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@sshojiro
Last active May 9, 2019 17:02
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayesian Gaussian Mixture Model \n",
"\n",
"[Pythonで体験する](https://www.amazon.co.jp/Python%E3%81%A7%E4%BD%93%E9%A8%93%E3%81%99%E3%82%8B%E3%83%99%E3%82%A4%E3%82%BA%E6%8E%A8%E8%AB%96-PyMC%E3%81%AB%E3%82%88%E3%82%8BMCMC%E5%85%A5%E9%96%80-%E3%82%AD%E3%83%A3%E3%83%A1%E3%83%AD%E3%83%B3-%E3%83%87%E3%83%93%E3%83%83%E3%83%89%E3%82%BD%E3%83%B3-%E3%83%94%E3%83%AD%E3%83%B3/dp/4627077912)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from os import makedirs\n",
"makedirs('data', exist_ok=True)\n",
"\n",
"from scipy.stats import poisson\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"plt.rcParams['figure.figsize'] = [12, 8]\n",
"plt.rcParams['font.size'] = 24\n",
"\n",
"# from urllib.request import urlretrieve\n",
"# urlretrieve('https://git.io/vXt6b', 'data/mixture_data.csv')\n",
"\n",
"from scipy import stats"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"see=lambda m:[s for s in dir(m)if not s.startswith('_')]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"a = [#poisson(10),\n",
" poisson(100),\n",
" poisson(140)\n",
" ]\n",
"b=[]\n",
"for i in range(len(a)):\n",
" b.append(a[i].rvs(size=1500))\n",
"c = np.concatenate(b)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n",
" 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"data = np.loadtxt('data/mixture_data.csv',\n",
" delimiter=',')\n",
"\n",
"plt.hist(data, bins=20, color='k',\n",
" histtype='stepfilled', alpha=.8)\n",
"plt.title('Histogram of the dataset')\n",
"plt.ylim([0, None])\n",
"plt.xlabel('Value')\n",
"plt.ylabel('Count')\n",
"\n",
"print(data[:10], '...')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gaussian Mixture Model\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"prior assignment with p = 0.96:\n",
"[0 0 0 0 0 0 0 0 0 0] ...\n"
]
}
],
"source": [
"import pymc as pm\n",
"\n",
"p = pm.Uniform('p', 0., 1.)\n",
"assignment = pm.Categorical('assignment', [p, 1-p], size=data.shape[0])\n",
"print('prior assignment with p = %.2f:' % p.value)\n",
"print(assignment.value[:10], '...')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"taus = 1. / pm.Uniform('stds', 0, 33, size=2)**2\n",
"centers = pm.Normal('centers', [120, 190],[.01, .01],size=2)\n",
"\n",
"@pm.deterministic\n",
"def center_i(assignment=assignment, centers=centers):\n",
" return centers[assignment]\n",
"\n",
"@pm.deterministic\n",
"def tau_i(assignment=assignment, taus=taus):\n",
" return taus[assignment]\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"observations = pm.Normal('obs', center_i, tau_i,\n",
" value=data, observed=True)\n",
"model = pm.Model([p, assignment, taus, centers])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 50000 of 50000 complete in 33.0 sec"
]
}
],
"source": [
"mcmc = pm.MCMC(model)\n",
"mcmc.sample(50000)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1b2fa9c95f8>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"colors = ['#348ABD','#A60628']\n",
"line_width = 1\n",
"center_trace = mcmc.trace('centers')[:]\n",
"if center_trace[-1, 0]< center_trace[-1, 1]:\n",
" colors = ['#A60628','#348ABD']\n",
" \n",
"plt.subplot(311)\n",
"plt.plot(center_trace[:,0],\n",
" label='trace of center 0',\n",
" c=colors[0],lw=line_width)\n",
"plt.plot(center_trace[:,1],\n",
" label='trace of center 1',\n",
" c=colors[1],lw=line_width)\n",
"plt.title('Traces of unknown parameters')\n",
"leg = plt.legend(loc='upper right')\n",
"leg.get_frame().set_alpha(.7)\n",
"\n",
"plt.subplot(312)\n",
"std_trace = mcmc.trace('stds')[:]\n",
"plt.plot(std_trace[:,0],\n",
" label='trace of standard deviation of cluster 0',\n",
" c=colors[0],lw=line_width)\n",
"plt.plot(std_trace[:,1],\n",
" label='trace of standard deviation of cluster 1',\n",
" c=colors[1],lw=line_width)\n",
"plt.legend(loc='upper left')\n",
"\n",
"plt.subplot(313)\n",
"p_trace = mcmc.trace('p')[:]\n",
"plt.plot(p_trace,\n",
" label='$p$: frequency of assignment '\n",
" 'to cluster 0', color='#467821', lw=line_width)\n",
"plt.xlabel('Steps')\n",
"plt.ylabel('Value')\n",
"plt.ylim(0, 1)\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Observation of MCMC results\n",
"\n",
"1. MCMC converges to the state where stochastic variables variate routinely, which is the 'convergence' of MCMC algorithm.\n",
"1. The first thousands of points are irrelavant to the posterior distributions. Therefore, they must be eliminated.\n",
"1. A sequence of points seem to correlate each other."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Successive results of MCMC"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 100000 of 100000 complete in 69.2 sec"
]
}
],
"source": [
"mcmc.sample(100000)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Steps')"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"center_trace = mcmc.trace('centers', chain=1)[:]\n",
"prev_center_trace = mcmc.trace('centers', chain=0)[:]\n",
"\n",
"x = np.arange(50000)\n",
"plt.plot(x, prev_center_trace[:,0],\n",
" label='previous trace of center 0',\n",
" lw=line_width, alpha=.4, c=colors[0])\n",
"plt.plot(x, prev_center_trace[:,1],\n",
" label='previous trace of center 1',\n",
" lw=line_width, alpha=.4, c=colors[1])\n",
"x = np.arange(50000, 150000)\n",
"\n",
"plt.plot(x, center_trace[:, 0],\n",
" label='new trace of center 0',\n",
" lw=line_width, c=colors[0])\n",
"plt.plot(x, center_trace[:, 1],\n",
" label='new trace of center 1',\n",
" lw=line_width, c=colors[1])\n",
"plt.title('Traces of unknown center parameters '\n",
" 'after sampling 100,000 more times')\n",
"leg = plt.legend(loc='upper right')\n",
"leg.get_frame().set_alpha(.8)\n",
"plt.ylabel('Value')\n",
"plt.xlabel('Steps')\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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sl3n4mFx/flM139VlJJ2+vyaX4SngqKoyltXv1XkmdQA8l9SOF+TP65XtC8rWd9WweseqY2h8jDie1GdoBanT+dtq5PfyvE7vA75IRx+C3fJ6Xp7zcD0dHQw3J91F8wLp8gukMyo/JZ3FXEq64+TwZvObx/sSad+2DPgf8h0a9f6UJzQzM7O12IB9dLGZmZm1jwMCMzMzc0BgZmZmDgjMzMyM9HAKAyRNJb3oZWFE7JrTRpB6jY4j9Sb9cES8IEmkh8hUHpd5TETcm6c5mo4X6pwZERfm9D1JPcqHk249+3w06NG5xRZbxLhx49pXyH7unnvueS4iRvZ1PmxwWdvaEbgtWdc4IOgwjXRrz/RC2kmkR7OeJemk/P0rpAdyjM9/+5BuD9knBxCnkp4PH8A9kq6NiBfyOFNIt53dQHrC3G/rZWjcuHHMnDmzbQXs7yTVe0KkWZesbe0I3Jasa3zJIIuI20j3hxYdQnrKHfn/5EL69EjuADbND7Y5EJgREYtzEDADmJSHbRwRf8lnBaYX5mVmZtbnHBDUt1Wkp0ZVnh5VeZb0tnR+lvS8nFYvfV5J+hokTZE0U9LMRYsWtaUQZmZmjTgg6Jqy55VHF9LXTIw4PyImRMSEkSN75xLgpcN24tJhzT4t2Mz6E7dfaxcHBPU9m0/3k/8vzOmVl+JUjCI9frRe+qiSdDMzs37BAUF919Lx0o+jSc/lrqQflV90MRFYmi8p3AgckF/+shlwAHBjHrZc0sR8h8JRhXmZmZn1Od9lkEm6lPTCjC0kzSPdLXAW6d3zx5FeGlJ5A+MNpFsO55BuOzwWICIWSzqD9JIbgNMjotJR8TN03Hb4WxrcYWBmZtabHBBkkd6BXmb/knEDOKHGfKYCU0vSZwK7diePZmZmPcWXDMzMzMwBgXVwb2Uzs7WXA4K1nAMAMzMDBwRWwmcKzMzWPg4IzKxtJE2VtFDSA4W0EZJmSJqd/2+W0yXpXElzJN0naY/CNEfn8WfnF4ZV0veUdH+e5tx8G6+ZtYEDAjNrp2mkF3cVVV4SNh64KX+Hzi8Jm0J6AVjlLaOnkl4ctjdwaiWIoOMlYZXpqpdlZl3kgMDM2sYvCTMbuPwcgrWU+whYL+r0kjBJvfKSMNKZBMaMGdOGIpgNfj5DYGZ9ZVC9JMxsoHNAYGY9zS8JMxsAHBBYTb790NrELwkzGwDch8DM2sYvCTMbuBwQmFnb+CVhZgOXLxmYmZmZAwIzMzNzQGBmZma4D8Fax3cNWLMk/Yp0Hf+3EbGqr/NjZj3LZwjMrJafAh8DZks6S9KOfZ0hM+s5DgjMrFRE/D4iPg7sATwJzJB0u6RjJQ3t29yZWbs5IDCzmiRtDhwDfBL4K/BDUoAwow+zZWY9wH0IzKyUpKuAHYFfAB+ovKAIuFzSzL7LmZn1BAcEZlbLBRFxQzFB0rCIWBkRE/oqU2bWMxwQrCV8d4F1wZmkxwsX/YV0ycDMBhkHBNZQJZj46MqH+zgn1hskvRHYFhgu6W10vHZ4Y2D9PsuYmfUoBwRmVu1AUkfCUcDZhfTlwCl9kSEz63kOCMysk4i4ELhQ0r9FxK/6Oj9m1jscEJhZJ5KOiIiLgHGSvlQ9PCLOLpnMzAY4BwRmVm2D/H/DPs2FNeTOwtZODgjMrJOIOC///0Zf58U6cwBgPclPKjSzUpK+K2ljSUMl3STpOUlH9HW+zKxnOCBogqQnJd0vaVblCW2SRkiaIWl2/r9ZTpekcyXNkXSfpD0K8zk6jz9b0tF9VR6zJh0QEcuAg4F5wFuAE/s2S2bWUxwQNO/dEfHWwhPaTgJuiojxwE35O8D7gPH5bwrpjXFIGgGcCuwD7A2cWgkizPqpyguMDgIujYjFfZkZM+tZDgi67hDgwvz5QmByIX16JHcAm0ramnRv94yIWBwRL5BeDjOptzNt1oLrJD0CTABukjQSeLmP82RmPcSdCpsTwO8kBXBeRJwPbFV52UtELJC0ZR53W2BuYdp5Oa1WeieSppDOLDBmzJhuZ9ydkKyrIuIkSd8BlkXE65JeJAW8ZjYIOSBozjsiYn4+6M/Iv5pqUUla1EnvnJCCjfMBJkyYsMbwvnTpsJ38+OK1z06k5xEU9xXT+yozZtZzHBA0ISLm5/8LJf2a1AfgWUlb57MDWwML8+jzgNGFyUcB83P6vlXpt/Rw1s26TNIvgDcDs4DXc3LggMBsUHIfggYkbSBpo8pn4ADgAeBaoHKnwNHANfnztcBR+W6DicDSfGnhRuAASZvlzoQH5DSz/moC6ezYZyPic/nvP7o6M9+t03WXDtvJl/+sx/kMQWNbAb+WBGl9XRIR/yvpbuAKSccBTwOH5fFvIPXKngO8BBwLEBGLJZ0B3J3HO929tq2fewB4I7CgjfN8d0Q8V/heuVvnLEkn5e9fofPdOvuQ7tbZp3C3zgTS2Yp7JF2bO+qaWTc4IGggIh4Hdi9Jfx7YvyQ9gBNqzGsqMLXdeTTrIVsAD0m6C1hZSYyID7ZxGYfQcSntQtJltK9QuFsHuENS5W6dfcl36wBIqtytc2kb82S2VnJAYGa1nNbm+Q3Yu3XM1gYOCMysVETcKmksMD4ifi9pfWBIN2bpu3XM+jF3KjSzUpI+BVwJnJeTtgWu7ur8infrAJ3u1snLa/ZunbJ0M+smBwRmVssJwDuAZQARMRvYsu4UNfhuHbP+z5cMzKyWlRHxSr7Dhvxwoq6efvfdOmb9nAMCM6vlVkmnAMMlvRf4LHBdV2bku3W6xs8esN7kSwbWEj8gZa1yErAIuB/4NOlX+9f6NEdm1mN8hmCQ8kHbuisiVkm6Grg6Ihb