{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## ランダムウォークの数理\n", "\n", "二つ(+1,-1)の状態をとるランダムウォークは二項分布 $_{10} C _r (\\frac{1}{2})^r (\\frac{1}{2})^{10-r} = _{10} C _r (\\frac{1}{2})^{10}$ に従う\n", "\n", "# 参考文献\n", "[1] 「なるほど確率論   著者:村上雅人」 \n", "[2] 「ランダム・ウォーク 乱れに潜む不思議な現象   著者:津野義道」" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "times = 10\n", "state = 0\n", "ran_num = 0.0\n", "for i = 1:times\n", " ran_num = rand()\n", " if ran_num >= 0.0 && ran_num <= 0.5\n", " state += 1\n", " elseif ran_num > 0.5 && ran_num<= 1.0\n", " state -= 1\n", " end\n", " print(\"$state ,\")\n", "end" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "約20%の確率で6の状態にいる." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.205078125" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 2項分布の計算\n", "((factorial(10)/(factorial(10-6)))/factorial(6)) * (1/2)^(6) * (1/2)^4" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "using PyPlot\n", "using Plots" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "binomial_dist (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function binomial_dist(n)\n", " state = 0\n", " global X = []\n", " for i = 0:n\n", " ran_num = rand()\n", " if ran_num >= 0.0 && ran_num <= 0.5\n", " state += 1\n", " elseif ran_num > 0.5 && ran_num<= 1.0\n", " state -= 1\n", " end\n", " #print(\"$state ,\")\n", " # 組み合わせの計算をしているところ\n", " var = (1 * i)+(-1 * (n - i))\n", " #print(\"var: $var , \\n\")\n", " # mpmathとかのインポートエラーになるのでダメ\n", " # p = ((factorial(big(n)))/(factorial(big(n-abs(var))))/factorial(big(abs(var)))) * (1/2)^(abs(var)) * (1/2)^(n-abs(var))\n", " p = binomial(n,abs(var)) * (1/2)^(abs(var)) * (1/2)^(n-abs(var))\n", " #p = ((factorial(n)/(factorial(n-abs(var))))/factorial(abs(var))) * (1/2)^(abs(var)) * (1/2)^(n-abs(var))\n", " #print(\"p: $p \\n\")\n", " push!(X,p)\n", " end\n", " end" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "binomial_dist(15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "きちんと二項分布になっている.  \n", "このシミュレーションでは二項分布 $_{15} C _r (\\frac{1}{2})^r (\\frac{1}{2})^{15-r} = _{15} C _r (\\frac{1}{2})^{15}$ に従う" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "0.00\n", "\n", "\n", "0.05\n", "\n", "\n", "0.10\n", "\n", "\n", "0.15\n", "\n", "\n", "0.20\n", "\n", "\n", "0\n", "\n", "\n", "2\n", "\n", "\n", "4\n", "\n", "\n", "6\n", "\n", "\n", "8\n", "\n", "\n", "10\n", "\n", "\n", "12\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "y1\n", "\n", "\n" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "histogram(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 例えば-10の状態と+10の状態では15C10と15C10で同じ確率になるので二つの凸が発生する." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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IzQ2eMHvvvfdi9erVWLhwIdavX4/f/e53OHDgAE6cODHq65SVlaGrq0t61NVx5HesOvh5Mxq6BpASb8JXFo5eBxYOcZuKhcZEAYEW8cgEOEDgxuQPVQ3oc3oi9rqkbSEFOOnp6TAYDCOyNc3NzSOyOuGora3FgQMHsHnz5gmvXbJkCUwmE6qrq0f9usViQXJyctCDYpO4d3/HkplTLi4eiq3iRMF6nR7Ud4odVJHZogKAFbPTUJgWj16nB386xWJjmpyQAhyz2YySkhKpy0lUUVGBlStXTnkxL774IjIzM3HLLbdMeO3p06fhdruRkzO1dl/StobOfvzjc39x8V0R3J4COOyPaLjqwWA/I8mCGfFT66AaSq/X4a7B2VWcbEyTFfIW1bZt2/Dcc8/hhRdewKeffor7778fdrsd9913HwBg48aNKCsrk653uVw4efIkTp48CZfLhfr6epw8eRJnz54Nel2fz4cXX3wR3/rWt2A0GoO+du7cOezYsQMffPABLly4gP379+Mb3/gGFi9ejC984Qvh/LspRrx2vA4+Abh2dirmZETujhII1Bi09jrR0eeK6GsTqdFUz6Aaz50lM2E26PHhxS58XN8V8dcn7Qk5wFm3bh3Ky8uxY8cOXH311fjnP/+J/fv3o6DAf66P3W5HY2PgcLSGhgYsXrwYixcvRmNjI3bt2oXFixeP2IY6cOAA7HY7vvOd74x4T7PZjL/97W+4+eabcdlll+GHP/whSktLceDAARgMkdtyIG3xeH1DiovDO3dqPIkWI/JmxAHgNhUREPg5iGT9jSgt0YKbB2voXmbLOE2CceJLRtqyZQu2bNky6tcOHjwY9OfCwkIIgjDha5aWlo55XX5+Pt59992Q10mx7e+fNeNStxOpCWbcfMXUa8RGU5yViPrOfpxp7sXy2WlReQ8itTgz2CJeHMH6m6HuvmYW/nSqAX88WY/tt8xHoiWsX2EUI3gWFWmWuFf/jZKZsBijk+kT71SrmcEhkn4OopHBAfxbzbMzEtDn8uLNk/VReQ/SDgY4pEl17Q68e6YFAKTixGhgqziRX8+AG41dAwCAeREYpjkanU4nHZT7yjH7pHYHKHYxwCFN2ne8DoLgP8umMD0hau8jZXA4zZhinDjBODPJAlu8KWrvc8eSmTAb9Tjd0I0PL7LYmMbGAIc0x+31Yd8H/sGOkZxcPJq5gxmc1l4X2tlJRTEs2ttTopQEM25Z5B8PwvOpaDwMcEhz/vbpJbT0OJGeaMFNC6JTXCxKsBgxM4WdVETiPKhoFRgPJd64/PFUA7oHeNgtjY4BDmmO2EK6dulMmAzR/xZnoTFRdFvEh1takILizET0u714s4rFxjQ6BjikKbVtfThU3QqdLrrFxUNxojHR0DOoop/B0el0UhbnZRYb0xgY4JCmvPq+v/ZmVXEG8lPjp+U9xY4RblFRrOrqd6Op299BNTdKHVTD3b54JixGPT5r6sEJe+e0vCepCwMc0gyXx4ffVQ4WF09T9gYY2knFDA7FprODXYTZyVbY4qLXQTWULd6Er16ZC4DFxjQ6BjikGe980oTWXhcykyy4cX7mtL3v3MxE6HRAe58Lrb3OaXtfIqWYzgLjocRtqj9/2IAuB4uNKRgDHNIM8S5u3bL8aSkuFsWZDeykopg2nQXGQy2ZNQOXZyfB6fHh91UXp/W9SfkY4JAmnG/tw+FzbdDp/AHOdBPrcDjRmGLRdBYYDzW02JiTjWk4BjikCa8Onjt1w7wMzEyZnuLioYqzWGhMsUv8vi+e5gwOAHx9cR7iTAZUN/fig9qOaX9/Ui4GOKR6To8Xv6v0p6fvXl4gyxrEO1dmcCjWdDncaO7x156JZ7NNp2SrCbdexcnGNBIDHFK9tz9uQnufC9nJVnzpsgxZ1iDWHpxp7mGanGLKmcEOqhybFUnW6emgGk68sXnro0Z08MgUGsQAh1RvaHGxcRqLi4eak+HvpOp0uNHCTiqKIXJuT4mummnDgpxkuDw+vH6CxcbkxwCHVO1scy+OnW+HXgesv2b6i4tFcWYDZg0OFjzLbSqKIVKBsQzbU6KgYuP3WWxMfgxwSNXE4uIvX56JHFucrGsp5kRjikHVzfK0iA/3tatzEW82oKalD8fOt8u6FlIGBjikWgNur5SOFu/e5CQWGp/hRGOKIXIN+RsuyWrC167mZGMKYIBDqvWXjxvR6XAjb0Ycrp83fZOLx8JTxSnWdDpcaBE7qGTO4ADA3df4i43FxgOKbQxwSLWGFhcb9DqZVxN8qjhrACgWiNmbvBlxSLQYZV4NsGimDYvybHB5A+fSUexigEOqdOZSD45f6IBBr5NlcvFo5mQkQq/zn6ws3tUSaVmgg0re7amhxO3qV9+v441GjGOAQ6okZm9uvDwTWclWmVfjZzUZUJCWACBwZ0ukZdUynUE1ntuuykWixYjzrX04cq5N7uWQjBjgkOoMuL34vYKKi4cSJ7myk4pigVRgLGOL+HAJFqNUbPzy+yw2jmUMcEh1/vxhI7oHPJiZEofriuWZXDwWqdC4mQEOaZ9SWsSHu2dwsvE7p5vQysGbMYsBDqnOK8dqAQB3XTMLegUUFw81tNCYSMva+1xo7fV3Ks1VUAYHABbkJuPq/BlwewX89gNONo5VDHBIVT5r6sYJeyeMeh2+sXSm3MsZYeiwPxY4kpaJ27AzU+KQoIAOquECxcZ2+Hz8WYxFDHBIVcTi4tIrspCZpIzi4qFmZyRArwN6Bjy41M3UOGmXEguMh7r1ylwkWY2wtzvwr3Otci+HZMAAh1TD4fLgjRP1AAIDvZTGajKgUOqkYh0OaZdSJhiPJc5swO2L8wAALx9lsXEsYoBDqvGnUw3ocXpQkBaPlXPS5F7OmAJ1OAxwSLvE7+95mcrM4ADA3YPFxhWfXkJz94DMq6HpxgCHVOOV9/2TSZVYXDxU4MgGFhqTdlUPnrmm1C0qALgsOwklBSnw+gT8tpLFxrGGAQ6pgsPlwam6TgDAvw+mnZVKPJPnDFvFSaNae51o73NBp1NeB9Vw4ufF0RoO/Ys1YQU4e/bsQVFREaxWK0pKSnDo0KExrz19+jTuuOMOFBYWQqfToby8fMQ1jzzyCHQ6XdAjOzs76BpBEPDII48gNzcXcXFxuOGGG3D69Olwlk8qVNPSBwBITTArZnLxWMRTxc/yTCrSKDE7OTMlDnFmg8yrGd/8HP8Nx9lmZlRjTcgBzr59+7B161Zs374dVVVVWLVqFdasWQO7ffQiLofDgdmzZ+Oxxx4bEbQMdcUVV6CxsVF6fPTRR0Fff+KJJ7B7924888wzOH78OLKzs3HTTTehp4d3ybHgXIv/w2luhrLvFgGgKD0BBr0OPU4PmrjvTxokDfhTcP2NaM7gZ0Zj1wB6nR6ZV0PTKeQAZ/fu3di0aRM2b96M+fPno7y8HPn5+di7d++o1y9btgxPPvkk1q9fD4vFMubrGo1GZGdnS4+MjMCEWkEQUF5eju3bt+P222/HwoUL8etf/xoOhwOvvPJKqP8EUiHx7mtOZoLMK5mYxWhAYVo8AA78I20KHLKp/ABnRrwZ6YlmAEBNC38eY0lIAY7L5UJlZSVKS0uDni8tLcXhw4entJDq6mrk5uaiqKgI69evR01NjfS18+fPo6mpKeh9LRYLrr/++jHf1+l0oru7O+hB6iVmcOaoIIMDDC00ZoaRtEcM3OcptEV8OPFz4xwDnJgSUoDT2toKr9eLrKysoOezsrLQ1NQU9iKWL1+O3/zmN/jrX/+KX/7yl2hqasLKlSvR1uYvChNfO5T33blzJ2w2m/TIz88Pe30kv0AGRx0fqFKhMQMc0hhBEBQ/5G848XODdTixJawiY50uuEVXEIQRz4VizZo1uOOOO7Bo0SKsXr0ab731FgDg17/+ddjvW1ZWhq6uLulRV1cX9vpIXh6vDxdaHQDUUYMDBO5suUVFWtPa60KHww2dTj0ZVfFz41xzn8wroekU0gEi6enpMBgMI7Imzc3NI7IrU5GQkIBFixahuroaAKTi5KamJuTk5EzqfS0Wy7g1P6QedR39cHl9sJr0yJsRJ/dyJkW8sz3b3DvlGwAiJRGzN7NS4xXfQSWSMjjcooopIWVwzGYzSkpKUFFREfR8RUUFVq5cGbFFOZ1OfPrpp1IwU1RUhOzs7KD3dblcePfddyP6vqRM5wbTyrPTExU94G+owrQEGPU69Do9aOhiJxVph1RgrIIOKpE4q6e2rQ9ur0/m1dB0CfkI2G3btmHDhg1YunQpVqxYgWeffRZ2ux333XcfAGDjxo3Iy8vDzp07AfgDkU8++UT63/X19Th58iQSExMxd+5cAMADDzyAW2+9FbNmzUJzczP+67/+C93d3fjWt74FwL81tXXrVjz66KMoLi5GcXExHn30UcTHx+Puu++OyH8IUi7xrkst9TcAYDbqUZSegOrmXpy51KOazBPRRM40q6vAGABykq2IMxnQ7/bC3u5QzdYaTU3IAc66devQ1taGHTt2oLGxEQsXLsT+/ftRUOA/88Nut0OvDySGGhoasHjxYunPu3btwq5du3D99dfj4MGDAICLFy/irrvuQmtrKzIyMnDttdfi6NGj0msCwE9+8hP09/djy5Yt6OjowPLly/HOO+8gKUk9dxEUHjGDo5b6G1FxViKqm3tRfakHX7osU+7lEEWE2gqMAUCv12FOZgI+ru/GueZeBjgxIuQABwC2bNmCLVu2jPo1MWgRFRYWTjjN9bXXXpvwPXU6HR555BE88sgjk10maUQgg6P8GThD+VP4TSw0Js0QBEHxp4iPZU5GIj6u78bZll6UTnw5aQDPoiJFEwQhkMFR0RYVwFk4pD0tPU509buhV1EHlYidVLGHAQ4pWkuvE90DHuh1/sJdNRFrFKqbe+Hz8UwqUj8xe1OQlgCrSR0dVCJ2UsUeBjikaOLdVn5qvOo+UAvTE2Ay6OBweVHf2S/3coimLNBBpa7sDRDIANc08xDcWMEAhxTtrMqOaBjKZPB3UgGBwwmJ1Ew6ZFNFBcaigrR46HVAj9OD5h6n3MuhacAAhxRNrfU3omKpDodpcVK/apUWGAP+Q3ALBre5z/HIhpjAAIcULXDIprrqb0TzMsUzqfiBSurm76BSbwYHCHyOsA4nNjDAIUVTewYnUGjMLSpSt+aeQMG/uPWqNmKhMTM4sYEBDilW35BjDtRYgwMEb1Gxk4rUTMzeFKqwg0okfo4wgxMbGOCQYtW0+Duo0hPNmBFvlnk14SlMi4fZoEe/m51UpG5qHfA31NxMzsKJJQxwSLHE+pvZKs3eAIDRoMfswX3/Mxz4RyqmxiMahhMzOE3dA+h1emReDUUbAxxSrLMqr78RidtULDQmNZNm4Kg4wLHFmZCRZAHAOpxYwACHFOucimfgDDVvMEDjkQ2kVoIgSC3iajpFfDRiJ9U51uFoHgMcUizNZXDYSUUq1dQ9gB6nBwa9TrUdVCLx8+QsMziaxwCHFMnj9eFCm78QUK0zcETiHe9ZnklFKiVurxamxcNiVGcHlUjMCDODo30McEiR7O0OuL0C4kwG5Nri5F7OlMxK9XdSDbh9qOtwyL0copBpocBYxAxO7GCAQ4p0brBFfHZGAvR6ncyrmZrgTip+qJL6aKHAWCRmcGrbHHB7fTKvhqKJAQ4pknh3pfYCY9E8qZOKdTikPmc0UmAMADk2K+LNBnh8AmrbmFHVMgY4pEji/rjaC4xF0pENDHBIZQRBkG44tLBFpdPpWIcTIxjgkCJpLYPDWTikVg1d/qF4Rr0OhWnqLvgXSYdusg5H0xjgkOIIgqDBDI4/wDnX0gsvO6lIRcRt1aL0BJiN2viVIR3ZwAyOpmnju5U0paXHiZ7BU4sL0+PlXk5EzEqNh8Woh9PjQ1079/1JPc5e0s72lEjaomIGR9MY4JDiiCf9+oMCdc/cEBn0gX1/FhqTmgQ6qLSRTQWGZnD6IAjMqGoVAxxSnHMaq78RSYXGvGskFTmjoQJjUUFaAgx6HXqdHlzqdsq9HIoSBjikOOIMHK3U34iK2SpOKiMIAs5KQ/608/NoNupRkOrf/mYdjnYxwCHF0VoHlWgeO6lIZeo7+9Hn8sJk0KFAIx1UotkQD/qLAAAgAElEQVQZnGisdQxwSHGkU8Q1lsER74DZSUVqIZ4gXpSeAJNBW78u2Emlfdr6jiXV63V60Ng1AACYq7EMTn5KPKwmPVweH2oHDxIlUjItHdEwHGfhaB8DHFKUmsG7qfREC2zxJplXE1l6vU66a+Q2FamBdERDpvYCHGZwtI8BDilKoP5GW/v9IvEXBY9sIDWobtZegbFI3AK/1O1E94Bb5tVQNDDAIUXR2gTj4aROKqbFSeF8PkGqwdHiFlWy1YTMJAsAoKaFW8ZaxACHFEWrHVSi4kweuknqUN/Zj363F2aDHoVp2pgoPtwcdlJpGgMcUhStzsARia3iNS198Hh9Mq+GaGxigfHsjAQYNdZBJWIdjraF9V27Z88eFBUVwWq1oqSkBIcOHRrz2tOnT+OOO+5AYWEhdDodysvLR1yzc+dOLFu2DElJScjMzMTXv/51fP7550HX3HDDDdDpdEGP9evXh7N8Uii314cLrf4AR2st4qKZKXGIMxng8vpwoY1nUpFyndHw9pSInVTaFnKAs2/fPmzduhXbt29HVVUVVq1ahTVr1sBut496vcPhwOzZs/HYY48hOzt71GveffddfO9738PRo0dRUVEBj8eD0tJS9PUF74vee++9aGxslB6/+MUvQl0+KZi93QGPT0C82YCcZKvcy4mKoZ1U3KYiJRO/P+dp9GYDAOYOFv0zg6NNxlD/wu7du7Fp0yZs3rwZAFBeXo6//vWv2Lt3L3bu3Dni+mXLlmHZsmUAgAcffHDU13z77beD/vziiy8iMzMTlZWVuO6666Tn4+PjxwySSP3Eu6jZGQnQ63UyryZ6irMS8VF9F85c6sWaRXKvhmh0Z5q1OwNHNCfTn8GpbXPA5fHBbNTmVlysCun/TZfLhcrKSpSWlgY9X1paisOHD0dsUV1dXQCA1NTUoOdffvllpKen44orrsADDzyAnp6x74CdTie6u7uDHqRsUgeVRguMRWIdjtiCS6Q0Pp8g3XBosUVclJ1sRYLZAK9PgL2dnVRaE1KA09raCq/Xi6ysrKDns7Ky0NTUFJEFCYKAbdu24Ytf/CIWLlwoPX/PPffg1VdfxcGDB/Hwww/j9ddfx+233z7m6+zcuRM2m0165OfnR2R9FD1a76ASSaeKc9gfKdTFjn4MuP0ZDa2dQTWUTqeT6v1Yh6M9IW9RAf5viqEEQRjxXLi+//3v48MPP8R7770X9Py9994r/e+FCxeiuLgYS5cuxYkTJ7BkyZIRr1NWVoZt27ZJf+7u7maQo3Ba76ASFQ/u+9e09sLt9WnujB9SP7GDak5GIgwa3i4G/BnjDy92SZ8/pB0hfbKmp6fDYDCMyNY0NzePyOqE4wc/+AH++Mc/4h//+Admzpw57rVLliyByWRCdXX1qF+3WCxITk4OepByCYKAc83aPGRzuLwZcYg3G+D2CjyTihTpjIYnGA/HDI52hRTgmM1mlJSUoKKiIuj5iooKrFy5MuxFCIKA73//+/j973+Pv//97ygqKprw75w+fRputxs5OTlhvy8pR3OPE71ODwx6HQo0OlRMpNfrpIF/PJOKlEjcPp2n4QJjkbglzk4q7Ql5i2rbtm3YsGEDli5dihUrVuDZZ5+F3W7HfffdBwDYuHEj8vLypI4ql8uFTz75RPrf9fX1OHnyJBITEzF