{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#
**Modélisation statistique avancée - Contrôle**
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20 Décembre 2024
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irene.balelli@inria.fr
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Partie I. Questions de cours** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**1.** Décrire les avantages et inconvenients d'un approche statistique non paramètrique versus un approche paramètrique." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**2.** Quels paramètres doivent être fixés pour réaliser une estimation de la densité par histogrammes ? Comment peuvent-ils affecter le résultat ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Soit $K(x):=a(1-x^2)^2\\mathbb{I}_{[-1,1]}(x)$, où $\\mathbb{I}_{[-1,1]}(x)$ denote la fonction indicatrice, *i.e.* $\\mathbb{I}_{[-1,1]}(x)=1$ si $x\\in[-1,1]$, 0 sinon, et $a\\in\\mathbb{R}$. Nous souhaitons proposer $K$ comme fonction noyau.\n", "\n", "**3.** $K$ est bien une fonction symétrique ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$K(-x)=a(1-(-x)^2)^2\\mathbb I_{[-1,1]}(-x) = K(x)$ car $(-x)^2=x^2$ et $\\mathbb I_{[-1,1]}(x)$ est symetrique vue que l'intervalle $[-1,1]$ l'est." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**4.** Déterminer $a$ tel que $K$ soit une fonction de densité." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On cherche $a$ t.q. $\\int_{\\mathbb R}K(x)dx=1$ :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{eqnarray}\n", "\\int_{\\mathbb R}K(x)dx &=& \\int_{\\mathbb R}a(1-x^2)^2\\mathbb{I}_{[-1,1]}(x)dx \\\\\n", "&=& a\\int_{-1}^1(1-x^2)^2dx \\\\\n", "&=& a\\int_{-1}^1(1+x^4-2x^2)dx \\\\\n", "&=& a\\left[x+\\frac{1}{5}x^5-\\frac{2}{3}x^3\\right]_{-1}^1 \\\\\n", "&=& a\\left[\\left(1+\\frac{1}{5}-\\frac{2}{3}\\right)+\\left(1+\\frac{1}{5}-\\frac{2}{3}\\right)\\right]\\\\\n", "&=& a\\frac{16}{15}\n", "\\end{eqnarray}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "D'où :\n", "\n", "\\begin{equation}\n", "\\int_{\\mathbb R}K(x)dx = 1 \\Leftrightarrow a\\frac{16}{15}=1 \\Leftrightarrow a=\\frac{15}{16}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Bonus.** Démontrer que $R(K):=\\int_{\\mathbb{R}}(K(x))^2dx=\\frac{5}{7}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{eqnarray}\n", "R(K) &=& \\int_{-1}^1\\frac{225}{256}(1-x^2)^4dx\\\\\n", "&=& \\frac{225}{256}\\int_{-1}^1(1+x^8+6x^4-4x^2-4x^6)^4dx\\\\\n", "&=& \\frac{225}{256}2\\left[x+\\frac{1}{9}x^9+\\frac{6}{5}x^5-\\frac{4}{3}x^3-\\frac{4}{7}x^7\\right]_{-1}^1\\\\\n", "&=& \\frac{225}{256}2\\left(1+\\frac{1}{9}+\\frac{6}{5}-\\frac{4}{3}-\\frac{4}{7}\\right)\\\\\n", "&=& \\frac{225}{256}\\frac{256}{315} = \\frac{5}{7}\n", "\\end{eqnarray}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Partie II. Application** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Soit $U$ une variable aléatoire à valeurs dans $\\{1,2,3\\}$ telle que:\n", "\\begin{equation}\n", "\\begin{cases}\n", "P(U=1)=p_1 \\\\\n", "P(U=2)=p_2 \\\\\n", "P(U=3)=p_3\n", "\\end{cases}\n", "\\end{equation}\n", "avec $p_i>0, i=1,\\dots,3$ et $p_1+p_2+p_3=1$.\n", "Soit $X$ une variable dépendante de $U$ et distribuée de la manière suivante :\n", "\\begin{equation}\n", "X|U\\sim\\begin{cases}\n", "\\mathcal{N}(\\mu_1=3,\\sigma_1=p_1)\\textrm{ si $U=1$} \\\\\n", "\\mathcal{N}(\\mu_2=6,\\sigma_2=p_2)\\textrm{ si $U=2$} \\\\\n", "\\mathcal{N}(\\mu_3=7,\\sigma_3=p_3)\\textrm{ si $U=3$}\n", "\\end{cases}\n", "\\end{equation}\n", "On peut donc montrer que la variable $X$ a pour densité :\n", "\\begin{equation}\n", "f_X(x)=p_1\\psi(\\mu_1,\\sigma_1)+p_2\\psi(\\mu_2,\\sigma_2)+p_3\\psi(\\mu_3,\\sigma_3),\n", "\\end{equation}\n", "où $\\psi(\\mu,\\sigma)$ est la fonction de densité d'une variable gaussienne de moyenne $\\mu$ et déviation standard $\\sigma$,\n", "\\begin{equation}\n", "\\psi(\\mu,\\sigma)=\\frac{1}{\\sqrt{2\\pi\\sigma}}e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^2}\n", "\\end{equation}\n", "\n", "**1.** Choisir 3 valeurs opportuns pour les quantités $p_1, p_2$ et $p_3$ et générer un échantillon de taille $N=500$, $\\mathcal{D}_{500}$, suivant la loi de $X$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np # linear algebra\n", "from scipy.stats import norm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Les observations dans l'échantillon généré de taille 500 sont comprises dans l'intervalle [2.48,8.66].\n" ] } ], "source": [ "p1, p2, p3 = .2, .3, .5\n", "\n", "mu1, mu2, mu3 = 3, 6, 7\n", "\n", "N=500\n", "\n", "s1, s2, s3 = int(p1*N), int(p2*N), N-(int(p1*N)+int(p2*N))\n", "\n", "X1, X2, X3 = norm.rvs(loc=mu1, scale=p1,size=s1), norm.rvs(loc=mu2, scale=p2,size=s2), norm.rvs(loc=mu3, scale=p3,size=s3)\n", "\n", "D500 = np.concatenate((X1,X2,X3))\n", "np.random.shuffle(D500)\n", "\n", "# Min and Max of the sample\n", "min_x = min(D500)\n", "max_x = max(D500)\n", "\n", "print(f'Les observations dans l\\'échantillon généré de taille {len(D500)} sont comprises dans l\\'intervalle [{round(min_x,2)},{round(max_x,2)}].')