1dX7MrGf5DIGZdZI78p0m6TngEeBRSYskfb2v82ZmPccBgZlV+wLp7oK9ImLziBhBenzwOyR9sW+zZmY9xQGBmVU7CvhoRDxRScidAo/Iw8xsEHJAYGbVhla9gAiA3I9gaB/kx8x6gQMCM6v2SheHmdkA5rsMzKza7pKWlaQLWK+3M2NmvcMBgZl1EhHdeYGRmQ1QDgisSyrPOfjoyof7OCdmg4+fI2J9wX0IzMzMzAHBYORfF2YDl9uv9RUHBGZmZuaAwMzMzBwQmJmZGQ4IrJv8OmQzs8HBtx2amfUDDqytr/kMgZmZmfkMwWDiXxhmZtZVPkNgbeG+BGZmA5sDAjMzM3NAYGZmZu5DYGbWp3ypzfoLBwSDQH/aofgtiGZmA5MvGfQiSZMkPSppjqST+jo/ZgOV25JZ+/kMQS+RNAT4MfBeYB5wt6RrI+Khrs6zP50ZMOstPdGWzMwBQW/aG5gTEY8DSLoMOAQYlDuxYrDiywfWZoOiLTmgt/7GAUHv2RaYW/g+D9ineiRJU4Ap+esKSY+2uJwtgOe6lMP2zaPT9B+Tmp1ubDeWaWuPhm2pDe0I2tOWem1eVe3Mbcla5oCg95QdFWONhIjzgfO7vBBpZkRM6Or07ZhHO/JgVkfDttTddgTtrcf9dV5mRe5U2HvmAaML30cB8/soL2YDmduSWQ9wQNB77gbGS3qTpDcAhwPX9nGezAYityWzHuBLBr0kIl6T9O/AjcAQYGpEPNgDi+rWadI2zaMdeTArNcDaUn+fl9lqiljjMraZmZmtZXzJwMzMzBwQmJmZmQOCAUfSVEkLJT1QSDtM0oOSVkmaUDX+yfnxro9KOrDG9N+T9Iik+yT9WtKmtaavk4cz8vSzJP1O0jY5XZLOzfO4T9IePbl+zLqiRp0eIWmGpNn5/2ZNzmu0pJslPZzb5ee7Oj9J60m6S9Lf8ry+kdPfJOnOPK/Lc+dKs25xQDDwTAMmVaU9APwrcFsxUdLOpB7Yu+RpfgJML5l+BrBrROwG/B04udb0+bGxZXn4XkTsFhFvBa4Hvp7T3weMz39TgJ+2WmCzXjCNNev0ScBNETEeuCl/b8ZrwJcjYidgInBCbktdmd9KYL+I2B14KzBJ0kTgO8AP8rxeAI5rMm9mNTkgGGAi4jZgcVXawxFR9iS2Q4DLImJlRDwBzCHtYKqn/11EvJa/3kG6r7vW9HvXyMOywtcN6HhQzCHA9EjuADaVtHVrpTbrWWV1mlR3L8yfLwQmNzmvBRFxb/68HHiY9HTFlueX282K/HVo/gtgP+DKVvNmVo8DgsGt7BGv2zaY5hPAb7syvaRvSpoLfJyOMwRdyYNZf7BVRCyAdJAHtmx1BpLGAW8D7uzq/CQNkTQLWEg6m/cYsKQQxLtNWVs4IBjcmnpc8uqRpa+STnde3JXpI+KrETE6T//vXZmH2WAhaUPgV8AXqs6gtSQiXs+X4kaRXuxU9lYktynrNgcEg1vTj3iVdDRwMPDx6Hg4RVcfEXsJ8G/dnIdZX3u2cnkr/1/Y7ISShpKCgYsj4qruzg8gIpYAt5D6JWwqqfJgObcpawsHBIPbtcDhkoZJehOpY99d1SNJmgR8BfhgRLzU6vR5HuMLXz8IPFKYx1H5boOJwNLKaVOzfu5a4Oj8+WjgmmYmkiTg58DDEXF2d+YnaWTlrh9Jw4H3kPok3Awc2mrezOrxkwoHGEmXAvuSXoH6LHAqqTPUfwMjgSXArIio3CL4VVK/gNeALwBHlUx/MjAMeD4v5o6IOL5s+oj4bY08HATsAKwCngKOj4h/5J3jj0g9uF8Cjo2Ime1fM2ZdV6NOXw1cAYwBngYOi4jqjodl83on8EfgflJ7ADiF1I+gpflJ2o3UaXAI6QfcFRFxuqTtgMuAEcBfgSMiYmULRTZbgwMCMzMz8yUDMzMzc0BgZmZmOCAwMzMzHBCYmZkZDgjMzMwMBwRmZg1JuqXyts9C2hck/aTONCtqDTPrjxwQmJk1dinpzZ9Fh+d0s0HBAYGZWWNXAgdLGgarX1q0DTBL0k2S7pV0v6RDqieUtK+k6wvffyTpmPx5T0m3SrpH0o1+E6j1JQcEZmYNRMTzpMd2T8pJhwOXA/8EPhQRewDvBr6fn87ZUH7fwX8Dh0bEnsBU4JvtzrtZs9ZtPIqZmdFx2eCa/P8TpLd5fkvSu0iPKd4W2Ap4pon57QDsCszIMcQQwO/5sD7jgMDMrDlXA2dL2gMYHhH35lP/I4E9I+JVSU8C61VN9xqdz8ZWhgt4MCLe3rPZNmuOLxmYmTUhIlaQXj88lY7OhJsAC3Mw8G5gbMmkTwE757eGbgLsn9MfBUZKejukSwiSdunJMpjV4zMEZmbNuxS4io47Di4GrpM0E5hFx2u/V4uIuZKuAO4DZpPeTkhEvCLpUODcHCisC5wDPNjjpTAr4bcdmpmZmS8ZmJmZmQMCMzMzwwGBmZmZ4YDAzMzMcEBgZmZmOCAwMzMzHBCYmZkZDgjMzMwMBwRmZmaGAwIzMzPDAYGZmZnhgMDMzMwYwAGBpBWStuuhee8raV7h+4OS9m3TvD8u6XeF7yFp+3bMO8+vx9ZLnWUOl3SdpKWSftmby+5J3SlXcbu6rtacv+tqQQ+s3yclvafJcY+R9Kc2LPMUSRd0Y/q21d8WlilJ/yPpBUl3tTht0+t4IGgYEOQC/zM33mfzituwqwuUNC5X/G69ejkiNoyIx7szjxaWtUtE3FJvnGbLFREXR8QB7ciXpFskfbJq/r22XgoOBbYCNo+Iw3prodU70HbXVeB44GBgy+6Uq6vbRNI0SWe2uKy6dVXSuyX9Ja+7JxvMy3U1a9d+a7CLiG9FxCcbj1lev5vZ1/aAdwLvBUZFxN69vGwknSbpojbPc1dJN0p6TlLTrzRu9gzBByJiQ2APYC/ga13JZDt0t0H2ZYMexDuTscDfI+K1vs4ITdbVJrfFtvn/613My5AuTlehbk1cXsYXgSu6OO1g0J/qalsM4m3VW8YCT0bEi32dka6osf1fJbXz41qaWUTU/QOeBN5T+P494Pr8eRvgWmAxMAf4VGG8vYGZwDLgWeDsnP40EMCK/Pf2nP4J4GHgBeBGYGxhXgGcAMwGniikbZ8/bwJMBxYBT5EOAuvkYccAfwZ+kPN5ZkkZhwPT8rIfAk4E5pWtg1bKVbbsnPanqrL9B/A48Fxev5W8nwZcVBh3XB5/XeCbpAPVy3l5P+rCevkT8P9yuZ8A3lenHuwE3AIsAR4EPpjTvwG8QqqAK4DjSqYdApwCPAYsB+4BRufI8vXjAAAcvklEQVRhOwIz8vp5FPhwYbppwI+B3+Tp7gTenIfdlsv6Yl7uR/J2+iowK+fzH8Cthbr6Uv5bmfO7bi7XPcBreX0uAc7O5YrC38uU19W/53VbKVelrgYwt7BNTi5skz/n5Ve2yQ+AhTlvL+Zt9mLOzyu5fNfl6bfL5VyVh11Nrquk+vIi8HtS/TyT+nV1Fa6r1dO20r7fDPwBeD6vj4uBTav2G/8J3AcsBS4H1isMPxFYAMwn1ani+ng/8Necj7nAaSXr9ricr9ty+pF53T1PagdPUth3V5Vzc9K+exlwF3BG1bYubZfAROAZYEhh3A8B99WoB7/M4y8ltdldcvqUvB2q6/fqPAPDgHPy+pmfPw/Lw/YF5gFfJrWdBcCxdepE6bEqr8OXSfVzBfCNGtN/itTml5OOEXuU5HcaheNLJY+F718h7ZOW53W6PzCJznXyb4X28PNcrn+Q2uOQZo9phWVuD0St4WuM33CEzgUeTWpgZ+TvtwI/AdYD3kpqzPvnYX8BjsyfNwQmVu8oCsuYnDfSTqQdyNeA26t2RDOAEcDwkp3JdOAaYKM8/7+TG3teea8Bn8vzHl5SxrOAP+b5jwYeoHZA0Eq51lg25TvZm/Oyx+S8f7LRTjZ/v6UybtX8ml0vr5Iq+hDgM6RGp5L1MzRvn1OANwD7kSr1DmX5LJn+ROB+YAfSr97dSTukDUg7u2Pz+tmDtGOt7DSmkSr83nn4xcBlZWXN3+eTDhj7kKL+eaSDwjBSXV0G/A04kFRXD8jlejqvj0q5Kju/c0q2abGufoW0s7u3UK5KXY1COYoBwfQ8/l/yNplHql+b0lFfvprL+ws672DWyct7inTa+x2kncmiwnYI4Ot53DupX1efdF1dY/pW2vf2pFPNw4CRpAPeOVX7jbtIB6MRpAPK8XnYJFLAsSupHVxStT72Bf4lb8fd8riTq/IyPU87HNiZdEB5V87P2Xl71goILiP9gtwg5+EflW1N43b5GPDewrx+CZxUox58Im/TysF9VmHYNKoOZnTe154O3AFsmdfv7XQce/bN5Ts9b/ODSAH1ZjXKW+9YdQyFel4y7WF5/exFaufbk3+w0mRAQNr3zQW2KWzDN5ets5x2NXBe3hZbkurRp5s9plXV0ag1fI3xG46QCryCtGN9Kq/U4aQD5+vARoVxvw1My59vI0XkW1TNbxxrNqzfUojWSY3gpcJKD2C/sp0JaQexEti5MOzTwC2Flfd0gzI+DkwqfJ9C7YCglXKtsezqypenKS77s8BNNRpXp2VQZyfb5HqZUxi2fp72jSXr5/+QDkTrFNIuJf9qqc5nyfSPAoeUpH8E+GNV2nnAqYUGdkFh2EHAI9VlLXxfRjpAFuvq30nXjV/PaZ8o1NUbcrlWb9OqcpUFBKvrai7XZErqKp137gGcXNgmp9Cx8z07Tz+RtAN+urCsaXTewexD2hEU68tVwIuF7fAyzdfV6oDAdbWF9l0y7WTgr1X7jSMK378L/Cx/ngqcVRj2Fqrqc9W8zwF+UJWX7QrDv07nYHkDUltYIyDI6/tVYMdC2rfoqJON2uWZwNT8eSPSWalK/a+5fklBbwCblNXvwjqr1N/HgIMKww4k11nSwfafdG6bC8kBXNU8Gx2rjqF+QHAj8Pkaw4r57VQeOgcE2+f8vQcYWjWPTuuMFOyvpHCgBz4K3FyrrdbJe0sBQbN9CCZHxKYRMTYiPhsR/yRFvYsjYnlhvKfouO56HKmSPyLpbkkH15n/WOCHkpZIWkL6VajCvCBFV2W2IP0SeKpGPupNW7FN1ThP1RqR1srVzLKrx3kq56e7mlkvz1Q+RMRL+WNZJ7xtSKe/V9WZVz2jSY272lhgn8p2z9v+48Aby/JIOnDW6yS4Luk0OKRTbh8DRpFOfy4mn8Yv5H9U/r56m5Ia8cQ6y1hdV/M002m9rj5XSPsdKeD+MfBD4A2SNq6z7CHAFYX1NYnOfYGK18ZdV8vnVU/T60zSlpIuk/QPScuAi3JZimrV37r7HEn7SLpZ0iJJS0kdXKvnXZy+0/wiXQ9/vkbWR5LaSq3lN2qXlwD/KmkY8K/AvRGxxj5T0hBJZ0l6LK+fJ/Og6nLUsg1r1olifXs+OvcFqbV/aHSsaqTW/qtpETEH+ALp4L8w15tabWcs6azHgsL6P490pqCimbbasu7cdjgfGCFpo0LaGNKpFSJidkR8lFSI7wBXStqAtFOuNpd0OmTTwt/wiLi9ME7ZdJB2rq+SVuIa+WgwbcUC0kYvTl+qxXI1s2xKlj0/f36R9GuoonigbDTvZtZLs+YDoyUV60sr85pLut5aln5r1XbfMCI+04U8QvoVcEnV/NYHLiSdshUd62wM6XT9aOCxwjadA7ynmbpKOvtwZJN1dTgd22THQvoY4KGI2JN0qWA46RJL2Xzmkg74H66UD/g8NXb8rqutz6vFdfbtnL5bRGwMHEHzHUEb7XMuIV3zHh0RmwA/K5l3MU+d5idpfdJluTKLSPWo1vLrtsuIeIh0QH0fKei+pMZyPgYcQvpVvAnpzAaFcjSqb/NZs07MrzFuo/nUPFY1odb+q1rdNhARl0TEO0llClL9gvJ2vpJ0lqqy/jeOiF2Ks2sy7y3pckAQEXNJ13S+LWk9SbuRouuLASQdIWlkjtSX5MleJ1XGVaTOURU/A06WtEuedhNJTd0SFBGvk66FfVPSRpLGAl8iRevNuiIvfzNJo0jXZkq1WK5mnZiXPZq0g788p88C3iVpjKRNSKedi56ttbw2rZeKO0mV/b8kDc33CX+AdB2yGRcAZ0gan+/53U3S5sD1wFskHZnnO1TSXpJ2anK+1eVfDhycf11J0gaS3k/aTrcDmwFDC3X1v3O5LpG0Nen6656k7fk66RdHULuuXkBav5+rlKtOXg8kXUe9gXRJakjeJqcAf5Y0lLQTWEXHXQ3V5buLdPD/iaStJY0hdVobWrbAGnV1FenSyqq8LtaT9IY6+a42qOtqi+17I/LlVEnb0hHINeMK4BhJO+eD96lVwzci/ap9WdLepINrPVeS6v478/Y8nRr797y+rwJOk7S+pJ2BowujNNMuLyF1MH0XqQ9BmY1Idfp50oHyW1XDa9aJ7FLga5JGStqCdFmk5TrR6FjVhAuA/5S0Z27n2+c6Wm0WcJCkEZLeSDojAICkHSTtl8+qvEy63FFs5+MqQWxELCCdOfy+pI0lrSPpzZL+b7Nlzvlcj3TmjVzuYQ0nbOIaxJPU7pgyilR5FpNOqRxfGHYR6ZrJClJHxMmFYaeTGtgSOjrtHEnqeFbpVTu1MP4a19aKaaQd/UV5nnPJnaoK11tqXh/K46xPOvW7hMZ3GTRdrrJlV6fRuef288D36dyD98d5fnNInaqK12XfTvqV+gJwbnfXS9l6LgzbhdQxZ2leRx8qDDuN+tdlh5A6ij5BOmjfTbrnF1Jnm9/kPD5P6rX91mhwTS5/P570y2gJ8OG8nU7K81+Sh/2StGMaRTrAL6NQV3O5niXt7FeROhhOLpTrPurX1aW5TJVyBfm6HZ37EPwxj3NHnuereZtMy99X5OELgQ3zdOPpuGPi6py2XV6PlcDhKTp3KlxBnbqa12FU/d1boz50SmPtqKuttO9dSHeWrMjb6cvU2G+ULZtUV5+h/C6DQ+m4e+V64EeVaanRn4F0UH+a5u4yGJnnW+sug5rtMg8fQ6qDv6ma7+oykk7fX5PL8BRwVFUZy+r36jyTOgCeS2rHC/Ln9cr2BWXru2pYvWPVMTQ+RhxP6jO0gtTp/G018nt5Xqf3AV+kow/Bbnk9L895uJ6ODoabk+6ieYF0+QXSGZWfks5iLiXdcXJ4C/mt1JHi35P1pomI1EvXzMzM1m4D9tHFZmZm1j4OCMzMzMwBgZmZmTkgMDMzM9LDKQyQNJX0ZruFEbFrThtB6jU6jtSb9MMR8YIkkR4iU3lc5jERcW+e5mg6XqhzZkRcmNP3JPUoH0669ezz0aBH5xZbbBHjxo1rXyH7uXvuuee5iBjZ1/mwwWVta0fgtmRd44CgwzTSrT3TC2knkR7Nepakk/L3r5AeyDE+/+1Duj1knxxAnApMIN3mcY+kayPihTzOFNJtZzeQnjD323oZGjduHDNnzmxbAfs7SfWeEGnWJWtbOwK3JesaXzLIIuI20v2hRYeQnnJH/j+5kD49kjuATfODbQ4EZkTE4hwEzAAm5WEbR8Rf8lmB6YV5mZmZ9TkHBPVtFempUZWnR1WeJb0tnZ8lPS+n1UufV5K+BklTJM2UNHPRokVtKYSZmVkjDgi6pux55dGF9DUTI86PiAkRMWHkyL69BLjX9/7AXt/7Q5/mwWwgcZuxgcwBQX3P5tP95P8Lc3rlpTgVo0iPH62XPqok3czMrF9wp8L6riU9H/ys/P+aQvq/S7qM1KlwaUQskHQj8C1Jm+XxDgBOjojFkpZLmkh6+cpRpBfr9Ev+hWPWGrcZGwwcEGSSLiW9MGMLSfNIdwucRXr3/HGkl4ZU3sB4A+mWwzmk2w6PBcgH/jNIL7kBOD0iKh0VP0PHbYe/pcEdBmZmZr3JAUEW6R3oZfYvGTeAE2rMZyowtSR9JrBrd/JoZmbWUxwQ2Go+7WlmtvZyp0IzMzNzQGBmZmYOCMzMzAwHBGZmbecHFNlA5IDAGu68vHOzdpC0qaQrJT0i6WFJb5c0QtIMSbPz/83yuJJ0rqQ5ku6TtEdhPkfn8Wfnt4uaWRs4IDCz3vJD4H8jYkdgd+BhOt4oOh64KX+Hzm8UnUJ6W2jlleSnkh4ItjdwauFBYGbWDQ4IzKzHSdoYeBfwc4CIeCUiltCmN4r2YlHMBi0HBGbWG7YDFgH/I+mvki6QtAHte6NoJ35rqFnrHBCYWW9YF9gD+GlEvA14kY7LA2W69ebQ/vTWULOBwgGBmfWGecC8iLgzf7+SFCC0642iZtZNDgjMrMdFxDPAXEk75KT9gYfoeKMorPlG0aPy3QYTyW8UBW4EDpC0We5MeEBOM7Nu8rsMzKy3fA64WNIbgMdJbwldh/a9UdTMusEBgTVtr+/9gbtP3K+vs2EDVETMAiaUDGrLG0XNrHscEJiZdZEf2GWDifsQrOW8Q7NWSfqVpPdL8v7DbBBxgzazVv0U+BgwW9JZknbs6wyZWfc5IDCzlkTE7yPi46TbBp8EZki6XdKxkob2be7MrKscEJhZyyRtDhwDfBL4K+k9BXuQHiVsZgOQOxWaWUskXQXsCPwC+EDl0cPA5ZJm9l3O+p9KHx3fnWMDgQMCM2vVBRFxQzFB0rCIWBkRZbcVmtkA4EsG1pK9vvcH35lgZ5ak/aXXc2FmbeUzBGbWFElvJL1ZcLikt9HxoqGNgfX7LGNm1hYOCMysWQeSOhKOAs4upC8HTumLDJlZ+zggMLOmRMSFwIWS/i0iftXX+TGz9nJAsJZyPwBrlaQjIuIiYJykL1UPj4izSyYzswHCnQrNrFkb5P8bAhuV/DUkaYikv0q6Pn9/k6Q7Jc2WdHl+EyKShuXvc/LwcYV5nJzTH5V0YPuKZ7Z28xkCM2tKRJyX/3+jG7P5PPAwqSMiwHeAH0TEZZJ+BhxHejTyccALEbG9pMPzeB+RtDNwOLALsA3we0lviYjXu5EnM8NnCMysRZK+K2ljSUMl3STpOUlHNDHdKOD9wAX5u4D9gCvzKBcCk/PnQ/J38vD98/iHAJflZx48AcwB9m5X2czWZg4IzKxVB0TEMuBgYB7wFuDEJqY7B/gvYFX+vjmwJCJey9/nkW5rJP+fC5CHL83jr04vmWY1SVMkzZQ0c9GiRS0UzWzt5YCgCZKelHS/pFmVR7NKGiFpRr72OUPSZjldks7N1zjvk7RHYT5H5/FnSzq6r8pj1k2VFxgdBFwaEYsbTSDpYGBhRNxTTC4ZNRoMqzdNR0LE+RExISImjBw5slH2zAwHBK14d0S8tfBo1pOAmyJiPHBT/g7wPmB8/ptCuh6KpBHAqcA+pFOcp1aCCLMB5jpJjwATgJskjQRebjDNO4APSnoSuIx0qeAcYFNJlb5Mo4D5+fM8YDRAHr4JsLiYXjKNmXWDA4KuK17jrL72OT2SO0g7vK1JD3WZERGLI+IF0lvhJvV2ps26KyJOAt4OTIiIV4EXSfW+3jQnR8SoiBhH6hT4h/wK5ZuBQ/NoRwPX5M/X5u/k4X+IiMjph+e7EN5ECrzvalvhzNZivsugOQH8TlIA50XE+cBWlbe8RcQCSVvmcWtd42z62ifpzAJjxoxpdzn8/AFrl51IzyMo7kOmd2E+XwEuk3Qm6TXKP8/pPwd+IWkO6czA4QAR8aCkK4CHgNeAE3yHgVl7OCBozjsiYn4+6M/Ip0tr6fa1T+B8gAkTJqwx3KyvSfoF8GZgFlA5GAdNBgQRcQtwS/78OCV3CUTEy8BhNab/JvDNFrNtZg04IGhCRMzP/xdK+jVpB/aspK3z2YGtgYV59FrXOOcB+1al39LDWe8xfs/7Wm0CsHM+hW9mg4T7EDQgaQNJG1U+AwcAD9D5Gmf1tc+j8t0GE4Gl+dLCjcABkjbLnQkPyGlmA80DwBv7OhN9rZXLb75UZwOBzxA0thXw6/RMFNYFLomI/5V0N3CFpOOAp+k4vXkD6XasOcBLwLEAEbFY0hnA3Xm805u5XcusH9oCeEjSXcDKSmJEfLDvsmRm3eWAoIF8jXP3kvTngf1L0gM4oca8pgJT251Hs152Wl9nwMzazwGBmbUkIm6VNBYYHxG/l7Q+MKSv82Vm3eM+BGbWEkmfIr1f4LyctC1wdd/lyMzawQGBmbXqBNKTB5cBRMRsYMu6U5hZv+eAwMxatTIiXql8yQ8n8i2IZgOcAwIza9Wtkk4Bhkt6L/BL4Lo+zpOZdZMDAjNr1UnAIuB+4NOkW22/1qc5MrNu810Ga4meejCKn1i49omIVZKuBq6OiEV9nR8zaw+fITCzpuSnb54m6TngEeBRSYskfb2v82Zm3eeAwMya9QXS3QV7RcTmETEC2Ad4h6Qv1ptQ0mhJN0t6WNKDkj6f00dImiFpdv6/WU6XpHMlzZF0n6Q9CvM6Oo8/W9LRtZbZ3+z1vT/4EcbWrzkgMLNmHQV8NCKeqCTkJ3kekYfV8xrw5YjYCZgInCBpZ1J/hJsiYjxwU/4O8D5gfP6bAvwUUgABnEoKRPYGTq0EEWbWPQ4IzKxZQyPiuerE3I9gaL0JI2JBRNybPy8HHiY90OgQ4MI82oXA5Pz5EGB6JHcAm+a3ih4IzIiIxRHxAjADmNT9opmZAwIza9YrXRzWiaRxwNuAO4Gt8ttAyf8rDzjaFphbmGxeTquVXr2MKZJmSpq5aJH7PZo1w3cZmFmzdpe0rCRdwHrNzEDShsCvgC9ExLL8FtHSUUvSok5654SI84HzASZMmOCHJpk1wQGBmTUlIrr1AiNJQ0nBwMURcVVOflbS1hGxIF8SWJjT5wGjC5OPAubn9H2r0m/pTr7MLPElAzPrcUqnAn4OPBwRZxcGXQtU7hQ4GrimkH5UvttgIrA0X1K4EThA0ma5M+EBOc3MuslnCAY53+Zk/cQ7gCOB+yXNymmnAGcBV0g6DngaOCwPuwE4CJgDvAQcCxARiyWdAdydxzs9Ihb3ThHMBjcHBGbW4yLiT5Rf/wfYv2T8IL1VsWxeU4Gp7ctda/pbkO2nhVq7+JKBtYUfumJmNrA5IDAz60UOnq2/ckBgZmZmDgjMzMzMnQoHLZ+SNDOzVvgMgZlZH3BfAutvHBBYW3knZ2Y2MDkgMDMzMwcEg5F/oZuZWascEJiZ9SFfZrP+wncZWI/Y63t/8KNUzdqk+vHEDiCsJzggMDNrQk8fhP1OAutrvmQwiPjUo9nA5zZsfcVnCHqRpEnAD4EhwAURcVYfZ6lH+ReP9ZTB3pZqBQUOFqwnOSDoJZKGAD8G3gvMA+6WdG1EPNTdeXsnYWuTnmxLZmszBwS9Z29gTkQ8DiDpMuAQoMs7sYESCFTn02cMrJva3pbqGSjtzKy7HBD0nm2BuYXv84B9qkeSNAWYkr+ukPRo/rwF8FyP5rC2ti5b/1Vz0Nh2LcMGtYZtqU47ape+aI91l1nVrtyWrGUOCHqPStJijYSI84Hz15hYmhkRE3oiY4305bLNSjRsS7XaUdsy0Adtwu3QeprvMug984DRhe+jgPl9lBezgcxtyawHOCDoPXcD4yW9SdIbgMOBa/s4T2YDkduSWQ/wJYNeEhGvSfp34EbSrVJTI+LBFmbRY6c/+/myzTppQ1tqh75oE26H1qMUscZlbDMzM1vL+JKBmZmZOSAwMzMzBwT9hqSpkhZKeqCQtrukv0i6X9J1kjYuDDtZ0hxJj0o6sBvLHS3pZkkPS3pQ0udz+ghJMyTNzv83y+mSdG5e9n2S9uhOuc36u1bbSBuWt56kuyT9LS/vGzn9TZLuzMu7PHeoNGsbBwT9xzRgUlXaBcBJEfEvwK+BEwEk7UzqWb1LnuYn+XGuXfEa8OWI2AmYCJyQ538ScFNEjAduyt8B3geMz39TgJ92cblmA0WrbaS7VgL7RcTuwFuBSZImAt8BfpCX9wJwXJuWZwY4IOg3IuI2YHFV8g7AbfnzDODf8udDgMsiYmVEPAHMIT3OtSvLXRAR9+bPy4GHSU+COwS4MI92ITC5sOzpkdwBbCpp664s22wg6EIb6e7yIiJW5K9D818A+wFXtnt5ZhUOCPq3B4AP5s+H0fEwlrJHt27b3YVJGge8DbgT2CoiFkDaIQJb9uSyzQaCJttIO5YzRNIsYCHpx8BjwJKIeC2P4nZnbeeAoH/7BOn05D3ARsArOb2pxyC3QtKGwK+AL0TEsnqjtnvZZgNBC22k2yLi9Yh4K+kpjHsDO5WN1pN5sLWPA4J+LCIeiYgDImJP4FLSrwRo86NbJQ0l7egujoircvKzlUsB+f/Cnli22UDQYhtpm4hYAtxC6ruwqaTKw+Tc7qztHBD0Y5K2zP/XAb4G/CwPuhY4XNIwSW8idfC7q4vLEPBz4OGIOLsw6Frg6Pz5aOCaQvpR+W6DicDSymlTs8GoC22ku8sbKWnT/Hk48B5Sv4WbgUPbvTyzCj+psJ+QdCmwL+kVp88CpwIbAifkUa4CTo68wSR9lXRJ4TXSKczfdnG57wT+CNwPrMrJp5CukV4BjAGeBg6LiMV55/gj0t0NLwHHRsTMrizbbCBotY20YXm7kToNDiH9aLsiIk6XtB1wGTAC+CtwRESs7O7yzCocEJiZmZkvGZiZmZkDAjMzM8MBgZmZmeGAwMzMzHBAYGZmZjggMDNrSNIt1W8VlfQFST+pM82KWsPM+iMHBGZmjV1KesNo0eE53WxQcEBgZtbYlcDBkobB6pccbQPMknSTpHsl3S/pkOoJJe0r6frC9x9JOiZ/3lPSrZLukXSj3xxqfckBgZlZAxHxPOnx4JNy0uHA5cA/gQ9FxB7Au4Hv56d5NpTfj/DfwKH5fSVTgW+2O+9mzVq38ShmZkbHZYNr8v9PkN7++S1J7yI91nhbYCvgmSbmtwOwKzAjxxBDAL8XxPqMAwIzs+ZcDZwtaQ9geETcm0/9jwT2jIhXJT0JrFc13Wt0PhtbGS7gwYh4e89m26w5vmRgZtaEiFhBehXxVDo6E24CLMzBwLuBsSWTPgXsnN9Ougmwf05/FBgp6e2QLiFI2qUny2BWj88QmJk171LSm0crdxxcDFwnaSYwC3ikeoKImCvpCuA+YDbpTYVExCuSDgXOzYHCusA5wIM9XgqzEn7boZmZmfmSgZmZmTkgMDMzMxwQmJmZGQ4IzMzMDAcEZmZmhgMCMzMzwwGBmZmZAf8fKzksXXyB1gAAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"_i = list(range(1,5))\n",
"\n",
"for i in range(2):\n",
" plt.subplot(2,2,_i[2*i])\n",
" plt.title('Posterior distribution of center'\n",
" 'of cluster %d' % i)\n",
" plt.hist(center_trace[:, i], color=colors[i],\n",
" bins=30, histtype='stepfilled')\n",
" plt.subplot(2,2,_i[2*i+1])\n",
" plt.title('Posterior distribution of standard deviation '\n",
" 'of cluster %d' % i)\n",
" plt.hist(std_trace[:,i],color=colors[i],bins=30,\n",
" histtype='stepfilled')\n",
" plt.xlabel('Value')\n",
" plt.ylabel('Density')\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib as mpl\n",
"\n",
"assignment_trace = mcmc.trace('assignment')[:]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Value of data point')"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"cmap = mpl.colors.LinearSegmentedColormap.from_list('BMH',colors)\n",
"\n",
"plt.scatter(data, 1-assignment_trace.mean(axis=0),\n",
" cmap=cmap,\n",
" c=assignment_trace.mean(axis=0), s=50)\n",
"plt.ylim(-.05, 1.05)\n",
"plt.xlim(35, 300)\n",
"plt.title('Probability of data point belonging to cluster 0')\n",
"plt.ylabel('Probability')\n",
"plt.xlabel('Value of data point')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inspection using the clusters"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"c:\\users\\shojiro_shibayama\\miniconda3\\envs\\bayesian\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6521: MatplotlibDeprecationWarning: \n",
"The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
" alternative=\"'density'\", removal=\"3.1\")\n"
]
},
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Visualizing clusters using posterior-mean parameters')"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"norm = stats.norm\n",
"\n",
"x = np.linspace(20, 300, 500)\n",
"posterior_center_means = center_trace.mean(axis=0)\n",
"posterio_std_means = std_trace.mean(axis=0)\n",
"posterior_p_mean = mcmc.trace('p')[:].mean()\n",
"\n",
"plt.hist(data ,bins=20, histtype='step',\n",
" normed=True, color='k', lw=2, label='histogram of data')\n",
"y = posterior_p_mean * norm.pdf(x,\n",
" loc=posterior_center_means[0],\n",
" scale=posterio_std_means[0])\n",
"plt.plot(x, y, lw=3, color=colors[0],\n",
" label='cluster 0 '\n",
" '(using posterior-mean parameters)')\n",
"plt.fill_between(x, y, color=colors[0], alpha=.3)\n",
"\n",
"y = (1 - posterior_p_mean) * norm.pdf(x,\n",
" loc=posterior_center_means[1],\n",
" scale=posterio_std_means[1])\n",
"plt.plot(x, y, lw=3, color=colors[1],\n",
" label='cluster 1 '\n",
" '(using posterior-mean parameters)')\n",
"plt.fill_between(x, y, color=colors[1], alpha=.3)\n",
"plt.legend(loc='upper left')\n",
"plt.title('Visualizing clusters using posterior-mean parameters')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Never mix up parameters with different evolution indexes\n",
"\n",
"What if two stochastic variables x and y have a relationship $x+y=10$? Obviously, x at i-th index and y at j-th index are never samplmed. It's appearantly meaningless."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\r",
" [-----------------100%-----------------] 500 of 500 complete in 0.1 sec"
]
},
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Displaying (extreme) case of dependence between unknowns')"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = pm.Normal('x', 4, 10)\n",
"y = pm.Lambda('y', lambda x=x: 10 - x, trace=True)\n",
"ex_mcmc = pm.MCMC(pm.Model([x, y]))\n",
"ex_mcmc.sample(500)\n",
"\n",
"plt.plot(ex_mcmc.trace('x')[:], color=colors[0])\n",
"plt.plot(ex_mcmc.trace('y')[:], color=colors[1])\n",
"plt.xlabel('Steps')\n",
"plt.ylabel('Value')\n",
"plt.xlim(0,500)\n",
"plt.title('Displaying (extreme) case of dependence between unknowns')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### How do we predict the cluster assigned to a datum?\n",
"\n",
"\n",
"The fast way is to calculate, letting $L_{x_n}$ the cluster for $x_n$ of sample $n$,:\n",
"\n",
"$$\n",
" P(L_{x_n}|x_n) = \\frac{P(x_n|L_{x_n})P(L_{x_n})}{P(x_n)},\n",
"$$\n",
"\n",
"and compare\n",
"\n",
"$$\n",
" P(L_{x_n}|x_n) \\ \\ \\rm{vs.} \\ \\ \\it{P}(L_{x_m}|x_m) .\n",
"$$\n",
"\n",
