{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Quasi-Bayesian Mixture Estimation" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Bayesian RLS (regression with a known variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume a row regressor $x_{t} \\in \\mathbb{R}^{n}$, determining via the column regression coefficients vector $\\beta \\in\\mathbb{R}^{k}$ the scalar regressand $y_{t}\\in\\mathbb{R}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Model**\n", "$$\n", "y_{t}|x_{t}, \\beta \\sim \\mathcal{N}(x_{t}\\beta, \\sigma^{2})\n", "$$\n", "\n", "with a pdf\n", "\n", "$$\n", "\\begin{align*}\n", "p(y_{t}|x_{t}, \\beta) &\\propto \\exp\\left\\{-\\frac{1}{2\\sigma^{2}} (y_{t} - x_{t}\\beta)^2\\right\\} \\\\\n", "&= \\exp\\left\\{ -\\frac{1}{2} \\left[ \\sigma^{-2}y_{t}^{\\intercal}y_{t} \n", "+ \\operatorname{Tr} \n", "\\left(\n", "\\begin{bmatrix}\n", "\\beta\\beta^{\\intercal}\\\\\n", "-2\\beta\n", "\\end{bmatrix}^{\\intercal}\n", "\\begin{bmatrix}\n", "x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\\\\n", "x_{t}^{\\intercal} y_{t} \\sigma^{-2}\n", "\\end{bmatrix}\n", "\\right)\n", "\\right] \\right\\}\n", "\\end{align*}\n", "$$\n", "\n", "where $\\eta = \\begin{bmatrix}\n", "\\beta\\beta^{\\intercal}\\\\\n", "-2\\beta\n", "\\end{bmatrix}^{\\intercal}$ and\n", "$T = \\begin{bmatrix}\n", "x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\\\\n", "x_{t}^{\\intercal} y_{t} \\sigma^{-2}\n", "\\end{bmatrix}$\n", "are the natural parameter and the sufficient statistic, respectively.\n", "\n", "**Prior**\n", "$$\n", "\\beta|V_{t-1} \\sim \\mathcal{N}(\\beta_{t-1}, V_{t-1})\n", "$$\n", "\n", "with a pdf\n", "\n", "$$\n", "\\begin{align*}\n", "\\pi(\\beta|V_{t-1}) &\\propto \\exp\\left\\{-\\frac{1}{2} (\\beta - \\beta_{t-1})^{\\intercal} V_{t-1}^{-1} (\\beta - \\beta_{t-1})\\right\\} \\\\\n", "&= \\exp\\left\\{ -\\frac{1}{2} \\left[ \\beta_{t-1}^{\\intercal}V_{t-1}^{-1}\\beta_{t-1}\n", "+ \\operatorname{Tr} \n", "\\left(\n", "\\begin{bmatrix}\n", "\\beta\\beta^{\\intercal}\\\\\n", "-2\\beta\n", "\\end{bmatrix}^{\\intercal}\n", "\\begin{bmatrix}\n", "V_{t-1}^{-1} \\\\\n", "V_{t-1}^{-1} \\beta_{t-1}\n", "\\end{bmatrix}\n", "\\right)\n", "\\right] \\right\\}\n", "\\end{align*}\n", "$$\n", "\n", "where $\\beta_{t-1}^{\\intercal}V_{t-1}^{-1}\\beta_{t-1}$ can be absorbed into the normalization constant.\n", "\n", "**Posterior**\n", "$$\n", "\\beta|V_{t} \\sim \\mathcal{N}(\\beta_{t}, V_{t}) \\qquad\\text{where}\\qquad\n", "V_{t}^{-1} = V_{t-1}^{-1} + x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\qquad \\text{and}\\qquad\n", "\\beta_{t} = (x_{t}^{\\intercal} x_{t} \\sigma^{-2} + V_{t-1}^{-1})^{-1} (x_{t}^{\\intercal} y_{t} \\sigma^{-2} + V_{t-1}^{-1}\\beta_{t-1})\n", "$$\n", "\n", "**Note:** *a popular choice for a one-shot estimation is the prior $\\beta|\\sigma^{2} \\sim \\mathcal{N}(\\beta_{0}, \\sigma^{2}V_{0})$ with $V_{0} = (x_{0}^{\\intercal}x_{0})^{-1}$. Notice, that putting then the factors $\\sigma^{2}$ cancel in the posterior estimation of $\\beta$ and the well-known formulae $\\hat{\\beta}_{t} = (x_{t}^{\\intercal} x_{t} + V_{0}^{-1})^{-1} (x_{t}^{\\intercal} y_{t} + V_{0}^{-1}\\beta_{t-1})$ are recovered. However, we will need the 'weighting' factor $\\sigma^{2}$ for the diffusion. Note also the coincidence of these formulae with the measurement update of the Kalman filter: this is where this filter and the recursive least squares coincide.*\n", "\n", "\n", "**Predictive**\n", "$$\n", "y_{t+1}|X_{t}, Y_{t} \\sim \\mathcal{N}(x_{t}\\beta_{t}, \\sigma^{2})\n", "$$" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Quasi-Bayesian mixture estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a mixture of $K$ RLS models in the form\n", "$$\n", "p(y_{t}|x_{t}, \\phi, \\beta) = \\sum_{k=1}^{K} p_{k}(y_{t}|x_{t}, \\beta_{k})\n", "$$\n", "where the unknown parameters $\\phi = [\\phi_{1},\\ldots,\\phi_{K}]$ are the component weights and $\\beta = [\\beta_{1},\\ldots,\\beta_{K}]$ are the regression coefficients. Their estimation exploits the principles described in the paper, Section II. In particular, the estimation of $\\beta$ employs the prior, posterior and predictive pdfs given above." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Diffusion quasi-Bayesian mixture estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The diffusion quasi-Bayesian estimation presented in the paper is applied to the mixture of two RLS models with unknown regression coefficients.\n", "\n", "* Adaptation phase - the node $i$ incorporates the measurements $x_{t}^{[j]}$ and $x_{t}^{[j]}$ of its neighborhood $j\\in\\mathcal{N}_{i}$. It exploits their noise variances $(\\sigma^{2})^{[j]}$ for evaluation of the posterior pdf, see the theory above.\n", "* Combination phase - the node $i$ forms a convex combination of the posterior sufficient statistics - c.f. the theory above." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Python code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we give the python code producing the results in the paper. First, some initializations:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np # numerical package\n", "from scipy.stats import norm # normal distribution from scientific package\n", "from copy import deepcopy # deepcopy of python data types\n", "import networkx as nx # graph package\n", "from prettytable import PrettyTable # pretty printing of tables\n", "\n", "np.set_printoptions(precision=4, suppress=True) # printing: n-digits precision, no scientific format\n", "seed = 1234 # seed for reproducible results" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Setting the diffusion network:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "nnodes = 25 # number of network nodes\n", "mode = 'null' # Diff. mode: 'ATC' - adapt-then-combine, 'null' for no coop.