37lwAwPe+9z288sorePPNN5GUlCRliGw2G+Li4nDu3Dm8/PLL+Ld/+zekp6fjk08+wY9//GMsXrwYX/jCFyLyH4LkJWZvZqXGw2I0yLya6CvOSsKpi104c6kH/7aIQTopi3SKuMazqQAwd7CT6lxzb0TLLUh+IQc469atQ1tbG3bs2IHGxkYsXLgQ+/fvR0FBAQDAbrdDrw8khhoaGrB48WLpz7t27cKuXbtw/fXX4+DBgwCAvXv3AvAP8xvqxRdfxLe//W2YzWb87W9/w//8z/+gt7cX+fn5uOWWW/Czn/0MBoP2fxnGgrMtsVFgLGKhMSmVd0gHlZZbxEUFaQkw6nXoc3nR1D2AHFuc3EuiCAmryHjLli3YsmXLqF8TgxZRYWEhBEEY9/Um+np+fj7efffdkNZI6hKov9Fux8ZQ0qGbHPZHClPX7oDT44PFqMesVG1vFwOAyaDHrLR41LT04VxzHwMcDWH7BinC2RiZgSMSaxvOt/bB5eGZVKQcsdRBJZorHbrJGw4tYYBDinCuWdtnUA2Xa7Mi0WKExyfgAjupSEGqY2DA33BzpEM3+bOoJQxwSHY9A240dQ8AiJ0aHJ0ucCYVt6lISaQC4xiovxEFMjisidMSBjgku5rBu6aMJAtscSaZVzN92CpOSnQmhlrERYEMDn8WtYQBDskucERDbBQYi6QzqZjBIYXw+gTpl3wsbVHNHvzsae5xonvALfNqKFIY4JDspEM2Y6T+RlScxS0qUpbaNn/Ru9WkR36K9juoRMlWE7KSLQACHZ2kfgxwSHaxcsjmcGIG50KbA06PV+bVEAW2p+ZmJkIfIx1Uojmsw9EcBjgku1jN4OTYrEiyGOH1CTjfyu4Nkp+4XTovM3bqb0Rz2UmlOQxwSFZurw+1bQ4AsZfB0el0mMuJxqQg1TE0wXg4ZnC0hwEOyaq2zQGPT0C82YAcm1Xu5Uw78U6ZhcakBGI9WCwVGIvEDE4NO6k0gwEOyWpo/U0sHnIXKDTmhyrJy+P1SSMbYqlFXCRmcGrbHZwurhEMcEhWsVp/IxJ/kZzhiHiSWW27Ay6vD3EmA/JmxN55TFnJFiQO1sTVcrq4JjDAIVmdi9EZOCIxwKllJxXJrFqaYBx7HVSAvyZO/BxiHY42MMAhWcV6Bicr2YIkq/+usYbdGyQjcZu0OAY7qEScaKwtDHBINoIgSC2ZsdZBJdLpdIFtKhYak4xiucBYxE4qbWGAQ7K51O1Er9MDg16HgrTY3KICAr9Q2CpOcqqOwTOohuMsHG1hgEOyEe+SClLjYTbG7reiuCXADA7Jxe31oaY1treLgUAG51xLL3w+QebV0FTF7m8Vkp24zz0nhj9QgSGHbjItTjKpbeuD2+ufRxWLHVSigrR4GPU6OFxeNHUPyL0cmiIGOCSbWD2Dajhxi6q2rQ8DbnZS0fQLFBjHZgeVyGTQoyDNf8go63DUjwEOySbWO6hEGUkWJFuN8Ans3iB5nJFaxGO3/kY0l51UmsEAh2RzNsZn4IiGdlKx0JjkECgwju2bDYCdVFrCAIdk0T3gRnOPEwBrcIDAnTMLjUkOzOAEMIOjHQxwSBbiBOPMJAuSrSaZVyO/eTyTimTi8vhwvjV2z6AaLpDBYau42jHAIVmIcyZivf5GJP5iOcszqWia1bb1weMTkGgxItdmlXs5shMzyq29TnQ53DKvhqaCAQ7Jgh1UwcRTxWvbHeykomklZg3nZiZCp4vdDipRosWI7GR/oHeW21SqxgCHZMEOqmAZiRbMiDdBEFjcSNOLRzSMxDocbWCAQ7I4xwxOEJ1Oh3mZ4sA/blPR9BG/31h/EyB2dp7jzYaqMcChaefy+FDb7gDADM5QxSw0JhlIQ/4Y4EiYwdEGBjg07Wrb+uAdLGrMSrbIvRzFCMzCYQaHpofL48MFqYOKNxsizsLRBgY4NO2kM6gyEljUOAQzODTdzrf6O6iShhTWUiCDY293wOlh0b9aMcChaSe2iLP+JpiYwanrcKDfxQ9Vir7AgD92UA2VkWRBksV/fEptm0Pu5VCYGODQtJNaxFl/EyQ90YLUBDM7qWjaVF9igfFodDqd9PnEn0X1CivA2bNnD4qKimC1WlFSUoJDhw6Nee3p06dxxx13oLCwEDqdDuXl5WG9ptPpxA9+8AOkp6cjISEBt912Gy5evBjO8klmgS0qBjjDFWeK21Ssw6HoY4Hx2MTPJ3ZSqVfIAc6+ffuwdetWbN++HVVVVVi1ahXWrFkDu90+6vUOhwOzZ8/GY489huzs7LBfc+vWrXjjjTfw2muv4b333kNvby+++tWvwutlKl9NBEGQPjDYQTWSeCd9hq3iNA3E77Ni/iyOIH4+cdifeoUc4OzevRubNm3C5s2bMX/+fJSXlyM/Px979+4d9fply5bhySefxPr162GxjN4xM9FrdnV14fnnn8dTTz2F1atXY/HixXjppZfw0Ucf4cCBA6O+ptPpRHd3d9CD5NfUPYA+lxdGvQ4FafFyL0dxxE4WnipO0eb0eKX6Em5RjSTNwmGAo1ohBTgulwuVlZUoLS0Ner60tBSHDx8OawGTec3Kykq43e6ga3Jzc7Fw4cIx33fnzp2w2WzSIz8/P6z1UWSJ+9kFafEwGVgCNtzcTJ4qTtOjpsU/riHJynENo5Fm4TT3wecTZF4NhSOk3zCtra3wer3IysoKej4rKwtNTU1hLWAyr9nU1ASz2YyUlJRJv29ZWRm6urqkR11dXVjro8jiBOPxiRmcix396HN6ZF4NadmZIQXG7KAaKT81HiaDDv1uLxq7B+ReDoUhrFvo4T8MgiBM+QcknNcc7xqLxYLk5OSgB8lP3M9mB9Xo0hItSEswA2D3BkWXuA3KAX+jMxn0KEjzb1PxZ1GdQgpw0tPTYTAYRmRNmpubR2RgIvma2dnZcLlc6OjoiNj7kjzONftn4MxlBmdMgYF/3Kai6JFm4GSy/mYsc9lJpWohBThmsxklJSWoqKgIer6iogIrV64MawGTec2SkhKYTKagaxobG/Hxxx+H/b4kD2ZwJiYWfPKukaJJ/P5igfHY5mQOZnBYaKxKxlD/wrZt27BhwwYsXboUK1aswLPPPgu73Y777rsPALBx40bk5eVh586dAPxFxJ988on0v+vr63Hy5EkkJiZi7ty5k3pNm82GTZs24cc//jHS0tKQmpqKBx54AIsWLcLq1asj8h+Coq+r342WHieAQIcCjSTOJGEGh6JlwO3FhTaeQTWRQKExAxw1CjnAWbduHdra2rBjxw40NjZi4cKF2L9/PwoKCgAAdrsden0gMdTQ0IDFixdLf961axd27dqF66+/HgcPHpzUawLAz3/+cxiNRqxduxb9/f248cYb8atf/QoGgyHcfztNM7HdMivZgiSrSebVKNe8TJ5JRdFV09IHnwDY4kzISGIH1VikYX/M4KhSyAEOAGzZsgVbtmwZ9Wti0CIqLCyEIEzcYjfeawKA1WrF008/jaeffjqktZJycMDf5IhbBvWd/k6qBEtYP6ZEY6puFjuoeAbVeMQAp7XXhU6HCzPizTKviELBQSQ0bc7yiIZJSUkwIz3Rf1ddzdQ4RUHgkE3W34wnwWJEjs1/yjqzOOrDAIemjdRBxQzOhOaxk4qiSNz+nMefxQkNHfhH6sIAh6YND9mcPHGbqpoBDkUBTxGfPPHzip1U6sMAh6aF0+OFvd1/7g0zOBMLzMLhhypF1oDbi9rBn0VuUU1sDjupVIsBDk2L2jYHvD4BiRYjMtm1MSFmcChazjb3QhCAlHgT0hNZNDsRcaQFMzjqwwCHpoV0BlUmuzYmY97gdNmGrgH0DLhlXg1pidhBVcwzqCZFzDjXtTsw4PbKvBoKBQMcmhZnpUM2OeBvMmzxJinTxUJjiqTPm3gGVSgyEi1IshrhEyANRyR1YIBD00IsMGb9zeRdOdMGAKiyd8q8EtKSKrv/TL8r82bIvBJ10Ol07KRSKQY4NC04Ayd0SwpSAAAn7B0TXEk0OW6vD6cu+gNm8fuLJiZ1UrHQWFUY4FDU+XwCZ+CEYcks/y+gytqOSU0DJ5rIp43dGHD7YIszYXY6t4snS8rgsNBYVRjgUNQ1dg+g3+2FUa/DrNR4uZejGlfNnAGDXodL3U7Ud/bLvRzSgMpafzZwyawZ0OtZYDxZzOCoEwMcijqxg6owPQEmA7/lJivObMAVuckAAr+YiKZC/D4q4fZUSMQMTk1rL3w+ZlPVgr9tKOrYQRU+cZuKhcYUCeL3EetvQpOfEgezQY8Bt4/ZVBVhgENRxw6q8Il32szg0FQ1dvWjvrMfBr0OV81kB1UojAY9CtP92+usw1EPBjgUdYEMDgOcUIkBzieN3XC4PDKvhtTsRK0/ezM/JwkJFqPMq1Ef1uGoDwMcirpzLeygClfujDhkJ1vh9Qk4Vdcl93JIxQIFxtyeCkegk4qzcNSCAQ5FVZfDjdZeJwBgNjM4YSnhPByKgEo7C4ynQszg8NBN9WCAQ1ElDvjLsVmRyLR4WKSBf6zDoTANuL04Xe/PADKDEx7OwlEfBjgUVedYfzNlUqGxnQP/KDwf1XfB4xOQmWTBzJQ4uZejSrMHu0Db+lzo6HPJvBqaDAY4FFXsoJq6BTnJsBj16HS4UdPK/X8K3dD5NzxBPDzxZiPyZviDQ2Zx1IEBDkXVuRbOwJkqs1EvtfWyXZzCwQF/kSFmcRjgqAMDHIoqqUWcGZwpYR0OhUsQBOn7ZjHrb6ZEzESzVVwdGOBQ1Dg9XtjbHQCAuazBmZIls5jBofDUtjnQ1ueC2aDHwrxkuZejalInFVvFVYEBDkXNhVYHfAKQZDUiI8ki93JUTczgVDf3oqvfLfNqSE3EoHjRTBssRoPMq1E3ZnDUhQEORU2g/iaRhY1TlJ5oQWGaf1R8FefhUAhOcP5NxIgZnLoOBwbcXplXQxNhgENRwyMaIot1OBQOTjCOnPREM5KtRggCcJ4djYrHAIeihi3ikTV0Hg7RZPQMuPH5pR4AwJICHrA5VTqdjgP/VIQBDkVNIIPDFvFIEAOck/ZOeLw+mVdDanCyrhOCAOSnxiEzySr3cjSBh26qBwMcigqfT0AND9mMqOLMJCRajOhzeaW7cqLxSPNvuD0VMTx0Uz0Y4FBUNHT1o9/thcmgw6zUeLmXowkGvQ6LB9vFT9g7ZV4NqQEH/EUeMzjqwQCHokK8uylMS4DRwG+zSBELRVloTBPx+QScHAyElzDAiRgxg1PT0gufj2fDKRl/81BUsIMqOqRCYwY4NIHq5l70OD1IMBtwWVaS3MvRjJkpcTAb9HB6fKjv7Jd7OTSOsAKcPXv2oKioCFarFSUlJTh06NC417/++utYsGABLBYLFixYgDfeeCPo6zqdbtTHk08+KV1TWFg44usPPvhgOMunacAOqui4etYM6HSAvd2B5p4BuZdDCiYGwVfPmsEsagQZDXoUpfsbJ86yk0rRQv6u37dvH7Zu3Yrt27ejqqoKq1atwpo1a2C320e9/siRI1i3bh02bNiAU6dOYcOGDVi7di2OHTsmXdPY2Bj0eOGFF6DT6XDHHXcEvdaOHTuCrnvooYdCXT5Nk8AZVOygiqRkq0m6Gz9RyzocGhvn30SP+Ll2jnU4ihZygLN7925s2rQJmzdvxvz581FeXo78/Hzs3bt31OvLy8tx0003oaysDJdffjnKyspw4403ory8XLomOzs76PHmm2/iS1/6EmbPnh30WklJSUHXJSaOnR1wOp3o7u4OetD0qREzOBlMjUeaeGDiCc7DoXGI3x+sv4m8uRmchaMGIQU4LpcLlZWVKC0tDXq+tLQUhw8fHvXvHDlyZMT1N99885jXX7p0CW+99RY2bdo04muPP/440tLScPXVV+O///u/4XK5xlzrzp07YbPZpEd+fv5E/zyKkE6HC629/v9vZnMGTsSVcKIxTaCt1ylN2l2SzwAn0ubwTCpVMIZycWtrK7xeL7KysoKez8rKQlNT06h/p6mpKaTrf/3rXyMpKQm333570PM/+tGPsGTJEqSkpOD9999HWVkZzp8/j+eee27U1ykrK8O2bdukP3d3dzPImSbiXU2uzYoES0jfYjQJYoDzYX0XnB4vD1CkEaoGu6eKMxNhizfJvBrt4ani6hDWb5/hBycKgjDuYYqhXP/CCy/gnnvugdUaPHXz/vvvl/73lVdeiZSUFNx5551SVmc4i8UCi4UnWMshUH/DAuNoKEyLR2qCGe19Lpxu6GaNBY1QyQM2o0rMTLf3udDe50JqglnmFdFoQtqiSk9Ph8FgGJF9aW5uHpGlEWVnZ0/6+kOHDuHzzz/H5s2bJ1zLtddeCwA4e/bsZJdP00S8q2GLeHTodDrOw6FxSQXGDHCiIt5sRN6MOACsw1GykAIcs9mMkpISVFRUBD1fUVGBlStXjvp3VqxYMeL6d955Z9Trn3/+eZSUlOCqq66acC1VVVUAgJycnMkun6YJMzjRx3k4NBa314dTdYMD/pjdixrW4ShfyFtU27Ztw4YNG7B06VKsWLECzz77LOx2O+677z4AwMaNG5GXl4edO3cC8NfOXHfddXj88cfxta99DW+++SYOHDiA9957L+h1u7u78dvf/hZPPfXUiPc8cuQIjh49ii996Uuw2Ww4fvw47r//ftx2222YNWtWOP9uiiJpBg4zOFGzZPDIhsrajgm3iCm2fNLQDafHhxnxJsxOZ5F/tMzNSMQ/z7SwVVzBQg5w1q1bh7a2NmkmzcKFC7F//34UFBQAAOx2O/T6QGJo5cqVeO211/DQQw/h4Ycfxpw5c7Bv3z4sX7486HVfe+01CIKAu+66a8R7WiwW7Nu3D//3//5fOJ1OFBQU4N5778VPfvKTUJdPUTbg9qKu3QGAM3Ci6cqZM2DU69Dc40R9Zz9mpvC8L/IbOv9Gr2fgGy3i5xuH/SlXWEXGW7ZswZYtW0b92sGDB0c8d+edd+LOO+8c9zW/+93v4rvf/e6oX1uyZAmOHj0a8jpp+l1o64NPAJKtRmQkssg7WuLMBlyRm4xTF7tQWdvBAIckJ1hgPC04C0f5OL+bImpo/Q23TaJrCefh0ChOcILxtBBrcC529GPA7ZV5NTQaBjgUUeea/R1UrL+JPqnQmBONaVBDZz8augZg0OtwVb5N7uVoWlqCGTPiTRAEoIbzcBSJAQ5FlLgfzQ6q6BMDnE8be9Dn9Mi8GlICcXtqfk4S4s0cshlNOp1OGoXBOhxlYoBDESV2FDCDE305tjjk2Kzw+gScusiDNylQYFzC7alpIdXhsJNKkRjgUMT4fAJqWpnBmU5iHY44mp9i2wkO+JtW7KRSNgY4FDH1nf0YcPtgNuiRnxIn93JigninzoF/NOD24nRDNwB2UE2XuZnM4CgZAxyKGPEupjA9HkYDv7Wmg3SyuL0DPp8g82pITh9e7ILHJyAr2SIdI0DRJdbg1LT2wcufP8XhbyGKGKn+httT02ZBbjKsJj06HW7UtLKTI5ZJ9TcFKRzRME1mpsTDbNTD5fGhvqNf7uXQMAxwKGJ4yOb0Mxn0uHKm/9gGzsOJbZWcfzPtDHqddBwGB/4pDwMcihhmcOQxdJuKYpMgCNL//ywwnl48dFO5GOBQxIh3MMzgTK8lLDSOeRfaHGjvc8Fs1OOK3GS5lxNT5vDIBsVigEMR0dHnQlufCwAwO4OHbE4n8WTx6uZedDncMq+G5CBuT16ZZ4PFaJB5NbFlLjM4isUAhyJCvHvJmxHHCarTLC3RgqLBOoATdczixKJKHrApmzkZrMFRKgY4FBHi3QuzN/IQt6lYaBybxP/fF7PAeNrNTk+ETgd0ONxo63XKvRwaggEORYR498ICY3lIB28ywIk53QNufH6pBwCwpGCGzKuJPXFmgzR36BwP3VQUBjgUEWIGhwXG8hADnFN1nfB4fTKvhqbTSXsnBAGYlRqPzCSr3MuJSdKhm6zDURQGOBQR4p0LMzjyKM5MRJLFiD6XV7qbp9gwdMAfyUM6soF1OIrCAIembMDtRV2HAwAzOHLR63W4ehYH/sUizr+RHzM4ysQAh6bsfGsfBAGwxZmQnmiWezkxi3U4scfrE3By8CT5EhYYy4YZHGVigENTFqi/SeAZODKSAhxONI4Z1c096HF6kGA24LLsJLmXE7PEVvH6zn70u7wyr4ZEDHBoythBpQxX58+ATgfUtfejuWdA7uXQNBCzdVfPmgGDnjcXcklLtCAl3gRBAGpamcVRCgY4NGXsoFKGJKsJl2X57+JP1HbKvBqaDlKBMbenZMc6HOVhgENTxg4q5VjCgzdjilhQzgJj+QXqcDgLRykY4NCUeH0CanjIpmKU8ODNmNHa68SFNn/3IicYy086dJMZHMVggENT0tDZD6fHB7NBj/zUeLmXE/PEQuOPLnbB6WGxo5ZVDXZPzctKhC3OJPNqiJ1UysMAh6ZE3G8uSk9gkaMCFKTFIy3BDJfXh4/ru+VeDkWRmKVbwuyNIogZnJrWPnh9gsyrIYABDk0RO6iURafTBepwuE2laay/UZa8lDhYjHq4PD5cHBx8SvJigENTMnQGDilDCQuNNc/l8eHUxcEBfwxwFMGg16Eo3f85yE4qZWCAQ1MiZnDmMIOjGOKWxQe1HRAEpsq16JPGbjg9PsyIN2F2Om8ulIJ1OMrCAIemhDNwlOfKmTYY9Tq09DhxsaNf7uVQFAydf8Pp4crBWTjKwgCHwtbe50KHww2AAY6SWE0GXJFnA8BtKq3iAZvKxFk4yhJWgLNnzx4UFRXBarWipKQEhw4dGvf6119/HQsWLIDFYsGCBQvwxhtvBH3929/+NnQ6XdDj2muvDbrG6XTiBz/4AdLT05GQkIDbbrsNFy9eDGf5FCHiXUrejDjEmQ0yr4aG4jwcbTvBDipFGprB4faw/EIOcPbt24etW7di+/btqKqqwqpVq7BmzRrY7fZRrz9y5AjWrVuHDRs24NSpU9iwYQPWrl2LY8eOBV33la98BY2NjdJj//79QV/funUr3njjDbz22mt477330Nvbi69+9avwejnrQy7soFIuniyuXQ2d/WjsGoBBr8NV+Ta5l0NDzM5IgE4HdPW70dbnkns5MS/kAGf37t3YtGkTNm/ejPnz56O8vBz5+fnYu3fvqNeXl5fjpptuQllZGS6//HKUlZXhxhtvRHl5edB1FosF2dnZ0iM1NVX6WldXF55//nk89dRTWL16NRYvXoyXXnoJH330EQ4cOBDqP4EihPU3yrWkYAYA4LOmHvQ5PSAp5DUAACAASURBVDKvhiJJDFoX5CQj3myUeTU0lNVkwMyUOACsw1GCkAIcl8uFyspKlJaWBj1fWlqKw4cPj/p3jhw5MuL6m2++ecT1Bw8eRGZmJubNm4d7770Xzc3N0tcqKyvhdruDXic3NxcLFy4c832dTie6u7uDHhRZzOAoV44tDrk2K7w+QWonJm2QCoxZf6NIczPYSaUUIQU4ra2t8Hq9yMrKCno+KysLTU1No/6dpqamCa9fs2YNXn75Zfz973/HU089hePHj+PLX/4ynE6n9BpmsxkpKSnjvs5QO3fuhM1mkx75+fmh/FNpEjgDR9k48E+bWGCsbOykUo6wioyHtyUKgjBuq+JE169btw633HILFi5ciFtvvRV/+ctfcObMGbz11lvjrmO89y0rK0NXV5f0qKurm+ifRSHod3lR3+lvQWYGR5lYh6M9/S4vPmnwZ6OZwVEmdlIpR0gBTnp6OgwGw4isSXNz84gsjSg7Ozuk6wEgJycHBQUFqK6ull7D5XKhoyP4g3q817FYLEhOTg56UOTUtPZCEIAZ8SakJpjlXg6NIjDRuBM+no2jCR9e7ITHJyAr2YJcm1Xu5dAoxKGnPFVcfiEFOGazGSUlJaioqAh6vqKiAitXrhz176xYsWLE9e+8886Y1wNAW1sb6urqkJOTAwAoKSmByWQKep3GxkZ8/PHH474ORY94dzI3I5GDxhRqfk4yrCY9uvrdqGnlh60WVNoD9Tf8uVMmsQanvrMfDhcL/OUU8hbVtm3b8Nxzz+GFF17Ap59+ivvvvx92ux333XcfAGDjxo0oKyuTrv/Rj36Ed955B48//jg+++wzPP744zhw4AC2bt0KAOjt7cUDDzyAI0eO4MKFCzh48CBuvfVWpKen49///d8BADabDZs2bcKPf/xj/O1vf0NVVRW++c1vYtGiRVi9enUk/jtQiNhBpXwmgx5XzfR3U52oZaGxFnD+jfKlJJilrHYNt6lkFXKP4bp169DW1oYdO3agsbERCxcuxP79+1FQUAAAsNvt0OsDcdPKlSvx2muv4aGHHsLDDz+MOXPmYN++fVi+fDkAwGAw4KOPPsJvfvMbdHZ2IicnB1/60pewb98+JCUlSa/z85//HEajEWvXrkV/fz9uvPFG/OpXv4LBwAFzcmAHlTqUFKTg2Pl2VNZ2YO0yFtqrmSAI7KBSibkZiXi/rx3nWnqxMI+ziuQS1hCFLVu2YMuWLaN+7eDBgyOeu/POO3HnnXeOen