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**2.** Representer sur une figure l'estimation de la densité de $\\mathcal D_{500}$ par histogrammes, $\\hat f_b^{\\textrm{Hist}}$, avec un nombre de bins $b=5,10,20,50$. Quelle choix de $b$ vous semble le plus adaptée à votre échantillon ?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "plt.style.use('ggplot')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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KUMXExOj06dPhbsPUGKPGNWWM4uLimnwJEAAIBT6BmsBms1nqhGicoKpxjFHjGCMAkYLDWAAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNK4NhYAtIDP55PH42lwGcMwVF5eLrfb3azrh9ntdhmGEWiLAL5B2AGAZvL5fMrJydGuXbtCUj87O1v5+fkEHiBIOIwFAM3k8XhCFnQkaefOnY3uNQLQdOzZAYAArNuxR3aHo87HDBlyJjjlKnHJp8YPY3ncbo0bMjDYLQJtHmEHAAJgdzgaDDuOuDhVVJxuUtgBEBocxgIAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZmyjMor1+/XmvWrJHL5VJqaqqmTp2q9PT0Rp+3ZcsWPf300xo8eLBmzpzZCp0CAACzM92ena1bt2rZsmWaNGmScnNzlZqaqnnz5qm0tLTB5x07dkx/+tOfdNFFF7VSpwAAIBKYLuysXbtWY8aM0ejRo5WSkqJp06YpJiZGBQUF9T7H6/Xq2Wef1U033aSkpKRW7BYAAJidqQ5jVVVV6cCBA8rJyfHfFxUVpczMTO3bt6/e561atUrx8fG68sor9eGHHza4jsrKSlVWVvpvG4Yhu93u/7ktOPc628rrbQnGqHFteYyqv2bjm38NLWcYhppyHdDqdQzDiIixbepYNPb8usYoEscjFNrythYspgo7ZWVl8nq9cjqdNe53Op06cuRInc/56KOP9NZbb+mJJ55o0jry8/O1atUq/+1evXopNzdXnTt3bnHfkSo5OTncLZgeY9S4tjhG5eXl/p+dCU454uIaXN6Z4GxS3fbtY/w/JycnK66RumbQ3LGoT11jFInjEUptcVsLFlOFnebyeDx69tlnNX36dMXHxzfpORMnTtSECRP8t88l5eLiYlVVVYWkT7MxDEPJyckqKiqSz9eEPzfbIMaocW15jNxut/9nV4lLFRWn61zOMAw5E5xylbiaNEaeanWLiorkcDgCbzbEmjoW9WlojCJxPEKhLW9rDbHZbE3eUWGqsBMfH6+oqCi5XK4a97tcrlp7eyTp6NGjKi4uVm5urv++c2+EyZMna+HChbWScHR0tKKjo+tcf1t7E/l8vjb3mpuLMWpcWxyj6q/X982/uhf8dvl6l6mxeLW6ETKuTR6Legt8W+e7z43E8QglxqDlTBV2bDab0tLSVFhYqCFDhkg6O/m4sLBQY8eOrbV8165dNX/+/Br3rVixQqdOndLtt9+uTp06tUrfAADAvEwVdiRpwoQJWrx4sdLS0pSenq5169apoqJCo0aNkiQtWrRIiYmJmjJlimJiYtSjR48azz93TPe79wMAgLbJdGFn2LBhKisrU15enlwul3r27KlZs2b5D2MdP36cGekAAKDJTBd2JGns2LF1HraSpIcffrjB595zzz0h6AgAAEQq051UEAAAIJgIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNIIOwAAwNJs4W4AANA6fD6fPB5PUGu63e6g1mvt9djtdhmGEZLaMA/CDgC0AT6fTzk5Odq1a1e4W2mRrKyskNTNzs5Wfn4+gcfiOIwFAG2Ax+MJadDJHjJUsXZ7UGvG2u0aeGl2UGt+186dO4O+twvmw54dAGhj1u3YI7vDEdSa/ZKcOnTydFBrGoahF/JWK6ndmaDX9rjdGjdkYFBrwrwIOwDQxtgdjqCHnVAdBjIMQ464ONm9/LpCy/HuiUCBTjI0DEPl5eVyu93y+Xy1HmfCHhB+wZ6Q21oTiQEzIuxEmNaYZMiEPSD8QjUhF2iLmKAcYUI9yVBiwh4QLq0xITcUE4kBs2PPTgRr6SRDQ4acCU65Slzy6dvDWEzYA8IrlBNyzwnFRGLA7Ag7EaylkwwNnZ3wV1FxukbYARB+oZ6Qy+FptEUcxgIAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZG2AEAAJZmC3cDABAqPp9PHo8n6HXdbnfQawIIHcIOAEvy+XzKycnRrl27wt0KgDDjMBYAS/J4PCEPOtlDhirWbg/pOgAEjj07ACxv3Y49sjscQa/bL8mpQydPB70ugOAi7ACwPLvDEZKwYxhG0GsCCD4OYwEAAEsj7AAAAEsj7AAAAEsj7AAAAEsj7AAAAEsj7AAAAEsz5VfP169frzVr1sjlcik1NVVTp05Venp6nctu375d+fn5Kioq0pkzZ5ScnKzvf//7GjFiRCt3DQAAzMh0YWfr1q1atmyZpk2bpj59+ui1117TvHnztHDhQnXs2LHW8uedd55uuOEGde3aVTabTbt379Zzzz2n+Ph4DRo0qPVfAAAAMBXTHcZau3atxowZo9GjRyslJUXTpk1TTEyMCgoK6ly+f//+GjJkiFJSUpScnKxx48YpNTVVH330USt3DgAAzMhUe3aqqqp04MAB5eTk+O+LiopSZmam9u3b1+jzfT6fCgsLdeTIEd166611LlNZWanKykr/bcMwZP/m2jaRcDbU6j0a3/xraQ3DMCRftfur1TIMIyLGI1RqjBHqZPYxCsa20qT1NFC3vm0t0LqBCsdY1PucJo5RsHuOpM87s29rkcBUYaesrExer1dOp7PG/U6nU0eOHKn3eW63W9OnT1dVVZWioqL04x//WAMHDqxz2fz8fK1atcp/u1evXsrNzVXnzp2D8hpCrby83P+zM8EpR1xci2s5E5w1brdvH+P/OTk5WXEB1LaK5OTkcLdgemYdo2BuK/UxqtxKSExodLnvbmvBqtsSoaodaN2GxigUPUfi551Zt7VIYKqw01KxsbF68sknderUKX3wwQdatmyZunTpov79+9daduLEiZowYYL/9rmkXFxcrKqqqlbruaXcbrf/Z1eJSxUVzb8IoWEYciY45Spxyef79k8pT7XaRUVFcoTgWkKRwjAMJScnq6ioqMYY4VtmH6NgbCuN6dAhRiUnSup9vL5tLdC6gQhV7ZbWbcoYhaLnSPq8M/u2Fi42m63JOypMFXbi4+MVFRUll8tV436Xy1Vrb091UVFR/sTbs2dPffnll1q9enWdYSc6OlrR0dF11omEN1H1Hn3f/Gt+kW9rVX9+jZ99vogYj1BjHBpn1jEKyrbSlPU0VLeebS3gugEKy1jU/6Sz/9PIGAW750j8vIuUPs3IVBOUbTab0tLSVFhY6L/P6/WqsLBQffv2bXIdr9dbY14OAABou0y1Z0eSJkyYoMWLFystLU3p6elat26dKioqNGrUKEnSokWLlJiYqClTpkg6Owend+/e6tKliyorK/Xee+9p06ZNuuOOO8L4KgAAgFmYLuwMGzZMZWVlysvLk8vlUs+ePTVr1iz/Yazjx4/XmJFeUVGhJUuW6KuvvlJMTIy6deumn/70pxo2bFiYXgEAADAT04UdSRo7dqzGjh1b52MPP/xwjduTJ0/W5MmTW6ErAAAQiUw1ZwcAACDYCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSCDsAAMDSAgo7v/3tb7V582adPn06WP0AAAAEVUDXxjp69KieffZZxcbGKjs7WyNGjFBmZmaNC3UCAACEU0Bh5+mnn9b+/fu1adMmbdu2TZs2bZLT6dTw4cN1xRVXqGfPnkFqEwAAoGUCvup5enq60tPT9cMf/lB79uzRpk2b9Oabb2rt2rVKSUnRiBEjNHz4cJ1//vnB6BcAAKBZAg4750RFRWnQoEEaNGiQysvL9fvf/17/+Mc/tHz5cv35z39W//79NX78eF1yySXBWiUAAECjghZ2JOmjjz7Su+++q+3bt+vkyZPq3r27RowYIZvNpoKCAuXm5uqGG27QzTffHMzVAgAA1CvgsPPFF1/o3Xff1ZYtW3T8+HF17NhRI0eO1IgRI2rM2Rk3bpxeeOEFvf7664QdAADQagIKO7/85S916NAhRUdHa/DgwbrjjjuUlZWlqKi6v9Hev39/vfXWW4GsEgAAoFkCCjtxcXGaPn26LrvsMjkcjkaXz87O1qJFiwJZJQAAQLMEFHZ+8pOfKD4+XjExMXU+fvr0aZWVlalTp06SpPbt26tz586BrBIAAKBZAjqD8j333KMdO3bU+/iuXbt0zz33BLIKAACAgIT02lhVVVX1zt8BAABoDc0+jOV2u+V2u/23v/76ax0/frzWcuXl5dq6daucTmdADQIAAASi2WHntdde06pVq/y3ly5dqqVLl9a7PF8zBwAA4dTssJOVlaXY2Fj5fD69/PLLuvzyy