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@RuizSerra
Created March 13, 2024 04:23
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dynamic Bayesian thermostat\n",
"\n",
"Python implementation of the _Dynamic Bayesian thermostat_ from Buckley _et al._ (2017) [^1]\n",
"\n",
"Original MATLAB implementation by Christopher L. Buckley, Chang Sub Kim, Simon M. McGregor and Anil K. Seth.\n",
"\n",
"Python implementation by Jaime Ruiz Serra.\n",
"\n",
"\n",
"[^1]: Buckley, C. L., Kim, C. S., McGregor, S. & Seth, A. K. The free energy principle for action and perception: A mathematical review. Journal of Mathematical Psychology 81, 55–79 (2017) [DOI:10.1016/j.jmp.2017.09.004](https://doi.org/10.1016/j.jmp.2017.09.004)\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%config InlineBackend.figure_format = \"retina\"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Simulation params\n",
"sim_time = 100\n",
"dt = 0.0005\n",
"timesteps = np.arange(0, sim_time, dt)\n",
"N = len(timesteps)\n",
"\n",
"# Generative model params\n",
"T0 = 100 # initial temperature\n",
"Td = 4 # desired temperature\n",
"action_time = sim_time/4 # onset time of action\n",
"\n",
"# Initialise states\n",
"rho_0 = [0] # sensor states\n",
"rho_1 = [0]\n",
"\n",
"mu_0 = [0] # brain states\n",
"mu_1 = [0]\n",
"mu_2 = [0]\n",
"\n",
"# Variances\n",
"omega_z0 = 0.1 # sensory\n",
"omega_z1 = 0.1\n",
"omega_w0 = 0.1 # hidden state\n",
"omega_w1 = 0.1\n",
"\n",
"# Sensory noise in generative process\n",
"zgp_0 = np.random.rand(N) * omega_z0\n",
"zgp_1 = np.random.rand(N) * omega_z1"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Initial action\n",
"a = [0]\n",
"\n",
"# Initialise generative process\n",
"x_dot = [a[0]]\n",
"x = [2]\n",
"T = [T0/(x[0]**2 + 1)]\n",
"Tx = [-2 * T0 * x[0] * (x[0]**2 + 1)**-2]\n",
"T_dot = [Tx[0] * x_dot[0]]\n",
"\n",
"# Init sensory input\n",
"rho_0 = [T[0]]\n",
"rho_1 = [T_dot[0]]\n",
"\n",
"# Init error terms\n",
"epsilon_z_0 = rho_0[0] - mu_0[0]\n",
"epsilon_z_1 = rho_1[0] - mu_1[0]\n",
"\n",
"epsilon_w_0 = mu_1[0] + mu_0[0] - Td\n",
"epsilon_w_1 = mu_2[0] + mu_1[0]\n",
"\n",
"# Init Variational Free Energy (VFE)\n",
"vfe = [\n",
" 1/omega_z0 * epsilon_z_0**2/2\n",
" + 1/omega_z1 * epsilon_z_1**2/2\n",
" + 1/omega_w0 * epsilon_w_0**2/2\n",
" + 1/omega_w1 * epsilon_w_1**2/2\n",
" + 1/2 * np.log(omega_w0 * omega_w1 * omega_z0 * omega_z1)\n",
"]\n",
"\n",
"# Learning params\n",
"k = 0.1\n",
"ka = 0.01"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"for i in range(1, N):\n",