1cXBz++te/TvieVqsVTz/9NJ5++umQ1krRIe4vz8lkB5WSiXf6lTyyQfXOt/ahw+GG2ajHFbn8palkczIT8P6FdtbhyIxnUVHIvD4BNa1iDU7SBFeTnMRW4rPNveh0cLKqmp2w+7cZr5ppg9nIj24lk1rFOQtHVvwpoZDVd/TD5fHBbNQjb3BqJylTaoIZs9P9WbYqO+tw1KyS9TeqEeikYg2OnBjgUMjOtvQAAGanJ8CgZyeH0kkD/7hNpWpSgTHrbxRP7KQ639oHj9cn82piFwMcCpl4VzKHBcaqwIF/6tfV78aZZv+NBTM4ypc3Iw4Wox4urw8XO/rlXk7MYoBDIWOLuLqIAc7Juk7eTarUybpOCAJQkBaPjCSL3MuhCej1OszmkQ2yY4BDIWOLuLrMzUhEktUIh8uLz5p65F4OhUFqD2f2RjUCRzYwwJELAxwKiSAIUmcAD9lUB71eh8WzWIejZlU8YFN1xM9HZnDkwwCHQnK0ph2dDjcsRj23qFREvPNnHY76eH2C1AHH+hv1EGcV/ePzZgy4vTKvJjYxwKGQPPvPcwCAbyydCauJU6TVooSdVKp15lIPep0eJJgNuCybc6fU4obLMpA3Iw6tvS78/kS93MuJSQxwaNLOXOrBPz5vgU4HbP7ibLmXQyG4Kt8GvQ6oa+9Hc/eA3MuhEIhZt8WzUjiWQUVMBj2+88UiAMBzh2rg8wkyryj2MMChSXv2nzUAgK9ckY3CdNbfqEmS1YTLspMBMIujNpx/o17rl+Uj2WpETWsfKj69JPdyYg4DHJqUpq4BvHnSn2b97nXM3qjRkln+k8VZh6Mu4jliPGBTfRIsRnzzWv9B1OINIk0fBjg0KS8ePg+3V8A1halSRw6pCwf+qU9rrxO1bQ7odMDV+TPkXg6F4dsrC2E26FFZ24HK2na5lxNTGODQhHoG3HjlqB0AszdqJgY4H9d3w+lhV4caiNtTxZmJsMWZZF4NhSMz2Yp/X5wHAPjFu8ziTCcGODSh196vQ4/TgzkZCfjy5ZlyL4fCNCs1HumJZri8Pnxc3y33cmgSuD2lDfde5y82rvj0Emo4+G/aMMChcbm9Przwr/MA/NkbPbs4VEun00lzVE5wm0oVTvAEcU2Ym5mE1fMzIQjALw+dl3s5MYMBDo3rT6ca0Ng1gPREC74+mGYl9WIdjnq4PD6cutgFgBkcLfjudXMAAK+fuIiWHqfMq4kNDHBoTIIgSJX//+cLhbAYOdhP7cRW40p7BwSBczmU7HRDF1weH1LiTSjiWAbVW1aYgqvyZ8Dl8eE3Ry7IvZyYwACHxvTP6lZ81tSDeLMB31xeIPdyKAIW5dlgMujQ0uPExY5+uZdD4zgxeDxDSUEKdDpuDaudTqfDfww2afy/o7VwuDwyr0j7GODQmMRjGdYty4ctnh0cWmA1GaQzcrhNpWwnhkwwJm24+YpsFKTFo9Phxv8er5N7OZrHAIdG9XF9F/51tg0GvQ6bBseNkzbwXCrlEwQBHwzOTGH9jXYY9DpsFo9veO88PF6fzCvSNgY4NCqx9uaWRTmYmRIv82ooklhorHwNXQO41O2EQa/DVTM54E9L7izJR2qCGRc7+vGXj5vkXo6mMcChES52OPDWR40AONhPi8QA59PGbvQ5WQegRGLweUVuMuLMLO7XkjizARuGHN/AYv/oYYBDIzz/3nl4fQK+MDcNC/Nsci+HIiwr2Yq8GXHwCcCpuk65l0Oj4Pwbbdu4ogAWox4f1XfhaA2Pb4gWBjgUpMvhxr7B4jdxbgNpzxJuUynaCU4w1rS0RAu+sXQmgEAzB0UeAxwK8tKxWjhcXlyenYTritPlXg5FSYl4sjgLjRXH4fLgdIP/KI0lDHA0a/MXZ0OnA/7xeQvOXOqRezmaxACHJANuL1781wUA/tobzt7QrpKCVABAlb0TPh9rAJTkw4td8PoEZCdbkWuzyr0cipLC9AR85YpsAIGmDoosBjgk+UNVPVp7ncixWXHrVblyL4ei6PKcJMSZDOjqd6OmlYf/KYm4bcgBf9onNnG8ebIeTV0DMq9GexjgEADA5xPwy0P+u4jvfKEIJgO/NbTMZNDjqnwO/FMiqcCY21Oat3hWCq4pTIXbK+DFwzyEM9L4W4wAAH//rBnnWvqQZDFi/TX5ci+HpgHn4SiPIAgsMI4xYhbnlaN29Ay4ZV6NtjDAIQCBPeC7r52FJCuPZYgFYgsyAxzlON/ahw6HGxajHgtykuVeDk2DL1+eiTkZCehxevDa+zy+IZIY4BCq7B14/0I7TAYdvvMFHssQK8Qzjs619KHT4ZJ5NQQEgs0rZ9pgNvLjORbo9Topi/PCv87DzeMbIiasn6A9e/agqKgIVqsVJSUlOHTo0LjXv/7661iwYAEsFgsWLFiAN954Q/qa2+3GT3/6UyxatAgJCQnIzc3Fxo0b0dDQEPQahYWF0Ol0QY8HH3wwnOXTMGL25mtX5yErmV0bsSI1wYzZGQkA/N1UJD9xe4r1N7Hl64vzkJFkQWPXAP50qmHiv0CTEnKAs2/fPmzduhXbt29HVVUVVq1ahTVr1sBut496/ZEjR7Bu3Tps2LABp06dwoYNG7B27VocO3YMAOBwOHDixAk8/PDDOHHiBH7/+9/jzJkzuO2220a81o4dO9DY2Cg9HnrooVCXT8NcaO3D26f956HwWIbYU8JtKkWROqg4wTimWIwGfHtlIQAe3xBJIQc4u3fvxqZNm7B582bMnz8f5eXlyM/Px969e0e9vry8HDfddBPKyspw+eWXo6ysDDfeeCPKy8sBADabDRUVFVi7di0uu+wyXHvttXj66adRWVk5ImhKSkpCdna29EhMTAzjn0xDPfdeDQQBuOGyDMzLSpJ7OTTNWGisHF39bpy55G/ZZwYn9nxzeQHizQZ81tSDf1a3yr0cTQgpwHG5XKisrERpaWnQ86WlpTh8+PCof+fIkSMjrr/55pvHvB7A/9/enUc1dad9AP9mIWELQRYJICAoCoIbUJVN7TvWqbVqV7Qo9tRxe9UiMKfVTrVTOyMM+k7HVkVFO13GttJ3xrXqW3HKoBQQCuKKW0UWISKIJLIESO77BxCL4AKS/ODm+ZzD8XC5kO+VcPPkt6K2thYCgQC2th130U1MTIS9vT3GjBmD9evXo6np4eMGNBoNVCpVhw/SUfU9Df735zIA1HpjqtoLnILSu2ihvn+mTrd1Tw22t4SDtZRxGmJsckszzH6mdQYrbd/QO7pV4FRVVUGr1cLJyanDcScnJyiVXW/7rlQqu3V+Y2MjVq9ejcjISNjY3J9FsHLlSuzZswdpaWlYsWIFNm3ahGXLlj00a0JCAuRyuf7DzY2mPj/oq6xiaFp0GOkqR7CXPes4hIEhjtawMRejoVmLS0paLp4lWv+G/C7MEyKhAD9dq8b5m7Ws4/R7PRpk/ODqmhzHPXLFzSc9v7m5GXPmzIFOp0NSUlKHr8XGxmLSpEkYNWoUFi5ciO3bt+Ozzz5DdXV1l4/53nvvoba2Vv9RWkrT736toUmLr7JuAKBtGUyZUCjQz6bKp32pmMpvG+hNO4ibrkEDLDF9pDMA2r6hN3SrwHFwcIBIJOrU+lJZWdmplaadQqF4ovObm5sRERGBoqIipKamdmi96cqECRMAANeuXevy61KpFDY2Nh0+yH3/zCtFTX0zBg2wwDR/Bes4hCEah8OeVsfpu6hogT/T1j5c4PC5CpTV1DNO0791q8CRSCQIDAxEampqh+OpqakICQnp8nuCg4M7nX/s2LEO57cXN1evXsXx48dhb//47pLTp08DAJydnbtzCQStN9NdGa3Lgi8M84SYtmUwaVTgsHdZqUZdkxbWUjEN9jdx/q5yhA61h1bH4bMM2r7haYi7+w1xcXGIiopCUFAQgoODkZycjJKSEixduhQAMH/+fLi6uiIhIQFA69iZiRMnIjExEbNmzcKBAwdw/PhxZGRkAABaWlrw2muvIT8/H99//z20Wq2+xcfOzg4SiQRZWVnIzs7Gs88+C7lcjtzcXMTGxmLmzJlwd3fvrf8Lk/HDBSWKq+tha2mGiGdobJKpG+1mC6EAKKtpwC1VI62FxEBeW+vNWHdbiITUXWzqFk8cgp+uVSMltxQxvxkGuSWtLt8T3S5wZs+ejerqav2aNP7+/jhy5Ag8PDwAACUlJRAK77cIhISEYM+ePVizZg3Wrl2LIUOGICUlBePHjwcAlJWV4eDBgwCAMWPGdHistLQ0TJ48GVKpFCkpKVi3bh00Gg08PDywaNEivPvuuz2+cFPFcRx2tPXtRk3wgKWk208BwjPWUjF8FDa4WKFCfnENpo2kVlFj0w8wpvE3BMBEbwf4KGS4pFRj96liLH92KOtI/ZKAM5EVhVQqFeRyOWpra016PM6p69WYnZwNiViIn1b9FxxlNB2VAGv2n8Pu7BIsDPPEmhdHsI5jciZuSEPJnXp8tWAcJg5zZB2H9AF788sQ990ZOMqkyFj1LKRiEetIzPT09ZsGX5iY9pH5rwYMouKG6LWPw6GZVMZ3W61ByZ16CATAGHfbx38DMQkzRrvAWW6O22oN9p++yTpOv0QFjgm5ekuNf1+qhEAALAqnTTXJfYHudgCA8zdVaGzWMk5jWtqLymEDZbAxp7EWpJWZSKjf/Dj5xHXodCbR2dKrqMAxITtPtrbePOfrBC9H2uaC3OdmZwEHaymatDpcKKcFxoyJFvgjDzNnnBtkUjF+uV2HHy9Vso7T71CBYyIqVY3Yf7p1l9olk2hbBtKRQCBAoEdr9whNFzcu/QabVOCQB8jMzRA5oXWmMC38131U4JiIzzNvoEmrQ6DHAAR62LGOQ/ogWg/H+DQtWpxtW5KfChzSlQWhnjATCZBz445+MUjyZKjAMQH3NC3YnV0MgDbVJA/XPkU5r/guTGRyJXMXylVoatHBzkqCwfaWrOOQPsjJxhyzxrgCoFac7qICxwTsySmBurEFXg5WeM636y01CPF3lcNMJEDVPQ3KahpYxzEJ99e/saX94MhDtb8x/b8LStyoqmOcpv+gAofnmrU6/L19W4ZwLwhplVTyEOZmIvi7ygFQN5WxtM+gogHG5FGGOcnw7HBHcBywK4NacZ4UFTg8d/hsBcprG+FgLcErAa6s45A+LtCdxuEYC8dx9wcY0wrG5DEWTxwCAPjfn8tQfU/DOE3/QAUOj/16W4b5wYNhbma6K2GSJ0MDjY3n5t0G3FJpIBYKMGoQLfBHHm2Clx1GusqhadHhq6