9WrV68ayxiGofbt2ystLU29e/cOWrMAAADN1eyw07dvX/Xt21eSVFFRoaFDh6pHjx5BbwwAACAYAvrq+Y033hisPgAAAEKiWWHn3FydG264QVFRUTXm7jRk0qRJze8MAAAgCJoVdv7yl79IknJychQVFeW/3RjCDgAACJdmhZ2VK1c2eBsAAMBsOOMfAACwtIAmKNeloqJCW7ZsUVVVlS6++GKuhQUAAMIqoLDz/PPPa//+/VqwYIGks5eHmD17tg4fPixJcjgcmjt3bq3z8AAAALSWgA5j/fvf/9aQIUP8tzdv3qzDhw/rpz/9qRYsWCCn09nkScwAAAChEFDYcblcNQ5T7dixQ2lpaRo+fLhSUlI0ZswY7d+/P+AmAQAAWiqgsNO+fXv/RUHPnDmjvXv3Kisry/94bGxsjYuGAgAAtLaA5uykpaVp48aN6t+/v3bt2iWPx6PBgwf7Hz969Kg6duwYcJMAAAAtFdCencmTJ6u0tFS/+tWvtGrVKg0dOlTp6en+x3fs2KF+/foF3CQAAEBLBbRnp3fv3lq4cKE+/vhjxcXFKSMjw/9YeXm5rrnmmhr3AQAAtLaAz7MTHx+v7OzsWvfHxcVp3LhxgZYHAAAISFBOKujxeFRcXKzy8nL5fL5aj7N3BwAAhEtAYefrr7/WH/7wB23fvl1er7fe5biGFgAACJeAws4LL7ygf/7zn7r22mt14YUX6rzzzgtWXwAAAEERUNh5//33NX78eN12223B6gcAACCoAj6pIBf6BAAAZhZQ2Lniiiu0Y8eOYPUCAAAQdAEdxrrsssu0d+9ezZs3T1dddZXOP/98RUXVzk9paWmBrAYAAKDFAgo7c+fO9f+8Z8+eepfj21gAACBcAgo7d999d7D6AAAACImAws6oUaOC1AYAAEBoBDRBubqSkhIdPHhQp06dClZJAACAgAUcdnbu3Kn7779fd911lx588EHt379fklRWVqaZM2fybS0AABBWAYWdXbt2af78+erQoYNuvPHGGo/Fx8crMTFRb7/9diCrAAAACEhAYeeVV15RRkaGHn30UV1zzTW1Hu/bt68+++yzQFYBAAAQkIDCzqFDh/S9732v3sc7duyosrKyQFYBAAAQkIAvF9HQhOSjR49ycVAAABBWAYWd/v3765133tGZM2dqPeZyubRx40ZlZWUFsgoAAICABBR2brnlFp04cUK//vWvtWHDBknSv/71L61YsUK/+MUvJEmTJk0KvEsAAIAWCuikgl27dtUjjzyipUuX+i8JsWbNGklSRkaGfvzjHyspKSnwLgEAAFoooLAjSd27d9ecOXN08uRJFRUVyefzqUuXLoqPjw9GfwAAAAFpcdiprKzUpk2b9P777+vo0aPyeDyy2+1KTk7WoEGDNHz4cNlsAWcpAACAgLQojRw6dEhPPPGEiouLJUkOh0OxsbEqKyvTZ599pm3btunVV1/VzJkzlZKSEtSGAQAAmqPZYefUqVPKzc1VWVmZbrnlFo0YMUKJiYn+x0+cOKF33nlHr776qnJzc/Xkk08qNjY2qE0DAAA0VbO/jVVQUKDjx4/rV7/6lXJycmoEHUlKTEzUxIkT9eCDD+rYsWNcLgIAAIRVs8PO7t27lZWVpf79+ze43IABAzRw4ED985//bHFzAAAAgWp22Dl06JAyMjKatOyAAQN06NChZjcFAAAQLM2es3Py5Ek5nc4mLduxY0edPHmyuavQ+vXrtWbNGrlcLqWmpmrq1KlKT0+vc9k333xT7777rg4fPixJSktL0y233FLv8gAAoG1p9p6dqqqqJn+lvF27dqqqqmpW/a1bt2rZsmWaNGmScnNzlZqaqnnz5qm0tLTO5ffu3avLL79c//M//6PHHntM559/vh577DGdOHGiWesFAADW1KKvnh87dkwHDhxo0nLNtXbtWo0ZM0ajR4+WJE2bNk27d+9WQUGBcnJyai1/77331rh91113afv27frggw80cuTIZq8fAABYS4vCzsqVK/2XhwimqqoqHThwoEaoiYqKUmZmpvbt29ekGhUVFaqqqqr3auuVlZWqrKz03zYMQ3a73f+z2VXv0fjmX0trGIYh+ardX62WYRgRMR6hUmOMUCezj1EwtpUmraeBuvVta4HWDVQ4xqLe5zRxjILdcyR93pl9W4sEzQ47d999dyj6kCSVlZXJ6/XWmhPkdDp15MiRJtV4+eWXlZiYqMzMzDofz8/P16pVq/y3e/XqpdzcXHXu3LnFfbem8vJy/8/OBKcccXEtruVMcNa43b59jP/n5ORkxQVQ2yqSk5PD3YLpmXWMgrmt1MeocishMaHR5b67rQWrbkuEqnagdRsao1D0HImfd2bd1iJBs8POqFGjQtBGcKxevVpbtmzRww8/rJiYmDqXmThxoiZMmOC/fS4pFxcXN3t+UTi43W7/z64SlyoqTje7hmEYciY45Spxyef79k8pT7XaRUVFcjgcgTUbwQzDUHJysv96b6jN7GMUjG2lMR06xKjkREm9j9e3rQVaNxChqt3Suk0Zo1D0HEmfd2bf1sLFZrM1eUeFqS5eFR8fr6ioKLlcrhr3u1yuRr8B9re//U2rV6/WnDlzlJqaWu9y0dHRio6OrvOxSHgTVe/R982/5hf5tlb159f42eeLiPEINcahcWYdo6BsK01ZT0N169nWAq4boLCMRf1POvs/jYxRsHuOxM+7SOnTjJr9baxQstlsSktLU2Fhof8+r9erwsJC9e3bt97n/fWvf9Urr7yiWbNmqXfv3q3RKgAAiBCmCjuSNGHCBG3cuFFvv/22vvjiCy1ZskQVFRX+w2eLFi3S8uXL/cuvXr1aK1eu1N13362kpCS5XC65XC6dOnUqTK8AAACYiakOY0nSsGHDVFZWpry8PLlcLvXs2VOzZs3yH8Y6fvx4jRnpGzZsUFVVlZ566qkadSZNmqSbbrqpNVsHAAAmZLqwI0ljx47V2LFj63zs4YcfrnF78eLFrdARAACIVKY7jAUAABBMhB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBphB0AAGBptnA3AHNyu91Br2m322UYRtDrAgDQEMIO6pSVlRX0mtnZ2crPzyfwAABaFYex4Bdrt2vgpdkhq79z5055PJ6Q1QcAoC7s2YGfYRh6IW+1ktqd0aGTp4NW1+N2a9yQgUGrBwBAcxB2UINhGHLExcnu5a0BALAGDmMBAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLs4W7AQAAwsntdge9pt1ul2EYQa+LliHsAADatKysrKDXzM7OVn5+PoHHJDiMBQBoc2Ltdg28NDtk9Xfu3CmPxxOy+mge9uwAANocwzD0Qt5qJbU7o0MnTwetrsft1rghA4NWD8FB2AEAtEmGYcgRFye7l1+FVsdhLAAAYGmEHQAAYGmEHQAAYGmEHQAAYGmEHQAAYGlMQQ8hn88X9PMshOJMnwAAWBlhJ0R8Pp9ycnK0a9eucLcCAECbxmGsEPF4PCENOtlDhirWbg9ZfQAArII9O61g3Y49sjscQa3ZL8kZ1LN+AgBgVYSdVmB3OIIedri4HAAATWO6sLN+/XqtWbNGLpdLqampmjp1qtLT0+tc9vDhw1q5cqU+++wzFRcX64c//KHGjx/fyh0DAAAzM9Wcna1bt2rZsmWaNGmScnNzlZqaqnnz5qm0tLTO5SsqKtSlSxdNmTJFTqezdZsFAAARwVRhZ+3atRozZoxGjx6tlJQUTZs2TTExMSooKKhz+fT0dP33f/+3Lr/8ckVHR7dytwAAIBKYJuxUVVXpwIEDyszM9N8XFRWlzMxM7du3L4ydAQCASGaaOTtlZWXyer21Dkc5nU4dOXIkaOuprKxUZWWl/7ZhGLJ/8xXuYE76rV7L+OZfsLW05rneDMOQfMGt3VgtwzAiYnJ1jTFCncw+Rq2xDZ6r3VgPDW1rLakbqHCMRb3PaeIYRcp4hOLzzuzbWiQwTdhpLfn5+Vq1apX/dq9evZSbm6vOnTsHdT3l5eX+n50JTjni4oJa36hyKyExIaAazgRnyGpX1759jP/n5ORkxQV5LEIpOTk53C2YnlnHKNTboNT0baW+bS3Qui0RqtqB1m1ojCJpPEL5eWfWbS0SmCbsxMfHKyoqSi6Xq8b9LpcrqJOPJ06cqAkTJvhvn0vKxcXFqqqqCtp6ql/WwVXiUkVFcM+J06FDjEpOlLTouYZhyJnglKvEJZ+v9p9SgdSui6faWBQVFckR5K/hh4JhGEpOTlZRUVGdYwTzj1Got0Gp8W2lsW2tpXUDEaraLa3blDGKpPEIxeed2be1cLHZbE3eUWGasGOz2ZSWlqbCwkINGTJEkuT1elVYWKixY8cGbT3R0dH1TmYO5puoei3fN/+CrcU1v3maz1d/X8Hst3otn88XURtrpPUbDmYdo9bYBs/VbuBBfy/NXX+o+g1l7RbVbeIYRcp4hPLzzqzbWiQwTdiRpAkTJmjx4sVKS0tTenq61q1bp4qKCo0aNUqStGjRIiUmJmrKlCmSzk5q/uKLL/w/nzhxQgcPHlRsbCy7+wAAgCSThZ1hw4aprKxMeXl5crlc6tmzp2bNmuU/jHX8+PEaE7ROnDihmTNn+m+vWbNGa9asUUZGhh5++OFW7h4AAJiRqcKOJI0dO7bew1bfDTBJSUnKy8trha4AAECkMs15dgAAAEKBsAMAACyNsAMAACyNsAMAACyNsAMAACyNsAMAACyNsAMAACyNsAMAACyNsAMAACzNdGdQBtD2+Hw+eTyeoNasftVzAG0bYQdAWPl8PuXk5GjXrl3hbgWARXEYC0BYeTyekAad7CFDFWu3h6w+APNjzw4A01i3Y4/sDkdQa/ZLcurQydNBrQkgshB2AJiG3eEIetgxDCOo9QBEHsIOAAAhEKxJ8oZhqLy8XG63Wz6fT3a7nRDfTIQdAABCICsrKyR1s7OzlZ+fT+BpBiYoAwAQJLF2uwZemh3SdezcuTPop2qwOvbsAAAQJIZh6IW81UpqdyZoE+MNGXImOPWfL4/o2iGZQanZ1hB2AAAIIsMw5IiLk90bnF+xhr6pF+TJ+20Jh7EAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAIClEXYAAICl2cLdANoWt9sdkrp2u12GYYSkNgAgshF20KqysrJCUjc7O1v5+fkEHgBALRzGQsjF2u0aeGl2SNexc+dOeTyekK4DABCZ2LODkDMMQy/krVZSuzM6dPJ0UGt73G6NGzIwqDUBANZC2EGrMAxDjrg42b285QAgUKGY/2jluY/85gEAIMKEYv6jlec+MmcHAIAIEOr5j1ae+8ieHQAAIkCo5j+2hbmPhB0AACIE8x9bhsNYAADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0pjODQAAJIXmzMznhPMMzYQdAAAgKTRnZj7nk08+kcPhCFn9hnAYCwCANizUZ2Y2A/bsAADQhoXqzMzVdY+zKTY6fJGDsAMAQBsX6jMzO+Ki5asMTZBqCg5jAQAASyPsAAAASyPsAAAASyPsAAAASyPsAAAAS+PbWACaxOfzyePx+G8bhqHy8nK53W75fL4W1w3lGVsBQCLsAGgCn8+nnJwc7dq1K9ytAECzcRgLQKM8Hk/Ig072kKGKtdtDug4AbZMp9+ysX79ea9askcvlUmpqqqZOnar09PR6l9+2bZtWrlyp4uJiJScn69Zbb9Ull1zSih0Dbce6HXtkdzhkyJAzwSlXiUs+tfww1jn9kpwhO3srgLbNdGFn69atWrZsmaZNm6Y+ffrotdde07x587Rw4UJ17Nix1vIff/yxnn76aU2ZMkWXXHKJNm/erCeffFK5ubnq0aNHGF4BYG12h8MfdhxxcaqoOB2UsBOuqyEDsD7ThZ21a9dqzJgxGj16tCRp2rRp2r17twoKCpSTk1Nr+XXr1mnQoEG67rrrJEmTJ0/WBx98oPXr1+vOO+9szdYRZsGc6BqsybdWwSRiAJHMVGGnqqpKBw4cqBFqoqKilJmZqX379tX5nH379mnChAk17svKytLOnTvrXL6yslKVlZX+24ZhyG63y2YL7lC0b99eF198sSSpQ2x7tY+JDmp9W7t2imthTcMw1D7KUFz76Dp/kQdSuyGhqGvzfjvOt99+e1Bro6bvvp8bex81VyS975pau6VjFM6eW7tuU8aoLY1HXb47RpHQ83dF29rJpyB//jfj97apwk5ZWZm8Xq+cTmeN+51Op44cOVLnc1wuV63DWx07dpTL5apz+fz8fK1atcp/+/LLL9d9992nhISEgHqvy+7du4Nes7pOgbbc4fzQ1W7FuqEeZzSigfdRc0XS+65ZtVswRmHvubXrNjJGbW486lJtjCKmZ5Noc9/GmjhxopYuXer/b9q0aTX29LQFHo9HDz74YI1zpqAmxqhxjFHjGKPGMUaNY4wCZ6o9O/Hx8YqKiqq1V8blctXa23OO0+lUaWlpjftKS0vrXT46OlrR0aHZTRcpfD6fPvvsM+aiNIAxahxj1DjGqHGMUeMYo8CZas+OzWZTWlqaCgsL/fd5vV4VFhaqb9++dT6nb9+++uCDD2rct2fPHvXp0yekvQIAgMhgqrAjSRMmTNDGjRv19ttv64svvtCSJUtUUVGhUaNGSZIWLVqk5cuX+5cfN26c3n//fa1Zs0Zffvml8vLy9Omnn2rs2LFhegUAAMBMTHUYS5KGDRumsrIy5eXlyeVyqWfPnpo1a5b/sNTx48drnI+jX79+uvfee7VixQr9+c9/1gUXXKBf/vKXnGOnAdHR0Zo0aVKbP5zXEMaocYxR4xijxjFGjWOMAmf4OAgIAAAszHSHsQAAAIKJsAMAACyNsAMAACyNsAMAACzNdN/GQui88cYbeuONN1RcXCxJSklJ0aRJk/zXPEJNq1ev1vLlyzVu3Diuu/WNvLy8GpdbkaSuXbtq4cKF4WnIpE6cOKGXXnpJ//rXv1RRUaHk5GTNmDFDvXv3DndrpnDPPff4P4eq+6//+i/dcccdYejIfLxer/Ly8rRp0ya5XC4lJiZq5MiR+sEPflDjG8loGsJOG5KYmKgpU6boggsukM/n0zvvvKMnnnhCTzzxhLp37x7u9kxl//792rBhg1JTU8Pdiul0795dc+bM8d+OimIHcXUnT57UnDlz1L9/f82aNUvx8fH6z3/+o7i4uHC3ZhqPP/64vF6v//ahQ4f02GOP6Xvf+14YuzKX1atXa8OGDbrnnnuUkpKiAwcO6LnnnpPD4dC4cePC3V7EIey0IYMHD65x+5ZbbtEbb7yhTz75hLBTzalTp/Tss89q+vTpevXVV8PdjulERUXVezkWSH/96191/vnna8aMGf77kpKSwtiR+cTHx9e4vXr1anXp0kUZGRlh6sh89u3bp8GDB+uSSy6RdPY9tHnzZu3fvz/MnUUm/iRro7xer7Zs2aKKiop6L8XRVi1ZskQXX3yxBg4cGO5WTKmoqEjTp0/XT37yEz3zzDM6fvx4uFsylV27diktLU1PPfWU7rjjDs2cOVNvvvlmuNsyraqqKm3atEmjR4/m8Ew1ffv2VWFhoY4cOSJJOnjwoD7++GOmHbQQe3bamEOHDmn27NmqrKxUbGysHnjgAaWkpIS7LdPYsmWLPvvsMz3++OPhbsWU+vTpoxkzZqhr164qKSnRqlWrNHfuXC1YsEB2uz3c7ZnCsWPHtGHDBo0fP14TJ07Up59+qhdffFE2m81/2Rt8a8eOHSovL2dsviMnJ0cej0c/+9nPFBUVJa/Xq8mTJ+uKK64Id2sRibDTxnTt2lVPPvmk3G63/vGPf2jx4sX6zW9+Q+DR2UuRLF26VA899JBiYmLC3Y4pVf+rMjU11R9+tm3bpiuvvDKMnZmH1+tV7969NWXKFElSr169dOjQIW3YsIFf6HUoKCjQoEGDlJiYGO5WTGXbtm3avHmz7r33XnXv3l0HDx7U0qVLlZCQwPuoBQg7bYzNZlNycrIkKS0tTZ9++qnWrVunO++8M8ydhd+BAwdUWlqqBx980H+f1+vVhx9+qPXr12v58uVMxv2OuLg4de3aVUVFReFuxTQSEhJq/fGQkpKi7du3h6kj8youLtaePXv0wAMPhLsV03nppZd0/fXX6/LLL5ck9ejRQ8XFxVq9ejVhpwUIO22c1+tVZWVluNswhczMTM2fP7/Gfc8//7y6du2q66+/nqBTh1OnTqmoqIhd69X069fPP8/inCNHjqhz585h6si8CgoK1LFjR/8kXHyroqKi1mdOVFSUuJxlyxB22pDly5dr0KBB6tSpk06dOqXNmzdr7969mj17drhbMwW73a4ePXrUuK99+/bq0KFDrfvbqmXLlmnw4MHq1KmTSkpKlJeXp6ioKA0fPjzcrZnG+PHjNWfOHL366qsaNmyY9u/fr40bN7L39Du8Xq/efvttjRw5Uu3atQt3O6Zz6aWX6tVXX1WnTp2UkpKigwcPau3atRo9enS4W4tIhJ02pLS0VIsXL1ZJSYkcDodSU1M1e/ZsvnWEJjtx4oSefvppff3114qPj9eFF16oefPm1foqcVuWnp6uBx54QMuXL9crr7yipKQk/fCHP2Tv13d88MEHOn78OL+86zF16lStXLlSS5YsUWlpqRITE3X11Vdr0qRJ4W4tIhk+9okBAAALYxICAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwNMIOAACwtP8PF8wgaa97s0cAAAAASUVORK5CYII=", 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/XqmpqTpw4EBEb+dgt9t1+PBhdezYkcADhMjj8ejw4cP17iMGAK3NVGFn9erVGjt2rMaMGSNJmjZtmrZv367i4mLl5+c3aP/GG2+osrJS9913n+8WA4HuYB2q2NhYJSUlqbKyMqLzjbb4+HgdPXo02mWYGn0UWDB9lJSUFPQtQACgJZhmD1RbW6tdu3bVCzUxMTG+ewj5895776lv3776y1/+om3btik5OVnnnHOO8vPzGz0KU1NTU28QNMMwfHfBPn4n8BPFxcWFdONIszMMQ+np6SotLWWAqkbQR4HRR4Ed36c0tm+xgrrrZvz406BNnWmGYdR/Tzvoo3DRR+EzTdipqKiQx+NpcH8ih8OhvXv3+n3Pvn37VFZWppEjR+ruu+9WaWmpFi9erGPHjunyyy/3+56ioqJ6d/ju3bu3CgoKgh6F0UrS09OjXYLp0UeB0UeBWbmPqqqqfI8dKQ7Z/ZyyTEiI9z1OT0/3e1rTyn0UKfRR85km7DSH1+tVcnKypk+frpiYGGVlZengwYN6+eWXGw07EydOVF5enu/58aRcVlam2traVqk72vgXeWD0UWD0UWDtoY9cLpfvsfOQU9XVDU9ruuu0KS0tbXC7CKv3UbjoI/9iY2Pb3u0ikpOTFRMTI6fTWW+60+ls9G7UDodDsbGx9U5Zde/eXU6nU7W1tX6vE4iLi1NcXJzf+bW3D5HX62136xwq+igw+igwK/dR3fXy/vjToE2daY31hZX7KFLoo+YzzdeLYmNjlZWVpZKSEt80j8ejkpKSendcrqt///4qLS2t99XW7777TikpKVwQCQAAJJko7EhSXl6e1q9frzfffFPffPONFi9erOrqao0ePVqStHDhQi1btszX/uc//7kqKyu1ZMkS7d27V9u3b1dRUZEuuuiiKK0BAAAwG1Md/hgxYoQqKipUWFgop9OpXr16aebMmb7TWAcOHKh3NXrnzp01a9Ys/e1vf9Mdd9yh1NRUXXzxxX6/pg4AANonU4UdSRo3bpzGjRvn97W5c+c2mNavXz/NmzevhasCAABtlalOYwEAAEQaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFgaYQcAAFhabLQLAAAr8Hq9crvd9aYZhqGqqiq5XC55vV5Jks1mk2EY0SgRaLcIOwAQJq/Xq/z8fG3bti1g29zcXBUVFRF4gFbEaSwACJPb7Q4q6EjS1q1bGxwBAtCyOLIDABG0ZssO2ex2SZIhQ44Uh5yHnHK5qjR+2OAoVwe0T4QdAIggm91eL+zYk5JUXX1UXnmjXBnQfnEaCwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWBphBwAAWJopbwS6du1arVq1Sk6nU5mZmZo6daqys7P9tn3zzTf15JNP1psWFxen5557rjVKBQAAJme6sLNp0yYtXbpU06ZNU9++ffXKK69o3rx5WrBggTp16uT3PTabTY899lgrVwoAANoC053GWr16tcaOHasxY8YoIyND06ZNU3x8vIqLixt9j2EYcjgc9f4DAACQTHZkp7a2Vrt27VJ+fr5vWkxMjHJycrRz585G33fkyBHNmDFDXq9XvXv31lVXXaUePXr4bVtTU6Oamhrfc8MwZLPZfI/bg+Pr2V7Wtznoo8Doo5/U7QPjx5+60w3jp2m+5xbpt8bWvV6bJtadz1Fg9FH4TBV2Kioq5PF4GhyZcTgc2rt3r9/3dOvWTTfddJMyMzPlcrn08ssv65577tEjjzyik08+uUH7oqIirVixwve8d+/eKigoUJcuXSK6Lm1Benp6tEswPfooMPpIqqqq8j12pDhkT0qq97ojxaH4+Djf8/T0dCWd0KatCrTukpSQEO973Ni68zkKjD5qPlOFnebo16+f+vXrV+/57373O61bt06TJ09u0H7ixInKy8vzPT+elMvKylRbW9vyBZuAYRhKT09XaWmpvF5vtMsxJfooMProJy6Xy/fYecip6uqjkn48xZ7ikPOQU646oaC0tFR2u73V62wJja17Xe46bU5cdz5HgdFH/sXGxgZ9oMJUYSc5OVkxMTFyOp31pjudzqCvw4mNjVXv3r1VWlrq9/W4uDjFxcX5fa29fYi8Xm+7W+dQ0UeB0Uf19x3eH39+fOJ73TdN1uqzRte9bpsg1t1KfdJS6KPmM9UFyrGxscrKylJJSYlvmsfjUUlJSb2jN03xeDzavXu3UlJSWqpMAADQhpjqyI4k5eXladGiRcrKylJ2drbWrFmj6upqjR49WpK0cOFCpaamasqUKZKkFStWqG/fvkpPT1dVVZVefvlllZWVaezYsVFcCwAAYBamCzsjRoxQRUWFCgsL5XQ61atXL82cOdN3GuvAgQP1rkivrKzU008/LafTqaSkJGVlZen+++9XRkZGlNYAAACYienCjiSNGzdO48aN8/va3Llz6z2/7rrrdN1117V8UQAAoE0y1TU7AAAAkUbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlhYb7QIAIJq8Xq/cbnfAdjabTYZhtEJFrac9rzvaF8IOgHbL6/UqPz9f27ZtC9g2NzdXRUVFlvmj357XHe0Pp7EAtFtutzuoP/aStHXr1qCOgrQV7Xnd0f5wZAcAJK3ZskM2u73BdLfLpfHDBkehotbTntcd7QNhBwAk2ex2v3/w24P2vO5oHziNBQAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALI2wAwAALM2Udz1fu3atVq1aJafTqczMTE2dOlXZ2dkB3/fOO+/oscce09ChQ3XnnXe2QqUAAMDsTHdkZ9OmTVq6dKkmTZqkgoICZWZmat68eSovL2/yffv379ff//53nXbaaa1UKQAAaAtMF3ZWr16tsWPHasyYMcrIyNC0adMUHx+v4uLiRt/j8Xj0xBNP6IorrlBaWlorVgsAAMzOVKexamtrtWvXLuXn5/umxcTEKCcnRzt37mz0fStWrFBycrLOP/98ffzxx00uo6amRjU1Nb7nhmHIZrP5HrcHx9ezvaxvc9BHgVmhj+rWbvz406BNnWmGYfhd38bmU7ePgplPa2rpdQ92Plb4HLU0+ih8pgo7FRUV8ng8cjgc9aY7HA7t3bvX73s++eQTvfHGG3rwwQeDWkZRUZFWrFjhe967d28VFBSoS5cuza67rUpPT492CaZHHwXWlvuoqqrK99iR4pA9KalBm4SEeN/j9PR0JflpE2g+jhSH4uPjAs6nNbXWugc7n7b8OWot9FHzmSrshMrtduuJJ57Q9OnTlZycHNR7Jk6cqLy8PN/z40m5rKxMtbW1LVKn2RiGofT0dJWWlsrr9Ua7HFOijwKzQh+5XC7fY+chp6qrjzZo467TprS0VHa7Pej5GIYhR4pDzkNOueqEgsbm05paet2DnY8VPkctjT7yLzY2NugDFaYKO8nJyYqJiZHT6aw33el0NjjaI0n79u1TWVmZCgoKfNOOfxAmT56sBQsWNEjCcXFxiouLkz/t7UPk9Xrb3TqHij4KrC33Ud26vT/+NGhTZ1pj69rofLx13hfEfFpTi697M+YT7T4xO/qo+UwVdmJjY5WVlaWSkhINGzZM0g8XH5eUlGjcuHEN2nfr1k0PP/xwvWnPP/+8jhw5ouuuu06dO3dulboBAIB5mSrsSFJeXp4WLVqkrKwsZWdna82aNaqurtbo0aMlSQsXLlRqaqqmTJmi+Ph49ezZs977j58LPnE6AABon0wXdkaMGKGKigoVFhbK6XSqV69emjlzpu801oEDB7gi3Q+v1yu32x1UW8MwVFVVJZfL5feQqM1mo4+BFlT3Ohd/2us2GMp+LBjttR/RkOnCjiSNGzfO72krSZo7d26T77355ptboCJz83q9ys/P17Zt2yIyv9zcXBUVFbGTAFrIkCFDmny9PW6Dkd6PSe2zH+Gf6QYVROjcbndEdxBbt26N6L+uAEiJNpsGn5UbVNv2uA1Gej8mtc9+hH+mPLKD5luzZYdsTXyltedJ8dpTWeP7Omzdb0m4XS6NHza4NcoE2h3DMPR04UqldTim3ZUNv54tsQ0eF2g/Jv2wL6MfESzCjsXY7PYmdxL2pATZPEdlT0pSdfVRv18TBdAyDMOQPSlJNg+73qYE2o9Jx/dl9COCE9ZprD/96U/auHGjjh71n64BAACiLaxYvG/fPj3xxBNKTExUbm6uRo0apZycHC4GAwAAphFW2Hnsscf0+eefa8OGDdq8ebM2bNggh8OhkSNH6txzz1WvXr0iVCYAAEDzhH3CMzs7W9nZ2br22mu1Y8cObdiwQa+//rpWr16tjIwMjRo1SiNHjtTJJ58ciXoBAABCErGru2JiYnT66afr9NNPV1VVlf785z/r3//+t5YtW6Z//OMfGjhwoCZMmKAzzzwzUosEAAAIKKKXsn/yySd6++239e6776qyslI9evTQqFGjFBsbq+LiYhUUFOiyyy7TlVdeGcnFAgAANCrssPPNN9/o7bff1jvvvKMDBw6oU6dOOu+88zRq1Kh61+yMHz9eTz/9tF599VXCDgAAaDVhhZ077rhDu3fvVlxcnIYOHarrr79eQ4YMUUyM/2+0Dxw4UG+88UY4iwQAAAhJWGEnKSlJ06dP19lnny17gAGgpB/uU7Jw4cJwFgkAABCSsMLOb37zGyUnJys+Pt7v60ePHlVFRYU6d+4sSUpISFCXLl3CWSQAAEBIwhpB+eabb9aWLVsafX3btm3t8i7kAADAPFr0rue1tbWNXr8DAADQGkI+jeVyueRyuXzPDx8+rAMHDjRoV1VVpU2bNsnhcIRVIAAAQDhCDjuvvPKKVqxY4Xu+ZMkSLVmypNH2fM0cAEJX9x+VzWWz2bhXIaBmhJ0hQ4YoMTFRXq9Xzz33nM455xz17t27XhvDMJSQkKCsrCz16dMnYsUCQHsxZMiQsOeRm5uroqIiAg/avZDDTr9+/dSvXz9JUnV1tYYPH66ePXtGvDAAaG8SbTYNPitXO97bGpH5bd26VW63O6ihQQArC+ur55dffnmk6gCAds8wDD1duFJpHY5pd+XRJtv2PCm+0TZul0vjhw1uiRKBNimksHP8Wp3LLrtMMTEx9a7dacqkSZNCrwwA2iHDMGRPSpLN0/Tu2Z6UELANgB+EtKX885//lCTl5+crJibG9zwQwg4AAIiWkMLO8uXLm3wOAABgNoz4BwAALC3iJ3yrq6v1zjvvqLa2VmeccQb3wgIAAFEVVth56qmn9Pnnn2v+/PmSfrg9xKxZs7Rnzx5Jkt1u15w5cxqMwwMAANBawjqN9d///lfDhg3zPd+4caP27Nmj3/72t5o/f74cDkfQFzEDAAC0hLDCjtPprHeaasuWLcrKytLIkSOVkZGhsWPH6vPPPw+7SAAAgOYKK+wkJCT47t9y7NgxffTRR/WGOE9MTIzI/V0AAACaK6xrdrKysrR+/XoNHDhQ27Ztk9vt1tChQ32v79u3T506dQq7SAAAgOYK68jO5MmTVV5errvuuksrVqzQ8OHDlZ2d7Xt9y5Yt6t+/f9hFAgAANFdYR3b69OmjBQsW6NNPP1VSUpIGDBjge62qqkoXXXRRvWkAAACtLexxdpKTk5Wbm9tgelJSksaPHx/u7AEAAMISkUEF3W63ysrKVFVVJa/X2+B1ju4AAIBoCSvsHD58WH/5y1/07rvvyuPxNNqOe2gBACQ1+IauYRiqqqrim7toUWGFnaefflrvvfeeLr74Yp166qk66aSTIlUXAMCC6g5PArSWsMLOBx98oAkTJuiaa66JVD0AAItJtNk0+Kxc7Xhva8C2ucOGK9Fma4Wq0