dpvf70d5eXmbf9u7d+8WsW2Jx+OIx+PN/45E5PdUExFRx7a7cxPA/ERERO3HeyciIvq+jD5JN3PmTHzyySfw+Xy45pprmn9fXV0NACgoKGj+PIXva/qMhqbYttx5553Iz89v/unevXvmGk9ERD9Kuzs3AcxPRETUfrx3IiKi78vYIt3HH3+MX/ziFwCAO+64A3369Gkua3qM2+dL/80mfr8fABCNRtPG3HDDDaitrW3+WbduXSaaTkREP1J7IjcBzE9ERNQ+vHciIqK2ZOTtrqtWrcL48eMRi8Vwzjnn4Ne//nWL8kBg+1cyJxLpv+q76VHsoOYrv/1+f3NCIiIi0tlTuQlgfiIiInO8dyIionR2+Um6TZs2YfTo0di4cSPGjRuHJ554otVj2U2PY9fU1EAp1WY9TY9q7/jV5ERERDuDuYmIiPZGzE9ERKSzS0/SVVVVYfTo0fjPf/6DI488ErNnz4bX620V169fPwDbX/HZsGEDunbt2ipm5cqVLWLbw91YBbc7mbY8ESoW6/A1btOW5/tSYh11Sflwhjv1F2Nyt60WY5xArhgTcLc+FzuKI0+uwyOv4/qi+s9qAoCuOfliTNxpexKyI1fbH8vx3/KY/IG42/ydxZiusY1ijGoMiTFje+ifvnlnjdzeY3rI5+k/ten7f5OKoL4/AECJcHwBwCV8NldtuPX1/X15KibG1CQDYkxZbL0YYwfk9kRtt347nvSvZDfZnJJfqS4NydeTwWUAv0c+UY5Pf825bLmOLY36ca8uKo+L2bC35CYAcEdr4PbYacvtHDk/uRv111y+fGmjLumIMSb5KVy1RoxRwQIxplOaz1hqEld7MD+F5HwaT3OTvCO3cEl5EvViHXsyP53YTT9mLVwr56cjK+TztCoi56duBvmpQIwAXDX6813nzhHryHUaxJiapHx8u0QN8pNfzk+NQn7q4pev7c3xzOQn2yA/BU3yk6U/Dy5HruM7TX7aW3MTsPfkp32Kg8jLSz9HNZgOwg/9ta2Q/q267eGplt+imyrMzGftSduyDbZjcJmge6485llKvraVwZmS5pXSvRUA1MbltuT7M/MpWlJz4gYD0UFl8li/JZp+btakNCiP9fo7vf+LMRgX95TRDR+JMbZ1jBhTI/SJoqC8LlId2F+MyTW4t3dFa8WY/AyMESbX5MZGfUydcG/VZKevpvr6eowdOxZLly7F8OHDMXfu3LSPW1dUVKBLly4AgPfff7/NmKbfH3zwwTvbJCIi6uCYm4iIaG/E/ERERCZ2apEuHo/jlFNOwYcffoj99tsPb7zxBnJz078SbVkWTj31VADAo48+2qp88eLFWLZsGbxeL04++eSdaRIREXVwzE1ERLQ3Yn4iIiJT7V6ks20bZ511FubPn48+ffrgH//4B4qKisS/u+666+Dz+fDWW2/hnnvuaf58hTVr1mDixIkAgMmTJze/akRERGSKuYmIiPZGzE9ERNQe7f5Muv/5n//BSy+9BABwuVw488wz24wrKyvD7Nmzm//dq1cvzJw5ExdddBGmTJmCGTNmoFOnTli6dCmSySSGDRuGe+65Z+f2goiIOjTmJiIi2hsxPxERUXu0e5Gu6eu+AWD58uVYvnx5m3E9evRo9bvzzz8fffv2xZ133onFixfjyy+/RO/evXH22Wfj+uuvb/66cSIiovZgbiIior0R8xMREbVHuxfpLrzwQlx44YU7vcGRI0di7ty5O/33RERE38fcREREeyPmJyIiao/MfFcyERERERERERER7TQu0hEREREREREREWVZu9/uuldyUtt/0nBbchXKG9SWR+EV6wh75Q3VJx0xJreoQoyxEo1ijOMPa8vdSqwCnkS9wXZyxBiT9lpefXsB+Vwm/XliHUFH3vH1ns5iTKegfPl47Ji2/LhSW6zjP7VJMaZXvtw/F6+Xz+XIriExJl7QXVueK+wzAMTd8nZyDK7bVFHrz2/5vuqYfIwLA/qNKYOhsrOKijExW75WgrEqMUaFisWYqrh+rAl45APcVVVryyOqTqyjw1PO9p9dqcLj15ZHHflchgzOdzQlj42hQv31DwBWUh4DHJ9+DDDKT0k5ryifPrcDhvnJJ+cWt/CyZ9Ij57iQwX6vTcr5qUsG8tPRJfLYuSoi56ceeXtPfsox6DNxg7mI3KuARKGcn+oSBnNCn3DtGgwvnT1xMSbuyMc3EN0mxsSCcn6qSeovFp9brAJdnfRtiTjMTRJvrAZeb/pr3AnkinW4Evp5TyLgE+swuUezC7rKbUkZ5B2P/Pl9KYMclwmWybzAJMaSn7fZFtWP5aUh+YIrSunngwBg++Vr3yDFicfGJyVbADFb3lJJUN7v699o+/Mjd3TXif3EGIlJ/22Afi4IAEGDud7GnkeKMW9+/p0Yc/b+nbTlHoPkpAz6r/LK8y/HI481JtdcQunbE5enRaiILNOWR+rk+Q7AJ+mIiIiIiIiIiIiyjot0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoy7hIR0RERERERERElGVcpCMiIiIiIiIiIsoyLtIRERERERERERFlmSfbDcgEJ9wJTm5e2vKErcQ6/L6Qtjwed8Q6crctF2MKArlijJ1XJsYkfWExxhuv12/HoA7ll2NMxOAVYyyDejwufZTHSYh1OJZPjCl3N4oxdSn52IS9AX2AnRLrqAjKx27xev25BoCR3eT2/u+WqBgzuFjfHuUR9hmAPyEfX1fDNjGmPq+bGFMYcIsx1TFbW+51y0OlbTCchoX+CwCxYLEYE6zbKMYEQl205TmpOrGOrZ4ibXmdwXHp6JxAHpxg+vyUlFMLfJnIT7VyfvL5c8SYVH5XOcarby8AeGMRbXnSl/6YNXELxwUA5OwPJCy/GGOSn7wZyE8Jg/zUzZOh/OQRtuWW81O3vS0/FenHe8egz/hTMTHGXbtJjGks7CnG5Prk18pr4vr8FPTI5yBpkJ9yDDp5NKDPCQAQbNgsxqSCnfRtsRvEOrZ6S9KW1Ul9m8TcBCXnlWQgX1v+bV1SrKP32oViDMr7iyFOXmcxxuR+0OfWXwiWwXGxDOa4jsn9lSWPDya5qTSkHxc9td+KdZjkfhNVwnwbAIoM5u2SoHAeAcCgO+CuE/uJMZ9tlnPTAZ2D2vKkW753CkHue57v5Lle56IKMebs/fVjNCD3vU1Rub2dQ3IfrzeYKAdM7j0N7p28whpMIFot1lFVsq+2vM6nn/824ZN0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoy7hIR0RERERERERElGVcpCMiIiIiIiIiIsoyLtIRERERERERERFlGRfpiIiIiIiIiIiIssyT7QZkgpWIwkqk3xW/LyTWkVL68rBPXs+MlfYXYzyWGAIrFhFjfHZSbk+wWFvemHDEOooSW8QYO7ezGOOH3F4I5wAAam19l41bcpfOdSXkpngDYowXBidT6Y/xd05QrKLEYDMju8p9/H+3RMWYwaVye76p1h+/AUG5/8LjE0NShd3FGPksAQ1Jg37u1x/k9fW2WEd3X1xui50jxsRScnt9BtdcuLFKW17lKRTrCAoDVtLL13lEytGOAz63XEXc1g+OJvmpobifGON3y4ONO1orx4gRQIMvT1seN7huAwb5yTHJTy