xi1nH6BSpweCzjWhUKK1SwMBMhaoIH6zikH2jvKrmkVOGepoVxGn5rLyL9XGxgIaE3H+TRBAKBfizOV1k30NBEC3I+DhU4PNY+4j4iaBAGWEkYpyH9gZONOQYNsICOA/78/UVa1dhASqrrse0/vwAAxlL3FHlC0/wVGDTAAjX1zfhnXinrOH0eFTg8dbFchZNXqyAUtA4uJuRJLX92KAQCYE9uKV7bnonSO/WsI/FK6sVbmL75JC4p1RhgaYZ5bQu5EfI4YpEQC8Nat2/YlVEELW3f8EhU4PBU+7YM00Y6w82O1tcgT+6Nce744q1xGGBphvM3VZj+6UmkXrzFOla/16LVIeFoIRZ99TPUjS0Y626Lw9HhGDpQxjoa6UcinnGDraUZiqvr8cMFJes4fRoVODxUfrcBh860bctAC/uRHpg0zBGHo8Mx1t0WqsYWLPrqZyQcLUSLVsc6Wr90S9WIyJ2nsCO99Y3HglBPpCwOhoutBeNkpL+xlIj1Yyp3nLhOi3I+AhU4PPT3jCK06DhM8LKj2Rmkx1xsLZCyOFi/o/GO9OuI3HUKlapGxsn6l8xrVZj+6Unk3LgDa6kYSXMD8MGMEZCI6fZLemZ+8GBIxEKcKb2LnKI7rOP0WfQXxjO1Dc34NqcEALCkbd0EQnpKIhbigxkjkDQ3ANZSMXKK7uCFTzOQ+UsV62h9nk7HYcuPVzHvs1OoutcEH4UMB1eE4oWRzqyjkX7OUSbFqwGDANwfjkA6owKHZ745VYK6Ji2GOVlj8nBH1nEIT7ww0hkHV4TCRyFD1T0N5u06ha1p16CjQY5dqqlrwoIvc/E/x65AxwGvBw7CvmWh8HK0Zh2N8MSicE8IBMDxwkpcq1SzjtMnUYHDI5oWLT7/qXVbhkXhXrS3DelVXo7W2LcsFK8HDoKOAzb+cBm/+zIXNXVNrKP1KadLavDi5gz85/JtSMVCbHh1FDa+PprWuiG9ysvRWr+34M4TRYzT9E1U4PDIgYJyVKo1cLKR6nefJaQ3WUhE2Pj6aGx4dRSkYiHSLt/Gi5szUFB6l3U05jiOw5eZNxCxIws37zZgsL0l9i0LRcQzbqyjEZ5aMql1Esm+0zdpbFwXqMDhCZ2Ow862hf3eCvWkAYzEoCKeccO+ZaEYbG+Jm3cb8Pr2THyVdcNkZ3Tc07Tg7W9P448HL6BZy+F5PwUOvh2GES42rKMRHgv0sEOgxwA0aXX4IvMG6zh9Dr0K8sR/rlTiauU9WEvFiBxPC4cRwxvhYoODb4fheT8FmrUcPjhwAdF7Ckxui4fLSjVmbsnA92crIBYKsGa6L7bNC4CNuRnraMQEtG/fsDu72OT+9h6HChyeaF9f441xbnRjJUZjY26GbfMCsGa6L8RCAQ6dKcfMLRm4css0Bj3uzS/DrK0ZuH67Dgobc6QsmYCFNP6NGNFzvk7wcrCCqrEFKbm0fcOvUYHDA2dK7+JU0R2IhQK81bZmCSHGIhAIsDDcCylLJkBhY47rt+swa8tP2JtfxjqawTQ2a/He3rOI++4MGpt1CPd2wOHoMAR62LGORkyMUCjQb8fz94wiNNNinHpU4PBA+6aaM0e70MqohJlADzscjg5DuLcDGpq1iPvuDN7be453G3YWV9fh1W2Z+DanFAIBEDPFG1+8NQ721lLW0YiJeiXAFQ7WEty824Aj5ypYx+kzqMDp50qq63H0fOsTehFty0AYs7eW4ou3xiFmijcEAuDbnBK8ui0TJdX82LDzhwtKvLg5AxfKVbCzkuDLt8YhZsowiITUJUXYMTcT4c3gwQBahyuY6mD/B1GB08/tyrgOHQdMHOYIX2easUHYEwkFiJkyDF++NQ52VhJcKFdh+uaTONaPNwZs1uoQf6QQS/6RB3VjCwLcbXE4OgwTh9FimqRvmDfBAxZmIlysUOGna9Ws4/QJVOD0Y3fqmvDdz62DyhaHU+sN6VsmDnPE4egwBLjbQt3YgsX/yEPCkcJ+N0ZAWduIyJ3Z+q7g34V5ImVJMJzl1B1M+o4BVhJEBLVu37DjxC+M0/QNVOD0Y//IKkZjsw4jnG0QOtSedRxCOnGWWyBlSTB+F9a2YeeJ64jcmY1b/WRRsp/aNsrMvVEDmVSMbXMDsPbFETAT0a2T9D0Lw70gFAAnr1bhYrmKdRzmBJyJdNapVCrI5XLU1tbCxqb/deXUN7Xgyq17uFShQmGFCoVKNQpK76KpRYdP5oyhlYtJn3f0XAXe/edZqDUtcLCW4JM5YxE61IF1rC7pdBy2pl3Dx8evgOMAH4UM2+YFwtPBinU0Qh5p+Tf5OHy2Ag7WEoweZAtfZxv4OMvgo7CBp4NVvxwv1tPXbypw+hiO41BW04DCChUuKdW4pFShsEKNG9V16Oo35aOQ4dDbYfSOkvQLRVV1+O/debikVEMoAGKnDMPyZ4dC2IduunfqmhCbUoD0K7cBALOD3LBulh/MzWgvKdL3XSxX4eWkn6Bp6dwVLBULMVwhg4+iteDxdbaBj0KGAVYSBkmfHBU4j9EXC5x7mhZcVqrbihkVLlWocUmpfuhqlA7WUvg6tz45W5+YNvB2sqbihvQrjc1afHDgPL77uXWdnMnDHfG3iDF94iabX1KDFV/no7y2EVKxEH96yR8RQbSXFOlf1I3NKKy4/9pSWKHGZaUaDQ9ZskFhYw4fZ5m+4PF1bm3t6SuvLUYtcJKSkrBx40ZUVFTAz88PmzZtQnh4+EPP/9e//oW1a9fil19+wZAhQ7B+/Xq8/PLL+q9zHId169YhOTkZNTU1GD9+PLZu3Qo/Pz/9OTU1NYiOjsbBgwcBADNnzsTmzZtha2v7RJlZFjg6HYeSO/X6J1p760zJna6nzkpEQgwdaN36hFPcb150lNE6G4Q/vvu5FGv3n4emRQcXuTm2zg3AWPcBTLJwHIcvMm8g/kghmrUcBttbImluIO0lRXhDp+NQfKe+dZjDr95Yl95p6PJ8iUgIbyfrtpYemf5fFus9Ga3ASUlJQVRUFJKSkhAaGoodO3Zg165duHjxItzdO++BlJWVhfDwcPzpT3/Cyy+/jH379uGDDz5ARkYGxo8fDwBITEzE+vXr8cUXX2DYsGH485//jBMnTuDy5cuQyWQAgGnTpqGsrAzJyckAgMWLF2Pw4ME4dOjQE+U2VoGjamzWt8oUVrR2MV1WqlHf1HXl7GQj1TcVtj+JvBz7TuVMiCFdLFdh2dd5uFFdDzORALHPDcNwJ5nRc+zNv4nDbQukTfNXIPG1UbTlCTEJ6sZmXLmlxsUKNS61D42oUKHuIa9ZjjKpvpWn/TVriKO1QTd4NlqBM378eAQEBGDbtm36Y76+vnjppZeQkJDQ6fzZs2dDpVLh6NGj+mPPP/88BgwYgG+//RYcx8HFxQUxMTFYtWoVAECj0cDJyQmJiYlYsmQJCgsLMWLECGRnZ+uLouzsbAQHB+PSpUsYPnz4Y3MbqsApv9uAb3NK9AXNzbsPqYbFQgx3auv7/NUTw64PNMsTwpKqsRmr/nkWR8+zXSdHLBTgDy/44q3QwbSXFDFpOl3bWFD90InWyS3Fd+q7HAsqFgowdKA1fJ1tMMLZBgvDPXv1b6inr9/i7jxIU1MT8vLysHr16g7Hp06diszMzC6/JysrC7GxsR2O/fa3v8WmTZsAAEVFRVAqlZg6dar+61KpFJMmTUJmZiaWLFmCrKwsyOVyfXEDABMmTIBcLkdmZmaXBY5Go4FGo9F/rlIZZspcnaYFm3+81uGYi9y8QxHj6yzDYHsriKlVhpBObMzNkDQ3ALuzi7Hv9E1odcYfFmhjYYaYKcMQ6MGmi4yQvkQoFMDd3hLu9pb4rZ9Cf7xO04Irt1rHihZWtBY/hUoV1I0tbZNi1DhdUtNnVtXvVoFTVVUFrVYLJyenDsednJygVHb97kupVD7y/PZ/uzqnuLhYf87AgQM7/eyBAwc+9HETEhKwbt26J7iqp+PpYIU3xrlhuNP9gb9yS2raJqQ7BAIBooIHI6ptuXlCSN9jJRVjrPuADmPlOI5DeW0jCstbx/T0pdmG3Spw2j3Y9MRx3CObo57k/Med09XPf9Tjvvfee4iLi9N/rlKp4ObW+7MhxCIhEl4Z1es/lxBCCOnrBAIBXG0t4GprgSkjnB7/DUbUrQLHwcEBIpGoU6tJZWVlpxaYdgqF4pHnKxStzV9KpRLOzs4PPefWrVudfvbt27cf+rhSqRRSKc06IoQQQkxRtwaFSCQSBAYGIjU1tcPx1NRUhISEdPk9wcHBnc4/duyY/nxPT08oFIoO5zQ1NSE9PV1/TnBwMGpra5GTk6M/59SpU6itrX3o4xJCCCHEdHW7iyouLg5RUVEICgpCcHAwkpOTUVJSgqVLlwIA5s+fD1dXV/2MqpUrV2LixIlITEzErFmzcODAARw/fhwZXmFgDwAACVtJREFUGRkAWpu3YmJiEB8fD29vb3h7eyM+Ph6WlpaIjIwE0DpL6/nnn8eiRYuwY8cOAK3TxF988cUnmkFFCCGEENPS7QJn9uzZqK6uxkcffYSKigr4+/vjyJEj8PDwAACUlJRAKLzfMBQSEoI9e/ZgzZo1WLt2LYYMGYKUlJQOM6LeffddNDQ0YNmyZfqF/o4dO6ZfAwcAvv76a0RHR+tnW82cORNbtmzp8YUTQgghhL9oqwZCCCGE9Fk9ff2mhVkIIYQQwjtU4BBCCCGEd6jAIYQQQgjvUIFDCCGEEN6hAocQQgghvEMFDiGEEEJ4hwocQgghhPAOFTiEEEII4Z0e7SbeH7WvZ6hSqRgnIYQQQsiTan/d7u66xCZT4KjVagCAm5sb4ySEEEII6S61Wg25XP7E55vMVg06nQ7l5eWQyWQQCAS9+rNVKhXc3NxQWlpqEttA0PXyG10vv5na9QKmd818u16O46BWq+Hi4tJhr8vHMZkWHKFQiEGDBhn0MWxsbHjxZHpSdL38RtfLb6Z2vYDpXTOfrrc7LTftaJAxIYQQQniHChxCCCGE8I7oww8//JB1CD4QiUSYPHkyxGLT6PWj6+U3ul5+M7XrBUzvmk3tertiMoOMCSGEEGI6qIuKEEIIIbxDBQ4hhBBCeIcKHEIIIYTwDhU4hBBCCOEdKnAIIYQQwjtU4DylpKQkeHp6wtzcHIGBgTh58iTrSAaTkJCAZ555BjKZDAMHDsRLL72Ey5cvs45lFAkJCRAIBIiJiWEdxaBu3ryJefPmwd7eHpaWlhgzZgzy8vJYxzKIlpYWrFmzBp6enrCwsICXlxc++ugj6HQ61tF6xYkTJzBjxgy4uLhAIBBg//79Hb7OcRw+/PBDuLi4wMLCApMnT8aFCxcYpX16j7re5uZmrFq1CiNHjoSVlRVcXFwwf/58lJeXM0z8dB73+/21JUuWQCAQYNOmTUZMyB4VOE8hJSUFMTExeP/993H69GmEh4dj2rRpKCkpYR3NINLT07F8+XJkZ2cjNTUVLS0tmDp1Kurq6lhHM6jc3FwkJydj1KhRrKMYVE1NDUJDQ2FmZoajR4/i4sWL+Otf/wpbW1vW0QwiMTER27dvx5YtW1BYWIgNGzZg48aN2Lx5M+tovaKurg6jR4/Gli1buvz6hg0b8PHHH2PLli3Izc2FQqHAc889p9+YuL951PXW19cjPz8fa9euRX5+Pvbu3YsrV65g5syZDJL2jsf9ftvt378fp06dgouLi5GS9SEc6bFx48ZxS5cu7XDMx8eHW716NaNExlVZWckB4NLT01lHMRi1Ws15e3tzqamp3KRJk7iVK1eyjmQwq1at4sLCwljHMJrp06dzCxYs6HDslVde4ebNm8cokeEA4Pbt26f/XKfTcQqFgvvLX/6iP9bY2MjJ5XJu+/btLCL2qgevtys5OTkcAK64uNhIqQznYddbVlbGubq6cufPn+c8PDy4v/3tbwzSsUMtOD3U1NSEvLw8TJ06tcPxqVOnIjMzk1Eq46qtrQUA2NnZMU5iOMuXL8f06dMxZcoU1lEM7uDBgwgKCsLrr7+OgQMHYuzYsdi5cyfrWAYTFhaGf//737hy5QoA4MyZM8jIyMALL7zAOJnhFRUVQalUdrh/SaVSTJo0yaTuXwKBgLctlDqdDlFRUXjnnXfg5+fHOg4TpruG81OqqqqCVquFk5NTh+NOTk5QKpWMUhkPx3GIi4tDWFgY/P39WccxiD179iA/Px+5ubmsoxjF9evXsW3bNsTFxeEPf/gDcnJyEB0dDalUivnz57OO1+tWrVqF2tpa+Pj4QCQSQavVYv369XjjjTdYRzO49ntUV/ev4uJiFpGMqrGxEatXr0ZkZCRvdtt+UGJiIsRiMaKjo1lHYYYKnKckEAg6fM5xXKdjfLRixQqcPXsWGRkZrKMYRGlpKVauXIljx47B3NycdRyj0Ol0CAoKQnx8PABg7NixuHDhArZt28bLAiclJQW7d+/GN998Az8/PxQUFCAmJgYuLi548803WcczClO8fzU3N2POnDnQ6XRISkpiHccg8vLy8MknnyA/P5/3v89HoS6qHnJwcIBIJOrUWlNZWdnpXRHfvP322zh48CDS0tIwaNAg1nEMIi8vD5WVlQgMDIRYLIZYLEZ6ejo+/fRTiMViaLVa1hF7nbOzM0aMGNHhmK+vL28Hzb/zzjtYvXo15syZg5EjRyIqKgqxsbFISEhgHc3gFAoFAJjc/au5uRkREREoKipCamoqb1tvTp48icrKSri7u+vvX8XFxfj973+PwYMHs45nNFTg9JBEIkFgYCBSU1M7HE9NTUVISAijVIbFcRxWrFiBvXv34scff4SnpyfrSAbzm9/8BufOnUNBQYH+IygoCHPnzkVBQQFEIhHriL0uNDS007T/K1euwMPDg1Eiw6qvr4dQ2PEWKBKJeDNN/FE8PT2hUCg63L+ampqQnp7O2/tXe3Fz9epVHD9+HPb29qwjGUxUVBTOnj3b4f7l4uKCd955Bz/88APreEZDXVRPIS4uDlFRUQgKCkJwcDCSk5NRUlKCpUuXso5mEMuXL8c333yDAwcOQCaT6d/9yeVyWFhYME7Xu2QyWaexRVZWVrC3t+ftmKPY2FiEhIQgPj4eERERyMnJQXJyMpKTk1lHM4gZM2Zg/fr1cHd3h5+fH06fPo2PP/4YCxYsYB2tV9y7dw/Xrl3Tf15UVISCggLY2dnB3d0dMTExiI+Ph7e3N7y9vREfHw9LS0tERkYyTN1zj7peFxcXvPbaa8jPz8f3338PrVarv3/Z2dlBIpGwit1jj/v9PljAmZmZQaFQYPjw4caOyg7bSVz939atWzkPDw9OIpFwAQEBvJ4yDaDLj88//5x1NKPg+zRxjuO4Q4cOcf7+/pxUKuV8fHy45ORk1pEMRqVScStXruTc3d05c3NzzsvLi3v//fc5jUbDOlqvSEtL6/Lv9c033+Q4rnWq+B//+EdOoVBwUqmUmzhxInfu3Dm2oZ/Co663qKjoofevtLQ01tF75HG/3weZ4jRxAcdxnJFqKUIIIYQQo6AxOIQQQgjhHSpwCCGEEMI7VOAQQgghhHeowCGEEEII71CBQwghhBDeoQKHEEIIIbxDBQ4hhBBCeIcKHEIIIYTwDhU4hBBCCOEdKnAIIYQQwjtU4BBCCCGEd/4fo77glBdyFeIAAAAASUVORK5CYII=", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "PyPlot.plot(X)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ims = [] = Any[]\n", " 0.000512 seconds (1.57 k allocations: 59.375 KiB)\n" ] } ], "source": [ "@show ims = []\n", "@time for i = 1:50\n", " binomial_dist(i)\n", " push!(ims,X)\n", "end" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ims = Any[] = Any[]\n", " 0.000624 seconds (1.57 k allocations: 59.375 KiB)\n" ] } ], "source": [ "@show ims = Any[]\n", "@time for i = 1:50\n", " binomial_dist(i)\n", " push!(ims,X)\n", "end" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "binomial_repitition (generic function with 1 method)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function binomial_repitition()\n", " @show ims = Any[]\n", " @time for i = 1:50\n", " binomial_dist(i)\n", " push!(ims,X)\n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.000009 seconds (16 allocations: 1.031 KiB)\n" ] }, { "data": { "text/plain": [ "binomial_repitition (generic function with 1 method)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# functionで囲ったほうが早くなる.\n", "@time binomial_repitition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1から50までの二項分布をプロットする." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.744225 seconds (136.02 k allocations: 7.230 MiB)\n", " 11.131688 seconds (91.69 k allocations: 4.609 MiB)\n" ] }, { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "using PyPlot\n", "using PyCall\n", "@pyimport matplotlib.animation as anim\n", "\n", "########## display file\n", "function displayfile(mimetype, filename)\n", " open(filename) do f\n", " base64text = base64encode(f)\n", " display(\"text/html\", \"\"\"\"\"\")\n", " end\n", "end\n", "\n", "########## initialize the frame\n", "#xs = [ims[i][1] for j in 1:2, i in 1:length(ims)]\n", "#ys = [ims[i][2] for j in 1:2, i in 1:length(ims)]\n", "#xmin, xmax = minimum(xs)-0.5, maximum(xs)+0.5\n", "#ymin, ymax = minimum(ys)-0.5, maximum(ys)+0.5\n", "function initframe()\n", " xlim(xmin, xmax)\n", " ylim(ymin, ymax)\n", " grid(ls=\":\")\n", "end\n", "\n", "########## update the frame\n", "function updateframe(t)\n", " # clf() #←全部消して書き直す場合にはコメントを外す\n", " #---------- フレームのアップデート開始\n", " if t ≥ 1\n", " X = ims[t]\n", " PyPlot.plot(X, lw=1.0)\n", " end\n", " title(\"t = $t\")\n", " #---------- フレームのアップデート終了\n", " # plot() #←念のためのおまじない. []と書いてもよい. いらない場合も多い.\n", "end\n", "\n", "########## filename\n", "filename = \"randomwalk.gif\"\n", "\n", "######### Construct Figure and Plot Data\n", "fig = figure(figsize=(6.4, 4.8))\n", "\n", "# Create the animation object by anim.FuncAnimaton\n", "frames = collect(0:length(ims))\n", "#@time myanim = anim.FuncAnimation(fig, updateframe, init_func=initframe, frames=frames, interval=100)\n", "@time myanim = anim.FuncAnimation(fig, updateframe, frames=frames, interval=500)\n", "# Convert it to an animated GIF file by Imagemagick.