\n", "edge_prob = .2 # probability of an edge\n", "\n", "if mode == 'ATC':\n", " # We generate a network of nnodes, interconnected with probability 0.2\n", " G = nx.binomial_graph(nnodes, edge_prob, seed=seed)\n", " adjacency_matrix = nx.adjacency_matrix(G)\n", " np.fill_diagonal(adjacency_matrix, 1) # The nodes are self-adjacent\n", "elif mode == 'null':\n", " adjacency_matrix = np.eye(nnodes) \n", " G = nx.from_numpy_matrix(adjacency_matrix)\n", "\n", "# Plot the network (first node is 1, not 0)\n", "G = nx.convert_node_labels_to_integers(G, first_label=1)\n", "nx.draw(G, node_color='yellow')\n", " \n", "# Adapt weights\n", "if mode == 'ATC': \n", " # Measurements are shared \n", " adapt_weights = adjacency_matrix.copy()\n", "elif mode == 'null': \n", " # Measurements are not shared\n", " adapt_weights = np.eye(nnodes)\n", "\n", "# Combine weights are always uniform\n", "combine_weights = adjacency_matrix.copy() \n", "np.fill_diagonal(combine_weights, 1)\n", "normsum = combine_weights.sum(axis=1)\n", "combine_weights = combine_weights / normsum\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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bN+5jb29vsrhLKul2LmJu3rxJnz6dWbw4CT+/ghMvqMcCfvVVBt7ed+nduyPp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\na1e5fv26gSMTQoinU7VqVa5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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Simulation of data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: `beta0` and `beta1` below correspond to $\\beta_2$ and $\\beta_1$ in the paper. That is, indexing in the code runs from 0 and the components are swapped wrt the paper." ] }, { "cell_type": "code", "collapsed": false, "input": [ "ndat = 600 # number of simulated data\n", "beta0 = np.array([.3, 1.3, -.9]) # coeffs. of the 1st component\n", "beta1 = np.array([.3, 0., .9]) # coeffs. of the 2nd component\n", "np.random.seed(seed)\n", "X = np.random.normal(size=(ndat, 3)) # regressors" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "Y1 = np.dot(X, beta0) # simulated data with 1st component\n", "Y2 = np.dot(X, beta1) # simulated data with 2nd component\n", "Y = Y2 # final data consist of 2nd component, later 1st component will replace some points\n", "\n", "# time indices where the 1st component will occur\n", "beta0_set = set(range(50, 70)) \\\n", " | set(range(120, 130)) \\\n", " | set(range(170, 190)) \\\n", " | set(range(210, 220)) \\\n", " | set(range(240, 250)) \\\n", " | set(range(300, 315)) \\\n", " | set(range(400, 420)) \\\n", " | set(range(510, 530))\n", "beta0_tuple = list(beta0_set)\n", "Y[np.array(beta0_tuple)] = Y1[np.array(beta0_tuple)] # here we do the replacement\n", "\n", "# Measurements of nodes\n", "YY = Y[:,newaxis] * np.ones((ndat, nnodes))\n", "noise_std_array = np.zeros(nnodes)\n", "for i in range(nnodes):\n", " noise_std = .05 * (i+1)\n", " np.random.seed(seed)\n", " YY[:,i] += np.random.normal(scale=noise_std, size=(ndat))\n", " noise_std_array[i] = noise_std" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Objects for RLS modelling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components will be represented by the `QB_RLS_component` class. It's documented in the code..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "class QB_RLS_component():\n", " def __init__(self, prior_invV, prior_beta, noise_std, kappa):\n", " \"\"\"Constructor\"\"\"\n", " self.prior_invV = prior_invV # sufficient statistic 1\n", " self.beta = prior_beta # prior/posterior mean\n", " self.prior_invV_beta = self.prior_invV.dot(self.beta) # sufficient statistic 2\n", " self.noise_std = noise_std # known noise st.dev.\n", " self.kappa = kappa # component's Dirichlet hyperparameter \n", " self.log_beta = [] # list for logging the beta estimates\n", " \n", " def predictive_loglikelihood(self, xt, yt, noise_std): \n", " \"\"\"Predictive loglikelihood\"\"\"\n", " mean = np.dot(xt, self.beta)\n", " return norm.logpdf(yt, loc=mean, scale=noise_std)\n", " \n", " def update(self, xt, yt, w, noise_std=None):\n", " \"\"\"Update of component's hyperparameters\"\"\"\n", " if noise_std is None: # Use own noise st. dev. if unset\n", " noise_std = self.noise_std\n", " xTx = np.outer(xt, xt)\n", " xTy = xt * yt\n", " self.prior_invV += w * xTx / noise_std**2 # update of suff. stat. 1\n", " self.prior_invV_beta += w * xTy / noise_std**2 # update of suff. stat. 2\n", " self.beta = np.linalg.inv(self.prior_invV).dot(self.prior_invV_beta) # calculate posterior mean (beta)\n", " self.kappa += w # update Dirichlet hyperparameter\n", " \n", " def savelog(self):\n", " \"\"\"Logging of the beta estimate\"\"\"\n", " self.log_beta.append(self.beta.copy())" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next is the class `QB_RLS`, for quasi-Bayesian estimation of a mixture of RLS models." ] }, { "cell_type": "code", "collapsed": false, "input": [ "class QB_RLS():\n", " def __init__(self, components):\n", " \"\"\"Constructor\"\"\"\n", " self.components = components # list of 'QB_RLS_component' components\n", " self.ncomponents = len(components) # number of components\n", " self.log_w = [] # list for logging components' weights\n", " \n", " def update(self, xt, yt, weight=1., noise_std=None):\n", " \"\"\"Mixture update\"\"\"\n", " if noise_std is None:\n", " noise_std = self.noise_std\n", " predictive_likelihoods = np.zeros(self.ncomponents)\n", " Dirichlet_hyperparams = np.array([comp.kappa for comp in self.components])\n", " comps_weights = Dirichlet_hyperparams/Dirichlet_hyperparams.sum()\n", " \n", " predictive_liks = np.array([comp.predictive_loglikelihood(xt, yt, noise_std) for comp in self.components])\n", " w = np.log(comps_weights) + predictive_liks\n", " w -= w.max()\n", " w = np.exp(w)\n", " w /= w.sum()\n", " w *= weight\n", " \n", " for k in range(self.ncomponents):\n", " self.components[k].update(xt, yt, w[k], noise_std)\n", " self.log_w.append(w)\n", "\n", " @property\n", " def statistics(self):\n", " \"\"\"Statistics of the mixtures' components\"\"\"\n", " statistics = []\n", " for component in self.components:\n", " statistics.append({'invV': component.prior_invV.copy(),\n", " 'invV_beta': component.prior_invV_beta.copy(),\n", " 'kappa': component.kappa})\n", " return statistics\n", " \n", " def savelog(self):\n", " \"\"\"Force logging\"\"\"\n", " for component in self.components:\n", " component.savelog()\n", " \n", " def adapt(self, xt, yt_array, noise_std_array, adapt_weights):\n", " \"\"\"Diffusion adapt step\"\"\"\n", " for i in range(yt_array.shape[0]):\n", " if adapt_weights[i] != 0:\n", " self.update(xt, yt_array[i], adapt_weights[i], noise_std_array[i])\n", " \n", " def combine(self, statistics, combine_weights):\n", " \"\"\"Diffusion combine step\"\"\"\n", " for k in range(self.ncomponents):\n", " self.components[k].prior_invV *= 0\n", " self.components[k].prior_invV_beta *= 0\n", " self.components[k].kappa = 0.