6D5OPIOawmqc8/bpdBfnKnxBiT/OSzDK5Npd/WViXngwJ5Kz+4/GRyfONFPcUYk+ug3qCfFwv5aU2d3Gd6BuT+22gwH4katNdvkp/q9ddulVc/fwWAoDf9cWFukinLBaUZJyyDMWRjnb5fVeR5xTpS+48WY0x4t60WY0Iu+aqU5p66Y9Yc4w+LMZlikL1EqfyuYozBrYhRW4oC8jmwhHsno3Ng0BaXyU4ZOKCzPHaurtVfK33cNWIdyiffQyQ7yWsRJlYKuRQA+hXq7+W+3too1tG5Qj8XBABhCmwslVcmxniq12nL63K7iXX4hY4Vd5vlJ2YxIiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWebJdgMyod7yw7ICactzUzGxDtvya8s9Lkusw5OoF2Pglg+5E8gTY+qTjhiTH6/Vlts+eTu2v7MY02DQlrBbXg9OWfKxyRGq8desE+tozOsmxvgtW4xxlBgCd91mbXknf65Yh6u6WoyJF3QXYwYXe8WYb6oTYkz/Qp+2fEODfK7L0SjGuOyUGNPgzhFjvAbXrg19THFIrqPGdosxBYjLbXHrjy8AJJR8jFWgSFteaEfFOhpUUL8Ng2ugo2tUXnhU+msvJyFfC45bfx5MEnkg1SDGKE0ebWIH88UYk5yQF6/Rlrv8BXJbDPJTNCV30pAljzW2S74uw0KIP/KtWEd9uFyMCcrDEZTBxelq3KYtL/HJ46urJkP5qUgePzORn9bXy2NnN0ueM3oM+kyDS3/dAkDALZ/MlJCfuuRkJj/lIynGJFzyaGMb5IV4sERbXqjkXNmg0s/bmZsywJH7eNdceV65p0Tye4gxIbfcMSIJff7yGVyzJte1CekeAgCccKkYoyz9uGcZnGtlcO1nimfrSm15vKSvWIfB1H+P6pmvv1ZW1Mpzq14+eR6SKVIuBYCNDfp+c0SFvM5gIs8n522DaSeSBjfu0aB+DibPkoH6hH4NoUEob8In6YiIiIiIiIiIiLKMi3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjJPthuQCQGPC0FP+vXGJAJiHcFotbbcCeSKdcS9YTGmMemIMQWulBgT9MinLubO19dhyW2BY4shAYO22AbrwfUJg2Pj0R+bREF3sY5kSt5Og22JMSUqIsbYOcX6AEs+LrXhrmJMrh0TY5RHvg4GBOV92tCgb3NZjtwfnl4aF2PO7Z8jxoTjVWKM8sv1xJX+2ATdcn9wW3JMTPnFmFyPXA8ceYyAUE3KGxKryEnUa8ttu1FuRwcX9FgIas5pUhmcByk/GfTxpE/OT2ZjcEKMCXh8YkzUVaAt97uUWAeUHON3y2OssuT21sV3PT/Z+fJYnjKYI1RlKD85GchPdW657+Uk5XHC8cnXgUl+Wl+vb3PXsJyfnv0iKsac3TcoxpjkJ5O5ZQr6/ukzyE+WQX5KCNsBgHyvwbwRcox0WaYM5u26fmU78pyI9JRLvlakXmUwimdM0jHYmuZesUmefBmIErbcFpPr1s7tLMaY7La01ybnujom3w8GvfLxDSIpxiRL+2rLTZ4wMphJGzHpwybbkurplS93vGtf/VqMuX+43OJkp/5ijBXXz/8BoCwnT1ueqevflZDnED6DOYQyOFMBt1tb7qn9VqwjJMz1PAn9NprwSToiIiIiIiIiIqIs4yIdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZ5sl2AzLBrVJwq1Ta8kbHLdYR9ebrt+FYYh0NSVuMKfXJMVYq/b408fgMTp3mmABATUJeow0bbMcjHxpYqZgY43b55Irc+hi3Ix+7lCPvd4ldI8ZsdReIMT6h3yixBiBPyccu7g6JMf5Eo7wxj3wOyqGv5+mlcbGOc/YvFWPmLNsmxhzXu1CMCbsNXosQToQ7slGsIhHsLMa4LPliidtyr7As+bp0CZva0ihfK2UBfX9QHq9YR0dnKQeWctKWJ2y5T0j5yUpffbO4QX4q9hrkJ9sgPwnjNAB4LP22quLyccnzy7ndbZKf7IRcj8sg50oxmn7QxDY4lyWqXozZYoXFGJ/Q9wwOHXKdBjEm7pXb4jeYIyhvQIzpZunrefaLqFjHWfvJ+enFr6vEmKN7yfkpxyXnJ0dICf7It2IdDaEyMcYtJQ0ACYPX9pWSc5hH2NZ3Rvkp/fWm3PLYQHom139KONVVUTmnhLzylsJeud/l+Qz6phghc8UiYozfL495JkfYpL0mc8agcKNWHZPPU2HAIN82VosxyaA8LkaT+kSYY9AfMnGuTWViW9I4DwD/b/wAMebyV5aJMTNOlo/f+mRQjJHWK7pD7g+JHDnfwiff4241GGtKgnIfli6nWLhcrEOqJGpwzQJ8ko6IiIiIiIiIiCjruEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWcZFOiIiIiIiIiIioizjIh0REREREREREVGWebLdgIywXNt/0nBbchUht7CJeJ1YR1jZYoxSQTHGspMG9ThiTFTpd6rAI2/HFW0QY3THvkm1O1eux4ASyl1OSqwj3x+Qt6O8YkxRQOg0ACC1x+DY1STl9uYY9HFXwzYxJlXYXa7H1u/Tuf1zxDrmLJPbcvrAYjHmgw1y/zy0WOo1gNvj05bXBDuLdRTUfyvGGB3fVEyMiVtyn0g6+v0u98jbcdxhbbly648byTwu+eINQZ9bXHGDcdpgbFQe+dq1UnG5Hq/cP6X8VOQ1yE+NNWIMXPI0p8ol5yePwUuaShjPTa5to/wUl3NPsd8gPxnMIyQ1yZAYI896AHftJjEmXtRTjPFY+n5+dl+5NS9+XSXGTBhQJMYsXl8vxozqJHcs6XqqCZWJdezR/OSS+3AqA/kp5Uqfn2wXc9Ou2tQo54xtQsxgrzzXczyFYoyCPM5kii1MGb0Reayy88vFGMevn18BgHCZAAD8Bje5MWGnig3uBx3IOcUOyefS5Okgt8G8aE8xaYnBaYK7sVq/HYNjZ7KdGScPFGPu/5ecD34+XM4r0j2sjVKxCo+dEGNM7jVKggZzHgPS5eQ2uN6kPJlS8jwa4JN0REREREREREREWcdFOiIiIiIiIiIioizjIh0REREREREREVGWcZGOiIiIiIiIiIgoy7hIR0RERERERERElGVcpCMiIiIiIiIiIsoyLtIRERERERERERFlGRfpiIiIiIiIiIiIssyT7QZkQnVcIRVXacvDPnktMqEsbbnfkuuI+nPFGDt9M5vleOUY22B9NeDWl8dteUO+UKHcGAP5yhFjXNFaMSbm0bfHb9AWy6AtcMmXhsm5jDv6k1CfkNtSFlsvxqSKeogx9XndxJiAGAE0uHO05eF4lVjHcb3lfvXBhgYx5pByfVsA4OvqhBjTM9+nLS+sWSHWESvpK8Z4UzExptrWtwUASrctk+sp6q8tj7hCYh3ulL6TR4VyAmoTgKPpgj63wTEUxiO/SxjsATT68uTtGAjJ3TMj+SnhyBvy5hTLjTFQkKn85N5D+clgPmJyZUZt/bynISm3pUtUzk+JQjk/NRb2FGPkXg40uILacpP8dHQvOT8tXl8vxozsFhZjzPKT/nwX1q4U62gs6i3G+DOUn0qqvhFjagr1+TJpkJ+