\n", "@time myanim[:save](filename, writer=\"imagemagick\")\n", "\n", "sleep(0.1)\n", "\n", "# Display the movie.\n", "displayfile(\"image/gif\", filename)\n", "\n", "# Don't display the axes of figure().\n", "clf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この画像の意味は取りうる確率が小さくなっていることを意味している.  \n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "binomial_dist_plot (generic function with 1 method)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function binomial_dist_plot(n)\n", " state = 0\n", " p = Float64\n", " global X = Any[]\n", " for i = 1:n\n", " ran_num = rand()\n", " if ran_num >= 0.0 && ran_num <= 0.5\n", " state += 1\n", " elseif ran_num > 0.5 && ran_num<= 1.0\n", " state -= 1\n", " end\n", " # 組み合わせの計算をしているところ\n", " var = (1 * i)+(-1 * (n - i))\n", " p = binomial(n,abs(var)) * (1/2)^(abs(var)) * (1/2)^(n-abs(var))\n", " push!(X,p)\n", " end\n", " PyPlot.plot(X)\n", " end" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "binomial_dist_plot(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "これは$_{10} C _r (\\frac{1}{2})^{10}$のときの二項分布である.見方としては,3〜4の値の状態にいる可能性が20%であり, \n", "同様に6,7くらいが確率が最大の20%である," ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "random_walk (generic function with 1 method)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using PyPlot\n", "function random_walk()\n", " value = 0\n", " value_array = Int64[]\n", " for i = 1:10000000\n", " ran_num = rand()\n", " if ran_num >= 0.0 && ran_num < 0.5\n", " value += 1\n", " else \n", " value -= 1\n", " end\n", " push!(value_array, value)\n", " end\n", " PyPlot.plot(value_array)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ランダムウォークに傾向のようなものはあまりない.上がったときはそのまま上がり続け下がってるときは下がることが多いというようなことは見て取れなくもない." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random_walk()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random_walk()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1-element Array{PyCall.PyObject,1}:\n", " PyObject " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random_walk()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "連続時間の数理ファイナンス理論では,株価の変動は収益率の変動に起因すると考えられている. \n", "変動はブラウン運動で表現される.$S_t$を$t$時点における株価とすれば,$S_t$の変動はブラウン運動$B_t$を用いて \n", "$S_t = S_0 exp(\\alpha t + \\sigma B_t)$と表されることを仮定する.[2]\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "二次元ランダムウォーク" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.000036 seconds (14 allocations: 1.397 KiB)\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "-25\n", "\n", "\n", "0\n", "\n", "\n", "25\n", "\n", "\n", "50\n", "\n", "\n", "-60\n", "\n", "\n", "-40\n", "\n", "\n", "-20\n", "\n", "\n", "0\n", "\n", "\n", "20\n", "\n", "\n", "Brownian motion\n", "\n", "\n", "\n", "\n", "\n", "\n", "y1\n", "\n", "\n" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "using GR\n", "\n", "# 座標の初期値\n", "x = 0.0\n", "y = 0.0\n", "\n", "xlist = Float64[]\n", "ylist = Float64[]\n", "@time function brown_plot(x,y)\n", " for i = 1:10000\n", " # 正規分布に従う乱数の生成(rand()は一様分布,randn()は正規乱数)\n", " x  += randn()\n", " y += randn() \n", " push!(xlist, x)\n", " push!(ylist, y)\n", " end\n", "end\n", "\n", "brown_plot(x, y)\n", "gr()\n", "Plots.plot(xlist, ylist,title=\"Brownian motion\",lw=0.4)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.000049 seconds (15 allocations: 1.575 KiB)\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "Brownian motion\n", "\n", "\n", "\n", "\n", "\n", "y1\n", "\n", "\n" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "using GR\n", "\n", "# 座標の初期値\n", "x = 0.0\n", "y = 0.0\n", "z = 0.0\n", "\n", "xlist = Float64[]\n", "ylist = Float64[]\n", "zlist = Float64[]\n", "\n", "@time function brown_plot(x,y,z)\n", " for i = 1:10000\n", " # 正規分布に従う乱数の生成(rand()は一様分布,randn()は正規乱数)\n", " x += randn()\n", " y += randn()\n", " z += randn()\n", " push!(xlist, x)\n", " push!(ylist, y)\n", " push!(zlist, z)\n", " end\n", "end\n", "\n", "brown_plot(x, y, z)\n", "gr()\n", "# lw は線の太さ\n", "Plots.plot(xlist, ylist,zlist, title=\"Brownian motion\",lw=0.4)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: replacing module PlotlyBase\n" ] }, { "ename": "LoadError", "evalue": "\u001b[91mUndefVarError: AbstractTrace not defined\u001b[39m", "output_type": "error", "traceback": [ "\u001b[91mUndefVarError: AbstractTrace not defined\u001b[39m", "", "Stacktrace:", " [1] \u001b[1minclude_string\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::String, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./loading.jl:522\u001b[22m\u001b[22m" ] } ], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "using Plots\n", "gr()\n", "w = cumsum(randn(10000,3))\n", "Plots.plot(w[:,1],w[:,2],w[:,3], title=\"Brownian motion\",lw=0.4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ぐりぐり出来るランダムウォーク.(黒木さんのコードを引用)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n" ] }, "metadata": {}, "output_type": "display_data", "source": "julia" }, { "data": { "text/html": [ "
\n", " \n" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "plotly()\n", "N = 10000\n", "rw(N) = cumsum(randn(N))\n", "plot(rw(N), rw(N), rw(N), size=(500, 500))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.6.2", "language": "julia", "name": "julia-0.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }