talks/logistic_regression_phases.ipynb

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    "# Classifying phases of the Ising Model with Logistic Regression\n",
    "\n",
    "This notebook is modified a notebook and demonstration originally developed in [Pankaj Mehta's ML for physics course](http://physics.bu.edu/~pankajm/PY580.html).\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "#### Preamble"
   ]
  },
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   "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",
    "\n",
    "## Machine learning package\n",
    "import sklearn\n"
   ]
  },
  {
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    "### The road to deep learning\n",
    "\n",
    "1. Many trainable parameters (giant matrix multiplications)\n",
    "\n",
    "2. **Nonlinearity (increases expressivity) <-- Today**\n",
    "\n",
    "3. Training (gradient descent plus the chain rule)"
   ]
  },
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    "## Overview\n",
    "\n",
    "+ We will show Logistic models can classify the states of the 2D Ising model according to their phase. \n",
    "\n",
    "+ Recall that the energy function of the classical Ising model is given by the Hamiltonian\n",
    "\n",
    "  $$ H = -J\\sum_{\\langle ij\\rangle}S_{i}S_j,\\qquad \\qquad S_j\\in\\{\\pm 1\\} $$\n",
    "\n",
    "  where the lattice site indices $i,j$ run over all nearest neighbors of a 2D square lattice, and $J$ is some arbitrary interaction energy scale. We adopt periodic boundary conditions. \n",
    "\n",
    "+ In two dimensions, Onsager proved that this model undergoes a thermal phase transition in the thermodynamic limit from an ordered ferromagnet with all spins aligned to a disordered phase at the critical temperature $T_c/J=2/\\log(1+\\sqrt{2})\\approx 2.26$. \n",
    "\n",
    "+ For any finite system size, this critical point is expanded to a **critical region** around $T_c$.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/2d_ising.png\" alt=\"2D Ising Phase Diagram\" style=\"width: 700px;\"/>\n",
    "\n",
    "\n",
    "## The 2D Ising Dataset\n",
    "\n",
    "+ We consider the 2D Ising model on a $40\\times 40$ square lattice, and use Monte-Carlo (MC) sampling to prepare $10^4$ states at every fixed temperature $T$ out of a pre-defined set $T\\in[0.25,0.5,\\cdots,4.0]$. \n",
    "\n",
    "+ Using Onsager's criterion, we can assign a label to each state according to its phase: $0$ if the state is disordered, and $1$ if it is ordered. Our goal is to predict the phase of a sample given the spin configuration.\n",
    "\n",
    "+ It is well-known that, near the critical temperature $T_c$, the ferromagnetic correlation length diverges which, among other things, leads to a critical slowing down of the MC algorithm. Therefore, we expect identifying the phases to be harder in the critical region. With this in mind, consider the following three types of states: ordered ($T/J<2.0$), critical ($2.0\\leq T/J\\leq 2.5$) and disordered ($T/J>2.5$).\n",
    "\n",
    "+ We use both ordered and disordered states to train the logistic regressor and once the supervised training procedure is complete, we evaluate the performance of our classification model on unseen ordered, disordered and critical states. "
   ]
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    "# Can we predict the phase, given only the microstate?\n",
    "\n",
    "+ For the Ising model, we saw that linear regression effectively finds the coupling matrix $J$ for a Hamiltonian\n",
    "\n",
    "+ Instead of regressing macroscopic energies, we will instead ask a qualitative question: Can we predict the phase of the system based on only the microstate? \n",
    "\n",
    "+ If we can successfully perform this operation, then we've essentially learned a computational surrogate for our experiments, which might be expensive to perform individually. The surrogates could be used to find critical points, for example."
   ]
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   "source": [
    "# Load the Ising dataset\n",
    "\n",
    "+ We load in the 2D Ising model dataset, which is hosted on Pankaj Mehta's [website](http://physics.bu.edu/~pankajm/MLnotebooks.html).\n",
    "+ We will wrap the import logic into a separate class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle, os\n",
    "from urllib.request import urlopen\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "## Dataloader\n",
    "class IsingSimulation:\n",
    "    \"\"\"\n",
    "    A container class for the Ising model simulation data.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        self.load_simulation()\n",
    "\n",
    "    def load_simulation(self):\n",
    "        \"\"\"\n",
    "        Load the compressed data and format it into a configuration amenable to \n",
    "        machine learning.\n",
    "        \"\"\"\n",
    "        ## URL of data\n",
    "        url_main = \"https://physics.bu.edu/~pankajm/ML-Review-Datasets/isingMC/\"\n",
    "        # The data consists of 16*10000 samples taken in T=np.arange(0.25,4.0001,0.25):\n",
    "        data_file_name = \"Ising2DFM_reSample_L40_T=All.pkl\"\n",
    "        # The labels are obtained from the following file:\n",
    "        label_file_name = \"Ising2DFM_reSample_L40_T=All_labels.pkl\"\n",
    "\n",
    "        # Ising model parameters used in the simulation\n",
    "        self.L = 40  # linear system size\n",
    "        self.J = -1.0  # Ising interaction\n",
    "        self.T = np.linspace(0.25, 4.0, 16)  # set of temperatures\n",
    "        self.T_c = 2.26  # Onsager critical temperature in the TD limit\n",
    "\n",
    "        # Load dataset into numpy\n",
    "        X_all = pickle.load(\n",
    "            urlopen(url_main + data_file_name)\n",
    "        )  # pickle reads the file and returns the Python object (1D array, compressed bits)\n",
    "        X_all = np.unpackbits(X_all).reshape(\n",
    "            -1, 1600\n",
    "        )  # Decompress array and reshape for convenience\n",
    "        X_all = X_all.astype(\"int\")\n",
    "        X_all[\n",
    "            np.where(X_all == 0)\n",
    "        ] = -1  # map 0 state to -1 (Ising variable can take values +/-1)\n",
    "        self.X_all = X_all\n",
    "\n",
    "        # LABELS (convention is 1 for ordered states and 0 for disordered states)\n",
    "        labels = pickle.load(\n",
    "            urlopen(url_main + label_file_name)\n",
    "        )\n",
    "        self.labels = labels\n",
    "        ##  pickle reads the file and returns the Python object (here just a 1D array with\n",
    "        ##  binary labels)\n",
    "        self.num_classes = np.unique(self.labels) # should be 2: ordered or disordered\n",
    "\n",
    "        \n",
    "    def reshape_datapoint(self, x):\n",
    "        \"\"\"\n",
    "        Given a single simulation snapshot, reshape into original square lattice\n",
    "        \"\"\"\n",
    "        return x.reshape(self.L, self.L)\n",
    "        \n",
    "    def find_magnetization(x, axis=-1):\n",
    "        \"\"\"\n",
    "        Given a single simulation snapshot, calculate the magnetization\n",
    "        \"\"\"\n",
    "        return np.mean(x, axis=axis)\n",
    "\n",
    "    def split_data(self, split_ratio=0.5):\n",
    "        \"\"\"\n",
    "        Split data into training and test sets\n",
    "        \n",
    "        Parameters:\n",
    "        split_ratio (float): ratio of training data to total data\n",
    "        \"\"\"\n",
    "\n",
    "        # pick random data points from ordered and disordered states\n",
    "        # to create the training and test sets\n",
    "        X_train, X_test, y_train, y_test = train_test_split(\n",
    "            self.X_all, self.labels, train_size=split_ratio, test_size=1.0 - split_ratio\n",
    "        )\n",
    "\n",
    "        return X_train, X_test, y_train, y_test\n",
    "\n",
    "    \n",
    "## fetch and pack the Ising dataset\n",
    "dataset = IsingSimulation()\n",
    "# dataset2 = IsingSimulation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
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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 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### plot a few representative Ising states\n",
    "fig, axarr = plt.subplots(nrows=1, ncols=3)\n",
    "\n",
    "axarr[0].imshow(dataset.reshape_datapoint(dataset.X_all[20001]), cmap='binary')\n",
    "axarr[0].set_title('$\\\\mathrm{ordered\\\\ phase}$',fontsize=16)\n",
    "axarr[0].tick_params(labelsize=16)\n",
    "\n",
    "axarr[1].imshow(dataset.reshape_datapoint(dataset.X_all[80001]), cmap='binary')\n",
    "axarr[1].set_title('Critical Region, $T \\sim T_c$',fontsize=16)\n",
    "axarr[1].tick_params(labelsize=16)\n",
    "\n",
    "axarr[2].imshow(dataset.reshape_datapoint(dataset.X_all[150001]), cmap='binary')\n",
    "axarr[2].set_title('$\\\\mathrm{disordered\\\\ phase}$',fontsize=16)\n",
    "axarr[2].tick_params(labelsize=16)\n",
    "\n",
    "fig.subplots_adjust(right=2.0)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.hist(dataset.labels)\n",
    "plt.xlabel('Ising Class')\n",
    "plt.ylabel('Number of Samples')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize this dataset by sorting all of the microstates by their magnetization:\n",
    "\n",
    "$$ m = \\frac{1}{N}\\sum_i S_i $$\n",
    "\n",
    "where $N = 1600$ is the total number of spins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b81cb067b41d4110b5ef215008d06da7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='i', layout=Layout(width='500px'), max=79), Output()), _d…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plotter(i)>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Create an interactive plot using ipywidgets\n",
    "\n",
    "from ipywidgets import interact, Layout\n",
    "import ipywidgets as widgets\n",
    "\n",
    "all_microstates = dataset.X_all[::2000].reshape(-1, 40, 40)\n",
    "magnetizations = np.mean(all_microstates, axis=(1, 2))\n",
    "all_microstates = all_microstates[np.argsort(magnetizations)]\n",
    "magnetizations = magnetizations[np.argsort(magnetizations)]\n",
    "# true_labels = dataset.y_all[::2000][np.argsort(magnetizations)]\n",
    "true_phase = dataset.labels[::2000][np.argsort(magnetizations)]\n",
    "\n",
    "def plotter(i):\n",
    "    fig = plt.figure(figsize=(6, 6))\n",
    "    plt.imshow(all_microstates[i], cmap='binary', vmin=-1, vmax=1)\n",
    "    plt.axis('off')\n",
    "    plt.title(f'Average magnetization: {magnetizations[i]:.2f}', fontsize=16)\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "\n",
    "interact(\n",
    "    plotter, \n",
    "    i=widgets.IntSlider(0, 0, len(all_microstates) - 1, 1, layout=Layout(width='500px'))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised learning to classify phases of the 2D Ising model\n",