QSt8/Y5oy2s4djcDtTT9SlMPg+i/RXyspdJXb0bBNjHF8Bv0hQ9z6YRHJTvq5lSmXwfUGjzwr91StEWPcwj2CsuWcYnLP4zHoMzDIcQH3ri9PCKdxe1MyFGPCztD9dCZcNUK+LueviYgxA4r112XPOvleJVG2vxhjci5NuL+cL8Ys73qYtrw0JPfN2ph+tlInlDfhk3RERERERERERERZxkU6IiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZTu1SPfSSy/h0ksvxbBhw1BWVgafz4eCggKMHDkSM2bMQCKR/tuqlixZglNOOQWlpaUIBoPYd999cfvttyMWM/iWGyIiojSYm4iIaG/E/ERERKZ2apHuD3/4Ax555BF88cUXCAaDOOCAAxAOh7FkyRJcc801GDlyJGpqalr93dNPP43DDz8cr7zyCvx+P/bZZx+sWLECt9xyC4444gg0Njbu6v4QEVEHxdxERER7I+YnIiIytVOLdJMnT8aCBQtQV1eHlStXorKyEuvXr8eSJUvQrVs3/Pvf/8aNN97Y4m9Wr16NSZMmwbZtTJ8+HevWrcPHH3+M5cuXY8CAAaisrMSUKVMyslNERNTxMDcREdHeiPmJiIhMWUoplckKZ8+ejZ/85CcoLy/Ht99+2/z7K6+8Eg8++CCOP/54vPnmmy3+ZvHixRg1ahS8Xi/WrVuHzp07G20rEokgPz8fmzdtQl5eXto4V2O1XJlytMVOIFeswhWrE2OcnGIxxkrJj6+7Ipt3eVvKFxLrgCWv45q0V7k8YkxUucUYt2Xp60jpzyMABNz6OgAgkGoQY6xkVIzZ6inSlod98j77kBJjqhLyPhUG5G01JOXj53XptxVQcbGOlDsgxngS9WLM140+MaZ/oRyzaG1EW35UuVyH8sj7BDv921maueVtWQn5lXPl0ddjW/I1KV0qkUgEnbt0QW1trXYM3hvsydwEtCM/NWyTKxPGT8cXlKswyE+2QX5yZSo/5emPpTK4DjKWnwy2FXXkMVYaG03GV6P8lJTPpWUnxZgqT6G2POSVj69JfqpJyvXk+uSY+gwcPz/k45Jyyf3Bm5TH4K8b5DHWJD+9u05/vo8o84p1mMzBpHkwYHatmIwRSrh2bYNzoLvcIpEIuvxAchOQnXunrcv+jbzccNq4VGF3sS63kL+cYL5cR52cL1L5XeV6orVijG3Qnj3FbXBv6oT0YzQAxG35Nt4t5CaTe6ewQT4w4d26UoxJlvTWljsGKxfCLhszOLziXBkApJBMLca4Yvr7GQBwApkZEx/5eKO2/Ipe8vzALpCvbRO+DZ+LMfGuB4gx0phmMk+WmOanjH9xxMCBAwGgxePXSim8+OKLAIBJkya1+puRI0di4MCBSCaTePnllzPdJCIi6uCYm4iIaG/E/ERERDvK+CLdkiVLAABDhw5t/t3atWuxceP21dZRo0a1+XdNv//www8z3SQiIurgmJuIiGhvxPxEREQ7Mnj+XWbbNjZu3IhXXnkFv/nNb5CTk4M777yzuXz58uUAAL/fj/Ly8jbr6N27d4vYtsTjccTj/30rXSQiP9JJREQd057KTQDzExERmeO9ExERpbNLT9Lde++9sCwLHo8H3bt3x5VXXoljjz0WH3zwAUaMGNEcV129/X33BQUFsNJ8plhhYWGL2LbceeedyM/Pb/7p3l3+vAQiIupY9nRuApifiIhIxnsnIiKS7NIiXdeuXTFq1CiMGDGi+QNLFyxYgGeffRa2bTfHxWLbP0TW50v/QbB+vx8AEI2m/zD+G264AbW1tc0/69at25XmExHRj9Cezk0A8xMREcl470RERJJdervrmWeeiTPPPLP53x9++CEuvfRS/P73v0dVVRUeeughAEAgsP1bDxOJ9N9s2PQodjCY/lvq/H5/c0IiIiJqy57OTQDzExERyXjvREREkox+ccTBBx+M119/HX6/H4888gjWrFkD4L+PY9fU1ECptr9kuOlR7aZYIiKiTGBuIiKivRHzExERfV/Gv921vLwcQ4YMgeM4+OyzzwAA/fr1A7D9FZ8NGza0+XcrV65sEUtERJQpzE1ERLQ3Yn4iIqIdZeTbXb8vlUq1+G9FRQW6dOmCTZs24f3338dPfvKTVn/z/vvvA9j+ilJ7WfEGWPFdW29MhIq15b5YrViH8siPk7vqt4gxG1zyK2L5+RViTNDd9gfNNrFi8jc8NXpzxRhbpf+8jCaJRNuvAu6oGHVijPKHteU1KXk7hUn9B8ADgBOQ91t55P3Od7m15S79KQIARG19HQBQGJArqo7ZYkyRX67Hhj4mrgJiHZBPE9wGx7dnvhyzaK3cz4+syNOWf7SpUaxjaBcxBLUpecgtjsifFxPNlz/4Od0r7018BkOmZ9tqfXldvVzJXmRP5yYAcEUjcHk150I5Yh2JQL623Ne4TazDJD95IhvFmI2eTmJMrkl+cun7pxWX+5ZJflKQ9zsWl89BMeT2SPkpvifzky8kxuS79IOAYzBONxrkp1yfnFdq4nJ+KjbITykhP6Ug5wyT/VZeOc/1zJcH2XfXyfOew7vrz/e/NjaIdRxUJrc3kpCvg6IM5SdbyE9Bg7mRLj95f2C5Cdjz+SlV0BWpPP3cR+Lk6O+dDC4lKK88Vplckwjq8yQA1CflPu53669br8HcyV23WYyxczuLMZaTEmN87l2/lfeZ3IxkSLKktxjjSsX0AR55PEvYcqeJGcTkmUyWDUjp32NwCoyuJ4Pcb8LkmrtkaJm2fKFBfjusUD6+UYO5k8eXI8aYsIUxzYS7QT8ndzfKxwXYDU/SrV69uvlVoAMOOAAAYFkWTj31VADAo48+2upvFi9ejGXLlsHr9eLkk0/OdJOIiKiDY24iIqK9EfMTERHtqN2LdP/+978xderU5kesd/TGG29gzJgxSKVSGDt2LPr06dNcdt1118Hn8+Gtt97CPffc0/yUx5o1azBx4kQAwOTJk9Gli8HjKERERDtgbiIior0R8xMREbVHuxfp6urqcNttt6FPnz4oKyvD8OHDccABB6CwsBBjxozBsmXLMHz4cDz55JMt/q5Xr16YOXMmXC4XpkyZgu7du2Po0KHo168fvv76awwbNgz33HNPxnaMiIg6DuYmIiLaGzE/ERFRe7R7ke6AAw7AjBkzcPLJJyMnJwfLli3DsmXLEAwGMWbMGDz++ONYvHgxSkpKWv3t+eefj3fffRfjx49HNBrFl19+id69e2PatGl47733kJOTmfcTExFRx8LcREREeyPmJyIiao92f9pkYWEhrr76alx99dU7tcGRI0di7ty5O/W3REREbWFuIiKivRHzExERtUfGvziCiIiIiIiIiIiI2oeLdERERERERERERFnW7re77o2Uxwvl8aUttxxbrMMXrdaWN/gL5DpclhjT6AqJMUElhiDglrcFJ6Utjvvy5LZAXwcA2B65G7ld8k4pSz42CaVfV46mkmIdVf5CMaY48q0Y4wTzxRjbl75fAsCWqHx8yzwJMUYZXMpetxyzvl6+VopD+r4XNOib7shGMaYm2FmMKaxZIcYcVd5NjPloU6O2fFgXuW++8k2VGHNyvwIxxvZ3F2Ma444YUxzTH2M7XCq3JadIX257xTo6OscXgOMLpi13yZc3fLFabXk0oD9PAOA2yE9Rg/