\n", " for i in range(len(statistics)):\n", " if combine_weights[i] != 0:\n", " self.components[k].prior_invV += combine_weights[i] * statistics[i][k]['invV']\n", " self.components[k].prior_invV_beta += combine_weights[i] * statistics[i][k]['invV_beta']\n", " self.components[k].kappa += combine_weights[i] * statistics[i][k]['kappa']\n", " self.components[k].beta = np.linalg.inv(self.components[k].prior_invV).dot(self.components[k].prior_invV_beta)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Estimation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "prior_invV = np.eye(3) * 1.\n", "prior_beta0 = np.array([0.5, 1., -1.])\n", "prior_beta1 = np.array([0.5, 0., 1.])\n", "\n", "diffnet = []\n", "\n", "for i in range(nnodes):\n", " components = []\n", " components.append(QB_RLS_component(prior_invV.copy(), prior_beta0.copy(), noise_std_array[i], 10.))\n", " components.append(QB_RLS_component(prior_invV.copy(), prior_beta1.copy(), noise_std_array[i], 10.))\n", " diffnet.append(QB_RLS(deepcopy(components)))\n", "\n", "print('Progress (out of {0}):'.format(ndat))\n", "for t in range(ndat):\n", " if t%10 == 0:\n", " print t,\n", " xt = X[t]\n", " yt_array = YY[t]\n", " \n", " # ADAPT\n", " for i in range(nnodes):\n", " diffnet[i].adapt(xt, yt_array, noise_std_array, np.ravel(adapt_weights[i]))\n", " \n", " # COMBINE\n", " if mode == 'ATC':\n", " diff_statistics = [node.statistics for node in diffnet]\n", " for i in range(nnodes):\n", " diffnet[i].combine(diff_statistics, np.ravel(combine_weights[i]))\n", " \n", " for node in diffnet:\n", " node.savelog()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Progress (out of 600):\n", "0 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "10 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "20 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "30 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "40 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ 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"stream": "stdout", "text": [ "490 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "500 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "510 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "520 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "530 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "540 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "550 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "560 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "570 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "580 " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "590\n" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# Printing table of final estimates\n", "est_tab = PrettyTable([\"Node\", \"1st component\", \"2nd component\"])\n", "for node in range(nnodes):\n", " est_tab.add_row([node+1, diffnet[node].components[0].beta, diffnet[node].components[1].beta])\n", "print est_tab\n", "\n", "# Plotting the evolution at nodes (note: python indexes from 0!)\n", "node_to_plot = 10\n", "\n", "plt.figure(figsize=(14,10)) \n", "plt.subplot(4,1,1)\n", "plt.title('Evolution of data')\n", "for tx in beta0_tuple:\n", " plt.axvline(tx, color='gainsboro')\n", "plt.plot(YY[:,node_to_plot])\n", "plt.hold(True)\n", "plt.grid(True)\n", "\n", "plt.subplot(4,1,2)\n", "plt.title('Evolution of weights (probabilities) of beta0')\n", "plt.fill_between(range(2, 2+len(diffnet[node_to_plot].log_w)), \n", " np.array(diffnet[node_to_plot].log_w)[:,0], np.zeros(len(diffnet[node_to_plot].log_w)), color='red')\n", "plt.hold(True)\n", "plt.grid(True)\n", "plt.xlim(xmax=len(diffnet[node_to_plot].log_w))\n", "\n", "plt.subplot(4,1,3)\n", "plt.plot(diffnet[node_to_plot].components[0].log_beta)\n", "plt.title('Estimates of beta0')\n", "plt.grid(True)\n", "\n", "plt.subplot(4,1,4)\n", "plt.plot(diffnet[node_to_plot].components[1].log_beta)\n", "plt.title('Estimates of beta1')\n", "plt.grid(True)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "+------+---------------------------+---------------------------+\n", "| Node | 1st component | 2nd component |\n", "+------+---------------------------+---------------------------+\n", "| 1 | [ 0.3052 1.2978 -0.896 ] | [ 0.3018 -0.0007 0.8978] |\n", "| 2 | [ 0.3136 1.2948 -0.8922] | [ 0.3042 -0.0021 0.8953] |\n", "| 3 | [ 0.3218 1.2926 -0.8878] | [ 0.3068 -0.0035 0.8927] |\n", "| 4 | [ 0.3295 1.2918 -0.8816] | [ 0.3095 -0.0036 0.8911] |\n", "| 5 | [ 0.3314 1.2879 -0.8754] | [ 0.3121 -0.0044 0.8893] |\n", "| 6 | [ 0.3173 1.2755 -0.8766] | [ 0.3102 -0.0089 0.8835] |\n", "| 7 | [ 0.179 1.245 -0.8418] | [ 0.3278 -0.0065 0.8801] |\n", "| 8 | [ 0.1175 1.1583 -0.8082] | [ 0.3594 0.0119 0.8814] |\n", "| 9 | [ 0.0921 1.104 -0.7854] | [ 0.3648 0.0107 0.884 ] |\n", "| 10 | [ 0.0883 1.0555 -0.7566] | [ 0.3708 0.0096 0.8874] |\n", "| 11 | [ 0.1009 0.9934 -0.7231] | [ 0.3788 0.0111 0.8926] |\n", "| 12 | [ 0.122 0.9309 -0.6845] | [ 0.3901 0.0137 0.8972] |\n", "| 13 | [ 0.136 0.8868 -0.6509] | [ 0.4018 0.0149 0.9002] |\n", "| 14 | [ 0.1438 0.8571 -0.627 ] | [ 0.4104 0.0145 0.9028] |\n", "| 15 | [ 0.1518 0.8371 -0.6099] | [ 0.4149 0.0126 0.9058] |\n", "| 16 | [ 0.166 0.824 -0.5956] | [ 0.4143 0.009 0.9098] |\n", "| 17 | [ 0.1917 0.8172 -0.5803] | [ 0.4067 0.0028 0.9153] |\n", "| 18 | [ 0.2324 0.8163 -0.5616] | [ 0.39 -0.0068 0.9221] |\n", "| 19 | [ 0.2857 0.8174 -0.5394] | [ 0.3647 -0.0178 0.9293] |\n", "| 20 | [ 0.3412 0.814 -0.5157] | [ 0.3374 -0.0262 0.9363] |\n", "| 21 | [ 0.3893 0.8039 -0.4932] | [ 0.3139 -0.0303 0.9429] |\n", "| 22 | [ 0.4285 0.7888 -0.4726] | [ 0.2951 -0.0314 0.949 ] |\n", "| 23 | [ 0.461 0.7709 -0.4536] | [ 0.2796 -0.0308 0.9548] |\n", "| 24 | [ 0.4888 0.7512 -0.4359] | [ 0.2663 -0.0293 0.9603] |\n", "| 25 | [ 0.5134 0.7306 -0.4193] | [ 0.2545 -0.0272 0.9655] |\n", "+------+---------------------------+---------------------------+\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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150gVn9xceh6rNbKxt6cHeP31/pWRwW4HensXjgjiYzBQmuprryVlTw02W3DF\nx2KJfeHKbqd5dijh80VHfHw+kVSHAluciLaPhJsbfv97cseMBUZjHDo748PWMdvqxGTSorNz+Nuk\nEi4XtdPDh+mYLVYEU3xoQW7oyxktRpWr22Dg3XfFCWgwfM+HSvEZN048Tkry+lclFy8GDh2iN8yI\nj9kcOHEz4hNe8dGguJgUn7Y2oKyM3HMmTQre4F0ukvVDGWBeL/3+ppuA996D38gNNpm2tQG7d9M7\na2yMbfNUZgDE+m5MJkAQUgLqzOmUE5+Rqvg0NZGv90hAY6POb2xK4fNR+ykpcWGo9yru7UXYVTi7\nXe7q9uGHVK9q/vMmExEfthiyf7/4OUCfe73U5ru7qU/7fEw1ZMRHdHUzmcT7rlkDvPVWJsaN8yAn\nx9MX16LBypVp+N3v+lUNAOSKz4kTRHoAUpoj3TMoHPE5dCi6rEyRghnXlKFN9JsJR3wSE72yGJ+k\nJC+Sk9WJz/LllO0oUhiNkRn9RiO1gfp64O23IyeZahhoxcfrJeOZvf9wxMfno3efk0PtOVLF5/Bh\n4IUXgn/PNgaOBGyRs7U1eiPz5MkErF6dGvXv1ODz0RiRmQksXAhs2qR+XijFB4h9dd1uF/vjUMFq\npbEr0oVGl4uSqYQ7n9VBNIrP55+Hr7u9e0WDP1qwsTlcf731VlpcM5loHrFaR5atwDxpWAIOpviw\nd6Km+IwW4vO1VnzMZprIjx8H5s4d+Ot3d9PANZiKj8kkTw0qVXy6u8XNRkMpPmJWt9Cv0mrVYvx4\nUfGZN48G4VCKT2srDfS7dgW/bm8vDe6XXkqDTTjFx2CgTmkyEblUrmJGE+MT67v57DMgP98TYLA7\nHFqkpkoVH+2I3LCvu5tW4EYCmpvjVX25PR5AqyVXt1hIWiTtwO2m1MxKd0mjkTYEDQZakRSTG1it\nwKOPAvffr058lIqPGvEByCDp6iIDMTGRJhMmzUtd3Vg/9nhoIWDNmlTk5Xmg0QDTp9OCx969yQOy\nwi+N8Tl5klLHAkBaWuQTXTji43BEphpEC6sVSEtbj+pqYPz4SIkPkJ4uJz6JicEVn1On5AZAOPT2\niivVocDqo7aWFo9CjaHhYLeTUtff9vDUU1SulStpoaqri1SccG7Jdju1YYqTilzxsVpDt7G33gJ+\n/evIyt7YCGRnr4+J+KxcmYZVqwYmjbnZTEqOTgeUlyPoog5TfNLS1IlPrO9yOBQfNtdESlJZ/1C2\nEeUCQCyULbjKAAAgAElEQVTE53e/A157TQh5jsGAmN2re3sjIz4Un62FyUS2mTJeOFKwBbeBBpsT\nz5yh+YipPbSnHL2jujqp/dg/VzefD7j66sF3l/vau7ox4rNzp3rDeeSR2OJHGLq7aY+bcJ39hhsi\ni2dRg9kMpKeLx8nJPr/iYzaLBlJnZxwSEvrr6qbB+PFAd3ccOjtFsjhxYvDJiSUoYIHbajAaKU5o\n4kTqZJG4ugE06aoRn0jQH+LjdAL/+Z/A7bf3Bhjs5Orm8xMfdv5Iw1AQn8OHEyIazIMpPm63Bjod\nUFDgHjR1ShBI+ZWugLKVyVCKDw3+Gn9/+u1vgUsuAW67LbjiM3481bnPF0h82Lvo7KR3IyU+UsVH\n6erW3R2H9HQyovLzabBatAjYvDkFe/YkDQjx6ewENBpWJ6JrrXIlWg3//Ccpi52dNE4NNfGx2YDi\nYjecTqCsTBzMk5KCK9wul0ZGfBwOMcZHLZ21wRDd+B1O8TlyRDwvNZXciWtr+5eJy24n16pQJOKx\nx0QjJhiee46yeW7aRISvq4sWvsK9O7OZniUhQVw1Hgjic/ZscOKgREMDUFnpRHt7fNRuYgcOJKom\nBooFBgPNdwDtj9LWpu5xEkzxYX061r7tcIwe4qM8/3/+R+49Io0bixRdXeHbXk9PbJ4kQOSKDxGf\nOP/5sRKfwUoU4nKRyzVAKj/L6gaIJCgnh2xnr5ds5f4oPjU1wJdfRrblQ3/wtXd1Y8TnwIHAF+bx\n0EZv/ZGEu7qI+ITqZF4vpW5mxKujg+IEIg+MoxUhhqQkr39V0mIRExJ0dcVh4sTgyQ10Ol8EWd1I\n8WlpiUd2tujyEkrxaWwEzj8/NPFhE8GkSRTM29ZGhlawyZQZAGx1XDkBRBrjk5ERm6vbU0/R6v11\n15lVFB8N0tK8/uQGwMhMcNDflKiR4B//yMKXXwamVpfC4SC5X434uFxk0OfmetDTM/B+3ABtZAvI\nB1sWtxNqImITs8WihdFIWZJefJHasRqhNJlokkhOpnZ98CApJ0rF5+xZ+j47m6kS8hgfu13T5xpK\n9dXeHocJE4BLL7UiP5+s1muvBT75JB2trfFBjaMTJyIn/Z2dQFERnS8db5ji43KJe/so8eqr5Mve\n2Ul9Jhri43T2P77DZgNmzKAVGqXiY7dr0d4eh6++ks+CjPiI8QOU1S0hgeYFj4fK9uc/0/cGQ+RG\nqM8XXvGZP5/IotEIzJhBxJzdJ1bY7eSaGKycRiOpSuGMvd5eykS2dSu11fp6WrAKR3wsFmovjMxH\nEr8BiG0uGEymyOfoxkbg4ovnIC3Ni66uyI1Mjwc4eDBpwFyRenpE4pOSQn1brf5sNpH4SOuAkexY\njczhcHVjbbe/ik9bm7zvSN0nIwFlYgUmTdIHfLd7N7B0Kf2tJD7NzdQO3G5gx47QSW+kxMflUl9Q\n9niYy6MWvb3kJRJrnI/JNDjZ1Nxu6tupqUSApPE9BgO128mTyWZj9R+NWqPM2suSfAy2u9yYdHVr\naKCMQ8HQ20uDtc9HFXzyJK2+mkxyssGMl0h92NUQTPHx+ShN6fLldB+PhzqZ0UhS3xNPRD5AmExy\n4kOKj0h8mCtOZ2ccKivV0+C63RqkpnojyupWUkJ/FxZSRhogPPFZuJDqItgqk9FI/s4TJhABbGqi\nv0O5ugHBFR+bDdi3L+SjwGSiOAo14++ZZ2gQDIaXXwaefhpISPAF1JnDQXXpdksVn8HtIu3t4ipx\npBgKxcfh0MBoDG1gtLbqkJ3tVSU+Hg8pPnFxtDLKlMCBgssF/Pvf1NakhoDJpIVGQxuCBoPVCqSm\nemGxaNHeThNDVhb9C+bqlp5ObkG7dhGxmTAhkPicPk3nxcWRkWi3S9NZ+/wLF+z/s2fjUVwM/PSn\nBtx4I80Ys2ZR3V94oT1oH7rjDlKaIyE/XV0Uz8dW35XEZ8sW4N571X/b20vxO7EQnzNnKHFDrCuv\nAD3fhAkuaLXqMT4bN6bg9dczZb9xOjUKVzdKbqDRAElJPthstJCzbBmN3T09kSs+NhsZFKGIj8Ui\nEuCZM8moSU7uP/HJzaX7q6kdzAgJ5TLDYjE//5xckidNotV39l5DqUVM8WHEJxrFJ1Qgf29v5CvE\nDQ2UKKWoyB2Vu1ttrQ42m2ZAFZ/sbPG4sFDdrUqaztpspn596tTAuLp1d/fPmyVasLkm0sUWNeJD\n+73JxxCLheoy0kUxtlCjZlzX1wNffSXGWrJxx+ejxYgDB5JQU5OAn/+cMrl6veoL1CaTFtnZHtTX\nA6++moXnnssOOIfNd0zxmTTJGbPi09sbG/FhyQuCwe2mPj5+PPrUbtEu7ekh0l5RQWo0q/9IScvp\n04ByL2GWFGiwic+YdHU7ejS07Pfee8DDD1OH0ulo8t6+nRqwlGywwTSUcdjeToHF0gH/6qvF1SyX\ni9wLlJ39xRcpYHPvXpEMnD1Lyk9hIRnkaitAGzcSqZNueqam+NhstGeP1CWmszO+j/iou7qlpnoj\ncnXLyAAyM70oLCT/5F/9ilZcgjXWpibqOJdcEtxHnSk+CQlk4O7eTWpSrMTniScEXH55aL/73l6q\nZzWC+eGHZKypwWymSeOcc0glUxrsTqdGFuMDDP5O5cuXi6vPkYJtJjeYZbPbtaob5krR2BiPSZOc\nIV3dAFpAiNbdLVyMT3U1GW1VVYGKT3l5eMUnN9cDm02DtjYxwUhWFvVdpaHGFihycoD33ycjJj1d\nTnxyc2khJieHPlNzdbNYNEhMFFWps2fjUFwMnH++A+efTy8zLg7Q66248kpL0E1DOzpofPr970NW\nkX+FtLQ0UPFhLjhGY3BCYzRSPet0NBaGIj42m3zfDuYWuHJl6DKGArnnbcGcOUBlpXhxto+P2awN\nMGiVrm4U48OywflgtdJYzDJVqSk++/cDP/pRYHmULrasPp59ltQxj0d0RTIagQsvpO+vvLL/xCcl\nhZ5b7R0wt5xQfYyRF6uVlKhp02iszs8PVCWUUCo+0RAf9ns1REt8ens3o6jIjb17k/DDH6rvHabE\ngQNJOP98R8R7doWDVPEBghMfqeKzaxfV9enT9Mzp6dEZiG636CLG5rxYXYruvz+y/XWk6OmhdtIf\nxcdkomOl4pOdHbniwxa49u8XAr4zm6nfmUw0fjPic+QI1bvZrIHNpkFPTxw6OoAnnsjFW29RgPUv\nfiEqOyaTFlOmONHQAGzZkoLu7sB5hM13BoMWZrMWEye6Yk5pbTJFF2PI8PLLwGWXBa87t5vIyTe/\nKcaqM3uhu5vGkkmTaIEqWuJjMJCLqsVCe+Z98QUpPhkZQ6P4jDlXN+ZPHsygY7sWswn8nHNoQs7N\nlVc4GxS6u2kSe/ll+XWamsjwv/VWcUDxeuklGgyiIcOYshQvvkiEoa1NTnyam4GpU4OvGn/+OX0e\nivgwxYepPmxSZ4qPcv8PgCbblJTIXN3S0oDMTA+KisiYeeaZ0L7+jY20WjxpUvDVRKb4AHTeyZP0\nXoK5TzAy2tJCz680Otrb6Xr33KNu9DF3k2CKT01NcNJVU0O71mu16sSHFB9ljE/kXeT48eBZfoKh\npib64EamMMRqTJ05E37ys9vDKz7NzfEoL3fB5dIEvCuXi4x9gAzvgY7z6eyktpmXF6j4lJQwVVi9\nTzDFJznZh9OnibADVN6UlMDBW6r4LF9O+wQpic+UKeSCFpz4+GC1avtcOzRwu4H29ni/H7YU//Ef\nHVi61IikJPW+2dkJvPIKBQuHclOyWIhI5eQEd3UL5brV20sGW15e6HGCjdfSsvT00L0/+SR4+cLB\naiVldts2+F0BAVHxsVq1Afueud3y5AZOJ8X40O/o8w0b6LvOTnXFZ8UKddWYPZ/VSn12xgw6PnSI\nAoXZXNHZKSo+cXHANdf0n/gkJcnbnBSREJ/eXhpXFywgg2nSJDK4cnPp81DtSKn4ROrqxtpVMGPI\nZKK+E4lreGMjkJfnQVGRGy+8kI2NG1Mjcs05eDAJc+faBszVTRrjA0Sm+Did1N/OnqX3UFISneKz\nZ4/oxsXaQizubh4P7bcX7XzT00Pusv2J8WF1pFR8onF1U27GLAVzm+zpITLV3k7tio0/drvWH+N3\n5Aiwd28STp9OgMmkwQsvAHv2JPVdR4tzznGgpoZIs5rNxeZOg4EUn4kTXRG5X/7614FlZ4pPtEmU\nqqvpPT7zjPr3LheNP089xVyD6Z9GIyo+GRlUb2z8jtTVjZ13+jTte/etb9FYMncuXa+tjVxqBwNj\n0tWNDdws4JFln2BoaaEBWkp8Zs6kv6UDiVTx2b6dNhuTruL29JABvGgRGYGAuFJgs4mZmViDkaKz\nE5g9W534lJSIq8ZKGAzA9dfTb6QMW0p84uNpomQGp9VKBmV3dxwqKtQVH5eLUjBHso9PWhqQleWV\n7R2UkEDPrTb4MOKjrF/lc7GJYOJE+j+c4lNcTARJpwu8rk6nx29/S4O92oTJ1L6MjMBBxGCg9xPs\n3tKsVuEVH4R0Ifz440Blac0a9Q0wQ+HUqUB/WSVMJhroGBgxj8Xdzecj98WtW0Of53RqZIrPG28A\nra3ywb25WYeSEndfXcp/31/FJ1yMD+s7ubny1U+TSYvMTDKUg/ldW620+p+a6kVNjTylvNrCBVN8\n8vLIzeyii9SJz8mTVB5APcbHatUgORlISfHCatX6Xd2USEz0IT5enJiksNvJuJ8yhRTqN98MXked\nnVTmlJToiQ9zjUpODk982NihJD5XX00JKCKZUHfvpv2ppLDZgGnT5gWcy4gPpZENr/gkJZFVkZzs\nQ1cXjS3Tp1O7UVN8Vq9WH0PYZ1Yr/ZZlRWKxC6wemeJTVkaLIZMmiW3K4SA3xWg2qmXGbrBMfA0N\n9H5C9TGTidrsM89QMo9Jk+jzSIiPVPExmyNLVQyEJz69vdSWw7ka+nz0jN/4xiUoLHTD49Fg3Di3\nagD6229nYP16MTaxqysOFRXOYXF1S0qi+i0oAO68k4xxRnyiWRlvb5eTibKy2BIcsHoOR3xuuEGe\ndIIRn/64urE6Uio+GRn0fsMl5gDEcX7cOH3AdyYT1U1TE9UPC4f49FNWdnFB+eBB4NixBDQ3x6Ol\nhSaprVuT+66jRXm5y++iqU58RMWHEZ9wio/XS55CUpdvr5fqg2y88M8vxe7dtPD10ks0linHE7db\nXHikzZtp7MnMpPeZnCz/HIi8TbLzamrIS+tXvyIRgXkPrV9PiYIiIcrvvBOd2+aYdHVjHZL9v2ED\nGSVPP03HUuKTng5cdRVw442B0rFU8WGZY6RxI3Y7DeIsIB8QJyarVTQslemsPR66/3nnUQPu6CCi\nwu5RUkINS211z2Cga5aWQrJJoZz4AEByshi8ScHXWiQleftcTdQVn0hd3UjxkRMfjSYw5SYDIz6h\npHmW1Q2g+oyLo/9DEZ+KClodHz8+0OhgAbfZ2cEzbKWnq6txTDIORXymTKG/dToEKBUsxoeSG4R2\nIfzrX8n1UgqLJfoB7NQpajseDw0ex48HniMIwG9+Q397PFQH5eWxrSLv20dkP5wxardr/Kk9Acrw\ndeSIXGPu6IjDuHFEfJTEub/Eh2H1avW2x/pOXl6gqxsRH3fQychiIfKRmupFbW1kxCc9nTbbfekl\n+kxKShjxaW6WKz4sfShzdbNatUhMBNLSfDCbtX5Xt2BITw9syywFsUZD7lhvvRX89+zc5OTAGB9G\nZIIRH6ojSm4Si+LT3U39ePLkyPbU+OQTYNUq+Wc2G/xualKwrG5Wa2DshjK5gZT4JCb6sH49PdPE\niUQMlVndmpupD6ot9EgVH0YAOjtF4sPmio4OUWGprJS3qT/+kdLpR7PPSCSKz6xZoQ1alhCmrIzc\nlqTEJyMjcsUnmkD3SIgPEN5t69Qp6lfp6V7o9VY89lgHpkxxoq4u8Nw9e5L8+98BZPDm5JBba6yb\nhkqhdHUrKgru6pacTKSnsZHGa6b4FBdHp/h0dMg3+4yV+LB3F26hrbpabkj39IgB8pEgFPFRKj4s\nW2Akqg9TudTaE6vPU6fIdigooD524gQprna7SHxWrKCsns3N8WhsjEd+PrB1a0rfdbTIyvKirAyY\nNcsWkvi0tsZDp/OhqMgdNrlBVxcZ+NJ+ZrFQG5kyJbo4n54eqs9rr6W+f/HFwEcfyc+hpFf0t1Tx\nycqisTklRfxcSnw8nvBzNav/kyepfh96iOwDtjBD20mQW3g4/Oxn0e1xNiZd3Wpq5CtX9fW0P8zj\nj9Oqh1LxWbKEJn/lSphU8Tl7lgbNTz8Vv2cTiZT4SAP4urup8yiNa4OBJonSUlHxmTyZytbcLAZJ\nq00iyrTPQDDi4/P7lVosWnR2xiEvz9OXTjZ4coNIFZ/p0x04/3z5d2pGjcNB9VBQEF7xYa5uEyeS\nEZmdHTqrW0UFdZri4kC16cgRARMmyImP1yvuxMwmcEZKWWIJIDrio9XSKjxTKny+QFe3YIqPx0Mu\nlCzuSSoVR0N82MpxTg61p7Vr1eOTWMA0QM/K3K5iUXxWrKD/w63eKZMb0Iq2fLgg4uNRJT4sqxsQ\nHfFZtoyCzwVBQG+v3B1VCrYKnZsb6OrGFJ+zZ9WJj1LxYa5ugDrxYQstpaVi+nml4sOUxGCubnFx\nRHbI798Ls1kTVPFhUDN0GZkByJgKZQAxxYet7LE6A+SKjxqhYf1s+vTIiY+03pjLSV5eZH3i6NHA\nNmmzAXV12wLOlSo+Sle3YMkNAFpUWr6cNofOzaX5hK02smdYswb4xjfUxztpjA/7vrU1UPGpr6d3\nzto/a1NtbcA//kGLddEsBESi+MybF97VTbpnHCM+OTk0fodSXaSKD3vHkaz+s3NCubolJ4cnPlu3\nkh1QXV2Nc8914qabzCgpcasSn46OeFlcht1OY7o0cVA4vPVW8DhRNVc3tcQt7J0B1A7GjaO5ymSK\nnvicPStXfEpLYyM+bJ4MRZCZ+iDts5G4uj34oDhHiX1P/L6tDQGuu4z4sLEyHLq6qL2cOiUEfMfa\nmJT4/N//Ub/IygJsNnJ1KyhwY9s24LLLrGhu1qGpSYebbiK37c5Ocl1LT/di3jzghhvMQb1sAKCp\nSYeMDC9yc91hkxuwNiK1i1i8V0VFZMSnp4fG4xUrRDdarZYUui++UJZRrvgwgsMylyYnBxIfi4UW\nWUMlGAPEuv7yS9E+BOTEp6oKeP750NfxeqkfRLOAOyZd3Q4fJvbKBvC2NnrB550nroxLiQ+Dmqtb\nfr5IfO66S+5r7nAEEh+p4sNWeJWKT2enuELmdpOrw7Rpclc3peLDfs8IQjjik5Tk9Q/cVisF42Vn\nM+KjntwgJSUwQ5kSFosWqanAr37Vjauukn/HGqzFQm58jY1U10VF1LlCKT7SiWDqVKrTUBMpczNs\nbyejSGnctbeTEiQlkJs3A3q9uGKWkSF25scfp8BigAaP8vLgpOvUKZH4ACyzG/3tdtMqemKiV0Z8\nGKFcvz4Fq1fTuSdPUtvYvVskvMwtMxriU1tL7WHCBDL2TSb11Q+rVQzWZAZlMEUsFHw+Sv4wdWp4\nw0WZ3IAMO3kb6+iIR36+uuLDsroB0RGfTZvEQfzdd8X+yMD6azBXN7NZi4wMIj5NTboA9zz2LMnJ\nXqSm+iJWfJT9lLVbFiRfWUmfByM+Op1Povh4I1J81Fzd2BgEiMHqavjlL4FbbqG2yYgPW7kH5MTH\nbg9M6GA00v0XLKBJLFQAvFTxYQSGtdOcnMgIuhrxYTE+SkiJj3JMVLq6OZ0aJCSIyQ2OHiW3o7w8\nGi+ysuTK2sGD9MzM3VVZJ7m58v1pmppEw5Tds6ZGXAwCxDZVV0cEecaM0P1B2ZciUXzmzg3v6iYl\nPuXl9H80MT4JCaGJj8dDffbVV8VYIPZ7Bp+P4tMAqvPy8vDEZ9s2Ij5SlJS4VN0FOzvjZPEWRHy9\nfvfSSLB8efAtHILF+KxeLU8LzxQfhoICIsQs5i4aVzfWvlgSp9JS+WLPRx+JHgGhEIniYzLRe4yG\n+NTV0R5R7PmDKT4TJwa6urGU4JEoPl1dNFcGi/EBaI7PyqL6/vBD4PLLmasvKT7Tp9NgNW+eDRqN\nD8eOJaCyErjkEjt27kzyE5+33gIuvTSY4kP/NzXFIz3di/x8j6p3QWOjGLvDFC9pP2N9kmVXC4fX\nXyc74IEHKOEUw5VXUh+Rvh+pqxuzY+126ussuYGaq1t7e/jx2mKhMgsC2RIMzE40GIBvf5uy7IVy\nY+vtFefPSDEmXd06OkiylxKfwkIyVo8coQpik7XUEFEa5t3dZIgwV7fFi6lDsNWGcIoPBT8HKj5d\nXTRhajRUrkOHiPi0txOjVyo+R48SaQOiVXy0/g1LDQaSXoMRH+bqFo742GyagHsxsNXcRx4hFYMR\nH5b+OpTiI01ucOGFlDEpI4PeUUcHHUthMIhGYm6ufDKnetMjJ0dugL7/PnXizz+XEx8Wj8VIQU0N\nlSESxQeAzGBnGx3Gx0MS4yMSynXrUvHHP1JH3buXjKO8PFIourtZFj75JL5xo6hUqeHUKTKEysrE\nbIZqkzlzSWKpTFn9RKv4rFlDBvmll0aq+MiJj7L9MTUynKtbaSm52F12WXhZu6eHztXr9Xj1VZrA\npH17/nyWpUfd1Y0pPsXFbjz9dA5uv70k4B5SxaenJzTx8XrlSgkDa7dmM40ljMAw4hMY40PEkVbu\nvejtjYPBECe7txLBXN3y8ujvUCrMwYMU//O//ysnPmquboB60G1GBvlq/+Y34RUfrZb6749/TP1U\nSnzCLQY4ndR31RSfiy6aE3B+KMVHSnzY3h1sokxK8mHBAlpYYcQnOzvQbVG6ICNNe9vbS+O+lPgc\nOkT3oX3X6LNgxKepifpCcXEgSXn7bTJefD5atPuv/xLvG0rx8XhorJ49m64ZLEiarS4zpKRQPGJ+\nfnQxPj09pGCoGcGff06ufH/4Axk9asSnvR34yU/omiYTzYeREp85khy6wRWfuADFJynJh5QUn6rH\nhBrOnAm9cKeM8Wlupmdau1b8XKr4ADTGnDpFbS0YgQ2Gs2fFNOrx8TQmShWfgwdFOyYUDAbqp6EU\nHzan9PRQu/rLX8LH+Cj3UwtGfChOWfwsFle3CROAlBR9wHdMPTx5kt5PYSHNpYz4UHIDDcaPdyEr\nizJplpS4sXNnMiZOpM1x6+t16O2NQ3o6LZTQApXaHnUaZGYCDocWaWlepKT4AuLRAcqoxpKTBiM+\n6enUtt99N7T7ucdDG8D++99kc86fL36XlUVK0DaJOK50dWNZN1mMj9LVjdnQzE03FMxm4IIL6B5S\n4sPsRKORuaaGvhari2jsmDHp6qbT0eoimxTa26kBT55M+00UFFBHaW0NVHyUrm6TJ4uKT3ExHbP4\nCTYo0Yae8pzobO+B1NRAxUfqZlJURArVtGm04sHSjUoVnxUriER4vcEVH+lkBNDk3N0dh4ICRnxI\n8UlLg6qfcrSubmpITaW6Wb6cFDeDgeqOGXGhBmrlChhLPGA0knvhww8Hns/2EFISn4YGGtg0GtFY\ncLlIsn74YUqNy1ZJ2Lvp6REngVDEp6uL3gMzGqmsasTHp6r4NDfH4+BBUnn27qUA91mzxGQGTDHr\n7hZXz//+98CAbSlYlrnSUiI+bFXQ45Hv7cMGxLNnRTfM7OzoBgyfj4jtsmWiIRwKDocGJlOcP+iU\nXKXE4YJWBeOQm+uBThc4cUml9ooKcXJUc1uTwmAg4nP4ML3X664T24fPR3XAFkDUXN2Y4vO97xmw\nc2cd2triA1adSPHxIS2NXpTU1U2ppBFJopVaKVi7ZUSU9RU2Pij38YmLo318GPE5cSIBeXlufx2p\nIZyrW0qKuBKsRHs7kfykpPDJDdhzOhxi22UxKgzhiE9eHvX5ujoyrNj4kZ0tEh+3mxR8ZUaqU6fU\nA+Ypxkdd8bHbtbBaNbDbtbLAaJdLzOrGjF5N39BYVubCT35Cf+fmqis+7H2yuv/pT0VF2WgUiQ97\nL/v3i/Vns9H3nZ2BdedwUN8uKVFXQFetoqQLdjtd5513aNwDQis+ra1U93l5IvlUg9LVDQC+/336\nTSjiY7XS3JudLbq6sSyBSrz1FvC735ERZjTSb5XqxqlT9H9bG30eTvHp7KRnVLpnl5YGEh+7Hejt\nlRMfm02D5GRa5IhE8fF4aB6KdL4rLKSxurFRdPWi+wYqPi0tIvGJVvEBqG0mJRFZlRKfurrgBuYr\nr4gGudFIdlAoxYf11e5uWgT9059ok/hQMT7vvy8nsFYrtSmlq9ukSYGKTzBXN5+PYriV9teECcFj\nPidOlCs+iYmkjIiKjxYpKV58/DFQVWVHcbEbTU06lJfT2NDQoPMrPoCYhCYwY6nGHyednu7ts1e8\nAe24u5vcwYDgrm4ZGTTHzZ0L/Pzn6vULUFxgbi4tHu7aRe6yUixcKJIsKqPc1c1oJNssOTlQ8XE6\nqZ9aLGJGylAwm6mPa7WBxIe5umVmBh9X2D5nwYiPmgcCw6hzdVuzZg3OPfdcTJ48Gf/93/+tek5x\nMRmBbEWirY0a8OTJ9FKLi6kym5vDu7pJFZ9x4+gFHT1K37OJRKcjAtPQIFd8mASrVHykbiZsAqys\npAbG1BGp4vPhh/QCu7ujUXwouQFdXwODIQ5ZWV5otWSsKVet3G4xnTULkleCstVpkJIS+B2rv02b\nKO97RQWVVRrEyQZqn4+C2KSQJjdgYBP9oUNEqNjAQbsdByc+9fVAaqrgr0eDgVSTigoyQNato3cg\nTW4QivhIJ4PGRiK6Gkn16XQ+/4DrcGiQkOCDTufzp31MSRGVtOZmHe65h4iDIIjEp6iIFBtGfJjf\nKkADVKjsTVLFp7aWYgvq6+n6S5aI50mJj9SgjMbVbflyGjRuuUU9MYQU5FJBxI/tZK2M8enqokFf\np0NYxUejodWviy+m56yrE9Oz1tbKDWEWuPnIIwK+/W3q76w+e3tpQGfurqmp6q5umZk0OObkeJGT\n47XwcOcAACAASURBVJFlKGLPQq5uNLoqFR/pQMxW5ZRQEh+djsoa3NWNiGNiIim0gpCCCy8MHS0c\njviwjVLVjFA27gHi/i/M0ADEhCZS4vPTn4oEVWkohyM+48bRe2xpofFZTfFZt46MKGUCj6NH1V1Y\nbDbg+PHtAfdj+/gwIi5VfUjx8fSlXBYTGwDAH//YhVtvpb/z8qjtqSk+OTmiat3QQC4mrE7Yyjcb\nu/fto3MZ8Rk/ns6VEh+Nho6PHBGJj7JNdneLcUJpacDdd4uZF6XER2n0NTSI9wzlUqp0dZOCPasa\nbrmF2ttPfiInPsrxw2AgRXnJEtHgsVqpXUjLzGIZTp+m95ifT236F79QV4O3bqV5KS6OYnwY1Fzd\n2tvlruIAxXZE4+rW3ByYaW7VKnGMUhKf/HwyAGfMkBMfpeKTn0//Z2SE9qCQoqNDXOwBROIzaRLN\nrWxera8P/v4efZT6HCv79OmREx+28Gy1Bnd1O3OGjPobb5QTH7bhLkNra3SKj8NB2cGkHiNdXUSU\nW1uFgHIw9dBmE2N8Zs2iNkuKD7m6JSX5cMUVzGajFbGJE4Hx491oaNDBbNYiPZ2MqPh4WnhRuni7\n3Rrk5tJiFiNJOTmegAUdo1FM69zWJhIQaZnZ3PLXvxKBDLaFx5//TEoqK5cSlZWiXUlllLu6GQz0\nf1KSuuLDtoRhik+o9NpmM40B5eXUnhgY8WGL/GrjyvPPU