    "\n",
    "+ Given an Ising microstatestate, we would like to classify whether it belongs to the ordered (label 0) or the disordered phase (label 1), without any additional information other than the spin configuration itself. \n",
    "\n",
    "+ As a supervised learning problem, the data consists of $X \\in \\{0,1\\}^{N\\times 1600}$, where $N$ is the number of experiments. Each row of $X$ is a flattened $40 \\times 40$ spin configuration. The labels $y\\in\\{0,1\\}^N$ are the ordered/disordered phase labels, based on whether the temperature is below or above the known critical temperature.\n",
    "\n",
    "+ This categorical machine learning problem is well suited for logistic regression. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Make our training and testing sets\n",
    "\n",
    "+ We need to hold out a testing set to avoid overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train shape: (80000, 1600)\n",
      "X_test shape: (80000, 1600)\n",
      "y_train shape: (80000,)\n",
      "y_test shape: (80000,)\n"
     ]
    }
   ],
   "source": [
    "## pick random data points from ordered and disordered states\n",
    "X_train, X_test, y_train, y_test = dataset.split_data()\n",
    "\n",
    "print(f\"X_train shape: {X_train.shape}\")\n",
    "print(f\"X_test shape: {X_test.shape}\")\n",
    "print(f\"y_train shape: {y_train.shape}\")\n",
    "print(f\"y_test shape: {y_test.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression\n",
    "\n",
    "+ Earlier, we used linear regression to fit the energy of the Ising model given observations of the spin configuration\n",
    "\n",
    "+ Our input variables, $X$, corresponded to snapshots of microstates. Our output variables, $y$, corresponded to energies\n",
    "\n",
    "+ Energy is a continuous variable, that changes relatively smoothly in response to small changes in microstates (such as individual spin flips)\n",
    "\n",
    "+ In contrast, the phase of the Ising model is a categorical variable, which can only take on two values: ordered or disordered\n",
    "\n",
    "+ Our input variables, $X$, correspond to snapshots of microstates. However, our output variables, $y$, will now correspond to phases\n",
    "\n",
    "Logistic classifier:\n",
    "$$\n",
    "\\hat y_i = \\dfrac{1}{1 + \\exp(- A \\cdot X_i)}\n",
    "$$\n",
    "Where $A$ is a learnable parameter vector that defines the relative weight of the different observed features in our dataset. Our goal will be for $hat y_i$ to match the true label (phase), $y_i$. However, because the logistic function is sigmoidal, $y_i$ will be $\\pm 1$ for most values of $X$.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'The Logistic Function')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = np.linspace(-10, 10, 200) # hypothetical A @ X\n",
    "\n",
    "## logistic function\n",
    "y = 1 / (1 + np.exp(-ax))\n",
    "\n",
    "plt.plot(ax, y, linewidth=3.5)\n",
    "## latex label for A @ X\n",
    "plt.xlabel(r'$A \\cdot X$', fontsize=16)\n",
    "plt.ylabel('$\\hat{y}$', fontsize=16)\n",
    "plt.title('The Logistic Function', fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/classification_vs_regression2.png\" alt=\"classification vs regression\" style=\"width: 750px;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approach\n",
    "\n",
    "**Idea: perform a linear regression, and then assign a label by applying a nonlinear function to the linear output**\n",
    "\n",
    "A logistic classifier has the form\n",
    "$$\n",
    "\\hat y_i = \\dfrac{1}{1 + \\exp(- A \\cdot X_i)}\n",
    "$$\n",
    "where $y_i \\in \\{0,1\\}$ , $A \\in \\mathbb{R}^{1600}$ is a learnable parameter vector that defines the relative weight of the different observed features in a given dataset $X_i \\in \\mathbb{R}^{1600}$.\n",
    "\n",
    "we can relate this to  linear regression problem through the use of a \"link function\" $g(.)$ that we apply to both sides of the equation:\n",
    "$$\n",
    "g(y_i) \\equiv \\log\\bigg(\\dfrac{y_i}{1 - y_i}\\bigg) = A \\cdot X_i\n",
    "$$\n",
    "\n",
    "So we just need to perform linear regression between our data and the transformed labels, $g(y_i)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other link functions exist for different data types\n",
    "\n",
    "+ Count data: logarithmic transform\n",
    "+ Power law data: double logarithm\n",
    "+ Poisson and Binomial: rate depends on linear transform\n",
    "\n",
    "This class of models is sometimes called [General Linear Models](https://en.wikipedia.org/wiki/Generalized_linear_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How do we fit our model?\n",
    "\n",
    "A seemingly obvious choice: transform our labels/regression targets with the link function $g$ and then fit a linear regression using standard methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.50\n"
     ]
    }
   ],
   "source": [
    "class LogisticClassifier:\n",
    "\n",
    "    def __init__(self, num_classes=2):\n",
    "        self.num_classes = num_classes\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        \"\"\"\n",
    "        Fit the model to the data X and labels y using gradient descent and\n",
    "        the logistic link function\n",
    "        \"\"\"\n",
    "\n",
    "        # convert yhat to g via inverse link function\n",
    "        g = self._inverse_link_function(y)\n",
    "\n",
    "        # moore-penrose pseudoinverse\n",
    "        self.A = np.linalg.pinv(X) @ g\n",
    "\n",
    "    def predict(self, X):\n",
    "        yhat = self._link_function(X @ self.A)\n",
    "        yhat = np.round(yhat).astype(int)\n",
    "        return yhat\n",
    "    \n",
    "    def _link_function(self, y):\n",
    "        return 1 / (1 + np.exp(-y))\n",
    "    \n",
    "    def _inverse_link_function(self, y):\n",
    "        return np.log(y / (1 - y + 1e-5) + 1e-5)\n",
    "        \n",
    "\n",
    "\n",
    "## Split the available experimental data\n",
    "X_train, X_test, y_train, y_test = dataset.split_data()\n",
    "\n",
    "## Train the model and predict the test set\n",
    "model = LogisticClassifier()\n",
    "model.fit(X_train, y_train)\n",
    "yhat = model.predict(X_test)\n",
    "print(f\"Accuracy: {np.mean(yhat == y_test):.2f}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Is this good?\n",
    "\n",
    "+ Generally, we want to compare the accuracy to the frequency of the *most common class* in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction disordered train  0.5647\n",
      "Fraction disordered test  0.5603\n"
     ]
    }
   ],
   "source": [
    "print(\"Fraction disordered train \", np.mean(y_train))\n",
    "print(\"Fraction disordered test \", np.mean(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ob9++vdm63a2tvuiKpuNy8+bNsXnz5gOu25lPJZYtW9bmr1a1pSOv+Y4dO+L888+Purq6uPDCC+OSSy6JKVOmRE1NTfTr1y8ef/zxOPXUU6OxsbHZvi655JIYMmRIfPvb346nn346nn766bjllluif//+ccEFF8Rtt92WPz+a+qi+vr7dc7fcP7mh95BNXSObikc2ySbYn3zqmp6STz2BfOo9+dQT3g8Vytddy8jgwYPz/79nz55I794zsM2paXhq03Z//OMf29z3H/7wh4LbsX+l+0DV82Jpan9bbUwp5Z9ba8Pfu0vTz8I3NDTE66+/3uo6TUOFm9YtV22Fb2tD4pten+uuu67dY/Kee+4pZbM75ZFHHont27fHn/3Zn8U999wTs2fPjqFDh+ZD6UDhecEFF8Rzzz0XW7ZsiR//+Mcxb968qKioiEWLFsWnP/3p/HpNfTRnzpx2+6i1n2iHciabZFN3kU2yCTpCPpV3PvUm8qn886k3vR9SpCsjtbW1MXbs2IiI+PWvf13wdkceeWRERLz88sutXkD27dsXL7/8csH7q6mpyX9//sknnyx4u85qav8LL7zQ6vJ169bFnj174qCDDmpzqG53mDBhQowZMyYi2v60rmn+7Nmzu61dHdH0KUprb0rq6uri//v//r8W85uG0u8/tLonabqw/9mf/Vmrn6i8934KrRkzZkz87d/+bdx1112xZs2a6NevX/zsZz+LLVu2RMSf+ujFF1+Mffv2Fa/xUAZkk2wqNdkkm6Az5FN551NvIJ96Tj71hvdDTRTpysxf//VfR0Tkb8hYiJNOOikGDhwYGzdujP/4j/9osfynP/1ph7/v/ld/9VcREfHtb3+74G2avtvd0WG7H/vYxyIiYtGiRfnvnu/vn/7pnyLi3Up7KYYkFyqXy8U555wTERF33313i+WrVq2Kl156KSorK9u8AWbWJk6cGBERTz31VItld911V6vbnHnmmVFVVRVLly7N3z+kJ2k6Lpvu/bC/N954o9XX8kCmTZuWH6rd9CnN5MmT46ijjopt27bFvffe28UWQ/mRTbKplGRTc7IJCiefyjefegP51Fw551NveD/URJGuzHz961+P4cOHx/e///346le/Gjt27Gi2fNu2bfGv//qvcfPNN+fn1dTUxOc+97mIePe74C+++GJ+2a9+9av4yle+EpWVlR1qx9VXXx21tbXx2GOPxbx58/Lf345499OlpUuXxs9+9rNm2zRdxDr6KzWf/OQnY8KECfH73/8+PvOZzzS7ceUPf/jD+Jd/+ZeIiLjmmms6tN8DOemkk+Lwww+Pf/u3f+vQdldffXVUVVXFo48+Grfddlv+07dXXnklLr744oh499dzmqr4TTZu3Bi5XC5yuVymXylp+gWr66+/vtmF9xe/+EXcdNNNUVHR8jaVY8eOjcsvvzwaGxvjYx/7WCxfvrzZ8pRS/Pd//3d88YtfbPWXgbL2oQ99KCIiHnjggXj88cfz87ds2RLnnntu/pe+9ldfXx/nn39+LF++vNmnO3v37o1/+qd/iu3bt8egQYNiypQp+WW33HJL5HK5uPTSS+Ouu+5qsd/169fHN7/5zfyvkEFPIptkUynJJtkEnSWfyjufOks+Zacn51Nn3w+VnUSnHXbYYSki0uLFiwtaf8OGDSki0mGHHXbA9VasWJFGjhyZIiJVVlamo48+Os2ePTtNnDgx5XK5FBHpb//2b5tts3PnzjRz5swUESmXy6Wjjz46HXXUUSmXy6XjjjsunX/++a229YYbbkgRkW644YYW7XjsscfSkCFD8u2YPn16Ovroo9OgQYNa3eamm25KEZEOOuigNGPGjHTyySenk08+OW3ZsiWllNKyZctSRKSTTz65xWM9+eSTqba2NkVEGjRoUDr++OPT+PHjU0SkiEjXX399i20O1PaUUlq8eHGKiHTRRRe1WNbR125/3//+91O/fv1SRKRx48alGTNmpMrKyhQRaebMmenNN99ssU3Tax8RacOGDR1+zPbaXeix9Yc//CGNGTMmRUSqrq5Oxx57bDr88MNTRKRrrrkmv//3trGxsTF9+tOfzj+HMWPGpBNOOCFNnz49f4xERHrxxRcLfi5N2yxbtqzgbdpqX5OTTz651X1+4hOfyD/eEUcckY499thUUVGRhgwZkm6//fYWx+X27dvz6w8aNChNnz49HX/88fnzMpfLpUWLFrV4/P/9v/93Ouigg1JEpCFDhqSZM2em448/Po0ePTq/v3/+538u+Plu2rQpjRgxIj8NGDAg/9rtP3/FihUF75PeTzY130Y2ySbZJJsoD/Kp+TZ9IZ86e72QTy3Jp8J05v1QuTGSrgzNmTMnXnjhhbjuuuti2rRpsWHDhvjVr34V/fr1i49//ONx5513xh133NFsm8GDB8fy5cvj61//ekyYMCFefvnl2LlzZ1xxxRXxxBNPRHV1dYfbccopp8TatWvjS1/6Uhx22GHx0ksvxebNm2PSpElx9dVXxwUXXNBs/WuuuSZuuOGGOOKII+KFF16IJ554Ip544olWh2G/1+zZs+P555+PL3zhCzFy5Mj41a9+FW+++Wacdtpp8fOf/zwWLFjQ4faXyoUXXhi//OUv46yzzopdu3bFCy+8EBMnTowbb7wxVqxY0eqw8q1bt0bEu7/CdMghh3R3k/NGjRoVK1eujPPOOy8GDhwYL7/8cgwbNiwWL14cCxcubHO7ioqK+MEPfhA///nP88P5n3322diyZUsceeSR8aUvfSmWL1+ev0dGubnvvvvi7//+7+Pwww+PV155JbZu3Rqf+MQn4qmnnorp06e3WH/IkCHxgx/8IC644IIYP358bNy4MX7961/H8OHD49Of/nQ8++yzMX/+/BbbXXrppfHcc8/F/PnzY9SoUfHrX/861q1bFyNHjoxPfvKT8eCDD8aFF15YcLv37t0bb7zxRn5q+jpEQ0NDs/nv/XUlKAXZJJtKRTbJJugK+VS++dTZ64V8ylZPzaeIzr0fKje5lNr4qRKgaL7zne/ElVdeGf/wD/8Q3/jGN7JuDgDIJgDKknyiLzOSDrrBypUrY8CAAXHJJZdk3RQAiAjZBEB5kk/0ZYp00A1Wr14dF1xwQYwcOTLrpgBARMgmAMqTfKIv83VXAAAAAMiYkXQAAAAAkLFMinRLly6NU045JYYPHx6DBg2K4447Lr773e/Gvn37smgOAMgmAMqSfALoO7r9667/+I//GNdee21EREycODEGDx4ca9eujX379sXcuXPjoYcein79Cqsd7tu3L15//fUYMmRI5HK5UjYbgPdIKcXOnTtj7NixBV+3y1UxsylCPgFkpTdlU4S/nQB6i4LzKXWjVatWpVwul/r165fuv//+/PznnnsujR49OkVEuu222wre3+bNm1NEmEwmkynDafPmzaWIjG5T7GxKST6ZTCZT1lNPz6aU/O1kMplMvXFqL5+6dSTdmWeeGUuXLo3Pf/7z8S//8i/Nlt1///3xd3/3dzFixIjYsmVLVFZWtru/urq6GDp0aGzevDlqampK1Wygl6utrT3g8rq6um5qSc9SX18f48ePjx07drTbh+Ws2NkUIZ8AstJbsimidH87AZCd9vKp24p09fX1MWrUqNizZ0+sWbMmTjjhhGbLGxsbY+TIkVFfXx//8R//EaeddlpB+6ytrY26ujp/BAGd1t5XPrrxs4wepTdcg0uRTU377el9A9AT9Zbrbyn/dgIgO+3lU7fdqOHZZ5+NPXv2RP/+/eO4445rsbyysjJmzZoVERFr1qzprmYB0IfJJgDKkXwC6Ju6rUi3bt26iIiYMGFCVFRUtLrOxIkTm637Xg0NDVFfX99sAoDOKkY2RcgnAIrL304AfVO3Fem2b98eERHDhg1rc52mZU3rvtfChQujtrY2P40fP774DQWgzyhGNkXIJwCKy99OAH1TtxXpdu/eHRERVVVVba5TXV0dERG7du1qdfm1114bdXV1+Wnz5s3FbygAfUYxsilCPgFQXP52AuibWh87XQL9+/ePiIg9e/a0uU5DQ0NERAwYMKDV5dXV1fkwAoCuKkY2RcgnAIrL304AfVO3jaQr5OtChQzrBoBikU0AlCP5BNA3ddtIusmTJ0dExKZNm+Kdd95p9Qao69evb7YuAJSSbAJ6u1wu1+46KaVuaAkdkWU+FXI8FHJcAdBx3TaSbsaMGVFZWRm7d++OZ555psXyxsbGeOqppyIiYvbs2d3VLAD6MNkEQDmSTwB9U7cV6WpqauKUU06JiIi77767xfIHH3ww6uvrY8SIEfHhD3+4u5oFQB8mmwAoR/IJoG/qtiJdRMR1110XuVwu7rrrrvjRj36Un//888/HV7/61YiI+NrXvnbAXzECgGKSTQCUI/kE0PfkUjffhOKb3/xmXH/99RERMXHixBg8eHCsXbs29u3bF2eeeWY8/PDDcdBBBxW0r/r6+qitrY26urqoqakpZbOBXqy9+6q4V0/retM1uJjZFNG7+gbo2fraPel62/W3FH87tcc96QBKp7186taRdBHvfiK0ZMmS+MhHPhJvvPFG/Pa3v42jjz46br/99g7/EQQAxSCbAChH8gmgb+n2kXTF1Ns+KQOyYSRd57gGt03fAOXCSDqaGEkHkL2yG0kHAAAAADSnSAcAAAAAGavIugEAWetNX/OhZ+mur6GV29fdfMUcuo/ziY7yVVaA7BhJBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGSsIusGAEBvVVtbm3UTIiIipZR1E5opp/bkcrl21ymkvYXspycpp9eoWIr1WhdLubWnJ+lt5xsANDGSDgAAAAAypkgHAAAAABlTpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMiYIh0AAAAAZKwi6wYAQF+VUuryPnK5XBFa0vMUo+8K1Vf7uJx012tQrMcp5PjszmO4GLqzbwDIRiHXaO+LSstIOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkLGKrBsAAH1VLpfLugk9lr4rrWL1b0qp2x6ruxTynGhbT3u9AfoS1+jsGUkHAAAAABlTpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMiYIh0AAAAAZEyRDgAAAAAyVpF1A+gbcrlcu+uklLqhJQDlo5DrXiHXTyhXjt+ewesEAOXBSDoAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgY4p0AAAAAJCxiqwbQN+QUsq6CdCn5HK5Ay53TpaH9l4nyEoh1wjHLwBAcRlJBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMlaRdQMAKL6UUtZNoIcp5JjJ5XLd0JLeqaf1bzm1pdwU0jfFugZ7HQCgbzGSDgAAAAAypkgHAAAAABlTpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMhYRdYNAACyl8vlsm5Cr6Z/+5ZCXu+UUje0BADoSYykAwAAAICMKdIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkrMNFug0bNsSiRYvic5/7XEyfPj0qKioil8vFzTff3O62q1evjrPPPjtGjRoVAwYMiGnTpsWCBQti9+7dnWo8ADSRTwCUG9kEQEdUdHSDO+64I+64444OP9B9990XF110UezduzfGjRsX48ePj7Vr18Y3vvGNWLJkSSxfvjwGDhzY4f0CQIR8AqD8yCYAOqLDI+lGjhwZZ511Vtx0003xyCOPxLnnntvuNhs3box58+bF3r1749Zbb43NmzfHM888E+vWrYspU6bEU089FV/72tc69QQAIEI+AT1LLpdrd6Lnk00AdEjqoosuuihFRFqwYEGb61xyySUpItJpp53WYtnKlStTRKTKysq0devWDj12XV1diohUV1fX4XYD0DXlfg0uh3wymUwmUzaTbGpJNplMJlP2U3v5VPIfjkgpxUMPPRQREfPmzWux/MQTT4ypU6dGY2NjPPzww6VuDgBEhHwCoPzIJoC+reRFuk2bNsWWLVsiImLOnDmtrtM0f82aNaVuDgBEhHwCoPzIJoC+rcM/HNFR69ati4iI6urqGDt2bKvrTJw4sdm6bWloaIiGhob8v+vr64vUSgD6GvkEQLmRTQB9W8lH0m3fvj0iIoYOHdrmDXCHDRvWbN22LFy4MGpra/PT+PHji9tYAPoM+QRAuZFNAH1byYt0u3fvjoiIqqqqNteprq6OiIhdu3YdcF/XXntt1NXV5afNmzcXr6EA9CnyCYByI5sA+raSf921f//+ERGxZ8+eNtdpGoY9YMCAA+6ruro6H0oA0BXyCYByI5sA+raSj6RrGo69Y8eOSCm1uk7TUO2mdQGg1OQTAOVGNgH0bSUv0k2ePDki3v3E5/XXX291nfXr1zdbFwBKTT4BUG5kE0DfVvIi3YQJE2LMmDEREbFy5cpW12maP3v27FI3BwAiQj4BUH5kE0DfVvIiXS6Xi3POOSciIu6+++4Wy1etWhUvvfRSVFZWxty5c0vdHACICPkEQPmRTQB9W8mLdBERV199dVRVVcWjjz4at912W/7+Cq+88kpcfPHFERExf/78/KdGANAd5BMA5UY2AfRdudTWHUnbsHLlyjj77LPz/37zzTejoaEhBg4c2OwXhp599tkYP358/t/33ntvfPazn419+/bFuHHj4uCDD461a9dGY2NjzJw5M5544okYNGhQhxpfX18ftbW1UVdXFzU1NR3aFoCuKbdrcDnmEwDZkE0tySaA7LWXTxUd3WFjY2O88cYbLea//fbb8fbbb+f/vXfv3mbLL7zwwjjiiCNi4cKFsWrVqnjhhRdi4sSJ8clPfjK+/vWv539uHAA6Qz4BUG5kEwAd0eGRdOWk3EZxAPQlrsFtM1oBIFuyqSXZBJC99vKpW+5JBwAAAAC0TZEOAAAAADLW4XvSAQBAT1PIHV5yuVw3tAQAoHVG0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIxVZN0AAKBtKaUDLs/lct3UEspBe8dDhGOiLfoFACh3RtIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMVWTdAACgbblcLusm9FgppaLsp5xeg3JqCwAAxWUkHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgY4p0AAAAAJCxiqwbAABQCrlcLusmZCKl1O46fbVvAADKmZF0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgYxVZNwAAgOLJ5XJZNwEAgE4wkg4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZq8i6AUD3yOVy7a6TUuqGlgBNinHOFXJu07d017XcsQcAUFxG0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGSsw0W6lFKsWLEirr766vjgBz8YQ4cOjaqqqhg7dmyce+65sWzZsgNuv3r16jj77LNj1KhRMWDAgJg2bVosWLAgdu/e3eknAUDfJpsAKEfyCYAOSR30+OOPp4hIEZH69euXjjzyyDRjxow0ePDg/Pzrr7++1W1/+MMfpoMOOihFRBo3blyaMWNGqqysTBGRZs2ald56660OtaWuri5FRKqrq+vo04A+p+n8PNAEHVFO1+ByyqaU/tQ33XHOFfI4pr41dZesn6fJdKCpHLIppfLKp0KzyWQymUylm9rLpw6/k3vsscfSEUccke688860bdu2/PyGhoZ07bXX5h94yZIlzbbbsGFDqq6uThGRbr311rRv376UUkobN25MU6ZMSRGRLr300g61pZz+QAQohkIu7OWinK7B5ZRNKflDyNS5qTfKuk9NfXcqh2xKqbzySTaZTCZT9lPRi3R1dXWpsbGxzeWnn356iog0d+7cZvMvueSSFBHptNNOa7HNypUrU0SkysrKtHXr1g61pZAnCdBTFHJhLxfldA0up2xqak/WbwBMPW/qjbLuU1Pfncohm1Iqr3ySTSaTyZT91F4+dfiedDU1NVFRUdHm8lNPPTUiIn7zm9/k56WU4qGHHoqIiHnz5rXY5sQTT4ypU6dGY2NjPPzwwx1tEgB9nGwCoBzJJwA6oui/7tp0E9MBAwbk523atCm2bNkSERFz5sxpdbum+WvWrCl2kwDo42QTAOVIPgGwv7Y/1umElFI8+OCDEdE8UNatWxcREdXV1TF27NhWt504cWKzdVvT0NAQDQ0N+X/X19d3uc0A9G6lzqYI+QRAx/nbCYD3KupIukWLFsWzzz4bVVVVcfnll+fnb9++PSIihg4dGrlcrtVthw0b1mzd1ixcuDBqa2vz0/jx44vXeAB6pVJnU4R8AqDj/O0EwHsVrUj3zDPPxGWXXRYRETfffHNMmjQpv6xpGHdVVVWb21dXV0dExK5du9pc59prr426urr8tHnz5mI0HYBeqjuyKUI+AdAx/nYCoDVF+brrhg0b4qyzzordu3fHpz71qbjqqquaLe/fv39EROzZs6fNfTQNxd7/fgzvVV1dnQ8kADiQ7sqmCPkEQOH87QRAW7o8km7r1q1x6qmnxpYtW+LMM8+Me+65p8Ww7Kbh2Dt27IiUUqv7aRqq3bQuAHSWbAKgHMknAA6kS0W6bdu2xamnnhq/+93v4uSTT44HH3wwKisrW6w3efLkiHj3E5/XX3+91X2tX7++2boAfVFKqd2JA+tJ2VTI6+146DtyuVy7U0/jGM6e16B89KR8AiAbnS7Svfnmm3HGGWfE2rVrY9asWbFkyZI2h1tPmDAhxowZExERK1eubHWdpvmzZ8/ubJMA6ONkEwDlSD4BUIhOFekaGhri7LPPjjVr1sQHPvCB+MUvfhFDhgxpc/1cLhfnnHNORETcfffdLZavWrUqXnrppaisrIy5c+d2pkkA9HGyCYByJJ8AKFSHi3R79+6N888/P/7zP/8zJk2aFI899lgMHz683e2uvvrqqKqqikcffTRuu+22/ND6V155JS6++OKIiJg/f37+UyMAKJRsAqAcyScAOiKXOngjih/96EfxqU99KiLevQfCwQcf3Op6hxxySDz44IPN5t17773x2c9+Nvbt2xfjxo2Lgw8+ONauXRuNjY0xc+bMeOKJJ2LQoEEFt6W+vj5qa2ujrq4uampqOvI0AOiicroGl1M2Rfypb9pTjHtB9cT7lNF5vfH+YY7h0irkmOmNr0E5ZFNEeeVTodkEQOm0l08VHd1h0899R0SsW7cu1q1b1+p6hx12WIt5F154YRxxxBGxcOHCWLVqVbzwwgsxceLE+OQnPxlf//rX8z83DgAdIZsAKEfyCYCO6PBIunJSTqM4APoa1+C2GUlHqfTgt21tcgyXlpF0NDGSDiB77eVTp3/dFQAAAAAoDkU6AAAAAMhYh+9JBwBA8fXGr7KSvd74VVYA6K2MpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMiYIh0AAAAAZEyRDgAAAAAypkgHAAAAABmryLoBANBb1dXVRU1NTUkfI6VUlP3kcrmi7KenKVb/0XmFvAa98fjsrmOvp/VdV/ulvr4+amtri9QaoFj66rUeOspIOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkLGKrBsAAL1VbW3tAZenlLqpJUC5yeVy3fI4hVxnuqstEe23pzvbAnQf5zYUxkg6AAAAAMiYIh0AAAAAZEyRDgAAAAAypkgHAAAAABlTpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQsYqsGwAAvVVdXV3U1NRk3YzI5XJZNwG6JKXU7jq98Tgv5HmXk+5q74Eep76+Pmpra7ulHQBQbEbSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMiYIh0AAAAAZEyRDgAAAAAypkgHAAAAABmryLoBAABAdlJK7a6Ty+WKsk57j1VIW+gdivVaF3LcAfQURtIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMVWTdAADoq3K5XLvrpJS6/DjF2EcxFfK829PTnlO5tbcYuuv47U6FtLcYx2+hj1VOelp7KX/FOpcAehMj6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYqsm4ALeVyuXbXSSl1Q0sAKKW+ei3vjc+7Nz6n9pTbcy5Gewp5D1Ys5fR+r5zaAgB9mZF0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgYxVZN4CWUkpZNwEAoM8p5D1YLpcryn4A2lKsaxHQ8xhJBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkLFOFel+8pOfxBe+8IWYOXNmHHLIIVFVVRVDhw6NE088Me64447Ys2dPm9uuXr06zj777Bg1alQMGDAgpk2bFgsWLIjdu3d3+kkAgGwCoBzJJwAKlUud+I34k046KVauXBnV1dUxduzYGDFiRGzZsiVee+21iIiYOXNmPP744zF06NBm2913331x0UUXxd69e2PcuHFx8MEHx9q1a6OxsTFmzZoVy5cvj4EDBxbcjvr6+qitrY26urqoqanp6NMAoAvK7RpcLtkUUX59AxRPLpdrd51OvL3OVG96TuV4/S2XfGrqG8pfIedbIectUH7ay6dOjaSbP39+LFu2LHbu3Bnr16+Pp556Kl599dVYvXp1HHroofH000/Hdddd12ybjRs3xrx582Lv3r1x6623xubNm+OZZ56JdevWxZQpU+Kpp56Kr33ta51pDgDIJgDKknwCoGCpyB544IEUEWns2LHN5l9yySUpItJpp53WYpuVK1emiEiVlZVp69atBT9WXV1diohUV1fX5XYD0DE96RrcndmUUvf2TUS0OwF9VyHXiN50HelJ2ZRSNn87mcp/KkTWbTSZTJ2b2sunov9wxNSpUyMi4u23387PSynFQw89FBER8+bNa7HNiSeeGFOnTo3GxsZ4+OGHi90kAPo42QRAOZJPAOyv6EW61atXR0TEcccdl5+3adOm2LJlS0REzJkzp9XtmuavWbOm2E0CoI+TTQCUI/kEwP4qirGTvXv3xpYtW+KnP/1pXHPNNTFo0KBYuHBhfvm6desiIvI3S23NxIkTm63bmoaGhmhoaMj/u76+vhjNB6AX6q5sipBPABTO304AtKVLI+luv/32yOVyUVFREePHj49LL700PvrRj8aTTz4ZJ5xwQn697du3R0TE0KFD2/wVmmHDhjVbtzULFy6M2tra/DR+/PiuNB+AXqi7sylCPgHQPn87AdCeLhXpxo0bF3PmzIkTTjghRo8eHRERy5Ytix/96Eexd+/e/Hq7d++OiIiqqqo291VdXR0REbt27WpznWuvvTbq6ury0+bNm7vSfAB6oe7Opgj5BED7/O0EQHu69HXX8847L84777z8v9esWRNf+MIX4lvf+lZs27Yt/vmf/zkiIvr37x8REXv27GlzX01DsQcMGNDmOtXV1flAAoDWdHc2RcgnANrnbycA2lPUH46YPXt2LF26NKqrq+N73/tevPLKKxHxp+HYO3bsiHd/LbqlpqHaTesCQDHIJgDKkXwC4L2K/uuuY8eOjWOPPTb27dsXzz//fERETJ48OSLe/cTn9ddfb3W79evXN1sXAIpFNgFQjuQTAPsrepEuIuKdd95p9t8JEybEmDFjIiJi5cqVrW7TNH/27NmlaBIAfVxvzaaUUrtTucnlcgecgOIp1jWivfO20HPX+d9Sb80nOq9Y5xtQHIVkaXtTXV1dQY9V9CLdxo0b858CTZ8+PSLevcicc845ERFx9913t9hm1apV8dJLL0VlZWXMnTu32E0CoI+TTQCUI/kEwP46XKR7+umn44YbbsgPsd7fL37xizj99NPjnXfeiTPOOCMmTZqUX3b11VdHVVVVPProo3HbbbflP7V75ZVX4uKLL46IiPnz5+c/NQKAQskmAMqRfAKgI3Kpg9+DWb58efzFX/xFRESMGTMmDj300NizZ09s2rQpduzYERERs2bNiqVLl8bIkSObbXvvvffGZz/72di3b1+MGzcuDj744Fi7dm00NjbGzJkz44knnohBgwYV3Jb6+vqora2Nurq6qKmp6cjTAKCLyukaXE7ZFFFefVOO2vuaTjl+RRd6s2J9da6Qc7fU53+5XX/LKZ+a+gaAjinGe9NC86nDI+mmT58ed9xxR8ydOzcGDRoUL730Urz00ksxYMCAOP3002Px4sWxatWqFiETEXHhhRfGL3/5yzjrrLNi165d8cILL8TEiRPjxhtvjBUrVnT4jyAAiJBNAJQn+QRAR3R4JF05KbdPygD6EtfgtumbAzOSDsqLkXR9g5F0AJ1T1iPpAAAAAIDiUqQDAAAAgIxVZN0AAKBv8XVWKC/deU46/wE6phi3EqBrCunfYuWbkXQAAAAAkDFFOgAAAADImCIdAAAAAGRMkQ4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjFVk3AOh7crlcUfaTUirKfoC+q5DrkWsNFE9755zzDaC5Yv3tRGkV63Uykg4AAAAAMqZIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGSsIusGAH1PSinrJgBERHldj3K5XLvrFNLeYu2nL9J3paf/AKBtRtIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMVWTdAACAcpbL5dpdJ6XU5X2QvfZeRwCAUjKSDgAAAAAypkgHAAAAABlTpAMAAACAjCnSAQAAAEDGFOkAAAAAIGOKdAAAAACQMUU6AAAAAMiYIh0AAAAAZKwi6wYAAJSzlFK37COXyxVlHQAAeiYj6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYqsm4AANAz5HK5dtdJKXVDSzgQr0Hv0d4557UGgN7FSDoAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgYxVZNwAA6BlSSlk3oVcrpH9zuVw3tAQAgCwYSQcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADJWkXUDKG+5XK7ddVJK3dASAEDmZq873xt5vQGgZ2gvs+vr66O2trbd/RhJBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjinQAAAAAkDFFOgAAAADImCIdAAAAAGSsIusGdEVKKSIi6uvrM25J36b/oW9qOvebrsX8iXyCvs25nx3Z1DZ9AlA67WV/ofnUo4t0O3fujIiI8ePHZ9ySvq22tjbrJgAZ2rlzp+vAe8gn6NtcE7Mnm1pqyiYAiq/QzGkvn3KpB3+ksm/fvnj99ddjyJAhkcvlor6+PsaPHx+bN2+OmpqarJvXK+nj0tK/paV/iyulFDt37oyxY8dGv37unrA/+dS99G9p6d/S08fFI5vaJpu6nz4uLf1bWvq3uArNpx49kq5fv35x6KGHtphfU1PjICoxfVxa+re09G/xGKXQOvmUDf1bWvq39PRxccim1smm7Ojj0tK/paV/i6eQfPLxEgAAAABkTJEOAAAAADLWq4p01dXVccMNN0R1dXXWTem19HFp6d/S0r9kxbFXWvq3tPRv6eljsuC4Kz19XFr6t7T0bzZ69A9HAAAAAEBv0KtG0gEAAABAT6RIBwAAAAAZU6QDAAAAgIwp0gEAAABAxhTpAAAAACBjvaZIt3Tp0jjllFNi+PDhMWjQoDjuuOPiu9/9buzbty/rppW9DRs2xKJFi+Jzn/tcTJ8+PSoqKiKXy8XNN9/c7rarV6+Os88+O0aNGhUDBgyIadOmxYIFC2L37t3d0PLyl1KKFStWxNVXXx0f/OAHY+jQoVFVVRVjx46Nc889N5YtW3bA7fVvYX7yk5/EF77whZg5c2YccsghUVVVFUOHDo0TTzwx7rjjjtizZ0+b2+pjSkk2dZ5sKi35VHqyiXImnzpPPpWObOoe8qnMpV5g4cKFKSJSRKSJEyemY445JvXr1y9FRJo7d27au3dv1k0sa5dddlm+//afFixYcMDtfvjDH6aDDjooRUQaN25cmjFjRqqsrEwRkWbNmpXeeuutbnoG5evxxx/P92e/fv3SkUcemWbMmJEGDx6cn3/99de3uq3+LdycOXNSRKTq6ur0vve9Lx1//PFp3Lhx+T6eOXNm2r59e4vt9DGlJJu6RjaVlnwqPdlEuZJPXSOfSkc2dQ/5VN56fJFu1apVKZfLpX79+qX7778/P/+5555Lo0ePThGRbrvttgxbWP4WLFiQzjrrrHTTTTelRx55JJ177rntBs2GDRtSdXV1ioh06623pn379qWUUtq4cWOaMmVKioh06aWXdtdTKFuPPfZYOuKII9Kdd96Ztm3blp/f0NCQrr322vyFcMmSJc22078ds3jx4rRs2bK0Z8+eZvNXr16dDj300BQR6ZJLLmm2TB9TSrKp62RTacmn0pNNlCP51HXyqXRkU/eQT+WtxxfpzjjjjBQR6fOf/3yLZffdd1+KiDRixIgWByBtu+iii9oNmksuuSRFRDrttNNaLFu5cmWKiFRZWZm2bt1ayqaWvbq6utTY2Njm8tNPPz3/qeX+9G/xPPDAAyki0tixY5vN18eUkmwqPtlUXPIpW7KJrMin4pNPxSObsiefstej70lXX18fjz/+eEREzJs3r8Xy8847L2pqauKNN95o9/vrFC6lFA899FBEtN7vJ554YkydOjUaGxvj4Ycf7u7mlZWampqoqKhoc/mpp54aERG/+c1v8vP0b3FNnTo1IiLefvvt/Dx9TCnJpmw4rztGPmVLNpEF+ZQN53bhZFP25FP2enSR7tlnn409e/ZE//7947jjjmuxvLKyMmbNmhUREWvWrOnu5vVamzZtii1btkRExJw5c1pdp2m+fj+wphtsDhgwID9P/xbX6tWrIyKaXSP0MaUkm7LhvC4u+VRasoksyKdsOLeLRzaVnnzKXo8u0q1bty4iIiZMmNBmxX3ixInN1qXrmvqyuro6xo4d2+o6+r19KaV48MEHI6L5xU7/dt3evXvj1VdfjTvvvDOuuuqqGDRoUCxcuDC/XB9TSrIpG87r4pFPpSGbyJp8yoZzuzhkU+nIp/LSo4t027dvj4iIYcOGtblO07Kmdem6pr4cOnRo5HK5VtfR7+1btGhRPPvss1FVVRWXX355fr7+7bzbb789crlcVFRUxPjx4+PSSy+Nj370o/Hkk0/GCSeckF9PH1NKsikbzuvikU/FJZsoF/IpG87t4pBNxSefylOPLtI1DXetqqpqc53q6uqIiNi1a1e3tKkv0O9d98wzz8Rll10WERE333xzTJo0Kb9M/3beuHHjYs6cOXHCCSfE6NGjIyJi2bJl8aMf/Sj27t2bX08fU0qOr2zo9+KQT8UnmygXjrFs6Peuk02lIZ/KU48u0vXv3z8iIvbs2dPmOg0NDRHR/HvrdI1+75oNGzbEWWedFbt3745PfepTcdVVVzVbrn8777zzzosVK1bEmjVrYuvWrfHkk0/G4YcfHt/61rfiS1/6Un49fUwpOb6yod+7Tj6VhmyiXDjGsqHfu0Y2lY58Kk89ukhXyJDKQoZ10zFNfbljx45IKbW6jn5v3datW+PUU0+NLVu2xJlnnhn33HNPiyHD+rd4Zs+eHUuXLo3q6ur43ve+F6+88kpE6GNKSzZlw3ndNfKp+8gmsiKfsuHc7jzZ1L3kU3no0UW6yZMnR8S7vzbyzjvvtLrO+vXrm61L1zX1ZUNDQ7z++uutrqPfW9q2bVuceuqp8bvf/S5OPvnkePDBB6OysrLFevq3uMaOHRvHHnts7Nu3L55//vmI0MeUlmzKhvO68+RT95NNZEE+ZcO53TmyKRvyKXs9ukg3Y8aMqKysjN27d8czzzzTYnljY2M89dRTEfFuVZjimDBhQowZMyYiIlauXNnqOk3z9fu73nzzzTjjjDNi7dq1MWvWrFiyZEmbQ4H1b/E1vRFt+q8+ppRkUzac150jn7Ijm+hu8ikbzu2Ok03Zkk/Z6tFFupqamjjllFMiIuLuu+9usfzBBx+M+vr6GDFiRHz4wx/u5tb1XrlcLs4555yIaL3fV61aFS+99FJUVlbG3Llzu7t5ZaehoSHOPvvsWLNmTXzgAx+IX/ziFzFkyJA219e/xbVx48b8p0DTp0+PCH1MacmmbDivO04+ZUc2kQX5lA3ndsfIpmzJpzKQergVK1akXC6X+vXrl+6///78/Oeeey6NHj06RUS65ZZbMmxhz3PRRReliEgLFixoc53169enqqqqFBHp1ltvTfv27UsppbRx48Y0ZcqUFBHpi1/8Ync1uWy988476a/+6q9SRKRJkyal119/vaDt9G/h/ud//id94xvfSL/73e9aLHvkkUfS1KlTU0SkM844o9kyfUwpyabik03FJZ9KSzZRruRT8cmn4pFNpSefyl+PL9KllNLNN9+cIiJFRJo4cWI65phjUr9+/VJEpDPPPDO98847WTexrK1YsSKNGDEiP1VXV6eISAMHDmw2f9OmTc22+/73v5/v53HjxqUZM2akysrKFBFp5syZ6c0338zoGZWP+++/P39sTp48Oc2ZM6fV6ROf+ESLbfVvYZYtW5bv4zFjxqTjjz8+HXPMMWno0KH5+bNmzUp//OMfW2yrjykl2dQ1sqm05FNpySbKmXzqGvlUOrKp9ORT+esVRbqUUlqyZEn6yEc+kmpra9PAgQPT9OnT0+233y5kCrD/iXqgacOGDS22XblyZTrrrLPS8OHDU3V1dZoyZUq68cYb065du7r/iZShxYsXF9S3hx12WKvb69/2bdu2Ld1xxx1p7ty5adKkSWnw4MGpqqoqHXLIIen0009PixcvTo2NjW1ur48pJdnUebKptORTackmyp186jz5VDqyqfTkU/nLpdTGb+gCAAAAAN2iR/9wBAAAAAD0Bop0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADKmSAcAAAAAGVOkAwAAAICMKdIBAAAAQMYU6QAAAAAgY4p0AAAAAJAxRToAAAAAyJgiHQAAAABkTJEOAAAAADL2/wM27sOCzF59bAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot some example prediction results\n",
    "\n",
    "fig, axarr = plt.subplots(nrows=1, ncols=3)\n",
    "\n",
    "yhat = model.predict(all_microstates.reshape(-1, 1600))\n",
    "\n",
    "ind = 12\n",
    "axarr[0].imshow(all_microstates[ind], cmap='binary')\n",
    "axarr[0].set_title(f'Prediction: {yhat[ind]}, True Phase {true_phase[ind]}', fontsize=16)\n",
    "axarr[0].tick_params(labelsize=16)\n",
    "\n",
    "ind = 40\n",
    "axarr[1].imshow(all_microstates[ind], cmap='binary')\n",
    "axarr[1].set_title(f'Prediction: {yhat[ind]}, True Phase {true_phase[ind]}', fontsize=16)\n",
    "axarr[1].tick_params(labelsize=16)\n",
    "\n",
    "ind = -12\n",
    "axarr[2].imshow(all_microstates[ind], cmap='binary')\n",
    "axarr[2].set_title(f'Prediction: {yhat[ind]}, True Phase {true_phase[ind]}', fontsize=16)\n",
    "axarr[2].tick_params(labelsize=16)\n",
    "\n",
    "fig.subplots_adjust(right=2.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is the uncertainty in our predictions?\n",
    "\n",
    "Suppose that our input $X \\in \\mathbb{R}^N$ has some uncertainty $\\sigma_X \\in \\mathbb{R}^N$. Then, our output label $\\hat{y} \\in \\mathbb{R}$ will have some uncertainty $\\sigma_y$. We can compute this uncertainty by taking the derivative of the model with respect to $X$:\n",
    "\n",
    "$$\n",
    "\\sigma_{\\hat{y}} = \\sqrt{\\sum_i \\bigg(\\dfrac{\\partial y}{\\partial X_i}\\bigg)^2 \\sigma_{X_i}^2}\n",
    "$$\n",
    "\n",
    "For a linear model, this would just be\n",
    "\n",
    "$$\n",
    "\\sigma_{\\hat{y}} = \\sqrt{\\sum_i A_i^2 \\sigma_{X_i}^2}.\n",
    "$$\n",
    "\n",
    "Now suppose our linear model arises after we transformed the labels using the link function $g(y) = \\log(y) - \\log(1 - y)$. Then, the error in the transformed labels is given by the chain rule:\n",
    "\n",
    "$$\n",
    "\\sigma_{g(y)} = \\sqrt{\\bigg(\\dfrac{\\partial g}{\\partial y}\\bigg)^2 \\sigma_y^2} = \\sqrt{\\bigg(\\dfrac{1}{y(1 - y)}\\bigg)^2 \\sigma_y^2} = \\dfrac{\\sigma_y}{y(1 - y)}\n",
    "$$\n",
    "\n",
    "We can replace $\\sigma_{g(y)}$ with the error in the linear model, $\\sqrt{\\sum_i A_i^2 \\sigma_{X_i}^2}$, and solve for $\\sigma_{\\hat{y}}$:\n",
    "\n",
    "$$\n",
    "\\sigma_{\\hat{y}} =  \\hat{y}(1 - \\hat{y})\\sqrt{\\sum_i A_i^2 \\sigma_{X_i}^2}\n",
    "$$\n",
    "\n",
    "Because linear regression assumes that the error in measurements is independent of $y$, using standard linear regression to fit a logistic model will overweight the importance of points with $y \\approx 0.5$, because the  residuals will be larger for these points. This is a problem because these points correspond points near the phase boundary, where the model should be the most uncertain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Expected Residual')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mse_loss = lambda yhat: yhat * (1 - yhat)\n",
    "\n",
    "## Plot the error function\n",
    "yhat = np.linspace(0, 1, 100)\n",
    "plt.plot(yhat, mse_loss(yhat), linewidth=3.5)\n",
    "plt.xlabel(\"Predicted Label\")\n",
    "plt.ylabel(\"Expected Residual\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "+ Linear regression with OLS (ie, matrix methods) assumes errors are normally distributed. Without any additional information, we might assume that the measurements ($X_i$) have normally-distributed errors, but that doesn't mean that $g(X_i)$ has normal errors\n",
    "\n",
    "+ In practice, this causes certain errors to be overweighted based on the gradient of the link function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "###  Can we fit our model that more strongly weights points farther from the phase boundary?\n",
    "\n",
    "+ A good choice of loss function for binary classification is the cross-entropy loss, which is the negative log-likelihood of the data given the model:\n",
    "\n",
    "  $$\n",
    "  \\mathcal{L}(y, \\hat{y}) =\\ -y\\log {\\hat {y}}-(1-y)\\log(1-{\\hat {y}})\n",
    "  $$ \n",
    "\n",
    "  where $\\hat y_i$ is the predicted probability of class $y_i$ and $i$ indexes over the training data. Notice that this function is zero when $\\hat{y} = y_i$ and grows quickly as $\\hat{y} \\rightarrow 1 - y_i$, but it also takes intermediate values in the \"transition\" region of the logistic function. The loss of a batch of training data is the sum over the loss of each individual data point.\n",
    "\n",
    "<!-- The loss function for logistic regression is given by the cross-entropy loss, which is the negative log-likelihood of the data given the model:\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = -\\sum_i \\bigg[ y_i \\log(\\hat y_i) + (1 - y_i) \\log(1 - \\hat y_i) \\bigg]\n",
    "$$\n",
    "\n",
    "where $\\hat y_i$ is the predicted probability of class $y_i$ and $i$ indexes over the training data. -->\n",
    "\n",
    "+ + Notice that the cross-entropy loss resembles the connection function $g(.)$. With some algebra, we can show that the cross-entropy loss is equivalent to the negative log-likelihood of the data given the model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13cbb1790>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LRbNXpbCiFio1N2kiIiIrorNHhUM/AIDy8nLMmDEDa9asQYcOHZq8t6amBqWlpRpfxubtpjmhVqUWUFTJ4R8iIrIinEzbuCeffBL33XcfRowY0ey9S5Ysgbu7e8OXUqk0en3c9I2IiKyezqEf6bfPByQOKl9//TVOnjyJJUuWtOj+l19+GSUlJQ1fGRkZRq6Qm74REZGVEwTtc36cPAEb8zjaQbJ9VDIyMvD000/jt99+a/EeEA4ODnBw0A4OxsTzfoiIyKrVlgP1VZptZrLiB5AwqCQkJCA3Nxd9+vRpaFOpVNi3bx+WL1+Ompoas9i1kUM/RERk1cx4Ii0gYVC55557kJSUpNH26KOPokuXLnjxxRfNIqQAjexOy6BCRETWwown0gISBhU3Nzd0795do83FxQVeXl5a7VLSuTstt9EnIiJrYcbn/ABmsOrH3PkqtINKZlGVjjuJiIgsUHG6dhvnqOi2Z88eqUvQovR0hlwG3L7HW2pehXQFERERGVL+Ze02rwjT19EI9qg0w8HWBkpPZ422/PIalFTVSVQRERGRAekKKt6dTF9HIxhUWiDCx1WrLTWvXIJKiIiIDKzgjqAiswE6hElTiw4MKi0Q7u2i1XaFwz9ERGTpqoqAijs2e+vQEbDVXvEqFQaVFojwZY8KERFZofwU7TbvKNPX0QQGlRbQ3aPCoEJERBYu/5J2G4OK5dHdo8KhHyIisnB3zk8BAC8GFYvj5WIPhaPmSu6rBRWoV6klqoiIiMgAzHzFD8Cg0iIymUyrV6VOJXDjNyIismwc+rEe4d7awz+cp0JERBZLVQcUpmm2OXUAnL2kqacRDCotFOGrPaGW81SIiMhiFV0D1HdsXuoVBchk0tTTCAaVFmKPChERWRVdE2nNbH4KwKDSYhE+7FEhIiIronN+SqTp62gGg0oLhXg5w0au2R3GHhUiIrJYFrDiB2BQaTEHWxsoOzhptBVU1KK4slaiioiIiNpA56nJ5rXiB2BQ0Yuuwwl55g8REVkknYcRdpSklKYwqOghXOc8FQ7/EBGRhaksBCoLNNs8w8zqMMJbGFT0wB4VIiKyChYy7AMwqOglXEdQYY8KERFZHAvYkfYWBhU96FqizJU/RERkcXTuocKgYvE8Xezh7mSn0ZZeWIk6Hk5IRESWxEKWJgMMKnqRyWRavSp1KgEZhZUSVURERNQKnKNivXTPU+GEWiIishCqOqDozsMIPQEX8zqM8BYGFT3pXvnDeSpERGQhiq4C6nrNNjOdnwIwqOhN914q7FEhIiILYUErfgAGFb2xR4WIiCyaBc1PARhU9BbiqX04YWo+e1SIiMhCWNCKH4BBRW/2tnKEejprtBVW1KKogocTEhGRBbCgPVQABpVW0TVP5dKNMgkqISIi0oNaDeRe0GyT25rlYYS3MKi0Qmd/N62205nFpi+EiIhIH4VXgJoSzTbvToCNne77zQCDSiv0UnbQaktMLzZ9IURERPrIPK7dFtTH9HXogUGlFXopPbTaGFSIiMjs6QoqwX1NX4ceGFRawcfNAUpPJ422nNJqZJdUSVQRERFRC2Se0G5jULFOuoZ/TrFXhYiIzFVtJXDjnGabvSvg01maelqIQaWVYnUM/5zKKDZ5HURERC2SfQoQVJptQb0BuY0k5bQUg0or9Qrx0GrjPBUiIjJbOifSxpm+Dj0xqLRSt0AF7G00374z14tRp1JLVBEREVETLHAiLcCg0moOtjboGqjQaKuuU+NiDjd+IyIiM5SZoN0WzB4Vq6ZzmTLnqRARkbkpuQ6UZWm2eYQArr7S1KMHBpU2iNUxT4Urf4iIyOxct7xlybcwqLRBrK4dajOKJKiEiIioCRY6kRZgUGkTpacTvFzsNdpS8ypQUlknUUVEREQ6WOBGb7cwqLSBTCbTPfzDAwqJiMhcqOqArFOabTb2QEBPScrRF4NKG+k+94fDP0REZCZunAPq7zjixb8HYOsgTT16YlBpo9gQHVvpc+UPERGZCwueSAswqLRZz2B3yGSabacyiiEIgjQFERER3U7X/BQLmUgLMKi0mZujHaJ8XTXaiivrcLWgUqKKiIiIbqNzIi2DSruic5ky56kQEZHUKguBgsuabc7eQIeOkpTTGgwqBsADComIyCxdP6ndFhwHrTkLZoxBxQB0LVE+frXQ9IUQERHdLv2QdpsFDfsADCoGEeXrBoWjrUbbhZwy3CitlqgiIiIiACm7tNuU/U1fRxswqBiAjVyGQVHeWu17L+VJUA0RERGA8jwg+5Rmm50LoLxLknJai0HFQO6O8tFqY1AhIiLJXPlDuy3sbsDWXrvdjDGoGMjdnbSDyoHL+VCpuZ8KERFJ4IqOYZ/Ie0xfRxvpHVQ+//xz/PLLLw3fv/DCC/Dw8MCAAQNw7do1gxZnSQI9nLT2UympqsNpnvtDRESmplbrnp8SOcL0tbSR3kHl7bffhpOTEwDg8OHDWL58Od599114e3vjmWeeMXiBlmSIjl6VfRz+ISIiU8s5A1Tma7Z5hgOeYdLU0wZ6B5WMjAxERkYCALZu3YoHH3wQjz/+OJYsWYL9+/cbvEBLMqQz56kQEZEZSPldu80Ce1OAVgQVV1dXFBQUAAB+++03jBgh/uCOjo6oqqpq6qFWr29HTzjaab6lpzOKUVxZK1FFRETULlnJsA/QiqAycuRIzJkzB3PmzMGlS5dw3333AQDOnTuHjh07Gro+i+JoZ4O7wr002tQCcCAlv5FHEBERGVh1CZB5TLPNxh7oOEiaetpI76CyYsUKxMfHIy8vD9999x28vMQP5oSEBDz00EMGL9DS6FymfJHDP0REZCJp+wB1vWZbSDxg7yJNPW1k2/wtmjw8PLB8+XKt9sWLFxukIEs3pLMP8LNm277LeRAEATILOluBiIgslBXNTwFa0aOyY8cOHDhwoOH7FStWoFevXpg+fTqKinhicLi3C4I7OGm03SitwcUbZRJVRERE7YYgACk6NnqzwP1TbtE7qDz//PMoLS0FACQlJeHZZ5/F2LFjkZqaioULFxq8QEsjk8l0bv7G4R8iIjK6/MtASbpmm1sA4NtVmnoMQO+gkpaWhq5dxR/4u+++w7hx4/D2229j5cqV2L59u17PtWrVKvTs2RMKhQIKhQLx8fF6P4c50rmfymUGFSIiMrLGdqO14KkHegcVe3t7VFZWAgB+//13jBo1CgDg6enZ0NPSUsHBwfj3v/+NEydO4MSJExg+fDgmTpyIc+fO6VuWWRkQ4QVbueZfiuNpRaioqW/kEURERAaga35KhOUO+wCtmEw7aNAgLFy4EAMHDsSxY8ewadMmAMClS5cQHBys13ONHz9e4/u33noLq1atwpEjR9CtWzet+2tqalBTU9Pwvb7ByFTcHO3QO7QDjqUVNrTVqtQ4kJKPe7v5S1gZERFZrZpy4OoBzTaZHAgfKkk5hqJ3j8ry5ctha2uLzZs3Y9WqVQgKCgIAbN++HaNHj251ISqVCl9//TUqKioQHx+v854lS5bA3d294UupVLb69YxN1/DPL2eyJaiEiIjahUs7gPpqzbagOMDZU5p6DEQmCIKkx/smJSUhPj4e1dXVcHV1xZdffomxY8fqvFdXj4pSqURJSQkUCoWpSm6R1LxyDH9/r0abk50NEv5vBJzt9e7IIiIiatpXDwEXt2m2jXoTGPAPaeppQmlpKdzd3Vv0+d2qT0yVSoWtW7fi/PnzkMlkiI6OxsSJE2FjY6P3c3Xu3BmnTp1CcXExvvvuO8ycORN79+5tmLB7OwcHBzg4OLSmZJML93FFt0AFzmX9OTxVVafCHxdyMa5noISVERGR1akqBi7v1G7vdr/JSzE0vYNKSkoKxo4di+vXr6Nz584QBAGXLl2CUqnEL7/8goiICL2ez97evuGQw7i4OBw/fhwfffQRVq9erW9pZmd8TKBGUAGAn09nM6gQEZFhXfgFUNdptoXEA+76zR01R3rPUZk/fz4iIiKQkZGBkydPIjExEenp6QgLC8P8+fPbXJAgCBrDO5bsvh4BWm1/XMxFWXWdjruJiIha6ex32m3dHjB9HUagd4/K3r17ceTIEXh6/jk5x8vLC//+978xcOBAvZ7rlVdewZgxY6BUKlFWVoavv/4ae/bswY4dO/QtyywpPZ0RG+KBxPTihrbaejV2Jt/AA70tP+USEZEZqMgHUvdotsnkQNeJkpRjaHr3qDg4OKCsTHs7+PLyctjb2+v1XDdu3MDDDz+Mzp0745577sHRo0exY8cOjBw5Ut+yzNZ4HcM8P3P1DxERGcr5HwFBpdnWcRDg5idNPQamd4/KuHHj8Pjjj+PTTz9Fv379AABHjx7FvHnzMGHCBL2e69NPP9X35S3OfT0D8K9fknH72qp9l/JQXFkLD2f9gh0REZGWs99rt3WfbPo6jETvHpVly5YhIiIC8fHxcHR0hKOjIwYOHIjIyEgsXbrUCCVaNj+FI/p11FzDXq8WsONsjkQVERGR1SjN1t7kTW4LROvXcWDO9O5R8fDwwA8//ICUlBScP38egiCga9euDSt3SNv4mEAcvW2XWkAc/vlLvxCJKiIiIquQ/AOAO7ZDCx9m8Zu83a7VO49FRkZqhJPTp0+jd+/eUKlUTTyqfRrT3R+LfjwHlfrPv0yHruQjr6wGPm6WsS8MERGZIV2rfaxo2AdoxdBPUyTe5NZsebk6YECEl0abWgC2n+WkWiIiaqXidCDzmGabjQPQRffu7pbKoEFFZsHHSBvb+Bjt1T8/nMqSoBIiIrIKSZu126JGAo7upq/FiAwaVKhx93bzh52NZpBLuFaESze0l3oTERE1Sa0GTn6u3d7dOjZ5u12Lg0ppaWmTX7r2VqE/uTvZYUS09pr2L4+mS1ANERFZtLQ9QNFVzTYHd6DTaCmqMaoWT6b18PBocmhHEAQO/TRjev8QbL9jWfJ3JzPx4ugucLLX/0BHIiJqp058pt0WMw2wdzF9LUbW4qCye/duY9bRLgyM8EaolzOuFVQ2tJVV1+OnM1mYGqeUsDIiIrIYpdnAhW3a7X0eNX0tJtDioDJkyBBj1tEuyOUyPNQvBP/efkGjfePRdAYVIiJqmcQN2lvmh8QDfl2lqcfIOJnWxKb0CdaaVHs6oxhnr5dIVBEREVkMtUr3JFor7U0BGFRMzsvVAaO7B2i1f3mMk2qJiKgZKb8DJRmabU4drOakZF0YVCQwo7/21vk/JF5HeU29BNUQEZHFOLFWu63XDMDO0fS1mAiDigT6h3kiwkdzZnZFrQo/nLouUUVERGT2ijOAy79qt1vxsA/QiqCybt06VFZWNn8jNUomk2F6/1Ct9o1H0nkMARER6XZyPSCoNdvC7ga8rftQYL2Dyssvvwx/f3/Mnj0bhw4dMkZN7cLk3kFwsNV8+5OzS5GYUSxNQUREZL7qa4HEL7Tb4x4zfS0mpndQyczMxIYNG1BUVIRhw4ahS5cueOedd5CTk9P8g6mBh7M97uupPal2zb5UCaohIiKzdnYzUHbHQbYuPkDn+6Spx4T0Dio2NjaYMGECvv/+e2RkZODxxx/Hxo0bERISggkTJuCHH36AWq1u/okIf71Le/hnx7kcXMkrl6AaIiIyS2o1cGCpdnvvRwBbe5OXY2ptmkzr6+uLgQMHIj4+HnK5HElJSZg1axYiIiKwZ88eA5VovXqHdEC/jp4abYLAXhUiIrrNpR1A/kXNNhsHoN/fpKnHxFoVVG7cuIH//Oc/6NatG4YOHYrS0lL8/PPPSEtLQ1ZWFh544AHMnDnT0LVapXlDw7XavjuZiZySagmqISIisyIIwIEPtNt7TQfctA+6tUZ6B5Xx48dDqVRi3bp1mDt3Lq5fv46vvvoKI0aMAAA4OTnh2WefRUZGRjPPRAAwrLMvOvu5abTVqQR8djBNooqIiMhsXDsEZB7XbJPJgQH/kKYeCegdVHx9fbF3716cPXsWCxYsgKenp9Y9AQEBSEvjB21LyGQynb0qG49cQ0llnQQVERGR2Ti4VLut60TAK8LkpUhF76Dy6aefIj4+vsl7ZDIZQkO1J4qSbuN6BiLIw0mjraJWhQ1Hr0lUERERSS7nLHD5N+32gQtMXoqUWjVHZdeuXRg3bhwiIiIQGRmJcePG4ffffzd0be2GnY0ccweHabWvPZiG6jqVjkcQEZHVO/iRdlv4MCCwl8lLkZLeQWX58uUYPXo03Nzc8PTTT2P+/PlQKBQYO3Ysli9fbowa24VpfUPg6aK5zCy/vBbfJmRKVBEREUmm6Cpw9jvt9kHPmLwUqckEPfdsDwoKwssvv4ynnnpKo33FihV46623kJWVZdACm1JaWgp3d3eUlJRAoVCY7HWN5aPfL+PD3y9ptAV5OOGP54bAwdZGoqqIiMjkfloAJNxxAGFgLDB3NyCTSVKSIenz+a13j0ppaSlGjx6t1T5q1CiUlpbq+3R0m0fiQ+FsrxlIrhdX4etjXEFFRNRuFFwRz/W506BnrCKk6EvvoDJhwgRs2bJFq/2HH37A+PHjDVJUe9XBxR4z+odotf/3j8uoqKmXoCIiIjK53W8Bwh3zE707AV3GSVOPxGz1fUB0dDTeeust7Nmzp2H1z5EjR3Dw4EE8++yzWLZsWcO98+fPN1yl7cTfh0biq2MZKL8tmOSX12LtwTQ8NTxKwsqIiMjoss/onpsy/J+AvH1OAdB7jkpYmPbqFJ1PLJMhNdW4W8Fb2xyVW3TNVXFzsMW+F4ahg4v1n+tARNRubXgQSNmp2WZFc1Nu0efzW+8eFW7kZnyzB4dh/eGrKKiobWgrq6nHqr1X8MrYaAkrIyIio7l6UDukAMCI160qpOirTYcSCoIAPTtkqAVcHWzx1PBIrfbPD11FdkmVBBUREZFRCQKwa7F2e9gQIHyoycsxJ60KKuvXr0ePHj3g5OQEJycn9OzZE1988YWha2vXpvcP0dqttqZejWW7LktUERERGc2lX4GMo9rtIxaZvhYzo3dQ+eCDD/D3v/8dY8eOxTfffINNmzZh9OjRmDdvHj788ENj1NguOdja4JmRnbTavzmRiSt55RJURERERqFWAX/8S7s9ejwQ1Mf09ZiZVk2mXbx4MR555BGN9s8//xyvv/66SeewWOtk2ltUagGjl+7D5VzNYDK0sw/WzuoLWTsesyQishonPgN+vmPHWZkceOII4NNZmpqMzKgbvmVnZ2PAgAFa7QMGDEB2dra+T0dNsJHL8Ny92n9J91zMw67zuRJUREREBlVZCOx6Q7s9ZrrVhhR96R1UIiMj8c0332i1b9q0CVFR3OfD0EZ19UO/ME+t9jd+TuaBhURElu6PN4GqIs02O2dg2CvS1GOG9F6evHjxYkybNg379u3DwIEDIZPJcODAAezatUtngKG2kclkeH18N4z7736obxukSy+sxJp9qfjHPQyHREQWKeuUOOxzp7ufA9yDTF6OudK7R2Xy5Mk4duwYvL29sXXrVnz//ffw9vbGsWPHcP/99xujxnava6ACD98VqtW+Yk8KrhdzuTIRkcURBGD7CwDumCbqGQ7EP6XzIe2VXkGlrq4Ojz76KDw8PLBhwwYkJCTg5MmT2LBhA2JjY41VIwFYOLIzPO/Ylba6To23fkmWqCIiImq1M5t0L0ce8y5g62D6esyYXkHFzs5O54GEZHzuznZ4XsfE2m1JOTiYki9BRURE1CrVpcBv/6fd3mkMEDXS9PWYOb2Hfu6//35s3brVCKVQc6bGKdEz2F2r/bUfzqKmnhNriYgswu63gYo7Vm7aOACj35amHjOn92TayMhI/Otf/8KhQ4fQp08fuLi4aFznicnGYyOXYfGEbrh/5SGN9it5FfjvrhSdS5mJiMiMpB8Fjv5Pu33gfHF+Cmkx6OnJpjgx+XbWvuFbY57/9jS+TcjUaLORy/DDkwPRPUi7x4WIiMxAXTWwejCQf0mzXREMPHUcsHeWpi4J8PRkK/fy2Gj8cSFX43RllVrAC5vP4IenBsLOpk1nTRIRkTHsfUc7pADAuA/aVUjRl96faG+88QYqKyu12quqqvDGGzp21yOD83Sxx+KJ3bTak7NL8fE+0/VoERFRC2WdAg5+pN3ecxrQ6V6Tl2NJ9B76sbGxQXZ2Nnx9fTXaCwoK4OvrC5XKdJM62+vQDwAIgoB5GxLw67kbGu32NnJse3oQIn3dJKqMiIg0qOqAj4cBN5I02118gCePAc7au49bO6Oe9SMIgs7D8E6fPg1Pz/b3ZktFJpPhXxO7Q+GoOXpXq1Lj+c1noFLrlT+JiMhYDizVDikAMPY/7TKk6KvFQaVDhw7w9PSETCZDp06d4Onp2fDl7u6OkSNHYurUqcasle7gq3DEa+O1h4AS04uxZj+HgIiIJJeTBOx7V7s9egLQbZLJy7FELZ5Mu3TpUgiCgMceewyLFy+Gu/ufq0vs7e3RsWNHxMfHG6VIatzk3kH46XQW9l7K02h//7eLGBjhjR469l0hIiITqK0ENs8GVLWa7Y4eYm8KtYjec1T27t2LAQMGwM7Ozlg1tVh7nqNyu+vFVRj1wV5U1GrODwr3dsHP8wfB2V7vxV1ERNRWPz+j+9DBSf8Dej1k+nrMiD6f33oHFQBQq9VISUlBbm4u1Gq1xrW7775b36drNQaVP317IgPPbz6j1f6Xvkr8e3JPCSoiImrHLvwCfD1duz16PDD1C0DHXM/2xKj7qBw5cgTTp0/HtWvXcGfGkclkJl31Q396sE8w9lzKwy9nsjXavz6egSGdfDCmR4BElRERtTOl2cAPOk5AdgsExi9r9yFFX3qv+pk3bx7i4uJw9uxZFBYWoqioqOGrsLDQGDVSC8hkMrw9qQeCPJy0rr30fRKyiqskqIqIqJ1Rq4EtfwOq7vw8lAEPrOYqn1bQO6hcvnwZb7/9NqKjo+Hh4QF3d3eNL5KOu7MdPpzWC/I7wnpJVR0WbDqFepVa9wOJiMgwDn0EpO3Vbh+0AAgz3dQIa6J3UOnfvz9SUlKMUQsZQL8wTzw1LFKr/VhaId777aIEFRERtRNp+4BdOnZoD+wNDHvV9PVYCb3nqPzjH//As88+i5ycHPTo0UNr9U/Pnpy4KbX590Rhf0o+EtOLNdpX701FrNIDo7tzvgoRkUGVZgGbHwOEO3qu7VyAyZ8ANtKvlLVUeq/6kcu1O2FkMlnDjrXcQt88pBdU4r7/7kdZdb1Gu6uDLX54aiAifFwlqoyIyMrU1wLr7gMyj2lf41JknXh6MiHEyxlLp/XC7M9PaLSX19Tj7xsSsOWJgXBx4P4qRERt9ts/dYeUPo8ypBhAq/ZRMRfsUWne+79dxH//0J5TND4mEMv+0kvnuU1ERNRCZ74Bvp+r3R7YG3hsB2DrYPqaLIBRDiV84oknUF5e3vD9F198ofF9cXExxo4d24pyyZgWjOiEwVHeWu0/nc7CJ/vZO0ZE1GrZp4GfntZud/IEpq5nSDGQFgeV1atXo7KysuH7J598Erm5uQ3f19TU4NdffzVsddRmNnIZPvpLrM79Vd7efh6/J9+QoCoiIgtXlgN89RBQV3nHBRnw4KeAh1KSsqxRi4PKnSNEhhgxWrJkCfr27Qs3Nzf4+vpi0qRJuHiRS2gNzdPFHitn9Ia9jeZ/bkEAnv46EeezSyWqjIjIAtVWiiGl9Lr2teH/BCKGm74mK6b3PiqGtHfvXjz55JM4cuQIdu7cifr6eowaNQoVFRVSlmWVYpQeeHNSd632iloV5nx+Arll1RJURURkYdRqYOvfgayT2te6jAMGLTR9TVZO0mUfO3bs0Ph+7dq18PX1RUJCgs7DDWtqalBTU9PwfWkpewL0MbWvEpdzy7Dmjrkp14ur8Pj6BHz9+F1wtLORqDoiIguwZwmQvFW73b8n8MDHgI4tPKht9Aoqr732GpydnQEAtbW1eOuttxq2zb99/kprlZSUAAA8PXWfhbBkyRIsXry4za/Tnr00Jhpp+RX4/XyuRvupjGI8v/kMPprWC/I79+AnIiJxhc++d7XbXf2Bh74G7F1MX1M70OLlyUOHDm3RUtbdu3e3qhBBEDBx4kQUFRVh//79Ou/R1aOiVCq5PFlPFTX1mLzqEC7klGldmzMoDP8c11WCqoiIzNiVP4CNUwF1nWa7rRPw6DYgqLc0dVkoo2z4tmfPnrbW1aSnnnoKZ86cwYEDBxq9x8HBAQ4OXO7VVi4Otvh0Vl9MXH4Q+eU1Gtc+OZAGX4UDHr87QqLqiIjMTFYisOlh7ZACAPf/jyHFyNo0mHbw4EGNHo7W+sc//oEff/wRu3fvRnBwcJufj5oX5OGENY/0gYOt9l+Bt7ddwPcnMyWoiojIzBRcATY8CNSWa18b9k+g2ySTl9TetCmojBkzBtev61ie1UKCIOCpp57C999/jz/++ANhYWFtKYf0FBvSAcun94auKSkvbD6DPRdztS8QEbUXZTeAL+4HKvO1r/WZBdz9nMlLao/aFFTaupfKk08+iQ0bNuDLL7+Em5sbcnJykJOTg6qqqjY9L7XcyK5+ePv+Hlrt9WoBT2w8icT0IgmqIiKSWHUJsPFBoPia9rUu44D7PgB4BIlJSLqOatWqVSgpKcHQoUMREBDQ8LVp0yYpy2p3/tIvBAtHdtJqr6xVYeZnx3D2eokEVRERSaSmTBzuyTmjfS1kADD5E0DOrRxMpU37qKxevRp+fn6tfrwFn4dodf4xPBJ5ZTX44ojmbw+l1fV4+NOj2PS3eHTyc5OoOiIiE6mtBL78i+7TkH27Ag99BdhpH0lCxtOmHpXp06dDpVJh69atOH/+vKFqIgnIZDK8PqEbxnT317pWVFmH6WuOIjVPx2QyIiJrUVcNbJoBXNOx+tRdCfz1O8DJw+RltXd6B5WpU6di+fLlAICqqirExcVh6tSp6NmzJ7777juDF0imYyOXYelfemFIJx+ta/nlNZi+5ijSC9q+sR8RkdmprwW+nSXul3InV3/gkR8ARaDJy6JWBJV9+/Zh8ODBAIAtW7ZAEAQUFxdj2bJlePPNNw1eIJmWg60NVj/cB/HhXlrXckqr8dCaI8goZFghIitSXwtsfhS4tF37mrO3GFK8uLeUVPQOKiUlJQ1b3O/YsQOTJ0+Gs7Mz7rvvPly+fNngBZLpOdrZ4NNZcYgL7aB17XpxFaauPoy0fB4cSURWoK4a+OZh4MLP2tccPYBHtgK+XUxdFd1G76CiVCpx+PBhVFRUYMeOHRg1ahQAoKioCI6OjgYvkKThbG+LtY/2RUywu9a17JJqTFt9GCm52lvwExFZjNpK4OuHgEs7tK85KICHtwD+2ts3kGnpHVQWLFiAGTNmIDg4GIGBgRg6dCgAcUioRw/+B7Umbo52WP9Yf3QL1D6HIbesBtNWH8GFHJ5gTUQWqLYC+HKq7jkp9q7AjM3cGt9MtPhQwtudOHECGRkZGDlyJFxdXQEAv/zyCzw8PDBw4ECDF9kYfQ41otYrrqzFI58dw5lM7f1UPJzt8MVj/dFDR88LEZFZqi4BvpwGpB/WvuagEFf3KPuZvq52RJ/P71YFldupVCokJSUhNDQUHTpoz2kwJgYV0ymtrsOsz47hZHqx1jVXB1t8/EgfDIjwNn1hRET6KM8FNjwA5CRpX3P0EId72JNidPp8frdq6OfTTz8FIIaUIUOGoHfv3lAqlUY/YZmko3C0w/rZ/dGvo6fWtfKaesz67Dh2nM2WoDIiohYqTAM+HaU7pDh5AjN/YkgxQ3oHlc2bNyMmJgYA8NNPPyEtLQ0XLlzAggUL8Oqrrxq8QDIfrg62WPdYXwyI0F66XKtS44mNJ/HVsXQJKiMiakbOWeCze4GiNO1rLj7ArF+AgJ6mr4uapXdQyc/Ph7+/uHvptm3bMGXKFHTq1AmzZ89GUpKOlEpWxdneFp/N6osR0b5a19QC8PL3SVixO4XHIxCR+bh2GFg7Fii/oX3NXQk8uh3w62r6uqhF9A4qfn5+SE5Ohkqlwo4dOzBixAgAQGVlJWxseEhTe+BoZ4P//bUPJvcO1nn9vV8v4p9bz6JepTZxZUREdzj7HbB+IlCj43BVny7AY78C3lGmr4taTO+g8uijj2Lq1Kno3r07ZDIZRo4cCQA4evQounThpjjtha2NHO892BNzB4fpvL7xaDrmrD+B8pp6E1dGRARAEIADHwKbHwNUNdrXg/uKPSnuQaavjfTSqlU/mzdvRkZGBqZMmYLgYPG36s8//xweHh6YOHGiwYtsDFf9mIfVe69gyfYLOq91DVDgs1l94e/OzQCJyERU9cC254CEtbqvR9wDTPsCsHcxbV3UwKTLk6XEoGI+vj2RgZe/T0K9WvuvU4C7Iz6b1RfRAfxvRERGVl0q9qKk7NR9vec0YMJywNbetHWRBqMuTwaAvXv3Yvz48YiMjERUVBQmTJiA/fv3t6pYsg5T4pRY92g/uDnYal3LLqnG5FWHsONsjgSVEVG7UZgKfDqy8ZAy5EXg/tUMKRZG76CyYcMGjBgxAs7Ozpg/fz6eeuopODk54Z577sGXX35pjBrJQgyK8sbmvw9AoI5hnspaFeZtSMB/d13miiAiMrzUvcCa4UCejmFouS0wcSUw7BVAJjN9bdQmeg/9REdH4/HHH8czzzyj0f7BBx9gzZo1OH/+vEELbAqHfszTjdJqzP78OM5e130O0H09AvCfKTFwsucqMSJqI0EAjn8CbH8REFTa1x0U4nyU8KEmL40aZ9Shn9TUVIwfP16rfcKECUhL07GRDrU7fgpHbHo8HiO7+um8/ktSNh783yFkFFaauDIisir1NcDPC8SJs7pCikcoMPs3hhQLp3dQUSqV2LVrl1b7rl27oFQqDVIUWT4XB1us/msfPDUsUuf1c1mlGL/8APZeyjNxZURkFUoygc9GAwnrdF/vOBiYuxvwjTZpWWR42jMfm/Hss89i/vz5OHXqFAYMGACZTIYDBw5g3bp1+Oijj4xRI1kouVyG5+7tjE7+bnj+29OoqdfcAK64sg6z1h7DwhGd8OSwSMjlHDsmohZI3SOu7Kks0H097jFgzLuAjZ1JyyLjaNXy5C1btuD9999vmI8SHR2N559/3qR7qACco2JJzmQWY+76E7hRqmPjJQAjon3x/tRecHfiPyxE1AhBAA4uBXa9AQg6dr6W2QBj3gH6zTV5aaQfo+2jUl9fj7feeguPPfaYWQzzMKhYltzSajz55Ukcv1qk87rS0wkrpvdGz2AP0xZGROavshDY+gRwabvu6y4+wINrgbDBpq2LWsVok2ltbW3x3nvvQaXSMWmJqBm+Ckd8OfcuPDqwo87rGYVVmLzqED47kMYlzET0p/SjwP8GNx5SgvsCj+9lSLFSek+mHTFiBPbs2WOEUqg9sLORY9H4bvjoL73gZKe9PLlOJeCNn5Pxty8SUFJZJ0GFRGQ21GrgwFJg7RigNFP3PX3nALN+4Zk9VkzvybRjxozByy+/jLNnz6JPnz5wcdE8K2HChAkGK46s18ReQejir8C8DQlIy6/Quv5b8g2cW7YfH/2lF+I6ekpQIRFJqjwX2Pp3IOV33ddtHYFxS4FeD5m0LDI9vSfTyuWNd8LIZDKTDgtxjorlK6+pxyvfJ+HH01k6r8tlwFPDozB/eCRsbVp14gMRWZpLv4rzUSrzdV/37gxMWQf4dTVpWWQ4Rt3wTa1WN/rFuSukL1cHW3z0l15Y8kAP2Ntq/3VUC8CyXZcxZfVhpBdwgzgiq1ZXBWx7HvhyauMhJWY68PhuhpR2hL+ikuRkMhke6heCH54ciHBv3ceuJ6YXY+yy/fj2RAYn2hJZo+wzwMfDgGMf675u5yye13P/KsBe978TZJ1aHFT++OMPdO3aFaWl2ue3lJSUoFu3bti3b59Bi6P2JTpAgZ/+MQhT+gTrvF5eU4/nN5/B418kIL9c934sRGRhVPXAvvduHijYyFlxfj2Ax/cAsTNMWhqZhxYHlaVLl2Lu3Lk6x5Lc3d3xt7/9DR9++KFBi6P2x8XBFu9NicGK6b2hcNQ913tn8g2M+nAfdpzNNnF1RGRQ+ZeBz+4F/ngTUDeyyi/+KWDuLsCns2lrI7PR4qBy+vRpjB49utHro0aNQkJCgkGKIrqvZwB2LLgb/cN0r/gprKjFvA0n8cymUyiurDVxdUTUJmo1cGSVuDfK9RO673H1Bx7eAtz7FmDrYNr6yKy0OKjcuHEDdnaNb29ua2uLvDweMEeGE+jhhC/n3oUXRneGnY3uc4C2JF7HiA/2YcfZHBNXR0Stkn9Z3Bdlx0tAfZXue7qMA/5+CIgYbtrayCy1OKgEBQUhKSmp0etnzpxBQECAQYoiusVGLsMTQyPx41OD0MXfTec9+eU1mLchAU9uPIm8Ms5dITJLqnrgwIfAqoFAxhHd9zi4A/d/DEzbALh4mbY+MlstDipjx47Fa6+9hurqaq1rVVVVWLRoEcaNG2fQ4ohuiQ5Q4MenBuHJYRFo7JDlX5KyMfLDvfj+ZCZXBhGZk5wk4JN7gN9fB1SN/DIRMRx44jAQMw2Q8SR1+lOLN3y7ceMGevfuDRsbGzz11FPo3LkzZDIZzp8/jxUrVkClUuHkyZPw8/Mzds0NuOFb+3QyvQjPfXsaqXnaO9reMjjKG29O6o5QLy5jJJJMbQWw59/A4RWA0Mg+W3YuwKg3gLjZDCjtiNFOT7527Rr+/ve/49dff234jVUmk+Hee+/FypUr0bFjxzYVri8Glfaruk6Fj3Zdxsf7UqFS6/4r7GArx/x7ovD43eGw4662RKZ1+Xfgl2eA4vTG7wkfBoz/COgQarq6yCwYLajcUlRUhJSUFAiCgKioKHTo0KHVxbYFgwolZZbg+c2ncSGnrNF7Ovu54c37u6MvzwwiMr7SbOC3V4Gz3zV+j4M7MPptoNcM9qK0U0YPKuaCQYUAoLZejVV7rmDF7hTUqtSN3vdgn2C8NKYLvF251JHI4FT14q6yu98Gahv/xQGd7wPuex9QcPFFe8agQu1SSm45XtmShGNphY3eo3C0xfOju2B6vxDYNDYrl4j0k34E+OVZ4MbZxu9xCwDGvgdEjzddXWS2GFSo3VKrBXybkIG3t11ASVUjO10C6B6kwOIJ3dAnlMNBRK1WliOu5Dn9VRM3yYC+c4B7/g9wdDdVZWTmGFSo3csrq8FbvyRj66msJu+b1CsQL42Jhr+7o4kqI7IC9TXAkZXAvv8AteWN3+fXAxj3IaDsa7rayCIwqBDddPhKAV774Swu5zb+j6mzvQ2eHBaJ2YPC4GhnY8LqiCyMIACXfgV+fRkoTG38Pns3YPg/xZ4UG91ndlH7xqBCdJvaejU+O5iGj36/jKq6RvZyABDcwQkvjemC+3oEQMaVCESacs6Kq3lS9zR9X48pwKg3ATd/k5RFlolBhUiHrOIqvL3tPH4+0/Spy71DPPB/47oiNkSaZfdEZqXsBrD7TSBxAyA0vqoOvl2BMe8CYYNNVxtZLAYVoiYcSS3A4p+ScT67tMn7xscE4vlRnRHi5WyiyojMSG2FuKPswY+anofi6CEO8/R5lMM81GIMKkTNUKkFfHUsHe//dhFFlY2vDrKzkeGvd4XiH8Oj4Olib8IKiSSiqgcSvwD2LAHKbzR+n0wOxD0GDHsVcObqOdIPgwpRC5VU1uG/f1zG54evok7V+P8V3BxsMW9oBB4bGAYne064JSskCMCFX4Bdi4H8S03fGzEcGPUW4NfVNLWR1WFQIdLT1fwK/Hv7Bew4l9PkfT5uDpg/PBLT+obA3pbnB5GVSNsH7HoDyDze9H3enYF73wIiR3Dre2oTBhWiVjqaWoC3tp3HmcySJu9TejrhmRGdMLFXEHe4Jct1PUEMKM2t5HH2Boa+xHkoZDAMKkRtoFYL+CUpG+/9ehHphZVN3hvl64pnRnbC6G7+kDOwkKXIOSvOQbnwc9P32TkDA/4hfjm4maY2ahcYVIgMoLZejY1Hr+G/f6SgsKK2yXujAxR4ZkQURnb14x4sZL5yL4gBJXlr0/fJbIDej4i9KNwPhYyAQYXIgMqq6/DJ/jR8sj8VFbWNbxgHAD2D3fH0PVEY3sWXgYXMR95FYN97QNJmAM38k9/tfnElj3eUSUqj9olBhcgICsprsHLPFXxx5Bpq65vY+ArioYfzh7OHhSSWe14MKGe/R7MBJXIEMPz/gMBepqiM2jkGFSIjyiquwrJdl7E5IRP16qb/7xMdoMD84ZG4l3NYyJRyzgL73gWSf2j+3pABwPBXgY6DjF8X0U0MKkQmkF5QiWV/XMb3JzPRTF5BpK8rnhgagfExgbCz4bJmMpKM48D+/wCXdjR/b3BfcYgnfCiXGpPJMagQmVBqXjmW7bqMH09nNRtYgjs4Yd6QCDzYJ5gnNZNhCAKQthfY9x/g6v7m7w+MFQMK90IhCTGoEEngSl45VuxOwdbE680GFh83Bzw6sCP+elcoFI52pimQrItaBZz/CTi4FMhKbP7+oDhxFQ8DCpkBBhUiCV3Nr8CK3Sn4PvE6VM0kFlcHW8zoH4LHBoXBT+FoogrJotVVA6e/Ag79Fyi80vz9yv7AkBfFbe8ZUMhMMKgQmYGMwkr8b+8VfHsiE7WqplcJ2dnIMLFXEOYODkdnf26sRTpUFgInPgWOfgxU5DZ/f9gQYPCzQNjdDChkdhhUiMzIjdJqfLI/FRuPpqOymX1YAGBIJx88fnc4BkR4cWkzAYWpwOGVwKmNQF3TOyUDADqNEQOKsq/xayNqJQYVIjNUWFGLzw9dxeeHr6K4sq7Z+6MDFHhsYEdM6BUIB1tOvG1XBAG4dgg4shK4uA0Qmu6Rg8wG6D4ZGPg04N/dNDUStYHFBJV9+/bhvffeQ0JCArKzs7FlyxZMmjSpxY9nUCFLVFlbj03HM7BmXyqySqqbvd/b1R5/vSsUf70rFN6uDiaokCRTXwuc+14MKNmnm7/f1gno/TAQ/xTQIdT49REZiD6f35Ieg1lRUYGYmBg8+uijmDx5spSlEJmMs70tHh0Yhr/eFYqfTmdhzf40nM8ubfT+/PJaLP39MlbuvoLxMYGYNaAjegS7m7BiMrqyG0DCWuDEZ0D5jebvd/YC+s4F+s0FXLyNXx+RhMxm6Ecmk7FHhdolQRBwMKUAa/anYu+lvBY9pk9oB8wa0BGju/tzAzlLlpkAHP0fcG4LoG5+OBBekUD8k0DMQ4Cdk/HrIzISi+lR0VdNTQ1qamoavi8tbfy3UCJLIZPJMCjKG4OivHEhpxSf7k/DD6eymlwplHCtCAnXiuDr5oCH+oVgev8QLm+2FHVV4tk7x9e0bP8TAAgdBMQ/IU6UlTOYUvtiUT0qr7/+OhYvXqzVzh4VsjZ5ZTXYePQaNhy5hvzy2mbvt5HLcG83Pzx8V0fcFe7J1ULmqDBNHNpJ/AKoKmr+frmdOEH2rr/zoECyOhYzmfZ2LQkqunpUlEolgwpZreo6FX48nYV1B68iuYl5LLeL8HHBjP6hmNw7GO7O3PVWUqp68dydE58BV3a17DHO3kDco0DfOYCbv3HrI5KI1QaVO3GOCrUXgiDgxLUirDt4FTvO5TS74y0AONjKMa5nIKb3D0HvEA/2sphSSSZw8gvg5OdAWXbLHhMYC/SfB3S7H7Dl6i6yblY7R4WovZLJZOjb0RN9O3oiu6QKG4+k4+vj6U0OC9XUq/HdyUx8dzITnf3c8FA/Je6PZS+L0ajqgcu/AgmfAyk7m9/7BBCHd7pNAvo9Lp5mzDBJpEXSHpXy8nKkpKQAAGJjY/HBBx9g2LBh8PT0REhISLOPZ48KtWc19SrsOJuD9YevIeFaC+Y8QOxlua9HAKb2VaJ/GOeyGERhGpC4Qdw5tqW9J4pgcXin90zA1ce49RGZIYsZ+tmzZw+GDRum1T5z5kysW7eu2cczqBCJzmWVYOPRdGxNvN6ibfoBIMzbBVPigvFg72D4csWQfuqqxJOLT64Hru5v+eMi7gHiHgM6jQZs2KFN7ZfFBJW2YlAh0lRWXYcfTmVhw5FruJBT1qLH2MhlGNrJB1PigjG8ix/sbbn8VSdBALJOAqe+BJK+BapLWvY4Z29x99jeMwHPMOPWSGQhGFSI2jlBEJCYUYyvj6Xjp9PZqKprWS9LB2c7TOwVhAf7BKN7EHe/BSDuGntmkxhQ8s63/HFhQ4A+M4Eu4zg5lugODCpE1KC0ug4/nsrCV8fScS6r5ZskdvF3w+TewZgYGwhft3Y2NFRXLR4GePorIGUXILQs6MHFF4idAfR+BPAMN26NRBaMQYWIdDp7vQSbjmdg66nrKKuub9Fj5DLg7k4+eKB3MEZ19YOjnZWe5CwIQMZRMZyc3QLUtHBoRyYHokYBsQ8Dne4FbLiqiqg5DCpE1KTqOnHF0KbjGTicWtDix7k62GJ0d388EBuE/uFesJFbwaqh/Mvi0M6Zb4Diay1/nGc4EPtXIGY6oAgwXn1EVohBhYhaLKOwEt+dzMTmhExkFlW1+HH+CkdM6BWICTGB6BaosKylzmU54nk7Sd+KE2Rbyt5V3Pek11+BkLu47wlRKzGoEJHe1GoBR9IKsDkhEzvO5rR4mTMARPq6YmJMICb0CkSol4sRq2yD6hJxSXHSt0DavpZtyAYAkAFhg8UTi7tOBOzN9OcjsiAMKkTUJhU19dhxNgffJ2bi0JUC6POvRIzSA+N7BmBcz0D4u0s8Cbe2Eri0Xew9ufwboGr+gMcGXpFiOOk5DfBQGq9GonaIQYWIDCaruAo/nMrClsRMXLpR3uLHyWRAv46eGBcTiDHd/eHtaqIlunXV4gGAZ78HLm4H6ipa/lhnL/HE4p7TgKA+HNohMhIGFSIyOEEQkJxdiq2J1/HDqSzkltU0/6Cb5DIgPsIL43oG4t5u/vB0sTdscfW1QOrum+FkG1DT8mXYsHUEOo8Bev4FiLyHq3aITIBBhYiMSqUWcCS1AD+cuo7tZ3NavNQZEHfCHRDhhbE9AtoWWuprgCu7geStwIVtLV9ODIhLisOHAT2mAF3uAxz57weRKTGoEJHJVNepsOdiLn48nYVd53NRU9/SSapiaLkr3BNjuouhxcetmeGhuirgyh9A8o/isI4+4QQAlP3FoZ1u9wOuvvo9logMhkGFiCRRXlOPnck5+Ol0NvZdykO9uuX/vMhkQN9QT4zu7o/R3f0R6OEkXqgpB1J2Ask/AJd+02/OCQD49wC6PyiGkw6h+j2WiIyCQYWIJFdcWYtfz+Xg5zPZOHSlACo9QosHyvCo93lMcDiJ0OJjkKuq9Xtx365iMOl2P+AdpWflRGRsDCpEZFYKymuw41wOtiVl4/CVAujKLIHIx0ibBNwrP45+8guwlbV8CAkA4NNF3Oek2wOAbxfDFE5ERsGgQkRmq6C8Br8l38C2M1koTEvEPTiBUTYn0F1+Ve/nUvt0gbzb/UDXSQwnRBZEn89vWxPVREQEqOrglXsYD+Vvw0Nl2wG7dL2f4qy6I7ar+mGHui9u5IZiiIcPRrq7YZhrHdydubSYyNowqBCRcVUWAim/i6t0Unbpv1IHwAl1J/yqisMOdV9kCH5/Xqipxy9J2fglKRs2chn6duyAEdF+uCfaD2He3OqeyBpw6IeIDEsQgPxLwKVfgUs7gPQjgNDyc4MAQJDbosCnP3bL+mNVTmekVrvpXUa4jwvu6eKL4V38ENexA+xs5Ho/BxEZB+eoEJFp1VUD1w7cDCe/AsXX9H8OOxcgagTQZRwQNRJw6iA+tUqNY2mF+O1cDnYm30BWiZ4rgAC4Odri7k4+GN7ZF0M7+8DLVNv5E5FODCpEZHzFGeJBf5d3Aml7gbpK/Z/D1Q/oNBroPBYIHwrYNX2IoSAIOJdVKoaW87k4n63HVvk3yWRAz2APDOvsg+FdfNE90B1yOc/0ITIlBhUiMrz6GnEYJ2UncPl3IO98657Ht6sYTDqPBQJjAXnrh2Qyiyqx63wudibfwNG0AtSp9P/nzNvVHnd38sGQTj64O8oHHQx9DhERaWFQISLDKEwTTyJO2QWk7tV/V1gAkNsBYYOBTmOATvcabXfYsuo67LuUj13nb2D3xVwUVdbp/RxyGRCj9MCQm8GlZ7AHbNjbQmRwDCpE1Dq1FcDVA2IwSfkdKLzSuudx8QWiRgGdRgERwwEH/SfDtoVKLeBkehH+uJCL3RdycSGnrFXP4+Fsh0GR3rj7Zm+Lv3vTQ1NE1DIMKkTUMmo1kHNGPOjvyh/i0I5a/54IQCYO40SNEntNAnq1aUjH0K4XV+GPC7nYcyEXB6/ko7pOz11vb+rs54bBUd4Y3MkH/Tp6wsnexsCVErUPDCpE1LiSTODKbiB1tzicU5nfuudxdAci7hHDSeQIwNXHsHUaSXWdCkfTCrH7Qi52X8zFtYJWTAIGYG8rR9+OHTAo0geDo7zRNUDBSblELcSgQkR/qi4Rh3NS94gBpeBy658roJe4dDhyJBDUB7Cx/D0jr+ZXYM/FXOy5lIfDVwpQU9+63hZPF3sMiPDCoEhvDIz0htLT2cCVElkPBhWi9qyuGsg8JvaWpO0FricAQus+fOHsLc4xiRwBRAwDXH0NW6uZudXbsu9SHvZdysPl3PJWP1eolzMGRnpjYIQ34iO84MnVREQNGFSI2hNVPZB9WgwlaXvFeSb1+m+KBgCQ2wLKu8RQEjkC8O9pVnNNTC2ruAr7LuVh/+V8HEjJR0lVa+bviKIDFBgY4YWBkd7oG+YJVwfL740iai0GFSJrplYDN84CV/cDafuAa4eAGv03PmvgFQmEDwMi7wE6DjL5Ch1LoVILOJNZjP2X87HvUh4SM4qhUrfun08buQw9g90RH+6FARHe6BPagRNzqV1hUCGyJmq1uLla2n4xnFw9AFQXt/75nL2AsCFir0n4MMBDabBS25Oy6jocSS3Egct52J+Sj9S8Vuwxc5O9jRy9lB64K8IL8eFeiA3xgKMdgwtZLwYVIkumVgO5ycC1g2IwuXYIqCxo/fPZOgGhA8Qt6sOHAn7d2/VwjrFkFVfhYEo+Dl0pwIGUfOSV1bT6uext5YhVeuCucC/0D/dE75AODC5kVRhUiCyJWgXkJInB5Noh8c+qotY/n8wGCI4Dwu4We06U/QBbHsJnSoIg4HJuOQ6m5ONgSgGOphagrKa+1c9nbyNHjNId/cPE4NIntAOc7TnHhSwXgwqROauvBbJP/RlM0o+0bY4JZIB/j5vB5G6x94TzTMxKvUqNpOslOHSlAEdSC3D8amGrN50DAFu5DN2D3NE/zBP9wjwRF+oJd2c7A1ZMZFwMKkTmpKYcyDwOpB8Wg0nmCaC+qm3P6RMtTnwNu1v809nTMLWSSdTUq3AqvRiHrhTgcGoBTqUXo1bV+uAik4m75vYL80TfjmJ48VNwu38yXwwqRFIqzwMyjog9JdcOiUuHBVXbntO7kxhIOg4WvyxkF1hqmeo6FU5eK8Lh1AIcvlKA05nFrToJ+nYhns7o29ETfTt2QN8wT4R7u0Am4865ZB4YVIhMRRCAghQxlNwKJwUpbX9eny5iMAkdKH65+bX9OcliVNWqkJhehCOpBTiSWohTGW3rcQHEnXPjQjsgrmMH9An1RPcgBRxsOUGXpMGgQmQsddXi/JL0I0DGUfGrLStyAAAywK+bGEg63gwmLt6GqJasRHWdConpxTiaVoBjaYVIuFbU6q3+b7G3lSMm2B19Qj0RF9oBvUM7cPdcMhkGFSJDKc0Wt6PPOCaGkqxTrTxd+DZyW/HMnNABYigJ6Q84dTBEtdRO1NarkXS9GMfSinAsrQAnrha1aVXRLeE+LugT0gF9bgaXSB9XHrRIRsGgQtQa9bXAjSQg4/jNcHIcKElv+/PaOQPBfcVgEnKX+L/tXdr+vEQ3qdQCLuSU4nhaIY5fLcKxq4Vt2sflFjdHW8SGdEDvEA/0DumAXiEeUDhydRG1HYMKUUuUZourcTKPiStxshJbf0bO7Vx8xEASEi/+6d8TsOE/7mQ6giAgvbASx68W4cTVQhy/Wogrbdg59xaZDIj0cUXvkA7oHeqB2BD2ulDrMKgQ3am2Ulx9c/3EzXCSAJRmGua5vTsByv5iKFHeBXhFiP+iE5mRgvIaJFwrQsK1Ipy4VoSkzJI2T9AFAFcHW8Qo3RGr7IBeSg/0CvGAtys3GKSmMahQ+6ZWAwWXxV6S6wliMLlxru1LhAHA1hEI6iPu9qrsL35xDxOyQNV1Kpy9XtIQXE5eK0JBRa1Bnlvp6YRet4KL0h3dAt15BABpYFCh9qU0WwwkWSf/HMJp006vt1EEiaEkuJ/4p39PwJYrI8j6CIKAqwWVOHmtCAnpYnC5eKMMhviEsJXLEB2gQIzSHTHBHuil9EC4jytsOGTUbjGokPWqKhKDyPWTN/9MAMqyDfPcNvbiapzgvuJZOcp+gHuwYZ6byAKVVdfhdEYJTqYXITG9CIkZxSiubOOqt5tc7G3QI1gMLj2DPdAz2B3BHZy4KV07waBC1qGmHMg5c1swOQkUphru+T1CboaSvkBQHBDQk4f3ETVBEASk5VfgZHoxTmUUITG9GBdyyqBSG+ZjxMvFHj2C3cXgEuSOnkp3+LrxKABrxKBClqe2ErhxVtynJCtR/Mq/CAhtn+wHALB3BQJj/+wtCYrjbq9EBlBZW48zmSU4lVGMU+nFOJVRjJxSA6yeu8lf4SiGlyB39Ah2R48gd3hxsq7FY1Ah81ZXBeScFXd4zTol/pl73jCTXQFAZgP4dRUnvd768ukCyDmZj8gUskuqxNCSWYzTGcVIyixBRa2B/v8NIMjDCd2DFOgR5I4ewR7oEeTOXXUtDIMKmY/aij9DSfZp8cuQoQQAOnQEAnvfDCW9gYAYbqhGZEZUagEpueU4nVGM05ni14XsMtQbaMgI+DO8dA90R/cg8cvHjT0v5opBhaRRVQzkJP0ZSLJPi8uEDTV8AwAuvmIYCez9558uXoZ7fiIyieo6Fc5lleJMZjHOZJbgdGYxUg2wKd3t/BQO6B7ojm5B7ugeqEC3IHcEujtywq4ZYFAh4yvLAbLPADmnxT+zTwPF1wz7Go4e4rySwNiboSRWXC7Mf2SIrFJpdR3OXi/BmcwSJN0ML5lFVQZ9jQ7OdugW6I5ugQp0DVSgW6A7wrxduFTaxBhUyHDUKnGlTc6Zm70lN/+syDXs6zgoxCGbW8EksBfQIYyhhKidK6yoRdL1kpsBRpzvklViuMm6AOBkZ4PoALeG4NI1QIHO/m7cpM6IGFSodWorxPkjt0JJTpK4o2tdpWFfx8FdXAoc2EvctyQwVgwlcrlhX4eIrFJ+eQ3O3gwvYogpxfViw/a8yGVAhI8rugYqEB2gQNcAsQeGxwMYBoMKNU0QgNIscTnwrTCSkwQUpAAw8F8HJ08xlAT0uhlMYthTQkQGV1hRK4aXrD8DTEahYcMLAPi6OSA6QHHzyw1dAxQI83aBrQ1/0dIHgwr9qa4ayDt/M4ycFcPJjbPiDq+G5hYgbjF/K5D49xR3dmUoISIJlFTVITmrFOduhpdzWaW4klcOAy42AgDY28rRyc8V0f5igOlyM8B4OHPJdGMYVNojQQBKMoAbyTfDyDnxqyDFsEuBb/GMAPx73OwtiQH8YwBXH8O/DhGRAVXVqnA+pxTnskpx7mZ4uXijDLX1BlydeJO/whFdAtzQxV/sfenir0C4jwvs2PvCoGL1qorFuSS5N8PIjWTx+5oSw7+WjT3g21UMJf49xF4S/+6Ag5vhX4uISAJ1KjWu5JXj3PVSnM8uRXK2GGRKqgxzrtHt7GxkiPBxRRd/N3T2V9z80w0B7WzZNIOKtaivAfIu3hZKkoHcZKD0unFez9lbDCF+3f8MJd5RgI2dcV6PiMhMCYKArJJqJGfdDC9ZpTifU4prBQZeXHCTm6MtOvuJoaWLvxs6+Yk9MO7O1vnvL4OKpVGrgMI0MYTknr/5ZzJQcMU4wzYyOeAVpRlK/LoDbv6cT0JE1ITymnpcyL7V81KG89mluJhThqo6I/xbDXH4qJO/Gzr7uaLTzSAT5esGJ3vLXjrNoGKu1GpxU7S8CzcDyXlxomveJUBVY5zXdOoghhC/7oBfNzGc+HQB7JyM83pERO2MSi0gvbAS57NLxRCTIwYYQ29Wd4tMBoR4OiPK1w2d/cUAE+XrhnAfF4vZ+4VBRWpqNVCSDuReEEPJrWCSf8nwe5LcIrcDvDuJh/HdHkzYS0JEJImy6jpculGG87f1vFzMKUNZTb1RXk8uAzp6uSDqZu9LlJ8bonxdEe7jAgdb8wowDCqmolYDxVfFeSR5F/6cT2LMQAIA7kpxgqtf15t/dhOHcmy5FI6IyJwJgoDrxVW4mFOGCzeDy8WcMlzJKzfoIY23s5HLEOrpjCg/V0T5ujX8KWUPDIOKoanqxDkk+bcFkryLQP5loN44XXsAxGEb3243A0m0GEp8owFHd+O9JhERmVxtvRqp+eUNweXSDTHIGGv4CBB7YEI8nRHp64ZIX1dE+boiys8VET6ucHGwNdrrAhYWVFauXIn33nsP2dnZ6NatG5YuXYrBgwe36LEGDypqlbjcN//Sn4Ek/5I4qVVt+GVqDexdxXkjt4cR32jA1Y/DNkRE7Vh5TT0u3xCDy6Ub5Q0hJrfMSPMabwp0d0SEr9jzEunrikhf8TgBVwMFGIsJKps2bcLDDz+MlStXYuDAgVi9ejU++eQTJCcnIyQkpNnHGzyoqOqAt/wBtXHGD2HrBPh0Anyi/wwjvtHiUA4DCRERtVBRRa0YXnLLcelmeLmcW47CilqjveYnj8RhRFc/gzyXxQSV/v37o3fv3li1alVDW3R0NCZNmoQlS5Y0+3ijDP0s7ycO8bSFraM4sdU3GvDpfDOYdAE8QgG5eU1oIiIi65FfXiOGlhvluJwr9sJcvlGGosq2jwrsfX4oQr1cDFClfp/fxh2EakJtbS0SEhLw0ksvabSPGjUKhw4d0vmYmpoa1NT82d1VWlpq+MJ8Orc8qNi5iBuiNQSSLuKfDCRERCQBb1cHeLs6YECEt0Z7fnkNLt8oR0qu2PNyK8jkl7esB8beVo7gDs7GKLlZkgWV/Px8qFQq+PlpdiP5+fkhJydH52OWLFmCxYsXG7cwn87A+TvaHD3Edu9ON8PIzUCiCALkPLOBiIjM260AEx/hpdFeVFGLlLxypNwMLyl55Ui5UYaskmqN+8K9XWAjl2aKgmRB5ZY7zzYQBKHR8w5efvllLFy4sOH70tJSKJVKwxbUcTBQXXIzlNzsJXHx4RwSIiKyOh1c7NHXxRN9O3pqtFfU1OPKrQCTWw5PCU+CliyoeHt7w8bGRqv3JDc3V6uX5RYHBwc4ODgYt7DwIeIXERFRO+XiYIuewR7oGewhdSmQbNzC3t4effr0wc6dOzXad+7ciQEDBkhUFREREZkTSYd+Fi5ciIcffhhxcXGIj4/Hxx9/jPT0dMybN0/KsoiIiMhMSBpUpk2bhoKCArzxxhvIzs5G9+7dsW3bNoSGhkpZFhEREZkJyXembQvJz/ohIiIivenz+c21tURERGS2GFSIiIjIbDGoEBERkdliUCEiIiKzxaBCREREZotBhYiIiMwWgwoRERGZLQYVIiIiMluSn57cFrf2qistLZW4EiIiImqpW5/bLdlz1qKDSllZGQBAqVRKXAkRERHpq6ysDO7u7k3eY9Fb6KvVamRlZcHNzQ0ymazVz1NaWgqlUomMjAxuxW8CfL9Ni++3afH9Ni2+36ZlqPdbEASUlZUhMDAQcnnTs1AsukdFLpcjODjYYM+nUCj4F92E+H6bFt9v0+L7bVp8v03LEO93cz0pt3AyLREREZktBhUiIiIyWwwqABwcHLBo0SI4ODhIXUq7wPfbtPh+mxbfb9Pi+21aUrzfFj2ZloiIiKwbe1SIiIjIbDGoEBERkdliUCEiIiKzxaBCREREZqvdBJWVK1ciLCwMjo6O6NOnD/bv39/k/Xv37kWfPn3g6OiI8PBw/O9//zNRpdZBn/f7+++/x8iRI+Hj4wOFQoH4+Hj8+uuvJqzW8un79/uWgwcPwtbWFr169TJugVZG3/e7pqYGr776KkJDQ+Hg4ICIiAh89tlnJqrW8un7fm/cuBExMTFwdnZGQEAAHn30URQUFJioWsu2b98+jB8/HoGBgZDJZNi6dWuzjzH656XQDnz99deCnZ2dsGbNGiE5OVl4+umnBRcXF+HatWs6709NTRWcnZ2Fp59+WkhOThbWrFkj2NnZCZs3bzZx5ZZJ3/f76aefFt555x3h2LFjwqVLl4SXX35ZsLOzE06ePGniyi2Tvu/3LcXFxUJ4eLgwatQoISYmxjTFWoHWvN8TJkwQ+vfvL+zcuVNIS0sTjh49Khw8eNCEVVsufd/v/fv3C3K5XPjoo4+E1NRUYf/+/UK3bt2ESZMmmbhyy7Rt2zbh1VdfFb777jsBgLBly5Ym7zfF52W7CCr9+vUT5s2bp9HWpUsX4aWXXtJ5/wsvvCB06dJFo+1vf/ubcNdddxmtRmui7/utS9euXYXFixcbujSr1Nr3e9q0acI///lPYdGiRQwqetD3/d6+fbvg7u4uFBQUmKI8q6Pv+/3ee+8J4eHhGm3Lli0TgoODjVajtWpJUDHF56XVD/3U1tYiISEBo0aN0mgfNWoUDh06pPMxhw8f1rr/3nvvxYkTJ1BXV2e0Wq1Ba97vO6nVapSVlcHT09MYJVqV1r7fa9euxZUrV7Bo0SJjl2hVWvN+//jjj4iLi8O7776LoKAgdOrUCc899xyqqqpMUbJFa837PWDAAGRmZmLbtm0QBAE3btzA5s2bcd9995mi5HbHFJ+XFn0oYUvk5+dDpVLBz89Po93Pzw85OTk6H5OTk6Pz/vr6euTn5yMgIMBo9Vq61rzfd3r//fdRUVGBqVOnGqNEq9Ka9/vy5ct46aWXsH//ftjaWv0/AQbVmvc7NTUVBw4cgKOjI7Zs2YL8/Hw88cQTKCws5DyVZrTm/R4wYAA2btyIadOmobq6GvX19ZgwYQL++9//mqLkdscUn5dW36Nyi0wm0/heEASttubu19VOuun7ft/y1Vdf4fXXX8emTZvg6+trrPKsTkvfb5VKhenTp2Px4sXo1KmTqcqzOvr8/Var1ZDJZNi4cSP69euHsWPH4oMPPsC6devYq9JC+rzfycnJmD9/Pl577TUkJCRgx44dSEtLw7x580xRartk7M9Lq/91ytvbGzY2NlrpOzc3VysF3uLv76/zfltbW3h5eRmtVmvQmvf7lk2bNmH27Nn49ttvMWLECGOWaTX0fb/Lyspw4sQJJCYm4qmnngIgfpAKggBbW1v89ttvGD58uElqt0St+fsdEBCAoKAgjSPto6OjIQgCMjMzERUVZdSaLVlr3u8lS5Zg4MCBeP755wEAPXv2hIuLCwYPHow333yTPeIGZorPS6vvUbG3t0efPn2wc+dOjfadO3diwIABOh8THx+vdf9vv/2GuLg42NnZGa1Wa9Ca9xsQe1JmzZqFL7/8kmPJetD3/VYoFEhKSsKpU6cavubNm4fOnTvj1KlT6N+/v6lKt0it+fs9cOBAZGVloby8vKHt0qVLkMvlCA4ONmq9lq4173dlZSXkcs2PNhsbGwB//qZPhmOSz0uDTcs1Y7eWt3366adCcnKysGDBAsHFxUW4evWqIAiC8NJLLwkPP/xww/23lls988wzQnJysvDpp59yebIe9H2/v/zyS8HW1lZYsWKFkJ2d3fBVXFws1Y9gUfR9v+/EVT/60ff9LisrE4KDg4UHH3xQOHfunLB3714hKipKmDNnjlQ/gkXR9/1eu3atYGtrK6xcuVK4cuWKcODAASEuLk7o16+fVD+CRSkrKxMSExOFxMREAYDwwQcfCImJiQ3LwaX4vGwXQUUQBGHFihVCaGioYG9vL/Tu3VvYu3dvw7WZM2cKQ4YM0bh/z549QmxsrGBvby907NhRWLVqlYkrtmz6vN9DhgwRAGh9zZw50/SFWyh9/37fjkFFf/q+3+fPnxdGjBghODk5CcHBwcLChQuFyspKE1dtufR9v5ctWyZ07dpVcHJyEgICAoQZM2YImZmZJq7aMu3evbvJf4+l+LyUCQL7woiIiMg8Wf0cFSIiIrJcDCpERERkthhUiIiIyGwxqBAREZHZYlAhIiIis8WgQkRERGaLQYWIiIjMFoMKERERmS0GFSLS2+uvv45evXo1fD9r1ixMmjTJ5HVcvXoVMpkMp06dMtpr3PmztoYp6iSyVgwqRFZi1qxZkMlkkMlksLOzQ3h4OJ577jlUVFQY/bU/+ugjrFu3rkX3mvpDe+jQoViwYIFJXouIDM9W6gKIyHBGjx6NtWvXoq6uDvv378ecOXNQUVGBVatWad1bV1dnsNNN3d3dDfI8RER3Yo8KkRVxcHCAv78/lEolpk+fjhkzZmDr1q0A/hzC+OyzzxAeHg4HBwcIgoCSkhI8/vjj8PX1hUKhwPDhw3H69GmN5/33v/8NPz8/uLm5Yfbs2aiurta4fufQj1qtxjvvvIPIyEg4ODggJCQEb731FgAgLCwMABAbGwuZTIahQ4c2PG7t2rWIjo6Go6MjunTpgpUrV2q8zrFjxxAbGwtHR0fExcUhMTGxze/Ziy++iE6dOsHZ2Rnh4eH4v//7P9TV1Wndt3r1aiiVSjg7O2PKlCkoLi7WuN5c7UTUOuxRIbJiTk5OGh+6KSkp+Oabb/Ddd9/BxsYGAHDffffB09MT27Ztg7u7O1avXo177rkHly5dgqenJ7755hssWrQIK1aswODBg/HFF19g2bJlCA8Pb/R1X375ZaxZswYffvghBg0ahOzsbFy4cAGAGDb69euH33//Hd26dYO9vT0AYM2aNVi0aBGWL1+O2NhYJCYmYu7cuXBxccHMmTNRUVGBcePGYfjw4diwYQPS0tLw9NNPt/k9cnNzw7p16xAYGIikpCTMnTsXbm5ueOGFF7Tet59++gmlpaWYPXs2nnzySWzcuLFFtRNRGxj0LGYikszMmTOFiRMnNnx/9OhRwcvLS5g6daogCIKwaNEiwc7OTsjNzW24Z9euXYJCoRCqq6s1nisiIkJYvXq1IAiCEB8fL8ybN0/jev/+/YWYmBidr11aWio4ODgIa9as0VlnWlqaAEBITEzUaFcqlcKXX36p0favf/1LiI+PFwRBEFavXi14enoKFRUVDddXrVql87luN2TIEOHpp59u9Pqd3n33XaFPnz4N3y9atEiwsbERMjIyGtq2b98uyOVyITs7u0W1N/YzE1Hz2KNCZEV+/vlnuLq6or6+HnV1dZg4cSL++9//NlwPDQ2Fj49Pw/cJCQkoLy+Hl5eXxvNUVVXhypUrAIDz589j3rx5Gtfj4+Oxe/dunTWcP38eNTU1uOeee1pcd15eHjIyMjB79mzMnTu3ob2+vr5h/sv58+cRExMDZ2dnjTraavPmzVi6dClSUlJQXl6O+vp6KBQKjXtCQkIQHBys8bpqtRoXL16EjY1Ns7UTUesxqBBZkWHDhmHVqlWws7NDYGCg1mRZFxcXje/VajUCAgKwZ88erefy8PBoVQ1OTk56P0atVgMQh1D69++vce3WEJUgCK2qpylHjhzBX/7yFyxevBj33nsv3N3d8fXXX+P9999v8nEymazhz5bUTkStx6BCZEVcXFwQGRnZ4vt79+6NnJwc2NraomPHjjrviY6OxpEjR/DII480tB05cqTR54yKioKTkxN27dqFOXPmaF2/NSdFpVI1tPn5+SEoKAipqamYMWOGzuft2rUrvvjiC1RVVTWEoabqaImDBw8iNDQUr776akPbtWvXtO5LT09HVlYWAgMDAQCHDx+GXC5Hp06dWlQ7EbUegwpROzZixAjEx8dj0qRJeOedd9C5c2dkZWVh27ZtmDRpEuLi4vD0009j5syZiIuLw6BBg7Bx40acO3eu0cm0jo6OePHFF/HCCy/A3t4eAwcORF5eHs6dO4fZs2fD19cXTk5O2LFjB4KDg+Ho6Ah3d3e8/vrrmD9/PhQKBcaMGYOamhqcOHECRUVFWLhwIaZPn45XX30Vs2fPxj//+U9cvXoV//nPf1r0c+bl5Wnt2+Lv74/IyEikp6fj66+/Rt++ffHLL79gy5YtOn+mmTNn4j//+Q9KS0sxf/58TJ06Ff7+/gDQbO1E1AZST5IhIsO4czLtnRYtWqQxAfaW0tJS4R//+IcQGBgo2NnZCUqlUpgxY4aQnp7ecM9bb70leHt7C66ursLMmTOFF154odHJtIIgCCqVSnjzzTeF0NBQwc7OTggJCRHefvvthutr1qwRlEqlIJfLhSFDhjS0b9y4UejVq5dgb28vdOjQQbj77ruF77//vuH64cOHhZiYGMHe3l7o1auX8N1337VoMi0Ara9FixYJgiAIzz//vODl5SW4uroK06ZNEz788EPB3d1d631buXKlEBgYKDg6OgoPPPCAUFhYqPE6TdXOybRErScTBCMM/BIREREZADd8IyIiIrPFoEJERERmi0GFiIiIzBaDChEREZktBhUiIiIyWwwqREREZLYYVIiIiMhsMagQERGR2WJQISIiIrPFoEJERERmi0GFiIiIzNb/A4AFWIQPbob2AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loss_cross_entropy = lambda y, yhat: -y * np.log(yhat) - (1 - y) * np.log(1 - yhat)\n",
    "\n",
    "## Plot the cross-entropy loss function\n",
    "yhat = np.linspace(0.01, 0.99, 100)\n",
    "plt.plot(yhat, loss_cross_entropy(1, yhat), label='True y=1', linewidth=3.5)\n",
    "plt.plot(yhat, loss_cross_entropy(0, yhat), label='True y=0', linewidth=3.5)\n",
    "plt.xlabel(\"Predicted Label\")\n",
    "plt.ylabel(\"Cross-Entropy Loss\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classification accuracy on training set:  0.693775\n",
      "Classification accuracy on test set:  0.6649\n"
     ]
    }
   ],
   "source": [
    "## Fit logistic regression model\n",
    "from sklearn import linear_model\n",
    "\n",
    "model_logistic = linear_model.LogisticRegression()\n",
    "\n",
    "model_logistic.fit(X_train, y_train)\n",
    "\n",
    "y_pred_train = model_logistic.predict(X_train)\n",
    "y_pred_test = model_logistic.predict(X_test)\n",
    "\n",
    "# plt.plot(y_pred_train, y_train, '.')\n",
    "print(\"Classification accuracy on training set: \", np.sum(y_pred_train == y_train) / len(y_train))\n",
    "print(\"Classification accuracy on test set: \", np.sum(y_pred_test == y_test) / len(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction disordered train  0.5647\n",
      "Fraction disordered test  0.5603\n"
     ]
    }
   ],
   "source": [
    "## What would I expect?\n",
    "print(\"Fraction disordered train \", np.mean(y_train))\n",
    "print(\"Fraction disordered test \", np.mean(y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Which datapoints does logistic regression fit well?\n",
    "\n",
    "Not all datapoints are created equal. We can compute the magnetization order parameter for each microstate, which corresponds to the mean bearing of all spins. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Classification accuracy')"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "## All observed microstates and their phase labels\n",
    "X_all = dataset.X_all.copy()\n",
    "y_all = dataset.labels.copy()\n",
    "\n",
    "\n",
    "## Compute magnetization and sort datapoints by magnetization\n",
    "magnetization = np.mean(X_all, axis=1)\n",
    "sort_inds = np.argsort(magnetization)\n",
    "magnetization = magnetization[sort_inds]\n",
    "X_all = X_all[sort_inds, :]\n",
    "y_all = y_all[sort_inds]\n",
    "\n",
    "## Bin the datapoints by magnetization and compute the classifier accuracy\n",
    "## in each magntization bin\n",
    "bin_width = 1000\n",
    "all_acc = []\n",
    "all_mag = []\n",
    "for i in range(0, len(X_all) - bin_width, bin_width):\n",
    "    X_batch, y_batch = X_all[i:i+bin_width], y_all[i:i+bin_width]\n",
    "\n",
    "    y_pred = model_logistic.predict(X_batch)\n",
    "    acc = np.sum(y_pred == y_batch) / len(y_batch)\n",
    "    all_acc.append(acc)\n",
    "\n",
    "    mag = np.mean(magnetization[i:i+bin_width])\n",
    "    all_mag.append(mag)\n",
    "\n",
    "\n",
    "plt.plot(all_mag, all_acc, '.')\n",
    "plt.xlabel('Microstate magnetization')\n",
    "plt.ylabel('Classification accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting the results\n",
    "\n",
    "+ Visually, it's clear that points near the critical point are harder to classify\n",
    "\n",
    "+ In finite-size systems, the critical point is expanded to a critical region, which means that there is a finite region of parameter space where the system is critical and thus harder to classify\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Is the model just counting average spin values?\n",
    "\n",
    "+ We can inspect the weights of the trained model to see which spins are most important for classification\n",
    "\n",
    "+ We can compare this to a null model in which the weights are just independent random values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'FFT of Random Coefficients')"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(model_logistic.coef_.reshape(40, 40))\n",
    "plt.title('Fitted Coefficients')\n",
    "plt.subplot(1, 2, 2)\n",
    "coeff_null = np.random.normal(loc=np.mean(model_logistic.coef_), scale=np.std(model_logistic.coef_), size=(40, 40))\n",
    "plt.imshow(coeff_null)\n",
    "plt.title('Random Coefficients')\n",
    "\n",
    "\n",
    "fft_coeff = np.fft.fftshift(np.fft.fft2(model_logistic.coef_.reshape(40, 40)))\n",
    "fft_null = np.fft.fftshift(np.fft.fft2(coeff_null))\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(np.abs(fft_coeff))\n",
    "plt.title('FFT of Fitted Coefficients')\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(np.abs(fft_null))\n",
    "plt.title('FFT of Random Coefficients')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the model particularly weights large wavenumbers, which correspond to high-frequency fluctuations in the spin configuration. This means that the model is not just counting the average spin value, but is instead looking at the spatial correlations in the spin configuration. If two neighboring spins disagree, then the model is more likely to be disordered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error scoring for classification\n",
    "\n",
    "+ The mean squared error could work, but for labelling problems where predictions take discrete values, other error functions may be preferable\n",
    "\n",
    "+ An intuitive metric would be the accuracy: $$Acc = \\dfrac{1}{N} \\sum_i^{N} \\mathcal{I}_{y_i, \\hat{y}_i}$$ where $\\mathcal{I}$ denotes the indicator function, which returns $1$ if the prediction $\\hat{y}_i$ equals the true label $y_i$, and zero otherwise. The accuracy is the fraction of microstates that were assigned the correct phase.\n",
    "\n",
    "+ Many other metrics exist for classification problems. For example, when classes are extremely imbalanced (ie, we only have a few observations of one phase, but many of another), the accuracy gives a deceptive picture of our method's accuracy. Other metrics to consider include the balanced accuracy, as well as the true positive rate, false positive rate, and confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set:  0.692125\n",
      "Cross-entropy on training set:  53773.99945276849 \n",
      "\n",
      "Accuracy on test set:  0.659475\n",
      "Cross-entropy on test set:  940926.0217409094\n"
     ]
    }
   ],
   "source": [
    "def cross_entropy(y, y_pred):\n",
    "    y_pred = np.clip(y_pred, 1e-15, 1 - 1e-15) # clip to avoid log(0)\n",
    "    return -np.sum(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred))\n",
    "\n",
    "def accuracy(y, y_pred):\n",
    "    return np.sum(y == y_pred) / len(y)\n",
    "\n",
    "print(\"Accuracy on training set: \", accuracy(y_train, model_logistic.predict(X_train)))\n",
    "print(\"Cross-entropy on training set: \", cross_entropy(y_train, model_logistic.predict_proba(X_train)[:, 1]), \"\\n\")\n",
    "\n",
    "print(\"Accuracy on test set: \", accuracy(y_test, y_pred_test))\n",
    "print(\"Cross-entropy on test set: \", cross_entropy(y_test, y_pred_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "confusion_matrix = metrics.confusion_matrix(y_test, y_pred_test, normalize=\"true\")\n",
    "\n",
    "plt.imshow(confusion_matrix, cmap=plt.cm.Blues, interpolation=\"nearest\")\n",
    "plt.colorbar(label=\"Fraction of predictions\")\n",
    "tick_marks = np.arange(2)\n",
    "plt.xticks(tick_marks, [\"disordered\", \"ordered\"])\n",
    "plt.yticks(tick_marks, [\"disordered\", \"ordered\"])\n",
    "plt.xlabel(\"Predicted label\", fontsize=16)\n",
    "plt.ylabel(\"True label\", fontsize=16)\n",
    "plt.title(\"Confusion matrix\", fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/confusion_matrix.png\" alt=\"Confusion Matrix\" style=\"width: 500px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are four quantities describing the confusion matrix for binary classification. By convention, \"positive\" is class 1 and \"negative\" is class 0.\n",
    "+ True positive rate (TPR): $\\dfrac{TP}{TP + FN}$\n",
    "+ False positive rate (FPR): $\\dfrac{FP}{FP + TN}$\n",
    "+ True negative rate (TNR): $\\dfrac{TN}{TN + FP}$\n",
    "+ False negative rate (FNR): $\\dfrac{FN}{FN + TP}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accuracy is a deceptive metric\n",
    "\n",
    "+ A COVID paper in 2020 claimed 98% accuracy predicing whether a patient had COVID or not based on CT scans of lung tissue\n",
    "+ + This was a result of the fact that the dataset was imbalanced: 98% of the patients did not have COVID\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Composite scores account for imbalance in training data\n",
    "+ Balanced accuracy: $\\dfrac{1}{2} \\left( \\dfrac{TP}{TP + FN} + \\dfrac{TN}{TN + FP} \\right)$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "+ Precision is the fraction of positive predictions that are correct: $\\dfrac{TP}{TP + FP}$\n",
    "+ Recall is the fraction of positive samples that are correctly predicted: $\\dfrac{TP}{TP + FN}$\n",
    "+ F1 score balances precision and recall: $\\dfrac{2}{\\dfrac{1}{TPR} + \\dfrac{1}{precision}}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The ROC curve\n",
    "\n",
    "+ The receiver operating characteristic (ROC) curve is a plot of the true positive rate (TPR) against the false positive rate (FPR) for the different possible thresholds of a binary classification model.\n",
    "\n",
    "+ For example, if we have a logistic regression model that outputs a **probability** of class 1, we normally would assume that a probability greater than 0.5 would be classified as class 1. However, we could change this threshold to be 0.6, 0.7, etc. The ROC curve shows how the TPR and FPR vary as we change this threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot the ROC curve\n",
    "from sklearn.metrics import roc_curve, auc\n",
    "\n",
    "fpr, tpr, _ = roc_curve(y_test, y_pred_test)\n",
    "roc_auc = auc(fpr, tpr)\n",
    "\n",
    "plt.plot(fpr, tpr, color=\"darkorange\", lw=2, label=\"ROC curve (area = %0.2f)\" % roc_auc)\n",
    "plt.plot([0, 1], [0, 1], color=\"navy\", lw=2, linestyle=\"--\")\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel(\"False Positive Rate\")\n",
    "plt.ylabel(\"True Positive Rate\")\n",
    "plt.title(\"Receiver operating characteristic\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.gca().set_aspect(\"equal\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification vs Regression\n",
    "\n",
    "+ Regression: Given datapoints $X_i$, our labels $\\hat{y}_i$ are *continuous values* that we want to interpolate\n",
    "+ Classification: Given datapoints $X_i$, our labels $\\hat{y}_i$ are an unordered set of integers denoting distinct classes\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/classification_vs_regression.png\" alt=\"Classification vs Regression\" style=\"width: 750px;\"/>\n",
    "\n",
    "[Image Source](https://www.javatpoint.com/regression-vs-classification-in-machine-learning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Can we get error bars on our scores? \n",
    "\n",
    "### Bootstrapping\n",
    "\n",
    "+ Many parametric models have well-defined error properties. For example, if we fit a Gaussian to a point cloud, we can read off the uncertainty of the centroid because the variance is actually a fitting parameter\n",
    "\n",
    "+ We have explicit equations describing linear and logistic regression; we can imagine propagating uncertainties in the inputs directly through the model.\n",
    "\n",
    "+ For a black-box or very complex model where we only have the ability to compute input/output pairs, we need to do something more creative.\n",
    "\n",
    "### Bootstrapping: randomly subsample the input data *with replacement*, and generate new predictions. \n",
    "+ + Why replacement? For finite datasets, we treat the dataset as an empirical approximation of the data population itself. We therefore want to approximate sampling the original population, while reducing dependence on the specificities of our original distribution. For example, resampling helps us avoid outliers.\n",
    "\n",
    "+ + Compared to full error propagation, bootstrapping is usually computationally expensive but conceptually simple. Extremely useful for non-differentiable models, small training datasts, or unusual feature distributions\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/boostrap.png\" alt=\"Bootstrapping\" style=\"width: 750px;\"/>\n",
    "\n",
    "[Image Source](https://dgarcia-eu.github.io/SocialDataScience/2_SocialDynamics/025_Bootstrapping/Bootstrapping.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap 0/100\n",
      "Bootstrap 10/100\n",
      "Bootstrap 20/100\n",
      "Bootstrap 30/100\n",
      "Bootstrap 40/100\n",
      "Bootstrap 50/100\n",
      "Bootstrap 60/100\n",
      "Bootstrap 70/100\n",
      "Bootstrap 80/100\n",
      "Bootstrap 90/100\n"
     ]
    }
   ],
   "source": [
    "def bootstrap(model, X, y, n=100, verbose=False):\n",
    "    \"\"\"\n",
    "    Bootstrap the data by fitting a model n times and finding the distribution of \n",
    "    accuracies and cross-entropies.\n",
    "    \n",
    "    Args:\n",
    "        model (sklearn model): model to fit\n",
    "        X (np.array): dataset to fit\n",
    "        y (np.array): labels to fit\n",
    "        n (int): number of bootstraps\n",
    "        verbose (bool): print progress\n",
    "\n",
    "    Returns:\n",
    "        accs (np.array): array of accuracies\n",
    "        cens (np.array): array of cross-entropies\n",
    "    \"\"\"\n",
    "    accs, cens = np.zeros(n), np.zeros(n)\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "    for i in range(n):\n",
    "        if verbose and i % (n // 10) == 0:\n",
    "            print(f\"Bootstrap {i}/{n}\", flush=True)\n",
    "\n",
    "        ## Pick random subsets of the full training dataset to use for fitting a model\n",
    "        subset_inds = np.random.choice(len(X_train), len(X_train))\n",
    "        X_train_subset, y_train_subset = X_train[subset_inds], y_train[subset_inds]\n",
    "\n",
    "        #X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.5)\n",
    "        model.fit(X_train_subset, y_train_subset)\n",
    "        y_pred_test = model.predict(X_test)\n",
    "        accs[i] = accuracy(y_test, y_pred_test)\n",
    "        cens[i] = cross_entropy(y_test, y_pred_test)\n",
    "    return accs, cens\n",
    "\n",
    "accs, cens = bootstrap(model_logistic, dataset.X_all, dataset.labels, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean accuracy:  0.66441375 +/- 0.0016948976739024656 %\n",
      "Mean cross-entropy:  370911.66186704295 +/- 1873.3239372397206\n"
     ]
    },
    {
     "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": [
    "print(\"Mean accuracy: \", np.mean(accs), \"+/-\", np.std(accs), \"%\")\n",
    "print(\"Mean cross-entropy: \", np.mean(cens), \"+/-\", np.std(cens))\n",
    "\n",
    "plt.hist(accs, bins=20)\n",
    "plt.xlabel(\"Accuracy\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.title(\"Accuracy distribution\")\n",
    "plt.show()\n",
    "\n",
    "plt.hist(cens, bins=20)\n",
    "plt.xlabel(\"Cross-entropy\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.title(\"Cross-entropy distribution\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression is powerful\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/nature_aftershocks.png\" alt=\"Nature Aftershocks\" style=\"width: 750px;\"/>\n",
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/nature_aftershocks_figure.png\" alt=\"Nature Aftershocks\" style=\"width: 750px;\"/>\n",
    "\n",
    "Source for image: [DeVries et al., Nature 2018](https://www.nature.com/articles/s41586-018-0438-y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/williamgilpin/cphy/main/resources/earthquake_response.png\" alt=\"Nature Aftershocks Reply\" style=\"width: 750px;\"/>\n",
    "\n",
    "Source for image: [Mignan & Broccardo, Nature 2019](https://www.nature.com/articles/s41586-019-1582-8)"
   ]
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