zkN8hPJmMAhLxslJ8s+TpQlvxapMfllutRATEmE/lpq69AjCmt3yTGOAE5P8U9+s+yqo7L+aCLXz4HMAgJeuSxZE2dnC+75Oj7ns+gb/oN8n9NqEyMKaxt/U2e33dEWbkY86+NDdry4WXyZ5LN+0+NGDOmt3zN2YVyfqqPyf2mNLpBv518+fjq5mBOis8g7AlSOmhIyhd/npJjvms0ufblOW7YK/cLVyyiLXcCBtdJrjx/NaFcmblNl86Dz52Z68UyOJcmIkp/7xQ2qMNkrA/YUTHGgTwvcgzmRVJzDKqAwcwqY33GYMooOqx7rhjz2gr9+gsAjOsr37fbefI3XNca3DsVOXX67Rjc+0O6DgyvE2YxIiIiIiIiIiKiLOMiHRERERERERERUZZxkY6IiIiIiIiIiCjLuEhHRERERERERESUZVykIyIiIiIiIiIiyjIu0hEREREREREREWUZF+mIiIiIiIiIiIiyjIt0REREREREREREWebJdgMywnJt/0nD8QXFKhKWTx+glFiHN1otxuSGCsUYKEcMsWIRuRpvQFteFU+JdZR5EgbbkbuRz2WJMXHHLcZYQjU9Q7ZYR9LtFWMclS+3xaBP1Mb17TE5vptTfjGms4qKMbbB5d7dFxdjamz9eXJLJwlAIthZjCmo/1aMiZX0FWM8cnMwtIu+/JVvqsQ6Tu5fJMZ8sKFBjDm4PEeMyffLr6/Uucu15SEkxTqcQJ6+XO6+JDDJT3Hoxyw5YwCBuJwzPML5BmCUn1yNci5Uwn5XGfQtk/HT9obEGLfBGJGAMEcAoIScYJKfUib5CblijGXL13fE0Z9Lo/wUN8hPHjmvJA3yU8+AvE9SfrIM8lNDqEyMMclPjUW9xRgf5HnYQWX6udy8/9SIdYzpUyDGvLuuTow5rLvc9woD8lyu0dtNW+5X8rm2NfNpOyW3gfQ2N8p9M9+vP84ug+vNzikWY4QpGgDAcuT2Kpc8zkjzHlue+hvllD0p7BKOjSUfF2XwXI/S3Is38UQ2ijHhPHkMlpicJ/jk+YEJg1tckUl7G5Ly/KsAMTHGMdhvk12SmmyyT+P6yusij3ws95nL95H3KT8o908b+vt/7zfvynX0OFBbrjzyWAXwSToiIiIiIiIiIqKs4yIdERERERERERFRlnGRjoiIiIiIiIiIKMu4SEdERERERERERJRlXKQjIiIiIiIiIiLKMi7SERERERERERERZRkX6YiIiIiIiIiIiLKMi3RERERERERERERZ5sl2AzKhNumCk0y/3ljgccQ6fMJypa0ssQ7lcosxViwi1xPIk+txbDEGqYS2OOwNiVU0WEExpj4qtyUsHWAAISspxrhrNmrLlTcg1uHzxMWYeq98DpKOkrcllFcrub2lIfnYxewcMSbskvtwg0E9BdAfv5jyi3W4LLktqcLuYow3FRNjlCUfv9qUfig8uV+BWMcHGxrEmEPK5eO7eH29GHNgmVyPz60/xq6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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Instantiate models\n",
    "from sklearn import linear_model\n",
    "model_ols = linear_model.LinearRegression()\n",
    "model_l2 = linear_model.Ridge()\n",
    "model_l1= linear_model.Lasso()\n",
    "\n",
    "# Set regularization range\n",
    "lambdas = np.logspace(-4, 5, 10)\n",
    "\n",
    "# Load data\n",
    "# define subset of samples\n",
    "n_samples = 400\n",
    "X_train, X_test = X_all[:n_samples], X_all[n_samples : 3 * n_samples // 2]\n",
    "y_train, y_test = y_all[:n_samples], y_all[n_samples : 3 * n_samples // 2]\n",
    "\n",
    "# define error lists\n",
    "train_error_ols, test_error_ols = list(), list()\n",
    "train_error_l2, test_error_l2 = list(), list()\n",
    "train_error_l1, test_error_l1 = list(), list()\n",
    "\n",
    "#Initialize coefficients for ridge regression and Lasso\n",
    "coeffs_ols, coeffs_ridge, coeffs_lasso = list(), list(), list()\n",
    "\n",
    "for lam in lambdas:\n",
    "    ### ordinary least squares\n",
    "    model_ols.fit(X_train, y_train) # fit model \n",
    "    coeffs_ols.append(model_ols.coef_) # store weights\n",
    "    # use the coefficient of determination R^2 as the performance of prediction.\n",
    "    train_error_ols.append(model_ols.score(X_train, y_train))\n",
    "    test_error_ols.append(model_ols.score(X_test, y_test))\n",
    "\n",
    "    ### ridge regression\n",
    "    model_l2.set_params(alpha=lam) # set regularisation strength\n",
    "    model_l2.fit(X_train, y_train) # fit model\n",
    "    coeffs_ridge.append(model_l2.coef_) # store weights\n",
    "    train_error_l2.append(model_l2.score(X_train, y_train))\n",
    "    test_error_l2.append(model_l2.score(X_test, y_test))\n",
    "\n",
    "    ### lasso\n",
    "    model_l1.set_params(alpha=lam) # set regularisation strength\n",
    "    model_l1.fit(X_train, y_train) # fit model\n",
    "    coeffs_lasso.append(model_l1.coef_) # store weights\n",
    "    train_error_l1.append(model_l1.score(X_train, y_train))\n",
    "    test_error_l1.append(model_l1.score(X_test, y_test))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    ### plot Ising interaction J\n",