J6EFXYSEhK40ScAoEmGYejpwpVK63BMuyuP1n9NhhwpDjkPOeWVV/3THA3aAOEKa5ydc889V1u2bIlULQAAizIMQ/akJNns9gb/1Z1uGEa0S4UFhXVk5+yzz9ZHH32kefPm6YILLtDJJ5+smJiG+SkrKyucxQAAADRbWGFnzpw5vsc7duxotB3fxgIAANESVti56aabIlUHAABAiwgr7IwePTpCZQAAALSMiIygLEmHDh1SeXm50tPTlZiYGKnZAgDC0NhgfaEO4hep+bS2QPXZbDYuim4Hwg47W7du1XPPPafvvvtOkjR79mwNGjRIFRUVuv/++zVp0iQNGzYs7EIBAKGL1CB+bXUwwEB15+bmqqioiMBjcWGFnW3btunhhx9Wv379NHLkSP3zn//0vZacnKzU1FS9+eabIYedtWvXatWqVXI6ncrMzNTUqVOVnZ3tt+27776roqIilZaW6tixY0pPT9cvfvELjRo1KpxVA4A2K1KD+LXVwQBDqXvr1q1yu92y2+2tUBmiJayw88ILL2jAgAH63//9Xx0+fLhe2JGkfv36ad26dSHNc9OmTVq6dKmmTZumvn376pVXXtG8efO0YMECderUqUH7k046SZdddpm6deum2NhYbd++XU8++aSSk5N1+umnh7N6ANAmNTWI34maGsQvUvNpbcHU7Xa5NH7Y4FauDNESVtjZvXu3rr322kZf79SpkyoqKkKa5+rVqzV27FiNGTNGkjRt2jRt375dxcXFys/Pb9B+4MCB9Z6PHz9eb731lj755BPCDoB2yzeIn6fp3Xyg0zeRmk9rC7ZutA9h3y7iyJEjjb6+b9++kG4OWltbq127dtULNTExMcrJydHOnTsDvt/r9aqkpER79+7V1Vdf7bdNTU2NampqfM8Nw5Dtx0OvZttYg1W3buPHn2DaG4YheetMr/M+wzDabH9EQr0+gl9W6KNgtp1gtovG5hPMttZobe2kjb8+CmY+4dbUlvZ3VtjWoi2ssDNw4EC99dZbmjBhQoPXnE6n1q9fr7POOivo+VVUVMjj8cjhcNSb7nA4tHfv3kbf53K5NH36dNXW1iomJka//vWvNXiw/8OTRUVFWrFihe957969VVBQ0Kbv8VVVVeV77EhxyJ6U1Ghbo9YlR4rD17auhIR43+P09HQlNTGf9iI9PT3aJZheW+6jYLadYLaLQPOpu60ZtS6lpKY0WVd7bHO8j4KZTySW1xb3d215W4u2sMLOVVddpVmzZunuu+/W2WefLUn6z3/+o5KSEt+1OpMmTQq/ygASExP10EMP6ciRI/rwww+1dOlSde3atcEpLkmaOHGi8vLyfM+PJ+WysjLV1ta2eK0toe5XK52HnKqubvy8eceO8XIecv504z3vT//cdNeZT2lpabu+YM8wDKWnp6u0tLReH+EnVuijYLadYLaLxuZjGEaDba1jx3gdOnioybraU5sT+yiY+USipra0v7PCttYSYmNjgz5QEVbY6datm+69914tWbLEd0uIVatWSZIGDBigX//610pLSwt6fsnJyYqJiZHT6aw33el0NjjaU1dMTIwv8fbq1UvffvutVq5c6TfsxMXFKS4uzu982uqHqG7d3h9/gmnv9dZvW++x19tm+yOS6IfA2nIfBbPtBLNdNDofb533NbKtNVpbe2njp4+CmU+4NbXF/V1bqdOMwr5yq0ePHpo9e7YqKyt9qbNr165KTk4OvZjYWGVlZamkpMT3dXWPx6OSkhKNGzcu6Pl4PJ561+UAAID2q9lhp6amRhs2bNAHH3ygffv2ye12y2azKT09XaeffrpGjhyp2NjQZ5+Xl6dFixYpKytL2dnZWrNmjaqrq323pli4cKFSU1M1ZcoUST9cg9OnTx917dpVNTU1ev/997VhwwZdf/31zV01AABgIc0KO7t379aDDz6osrIySZLdbldiYqIqKir05ZdfavPmzXrxxRd15513KiMjI6R5jxgxQhUVFSosLJTT6VSvXr00c+ZM32msAwcO1Lsivbq6WosXL9b333+v+Ph4de/eXb/97W81YsSI5qwaAACwmJDDzpEjR1RQUKCKigpdddVVGjVqlFJTU32vHzx4UG+99ZZefPFFFRQU6KGHHgr5Xlnjxo1r9LTV3Llz6z2fPHmyJk+eHOpqAACAdiIm1DcUFxfrwIEDuuuuu5Sfn18v6EhSamqqJk6cqD/84Q/av3+/3nzzzUjVCgAAELKQw8727ds1ZMgQv990qmvQoEEaPHiw3nvvvWYXBwAAEK6Qw87u3bs1YMCAoNoOGjRIu3fvDrkoAACASAk57FRWVjY55k1dnTp1UmVlZaiLAAAAiJiQw05tbW3QXynv0KFDmx2VGAAAWEOzvnq+f/9+7dq1K6h2AAAA0dSssLN8+XLf7SEAAADMLOSwc9NNN7VEHQAAAC0i5LBz/LYNAAAAbUHIFygDAAC0JYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgaYQdAABgabHRLgCBeb1eud3uRl93uVwRX2agedpsNhmGEfHlApEU6W2nsfYtsQ0CiBzCjsl5vV7l5+dr27ZtrbrcIUOGNPl6bm6uioqKCDwwrZbYdgJtFwDMidNYJud2u4PeWecOG65Em63Zy0q02TT4rNyg2m7durXJfzED0RapbSeU7SLcbRBAy+DIThuyZssO2ez2Rl/vn+bQ7sqjzZ6/YRh6unCl0joca3Q+bpdL44cNbvYygGgIZ9sJZrsIZj4Aooew04bY7PYmd9iROKVkGIbsSUmyefhowDrC3XaC3S44rQuYE6exAACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApRF2AACApcVGuwB/1q5dq1WrVsnpdCozM1NTp05Vdna237avv/663n77be3Zs0eSlJWVpauuuqrR9gAAoH0x3ZGdTZs2aenSpZo0aZIKCgqUmZmpefPmqby83G/7jz76SOecc47+93//V/fff79OPvlk3X///Tp48GArVw4AAMzIdGFn9erVGjt2rMaMGaOMjAxNmzZN8fHxKi4u9tv+lltu0UUXXaRevXqpe/fuuvHGG+X1evXhhx+2cuUAAMCMTBV2amtrtWvXLuXk5PimxcTEKCcnRzt37gxqHtXV1aqtrdVJJ53UUmUCAIA2xFTX7FRUVMjj8cjhcNSb7nA4tHfv3qDm8dxzzyk1NbVeYKqrpqZGNTU1vueGYchms/kem03dmowff5psH+D1uvM0DEPyhjafutMNwzBln0VCvT6CX2bvoxbZdkJs09i21hLLaqtt/PVRMPMJt6a2tC8z+7bWFpgq7IRr5cqVeueddzR37lzFx8f7bVNUVKQVK1b4nvfu3VsFBQXq0qVLa5UZkqqqKt9jR4pD9qSkRtsatS6lpKY0OT+j1iVHisM3v1Dnk5DwU7+mp6crqYl6rCA9PT3aJZieWfuoJbad5rapu6219LLaapvjfRTMfCKxvLa4LzPrttYWmCrsJCcnKyYmRk6ns950p9PZ4GjPiV5++WWtXLlSs2fPVmZmZqPtJk6cqLy8PN/z40m5rKxMtbW1za69pbhcLt9j5yGnqquPNtq2Y8d4HTp4qMn5dewYL+chpxwpDjkPOeX1Njy009R83HXqKS0tld1uD7QKbZJhGEpPT1dpaanfPoL5+6gltp1Q2xiG0WBba6lltdU2J/ZRMPOJRE1taV9m9m0tWmJjY4M+UGGqsBMbG6usrCyVlJRo2LBhkiSPx6OSkhKNGzeu0fe99NJLevHFFzVr1iz16dOnyWXExcUpLi7O72tm/BDVrcn740+T7QO8XneeXm/j8wtmutfrNWWfRVJ7WMdwmbWPWmTbCbWN96da6m07LbGsttrGTx8FM59wa2qL+7K2UqcZmeoCZUnKy8vT+vXr9eabb+qbb77R4sWLVV1drdGjR0uSFi5cqGXLlvnar1y5UsuXL9dNN92ktLQ0OZ1OOZ1OHTlyJEprAAAAzMRUR3YkacSIEaqoqFBhYaGcTqd69eqlmTNn+k5jHThwoN5FWuvWrVNtba0eeeSRevOZNGmSrrjiitYsHQAAmJDpwo4kjRs3rtHTVnPnzq33fNGiRa1QEQAAaKtMdxoLAAAgkgg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0gg7AADA0mKjXQAAANHkcrnCnofNZpNhGBGoBi2BsAMAaNeGDBkS9jxyc3NVVFRE4DEpTmMBANqdRJtNg8/Kjdj8tm7dKrfbHbH5IbI4sgMAaHcMw9DThSuV1uGYdlcebbJtz5PiG23jdrk0ftjgligREUTYAQC0S4ZhyJ6UJJun6T+F9qSEgG1gbpzGAgAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlkbYAQAAlsZtXKPM6/XK7XY3+rrL5WrFakITqDabzSbDMFqpGgAA/CPsRJHX61V+fr62bdsW7VKaZciQIU2+npubq6KiIgIPACCqOI0VRW63O+igkztsuBJtthauKLBEm02Dz8oNqu3WrVubPGoFAEBr4MiOSazZskM2u73R1/unObS78mgrVuSfYRh6unCl0joca7Qet8ul8cMGt3JlAAD4R9gxCZvd3mTYMdOpIMMwZE9Kks3DxwcAYH6m+2u1du1arVq1Sk6nU5mZmZo6daqys7P9tt2zZ4+WL1+uL7/8UmVlZbr22ms1YcKEVq4YAACYmamu2dm0aZOWLl2qSZMmqaCgQJmZmZo3b57Ky8v9tq+urlbXrl01ZcoUORyO1i0WAAC0CaYKO6tXr9bYsWM1ZswYZWRkaNq0aYqPj1dxcbHf9tnZ2fqf//kfnXPOOYqLi2vlagEAQFtgmtNYtbW12rVrl