"Note that the denominators can be ignored."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of belonging to cluster 1: 3e-05\n"
]
}
],
"source": [
"norm_pdf = stats.norm.pdf\n",
"\n",
"center_trace = mcmc.trace('centers')[:]\n",
"std_trace = mcmc.trace('stds')[:]\n",
"p_trace = mcmc.trace('p')[:]\n",
"\n",
"x = 175\n",
"\n",
"v = p_trace * norm_pdf(x,\n",
" loc=center_trace[:, 0],\n",
" scale=std_trace[:, 0]) > \\\n",
" (1 - p_trace) * norm_pdf(x,\n",
" loc=center_trace[:, 1],\n",
" scale=std_trace[:, 1])\n",
"print('Probability of belonging to cluster 1:', v.mean())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Tool to visualize posterior distributions\n",
"\n",
"`pymc.Matplot.plot` shows how distributions converge. 95% credible interval and mean of the posterior distributions are important information to tell if MCMC converges enough."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"from pymc.Matplot import plot as mcplot"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 25000 of 25000 complete in 15.7 secPlotting centers_0\n",
"Plotting centers_1\n"
]
},
{
"data": {
"image/png": 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tc3uS6OhoV8IVGRnpcxzX559/zooVK1iwYAFPPPFEvvGoSlUGQZtYVatWjXfffTdfWUyjNjQc83fX8fj/bKD2BeNcx1eNG8+cAyvYfOAkX3/1lav8nHPO4cILL8z3WPPmzXP9fc011+T7ledL48aNWbp0aaG333HHHdxxxx1e5TVq1PA5pmDEiBGMGDGCg+mZ9Hrya7Lz4LnnngPcTeC3v/0/lv56gN+futh1P88WhkA1MEV5JJLOdarqVI/m2Onif7Cfyspl1fbD7E3L4IVvtrPi/kE+z9t64GS+42On3DPSujy62GcLyYMf/cy7ybt48Vorofh5z3E277dWoI8Q4e9f/MrpM7nsP55J0zrViI4M2iGDAbE3LYMmHkl2WTi/HP1ZLqH1X78gvnltZo2OZ/6PfwTk+W0wyLGP6UfAVmCZo3wpcC1w2kdZmRKrmjVr0qxZMz755BMuv/xysrKyyM3N5cILL+Thhx9m3LhxxMbGsmfPHlcremHi4uJIT7f29Wzfvj2HDh1i9erV9O3bl+zsbLZu3UqnTp287rdjxw569+5N7969+eyzz9i1a5fPxGrkyJFce+213Hvvvezdu5dt27bRq1evEr/mvLw8du3axaBBg7jgggt4++23OXnyJHFxcZw44b17hFLhKGgTK39s2JV/zIBzp5aIMmYcs2fP5uOPP3Ydd+3a1ZX0lJfDJ7PIzs0j0iP2pb9aA0M9f/h2fGQRV3ZrysxruvL6qtSAPHet6u4PdV8/smtUieTUGd8Dx38/fIpxr6xxHWfl5BITVXzrUbciZpNt2nuCi593J6OeY3qcG0g/9cWvnMi0fi0nzlgGhFf3lZNn4nPtyz+wbLLvxLWknNXM3xbKDbvSQnlM2z6gHZAFfArUBA44bjsO1AFqAycKlOUjIhOBiWBNTvHHf/7zH26++WYeeeQRoqOjef/99xk2bBi//vorffv2BawlDN566y0iIwv//2b8+PHccsstVKtWjdWrV/PBBx9w5513cvz4cXJycrj77rt9JlaTJ09m27ZtGGMYMmQI8fHx+W5/9tlnAbjvvvsYPXo0HTt2JCoqin/+859FxlOY3NxcrrvuOo4fP44xhnvuuYfatWtz6aWXMmrUKD799FNeeOEF+vfvX+LHVsHNsy5VdiGdWBXkTER8JVZ70jI4lJ5F1+a1i32cu+66yzW7r7yJx/iwtlO/ZFjHhl7nnPPXL/Idf/S/Pcy8pqvfz/HGn3vRqGZVLnxuhc/bPbsah3VqxOJNB2jbMM61VtHrN/ZitJ+z926al8yMq+NpEBdDRIT/X8Rpp8+QnplD87rVeW1V8Us4OJOqcHfrf9e5/j7iGGu25rcjVK8SxXnNSr/qua8xVsXfp9RPZytjTBZWUoWILMRKoJo6bq4JpDn+FSwr+DhzgbkACQkJfl24tm3b8s0333iVF/YZ88sv7q5Wz4HeV111FVdddZXruGvXrqxY4f3/c8G92j766KMi4zt50t2SPHXqVKZOner3+aNGjWLUqFGANSvQaeXKlV73a9euHT/99FORj61Cm2fdqOzCKrH6x6ItgO8usvOnWx9uS+8d6BpPFAjGmID+kl+86UDxJ5XQwHb1fZa3aRDL9oMn6eLxBT2qRzMuPq8Rj3+2yZVYNYiL8Xl/X1ZuP0yfp75mbK/mPHVlF7/v1/VxqwUr0K1O6/44xs+7j3NNz+YAITUWa+eRU3y10T1D05B/plRZrpUzSfrXsu3sPpbB2xP6eJ2Tk5vHtAUbPe4TmpmViMQZY9Idh+cDL2B19T0DJAE/AGuBWwuUhb17773X7hBUmNC65BY2iZXnF05RXwBJM5cH7Mv7m80H+PO8ZBbdPYD2jeJK9Rjl/V3Vr7X3eAqA+4e35+YBrdl97DRnn1Uj323Vq0Tl6yIqzRfq/B938dSVXTh6qmSre4/+92pXQldae9MyqBIVQb3YGK78l7UooTNBWHLPANo2jMt3btXoSOrWqFKm5yyJU1k55OSafF2wvgz8x7J8x2VZHPb46WwiIiCuajTHM7JJPXIagPeSrYVoZzh+lHg+1+rfjvDfNe4xVf2fqZhtk8pBfxF5AqvVaqUxZo2IrBCRlcAfwHPGmDMFy+wMuLwsWrSIKVOm5Ctr1apVvqEPSpVGXFzpvgPDkV+JlYg0ARYCHYFYoAcwC8gFko0x9zjOC+h05dLyMakvYLo+vphLuzThics78+d5yYA1/sSfxGrj3uOcUy+WalUqptVkw7Rh1Cjkubo2r01khHglVYXpe85ZrP7tSPEnethx6CRDnl3uOn50wUa+/GUfl3dtWuh9ypJU7TueQeNa1ejnaJ30lUC/8M12nveYXefr3F5PLmVc77O5K6ltqWPxtGFXGo1qVaVhTWsm6cB/fMvhk2dKnOAXNs6tMMYYPv95Hxd2akT844uJjBB2/P1iHvzIu0tm7orf8h3nmfJdjLYiGWO+AL4oUPY08HRxZeHmwgsv9JrIo5QKLH9TkKPAENzN4zuBwcaY/kADETnPcwoz8BPWdOWAmLlkK/9evsPv84trYbnrndItcLh00wHSTmfznx925iuP9DH4xBjDqDnf0+3xxaRnZpOemc2I51dyx/z/0XbqF67HKG2D1b+WbS/2nLiYKKJKOVPOeCwdmZWTy2vje5b4MTyTKoB536dy4EQW/y7wJR4oN76+tthzcgrZu3H7wZN8t81aOPZgehazlm4NWFyX/XMVgx0D7MG9LpeTv/tVltS3Ww5y+9v/428LrYVYcx2ZUsHnBziTm/+65OTlBdX2Sap8fPbZZ3z22Wd2h6HCgNYlN7++dY0xmcaYYx7H+40xzl1/c7BarnqRf7qy96CNUnr+62089eVmv8//afdx/rVsO99sPsAr3/3m9QXx6frSbclx/4e+B19GRgj7j2fme57sXEPyzmMcO53N/B//IDPb+uJa89sRsnMNj3+2kVNZOa5ZbiX1zFdbij2n4ODxpfd6rCNVzNN6XrIaMVEV1spWFr8fPkXHR74q8pycQq530szlXP+q7y08ipOXZzhYzCbYRbU2zV3xG60e/IIVWw+RevhUiZ77RGY2TyzclG+7n4MnMun/zDes/8Maf/3G6vw/BPxJ5ts/9BWb9un0+HC3bt061q1bV/yJShVD65JbmcZYiUgXoJ4xZpOIdKMcpiuXlmfi8XsJv6wKk+Pxq95zTNcDH/1EZnYeT191Htf09H5decZjertHWadpi2hRxNYhgdamQSy9W9VljR/dbc447xjcJmBrJ5W3rBzfrVGeFm86wM4jp/jhtyOMTmgekOd94ZvtzFq6lfjmtbm2V3OfdQDgma82c+cQd/fiN5sPMPjchry1xkp8bnjNSuxK0kU4a8lWXl+Vyqsrf3fd77Of9rHraAavFbIch79D5vxJ3lVoc66irlRZaV1yK3ViJSJ1gRcB51Lj5TJdORA8B+CWRWFjTlytUb8fdX2penalea5c7eyOcU5z/+Po6YDEVpCv7knwfyB6UoeGfJCymxFdwm//J+eg8NlLtwXk8VY4uhA37Epjw640RsY3dbXwffnzPtd5/1q2g5oe2/r8eV4yqdNHUEjvpF+yc73v7HzrW9arzi97vFudJIB7TVYPgZZMVTj3tmBKlY3WJbdSDcARkSjgLWCyMcY5H3wt4OxrCsvpyrnFjOb1HLvi2ZV2PCPbvdK144byHr4ytpfv1hjnwP7inn5450Zs/dtFnNuoZmADq0AZxQz23nu86O47fxXMYTt4dEcWXMT1jI9WtYL16rdD/q8H4ytJcibVhXV7/rLnuN+PX5zF9wwI2GMppVQ48CuxEpFoEVkKxAOLgKlAT+BpEVkmIn2NMQcB53TlrsAn5RV0IHyzueTrReUWkw2t2HqIbQfSHY9/0FU+d4V7nFd5baJcUMO4qj7LnxkVz7jeLejdqm6xj1ElKrS3iHn6K//H5TkVNmB73/EMjheyxc/pIhI4U0wKe+GsFfnGRwGMfdn/3yQFJ1KAu1Vy8/50r9t+2XOc9KzALK46vFMjmtWpuK5sFXhbtmxhyxbt8lVlp3XJzd/B69nGmCRjTB1jzBBjzGPGmPrGmETHv9WO8542xlxgjLnWGFOyBYwqmHOphJIorsUKYPzrazlwIpN9BVpDnHctrynsQ85tAMDgcxswc3Q8tyS29nle09rVePKK80o9WzCUzPs+tcT38ZWM5OUZ+j71DRc87b2CNsDGvd7dbY99tpGUnUdZm3osX/nK7YfzHW85kO61J+OBE1l+7cnnKwnMzs0jObXwMXSXvOC9KnZpzbwmvviTVFB75513eOedd+wOQ4UBrUtuYbNAaGmUdNV0fxKrPWkZPPjRzyzbcjBfeXm3WD06shNfbz7IpfGNuaJbs3J5jsrgotneG2Z/kGItopmelUN2bp5fmz2/virV516O/q7T9eBHPxd7zopth73K2k790q/HD4TqVSr1x0dYaNeund0hqDChdcmtUn8yph45Tat6NTDG8M3mgwxq36BE+9sVJjM716tlynlcXj2BzetW57e/XxyQ+JUlPTObuKrR7D2e4Sp7adkO7hjSln3HM9i8L51BjpZCO/zptdItD6GU09ixY+0OQYUJrUtu4d8fVIRBjkUbP/7fHm56I5nrXl1T6LmdilkfydP3O7xXKK+IsVUVlVT1ONtrJY2wdN6jiwF4zmP24JFTZ/j8p330feobbpy3NqgW0Xxv7S67Q1BKqUqvUrdYAew6eto1Hur7HUdYue0wfVuf5bVcQUm3Eymo4F5soejzOy/g9JlcGteqygVPh+y+cSVy+kz+gd7GGG57270IXqsHvyh4F9s8/01glo9QSilVepW6xQqsjWU3eQw+vu7VNaUa9Fycj/63p0Tnn9sojsT29QMeR1l0alKLni3r0qxOdbo0q2V3OBWi4yOL8h0XXMU8mKQVMmtRqcI89thjPPbYY3aHocKA1iW3oE+sDqYHZq2honzusYgjwBMLN/k1UL08bd6fTm2PxSSDTdWosi0M+ftTF9O6vn8bQPvSv229Mj1/OKrIOtuuYWyFPZdSSoWSoE+sTmWVrQuutP6zOpWDJzJp99CXrPnNe8xUZedckb1NA/cX7COXdPT7/iJCYvv8A7/f+HMvv+8fpYP0vVTUGmkAzXX9qrAwbdo0pk2bZncYKgxoXXIL+sSqVb3iWzX6nnNWwJ/30c820evvX3MmJ4+/flz81PdAW3zPgBItBVHRbuh7Nr8+Pty1sfOkxNb8+YJWJXqMBy46N9/G0APbFd31OXHAObwwthtgLYJ5k8fzVYvWrVX82SuxLDo3raktVUopVYygT6yK07FxzWJXty6rHYcCs4lzSTSq5Xvl9GAhIq798FKnj2DK8HNL/BjRkRH5WryKc09SO9dq8BERwsOXdOSuIW0Z26uF3xsLh7Lv7h9U7s9Rt0aVQm8ThMdGdgagYZDXT6WUsktIJFb/uanwLqL5E/q41oZ6e0LvfOWhLDoiwmsXuOhI7+zhim5N2TBtWMUEVQJjevreq7AsRNz730U6Mql7hrbjqSvPq9BuMLs0r1v+3W9FXccIgT7n1GXWNfE8PML/bl8VvObPn8/8+fPtDkOFAa1LbiGRWF3Qxnug8rmN4piU2Jpa1aNd7VWeG9L2bR347sGK5LncwzOjurD03gE+u0WrRkdSKwgHuU+/qkup7nduozgAn68pMkKoVsWqsu0c5zk5V0OfOOCcUj2vsuQVMQD+ovMaIyJc0a2Zq7UylIjIvY69TBGRWSLynYjM9rjdqyzcbd26la1bt9odhgoDWpfcQiKx8jXWaGTXJu7uJ8d3gTMXGXFe4wqKrPSa1q5W5O2eg7MjRWjTIC5f4ugUzGO437u5L09e0bnY81Y9MJgv7uwPuAewR0dG8PhlnfIt6xApwqD2DXjpuh7cObhN/gdx1IHbEguUY40H86V53aLfAzs9e3U8DeJivMofGtEhoM/TqGb+Lr3C8qqfHx3GzSGctIpIDNYm8ohId6CGMaY/UEVEevoqszHcCjNmzBjGjBljdxgqDGhdcgvZBUIbxLm/EEZ2bcKPqUc5+6wapE4fYWNU/nv35j5FLrIZESG0bWi1yjjHW/kaRxRTxmUPylOvVnXZ/bpTAAAgAElEQVTp1aouT32xmZNZOYWe17R2NVeiWSPGqpKD2tfnhr4tuaFvS1o+8DlgvX4RYXjnRl6PkePICCJ9dJde07M5bzrWn1oxeRAD/mFd9/qxMew6muF1vt0uPq8RV/VoRr82Z7Fxzwl2HDrpaq38v/7n8LfPfw3Yc314az8+Xb+HZ76yFrCdOqIDOw6eZHjnRox6abXrvLiqwdcqWkL/B7wBPA70BZY6ypcCfYA8H2VrKzjGCte+fXu7Qwg5zs+jQAiV7yt/aF1yC4kWK4BbE1sD8MEtfXlhbDeu6t7Uddu43i3Y9uRFQT/g21OzOtXZ+NiF+coKtrTdPOAc3r+lL+f76AoFuLpHM+4Z2rbcYiyNSYmtiYnKX62+vm9gvuOiPkxiY6JYOWUQT15xntdtRc2SdCYevpZh6NTE3epVtYo7tppB2IUK8MLY7gA0rlWNpI4NuXlga4Z18k4mA6Fp7Wqu8WoT+rdibK8WPHRJRxJa1i2X57ODiEQDA40x3ziKagPOVYGPA3UKKSv4OBNFJFlEkg8dOlTOUSulQlXIJFb3Dz+X1OkjSGhZl0vjm+T7khUR1xibivbJbeeX+r7O1hmAH6cO4Z/juvPhpH7cN9TaJTwiQuhZxBfc367oHHQtCVOGn8uWv12Ur6yhR3dT56Y1i32MZnWqu2b/AcT7scr7mzf14vXxPakaHcnc63tQp3r+61I12no8ZxLR55y6Fbqg5r1D/dv5vX/bel7bKRU07VL/B47PHtPVZ/lDIzowob+1XIXzf6UwHv9/PfC2x3Ea4KyINR3HvsryMcbMNcYkGGMS6tcPrl0RSislJYWUlBS7w1BhQOuSW8gkVsGqa/PaXl90I+ObFHkfX4PQ61S3prn3OLsOdwwpuhVqxtXx3DmkbVB3AxZm4R39S3yft/6vN4vvGVDkOfViYxh0rrXg6LBOjVj38FD+fsV5/PSoNWMyKsKRWEUI3z8wmNfH93IlEo+N7MRbN/VmbK8WJY7NX3cOacv7t/TlTo/31nO81L/GWa1U/VoXv6L8jee3okPjwhPUmlXdCXvr+r6Xs7imZ3OmOmb29TjbSt7PD9/V7NsDk0TkK6ATUA8Y4rgtCfgBWO2jLOwtXLiQhQsX2h2GCgNal9z8GmMlIk2AhUBHIBZo4HlsjMlxnDcLSADWGWPuKpeIy2DT4xdSvUoUTyzcxKsrfw/Y4954fitSD59y7SN3RfemLNiwt9DzP761n1dZZAkWYurYuCajejQreaA2evyyTuw4eLJU942rGl3iljkR4dre7kTJ2QpkDDRxjOdytli1aRDL+W3qcTIrh/k//sGsa+K5590NpYq1KD1b1qVny7rUqR7N+W3q0a5hHP9d8we/Hz7FuY3i+P6BwV6DyQtjCjQvDT63Ad9sPgjAoHMb8Ol6q/5l5fjeuSDCo771OLsOm58YTtUwXWTVGDPF+beIrDTGPCYis0XkO2CDMeZHx22ZBcvCXffu3e0OQYUJrUtu/g5eP4r1a+7jQo7zzbQRkTki0tMYE1SDP6tXcQ6MblDqxKpNg1i2OxKEGVfHu8ofu6wz7ybvIjM7j/hmtXni8s48/MkvPh8jNsb7skeUYHpfeS+IWh5u6NvS1uc/q0YVjmdk57tyzjWbnEnGhZ0asuGRYdSqHu1XYlW7enSpNj6+8Xz3ivHO5C4yQlwJnz+K6rbzbBEtLFkq2N0YrklVQcaYCxz/9frhF4w/BsvbpZdeancIKkxoXXLzqyvQGJNpjDlW2LGDr5k2tnptfAILbrfGQHlOub+gDF0engsoFmw1ci5eGRUpXN/n7HzbtXiK8hgP9tGt/fyexu58al/LLqiivfHnXky7tGO+lcWd4/KcSYaIUKu675axcR6tXzFREXxz30Au6eJ7WY8mtapyYaeGfsXlTKwiSrh0fIuz8i8W6tmCdfsg95ITJVnZXimlVNkFcoxV0M2qGXxuQ7o0q83Wv13Eo5d2CshjFrWAonPKv3vfOu9zZ46Oz3fcvUUdHrzYv7WJsvOsveB8rcCuita8bvV8LUVgtTjeMrA1CWd7VVWv1f7rx8W4EqmR8U04p34sfxnmPb347LOq8/SoLvz7+gS+urv48WQJLa3n9tWKWZSZo+N55YYE6sfF0LBmDLWruxNGz8S9sC7m4gbIe7o7KbhmnqrASU9PJz093e4wVBjQuuQWyHWs/JpVA8wFSEhIqLD+rCpRgcsf/zmuO5PeWscfR0973XZt7xa8veYPV0uIMwerEhXBGccGuUM7+teS4Yu7RUznHARCo1pVeeAi33sc9m+bf9aXMfDitd0ZnXDINVOzdvUq1IuN4fDJLNd5yye79/M7t1HxMyCfvqoLkxJbU6eIPfp8iasaTVLHhgzpYA3YP5GZw8f/2+N1nufs2buT2nJdn7PZl5ZZolm0dyf5N6NRhZ6ZM2cCMG3aNJsjUaFO65JbIL+hw2ZWTWEtDanTR9CpSS2+uKs/a/46xOv2v13Wma0eSw04e2daenTbOGenlUbX5rWB/LO+VMWIc1zzAe3q59vOpXV97xmeJVE1OtKvBKwwImJ1YRayJpdnw9TdSe2oFxvDeX4sXwFwWdcmrjqnwlNsbCyxsdpdrMpO65Kbv7MCo4EvsbaEWCQifwWe9Dw2xqwJl1k1xX3RxcZEFToAvYrHN5lzPJbnmKiSdMEU9MyoLkwccA5nxXpvdaLKz6OXdmRcH9/b4px9VnXW/H60giPyX1GLqhZn9phuAYwk8ETkXWAx8F9jTKbd8YSi++67z+4QVJjQuuTmV2JljMnGaoXyVPC4Us6qKYprsLnHd5uvlcH9VTU6ks5N/WttUGV326DWnMrKZXyBsVnB6vUbe7Jlv+8xDkmOLsNwYoy5RkSGAW+LyHZgtjHGuz9UKaUqkPYpFaJebBUOnzxTpsdo2zCWYR0bcueQtrzy3W98sn5viZZVUPaafKHv8Ve+3DWkLaN7Ni/HaIo3qH0DBrX3TqDW/HUItQuZ7RjKRKQHcCnwG9a6es8CugusjQK5j55SoarSjoJe/eDgfMc/Ts0/ZurjW8/n/uHtqe4YT1OaLrzoyAjm3pBA56a1eG5Mt7DacFNZnK2STWpXdW0k7enCTg1tby1qWLNqSK7S74dE4GFjzF+MMSuAJ2yOJ+TMnTuXuXPn2h2GCgNal9wqbYtV41rVaFWvBr8fPgVAg7j8K143r1udWxPbsGjjATbsSuPVPyXYEaYKEYWtLfbv67XelKNMY0wagIjcYox5ye6AQs2+ffvsDkGFCa1LbpU2sQL82oTXuW5V3RJOh1eVQ4xjc+coXVvMDp4r64bGQLggM2HCBLtDUGFC65JbpU6s8grsC/L2hN6s25l/Qfma1axLFKZdKaqM7h9+LjWrRnNpMRtvq3JhRGQa1kq8mtmWQpMmWm9VYGhdcqvciZWjNerK7k0B6Ne6Hv1a59/u5rlrurHwp720a6jrcyhvNatGc/9w/we5V5RX/5TA9zuO2B1GuTLG/EVEOlp/ml/tjkcppaCSJ1a5jhar+4uY/VU/LsZrKxSlgt2QDg0Z0qH0q/yHAhGZBFwARIiIMcZca3dMoWbZsmUAJCYm2hqHCn1al9wq7axAgD87EqZwnIquVCXQyBgzzhgzVpOq0lm+fDnLly+3OwwVBrQuuVXqFqubB7bm5oGt7Q5DKVU6TUTkCuAUgDFmsc3xhJyBAwfaHYIKE1qX3Cp1YqWUCmkrgTisTd8rbFP3cKLdNipQtC65VequQKVUSNsG1DXGvAGk2R2MUkqBjS1WKSkph0VkZwnuUg84XF7xlCONu2Jp3BWrpHH73s26dMYDex1/DwAW+DpJRDoDc4FcYDvwZ2AmkACsc+5xKiKzCpaFu717rcunU+VVWWldcrMtsTLG1C/J+SKSbIwJuWWsNe6KpXFXLJvjPgXkiYgAdYs4b4sxph+AiLwO9AJqGGP6i8gcEemJlXTlKzPGrC33V2Czl19+GYBp06bZHIkKdVqX3HSMlVIqVC0E7gA+Bv5Z2EnGmGyPwywgCVjqOF4K9AHyfJTlS6xEZCIwEaBFixZljz4ING7c2O4QVJjQuuSmiZVSKlTtAqY4/i5y8LqIjAT+DmwF9gEnHDcdBzphtVjtKFCWjzFmLlaXIgkJCWExWH7ixIl2h6DChNYlt1BKrEJ122yNu2Jp3BXLzrjHYiVUNYDuwNDCTjTGLAAWiMgLQA7WTEIc/03DSqwKlimlVImFzKxAx6/FkKNxVyyNu2LZGbcx5jFjzOPGmCnAl4WdJyIxHocnsJKxIY7jJOAHYLWPMqWUKrFQarFSSikXEZmPuwvwQBGnDheRex1/b8MaJzVLRL4DNhhjfnQ8XmbBsnD37LPPAnDffffZHIkKdVqX3EIisQr2adAi0hJYA/wKnDHGDBORycBlwE5gvDEm21eZTfE2wRr42xGINcbk+LrG/pbZFTfQjALX3XFeUF17EekNzMLqbko2xtzjb4xBGPdx4H+OU640xhwVkXHAbcBR4FpjzAlfZYGOzxgz1s/zPgU+LVDsVXeD8bOlvJ08edLuEFSY0LrkFvRdgSLSHcc0aKCKY2p0MFpijEl0JFX1gUHGmAuAn4DLfZXZGOtRrG6PH8D3Nfa3zM64HVzX3fFagvHa7wQGO65bAxHp70+MQRj3ecDPjuud6EiqooFbsNaR+g9ws6+y8ghORBaIyJeOfwtE5O3yeJ5wdu+993LvvfcWf6JSxdC65Bb0iRXQF+9p0MFokIh8JyL3YK2Ts8xR7ozZV5ktjDGZxphjHkW+rrG/ZRXGR9yQ/7pDEF57Y8x+Y0ym4zAH6OIjnlCIOxfo4Lje0x3rR7XDSrZyPGL0VVYefgIucfzboBsxl1xcXBxxcXF2h6HCgNYlt1BIrGqTf2p0HRtjKcw+rC+TQVgDXxPwjjmYX4ev2Pwts1O+6y4iXQjiuB3x1cOacRYy19sZtzFmE9AWqyWqDnBpITFWVNxtgYaOf7qbulIqKITCGKs0gnwatDEmC2vhQURkIdaXSlPHzc6Y03yUBQtf19jX9POgmpLu47p3xvd1tv3ai0hd4EVgNNDDzxiDLW6MMUcd5Z8A3bDGLhWsExX1/+zDgLPv4bFyeo6w9tlnnwFw6aWX2hyJCnVal9xCocUq6KdBi4hn++f5WPuRDXQcO2Ne66MsWPi6xv6W2cbHdd+B7+ts67UXkSjgLWCyMWZ/CWIMqrhFpIaIRDpudl7vrUBnR7kzRl9l5eEsYLcx5i9A+3J6jrC2bt061q1bZ3cYKgxoXXIL+hYrY8y6EJgG3V9EnsBqPVlpjFkjIitEZCXwB/CcMeZMwTK7gnUMLv4SiAcWAX8FvK6xr+tu53vhI+4VjhW1XdfdcV6wXfurgZ7A09awJB50xF5kjEEa9z9F5BTwGzDNGJMrIi8D3wHHsGYAZhcsK6f4bsSPTZhV4S655BK7Q1BhQuuSmxhjz84M9erVMy1btrTluZVS9khJSTlc0g3YC+NY+uMY8ATwqjHmz4F4XH8kJCSY5OTkinq6kNHygc/tDqFEdj5tJQNnT1loy/OnTh9hy/Oq0hGRFH82nbetxaply5boB5NSlYuI7Azgw/m1CbNSSlWkYsdYichrInJQRH4p5HYRkedFZLuI/ORY60gppcpbE2PM5Y5/S+wOJhRt2bKFLVu22B2GCgNal9z8Gbw+DxhexO0XYU17bou1VcScsoellFLF6uZYuLadiLSzO5hQ9M477/DOO+/YHYYKA1qX3IrtCjTGrHBs2VKYy4A3jTVY6wcRqS0ijY0x+wIUo1JK5SMiF2OtkXUf1pZGBnjc1qBCULt2mo+qwNC65BaIMVZNgV0ex7sdZZpYKaXKyyXGmFtFZI4xRtewKqWxY/3ablGpYmldcgtEYiU+ynxONRSRiVjdhcTExATgqZVSlVQLERkGNHf8F2PMYptjUkqpgCRWu4HmHsfNcK8tk48xZi4wFyAuLs6edR6UUuHgfaCxx3/180QpFRQCkVgtAG4XkXeA3sBxHV+llCpPxpg37I4hHDz2mNWLOm3aNJsjUaFO65JbsYmViMwHEoF6IrIbmAZEAxhjXgK+AC7G2sblNNZqyEoppZQqQqAXVNUFR4ODP7MCixyR5pgNeFvAIlJKqQASkd7ALKxNxJONMfeIyGSsGc07gfGObXi8ymwLuoJo64IKFK1LbqGwCbNSSpXFTmCwMaY/0EBE+gODjDEXAD8Bl4tI/YJl9oWrlAplmlgppcKaMWa/MSbTcZgDdAGWOY6XAn2AXj7KlFKqxDSxUkpVCiLSBagHpAEnHMXHgTpAbR9lBe8/UUSSRST50KFDFRBx+Zs/fz7z58+3OwwVBrQuudm2CbNSSlUUEakLvAiMBnpgLWIMUBMr0UrzUZaP53IxCQkJYbG8w9atW+0OQYUJrUtumlgppcKaiEQBbwGTjTH7RWQtcCvwDJAE/AD4Kgt7Y8aMsTsEFSa0LrmFZVdgWloa7733XkAfc9++fQwdOpR+/frx5ptvBvSxlVLl6mqgJ/C0iCwDWgMrRGQl0BX4xBhzsGCZXcFWpPbt29O+fXu7w1BhQOuSW6VPrIwxWCtGFG369OlMmTKFFStWMGfOHDIyMsoappe8vLwij5VSJWeMmW+MqW+MSXT8W22MedoYc4Ex5lpjzBnHeV5lSilVUkGbWGVkZDB27FgGDhxIUlISAMnJyQwaNIj+/fszY8YMAB599FHGjRvHRRddxIABAzh9+jRz5sxh+fLlJCYmsmXLFr766iv69+9Pv379XIPrxo8fz6RJk0hKSiI5OZm+ffuSmJjIxIkTfcazdu1aBg8eTFRUFAkJCWzcuDHf7f/4xz8YPHgwPXr0YMmSJQBs376dIUOGMHDgQCZPngzAjBkz6Nu3L/369SMlJQWA7t27c/vtt/OnP/2JefPmcc011zBixAiWLl0a+AurlFIOKSkprs8hpcpC65Jb0I6xmjt3Lr169eKee+5xtdxMmTKFjz76iDp16nDFFVdw/fXXA1YT5COPPMLUqVNZunQpkyZNYseOHXzwwQfk5eVx4403smzZMqKiohg0aBCjR48GICEhgTlz5vDqq68ybtw4br/99kJbiXJycoiIsPLQWrVqcfTo0Xy333bbbUyePJnDhw9z9dVXM3ToUCZPnsyMGTPo1q0beXl57N+/nwULFrBq1SpSU1OZOHEiS5cu5dixY9x99920adOGefPmUaVKFT7/PLAr8iqlVEELFy4EoEePHjZHokKd1iW3oE2sNm/ezE033QTgSmh+/vlnrrjiCgCOHTvGrl27AOjWrRsAzZs359ixY/ke5/Dhw2zbto1hw4a5jp1TpXv27AnA6NGjefLJJ7nhhhtISkrihhtu8IonOjqa3NxcIiMjSUtLo27duvlu/+9//8ubb75JREQE+/fvB2D37t2u2CIiIkhNTSU+Pp6IiAjOOeccjh8/DkCdOnVo06aN67GccSmlVHnq3r273SGoMKF1yc32xCoxMRGAZcuW5Svv0KEDq1atIiEhgby8PCIiIoiPj+eDDz6gVq1a5ObmEhERwcKFCxER1/2MMa4kCKBevXp06NCBJUuWEB0dTXZ2NtHR0YA7YYuKimL69OkAdOzYkeuuu851m1NCQgLffvstiYmJpKSkuLoinWbMmMHGjRs5duwYF1xwAWAlehs2bCA+Pp68vDxatmzJ+vXrycvLIzU1ldq1a+eLw6ngsVJKlYdLL73U7hBUmNC65GZ7YlWYCRMmMH78eD788EOqVavGokWLmD59OldeeSV5eXlUqVKFTz7xPXGncePGZGRkMGrUKJ555hmmTp1KUlISERER1K9f32tg+4IFC3jxxRfJyspi+PDhPhObBx54gOuvv55HHnmESZMmUbVq1Xy3O8d+9e7dm5o1awLwzDPPMGHCBIwx9O7dm6effprLLruM888/HxHhhRdeCNDVUkoppVQwEH9mxJWHuLg4k56eXmiLlVIq/IhIijEmwe44yiohIcEkJyfbHUaZpaenAxAXFxeQx2v5QGiNDd359CUAnD1loc2RBEbq9BG2PXeg61Iw8vfzK2hbrOw0e/ZsPv74Y9dx165dee6552yMSCmlAm/mzJkATJs2zeZIVKjTuuQWNIlVMLVc3XXXXdx11112h6GUUuUqNjbW7hBUmNC65BY0iZUnZ5LlVFiy5es8f++rlFKV3X333Wd3CCpMaF1yC8rEypeyJEyBag3TpE0ppZRSRQmZxCpQ/G3lKkurmVJKKaUqp0qXWFWEkiZvJUnugmksmlIqtM2dOxeg0K28lPKX1iU3TaxCVHFJWVkeR5M2pSqHffv22R2CChNal9w0sQpTgejeLGuXqCZqSgW3CRMm2B2CChNal9z8SqxEZDgwG4gEXjHGTC9w+3jgH8AeR9GLxphXAhinCiJ2jSvTRE2pwGrSpIndIagACuQCrSVdbFTrkluxiZWIRAL/BIYCu4G1IrLAGLOpwKnvGmNuL4cYVYjzdyyZv2PNCj5mScuUUkqp8uJPi1UvYLsx5jcAEXkHuAwomFgpVeFKk2DpRAGlLJc/ZA04Xp/T1OZIVKhzfk76+iFc2fiTWDUFdnkc7wZ6+zjvKhEZAGwF7jHG7Cp4gohMBCYCxMTElDxapWxSlmU6ypKg+ZskavJXOBFpAiwEOgKxxpgcEZkFJADrjDF3Oc7zKgt33aKtAceaWKmyWr58OaCJFfiXWImPsoI7N38GzDfGZInILcAbwGCvOxkzF5gL1ibMJYxVqZBWmlYzX/cvzWNXckeBIcDHACLSHahhjOkvInNEpCeQW7DMGLPWxpgrxP+yG9sdggoTAwcOtDuEoOFPYrUbaO5x3AzY63mCMeaIx+HLwNNlD00pFShFJVtlTcqCvdXMGJMJZIq4fiP2BZY6/l4K9AHyfJSFfWKlLVUqULSlys2fxGot0FZEWmHN+hsDXOt5gog0NsY4F7EYCfwa0CiVUgHn7wehv92bpZmEYJPawA7H38eBTlgtVgXL8vEcytCiRYvyj1IpFZKKTawc4xFuBxZhLbfwmjFmo4g8DiQbYxYAd4rISCAHq9l9fDnGrJRSZZEG1HT8XdNxnOujLB/PoQwJCQlhMZThLDkFwBFTw+ZIVKjbu9fqyNJlF/xcx8oY8wXwRYGyRzz+fhB4MLChKaVUuVgN3Ay8ByQB87B+FBYsC3sjq1qdC69nJNgciQo2JV0T68ZqyYDvulTSNbFCXYTdASilVHkSkWgRWQrEY7W8R2ONufoOyDPG/GiMWVewzMaQK8zhvOoczqtudxgqDGhdctMtbZRSYc0Yk43VCuVpjY/zKsUSC54+y+podwgqTGhdctMWK6WUUkqpANHESimllFIqQDSxUkqpSuqaqhu4puoGu8NQYUDrkpuOsVJKqUqqumTbHYIKE1qX3DSxUkqpSuqdjC52h6DChNYlN02slFKqksqgit0hqDChdclNx1gppZRSSgWIJlZKKVVJ9YtOpV90qt1hqDCgdclNuwKVUqqSah91GIDvs1vaG4gKeUXVpZJuj1OUUNgeRxMrpZSqpFadOdvuEFSY0LrkpomVUkpVUltz69sdggoTWpfcdIyVUkoppVSAaIuVUkqFkECOV2kekQbArrzaAXtMVTlpXXLTFiullKqkkmK2kxSz3e4wVBjQuuSmLVZKKVVJ/ZFby+4QVJjQuuSmiZVSSlVSX59pa3cIKkxUVF0KZFc4lM/yDdoVqJRSSikVIJpYKaWUg4jMEpHvRGS23bEopUKTX12BIjIcmA1EAq8YY6YXuD0GeBPoARwBrjHGpAY2VKWUKj8i0h2oYYzpLyJzRKSnMWZtIB470N0XgXJjtWQAXs9IsDkSFeq0LrkV22IlIpHAP4GLgI7AWBHpWOC0m4Bjxpg2wCzg6UAHqpRS5awvsNTx91Kgj42xKKVClD8tVr2A7caY3wBE5B3gMmCTxzmXAY86/v4AeFFExBhjAhirUkqVp9rADsffx4FOnjeKyERgouPwpIhsKcVz1AMOlzrCAHu08JuCKs4iBCTOnU9fEoBQihT21/PRwMZRnIBdTylZM5Bf+/ZIcbmPiIwChhtj/s9xfD3Q2xhzu