    "    J_leastsq = np.array(model_ols.coef_).reshape((L, L))\n",
    "    J_ridge = np.array(model_l2.coef_).reshape((L, L))\n",
    "    J_lasso = np.array(model_l1.coef_).reshape((L, L))\n",
    "\n",
    "\n",
    "    fig, axarr = plt.subplots(nrows=1, ncols=3)\n",
    "    \n",
    "    axarr[0].imshow(J_leastsq,  cmap=\"RdBu_r\", vmin=-1, vmax=1)\n",
    "    axarr[0].set_title(f\"OLS \\n Train={train_error_ols[-1]}, Test={test_error_ols[-1]}\")\n",
    "    ## 3 sig figs\n",
    "    # axarr[0].set_title('OLS \\n Train$=%.3f$, Test$=%.3f$' %(train_error_ols[-1],test_error_ols[-1]))\n",
    "    axarr[1].set_title('OLS $\\lambda=%.4f$\\n Train$=%.3f$, Test$=%.3f$' %(lam, train_error_ols[-1],test_error_ols[-1]))\n",
    "    axarr[0].tick_params(labelsize=16)\n",
    "    \n",
    "    axarr[1].imshow(J_ridge,  cmap=\"RdBu_r\", vmin=-1, vmax=1)\n",
    "    axarr[1].set_title('Ridge $\\lambda=%.4f$\\n Train$=%.3f$, Test$=%.3f$' %(lam, train_error_l2[-1],test_error_l2[-1]))\n",
    "    axarr[1].tick_params(labelsize=16)\n",
    "    \n",
    "    im=axarr[2].imshow(J_lasso, cmap=\"RdBu_r\", vmin=-1, vmax=1)\n",
    "    axarr[2].set_title('LASSO $\\lambda=%.4f$\\n Train$=%.3f$, Test$=%.3f$' %(lam, train_error_l1[-1],test_error_l1[-1]))\n",
    "    axarr[2].tick_params(labelsize=16)\n",
    "    \n",
    "    # divider = make_axes_locatable(axarr[2])\n",
    "    # cax = divider.append_axes(\"right\", size=\"5%\", pad=0.05, add_to_figure=True)\n",
    "    # cbar=fig.colorbar(im, cax=cax)\n",
    "    \n",
    "    # cbar.ax.set_yticklabels(np.arange(-1.0, 1.0+0.25, 0.25),fontsize=14)\n",
    "    # cbar.set_label('$J_{i,j}$',labelpad=15, y=0.5,fontsize=20,rotation=0)\n",
    "    \n",
    "    fig.subplots_adjust(right=2.0)\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Performance $R^2$')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot our performance on both the training and test data\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.semilogx(lambdas, train_error_ols, \"b\", label=\"Train (OLS)\")\n",
    "plt.semilogx(lambdas, test_error_ols, \"--b\", label=\"Test (OLS)\")\n",
    "plt.title(\"Ordinary Least Squares\", fontsize=16)\n",
    "plt.xlabel(\"Regularization strength $\\lambda$\")\n",
    "plt.ylabel(\"Performance $R^2$\")\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.semilogx(lambdas, train_error_l2, \"r\", label=\"Train (Ridge)\", linewidth=1)\n",
    "plt.semilogx(lambdas, test_error_l2, \"--r\", label=\"Test (Ridge)\", linewidth=1)\n",
    "plt.title(\"Ridge Regression\", fontsize=16)\n",
    "plt.xlabel(\"Regularization strength $\\lambda$\")\n",
    "plt.ylabel(\"Performance $R^2$\")\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.semilogx(lambdas, train_error_l1, \"g\", label=\"Train (LASSO)\")\n",
    "plt.semilogx(lambdas, test_error_l1, \"--g\", label=\"Test (LASSO)\")\n",
    "plt.title(\"LASSO\", fontsize=16)\n",
    "plt.xlabel(\"Regularization strength $\\lambda$\")\n",
    "plt.ylabel(\"Performance $R^2$\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Understanding our result\n",
    "\n",
    "It looks like our coupling matrix is pretty sparse, and that the non-zero entries are concentrated along the off diagonal. This means that our Hamiltonian likely corresponds to the nearest-neighbor Ising model\n",
    "\n",
    "$$\n",
    "\\mathcal{H}(\\mathbf{s}^{(i)})=-J\\sum_{j=1}^L s_{j}^{(i)}\\, s_{j+1}^{(i)}\n",
    "$$\n",
    "\n",
    "\n",
    "+ When $\\lambda\\to 0$ and $\\lambda\\to\\infty$, all three models overfit the data, as can be seen from the deviation of the test errors from unity (dashed lines), while the training curves stay at unity. \n",
    "\n",
    "+ While the ordinary least-squares and Ridge regression test curves are monotonic, the LASSO test curve is not -- suggesting the optimal LASSO regularization parameter is $\\lambda\\approx 10^{-2}$. At this sweet spot, the Ising interaction weights ${\\bf J}$ contain only nearest-neighbor terms (as did the model the data was generated from).\n",
    "\n",
    "+ Notice how Lasso was able to correctly identify that the coupling matrix is non-symmetric, while OLS and Ridge both favored finding symmetric matrices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyperparameter tuning\n",
    "\n",
    "We can imagine that an even more general model would have both regularizers, each with different strengths\n",
    "$$\n",
    "\\mathcal{L}_{total} = \\mathcal{L}_{least-squares} + \\lambda_1 \\mathcal{L}_{lasso} + \\lambda_2 \\mathcal{L}_{ridge}\n",
    "$$\n",
    "This loss function is sometimes referred to as least-squares with an ElasticNet penalty.\n",
    "\n",
    "\n",
    "## Why not always use regularizers\n",
    "+ The issue: we have two arbitrary factors, $\\lambda_1$ and $\\lambda_2$, which determine how important the L1 and L2 penalties are relative to the primary fitting. These change the available solution space and thus model class\n",
    "+ These are not \"fit\" during training like ordinary parameters; rather they are specified beforehand, perhaps with a bit of intuition or domain knowledge, These therefore represent *hyperparameters* of the model\n",
    "+ Generally speaking, any \"choices\" we make---amount of data, model type, model parameters, neural network depth, etc are all hyperparameters. How do we choose these in a principled manner?\n",
    "+ A major question in machine learning: **How do we choose the best hyperparameters for a model?**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation set\n",
    "+ Hold out some data just for hyperparameter tuning, separate from the test set\n",
    "+ Don't validate on test, that leads to data leakage and thus overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best lambda on validation set 0.0005336699231206307\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# define train, validation and test data sets\n",
    "X_train, X_val, X_test = X_all[:400], X_all[400 : 600], X_all[600 : 800]\n",
    "y_train, y_val, y_test = y_all[:400], y_all[400 : 600], y_all[600 : 800]\n",
    "\n",
    "# the hyperparameter values to check\n",
    "lambdas = np.logspace(-6, 4, 100)\n",
    "\n",
    "all_validation_losses = list()\n",
    "\n",
    "for lam in lambdas:\n",
    "    model_l1 = linear_model.Lasso(alpha=lam)\n",
    "    model_l1.fit(X_train, y_train)\n",
    "    validation_loss = model_l1.score(X_val, y_val)\n",
    "    all_validation_losses.append(validation_loss)\n",
    "\n",
    "best_lambda = lambdas[np.argmax(all_validation_losses)]\n",
    "\n",
    "plt.semilogx(lambdas, all_validation_losses, label=\"Validation\")\n",
    "plt.axvline(best_lambda, color='k', linestyle='--', label=\"Best lambda\")\n",
    "plt.xlabel(\"Regularization strength $\\lambda$\")\n",
    "plt.ylabel(\"Validation Performance $R^2$\")\n",
    "\n",
    "print(\"Best lambda on validation set\", best_lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit best model \n",
    "model_l1 = linear_model.Lasso(alpha=best_lambda)\n",
    "model_l1.fit(X_train, y_train)\n",
    "\n",
    "y_test_predict = model_l1.predict(X_test)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(y_test, y_test_predict, \".k\")\n",
    "plt.xlabel(\"True value\")\n",
    "plt.ylabel(\"Predicted value\")\n",