/Lz833TYmJilJOTo507d0ZsOTU1NaqpqfE9NwxDth+/5dTa18XUXZ7x40+T7QO8HnSbH5drGIbkjfyy6k43DMNU1xsFq14fwS+z91HUtq8TPv++/3v9t2nNeszYxl8fBTOflqwplDatsb8z+7bWFpgm7FRUVMjj8TQ4HeVwOLR3796ILaeoqEgrVqzwPe/du7cKCgrUpUuXiC0jWFVVVb7HjhSH7ElJjbY1al1KSU1pcn7BtnGkOHzLbIllJSTE+x6np6crqYn1Mrv09PRol2B60eojr9fb5MCWHTp08D1uze3LX5u621pLL6uttjneR8HMp7VqCqZNa+7v2B81n2nCTmuZOHGi8vLyfM+PJ+WysjLV1ta2ai11d9TOQ05VVzf+1fKOHeN16OChJucXbBvnIaccKQ45Dznl9TY8tBPustx11qu0tFT2Jr5lZlaGYSg9PV2lpaV++wjR7SOv16tLL7006HGqWnP7qtvGMIwG21pLLauttjmxj4KZjxnqPq419nfsj/yLjY0N+kCFacJOcnKyYmJi5HQ66013Op0Rvfg4Li6u0et7orHD9j3+8afJ9gFeD7rNj8v1ehtfZjjLqjvd6/W26Y2zrdffGqLRRy6XK6QBORNsia23fdVt8+PDE7e1FllWW23jp4+CmU+L1hRCm9bc37E/aj7ThJ3Y2FhlZWWppKREw4YNkyR5PB6VlJRo3LhxUa4OgFm1lQE5AUSPacKOJOXl5WnRokXKyspSdna21qxZo+rqao0ePVqStHDhQqWmpmrKlCmSfrio+ZtvvvE9PnjwoL766islJiZybhNoJ9rSgJwAosNUYWfEiBGqqKhQYWGhnE6nevXqpZkzZ/pOYx04cKDejuvgwYO68847fc9XrVqlVatWacCAAZo7d24rVw8AAMzIVGFHksaNG9foaasTA0xaWpoKCwtboSoAANBWmWpQQQAAgEgj7AAAAEsz3WksAPB6vXK73Y2+3tRggkC0BPpc2mw2LpiPEsIOAFPxer3Kz88PehwdwCyGDBnS5Ou5ubkqKioi8EQBp7EAmIrb7Q5pwMDEH+9tB0RDos2mwWflBtV269atTR6xRMvhyA4A02LAQJidYRh6unCl0joca/Sz6Ha5NH7Y4FauDHURdgCYFgMGoi0wDEP2pCTZPPxJNStOYwEAAEsj7AAAAEsj7AAAAEsj7AAAAEvjaiq0KAbZAoDgNDaYpmEYqqqqksvlktfrDWpe7FvrI+ygRTHIFgAEFunBNNm31sdpLEQcg2wBQGhCGUwzGOxb6+PIDiKOQbYAoPlOHEzTkCFHikPOQ0555VXPk+LZt4aIsIMWwSBbANA8Jw6maeiH/Wl19VF55ZU9KYF9a4g4jQUAACyNsAMAACyNsAMAACyNsAMAACyNK5wAAGgljQ20GmgAVoSHsAMAQCsJNNAqWgansQAAaEGhDLSaO2y4Em22Fq6o/eHIDgAALSiYgVaP65/mCNgGoSPsAADQwoIdaJV7WbUMTmMBAABLI+wAAABLI+wAAABLI+wAAABL4wJlRF2gwbRsNhsX7QGACXm9Xrnd7qDaRnNfTthB1AUaZCs3N1dFRUUEHgAwEa/Xq/z8fG3bti2o9p999pnsdnsLV+Ufp7EQFaEMsrV169ag/+UAAGgdbrc76KATbRzZQVQEM8iW2+XS+GGDW7kyAECo1mzZIVsTR216JMUqMS56kYOwg6gJdpAtAIC52ez2JsOOPSlO3projQzNaSwAAGBphB0AAGBphB0AAGBphB0AAGBpXBnaggINthRoMD38hIEHo+/Ez7NhGKqqqpLL5ZLX6/VND/S7YLsAWke4+00rbauEnRYS6mBLaBoDD0ZXKJ/npn4XbBdA6wlnv2m1bZXTWC0klMGWcocNV6LN1sIVtT0MPGgeoXyem/pdsF0ALStS+02rbasc2WkFgQZb6p/maHRgvfaMgQfN6fjn2ZAhR4pDzkNOeeUN+XfBdgFEXkvsN62wrRJ2WkGgwZY49dI4Bh40n+OfZ0M//G6qq4/KK2/gNzYyn8awXQDNE+n9phW2VU5jAQAASyPsAAAASzPluYG1a9dq1apVcjqdyszM1NSpU5Wdnd1o+82bN2v58uUqKytTenq6rr76ap155pmtWDEAADAr0x3Z2bRpk5YuXapJkyapoKBAmZmZmjdvnsrLy/22//TTT/XYY4/p/PPPV0FBgXJzc/XQQw9p9+7drVw5AAAwI9Md2Vm9erXGjh2rMWPGSJKmTZum7du3q7i4WPn5+Q3ar1mzRqeffrouueQSSdLkyZP14Ycfau3atbrhhhtas3REWSQHuGpswLz2KtS+bax9WxqEDGgP2su2aqqwU1tbq127dtULNTExMcrJydHOnTv9vmfnzp3Ky8urN23IkCHaunWr3/Y1NTWqqanxPTcMQzabTbGxke2KhIQEnXHGGZKkjokJSoiPa7RtbIcOSmri9Yi3SYhTQoyhpIQ4v3/IW72eMNrEen7q5+uuu67J+SA8J36eDcOo9zkK9ndh2u2iBdqc2EfRrseMbRp8joKYjxnqbs02zemjSOw3I7mtxsV2kFeBf6+hCOXvtqnCTkVFhTwejxwOR73pDodDe/fu9fsep9OpTp061ZvWqVMnOZ1Ov+2Lioq0YsUK3/NzzjlHt956q1JSUsKq3Z/t27cH3bZzEIuPeJuOJ5urnma2CaWf0QLqfI4i/bswy2cs7DYnbGtRr8eMber0UTDzaZWazNYmxD5qzf1msL+zaDHdNTstbeLEiVqyZInvv2nTptU70tMeuN1u/eEPf2DE4SbQR4HRR4HRR4HRR4HRR+Ez1ZGd5ORkxcTENDgq43Q6GxztOc7hcDS4eLm8vLzR9nFxcYqLi+yhtLbG6/Xqyy+/5FqUJtBHgdFHgdFHgdFHgdFH4TPVkZ3Y2FhlZWWppKTEN83j8aikpET9+vXz+55+/frpww8/rDdtx44d6tu3b4vWCgAA2gZThR1JysvL0/r16/Xmm2/qm2++0eLFi1VdXa3Ro0dLkhYuXKhly5b52o8fP14ffPCBVq1apW+//VaFhYX64osvNG7cuCitAQAAMBNTncaSpBEjRqiiokKFhYVyOp3q1auXZs6c6TstdeDAgXr34ejfv79uueUWPf/88/rHP/6hU045RXfccYd69uwZpTUwv7i4OE2aNKndn85rCn0UGH0UGH0UGH0UGH0UPsPLSUAAAGBhpjuNBQAAEEmEHQAAYGmEHQAAYGmEHQAAYGmm+zYWWs5rr72m1157TWVlZZKkjIwMTZo0yXf/E9S3cuVKLVu2TOPHj+e+Wz8qLCysd7sVSerWrZsWLFgQnYJM6uDBg3r22Wf1n//8R9XV1UpPT9eMGTPUp0+faJdmCjfffLNvP1TXz3/+c11//fVRqMh8PB6PCgsLtWHDBjmdTqWmpuq8887TL3/5y3rfSEZwCDvtSGpqqqZMmaJTTjlFXq9Xb731lh588EE9+OCD6tGjR7TLM5XPP/9c69atU2ZmZrRLMZ0ePXpo9uzZvucxMRwgrquyslKzZ8/WwIEDNXPmTCUnJ+u7775TUlJStEszjQceeEAej8f3fPfu3br//vv1s5/9LIpVmcvKlSu1bt063XzzzcrIyNCuXbv05JNPym63a/z48dEur80h7LQjQ4cOrff8qquu0muvvabPPvuMsFPHkSNH9MQTT2j69Ol68cUXo12O6cTExDR6OxZIL730kk4++WTNmDHDNy0tLS2KFZlPcnJyvecrV65U165dNWDAgChVZD47d+7U0KFDdeaZZ0r64TO0ceNGff7551GurG3in2TtlMfj0TvvvKPq6upGb8XRXi1evFhnnHGGBg8eHO1STKm0tFTTp0/Xb37zGz3++OM6cOBAtEsylW3btikrK0uPPPKIrr/+et155516/fXXo12WadXW1mrDhg0aM2YMp2fq6Nevn0pKSrR3715J0ldffaVPP/2Uyw6aiSM77czu3bs1a9Ys1dTUKDExUbfffrsyMjKiXZZpvPPOO/ryyy/1wAMPRLsUU+rbt69mzJihbt266dChQ1qxYoXmzJmj+fPny2azRbs8U9i/f7/WrVunCRMmaOLEifriiy/0zDPPKDY21nfbG/xky5Ytqqqqom9OkJ+fL7fbrd/97neKiYmRx+PR5MmTde6550a7tDaJsNPOdOvWTQ899JBcLpf+/e9/a9GiRfrjH/9I4NEPtyJZsmSJ7rnnHsXHx0e7HFOq+6/KzMxMX/jZvHmzzj///ChWZh4ej0d9+vTRlClTJEm9e/fW7t27tW7dOv6g+1FcXKzTTz9dqamp0S7FVDZv3qyNGzfqlltuUY8ePfTVV19pyZIlSklJ4XPUDISddiY2Nlbp6emSpKysLH3xxRdas2aNbrjhhihXFn27du1SeXm5/vCHP/imeTweffzxx1q7dq2WLVvGxbgnSEpKUrdu3VRaWhrtUkwjJSWlwT8eMjIy9O6770apIvMqKyvTjh07dPvtt0e7FNN59tlndemll+qcc86RJPXs2VNlZWVauXIlYacZCDvtnMfjUU1NTbTLMIWcnBw9/PDD9aY99dRT6tatmy699FKCjh9HjhxRaWkph9br6N+/v+86i+P27t2rLl26RKki8youLlanTp18F+HiJ9XV1Q32OTExMeJ2ls1D2GlHli1bptNPP12dO3fWkSNHtHHjRn300UeaNWtWtEszBZvNpp49e9ablpCQoI4dOzaY3l4tXbpUQ4cOVefOnXXo0CEVFhYqJiZGI0eOjHZppjFhwgTNnj1bL774okaMGKHPP/9c69ev5+jpCTwej958802dd9556tChQ7TLMZ2zzjpLL774ojp37qyMjAx99dVXWr16tcaMGRPt0tokwk47Ul5erkWLFunQoUOy2+3KzMzUrFmz+NYRgnbw4EE99thjOnz4sJKTk3Xqqadq3rx5Db5K3J5lZ2fr9ttv17Jly/TCCy8oLS1N1157LUe/TvDhhx/qwIED/PFuxNSpU7V8+XItXrxY5eXlSk1N1YUXXqhJkyZFu7Q2yfByTAwAAFgYFyEAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABLI+wAAABL+/+y4LeLNw+D/gAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for