8c5vzjO2e043uE4p9AXXrXB2eayJ95h/Yb1+cq7xnctt7LyfOxQj0tjCO64giGGQMS1dc6tKcaYoOwrEJHbgEPGmPdE5EqgmTHm+QA/R3Kwvn5PGmdgaZyBFexx+pNYXQ1cWCCx6mWMucPjnI2OczwTq17GmCMFHsv1iy+2ceseF0/7TyBfi1IqyL13S79gTqy6AzcbY24WkX8B84wxPwb4OYL6C8FJ4wwsjTOwgj1Of7oCdwPNPY6bAXsLOWe3iEQBtYCjBR/IGDMXmAuQkJBg3r25b2liVkqFqPdusTuCwhlj1olIpoh8B2wIdFKllKoc/Ems1gJtRaQVsAcYA1xb4JwFwJ+A1cAo4BsdX6WUCjXGmLvK+SnmlvPjB4rGGVgaZ2AFdZzFdgUCiMjFwHNYyy28Zox5UkQeB5KNMQtEpCrwH6AbVkvVGOdg98IkJCSY5OTkMr8ApVToEJGg7QpUSqlA8GsdK2PMF8AXBcoe8fg7E7g6sKEppZRSSoUWXXldKaUCTESaiIhzzFaUoyzfqu4i0lJEDojIMhFZHAxx+orbV+zBGGeQXs/eIvK949rN8jhvsoisFJH/ikh0EMd53HE9l4lI3SCIs7NHnK+LiDjOC6odE2zbhDklJaW068AEo1BZo8Qf4fJawuV1QHi9lvZ2B1BBjgJDgI/B96ruwCFgiTHmumCJ08dxua5IH8g4HYLteu4EBhtjMh1J1HnAfmCQMeYCEZkCXA68H2xxGmN+Bn42xiRWcGyeCsa5xRjTD0BEXgcSRCQX++tnPrYlVlgXKCzGWgT71M+SCJfXEi6vA8LvtdgdQ0VwDI/IdGjcXeUAACAASURBVPygBt+run8GDHLMQvzIGDPL64EqOE4fcYPv2Cv0i8vPOCH4rud+j5tzgFysRbeXOcqWYk0Gq9DEys84ATo4rucq4MGKnpTmI85sj5uzgF3AVdhcPwvSrkCllCp/tYETjr+PA3WAfUA7YBCQJCJdbIqtOL5iD0ZBez0dsdQzxmwiiK9ngTgB2gIDsGK81LbAPIjISLEWJW+AtTdx0F1PTayUUqr8pQE1HX/XBNKMMVnGmFPGmBxgIdDZtuiK5hW7jbEUKlivp2Ns0otYe+pCkF5PH3FijDnqaKX6hCC5nsaYBcaYzljLP11CEF5POxOroF6HooT0tQSfcHkdoK8lHKzGGisCkAT8ICJxHrefj3ufwmDjFbuNsRQqGK+nY2D9W8Bkj+62tcBAx99BcT19xSkiNUQk0nFKsFzPGI/DE0AGQVg/bUusHKuwhwV9LcEnXF4H6GsJRSISLSJLgXhgERCNNVbkOyDPsap7fxFJEZHvgb3GmDV2x+mYHZbv2BizzkfsQRcnQXg9galAT+Bpx8y6vsaYg8AKEVkJdMVqDQq6OLG6Adc63vfmwAdBEOcDIrJcRJYDDYHFwVA/C/JrgVCllFJKKVU8W1qsRGS4iGwRke0i8oAdMZSGiDQXkW9F5FcR2SgidznK64rIEhHZ5viv7YPn/CUikSLyPxFZ6DhuJSJrHK/lXRGpYneM/hCR2iLygYhsdrw/fUPxfRGRexx16xcRmS8iVUPlPRGR10TkoGNgqbPM53sglucdnwE/iTWlXymlQl6FJ1aOPtt/AhcBHYGxItKxouMopRzgPmNMB6wpnbc5Yn8A+NoY0xb42nEcKu4CfvU4fhqY5Xgtx/AYyBjkZgNfGWPOxWo2/pUQe19EpClwJ5DgGJwZibU3Z6i8J/OA4QXKCnsPLsLqamgLTATmVFCMSilVruxoseoFbDfG/GaMOQO8A1xmQxwlZozZ5+jPxRiTjvXl3RQr/jccp72BteBb0BORZsAI4BXHsQCDcfelh8RrEZGaWFOCXwUwxpwxxqQRmu9LFFDNMZi0OtYU8pB4T4wxK7AW9PNU2HtwGfCmsfwA1BaRxhUTqVJKlR87EqumWIt6Oe12lIUUEWmJten0GqChMWYfWMkX1voaoeA54H4gz3F8FtY08BzHcai8N+dgrWL9uqNb8xURqUGIvS/GmD3ADOAPrITqOJBCaL4nToW9B2HxOaCUUgXZkVh5LZULhNQIehGJBT4E7jbGnCju/GAkIpcAB40xKZ7FPk4NhfcmCugOzDHGdANOEeTdfr44xh9dBrQCmgA1sLrMCgqF96Q4oVrXlFKqSHYkVruxpm46NQP22hBHqYi1YeaHwH+NMR85ig84uzEc/z1oV3wlcD4wUkRSsbpjB2O1YNUW9+arofLe7AZ2e0yv/gAr0Qq19yUJ+N0Yc8ixdcNHQD9C8z1xKuw9COnPAaWUKowdidVaoK1jplMVrMG5C2yIo8QcY5BeBX41xsz0uGkB8CfH338CPq3o2ErKGPOgMaaZMaYl1nvwjTFmHPAtMMpxWqi8lv3ALhFxbvA7BNhE6L0vfwB9RKS6o645X0fIvSceCnsPFgA3OGYH9gGOO7sMlVIqlNmyjpWIXHzWWWd93rJlywp/bqWUfVJSUo4aY85yJI4vYs0iPA3caIypFBs0K6XCm20LhCYkJJjkZP0cVaoyEZEUY0yC3XEopVR50U2YFQBZObk89MnPHD11xu5QlFJKqZCliZUCYOGGfbz1wx889cWvxZ+slFJKKZ80sQpzxhhmLt7C74dPFXlebp7VJfx+yu6KCEupCiUiN4jI144NZpuKyCwR+U5EZnuc41WmlFIlpYlVmNt7PJPnv9nOja8XveG30SWEVJhybBU00BgzxBiTCDQEahhj+gNVRKSnY6/CfGU2hqyUCmFRxZ+iQplzckJ2rnfi9P32w1z7yhrG9mrB9zsOV3RoSlWUC4FIEfkaa/mKzcBSx21Lsfb9zPNRtraC41RKhQFtsaok9qRl8NYPO/l593FX2XvJ1o4i83/8g51HTtsVmlLlrSFQxRgzBGtph9qAc8eE40CdQsryEZGJIpLs+Dex/MNWSoUibbEKQzsOnSQ2JoqGNatiLRdkeeiTXwCYenEHru3dggjxtasIHM/Ipla16AqJtbTOffhLOjSuyce3nm93KCr4HQeWO/7+BkgAajqOawJpQK6PsnyMMXOBuQD16tUzCQkJ/y7HmFUISUmxdgbr0aOHzZGo8pSSknLYGFO/uPM0sQpDQ561vkNSp4/wefuTX/zK0dNnfO/WBmScyfWZWE18M5kruzdleOfGAYu1tDKz8/jfH17ffUr58j0wwfF3V6w9CYcA72FtIzQPyAFuLlBWqJYtW6Lr8Ckn5w9YrRPhTUR2+nNeWHUF5uTmuWa3haJD6VnklTH+JZsO+HVehFBoi9V/1+zkYHomANsOpLuu6eJNB7jlrXVlik+pimaMWQ9kiMgyoCcwA8gUke+APGPMj8aYdQXL7Is4NKWnp5Oenv7/7d13eFRV+sDx75tGKEF6B1HpIAkQelcElSaiCOK6uC7oriI2Flk7ij9AwLorBtuuIuhaEUURNQiKSBERlKaChN57STm/P+6dzGQyk0ySydyZ5P08Dw8z59658849k5l3zj3F6TCUQ7T+3UpUYtXo/oX0e/prp8MolF1HTtN+8mKe/2prkY4z+r85fzFt3H3M535Vy5chyk+L1XNfbmXgc8vYe+wMlz31NY/M31CkmFRuGZlZRU6iVeCMMfcaY3oZY64xxpwzxowzxnQ3xtzusU+uMhW4mTNnMnPmzPx3VCWS1r9biUqsALbuO+F0CIWy+6jVQvTVpn0FfuyZ9Ew+XLsT7+WJjpw6x+JffLdgxcdG8+2vB/0ec++xszz7xZY8Yzp2Jp29x87kGdvq7YdoeN/H7D56Os/9CqvhfR+zcY/v5DGcNbp/IX+fo61/quSoUKECFSpUcDoM5RCtf7eI6mNljGHAc8uYNLgV1SuU4YcdhxmcVDffx/286xhvrNjO44NbEeWvmSZMeC/duPzXg1xQrTy1zov3+5jHFvzMnBV/ULNizn3+/Mr3tKx7ns/H/PP9n/KNZc6KP7JvnzibkWv7JdNTOXDinN++XABvfGcdY/mvB7m6bT2f+xw5dY49x87QrFZFn9vz8+n6PYV+rJM+3bAnoP0yswxZxhAbHR6/g9Izs8gyhjIx0U6HosLIPffc43QIykFa/27h8UkdoK827WPDrmMMfeFbBjy3lHHz1gb0uFGvfs+bK/5g3/GzxRxh4fnp7sSI2d/le3nT1dq12Kt/1fpdx4j2d+ACMAbGzf0hV/mBE9a6gg3v+5idR05zJj2Tl5f9XuBLXDf/ZxWXP7200P3jxKsX/ntr0rj6398U6ljh6MpnltL4/oVOh5Gt9/RUmj7wqdNhKKVUWIqoFqsdh9yXk46dyd2C4q3/s0tpVee87DnFg5BjFBvvlipPR0+n+yz/ZfcxVm47lJ1WvLTs9xzbM7MMr38X0CCGfG3ck3enxJ/SjvDDjiO8uOQ3qpaP46o2+bckuqzefhiwLmmWL1Pwt6R3vd799o8FPkY427Q3vDqEph22/g73HjuTq5VUqZKu4X0fF2qbL3m19qvIFVEtVt59iPyVffvzdt5++2027DrGW6t2ZCctRcmr3nvvPZo1a0ZycrLP7a+99hrnzp0rwjMU3H3v/cRDH27gbEZWsT7PziM5+0et+eNwrkuDmVlwzE4AD5w4S5MHFvJZgJe6XLLyyi5tfxw8xY5DJWcy04/X7c5z++rth0IUScF1fOILp0NQYSQlJYWUlBSnw1AO0fp3i5jEauzcH/jkp9xf1L4uHw177gvefvttjxL/mZUxxmdy5q1nz56sW7fO73Z/iVVWVmBJT2Fa037cYc3jtGxr8S9H43mOrv73t/R/dmmO7Zke23ccOsW5jCxueX11dmvburSjTFm4kbdW/oE/gZyqHk9+RfdpX+UoE6yEa8Ouo74fVADGGOas2O63lTDYZi35Nc/tQ19YHpI4CuvFfOJXpcfu3bvZvTvvHwqq5NL6dwvbS4GnT5/mL3/5C7t27SI2NpatyXdxdvcWDqe+AlmZlG3UifM6Xk21njfA0T10qBPHnp/TqDHsUY7/8Amfb/qKs99vomq/2zmy6yB7vppD/68qcveddzBixAhGjRpF2bJl2bx5M1OmTOGOO+6gTJkyNGnSxGfWXbVqVb+xLl++nLVr13LFFVdwzTXXcPjwYX7//Xf27dvHtGnTmDp1KmlpaWRkZPDmm2/SoEEDPvnkEx577DHi4uK45ZZb2F21LYc+n8Wig3/QcW5lbpwwldsGdsx+juEpy2lYtTx/6nw+VcuXybMze3HYdTTn6D/vJXDeWL6di2qUB8gx2/uXG60Rha99uy27rF/LWizdcoCxc39g/aP9ssvPZRa+5a3Hk1ayVdSm9R/TjnL/++t56vPNrHrgsiIdK1BZWYZZX//KyA7nc1658J7x3tv/LdzILT0vcjoMFQZGjx6d/06qxNL6dwvbFquUlBQ6dOjAkiVLWLRoEQBHlrxK9SH3U2vkNM7u/JnMk1bfHCrVYfrL8yhTvyVntv1IQpsrqdu8HbWun0JMlTrsSZ1DzeGT+WjRF8yaNYvMzEwAkpOT+eKLL1i3bh0jR44kNTWVWbNmBRzjnqNn+Hjdbjp37kxSUhILFy5k3LhxADRo0ICFCxdy8cUXk5KSQmpqKv/4xz948cUXycrKYuLEiXz++ecsWbKE4cOHM/fdD4mKr0CN4U/wR6MhTHzksRydwL/77RDzVu6g/7PL6DzlC/4Is7X9vt92KOD1BrMM/Muer8vzdVw6I9XvY46cOsexM75bkYLZd+5MuvXecHXML24Gw7KtB5j26SYe/HB9SJ6zoM5mZPLnV77n513HSC9C8qtKtjp16lCnTh2nw1AO0fp3C9sWq40bN3LzzTcDEBVl5X/n9m9n/3uPA5B15gQZx6xLYHE1L0QQYhKqkXXGmscqw05Ksk4d48zBnex960Gu/m4mRw8dZP/+/QC0b98egGHDhjF58mRuvPFG+vTpw4033hhQjCNmf8fvB05yWYsrcm1zHTszM5MJEyaw5ocfOHf2HK1atWT//v3Ur18/e86PqKgoju/ZxqnNyzmzw/pyjUmolqtvk4sxkLq54PNdFbe85sXy1Paxz7NvZxlDlFjJlueAhDPpmWzdd4I3v/+DSYNakjTpc78JlL8ruTsOnaJmxXh2HD6VvXbie2vSqFAmhr4taxXoWMXFGLKTleNeiaP3faes33mMJZv3c/R0OrW0s7pSSuUpbBOr5s2b880335CcnMwPdgfeuOoXUH3IRKLKlMdkZYJEcfrX7wHx+NI1EBVNVpbV8hBVriLx1etT9drHadumPk8MbkHF8taXgythi4mJYcqUKQC0aNGCG264IXtbXnbao6OyjCE2Nja7Jczz2GvXrmXv3r3s7DaR6ofWYc5tonr16qSlpXHy5EnKlSvHnO+2E1W5LuWadaNS1xHWq8jM8JtYQc7LbeGmINMmbDt4El+7N3vQPZx/wMXW2oT+kh5/s9V3n/YVNRLKZE+zsW1K/+wRg56XDI+eSifLGCqXjws47mDZsOsYS7dYPxA8X96RU+dImvS5z8ccPHGWWUt+ZcLlzYgJwdxWrkEFJ85mBDz3lip9UlNTAejVq5ejcShnaP27he2lwNGjR/Ptt9/So0cPuvTqA0ClXqPY//5k9sydyL7/PYLJcF+u8ZxxPbpCFbLSz7L//SfIOLqPGj1GsPetB3hp4ig6XjY413PNnz+f7t2706FDBy6//HKfSVVqaip9+vRh8+bN9OnTh7179+boEzRo0CCGDRvGyy+/nONxzZo149Pvf2HvvAfYtMbqiBwVFcXkyZO55JJLSO7cnbv+71+cqpVE1unj7Jk7kT1zJ3Ji/Zf8lOa/M3b4plXu1sJA3P5mzvmxTp7NyDVkedKCn/M8hueoyO0HT+bY5m/usqwsw9mMTH7bf4LESYto85jvJKYwMrMMGQW4ZObqf3bsdDqf/7yXhvd9zIxFm/3u/8hHPzN76e8s/iW4rZYN7/vY58SxGZlWfUbqqgYqNJYsWcKSJUucDkM5ROvfLWxbrMqWLctbb70FuOcGKVOrETWHP5Fjv0rdRmbfTmhzZfbtrH7/pLqrvHZ9atVJBKBr85qANYrP5brrruO6664D4NutBzh88lyu1ouePXuyJaoBb7apQ42EeJZ7XPb67reDjB07lrFjx+Z6HeXLl6fK8CnZ91+zW0pqtuxMq789z+A2dbnDnnyzSp8xOR47+ZNffJ0aILzn5NpUhCVmfE36mt8cWp56Ppnqd9uyLe7Rk2NeX8XiX/ZxTTv3bPD/W7WDqhV8t1pNWbiRMjFR3HVZk3xj6DNzCb8fOJmjVezIqXPEx0YTH+t/tvI1fxzJXusxr/nHXEmbr+kp5v+4i/Jx0Vxqv88L6s0Vf/DEkIvZcegUe46doX3DKhG9sLkKnZ49ezodgnKQ1r9bQImViHQEngIygVXGmLtEZDwwGNgOjDLGpPsqK6a4c8lrqRrPqQL2n/A/+/qZ9Eyuf2kFGT8uoNHpX8gyhkMnz3Fp1w7cMuExJn/yC5M/+YU7LmnEs1+6Lz+NenUlz41ow8DEwDvu3fbmGvYeO8sXGwvX6hDqvkAFseaPI4V+rL+1DYPhhpdXeDyPdd7fWZ2WXTb+Hf/TabimRQgksfr9wMlcZUmTPqdV3YosGNs94HgLw5WkBzo6MivLkOm1XI5ni+Gmxy/njSBNMqtKNr0EVLpp/bsFeilwO3CJMaY7UENEugO9jTHdgHXAVSJS3busWCL2I6+lW9Iz3VmIa+4nX1yXsGISB/D47HfoO/4FTvR5gKtve4AMj0mWPJMql7Fzf2Bd2hHG/HdVQJeBipoY/VGCJsksLdbvPFak1p/V2w9z+OQ5Fq4PXj+n+z9YT+P7FzL3e9/zizV94FPtVxUGXnvtNXbt2lVsxz948CC9e/emQoUK3H777X73a9iwIQcO5J43b/78+dn9VH1Zu3Ytn3zySVBiVSrcBdRiZYzx/GTNAFoDqfb9xcD1wCkfZf8LRpCBuO3NNX63nU7PzHH/yKlzvLM6jZu6XkC0n5auzXuPs/uYNXfTsdPpVAhgqZVBz1vr033+81427T3OnX2a+J18tKjrFv62X/u7FLdlWw7QrXE1v9v3HD3D8JTlvH5zR+pXKRfQMS/6Z+G/XIa+8G2O+4VNzn8/cJIbXlrBe3/vkp1QTXwv/0W5lXNee+01WrVqVaDh7BkZGcTEBNbbIz4+nscee4z169ezfn3Bp/0YNGgQycnJ7Nq1y2eMa9euZdWqVVx55ZU+Hl38CrrUjCo4V+KvUy4UsPO6iLQGqgFHAFdHmqNAZaCSjzLvx48RkVUisso15UF+vJdOCYakSZ/z+Me/8OHanTnKvfusuJKi9TuPFmiG6b/NWcPTi7fw6frdBV7WJVDB7riscvO8dOjLu2vS2HbwlN/WHpfb80j6Q2nnkdPsOXqG15dvZ+eR03zww878H6SKZOvWrfTp04fExETatm3Lr79anyNPPvkk7du3p3Xr1jz88MMAbNu2jebNmzN69GhatmxJ3759OX36NO+88w6rVq1i5MiRJCUlcfr0aVavXk3Pnj1p164d/fr1y57xulevXvzzn/+kZ8+ePPPMM/zvf/+jVatWJCYm0qNHD79xli9fnm7duhEfn/90Gs899xxt27bl4osvZuPGjYCV+F111VXMnj0713OeO3eOhx56iLfeeoukpKTsvrOqZJk9ezazZ892OoywEHDndRGpAjwPDAPaAa5VditiJVpHfJTlYIxJAVIAkpOTA/q9nXa4+C55nTqXsyXLc0LOw6fOse+Y1ar04te/0apuxQIf/9Y3fH+hXveiM8uUjOrSkMrl4nhqsf8RZyow+4+fZZc9HUaUCFv2Hqd6QhkqlXN3fp/66Ub+3usiFuSzHmCwbN3n7uT/6fo9XN4q51xdXad8CcDo7hcAcPBkaNe2LI1GjhzJfffdx5AhQzhz5gxZWVksWrSILVu28P3332OMYdCgQXz99dc0aNCALVu2MHfuXGbPns2wYcN49913ueGGG3j++eeZPn06ycnJpKenM3bsWD788EOqV6/OW2+9xf33388rr7wCwJEjR7JHZ1188cV89tln1K1blyNHCt/30VO1atVYs2YN//73v5k+fTovvfQSYCVntWvXZtKkSTmeMy4ujkmTJrFq1Sqef/75oMSgwk/t2rWdDiFsBNp5PQZ4AxhvjNkjIiuBvwPTgD7Ad4CvsiKrXbFsMA7jk2e3rOW/HmTqpxuz7z/35Vbane9udMvIDE5v8V92H2PF784srFs9oQx9mtfMN7GaeEUz/m/hxjz3Ka0G/+ubXP30TqdnctlTX1O3Ulm+ue+S7PIXUn/lhdTiW0vvtjfXULdyVw4cP0tcTBQ3vvJ99rZb31jNdxMv9bn0UZT9xk/5+rcix1ApApbgEZGGwArgF+CcMaZvKAbfHD9+nJ07dzJkyBCA7NagRYsWsWjRItq0aQPAiRMn2LJlCw0aNOCCCy4gKSkJgHbt2rFt27Zcx920aRPr16/nssusJZcyMzNzfKm5RjgDdO3alVGjRjFs2DCuvvrqorycbK7jtGvXjvfeey+7vGXLlowZM4Y1a9YE/TlV+BszZkz+O5USgbZYXQu0B6baE1NOBL4WkWXAH8DTxphzIpKjLBgBxscV31RbG3cf5/iZdH5KO8r1L+W+7LN6++Hs28Eacn7FM0vz36kYjLu0MWN6XBjQXESNalQIQUSRydfgh5eX/Q6Q54SuxeXT9Xv8LuTc6f++oH6VskwbmsiI2e7fOcGcXDaMZ/3w9rkx5gYAz4E2IjIBa/BNqncZRewj6q9/pTGGiRMncsstt+Qo37ZtG2XKlMm+Hx0dzenTud9TxhhatmzJ8uW+W77Lly+ffXvWrFmsWLGCjz/+mKSkJNauXZvnuqeBcMUYHR1NRkburhq+nlOp0iSgrMUYM9cYU90Y08v+t9wYM9UY080Yc70x5py9X66yoooJYAb0wnr9u+1c/Mgin0mVty0RPjniyI4NiI2OomHV8jnKXZeFALrbHbXDeY6sUDt+Jp1zGYFP9unvy7S45DHLCAA7Dp3OkVQBBGuy9r/1uoi5YzoF52DFr7eILBWRu4AO5Bxo08lPWZFUrFiRevXq8cEHHwBw9uxZTp06Rb9+/XjllVc4ccL6TNm5cyf79uXdZzIhIYHjx61LvU2bNmX//v3ZiVV6ejobNmzw+bhff/2Vjh07MmnSJKpVq8aOHTuK+rLy5es5PeNXqqQL25nXXfL74lD+zR3dKXttN9dUEmXjonn95g4APHVdIhOvaJ69f8Wy1mWduGj/k1iWNhc/sogmDywMeP9Qzy/mb1RrXlwtbEU14fJmNKtV8L6HDtgNNAF6Y3VTSCZEg29ef/11nn32WVq3bk2XLl3Ys2cPffv25frrr6dz585cfPHFXHPNNfkmHaNGjeLWW28lKSmJzMxM3nnnHSZMmEBiYiJJSUl8++23Ph83fvx4Lr74Ylq1akWPHj1ITEz0+xwNGzbk7rvv5rXXXqNevXr8/HPeKx54++GHH5gxY4bP5+zduzc///yzdl4vwWbMmMGMGTOcDiMshO3M6y7hvCZeuJpxbSIL1++h80VViYm2zp9nH7HujavnmECyQ8MqfL/tEJOvakWL2hXpclHOSwVL/9Gb7tO+Ck3wES7U87YW5u/jTHrgLXAlgTHmLHAWQEQWYCVQIRl807hxY7788stc5ePGjWPcuHG5yj2nOrj33nuzbw8dOpShQ4dm309KSuLrr7/O9XjXem0unn2g8uOrP1de+yQnJ2c/36hRo9i+fTsnTpzw+ZxVqlRh5cqVAceiIo+rBVZFQGKlCm5ou3oMtZdqGd+vKePmraV6Qhm/+//35g6cPpdJpXJx3Na7Ua7tgc7RpGBjEZbzKYxnv9gS0ueLRCKSYIxxNQl1BZ7Dmmev2AfflCZ333230yEoB2n9u4X9pUCAv/e6KFfZ0Lb1fOxZ8jx5TeuAJif1Z3BSXbZN6U/ZOP+X9+Jjo3OtjTjtmtYBP8ctPS7kourl898xSMb3axqy5yqo/s8uczoElVt3EVktIt8Cu4wxK3APvkkCPjDG7PMuczDeYvPZZ5+RlJSU459r1GJRJSQkkJCQEJRjqcij9e8WEYlVl4tyz35dt1L+E9mVBPGx0ZxXNvAh7a/e1D4ozzssuX6e22/o1CD79sQrmxeqr09hXeE1P5NSeTHGfGKMaWeM6WKM+YddFpLBN+GmX79+rF27Nse/999/3+mwlCpRIiKxMj56rpSmvlcFmeqhd9MaxRiJ20MDWua4H+VVH4OT8l7WYEyPC4Mek1LKOR999BEfffSR02Eoh2j9u0VEYuU9RQCUrikBMkM91CwAsdFC/9a1eenGZMAaeu8pv2ky7u1b+Mt5QZpSTCkVRGvWrGHNmvBYvkmFnta/W0QkVvWrlOPBAS1ylFX16hMUiGa1IvP6b34tVlXKx/HqqPY8MzwpqM/77Ig23HdFM5/bRIR/Xd+WPi1qAu6+XC4DE/Ne3iAuxvdb77uJl+YbV6jninLaqC4NnQ5BqXwNGDCAAQMGOB2GcojWv1vEjAqMj835RXx9x/OJi4liwrs/+dz/meFJjP/fOs5luoeWX1S9Ahv3RNYkdRdUK0/F+BgO+VnXzTOZCbZBiYVfpbxX0xpMvzaRe//3Y65t/VpaydiyCb0pHxdD2bhomj34KYDPJVi8ZZSyJqtQ9l/Lzwsj2/K3OfqrVOXWrl07p0NQDtL6d4uIFivIPfFidJRwXfsG9GxS3ef+g5PqlojLha3qnsfrN3dkh2qd+AAAIABJREFU0uCWubb9MulyByLKW73K7rUdr2lXjzUPXpZrn7YNKtv7lqNy+TjiY6P5+I5ufHBb1wI9R7Bb6FT+Lmkemj58SikVqSIosfLdSvGfv3Qg2V4s2bvDdK7EKsISrVh7cs/6VcpxY+eGubZ7t+IVpw9u68pbASxf8tHt3fj0zu7Z933VW7fGuUd5tqxzHkn1K+V7/FZ1K5IQH8u2Kf0ZnFQ33/196d3UdzIerlynsHvjamyZfEXInve65PrM+WvHHGXFucSUimybNm1i06ZNToehHKL17xYxn5J9W+Y/xH5kx/Nz3J83pnPOvjwRdgWpfuW8J+YM5cjIpPqV6Hhh/ou3Vi4fl+cyJ9um9KdlnfPyPU6f5jXYNqV/rkudBZnTq7OfeCuVi2Pz41dkr40YKp6teQWRZWdWvZrWIDZYC/0FoG7lsnRt5D5H5eKidYkp5de8efOYN2+e02Eoh2j9u0VMYlWzYjydLqwCwPt/75JjW4s61hd55XI553tKql+Jx3xcQguGC6sVz4SY3Ty+yCIsD8zXV/f2Cmi/nx7pyws3uK/XX3mxO6n27m9UuVwsD/Rvzu//d2Wu4zS1ByuIwIt/asegxDrccUkjHh7YgriYKGbdENo+Ade2q88/r2zGXX2acH7Vcj478FfxMSjDlVhFhzip8U6i3v9711I1zYkqmCZNmtCkSROnw1AO0fp3i5jO6wBPXpNI6ub9uS4Z3d+/OYMS69C4Zj6j/oL4nWCwFjFesmk/1RPKMHtpcBa2HdquLpMGt+SSGUuCcjynlbdbmG7v3YgLAkxGE+JzJsj/HtmO5b8eZMTs76hcLmfi8cNDff0eZ1BSHV77dhtRIvRrWYt+Xq2e5Yswo31BvfindvRtUTM7MRnXpzGb9x6n71M513tzJVEPDWhBzYrxvPn99uyyqBA3F/2l2wU57jf1GFUbG+osT4W9ESNGOB2CcpDWv1vEtFiB1dfoT53Oz/WruUxMNMkNq/h8jBRjx6ohberx9PA23N+/BZsfD07flyFt6pWoVoH42Gi2TL6Ce/oW7ZdMpwurcP+VzZk85GK/+zw7og0zrk3Mvt+4RgUAqlUo+NQcwdakZkKuem1QpRzVKpShy0VVedJeQqhJTXcrW//WtZnz107Z83Z5T8IaDHktDVUuznfiOePaRD69s0fQY1FKqZIgohKroirOdCUuJorVD/ShVV3//Yv8KednHb+SMl9TbHRUkZNFEWF0jwvzXN5nUGId+reuTUJ8DDOuTSQhPpbx/Zoyb0znIj13MMT4aG2Kj41m1QN9eHN0J65Nrs9Pj/TNnmvNc+8sO7MqjsTK8zJroIa2q8dF1SsEPRallCoJIupSYCA+v6sHZWL8LzhcFJMGt+ShDzf43V61QhkWjO3Oe2vSuPvt3PM3+fPzpMtpeN/H+e7XuEYFtuw7EfBxS6P42Gh+eqRf9v3bejcq9LEa1ajA1gKc73Jx0Zw6l+lzW8X4/Nd7TIiP5Xx7lYE6ldwd3ds2qMy8lTtoWiv4yUx6ZslI3pXzHn30UQAefvhhhyOJHIF87hdEcc5rmB+tf7cSl1jl6mfl8SPfusyyu1DHffWm9gGPSBucVJclm/fz4dpdhXoufz4a242z6VmMfn0V3/9+KKjHVrllBTAR6Ws3tWfUqysB6733444jOba/MiqZ/cfPcl65wBbSvqlLQ5rXSqCLxyCGa5Pr0aVRVerZo0Tvv7I5kz/5BYBbe15EizoVqVUxnmEvLg/oOTwFMlKxV4RNT6GUUk4qcYmVPz2aVOe23o2Y+fnmHOW9m1bnq03783xsu/MrZy9u/OyINtwx94c894+OEv55ZfNCJ1auXND78ll8bDTxsdG8cXPHHDPKq6KrW6ksO4+czlEWyBqN7ew51ADifYzyu6RZzQLFERUlOZIqsN4H9Tym3hjd48LsxMq15FBmluGadvV4Z3VaQM/TuEYFWtU9jxa13Zeur25bl/fW7My172s3dSjQa1Clk7ZUlG5a/26lpo9V9QplfC4NMnVoa5/lL/85Ofv25CGtsm+3sqd2yK//U82K8ax/tJ/f7T8+7H80m4u/54iLiSrQfE4qf6nje+Uqc43G815gGqz1+0Z0qJ9jBGNdu/XnwQEtWPPgZax9KPes88HkOTIvOkqY7tFxPz/9W9fmqeuSiIoSbulxIW0bVGLq0Na8Obpj/g9WSinlV6n/dq5RMZ7oKMm10PGlzWvS5aKqfPvrQcp7jI4qSCfsCmViqFI+zuc6f3l1wlah8+19l3D0dLrPiTez7EbBRj46aj8yKPf8aK5Lh5XLxfqcjyqYnrymNW0aVM5/Rz88R8tOvLJ59u0uF4V20lSllCppSnyLVV5pkKslqmys1dm9znnxfHFPTxbf3ROAf13flqevS6J+lbxnQM/LdxMvzV5C5YWRbfPcNyHeSuBK0GwLYa9OpbI0r+17JKerxSqQ+qhfpSyufuChWDT52uT6NKpR+M7sMToPlQqyuXPnMnfuXKfDUA7R+ncrdS1WN3VtyKvfbAPcS+BUrRDH0dPpPHd92xzDyCuXj+OqNoVbj84lLibK7yjFx65qRRP7y3Hu6E40rJYzgQvH8VozhyUWKdEMZxOvaEa5MjE8+MF6APq2qMl/lm/Pvux6QbXy/H7gZK7HrXukL3HRUdxjjwQNRWJVUAllYjh+NiP7/p+7NPS77zPDk0pki6qI3A1cbYzpJiJPAcnAGmPMOHt7rjIVuM2bN+e/kyqxtP7dSk1iZew05eGBLdmw61iOUXX/6NeUsXN/yNGR1x/XZJM3dDo/nz3z9yePY3S+KP91+MLB1XlMKBnpbulp9aVyJVYPDmjBbZc0Yutea8qFmhXL+EysXFMpuC4nR4dRk2OHC6rw/e+HuK59fRau35PdQT+vPnqFXdw6nIlIGSDRvt0WKG+M6S4iL4hIeyDTu8wYs9LJmCPN8OHDnQ5BOUjr363EJ1a++kS9fnMHTnvMN3R5q9psmVw7oOMlxMcWeK6QUV0b8umGPTlGkOWlOGeLV4GLiY6iRkI8W+zEyjVBZ7NavpdOynRo6Zm8vDWmE3uPnaV6QhlqnRfP4x//4nRITvkr8B9gEtAZWGyXLwY6AVk+yjSxKoCmTZs6HYJykNa/W4lPrFrao/hc0yWAtQROcU0i6kunC6s6OnGbKhrPvlbf3ncJFf1cJssKwxYrEaHWefFOh+EoEYkFehpj/iUik4BKwK/25qNAS6wWK+8y7+OMAcYANGjQoLjDVkpFqBKfWDWvXZGfJ/Xzu+5ZqL06qj27j54JaN8SsqJNxHPVgyA5ZkT35mqxCsc+VgBdG5XaEX9/At70uH8EcF33r2jfz/RRloMxJgVIAUhOTta/Ti+rV68GoF27dg5Hopyg9e8WHtlGMQuXpAqgd7Ma+e4TRg0eCqhRsQwAreudl+d+Q9rUJXXTfpr6uVTotOa1K/LkNa1pXa+S06GEWlMgSURuxWqJqga0Bt4G+gCvARnALV5lqgAWLFgA6BdraaX17xY+GYfK5hoKX7mY50JSgWlWqyILxnbz27fKZXBSXcc7fn92Zw/+OHSK0f9d5XP7tcn1QxyR84wxE1y3RWSZMeZREXlGRJYCPxpjvre3nfEuU4Fr2zbv6WRUyab176aJVRiqfV5ZJg9pxWXNC7Yciio+rerm3VoVLprWSqBprQQub1mLTzfscTqcsGOM6Wb/n2s6BZ1ioWgGDhzodAjKQVr/bppYhSnXHFtKFcaT17Zm0lW5Z4dXSilVvDSxUqoESoiPzbGOoVLF7fjx4wAkJIRnH0NVvLT+3Ur8kjZKKaWK38yZM5k5c6bTYSiHaP27aYuVUkqpIqtQofBrV6rIp/XvFlBiJSJ1gAVAC8B19t4AagIrjTH/sPcbDwwGtgOjjDHpQY9YKaUAEXkLWATMMcYENjmcKjb33HOP0yEoB2n9uwV6KfAQcCnwnX1/CNaQ5N5AWRFJFJHqQG971M064KqgR6tUiFRPKON0CCofxpjrgB3AmyIyTURK3iKHSqmIE1CLlf1r8IzHunsXYiVPAGux1t7aAaTaZYuB64H/eR5Hl4RQkeCHBy8jLka7H4Y7EWkHDAR+w2pRnwHoSrBKKUcVto/VJqAn8DHQG9gAHAeO2duPArlWHNYlIVQk0IlZI0Yv4EFjzBEAETnobDilW0pKCgBjxoxxOBLlBK1/t8L+LP8I6xLgF8BZYC++199SSqnicsYjqbrVGLPB6YBKs927d7N7926nw1AO0fp3K1SLlTEmExgLICIpWB1IzwF/B6ZhrbX1nd8DAKtXrz4gItsL8LTVgAOFiddhGndoadyhVdC4gznz7YUety8I4nFVIYwePdrpEJSDtP7dAh0VGAssBBKBz0RkEvAokAX81xiTZu/3tYgsA/4Ans7rmMaY6gUJVERWGWOSC/KYcKBxh5bGHVoOx21E5GHAALp0ucPq1KnjdAjKQVr/boF2Xk/HaoXy1MvHflOBqUUPSyml8maMuVdEWlg3zS9Ox6OUUqAThCqlIpSI/A3oBkSJiDHGXO90TKVZamoqAL169QrK8Rre93FQjqNCI9j1H8kiKbFKcTqAQtK4Q0vjDi0n465ljBnp4PMrD0uWLAH0i7W00vp3i5jEyp6qIeJo3KGlcYeWw3HXEZEhwEk7lkUOxlLq9ezZ0+kQlIO0/t0iJrFSSikvy4AErOlddF48h2lLRemm9e8WEdNLi8hTIrJURJ5xOhZfRKShiOwVkVQRWWSXjReRZSIyxx5V6bPMoXjriMgaETkjIjF2Wa5zHGiZU3H7Ou/2fmF17kWko4h8a5+3pwoSYxjGfdQ+36kiUsUuG2nvt0BEKvorKwZbgCrGmP+g8+YppcJE2CdWItIWKG+M6Q7EiUh7p2Py43NjTC9jTF9f6yaG2VqKOdZ+9HWOAy1zMm5b9nm3X0s4nvvtwCX2eashIt0DiTEM474Y+Mk+372MMYfsZO9WoAfwOnCLr7Jiim8UUMm+3cPfTiLSyiNBfFUsYfWjoSTYtWsXu3btcjoM5RCtf7ewT6yw1iFcbN9eDHRyMJa89LY/lO8COpBz3cROfsocYYw5Y4w57FHk6xwHWhYyPuKGnOcdwvDcG2P22OttAmQArX3EEwlxZwLN7fM9RUQEaIKVbGV4xOirrDicBLLsOKrksd8mY0wXO0EE67yG24+GiDd79mxmz57tdBjKIVr/bpGQWFUinzUIw8BurC+T3ljzfSWTO+Zwfh2+Ygu0zEk5zruItCaM47bjq4Z12SpizrcrbmPMz0BjrNahylgLIDsZ9wKgLfA+MNffTvY8fC5nsf5GC/yjQUTGiMgqEVm1f//+okdfwtSuXZvatWs7HYZyiNa/WyR0Xg/7NQiNMWexPrARkQVYXyp17c2umI/4KAsXvs5xZoBljvFx3lvh+zw7fu7t/kjPA8OAdgHGGG5xY4w5ZJd/ALQBPiT3eyJUf7M7gAn27Tw7r4vIIOAJYDNWQu6Z+LXEem//6lWWgy4inzddfLd00/p3i4QWq+VY/WoggDUInSAiCR53uwJbAdfYU1fMK32UhQtf5zjQMsf4OO+/4vs8O3ru7QECbwDjjTF7ChBjWMUtIuVFJNre7Drfm4FWdrkrRl9lxWEEcB3wF+Bfee1ojJlvjGkF7MS6rOlUMqiUKuHCPrEyxqwBzojIUiDLGPO90zH50F1EVovIt8AuY8wKwLVuYhLwgTFmn3eZU8GKSKyILMZe+xGIxesc+zrvTteFj7jv9j7vvs5zGJz7a4H2wFQRSQUuCiTGMIy7NbDSrv/6wDv2ZbbZwFLgz8CLvsqKIzhjzKPGmEnGmAlYa5n6JCJlPO4ew2rdCusfDUqpyCXGONOiXa1aNdOwYUNHnlsp5YzVq1cfKOgC7P6IyFzclwD3GmPu8rPfYOBu++4WYAzwFFb/rB+NMbfb+z3jXeZPcnKyWbVqVdFfRAkyY8YMAO65556gHC+SlrTZPnUAAOdPWOBoHNum9HfsuYNd/+FIRFYHsui8Y32sGjZsiH4wKVW6iMj2YB3LGDMiwP0+xOoL5mmcj/1ylanAnThxwukQlIO0/t3yTaxE5BVgALDP7qPgvV2AZ4ArgVPAKPuSkVJKFRsRmY91GRsgHTihCzE75+67785/J1Viaf27BdLH6jXg8jy2X4E1BLsxVhP7C0UPSyml8rUO60ffAKzLd5pUOSghIYGEhIT8d1Qlkta/W76JlTHma6wZr/0ZDPzXWL4DKomITmahlCpujYGa9r+LHI5FKaWA4PSxqos1n4xLml22OwjHVkopfx7E3Sn9UScDUfDRRx8BMHDgQIcjUU7Q+ncLxnQL4qPM51BDz5mL169fH4SnVkqVYlWBNGPMvUBTp4Mp7dasWcOaNdq9trTS+ncLRotVGtacNi71AJ8rMXrOXJyQkKAzFyuliuIm3J81PYD5DsZS6g0YMMDpEJSDtP7dgpFYzQduF5F5QEfgqDFGLwMqpYpboIswqxBo166d0yEoB2n9uwUy3cJcoBdQTUTSgIexhzgbY2YBn2BNtbAVa7qFm4orWKWU8rAAGIu1CHOeS9ooVRoEc1JVJycbjXT5Jlb5TcJnrKnbbwtaREopFZg6xpirnA5CWTZt2gRA06ba3a000vp3C/u1ApVSyo82ItJeRJqISBOngynt5s2bx7x585wOQzlE69/NsSVtlFKqsETkSuAocA/wC9ZI5EmOBlXKNWmiuW1ppvXvpomVUioSDTDG/F1EXjDG6BxWYWDEiICWblQllNa/m14KVEpFogYi0heoLyJ97dtKKeU4bbFSSkWi/wG1Pf7XefGUUmGhRLZYHTlyhLfffjuox3zvvfdo1qwZycnJQT2uUqrgjDH/8fr3X6djKu0effRRHn1Ur8qWVlr/bqU+sTLGYM0YkbeePXuybt26ooaWp6ysrDzvK6WUUiq8he2lwNOnT/OXv/yFXbt2ERsby+LFi1m1ahXjx48nIyODwYMHc++99/LII4+wZcsWDh06xMmTJ/n000954YUXWLJkCb169eLFF1/k999/Z/LkyWRmZjJ27FhGjBjBqFGjKFu2LJs3b2bKlCnccccdlClThiZNmpCSkpIrnqpVq+YZ75NPPsnChQs5evQoU6ZM4bLLLmPr1q3ccsstZGRk0KFDB5588kmmT5/Ou+++i4jw3HPP0a5dO9q2bUuXLl04evQol156KQsXLuTEiROMGzeOvn2164hSRSEiHYGngExglTHmLhEZDwwGtgOjjDHpvsocCzoCPfzww06HoByk9e8Wti1WKSkpdOjQgSVLlrBo0SIAJkyYwHvvvcfSpUv55ptv2Lt3L2BNSLZw4UK6d+/O4sWL+dvf/kbPnj1JTU2lcePGTJo0iS+++IJly5Yxa9YsMjMzAUhOTuaLL75g3bp1jBw5ktTUVGbNmlWoeG+77Ta+/PJLPvvsM5544gkAxo8fz/Tp01myZAlTp05lz549zJ8/n2+++YY33niDCRMmAHD48GHuvPNOXn/9dQDi4uL4+OOPNalSKji2A5cYY7oDNUSkO9DbGNMNWAdcJSLVvcucC1cpFcnCNrHauHEj3bt3ByAqygrzp59+YsiQIfTq1YvffvuNHTt2ANCmTRsA6tevz+HDh3Mc58CBA2zZsoW+fftyySWXcODAAfbv3w9A+/btARg2bBhpaWnceOONvPHGG4WKd86cOXTv3p2hQ4eya5e1LmxaWlp2bFFRUWzbto3ExESioqK48MILOXr0KACVK1emUaNG2cdyxaWUKjpjzB5jzBn7bgbQGki17y8GOgEdfJQppVSBhe2lwObNm/PNN9+QnJxMVlYWUVFRJCYm8s4773DeeeeRmZlJVFQUCxYswFqD1WKMITY2NrtVqlq1ajRv3pzPP/+c2NhY0tPTiY2NBdwJW0xMDFOmTAGgRYsW3HDDDdnbAjV9+nQ2bNjA4cOH6datG2Alej/++COJiYlkZWXRsGFD1q5dS1ZWFtu2baNSpUo54nAp6HMrpfInIq2BasARrMuCYE0yWhmoBBzzKvN+/BhgDECDBg2KO9yIM3fuXEDnMyqttP7dwjaxGj16NKNGjeLdd9+lbNmyfPbZZ0yZMoWrr76arKws4uLi+OCDD3w+tnbt2pw+fZprrrmGadOmcf/999OnTx+ioqKoXr16ro7t8+fP5/nnn+fs2bNcfvnlPhOb1NRUHn/8cTZv3kyfPn2YM2cONWvWzN7eu3dvunfvTseOHalYsSIA06ZNY/To0Rhj6NixI1OnTmXw4MF07do1u4+VUqr4iUgV4HlgGNAOqGtvqoiVaB3xUZaDMSYFSAFITk7W6R28bN682ekQlIO0/t0kkBFxxSEhIcEcP37ckedWSjlDRFYbY0I6Z4mIxADzgUeNMStEpAbwqjGmv4j8A9iGdRkwR5kxxu/Q4uTkZLNq1aoQRB85gr0Ib8P7Pg7KcUJh+9QBAJw/YYHDkQTPtin9C7R/aViEOdDPr7BtsXLSM888w/vvv599PykpiaefftrBiJRSRXAt0B6YancbmAh8LSLLgD+Ap40x50QkR5lj0UaokvyFqvKn9e+miZUP48aNY9y4cU6HoZQKAmPMXGCuV/FyYKrXflO9y5RSqqC0l7RSSqkiW716NatXr3Y6DOUQrX83bbFSSilVZAsWWP2L2rVr53Akygla/26aWCmllCqytm3bMvf7PyKq07kKnrZt2zodQtjQxEoppVSRDRw4kLHfaFJVWg0cONDpEMKG9rFSSimllAoSTayUUkoV2fHjxynLOafDUA45fvw4OjelJaDESkQuF5FNIrJVRO7zsX2UiOwXkbX2v78GP1SllFLhaubMmQwvu87pMJRDZs6cycyZM50OIyzk28dKRKKBfwGXAWnAShGZb4z52WvXt4wxtxdDjEoppcJchQoV2Hf8rNNhKIdUqFDB6RDCRiCd1zsAW40xvwGIyDxgMOCdWCmllCql7rnnHh0RWIrdc889TocQNgK5FFgX2OFxPw33YqWehorIOhF5R0Tq+zqQiIwRkVUisio9Pb0Q4SqllFJKha9AEivxUea9cvNHQENjTGtgMfAfXwcyxqQYY5KNMcmxsbEFi1QppZRSKswFklilAZ4tUPWAXZ47GGMOGmNcF9dnAwFPvdqrVy969eoV6O5KKaXCUEpKCgPLaA+R0iolJYWUlBSnwwgLgfSxWgk0FpELgJ3AcOB6zx1EpLYxZrd9dxDwS0EDcSVXqampBX2oUkoph+3evZtqOoFPqbV79+78dyol8k2sjDEZInI78BkQDbxijNkgIpOAVcaY+cAdIjIIyAAOAaOKEpR3C5ZnsuWZgOW1n6/jadKmlFLFY/To0Qx8bpnTYSiHjB492ukQwkZAS9oYYz4BPvEqe8jj9kRgYnBDyynQy4X5JVu+tueVeAWalBU1efP1eE0IlVKRok6dOhw05Z0OQzmkTp06TocQNnStQA95tYZ5bncpyn7+ErrCJFjBarnTRE4ppRQQ1Kkztk3pH7RjRQJNrCJMQZOo/PYLNU3elCqZUlNTSYrZydoMX7PxqJIuKWYngNY/ulZgqeQ5EjO/UZm+tuf1mEBHeRYkBqWKQkTqiMgaETkjIjF22VMislREnvHYL1eZCtySJUtoE6sdmEurNrG7tf5t2mKlcinMJcpAL4kW5rnz2s/z2IGWqVLnEHAp8D6AiLQFyhtjuovICyLSHsj0LjPGrHQw5ojTs2dPnl682ekwlEN+SK/tdAhhQxMrFZYKM/ozGM9XmOfQgQfhzRhzBjgjkj3XcWesiYyx/+8EZPko08SqAHr16sWoT086HYZyiF4CdNPESpU6hensX9iBC/6eL69kLL+4gqUUJ3+VgF/t20eBllgtVt5lOYjIGGAMQIMGDYo/SqVURNLESikHFWSkZlEufxblEmtesURoK90RoKJ9u6J9P9NHWQ7GmBQgBSA5Odl7Wa9Sb9euXVSVkzrlQilVVazWSq1/7byuVKlS0MEIgWwP1mNCaDlWnyuAPsB3fspUAcyePZtB8QVedEOVEIPif9H6t2mLlVKqSPJLysD/pdNQEJFYYCGQiLWCxD+x+lwtBX40xnxv75erTAWudu3a/LTzqNNhKIccyCrndAhhQxMrpVSJZoxJx2qF8rTCx37jQhNRyTRmzJigTiqpIstHZ1s4HULY0EuBSimllFJBoomVUkoppVSQaGKllFKqyGbMmMF18T86HYZyyHXxP2r927SPlVJKqSI7ceIE5ST//VTJVE7SnQ4hbGhipZRSqsjuvvtuOkxenP+OqkSad7q10yGEDU2slFJKFVlCQgKniXM6DOUQrXs37WOllFJKKRUkmlgppZQqso8++ogusducDkM5pEvsNq1/myZWSimlimzNmjU0jTngdBjKIU1jDmj927SPlVJKlVLBnCm9SfT5QTuWijzfnNP6dwmoxUpELheRTSKyVUTu87G9jIi8ZW9fISINgx2oUkqp8LU5szqbM6s7HYZyiNa/W74tViISDfwLuAxIA1aKyHxjzM8eu90MHDbGNBKR4cBU4LriCFgppZRSkSOYLaPbpvQP2rGKSyAtVh2ArcaY34wx54B5wGCvfQYD/7FvvwNcKiI6VZxSSpUS9aOOUD/qiNNhKIdo/buJMSbvHUSuAS43xvzVvv8noKMx5naPfdbb+6TZ93+19/Hbky2+xvlm8GPzWPvj2hzlSYlJxVZWnMeO9Lg0hvCOKxxiCEZcm1/4+2pjTDIRLjk52axatcrpMIosmC0JN5W1zserpyO+egts+9QBAJw/YYHDkTgnVPXvZIuViAT0+RVIYnUt0M8rsepgjBnrsc8Gex/PxKqDMeag17HGAGMAKtS+qN2VD79esFellIpob9/aRROrMBLMxOrSuC0AfHGucdCOGSk0sQpd/UdCYhXIqMA0oL7H/XrALj+vE26UAAAIvUlEQVT7pIlIDHAecMj7QMaYFCAFrA+mt27pHMDTK6VKirdvdToCVVxKY0Kl3LT+3QLpY7USaCwiF4hIHDAcmO+1z3zgz/bta4AvTX5NYUoppZRSJUy+LVbGmAwRuR34DIgGXjHGbBCRScAqY8x84GXgdRHZitVSNbw4g1ZKqeIgIk8BycAaY8w4p+PxJZiX75RSwRfQBKHGmE+AT7zKHvK4fQa4NrihKaVU6IhIW6C8Maa7iLwgIu2NMSudjitSlObO6yp09R/sHxbF0WdLl7RRSilLZ2CxfXsx0MnBWJRSESrfUYHF9sQix4FNjjx58FUDSsoiSSXltZSU1wEl67U0NcYkOB2ELyJyP7DaGPOpiPQBuhhjJnlszx7VDDQl78+vcKwzjSkwGlNgSmNM5xtj8p1e3sm1AjeVhGHXACKySl9LeCkprwNK3mtxOoY8HAEq2rcr2vezeY5qzk841pnGFBiNKTAak396KVAppSzLgUvt232A7xyMRSkVoTSxUkopwBizBjgjIkuBLGPM907HpJSKPE5eCgyoST1C6GsJPyXldYC+lpAJ4hQL4fg6NabAaEyB0Zj8cKzzulJKKaVUSaOXApVSSimlgsSRxEpELheRTSKyVUTucyKGwhCR+iLylYj8IiIbRGScXV5FRD4XkS32/5WdjjVQIhItIj+IyAL7/gUissJ+LW/ZyxiFPRGpJCLviMhGu346R2K9iMhd9ntrvYjMFZH4SKkTEXlFRPaJyHqPMp91IJZn7c+AdfbknGFPROqIyBoROSMiMfa/efbnwjSP/caLyDIRmSMisT6O8aWIfGtP61DsMdnvoaUi8rWIvCki0V7HGGV/Jqd6vo7ijMne76j9nKkiUsXrGAki8pGIfCMiN4YiJhFJ8ojndxG50+sYwT5PHe33wVKxZv33+d4J8fsp35gceD8Fep5C9n7KkzEmpP+wlsX5FbgQiAN+BFqEOo5Cxl4baGvfTgA2Ay2AacB9dvl9wFSnYy3Aa7obeBNYYN9/Gxhu354F/M3pGAN8Hf8B/mrfjgMqRVq9AHWB34GyHnUxKlLqBOgBtAXWe5T5rAPgSmAhIFgTca5wOv4AX2M8UBlIxeqjei0w0d72HJAIVAc+scsmANd6HeNZoAtQAUgNUUyVgUp22WRgoNcxRrn+fkJ1nuzby/I4xt3A9fZ3xtdAXChi8tj/Q6BRMZ+nWkC8fXsO0N37vePA+ymQmEL9fso3plC/n/L650SLVQdgqzHmN2PMOWAeMNiBOArMGLPbWCOHMMYcB37B+jIcjPXFjv3/Vc5EWDAiUg/oD7xk3xfgEuAde5eIeC0iUhHrS/1lAGPMOWPMESKzXmKAsiISA5QDdhMhdWKM+RprrVBP/upgMPBfY/kOqCQitUMTaeEZY84YYw57FF0IrLNvr8Wavb0D1pc3+J7BvTWw3BhzAjguIkWaMDWQmIwxh+2/CYAMINPHoe60WyAu9bEt6DHZt5vbrRBT7M8fT52BxcaYTKwf4E1DFBMiUh6oZYzZ6uNQwTxPe4y1JBxY9dKa3O+dUL+f8o3JgfdTIOcJQvh+yosTiVVdYIfH/TS7LKKISEOgDbACqGmM2Q1W8gXUcC6yAnka+AeQZd+vChwxxmTY9yOlbi4E9gOvinVZ8yX7gzGi6sUYsxOYDvyBlVAdBVYTmXXi4q8OSsTnANbs6z3t272xf8kDx+yyo3aZp2hj/4T2s704YgKsy0ZYc3Qt8nrMB1hfVkOB6d6XdooxpsZYP4oqAwO9HpPfeSyumACuAD718ZhiOU8i0hpr1vAj5H7Njryf8onJtU9I308BxOTk+ymbE4mVdxYJEFFDE0WkAvAucKcx5lh++4cjERkA7DPGrPYs9rFrJNRNDNYlqBeMMW2Ak1iXnSKKWP2PBgMXAHWA8lgf8N4ioU7yE6nvNW8fYbUwfgGcBfaSzwzu5Px172t7ccSEiJTBajUc7ZGoA2CMOWKMyTLG7Mfq4lAzFDEZYw7ZScEHQCuvx+R3HoslJtsQ4D3vBxTHebL7Aj0P3Izv1xzy91MAMYX8/RRITA6/n7I5kVilAfU97tcDdjkQR6HYneTeBeYYY1x/eHtdlzHs//c5FV8BdAUGicg2rMuxl2C1YFWyL0NB5NRNGpBmjFlh338HK9GKtHrpA/xujNlvjEnH+mDvQmTWiYu/OojozwEXY0ymMWasMeZSrC+4RcBK3C0hvmZwXyfW4IryQMVg/zjzExNYc/z82xjzs/dj7MvpiEhZrF/9+4s7JhEp79GS0RWr762n5cCl9j5JBHltWX/nyf6Mb26M+dH7McE+T/bf9RvAeGPMHny/d0L6fgowJgjh+ymQmJx+P3lyIrFaCTS2RxXEAcOB+Q7EUWD2NduXgV+MMTM9Ns0H/mzf/jNWp8ewZoyZaIypZ4xpiFUHXxpjRgJfAdfYu0XKa9kD7BAR1zXzS4Gfibx6+QPoJCLl7Pea63VEXJ148FcH84EbxdIJOOq6ZBjO7BFRi7E6hH8mIj3tEUhfAt8aY9KMMfuAr0VkGdYH+Af2Y5+zDzMNq8PvYuCJUMQkIp2Bq4Fx9rYhXjHdJSLLsfqtTLET+2KNCesLd6VYM93Xx+5H6BHTS8BIYCnwijHmbAhiAutH5pdejy2W84TVEbw9MFVEUoGL8HrvhPr9FEhMoX4/BRITIX4/5cWRCUJF5Eqs1pForBc4OeRBFIKIdMOqlJ9w90v6J1Y/q7eBBlhfjtcaY7w78YYtEekF3GuMGSAiF2K1YFUBfgBuKM43YLCISBLWH04c8BtwE9YPh4iqFxF5FLgOq4PmD8BfsfoehX2diMhcoBdWH4i9wMNYH3i56sBOHJ8HLgdOATcZY8J5gWallAqIzryulFJKKRUkOvO6UkoppVSQaGKllFJKKRUkmlgppZRSSgWJJlZKKaWUUkGiiZVSSimlVJBoYqWUUkopFSSaWCmllFJKBYkmVkoppZRSQfL/Q7eOcHUVwSoAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 720x432 with 6 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mcmc.sample(25000, 0, 10)\n",
"mcplot(mcmc.trace('centers', 2), common_scale=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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