    "plt.gca().set_aspect(1)\n",
    "\n",
    "\n",
    "# plot Ising interaction J\n",
    "J_lasso = np.array(model_l1.coef_).reshape((L, L))\n",
    "plt.figure()\n",
    "plt.imshow(J_lasso,  cmap=\"RdBu_r\", vmin=-1, vmax=1)\n",
    "plt.gca().set_aspect(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-validation\n",
    "\n",
    "+ We repeatedly split-up the train into multiple sub-splits for training and validation\n",
    "+ For example, if we have 100 train points, we can create five 80:20 \"splits\", and average the best hyperparameter across the splits\n",
    "+ If we perform $k$ subsplits, we refer to our procedure as k-fold cross-validation\n",
    "+ More elaborate splitting methods (random Monte Carlo, importance weighted, etc)\n",
    "\n",
    "\n",
    "<img src=\"../resources/cross_val.png\" alt=\"supervised_learning\" style=\"width: 750px;\"/>\n",
    "\n",
    "Image from [source](https://towardsdatascience.com/cross-validation-k-fold-vs-monte-carlo-e54df2fc179b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best lambda on validation set 0.005623413251903491\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Cross validation\n",
    "\n",
    "from sklearn import linear_model\n",
    "\n",
    "# define train, validation and test data sets\n",
    "X_train, X_test = X_all[:600], X_all[600 : 800]\n",
    "y_train, y_test = y_all[:600], y_all[600 : 800]\n",
    "\n",
    "# the hyperparameter values to check\n",
    "lambdas = np.logspace(-6, 4, 9)\n",
    "\n",
    "all_validation_losses = list()\n",
    "\n",
    "for lam in lambdas:\n",
    "\n",
    "    all_val_loss_lam = list()\n",
    "\n",
    "    for k in range(5):\n",
    "\n",
    "        # Create the training and validation subsets from the training data\n",
    "        X_train_k = np.concatenate([X_train[:k*100], X_train[(k+1)*100:]])\n",
    "        y_train_k = np.concatenate([y_train[:k*100], y_train[(k+1)*100:]])\n",
    "        X_val_k = X_train[k*100:(k+1)*100]\n",
    "        y_val_k = y_train[k*100:(k+1)*100]\n",
    "\n",
    "\n",
    "        model_l1 = linear_model.Lasso(alpha=lam)\n",
    "        model_l1.fit(X_train_k, y_train_k)\n",
    "        validation_loss = model_l1.score(X_val_k, y_val_k)\n",
    "        all_val_loss_lam.append(validation_loss)\n",
    "\n",
    "    all_validation_losses.append(np.mean(all_val_loss_lam))\n",
    "\n",
    "best_lambda = lambdas[np.argmax(all_validation_losses)]\n",
    "plt.figure()\n",
    "plt.semilogx(lambdas, all_validation_losses, label=\"Validation\")\n",
    "print(\"Best lambda on validation set\", best_lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit best model \n",
    "model_l1 = linear_model.Lasso(alpha=best_lambda)\n",
    "model_l1.fit(X_train, y_train)\n",
    "\n",
    "y_test_predict = model_l1.predict(X_test)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(y_test, y_test_predict, \".k\")\n",
    "plt.xlabel(\"True value\")\n",
    "plt.ylabel(\"Predicted value\")\n",
    "plt.gca().set_aspect(1)\n",
    "\n",
    "\n",
    "# plot Ising interaction J\n",
    "J_lasso = np.array(model_l1.coef_).reshape((L, L))\n",
    "plt.figure()\n",
    "plt.imshow(J_lasso,  cmap=\"RdBu_r\", vmin=-1, vmax=1)\n",
    "plt.gca().set_aspect(1)"
   ]
  },
  {
   "cell_type": "code",
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    "## How many free parameters are in our model?\n",
    "\n",
    "Linear regression:\n",
    "\n",
    "$$\n",
    "y_i = \\mathbf{A} \\mathbf{X}_i\n",
    "$$\n",
    "\n",
    "+ In our Ising example, the fitting parameters $\\mathbf{A}$ corresponded to our coupling matrix $\\mathbf{J}$\n",