b in [5,10,20,50]:\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111)\n", " \n", " bins = np.linspace(min_x, max_x, b+1)\n", " nu = (max_x-min_x)/b\n", " \n", " ax = sns.histplot(D500,\n", " bins=bins, # Here we impose the intervals as they have been defined in the previous cell\n", " stat='density', # Normalize such that the total area of the histogram equals 1\n", " color=\"skyblue\",\n", " alpha=.3\n", " )\n", " \n", " counts, _ = np.histogram(D500, bins=bins)\n", " f_hat = [0]+[count_i/(N*nu) for count_i in counts]\n", " sns.lineplot(x=bins,y=f_hat, drawstyle='steps-pre', color='k', label='Densité estimée, b=%i' %b)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**3.** Soit $K(x):=\\frac{15}{16}(1-x^2)^2\\mathbb{I}_{[-1,1]}(x)$. Définir une fonction qui permette de calculer pour tout $x\\in\\mathbb R$ la fonction suivante :\n", "\\begin{equation}\n", "\\hat f_{\\nu}^K(x):=\\frac{1}{N\\nu}\\sum_{i=1}^N K\\left(\\frac{x-x_i}{\\nu}\\right),\n", "\\end{equation}\n", "pour un $N$-échantillon $\\mathcal D_N=\\{x_1,\\dots,x_N\\}$ et un $\\nu\\in\\mathbb R$ donnés. Qu'est-ce que $f_{\\nu}^K(x)$ répresente ?" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def K(x):\n", " ind = 1 if abs(x)<=1 else 0\n", " return 15*((1-x**2)**2)*ind/16\n", "\n", "def f_hat_K_x(x,data,nu):\n", " N = len(data)\n", " return sum([K((x-xj)/nu) for xj in data])/(N*nu)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**4.** Choisir une des méthodes vues en cours pour déterminer le $\\nu$ optimal d'un estimateur à noyau, et l'utiliser pour déterminer le meilleur choix de $\\nu$ pour $\\hat f_{\\nu}^K$ et pour l'échantillon $\\mathcal D_{500}$ généré au point **1**." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def bw_silverman(X):\n", " # X : data (np.array)\n", " \n", " def _select_sigma(X):\n", " # X : data (np.array)\n", " \n", " q75, q25 = np.percentile(X, [75 ,25])\n", " iqr = q75 - q25\n", " std = np.std(X)\n", "\n", " A = min(std,iqr/1.34)\n", " return A\n", " \n", " sigma = _select_sigma(X)\n", " N = len(X)\n", " nu_opt = sigma * (3*N/4)**(-1/5)\n", " return nu_opt" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "La fenetre optimale par la règle de Silverman est 0.28\n" ] } ], "source": [ "nu_sil=bw_silverman(D500)\n", "print(f'La fenetre optimale par la règle de Silverman est {round(nu_sil,2)}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**5.** Sur une même figure, répresenter $\\hat f_b^{\\mathrm{Hist}}$ et $\\hat f_{\\nu}^K$. Utiliser la valeur de $b$ reteue au point **2** at la valuer de $\\nu$ retenue au point **4** pour $\\hat f_b^{\\mathrm{Hist}}$ et $\\hat f_{\\nu}^K$ respectivement. Commentez." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "b, nu = 20, nu_sil" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 0, 'x'), Text(0, 0.5, 'Density')]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_lin = np.linspace(1,9, 1000)\n", "f_hat_K = np.array([f_hat_K_x(x,D500,nu) for x in x_lin])\n", "\n", "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "bins = np.linspace(min_x, max_x, b+1)\n", "nu_H = (max_x-min_x)/b\n", "ax= sns.histplot(data=D500,\n", " bins=bins, \n", " stat='density', # Normalize such that the total area of the histogram equals 1\n", " color=\"skyblue\",\n", " alpha=.3)\n", "\n", "ax.plot(x_lin,f_hat_K,'b-', label='Densité estimée, K')\n", "\n", "counts, _ = np.histogram(D500, bins=bins)\n", "f_hat = [0]+[count_i/(N*nu_H) for count_i in counts]\n", "sns.lineplot(x=bins,y=f_hat, drawstyle='steps-pre', color='k', label='Densité estimée, Hist.')\n", "\n", "ax.set(xlabel='x', ylabel='Density')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Bonus.** Reproduire la même figure qu'au point **5** et rajouter aussi $f_X$. Quel estimateur vous semble-t-il mieux adapté ?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 0, 'x'), Text(0, 0.5, 'Density')]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_lin = np.linspace(1,9, 1000)\n", "\n", "fig = plt.figure(figsize=(12, 5))\n", "ax = fig.add_subplot(111)\n", "\n", "ax= sns.histplot(data=D500,\n", " bins=bins, \n", " stat='density', # Normalize such that the total area of the histogram equals 1\n", " color=\"skyblue\",\n", " alpha=.3)\n", "\n", "ax.plot(x_lin, p1*norm.pdf(x_lin,loc=mu1, scale=p1)+p2*norm.pdf(x_lin,loc=mu2, scale=p2)+p3*norm.pdf(x_lin,loc=mu3, scale=p3),'g-', lw=2, alpha=0.6, label='Densité réelle')\n", "\n", "ax.plot(x_lin,f_hat_K,'b-', label='Densité estimée, K')\n", "\n", "sns.lineplot(x=bins,y=f_hat, drawstyle='steps-pre', color='k', label='Densité estimée, Hist.')\n", "\n", "ax.set(xlabel='x', ylabel='Density')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 4 }