/t99tngxEctZolhVLm6eTwe3H///Viz\nZg2OHj2K9957D8eOHQs4T7kaJnV1Y7EUasRHLasbSzpgNlNHUCM+gLiJk9R3mbm6qSk+TDFgjH/c\nOPrHiA9TfI4fF13umprIIE5KiiTGR6749PRokZVFHZHtNi8Fxfh44XBocdNNlJ9eCdrEzxewas2Q\nmkoy6YwZYvmlA7xUwvz+9+W+79LkBgwaDTX63bvpezZwM7egrCwakNSID6tXRnyOHCE3joICWi1+\n+ml1xcfhoPdz7rnU2ZgLEzMeOjrEyYdBqlSw/T7IJYkSHyQkEKH0eoG2tjj853/S4B0XR0b8d75D\nig8zztmg3t1NE+Xp08GJj9tNhuDs2UT2ASI+DQ1EmJSqA0DtmSk+zED/wx/kA54SdjsZbg89RKvI\nWm1gu1Yrm0ZDg7nRqPXL+NIJoK2NMqcB8lgp8Roi8WGorCRjc/t2ImK1tRRvsXw5fe/xUBuZPZtW\nuG65Rd4+GMGVxvmxRBqM8JtMWpmBV1zsDngHlE2HFJ/4eLkho3R1U1NlATnxYa4veXnh9vHR9CU3\n8GHfviTMmhWa+ISL8QHUCYnbLWaRBMQAcqlyxWJ2pMSnvV30NWcxPqHuw+BwUP88coTGOSXxYRPb\n229TGZT+7EeP0kKCGvFRm+Skrm50njgmulwapKV5+3zXNaoxQgDVDQv2DaX4sJXvkyflio/ZTHNM\nba24km21in1ZOSZmZZGKGUzxYcTHZiOjZM4cMYW91NVN2R4iJT5KVzcpQik+hw5RNkO2Ms8WXpTv\n6pVXaNVZmixBjfgwxaemhtpXbi6NkS+/LHfVYfjyS7quEuPGedDdDZmnA6kKLphMogrocETn6ibd\n3oLhsceoDoBAV7e4OOC++4i4KYmPVPFJSqJ6SU8P7+rm8ZDLaGEhzV9nz9K1enroOpdcQvXP1Ma6\nOvXrsfgJFntjNNJWEz09wZMJKInPPfdQCvTSUhpXlAurW7eS21V+vvhbpvSpuboFU3yU8wc7j8XV\nAqKrW7AYH5awIyuLiBhbXyfFRwuHg9Q/htJSF1JTvcjJAcaPd6G+XgebjZJhMKSlBdpcLpcGCQmU\nIZcRn+xsOfHxeOgZjhyhem9tDdzfUEp8srPp3aolrfjkE3qXN9wQ+B3D+PFyQqtMZ20wUD0z4qOM\n8cnNpffR0SG6d//kJ+JCmBTsvW3aRHaQWFehFZ/nniPX6x//WFR9ADnxcThIYQ42jo0qV7ddu3ah\nsrIS5eXl0Ol0+O53v4tPVHa2KykhctPaKu6+y1zdAPouI0Nd8VESn8pKGhDYioyS+LDKY3E+PT10\nntTVTS3GR6r4AHT9ceNEH3+m+KxbR6vcBQWiz7dGQ+darXQOm+SkSEnx+omP1Sq6ugHBiQ9zyaqt\nhX+FHiDXA7OZUr6mpATP5ZmWRnUzY4ZYfinxYcRSbeNMNcUHoPe0bx/VD1vhZdfUaKge1YjP3Ll6\nfz0aDGIbAMhtLDWV6lCp+LS00HlZWTTptrRQx7/tNiq3OvHxSYiP1u/qZrUSKUpMpBiftjYgI8OL\nceOAv/2NXFKysuidL1ok1g8brLu6iPRdeCE9k88X6Ff9ySc0mcycSYoPQDI2W+mSrpQEU3xaW2ml\naMcO9ffq81GM2dtv06olW51Rc3V7/vlsLF9O1hrtOu5DRoYXRmMcXC4WxyC2LSI+noB6ZJD6GDOw\n7DWHDlH/e/hheepUljXx4ouB/Hw95s6Vtw82sUiJD9vvhg2eLMaHQW1lWJrcYNw46vcMSuKjltgA\nCFR8ADKO2KaWyhgf5urGkht4PBrMmhXa3zBcjA+gTkgYOWIkJzmZ2r/amMmUHauV/mbtNBbF56uv\n6H00N4uEkCk+JhO1wXvuCYxHOHqU+opacoN582YF3I+ls7ZYNMjM9MgMWlJ8qD2ywHY1sDoMpvhI\n3+9111Efksb4mExivCAjPjYb/Y4Z/1JkZdFzlpbSvdm+IwxSxSclhYjgoUNUt9KYVDaHMUiJT0GB\n3PiWQs3VjSHYFgyAfB5QKj5sVXjtWlrBZdtOMIPHZlMnPunpNA6w7JSrV9NimlqK7y+/hD8ZjzTG\nR6ulcbOlRVz+Jg8RN9LTvTAY4uDzwb/KH6niU1dHzyntd21t5LbMMlAp57sXXiAbRenqlqRYgxw3\nLjJXtzNnaOHntttoHunqonfc3U1l02opYdObb9I429SkrvgwV1tGfNi7KyoKNCx9PrK5WOrqnh6a\ne4uKaJ+W+HgxK9sDD4i/276dMqfl5ARXfNiiZHl5cMVHScSsVnrOVavEdsau4fXqA56VKT4A9enS\nUnIfA+SubtLxoLjYjZISV1/MthtdXXFITfXK5gPKwClvN2xMz8ryICNDnfiweWP2bIrzbWsLJD7K\nPjlxIlTj1p54glwONSF4e1mZnPhIs6oqFR+1dNbZ2SLxYWU7fZr6tsFAyaUY2NxbWiovE2vXasSn\nrY28ZdasISVO6lInJT67dlGZgrm/jipXt+bmZpQx6w5AaWkpmlUoXWkpTdLp6TSg22ziilxhIXXC\nUK5uq1fTCkRXFxlZPp/o7hFK8Tl9ml5uQYHo6qam+Chd3dLTaSBSU3xqa6mh5+eLfqcANZTx44Fj\nx+hZtYo3QJvsUdCzzaZBT48WmZnUuVJTfSrEhz7v7o5DV5fcHemPfwTeeisTFgtlfgsG5v7CFB8l\n8WH1q0Z81BQfQMx8t2hRIPEBqF6UWd3q6sRsQ9IUsFKSuWMHqRzMeGfEhwUOs+u1tlIHO+88GpzV\niI9UqWCrw/HxPlgsZMwzxae+ngbJYJBmxWPpe3ftov0DfD5qj1Onyg2+556jzFsArWKxdMkTJpC8\nz3LqA3TdggJR8WHEZ+NGasvSbEJSdHRQXWzYQIYUgxrxOX48AQcP0mqA3U51k5lJig/b8VpJfPLy\nQhGf4IrPoUPA/fcTka2qEl1c2Grq9dfTZKvVqis+LAUzGwOkCQ6YqxuDmuIjTW6gTC6gJD7KfTsY\nWLlYOnIAuPlmcSFDuY+PTkeZ7lg665wcDyorXYEXVrmHFNLFF0CdkEjd3AB6352dgWMmCzBnxnx/\niU9tLRF5FuPDYtG6u8VNQ2fNClR8amspWFZN8ZG6qjHQhE0LOnl5Hpniw7K4JSaibw809XGPER+p\n4sNiMaWfdXWRyv3FF6Liw1zdlMSHCLWYMECKrCyqv5ISatdFRXJ3NyXxSU2l+WP/flE9uPJK6stS\n/3cp8VEm1pEilKtbUZF6SmaXi+7N5geqU3HBwW6n7E1Ll1JfZivuLMYzmOIzd65c8enooLahTCHd\n2EjttqpKvdwFBZBlcGtvp8WYnBwPurq0cDhobIqLQ8QxPmfOUNyuNK6wvR244gpa9LJa1ZWzcePk\nq/VKVzdWXqmr28mT6iv8Z8/SPDB/vpgsiGXjYte86y7aR47cw9WJDzMopYpPVhYZyW++SSv2DH/7\nG82r3d1kOzHFRxr/mJxMtteLL4pz044dRHykLseM+DBiv3YtnZOZGbmrm9VK7cnjIVsJEBWfUDE+\ngFyRA0RXN7tdrvjMnm3Hz35Gg318PM0VTMFhYBk4pXC7pYoPVYQyxocZ/1dfTca+GvFRulGXlwd6\nb+zYQW1EGdOjRGkpvRs2Nqi5uqkpPmyOYtn1GhvJRu3tpTaweTOVf9Mm8Z2reSpRXYnEJytLTnw6\nOkT7hsXlsvOkxGfTJiqHMiGO2Uz1Napc3TShqKoEjY1LsWzZMqSlLcNvf/scMjMFP6PMzxfQ2yv4\niU9zswChL5orPZ1yuz/7rIBHHqHB6sABAUlJgt8AaG4WUF8v+F90ezv9fuJEMkhragSkpwv+yaeu\nTsDhw0JfwCTw0UcCjh8X/BNmR4eAtDS6f1kZ4HDQ9djks3u3AItFQH4+DfJarVje0lLg448FJCQI\n/mcXBAHV1dV+V7fOTgEJCRvR0qJDVpYHgiDA4xH8xic73+MhV7cTJ7YDEPyrn9XV1TAYBLz+elbf\n5LDRf3/2e3ZMg4+ApibBT9yOHRPQ3i7Wr8EgYONGOu7pod9/8QW9n6Qk+fX67oCiIgHnn0/ERxDo\n98yI/OUvBdjtgt+4EwQBBw8KMBgE//s6dUrwx3mx68fHU8M/eZK+T0igTr5ypQCdTujzywU+/1wA\nIGD8eJrU9+wRYDKJ5auurobDsck/4O7btwNOpwCdjgWMC+jq2gKnk4hPYmLw+ktLA6qrBXR2Cigr\no077+ecCUlNpT6K1awGTScCKFXR+XR1w6JCA7Gyx/fz97wI2b6by5uRQrNPq1fS9xQLk5grYu1fw\nr6TX1gqw2QRMnkwTm7L+BUHAhx8KfmNE+n1yMnD6tCDzmT9xYjsOHCDpyGYDNJqNcLs3obeXsuEA\nAlpbt/jP37ZNgMtFM6dOB+zaJb/e0aM7/O+S3b+uTkBzMxlzM2YImD9fwGOPsbgmAevXC8jOJgMv\nPv45CIK8fWzdStczGoG2NgHHjtFxbi7wxRd0f+bqVl1djerqapSWEvFhxwC935aWrWhv3+Kf2Fn9\nMOLDjuvrybBU1u/BgwK6uwWcPEmETvl9ayuNF2yFqq5uKwChz9XTg4qKL7Bzp1hf0vKx45YWwW+A\nsesz4sOOU1LY/gvi/dvbAZ1OPE5JQV9fFsu3d68Ao1Hwqxg7dlB/Z6uGR44I6OgQz//qK3pe6ftk\n13c6AbOZrj9vHk2edruAPXsEv6vb2rUCkpMFf+pW6e8pi5a8f375pQCfT8DevdUB9UOrlpuh0Wzs\nS2Sg8Y+HLhdzLRSwc+dOP/Fh30ufB6D3nZEB7N9P/S01lQwGi0XAzp1UP1ddRfPJ6dMCioqo/Zw+\nLcDtpvJWVFD5Dx2i90GLH/L24HLR/cRMmQJee03ASy8x10QBZ84IfvIkCALKygRUV5NxcuoUfZ+R\nQcoIqz9GfASB3idzLb7oIvn9T5+m+U/t/Y0fD5w4ETh+rF4t+D0VBEFATY0An4/Kp9MJ+Pe/Baxb\nR+/P6xV/T/FMAnp6BD/xYeN/TQ0ZwQcP0nzGSPzVVwvYvVt+/xdfFLBwIRFFQRDwOgu26msPVqvg\nj8Gsrq7Gjh0C8vPdyMnxYOvWnfjiC8H//nt7N+PIke2y3yv7W3V1NerqKJFCQwM9T3c3zY+33irg\nv/+b6p+VR1pfJ08KaGkRjxsaBNTWyp9HoxH8ik9np4DbbhP8iTOU/VerpfYlCESqHA6qH0Z8aK4W\n8O67RNQsFho/pfdbu1aAVktkUxBovszMJBVi+XIB990nnr92rYBNmwQ/8WlqEnDihCAbHzUawU/W\nP/9cwKpV9D6rqoDGRvF5Sf0U/LE4H3wAVFUJ2LdP8HtFCIKAtjbBv3i8c6e8Pjdvpv4/bx4lxFm7\nVoDLReUxmagtSc83GgV0ddFxVpa8Pmn824rm5q1+4lNdXY1Tp7bh+uvN/uOMjPV+BYeNF2lptNgs\nHT9cLg0MBgE+30Y/UbJYNmHPHrE869cLiIsTcOON5N3R2CjA6xVgNBKZWbKE7EtGfASBzmeKDyv/\nc89R0oMtWwL7p/S4uprGV6Y6OhwCtm+n7ymhAbWnpCQab1paaHxmrm5dXWSPsk3rN2wge/DMGXJP\nA4Q+m4r6c01NYHmOHRP8quhXXwkwmwU/8dm0id4nQONjfb2A/fsFlJeL9qQgCNi8mRaMDx2SX//H\nPxZw883P4cyZZXjzzWVYyoKEY0To7WYHCCUlJWiU6HCNjY0oZc7QEqxY8QYAejE7d4qr/wDw1FN6\nTJtG+7ZYLMBFF+n98ltaGpCerkd7OzHG4mJgwQI98vLElc+rrtJj8mTaadZuB845h36/cycRn6Qk\nPc45R1R8LrlEj6lTKZ3jP/4B7Nyph1YrrrYuWaL3+ys//zyg0+kRH09GnMEA+Hx63HADZXbbsgUo\nKxPLSxKh3r9SDFD63traWmzaRCtT55+vR3q6G83NGmRne6HX61FUZIHZ3Os/v6am1h/j09NDjtA2\nG+mtc+bMgctVgYsusuBXvypAfn4e9Pok1PYtt+ol2mVaGlBVpcfChbQyYTQCycl6zJ5N36emAna7\n3u+/bjAA11yjR3OzuLIpvR5Az1tZSTE3GzYAzz6rR2+vuBqzdCmdv349GbZ6vb4vA58AALj0Uj22\nbBEVnwsvlF9/9mw9Xn+drqfRUPkuvJC+o8lJjxkz6NlaWoDUVL3fDYnVT3Z2sZ/4VFZeiry8LMTH\nG/pWouajvNzkz8Z0wQVzodeLS//K+isv18PrhZ/41Nfrcffd5Mr14YcAoPf7fK9cCdx0k17mu/7d\n79L13nuPXJQOH9bjggvoO4uF3g9ARsZ3vgNMnkzH991HLo3K+tfr9WhpEVdhpd8nJwNZWXrMmUNt\ngVSpq/p8uM/A7QYyMuZj0iQbjEZnX/C4HvHxdng8zdi2LRmpqXpccEEnACN0Oh+mTtVj8mRxKX/i\nxHloaioEIG9vxcU0sd9+ux533UUrQQ0N9L3LJbaPqqoq6PV6fPqp2D527aK6YWnPFyygc3NzgQkT\n9Jg2rdav+DC3GIfD3RcgLbrJWK3AhRfOxcSJLv9Ezsq3bx+T9ul440Yah5T1e+21etjttEp99dWB\n3597rt6/+pWQAJx77jwAhUhMBL71LTMWLToXWVni6qK0fOw4IaEC//oXuc1Om6ZHcbGoOk+ZQvdj\nSsyCBXrs3w/88IfklsDGN/a+PR69bPX2G9/Q+1cFc3KAykqqf6b4ZGaK/QkArr5aL8uOp9fr/Qqm\nwwHMmaPHa6+REZaYSOPxggW06ECuFTSeVFTQeMvqq7eXfr9kiR7SuWzWLH2f0vBOQP2QEr8Q2dke\npKY6YLFoceutNB66XBrEx/uQkaFHQUG7P8aHja8MCxfq/YoUreLTeM/G5ClT9EhJobEkI4Pq88gR\nUnPIz1yPyy6j8ydOBJxOPYqK6Lv8fOqv0iYxebIeX30lqifnnafH//4vjR3f+Q4A6P0uhykpYv1u\n2kTz1SWX0PWuuorGzAcfpIv/8pdEXC68UI/du4n0dHXReChtUgkJesybJ39/DGVlQFeXHldcIf+e\nZb1jx0xVSEmh+ioro2dNSpJfjwKb9fB46PsjR+j71lZxp/q2Nj2qquj7xETg8cepPthqsl6vxz/+\nIbq56fV6mZfInDlzUFhYAaez1X+8bVsF8vI6kJPjQWHh5bjookIkJ1OjnTTpUtlqvlp/A8il7cYb\ngQMHqL6PHKH55847yZ545pnA+gOAb36T+o/DQc/j9crHd71ej+nTxRgfi0WPw4dF1VB6vbNnqb8v\nXUpuZfn5VN8sDoSdf+edFBu1YAHNF9J4C71eD52O+uOpU8D8+fo+9yx6hsce06OwUHQdslj0/lX+\nykpg5Uq9P3aPXS8zU1QpZ8zQ48QJUngTEqg/scRHViu5rDc3kz21ahVw4oTer3qy6zmd1P8SEoCp\nU+X9ZepUPcaNo7bZ3EzlLyyk8So+nsYbNp/SHK7Ht74F/OAHdM1p08SLkZpxBZKTvUhKMgR9/xdc\nkIdTp7z+8tXW1uKf/6SU1tLxw+XSoKREj6ysHowfT7LWBRfMRVeX6FIyZQqN1+eeS+25s1OPa68l\n1819+4Bjx+h5mQqr19P4wtw9WXtYsoTcSIuL5e1Nbb6vqKBFp8JCeftLSgJcLmq/rP2cf74eV10l\nKj4TJ+px6BCNxxMn0nhls1E68E2b5PaT2Uz22axZ8vuXl5OXkc1G8+OWLaISWVmp97v05+XR+JSb\nS3NrUxP93uMhUvjss8Dq1fL2YDLp/z97Zx4fVXX+/89Mkkkmk0lmshDIziqELWyClCVocQUKoggC\n4lL71boX+bpVRVGxWmyr1m/VitLWotbagoi2KoL8VESRRQUxhEBWICvZSSZzfn88nLnL3Dv7ZD3v\n1ysvuLPcOffcc895nvNsyMnJR2UlyTx5ecAGHhwcAJ1i8Zk4cSIKCgpw7NgxtLW14c0338Q8D5Fa\n06aRwMFdnAAK/M7IkARtLVe3khIK/OPKSWKi0uUjPZ0EaT1Xt7Q07Rif0lJqT2WldO6hQ4HXXqP/\nm82SWZHvGBcV0QBSu7oBdB0//KBtLuQ7VBYLZWujrG4dZ69Taa7v6ACMRqYw3/IAdKeT2v7ccyfx\n2GOVWLlSP2doYqLkCiVPbsCFUG5F4esON02uX0/auRbx8fTQDx+u7erG4Tv6tbV0PfPm5Sv6Ue7q\npuwnEqrsdurjvXsld8P4eLKCcPfIigrfXN3kMT5kWZJc3dLT9d2SuIm3uZkm6h9+oL7PzKQH+/33\n6V+uKG/ZQu5cWsyYASxYILmLAHTegQPJcrhnD01G/frRorl0KV2rVhaWo0clxUeOOnatpobGUUpK\nB4qLo1QxPuTqRvFvRhQWRuH669PwwQfeYnzcXd0AWlRzc6X4k+RkyXVI7lbGJ3Z1jE92tnsR4+Rk\neo8xKZ01Jy2t3c1vmqezzs1tw//8j/I9dXrs48fpN9VERpKl66uvlJltODy5AReE5G4HMTFMofTo\nwd2t7r2XNlAAbVc3vov6zTe0u6jlogIo5xuDgY7j45U1fRoapBhELVc3+TgbN05KLMLn2exseg75\n3MFd3Xg/9u9Pv6F2b42KonNz5YpbPtQCCu9DapMTZjNzubrRfCgViTxxIlLX1Q2gccMtPup4LauV\n2saPJ0+m8yckKGOmpk4lFxaTScqWdMklStdSgH6Hz08A/T8+nuYmPt7kyQ14XxYXK9erCy6QMkUB\n7q5udXXKAPX336caIZ5c3bhrndrtSh2/yeNiedX38nJ3tyJA39WNZ7FMTaUxEx9Pbf/qK/r94cMl\nFz3GKLsl39wA3McCBcUrkxskJ3cgKakD1dURZ11auZu4765uY8ZIApt8/bn4YqnemhqDgcYT70N5\n0hPOzJnk6kmlKeg5PnDA/VwnT1K/xcZSf/GYVrmrG0DB7hUV9PxoZdCqraU1yGajtVvulh4XR+fm\nCRIKCujaeZgAX3vl8wi/5wCNp+++ozkA0Hd1276dXOhTU+kZcTql5Eg8XtVkIuVFndAnNlZy4eKW\nd4A2ZeTubtxljCf90XJ1a2kxurm6qcnMdLhKHHC0XN14coNVq2qQn0+Tr83mVKwbclfhBQtoDHHX\nr+JisnqrE46oXd14Flz5fO+JzEw6N2M0V8ljPAHJ1Y33CY/x4THvFgv1H7+Xzc1UA3PSJJqL+PjS\nqmtHfUVj12qleVguw8j7Q+7qxi0+AF17cjKNP3WMz8GD0lpjMvnWH57oFMUnMjISzz//PC666CLk\n5ubiqquuwghe2VOD886jB0T+0HH0FJ/6enpAHn6YFiKAHgC54sMXb/lCkpxMDyLFcUhZ3fjAaGmh\nh72ykqxF8sBiLXiAV3Q0tbVfP5pA5D7fnhQf/mBaLHCl27XbpclbWUvF4Mo+BvBc7PQ+pXIlIWva\ntBZMmaKfQeoXv5ACU7WSG/Dr4rEStbX094c/UH9rkZ9PO+EDB9IOVkMDPex88pKft6GBhPTBg6Vg\nOZuNBn91tbvCQv1E95IrPvv2SRmV5IpPWhrdv6oq93snz+omxfjAFePDkxv4EuPDs7plZkqTvcFA\nE8aZM8DVV1ObGhooe9Hs2drnWrqUdq3k/rFNTdSPu3eToGWxUL/x8RgTIxVIk6On+Khj14qKqC7G\n0KFtKCgwnZ0IGRISKLlBS4sBycmkVNfWRiAqiuHQocAUn8GDlTU5eMwbTymvXrTUMT5DhijTWQPy\nidqAqCim+N30dIdrMeBQVjdtxSM9ncYrv55jx7QVH942QBp3cniMD3+OIiOpAWq/f0/Ex9M1HzhA\nMTIOB/WF/LmUx94UFUmfV8f4AO7zjcVCvxEbS0JVRATdi7Iy9xifqChazHjcGFeUuMWGP6NqxScm\nhpS+gwfp3EajMrMl3yDin+XjUl0HRd23ACWCoaB1mjTa2+n+A7Qp8MMPJt3kBgC1WV5oT167LD6e\n5jsudHDrd0IC9depU/S9d9+lxTs2luYYs5nm02nTlL+lVnxuuAF45x36ncOH6TV5jA8glXaQr1ez\nZpEHQXu7lCCBt5ErPlyQ4D76r7/uObkBID2DctRrgFzxMZtpXpV7LXB4kcS2NpqfuJB65IgkyAPU\nfwaDNB+MHi3F+XDjHC99oIWW4sNjfGpqIlwbHABtIqrTEmvB5xg+5+htvGnRr5+U4EA+ljhXXUWZ\nKnmigFtuoTlanSb61ClJ9hk7VlKCeFY3ztixdN+ys7UzQPLNy2HDpKyE8vt53nkU/8rrz8XErrRs\nEgAAIABJREFU0FhMTeUp45Wf5/cckDYr+dhLSqJz8AygPLlBWZlUsJxKROBsqnkSzmNjpU2i0aOl\neYGXFElPp2dAvgEVF0fX9uWXdMw3wYxGGsPqeUNKZ23UnfcBYMqUFsyc2ax4TSu5AXenlWO3d6C6\nWiqaLC/svmQJbVbyNb2khPrm8GHPyQ1aWqSSBb7AM7vxDSAeP87HDE9uAEjx5SYTzQ2UdIfmxPh4\naofNRvPUhg1KxVovxsdqpd/mY0Yuw8jnH24oKCtTKj4HD1JMtrpERWsrjYuqqh6W1Q0ALrnkEhw+\nfBhHjhzBfffd5/GzCQm066I14WgpPnx3Li6OMqnx3VG1xYcH9MoXEoOBhMPGRneLD9eIy8tpAnY6\nvWvfXNPlizkXCOQTSHo6TexaQZLSDhXf0XS6ivhZrU7U10u3jBep4u+PHi0lN2hpMboEQ2+YTNJi\nq5XcAKC+O36cBKC6Oso5f+GF0qSm5qabeKwGTdBff01/cnM8XZOkFA0aBJdfp81Gk5jd7p4dDJAm\nN674NDQoLT6FhTSBe7L4yAX2EycikZLS4UpuYDIxlcXHs+JDVhP6zW+/hctNLTubJq8rr6Rdtf/8\nh1LVehJCACklLEDjkSswl1zi/lm+sHH+9CcKNj56VBqH6r6TKz5Hj1I6T1J8olyFI3lyg5YWA/r1\nI6W6piYCM2Y04/LLgUGDqPO001lr37clS6hGiZysLBpbcsWHjwO1xYcH3ra1SWOAJzfgNa/kxMYy\nWCzKIGi5QKQmMpLGDHf5On5c6XIrx2qlZ04rhJEv5vyauMXHn0nbaqWq7LGx9OwUF9N8Jk9LL1d8\n+KL53//6pviQizCdnzIXkrBdUuJewJT/1vz5lJiD72w3NUkWH67Epqcrhb7ERFLGuODC43wAWtB4\n/8rHJVd85HEYHKORnl2LRZmtS674nHMOcOhQtEeLz6uv0i68rxYf3mdc8ZH3Z2wsjUE9ZS0lRTmO\nRo+m3fL0dJovEhL0FR95hrDkZJoLvvrKvTaZlsXn1CmyEntKZw1Iu8Vy1IlrJIXTu+Jz8qSUqEht\n8eFjUz0Hjholufps306bZ/JnSz0W6BmjDzBG9ys11eFSfOQFcGNj3TOiqmFMSs3O596KCv8VHz6G\n9cYCQHLE/Pm0fqoTUXCLD0BWnfPOkzYn5POHwUCbjxddpJ0BklvQaRPA/X5OnUquRXyDbMgQ+hx3\nAeXPNId7WQD0W3LhngvSfAzzdNbqDUduoebzosEgZXWrqFAWBFZbfKQNqO14/31aC3ndPD62tcY4\nz+rGy3roMXr0GSxbpuxEPYuPem3jWd3++Edg1SqloD9mDLmjyy0+UVE0J8rbm51N17lnDyV00MuY\nqwfP7KZee/ncIbf48LHJawtxxSc5mdp57BiNUZuNlBH5Oqyn+FBspTQm9BQfQKqjlpVFn3E66Zq1\nFJ8ff6Tr4YpPj7H4BMLll0vCoxw9i09ZmZQWmPPYY2Rm5PDaFfJ01gA99JGRktuNWvEpK6Md+7g4\n3zo9IcGz4pORQUqLJ4sPLbDM5eZG51UqPtziwx/mUaMkV7fmZoPPio+67eo6PoCUaW/gQJq0jh93\nr6atx+TJtDvjSfFRWycSEuhh0Ft0+APMFR9AafFpb1dafPQUH55G8+jRKAwe3IbISHZWoZQsPkVF\nVNlZD27ijY2VBAHuD5ubS4rOyJHUjtdeAxYv9txf/BrkFp/sbFokfFF8tm6lFKtFRfqubp4sPtzV\njY+3M2eMCsUnJcWBf/4T6N/ff4vPzJlK9xVAcumRu1dy1BafwYNpgbRYpEWZm86rqyOQlORewTc5\nGairk54bT4oPQALqsWO0e1Ve7j6vyNum5eYGSOmsuTAdiMXHaqVnYNEiWtA2bKCNHTlqxWfSJOof\nueLDBWktxYdbfOSKD0+PqxZMLRYSlEpLlbW5eDrUb76hsZWRobyPiYnU59zaK7cuyC0+asVHr+Ay\nAFdRSrOZqSw+9P7w4UBRUZRHQWfYMFpQtVKTW610nfx4xAh6piIiqJ3q+ZtbfPTafO21klVdDld8\nMjKUmeEAyd26tFQ5bi64gGIF5G5ugLviU11Nz8zJk3S/vFl81IUtPVl8YmJoXdRydUtIoDEYG6ss\nNVFQQMJ1UpK0QShHS/HxhNzic+BA9NnMmA4kJblbfCwW5tXVjaz+dG2MkZAViMVHy81Nzb59tCaM\nGePu7ia3+CxdShncuOKjnj/mz5csPlqKj91Oc8IXX7grPuedR1lwDx+m+zJoEF13YiL9qT1u+D0H\ntFN7y12kuMVHrfjwZCzyZy06mj7X0SH1hVzxKS2lsc4VH9oQoevbt0+/yLT8N1taaAPP07yvhSdX\nNzmJieTqtnMnyTJypVA6l2S9OO88Kf09h1vgp02jMAK9jLl6cMWHb4hz+Hwit/jweSomRlJ8LBbJ\n4lNUpNzU8MXiw92nfVV8jh6lcWI20zkPHiR5SW49BEghOvfcHujqFggPPQRXlW05eooP4O5ykpur\nnIC0XN0AWnhtNskMyx+6iAgaQMXFwIoVtLPiCzabJHByYVvt6qa+Bo7a1U2+g22zdaCuTtrudTgM\nZ02hkuIjr2buSXDw1Pa6OvcHl1t8uP8vLyjrC5Mn8wB/93ukVnx4bEdUFPWB3qLDH2abTepj3h7+\ngPXvL9W24DUM5MgtFYWFJgwZ0u4SnHg667KySFgsQFyc/oTJFR+LRbIIcqV91ChaXKKiaGL66CNy\nd/CGfNJobqbjXbukYFg5EydSPR9eAPDwYXKLO3FCW2jXsvhkZrYjO7sdJSVRZzcGnApXN5uNVxGP\nQGKi0qoidxnkOBwGzQrTWsgtPt5ifIYMcU9nzxfcmhptxUftEiP3/deCKz7l5XRuPSsNt/howV3d\nuBDEFR9/LD58HE+dSor0M8+4z4lqV7f58+n/csWHu6l5cnVTKz7qGB+Avn/xxdQvXPHhFp/oaCnt\n8IQJyhTEiYn0jPL5SJ7615PioxfjA9CcFxfnVMRutLVBYfFhzPMOL4cv6nJhLD5eaeGPiJDql/Dr\nUAstniw+lPDB/XWu+GRmKt2sOZmZ7i5OPMGBN8WHW3zsdklh08MfVzdvFp/4eOoLteLDXd0iIqRS\nBnK44sPje9SKj3os8HpOALB1axyuuooXXnbKFB/n2TY7vbq6UQwInYPPO4EqPlr9IocrA1qKj9zi\nw9FTfDhaig+/f9On07rDY3U5gwbRfV+3juZV/hx6Uny4q1t9vbtgzmv5yGN8vFl8ABJkuav2/v30\nL38O+venc8jd5DMy8rFrF92jbdv0i0xzKKaVu7r5r/ho1U5UC982G1l8du+mPtKymPNxVVEBVyIR\n9Ry7aBEl1yAPhsAtPvK1V27xkVt6+L88AQ+3+HDFR+7dxMdXWxs9n3rKh1rx4WNSS/FpbZVismpr\nJYsPd4/m69qhQ8BPfiLFDfYoV7dQoefqBujvzHK4kHDmjHICGTSIbgBfeLnFB6DXYmNJ4OfCuy9t\n5JOIvF4EJzlZGmhq+ETNFR9evBSAK9icQwOc6pGkp7cjOzswVzc5cXHSrqP84aGU1tRXtbX0cPuj\n+OzZQwK62i3IaqVzHTzo7s9ts2nHeQHuFp9+/aSHkadg5f3MA5jVgrjcUnH0aBQGDWpzCajchfDI\nEZOm1UR9DVzxSUwkIXPkSPfPDR1KxRB9mczUrm4WC+16aLlV3Xwz1WC44gqamI4fJ5eyjAz3awbc\nkxuQRcsBm8151rWNJzfgdXwMZ5NtOFFaGqUYk4C2xUdeQM0b3OKjFeNjsdAz6XRKrm68lgiHJzfQ\ns/hoKT6+WHz0EhtwrrxSP7mH3NWNLD70ur8WH4Du+8SJdE61tUw+p1VW0vgClM+NwUD33FeLD3d1\nUy/KGzfShlRFhbvFR74YLVgA/O//Ssd2u1JAT0nxrvjILR9aREczxMays8kNJIsPj3fkcZ6eXN04\nehYfQFuA5YqJXEHxZvHRIz2drLVyi4/8HHyjSD5upk+n+fTNN/UVH16osLKSxmh8vOcCiFqKjy/J\nDfRc3QCe/Y3GCGOk+HDXaF7TRk5GBt1/HrvhKb6Ht6etzQCnE9i61YJFi/jvd6Cuzuiq10Vt8e7q\nRhYB+j8X9PxVfCorteN79Bg71rPFhxOI4sPn03POUcZecAwGSpyyaxetTYMGSRuOWoqP2UzPPo9p\nVY8PLYuP2tOCz1fyZ81kovUzLs7d4hMZSd//6itljE9REVlReVZYLVmKwzd+Ghr0CxrrERfHNGN8\n1GsbX0/Ky+lPa+MIoGejf3/alAfcFbbnnqNYsOpqbauRJxIT6flXu7rxTHi+WnwSEmjtk49hPkfq\nJTbgxMV5j/EBJKUqIUFKgMMVH/4+d3c7eJA2GHlWwF5t8dFDS/HhN9FXxUdt8Rk0iDpfbfEB6HO+\nCviciy8mDRWgARUfr5wgDAaa5L1ZfGJj1RYf2oHn0K46CQDbtxfDag3e1c1opD5WT5K8rXKLjzxY\n1xM5OfRAqd3cANrxys2lIMuhQ6XYDoDa4M3iwxUfuSUpPp5e48JmWpp2ggQusJOwb0RqaodL8eEW\nn8rKSK8LsNzik50N3H+/tgB0zTXAypWezyW/htOnaRJzODzvchgM5BIBUPbBjAwKnNUTytXJDY4e\nBTIy2s/G9ESokhsYz+6UketlaWkkEhO9Kz56rm5ajBpFC5tWjI/RKAX2yt2ltCw+vig+jNEE7inI\nlSs+POOYHrffrh/jFh1Nc01zM1e6/Xd1i4qi9KDDh5NCc/vt7gsun9OOH6f7PnKkZOmU46viM2MG\nbfBouY+MG0dzrNziwxc2T9a9xESlAskVHx6X4cnioxXjA9D45DGQWjE+NhuQnOzwSdDJyKD+Ky72\nTfExm6nfjbLVMzaWFndPypreb3d0SIqP2sWPr2nycWOxUHzSpElK6zF3U+a1WLir2yWXeN4R57/j\nr8VHz9UtLk4KZOfjs7ycjvn6zbNcyTEYaC54/nn3+B5AO8anrY02rSIjJbdT7hkhL4DrydVtxw4z\nDhyIxpkzRtf9C7fFhzNmDFk5uFtPWxv9rlZmssbGwCw+BgO5T2kJ0fPmAePHkwI2aBC1m6xm2haf\nM2doTuSubvJzcpdj7sJlMJCipOXqJp/ro6Ppc+PHU3/zzJLyWLeGBmnup5phVAT7s8+ov72N75gY\nJxwOg08bIXK0XN2oSLLyc3yjdfp0SfnV6u+EBHrW+LqhpRzx9cxfiw/fbFO7ugF07/RifHhx04ED\nyaMkPp7GoZbFR8/NjWO1+u7qxj9jt5OlNy5OGhPceghIChH/TigUn06p4xNKEhJo8ZcLghER9JB4\nU3zi4tzTgwLkOpCeTuetrZU0ZIAGhr+Kz/33K4+1Knmnp+uls5ZbfBgcDnmMT4eGxYf+z/0r+eTe\n2moMyNWNfsd9IuHHgVh8DAZywTn/fPf3YmNJ0OImcZ45DvCs+PBdHLudXIHuuUd6Lz5e+b0BA7Sr\nznMXLW7tMRgkwdJkkmKnvFl84uJowePZndas0f6cL7E9HF4zgVt7vNUANhjIb/i112iH79xzociz\nL0cuYDoctMOfkeFARARDfb3xrDlZmdWNhBgnSkqifFZ8fFW88/JoYty/X1uQslol0ztPlamn+CQn\ne1Z8amoizlpbvVt8PGV08wbPtMcFj0Bc3QBpLF10kbarLRcsuQIRFUUCqVEl42kpPtzVzWKRYkDG\njKGUvb/7nTKJAic1lZ5VHuSsDrjWIjFROf9xxaeuTtpo4W30NcaHLD5OhUArV3wAYODAdp9c3ZKT\nSTDcvBlYtoxek6deVcNduNSvyf/1Fb55JLf4DBggva9l8QHI2qh2ezSZ6K+0lASr8nIShObMUc6r\nWmRl0QaIPHhYL7kBz+rGg9jVGAzUf2azlJXq229pY4vzpz9prx+jRlF8wwsveG4vb8/p0wY0NhrP\nWqFp8rbbnS6LjzdXt44OYPXqFFx5ZT3OP79ZofjU19M4l98PT6SlUd/7EuPDGTCAlJ4TJ+j/3EKi\nfn7lG7FaeLL4ACSQ82dWjtEIV3206mq4rGYXXeQulPPf5qmNtSw+5eU0foxGuv8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MAAAg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\n9WdlP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3/uaumVxkaj7NFTLjoqBwqoHChOVBYUUDlQXMclxcfhcDB79mxWr17N7t27WbZs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\n5lqObj1Kv5H9VGJ23FBBm9mGw+zAbrYTCAVYe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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Mean square errors" ] }, { "cell_type": "code", "collapsed": false, "input": [ "est_errors_beta0_norm = np.zeros((ndat, nnodes))\n", "est_errors_beta1_norm = np.zeros((ndat, nnodes)) \n", "\n", "for i in range(nnodes):\n", " est_errors_beta0_norm[:,i] += np.sum((np.array(diffnet[i].components[0].log_beta) - beta0) ** 2, axis = 1)\n", " MSE_beta0_nodes = np.cumsum(est_errors_beta0_norm, axis=1) / np.arange(1, ndat+1)[:,newaxis]\n", " MSE_beta0_net = np.mean(MSE_beta0_nodes, axis=1)\n", " est_errors_beta1_norm[:,i] += np.sum((np.array(diffnet[i].components[1].log_beta) - beta1) ** 2, axis = 1)\n", " MSE_beta1_nodes = np.cumsum(est_errors_beta1_norm, axis=1) / np.arange(1, ndat+1)[:,newaxis]\n", " MSE_beta1_net = np.mean(MSE_beta1_nodes, axis=1)\n", " np.save('{0}.npy'.format(mode), [MSE_beta0_net, MSE_beta1_net])\n", " np.save('nodes_{0}.npy'.format(mode), [MSE_beta0_nodes, MSE_beta1_nodes])\n", "\n", "# In this figure, betas correspond to the paper!\n", "plt.figure(figsize=(8, 4.5))\n", "for tx in beta0_tuple:\n", " plt.axvline(tx, color='gainsboro')\n", "plt.hold(True)\n", "plt.plot(np.log10(MSE_beta1_net), 'g', label=r'$\\beta_2$')\n", "plt.plot(np.log10(MSE_beta0_net), 'r', label=r'$\\beta_1$')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.ylabel(r'log(MSE) of $\\beta_{1}, \\beta_{2}$', fontsize=14)\n", "plt.xlabel('Time $t$', fontsize=14)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0V//EiRMZPHgwn3zyCVqtss9QUlLC2LFjmThxYrXt/OMD41kzaA096vUo972j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\nKsLGT0REpCL/B9RewOPHXxE5AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(np.arange(1, nnodes+1), np.log(MSE_beta0_nodes[-1,:]), 'v--', label=r'$MSE(\\beta_0)$')\n", "plt.hold(True)\n", "plt.plot(np.arange(1, nnodes+1), np.log(MSE_beta1_nodes[-1,:]), '^--', label=r'$MSE(\\beta_1)$')\n", "plt.grid()\n", "plt.legend(loc=4)\n", "plt.xlim(xmin=1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "(1, 25.0)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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