    "+ $\\mathbf{X}_i$ were our spin product microstates, and $y_i$ was their energies\n",
    "+ $\\mathbf{J} \\in \\mathbb{R}^{40 \\times 40}$ because our inputs (microstates) are on an $L = 40$ lattice, and so we had $1600$ free parameters\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "## What if we wanted to increase our model complexity?\n",
    "\n",
    "### Idea: \n",
    "\n",
    "$$\n",
    "y_i = \\mathbf{B} \\mathbf{C} \\mathbf{X}_i\n",
    "$$\n",
    "\n",
    "where $\\mathbf{B} \\in \\mathbb{R}^{40 \\times p}$ and $\\mathbf{C} \\in \\mathbb{R}^{p \\times 40}$, with $p$ being a hyperparameter that controls the complexity of the model. This \"hidden\" or \"latent\" dimensionality allows us to have a more complex model.\n",
    "\n",
    "However, the problem is that $\\mathbf{B} \\mathbf{C} \\equiv \\mathbf{A}\\in \\mathbb{R}^{40 \\times 40}$, so we don't gain any expressivity\n",
    "\n",
    "### Solution:\n",
    "\n",
    "$$\n",
    "y_i = \\mathbf{B} \\sigma(\\mathbf{C} \\mathbf{X}_i)\n",
    "$$\n",
    "\n",
    "where $\\sigma(.)$ is an elementwise nonlinear function, like $\\tanh(.)$. Now the model doesn't collapse, so we have $2 \\times 40 \\times p$ free parameters.\n",
    "\n",
    "This is a one-layer neural network, with a $p$ unit \"hidden\" layer. We can always go wider or deeper to further increase the model complexity."
   ]
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  },
  {
   "cell_type": "code",
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  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# Appendix\n",
    "\n",
    "Simulate the Ising model with nearest-neighbor interactions with periodic boundary conditions. The energy of a spin configuration $\\boldsymbol{\\sigma} = \\{\\sigma_1,\\dots,\\sigma_N\\}$ is given by\n",
    "\n",
    "$$\n",
    "E[\\boldsymbol{\\sigma}] = -J\\sum_{\\langle i,j\\rangle} \\sigma_i \\sigma_j\n",
    "$$\n",
    "\n",
    "where the sum is over all pairs of nearest neighbors on a $L\\times L$ square lattice, and $J$ is the coupling constant. The magnetization is given by\n",
    "\n",
    "$$\n",
    "M[\\boldsymbol{\\sigma}] = \\sum_{i=1}^N \\sigma_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class IsingModel:\n",
    "    \"\"\"\n",
    "    The Ising model with ferromagnetic interactions that encourage nearest neighbors\n",
    "    to align\n",
    "    \"\"\"\n",
    "    def __init__(self, L, random_state=None):\n",
    "        self.L = L\n",
    "        self.random_state = random_state\n",
    "        \n",
    "        self.J = np.diag(-np.ones(L - 1), 1)\n",
    "        self.J [-1, 0] = -1.0 # periodic boundary conditions\n",
    "\n",
    "    def sample(self, n_samples=1):\n",
    "        if self.random_state is not None:\n",
    "            np.random.seed(self.random_state)\n",
    "        return np.random.choice([-1, 1], size=(n_samples, self.L))\n",
    "\n",
    "    def energy(self, state):\n",
    "        return np.einsum(\"...i,ij,...j->...\", states, self.J, states)\n",
    "\n",
    "model_experiment = IsingModel(40, random_state=0)\n",
    "\n",
    "# create 10000 random Ising states\n",
    "states = model_experiment.sample(n_samples=10000)\n",
    "\n",
    "\n",
    "# calculate Ising energies\n",
    "energies = model_experiment.energy(states)\n",
    "\n",
    "print(\"Input data has shape: \", states.shape)\n",
    "print(\"Labels have shape: \", energies.shape)\n",
    "\n",
    "\n",
    "## Save data\n",
    "# states.dump(\"../resources/spin_microstates.npy\")\n",
    "# energies.dump(\"../resources/spin_energies.npy\")"
   ]
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