" # Generative process\n",
" x_dot.append(a[i-1])\n",
" x.append(x[i-1] + dt * (x_dot[i]))\n",
" T.append(T0 / (x[i]**2+1))\n",
" Tx.append(-2 * T0 * x[i] * (x[i]**2+1)**-2)\n",
" T_dot.append(Tx[i] * x_dot[i])\n",
"\n",
" rho_0.append(T[i] + zgp_0[i]) # sensory inputs\n",
" rho_1.append(T_dot[i] + zgp_1[i])\n",
"\n",
" # Generative model\n",
" epsilon_z_0 = rho_0[i-1] - mu_0[i-1] # error terms\n",
" epsilon_z_1 = rho_1[i-1] - mu_1[i-1]\n",
"\n",
" epsilon_w_0 = mu_1[i-1] + mu_0[i-1] - Td\n",
" epsilon_w_1 = mu_2[i-1] + mu_1[i-1]\n",
"\n",
" vfe.append(\n",
" 1/omega_z0 * epsilon_z_0**2/2\n",
" + 1/omega_z1 * epsilon_z_1**2/2\n",
" + 1/omega_w0 * epsilon_w_0**2/2\n",
" + 1/omega_w1 * epsilon_w_1**2/2\n",
" + 1/2 * np.log(omega_w0 * omega_w1 * omega_z0 * omega_z1)\n",
" )\n",
"\n",
" mu_0.append(\n",
" mu_0[i-1]\n",
" + dt * (mu_1[i-1] - k * (\n",
" - epsilon_z_0 / omega_z0\n",
" + epsilon_w_0 / omega_w0 \n",
" ) )\n",
" )\n",
"\n",
" mu_1.append(\n",
" mu_1[i-1] \n",
" + dt * (mu_2[i-1] - k * (\n",
" - epsilon_z_1 / omega_z1\n",
" + epsilon_w_0 / omega_w0\n",
" + epsilon_w_1 / omega_w1 \n",
" ))\n",
" )\n",
"\n",
" mu_2.append(\n",
" mu_2[i-1]\n",
" + dt * -k * (epsilon_w_1 / omega_w1)\n",
" )\n",
"\n",
" if timesteps[i] > 25:\n",
" a.append(\n",
" a[i-1] \n",
" + dt * -ka * Tx[i] * epsilon_z_1 / omega_z1 # active inference\n",
" )\n",
" else:\n",
" a.append(0)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'VFE')"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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BkWqfHT8N4T2zVmrZ1n1pigoAAAAAAKDpILkFtFKRdbQyMjI0ePDgWttFpiSUkie3nn/+eV111VUaNWqUPB6PDMPQjBkzGjhaAGhdOuVl6K/nDY8r8wUtXf/iIpV5A2mKCgAAAAAAoGlgzS00H5ntQmtQtSBrC8tU5Q9Gj7u1yVSbrJgn9TPbNdp7R0ZuDR06VE5n7ZeCSBLMNE0NGzYsof43v/mNNm7cqIKCAnXp0kUbN25slHgBoLWZMKijrjyhrx6fsy5atr6oXHe8tUwPnDec9bcAAAAAAECrRXILzYdpStkF6Y6iQVXtcynotKPHztxsKcOVkveOJK32N9VgZOTWgAEDlJWVlVD/xBNPaMCAAerVq5fuvfde3XbbbQ0dKgC0Wr84ZZD+t36Plmwujpa9uWirhnbL10+O65O+wAAAAAAAANKIaQmBNLEsW0HLjitzOlLzI1lWVqZ160IjAfaX3Jo/f36d7SZOnKhevXo1ZHgAgDC309Sj549Qrif+eaQ/zlyuuasL0xQVAAAAAABAepHcAtIkYFkJZU5HaqaYWrJkiWw7lFjr169fre2WLVumTZs2SZKGDx9eazsAQOPp2T5Lfzk3/hps2dJ1LyzS+qLyNEUFAAAAAACQPiS3gDQJ1Bi1ZRiGHClaPyWy3pYklZfXfmP0vvvui+7vb4QXAKDxfO+Izrpx4oC4sn2Vfl3x7AKVVvnTFBUAAAAAAEB6kNwC0iQQrDEloWnISENy6/XXX0/aZvr06Xruueeix4cffnijxwUAqN3PThqgyUd0jitbs6tMN7y0OGGaWwAAAAAAgJbMuf8mABpDzWkJnWZqEluStHjxYkmSaZp64YUX5PP5dM4556hDhw7avHmzXn75Zb333ntyuVzy+0MjAt544w117txZ559/fsriBABUM01D9583XBt2V2jF9pJo+X9X7tJfP1ilX35vcBqjAwAAAAAASB1GbgFpkjByy5GaH0fLsrRs2TJJ0jXXXKN27drptdde0/nnn6+TTz5Zl156qd577z1NmTJF1157bfS8m266SR999FFKYgQAJJflduqfF49Uu2x3XPljn67Va19vSVNUAAAAAAAAqUVyC0iTmmtupWrk1nfffaeKigpJ0sSJE/XZZ59p6tSpatOmjbKzs3XUUUfpkUce0dtvv60bb7xRRx55pLKzs3XCCSfosssuS0mMAIDadW+bpccuPCrh341fvf6NPl21K01RAQAAAAAApA7TEgJpkjhyK/XrbQ0bNkx9+vTRW2+9lbRtr169tGjRopTEBQCov6P7ttfvpx6h299cGi0LWLau+ddCvXTlMRrWvU36ggMAAAAAAGhkjNwC0iRxza3U/DhG1tvKy8tT7969U/KeAICG98Oje+qqE/rGlVX4gvrJjPnauLs8TVEBAAAAAAA0PkZuAWmSrmkJIyO3jjjiCBnGob/nE088oc8++0yStHTp0mjZp59+Kkk688wzdeaZZx7y+wAAEv3ye4O1o6RK/168LVpWVObThU/8T69cNVZd22SmMToAAAAAAIDGQXILSJN0TUsYGbk1bNiwBunvs88+0zPPPBNXNm/ePM2bN0+S1Lt3b5JbANBITNPQX84ZrqIyr+at2R0t37K3Uhc98T+9fNVYdcj1pDFCAAAAAACAhse0hEAa2LatYMK0hI2f3CosLNT27dslNVxya8aMGbJtu9bXb3/72wZ5HwBAcm6nqekXjdRhXfLiytcVleuiJ/6nveW+NEUGAAAAAADQOEhuAWkQtGzZNcqcjsb/cYxMSSg1XHILAJB+uRkuPXvZGPXrkB1XvmpnqX74xP+0u8ybpsgAAAAAAAAaHsktIA1qrrclSY4UjNyaOHFidETVuHHjGv39AACpU5Dj0b8uP0Y922XFla/YXqIL/vmldpVWpSkyAAAAAACAhkVyC0iDQDB+SkKHacg0UrPmFgCg5eqcn6F/XX60uuZnxJV/t7NM5z/+pXaWkOACAAAAAADNH8ktIA1qjtxymvwoAgAaRo92WXr5qrHq1iYzrnxdYbnOnf6F1hWWpSkyAAAAAACAhsEddSANEpNbjNoCADScUIIrcYrCTXsqdNZjn+ur9XvSFBkAAAAAAMChI7kFpEGwRnIrFettAQBal+5ts/TKVWPVtyA7rry4wq+Lnvif3l6yLU2RAQAAAAAAHBqSW0AakNwCAKRC5/wMvXTVMTqiW15cuS9o6WcvLtLfP10j27ZrORsAAAAAAKBpIrkFpEHN5JbTQXILANA4OuZm6OUrx+rkwR0T6u57f5Vuf3Op/EErDZEBAAAAAAAcHJJbQBrUXHPLYZDcAgA0nmyPU49fPEoXj+2VUPfiV5t12TMLVOYNpCEyAAAAAACAA0dyC0gDpiUEAKSawzT0u+8frt9MGaKaz1TM+a5Q5zz2udYXlacnOAAAAAAAgANAcgtIg4RpCUluAQBSwDAMXX58X/39h0fJ44z/GrhyR6lOf2Su3li4JU3RAQAAAAAA1A/JLSANglb82iaM3AIApNLkoV304pXHqF22O6683BfUz19Zop+/vJhpCgEAAAAAQJNFcgtIMdu2k0xLyI8iACC1jurZVm9ec6wGdMxJqHtj0Vad8ehnWrZ1XxoiAwAAAAAAqBt31IEUC1q27BpljNwCAKRDr/bZ+vd143T+6B4JdeuLyjXt7/P05GfrZds1/+UCAAAAAABIH5JbLYhhGPV6nXjiiekOtVWrOWpLYs0tAED6ZLmduvfsYXr0ghHK9Tjj6vxBW394d7kuf2aB9pT70hQhAAAAAABAPJJbQIoFazz9bhqGTJJbAIA0O2N4V8382fEa3qNNQt3HK3dp8sNzNHd1YeoDAwAAAAAAqMG5/yZobq6++mpdc801tdZnZ2enMBrUFEhYb4vEFgCgaejZPkuv/XSs/vrBKv1j9rq4up0lXv3oya90zsju+s2UIWqT5U5TlAAAAAAAoLUjudUCdezYUUcccUS6w0Atak5LSHILANCUuBymbps8ROP6FejnryxWUVn8dISvfb1Fn67apV9PGaIzj+wmw+DfMQAAAAAAkFpMSwikGMktAEBzcMLADpp1w/E6fkBBQl1RmU83vbxEZz/2ub7ZUpz64AAAAAAAQKtGcgtIsZrJLSfJLQBAE9UxN0PP/HiM/nDmEcrxJA74X7ipWFP/Nk+3vLpEu0qr0hAhAAAAAABojUhuASnGmlsAgObENA396Jhe+vDnJ2jikI4J9bYtvfr1Fp3019l6fM5a+QJWGqIEAAAAAACtCcmtFujVV1/VoEGDlJmZqdzcXA0YMECXXHKJPvnkk3SHBjEtIQCgeeqSn6l/XjxK/7x4lHq1z0qoL/MGdM+slTr1oTmatXS7bNtO0gsAAAAAAMChI7nVAi1fvlzfffedqqqqVFZWpjVr1ujZZ5/VSSedpGnTpmnfvn0H1e+WLVvqfG3fvr2BP0nL1JSSWzNmzJBhGDIMQxs3bqy13YoVK6LtXn755RRGCABoSgzD0KTDOumDm07QL783WNluR0Kb9UXluuZfC/X9/5un95ftkGWR5AIAAAAAAA0rcfEENFtZWVn6/ve/r5NPPlmDBw9WTk6OCgsLNXv2bE2fPl27d+/WW2+9palTp+rDDz+Uy+U6oP579OjRSJG3LgnJLSN9ya0lS5ZIktq2batevXrV2m7x4sXR/eHDhzd2WACAJs7jdOjqE/vp7KO66c/vr9LrC7cktFm6dZ9++vzX6tchW1ed0E9njugmt5PnqgAAAAAAwKEjudWCbN26VW3atEkonzRpkq6//npNnjxZixYt0uzZs/XYY4/pZz/7WeqDhCy76YzciiStjjzyyHq1y8rK0sCBAxs3KABAs9ExL0P3nzdcFx3TU797Z7kWby5OaLO2sFy3vv6NHvjwO112XB9dcHRP5Xj4CgoAAAAAAA4edxZakGSJrYhOnTrptdde05AhQ+Tz+fToo48ecHJr8+bNddZv375dY8aMOaA+D4RlWyr2Fjda/6myt6pU/qAVPd7n88kyk/8otvG0kWk03lPu33zzjSRpxIgRdbZbtGiRJGno0KEyTZ66BwDEG9Gzrd64+li9t2yH7v9wldYVlie02VFSpbtnrdCj/12ti8f21qXjeqsgx5OGaAEAAAAAQHNHcqsV6du3ryZNmqSZM2dqzZo12rZtm7p27Vrv87t3796I0e1fsbdY418en9YYUm32D2arXUa7Rul706ZN2rNnj6T9J7ci0xfub4QXAKD1Mk1DU4Z10amHd9K732zX9NlrtXJHaUK7kqqA/u+TNfrn3HU6d1R3XXl8P/Vsn5WGiAEAAAAAQHPFEIxW5rDDDovub926NY2RIN0iCSup7qTVtm3btGvXrv22AwBAkpwOU2eO6Kb3bjheT/94tMb0Sf6Qhjdg6fkvN+nEv36iHz/9ld5ftl2+gJW0LQAAAAAAQCxGbrUydo31ntB6RdbRysjI0ODBg2ttF5mSUEpMbm3dulWvvvqqZs2apZUrV2rHjh1q166dxo0bp1tvvVVHH310Y4QOAGgGDMPQhEEdNWFQR329ca+mz16rD5fvTGhn2dInqwr1yapCtc926+yR3XXeqB7q3zEnDVEDAAAAAIDmgORWK7N8+fLo/oFMSYiWJzJya+jQoXI6a78URJJgpmlq2LBhcXWPPvqo/vznP6tfv36aNGmSOnbsqNWrV+utt97SW2+9pRdffFHnnXdeo30GAEDzMLJXW/3z4lFas6tU/5i9Tm8t3ip/MPGBm93lPj0+Z50en7NOI3u11Q9G9dCUYV2U7eErKwAAAAAAqMadglZk3bp1+vDDDyWF1t/q1q1bmiM6MG08bTT7B7PTHcYhqfIFtK6oPHpsyNDgLrkyDCNp+zaeNo0WSyRptb+pBiMjtwYMGKCsrPg1UcaMGaM5c+bo+OOPjyufO3euTj75ZF199dWaOnWqPB5Pg8UNAGi++nfM1V/OHa6fnzJQT85dr5fmb1aZN5C07dcb9+rrjXv1u3e+1amHd9bkoV10/IACZbgcKY4aAAAAAAA0NSS3Woh33nlHkydPrnUEzs6dO3XOOefI7/dLkq699tpUhtcgTMNUu4zk63Y0F2UKKM/tjh47TEPtM/NTH0dZmdatWydp/8mt+fPn19rurLPOSnrO8ccfrwkTJuiDDz7Q0qVLNWrUqEOKFwDQsnTJz9RvTj9MN00aqJlLt+uV+Zu1YOPepG3LfUG9sWir3li0Vdluh04a0kmTj+isEwd1UJabr7IAAAAAALRG3BFoIa6//nr5/X6dffbZGjt2rHr37q3MzEwVFRXp008/1fTp07V7925J0nHHHdcsk1stQbDGmmcOM/mIrca2ZMmS6Ppr/fr1q7XdsmXLtGnTJknS8OHDD+g9XC6XJNU55SEAoHXL9jh13qgeOm9UD63ZVaZXF2zW6wu3qKjMl7R9uS+od5Zs0ztLtinDZerEgR01eWhnnTS4o3IzXCmOHgAAAAAApAt3nVuQbdu26dFHH9Wjjz5aa5uzzz5bTzzxBNPEpUnQqpHcqmU6wsYWWW9LksrLy2ttd99990X39zfCK9amTZv00UcfqXPnzho6dOhBxQgAaF36d8zRbacN0S9OHaSPV+zSKws269NVu2QlLs0lSaryW3r/2x16/9sdcjtMHd23nU4a3FEnDe6oXu2zUxs8AACIY9u2/EFbvqAlXyDmFQzKF7AVsCwFLFtBy1YgaMuyIy/Jsm3Zti3blkzDkGGEtqGXZIS3plldFqmPtjWVUBepdzoMOUxDbocpt9OU22HK6TDT/UcGAAAOEMmtFuKZZ57R7Nmz9cUXX2jdunUqKipSSUmJcnJy1KNHDx177LG65JJLNHbs2HSH2qpZNZNbaRy5FfH6668nnV5w+vTpeu6556LHhx9+eL369vv9+tGPfiSv16v77rtPDgdrowAA6s/lMPW9Izrre0d01s6SKr23dLtmLduh+Rv2yK4l0eULWpq7ukhzVxfpd+8sV+/2WTp+QAcdN6BAx/Rpr/wsRnUBAFCTL2CptMqv0qqAyrwBlXsDKvcFVOYNhva9AZV7gyr3hfYrfEFV+ELbKn9Qlf6gvH4rIYHlDVryB61a/91uikwj9B3E7TTlCSe8PC5HNAHmcZryuEx5nA55nKYyXDFbl6kMp0MZLocyXGZ0m+lyKNPtDG1dDmW6zbjjDJdZ6/rbAABg/0hutRDjx4/X+PHj0x0G9qPmtIRmmr7ILl68OPT+pqkXXnhBPp9P55xzjjp06KDNmzfr5Zdf1nvvvSeXyxVdp+2NN95Q586ddf7559far2VZ+slPfqI5c+boiiuu0I9+9KNUfBwAQAvVKS9Dl47ro0vH9dGu0ip98O1Ovbdsu75ctydhNHSsDbsrtGH3Rj335UYZhnRYlzyN7dteY/u11+g+7ZTHFIYAgBYkaNnaW+HT7jKfisq82l3u074Kn4or/Cqu9Ku4wq99ldXHJZV+lVT5VeW30h16k2HZkjdgyRuwVJrC9810OZTldijL41CWyxnauh3KdDmVXWM/0+1QttsZ3Wa5Q2VZboey3JH2TmW7HYxEAwC0CoZtN6dnadCUbdmyRT169JAkbd68Wd27d6/3uatXr1YgEJDT6dSAAQMaK8S021ZcqaIyb/S4bZZbPdplpTQGy7KUm5uriooKXXfddXrhhRe0Z8+ehHZTpkzRgAED9NBDD0XLLrvsMj3xxBNJ+7VtW5dffrmeeuopXXTRRXrmmWdkmgf+hbq1/F0AABy8PeU+fbh8h2Yt3aHP1xbJH6z/11nTkI7olq+RvdrqqJ5tdVSvtuqan8GT0wCAJsUbCGp3WXXCqrDMG90vqrG/p9xX6zS+aJ3cTlPZMUmvzHDSKyucFIskwrLcsdvq/bhEWkxbF0kzAMBBOJS8QV0YuQWkUFOYlvC7775TRUWFJGnixIm65pprdNttt2n27Nny+/0aNGiQLr30Ul177bXavHmzPv30U61evVojR47UZZddlrRPy7J0+eWX6+mnn9YFF1ygGTNmHFRiCwCA+miX7dYPRvfUD0b3VEmVX5+tLtJ/V+7Sp6sK4x4iScaypW+27NM3W/bp6XkbJEmd8jw6qmdbjezVViN6ttUR3fLkcTKtLgCg4di2rXJfUEWlXu0u96qw1JeQpIrdL6kKpDvkRuMwDTnDL4dpyOkwo+tjOczqtbEkybZDf3aRtbis6HFovS47ptyyY4/tVp3wi0wRubfC36D9uh1mOPEVSoBlukMjzjLcDmWFR6El309sUz09oyNu2sd0Ld8AAGh+SG4BKZQwLWEavrTFrrc1bNgw9enTR2+99VbStr169dKiRYvq7C82sfWDH/xAzz33HOtsAQBSJi/DpdOGdtFpQ7vIsmwt314SXn+rUF9v3CtvYP9TLu0s8eq9ZTv03rIdkkI3bg7vlqfh3dtoWPd8De2Wr74dcrjZAgCIY1m2iiv90YRUUZkvmrwqCievisqry5ryNIBO01C2JzS6J9vjDL9Co3dyPKHp8kJT4Tnj1o7yOENrUrmdpjyO6n13eN2q6jpHdD9V/57admLyy7JtBSxbgaAtf3itMG/Aiu7Hrh/mDQTlDVS38QUsVQVC64xFt/5g+BVfV+kLnVsZXqesKrw2WXPnC1ryVVraV9mwSbNYLocRXdsslPRyxG+d4bXPwmudhZJiieuhxa6RFl9ee5nTNBjNDzRRkQcdApaloBW6lgeD4a1lK2BZsqwa9dG68PU/WP3vgJXQpvo8y7IVtJO1qd6PPGQRaWfZiiu3bFtHdMvXhUf3SvcfXYtGcgtIoZrrgzjS8KUpst5WXl6eevfufUh9WZalyy67TDNmzNC5556r559/nsQWACBtTNPQEd3ydUS3fF19Yj95A0Et3lSsL9bt1hdrd2vRpuJ63VjyBS0t2lSsRZuKo2UZLlODO+fpsK55GtIlT0M652pAp1zlZ7J+FwC0NN5AULtKvNpV6lVhaZV2lXrDx1UqLA2V7yoNTQdY1xqQ6dAmy6X22W61zXKrTZZLbbLcapPpUn6mS22yXMoL7+dlupSX4VJehlN5mS55nGaLu6lvhEeAmWoanysQtFTpD6rSH1SVz1KFPxBOfkVeAVX4gir3hsv9oSRZuTcQ3U/WpsIbbBGJswh/0JY/GNB+BuM3CtNQdcKrRuIsIzZZ5kpSVjMR5zDlchpymqZcjtDW6TDkdphyOkJlLkeoLNrGYcoVHs3odBhymZF6km6tVSShE0mWRJIrkeRLMCHxYkUT+LHtA8HEBE7cObW2r+4z7rxgLeXRpJGVpH1t7x8uD8YkoWpJKDU3k4/wk9xqZCS3gBSqOXIrHU+AR0ZuHXHEEYf85ej3v/+9ZsyYoZycHA0cOFB//OMfE9qceeaZOvLIIw/pfQAAOBgep0NH922vo/u2140TpSp/UAs37tWCjXu1cNNeLdpUXO8nj6v8lhZvLtbizcVx5Z3yPBrQMVf9O+ZoQKccDeyUqwEdc9Qmy90InwgAcCgqfIGYpFUoWbUzJmm1sySUyCpu4KncDoXDNNQ+262CHI/a57jVIcejglxPXFlBjkcdcj1qm+WW28n08E2V02Eq12EqN6PhH4zxB61ogqzcG06IRY59QVXUOI5NmlV4q8sqfKGkWeS4JSXN6sOyFU02Sk3nOiCFEm9O04xO6+lwVE/tGZrWM5TMNQxVH6v6uHobKjdNxbQJTQuasJURbReKIbGdESk3Q+0T3y/cT+xx9PzqWOP7j4nVUDQ9HXtHzbYlW3bc1KU1y2xVT1dqK340Z6TMCu/EtrXC5yqubcx7xEx9Gp0G1Qrd87Ojo3lCo3trjvCxw4mqmiN8YpNUwZj+mmNCB9X4/9f4SG4BKWTV+F7oSMODN5GRW8OGDTvkvjZs2CBJKisr09133520Te/evUluAQCahAyXQ8f2L9Cx/QskhX7hXFdUHk507dXCjcX6blep7AP4HWRniVc7S7z6bE1RXHlBjkcDwgmvAR1z1LsgW73bZ6trm0ymNwSABuQPWnFrVRWWhqYHjCSvdpV6VRQeaVXmbRrrWGW4TBXkeGJe8Ymq2LL8TFdaprNH8+JymMrPNBt8RHls0qzCFxolFtmv9Aej28pImS+2LJws8yeWR0awHch3rtbOskOzCyiY7kgA1JfFRa7RkdwCUihhWsIU/5JSWFio7du3S2qY5NaMGTM0Y8aMQ+4HAIB0ME1D/TvmqH/HHJ03qockqaTKryWbQ1MSLt26T0u37NOOkqoD7jtyk/WLdbvjyt0OUz3bZ6l3+yz1aJelXu2y1Kt9tnq0y1KPdpnyOJneFwCq/EEVlXnjklaRhFXc+lZlTWeUVX6mSwU5brXP8ahDjURVdHRVeD/bw60YNA+NlTSTQqNfvOH1zLzh9cq8gdD6Zd6YNc+8/si2uqwqUhZbH1ce6a9GWbifqgCJNaClMwxFRzc6jPDWNOQwzery8EhIM7I1DDkdoW1sffXWlMMMjaI0DEX7NqNbRc81DUODOuem+4+hxeMbFZBCNaclTPUTeJEpCaWGSW4BANDS5GW4dPyADjp+QIdoWVGZV8u3lejbbSVasT30Wl9UrsBBTDPhC1pas6tMa3aVJdQZhtQhx6NubTPVrU2murXNVPfItm2WuuRnNMpURgDQ2GzbVoUvqN1lPhWWxSSoSmOTV+GEValXpU1khJXHaapjXigp1TE3Qx3zPOqYG9rvEC4vyPGoXTbTAQIHyjAMZbgcynA5JKX2+41t2/IH7eqEVzhJVhWTQItNnMUl08KJs6qYBFps4iyUoAvKF7TlD1jyBS0Fgpb8wdC6QoGgLX/MsT9Ilg0NyzAkRzhJEzuVpZmQqImpdyQvry3BU3NqzNjy5O9jyOEwa33/2BhdNfqIJIpcDjP+XEd14sppmnHxRBJOaPlIbgEpYoXn3o0VmVc4VSZOnJgQAwAAqFtBjkcnDOygEwZWJ7z8QUsbisq1eleZVu8s0+pdpVq9s0zrisoO+iaFbUu7wlNnLdpUnLRNjsepzvkZ6pKfoU55Geqcl6FO+aFtx1yPOuaFbrS6HNxkBdB4qvxBFVf4VVzp055yn/aW+7Wnwqc9ZT7trQiVRV57K3zaXe6TL9B01u7JcjvUMTe0TlXHvAx1iklcdcrLUKc8jzrkZigvw3nI6xQDaHoMw5DbacjtNJXucRWRNZoCVijpFQja8ltWqCwYKo8kx6yYtoGgpaAdahO3LpRVvWZU7FpUkbWhJEXXiKpeZyqy1lSNc63IulXx61VZMWtbVbcJlStmLaq4Na9iy2PXyYquZVWj/5i1rWxVr7sVywwvyJVsfTGpev0uQzFrhBmxa4NVrxsWu75X7Npgcf2G943wyBxDiiZeIqN4ImuIRRI1jpiRPI7wOmKOGuWRc2KTSZFRQM7wSKHk9bEJofgkFtBakNwCUsRK8nQ3a24AANA8uRymBnTK1YBOudLQ6vJA0NLGPRVavbNMa3aV6rudZVpfVK4NReUNMhKhzBuodeRXrHbZ7uiN2+grJ7Rtnx0aZdAu26222S6mQgRaqciUYPsq/dpX6VdxRWTr075Kv/ZW+EIJrIrQ/t4Kv/aFt5X+prfoi2lI7bJDa1VFrnsdczPCW09cMiuHaQEBNBFGZISNQ+FRbACA+uIbHZAiyRYRTPXILQAA0LicDlP9OuSoX4ccSZ2j5bZta3e5TxuKyrW+qFyb9lRo054Kbdxdoc17KrS73NegcURGTKzcUbrftjkeZzjR5Vb7bLfaZrnVNsulttlutclyqW2WW20yXWqTFTrOz3Qpy+1gNAOQZpZlq8wXUFlVQKVVAZV5/SqpCh2XVPlVWhVQSaVfJVV+lVQGokms0HGozBdsOqOpknE5DLXP9qggt3r9qtAr5jhc1zbLzcODAAAArQjJLSBFki3Lwe9eAAC0DoZhRG/EjurdLqG+tMqvLXsrtXVvpbbsrdDW4srQa29oW1TWsMmvWGXegMq8AW3aU1Hvc1wOQ/mZLuVluJSb6VJehlN5GS7lZUa2LuVmOEMvj0s5GU7leELH2Z7QvsdpkiBDqxIZKVXhC6rCF1CFL6hyb2hb5g0lpcp9oZ/Hcm9A5d6gSqvC++HysqrQtjS8bY48TjOclPKoQ2ySKsetgvDo0g7hhFV+povrBAAAAJIiuQWkSLBGdssMz7ULAGgebNvW+n3rtWjXIn27+1ttKNmg3ZW7VeIrkSlTTtOpdhnt1CWni3rn9dbQgqEa1mGY2me2T3foaAZyM1wa0sWlIV3yktZX+YPasa9K2/dVafu+Su0oqdLOfVXaUVKlHSVeFZZUqbDMm7JFyf1BW0VlvkNKujlMQ9luh3IzXMr2OJTldirb41Cmyxk9znI7lOV2KNPtUJbLoSxPTJnLqUy3Q5kuhzxOU+7Yl8MkeYZ6s21b/qAtbyCoKr+VuPUHVekP7Ye21a9Kf1CVPiu8DSWqKv3BcAIrpswXVIU/mPA7QXNnGFJehkvto1OdutUuK7zNDo38jB0Z2i7brRwP61gBAADg0JHcAlKk5rSELPAIAM3DppJNem31a/p448faVLqpzrbbyrdp2e5lcWWHtT9ME3pM0Cm9TlHfNn0bM1S0YBkuh3oXZKt3QXatbSzLVnGlX7tKq7SrxKvCUq92lXq1q7QqlIgq9aqwzKs95T7trfApyYzJKRW0bJVUBVRS1XijT9yO+IRXZN9To8wTlxRzJCTKIm3ikmgOR1wbl8OQ02HKaYbXzjANOUxTDsOQI3psxB3HLiAeWdS8ObIsO7oAfGTB+qAVWqw+GN4PWrYCliXLkgKWFT62o9tA0Ioe+4OWAsFQe18wXBe05bfC26Alf3jrC1jyBy15w1tfwJIvsg3vewPxx5H92CRWC8s5HZRcj1N5ma7o9KNts2KmJo3ZtolMXZrlVl6mi6kAAQAAkBYkt4AUsWr8xuxopjcvAKC1WFK4RNOXTNdnWz87pH6W716u5buX62+L/6YjOxypswacpe/1+Z4ynZkNFCkQYpqG2oVHRgzuXHfboGVrX6U/ujZX5LW3onpbXOGP2+6r9Kc9IXagfMFQMkPedEdSP4YRGt3vMAwZhsJJr1Diy4xJhhmGZMScYyjxe2Wyr5rJvn0ahiHbtmVLssPJqci+bddIWlmh/aBty44ksJrZ34mWLDISMifDqbwMp3IzQtOD5mdWTxWan+mKe+VlhLa5GU45HWa6PwIAAABQbyS3gBSpOUsQDzgCQNO0p2qPHl74sN5Y/UaD9724cLEWFy7WA18/oAuHXKgLBl+gfE9+g78PsD+OmERYfQUtW2VVAe2r9EdfJVV+lVT6VVoViO6XVAXCW390XaDIGkEtbUq2hmaHE0dB8efUWmS6QtNsZnsi69E5lOOpXpsudj/UxhFa6y7DqZxwAivSjhFUAAAAaE1IbqFJMM3QU4LBYFC2bTfbKVnqwrSE+2fbtoLBoCTJ4XCkORoArU3QCur11a/r4YUPq8RXUmu7jlkddVTHozSo3SB1ye6itp62kiRv0KtdFbu0pWyLvt39rZYVLVNloDJpH8XeYv1t8d/09LKndf7g83XZ0MuU506+1hLQVDhMQ/lZLuVnuQ7qfNu2VeW3VOYNqDyc8Cr3BlTuC6jMG1RFuCyyNlGFN7RWUex+ZC2jyuh+QFV+q4E/KRDiMA15nKYyXQ5luEJrv2W4Yo5jtpluhzwuU1kuZ/U6ce7EteOy3U5leULbTJeD3wkAAACAg0RyC02C2+2Wz+eTbdvyer3KyMhId0gNjmkJ96+iokJ2OAnodtf/SXIAOFTLipbpj1/+Ud/u/jZpfa47V9P6T9NpfU/TYe0Oq9dDGH7Lr4U7F+qTzZ/o/fXva3fV7oQ2FYEKPbXsKb2++nVdOfRKnT/4fLkdXP/QMhmGoczwDf4OuZ4G69ey7Oj0g74kayt5A8E61lyqbV2moLz+2tduCm2DcfWxa0IFGKFWL6YhOU1TTkdo3bHIOmWR9cnczvBaZmb1mmaRhJMrvM6Z2+mQy1Fd5naYctWynlrNddQyXA55YrYel0MZMVum6QMAAACaLpJbaBKys7NVVlYmSSopKWmZya2aI7dIbsWxbVt79uyJHuflMYIBQOMrrirWw4se1uvfvS47yTRgWc4sXT38av1g8A8OeI0sl+nS0V2O1tFdjtbNo27WnC1z9Op3r2re1nkJbfd59+kvC/6iF1a+oJ+P/Lkm9ZrUIkcxA43BNA1lmKERNE2FHV6nKmiF1qUKWJYsSwpYlgLhssjLqrGuVdCyQ9MT1qyzqttEvlbasuPWQat5FbNrfP9MuMrZii7EZSiUgDSkuHW9jPCaXw7TkGEY4XXAFF3/K3KcUGdWn+cwjCRJLIPrHAAAAICDRnILTUJOTo527twpSdq9e7ccDofatGnToqamS1hziwdBJYVuulRUVGjPnj3RBKdhGMrJyUlzZABaMsu29ObqN/XQwodU7C1O2mZy78m6edTN6pTd6ZDfz2W6dHLPk3Vyz5O1as8qPbn0Sf1n439k2fHTqW0t26qbZ9+sY7seq9uPvl298nod8nsDSD3DMOQIJ3ZCWs53WgAAAABoCgy75uN8wEHasmWLevToIUnavHmzunfvfkDnFxUVqbCwMK7M4XC0mCc6q/xB+WMyXJFpUlq7yDprEYZhqFu3bsrNzU1jVABasgU7Fui++fdpxZ4VSev75PfR7UffrmO6HNOocWzYt0GPLHpEH278MGm9y3Tpx0f8WJcPvfyAR40BAAAAAAA0BYeaN6gNyS00mEP9S2rbtrZv3659+/Y1Rnhpt7vMp0p/MHqcl+FUXubBLcjeUqUisWXbtoJ2MDT9mC1ZsmTbdnhan+ptpDxyTm3t4rZJpjSrLYZ6tatnf/VvVv/LfSo+S9L3SFqU5Nxa3re+73NIcSc5NxWfr0l9tnq2S/q+jfDZ6vtnvb18u95e+7YW7lqYtJ9MZ6auGnaVLj7sYrkcqbs+LylcogcWPFBrXN1yuumusXdpbNexKYsJAAAAAACgIZDcQpPXUH9Jq6qqVFxcrIqKCgWDwf2f0Ews2VKsveX+6HG/Dtnq0S4rjRGln61Q0shyWAq4Aio3y1UWKFOpr1SlvlJV+CtUFaySN+hVVSC0jd2vClbJH/QrYAcUtIIK2kEFrIACVkBBO6igFT6OqQ/aLefvFICGM6nXJN06+lZ1zu6clve3bVv/2fgf/eWrv2hX5a6kbab1n6abR92sfE9+iqMDAAAAAAA4OI2V3GLNLTQ5GRkZ6tw5PTcXG9MvP5ynhZuKo8d3T+umkwa03LVU/JZfO8p2aHPpZm0p26KtZVtVVFmk3ZW7VVhZqKLKIu2t2ntAo4kAoKH1ze+rW0ffqnHdxqU1DsMw9L3e39Px3Y7X9CXT9fzy5xWwA3Ft3lzzpuZunatfH/1rTew1MU2RAgAAAAAApB/JLSBFyr3xI4ay3S3jx8+yLW0p3aJVe1dp1Z5VWrV3ldbsXaPt5dsZJQWgyeqY2VGXDb1M5w46Vy6z6UwRm+3K1s2jbtbUflP1hy//kDBVYVFlkW769CZN6jVJtx99uwoyC9IUKQAAAAAAQPq0jLvrQDNQ7ot/Aj/b0zx//IJWUCv3rNSCnQv09c6vtWjXIhV7i9MdFlAnQ0ZimZGkLFm7JGXJi+rZX33fN0m7ZNL22er5Hgdy/qGcW5/P53K4NLRgqE7qeZIm9prYpJJaNfVv219Pf+9pvfbda3rg6wdU7i+Pq/9w44f63/b/6ZbRt2hqv6n1/vMEAAAAAABoCZrn3XWgGSr31kxuOdIUyYGr8Ffoi21f6JPNn2ju1rnaU7Wnwd/DaTqV585TnjtPOa4c5bpzle3KlsfpUYYjQx6HJ24/wxnauh1uOQ2nHKZDTtMZt+8wkm8Nw5ApM7qVEboJHlsuSaZhRsvjjsNlhmHEH9dyYz+ZQ7mxn4r+DqhtvZs1bPKntrZAS2Eaps4bdJ5O6H6C/vDlHzRny5y4+hJfie6Yd4dmrZulu469S91yuqUpUgAAAAAAgNQiuQWkSM1pCXOa+Mgty7b09c6v9daat/Thxg9VGag8qH5yXbnqnttd3XO7q1NWJ7XPbK8OmR1UkFmggswCtc1oqzx3njwOD4kKAEiic3Zn/d9J/6dZ62fp3q/uTRgt+8X2LzTt39N0w1E36PxB58thNp+HJwAAAAAAAA5G0767DrQQvoAlX9CKK2uq0xJW+Cv01pq39PyK57W5dHO9z2uX0U4D2w7UoLaDNKjdIPXJ76MeuT2U584jaQUAh8gwDE3pO0Vju47VvV/dq/fWvxdXXxmojJb/7tjfqV+bfmmKFAAAAAAAoPE1zbvrQAtTUWO9LUnKdjetH78SX4me/fZZvbjyRZX4Svbbvndeb43qPEpHdTxKIzuNVJfsLiSxAKCRtctop/tOuE+n9TlNf/jyD9pVsSuufknhEp37zrm6athV+skRP5HL0XTXFQMAAAAAADhYTevuOtBClXmTJLeayJpbvqBPL658Uf9c+k/t8+6rtZ1pmBrVaZQm9JigE3ucqO653VMYJQAg1ok9TtTITiP14NcP6tXvXo2r81t+/d/i/9MHGz/Q74/9vQ4vODxNUQIAAAAAADQOkltACtRcb0tqGiO3Pt/2uf7wxR+0pWxLrW365ffTmf3P1JS+U9Qhq0MKowMA1CXXnas7x96pyX0m67ef/1abSjfF1X+39zv9cNYPdclhl+jqI69WpjMzTZECAAAAAAA0rPTfXQdagZojt7LcDplm+qbw21u1V3+Z/xe9s+6dWtuc0P0EXXr4pRrVaRTTDQJAEza682i99v3X9Njix/TM8mdk2dVrPFq2pae/fVofb/pYvz32txrdeXQaIwUAAAAAAGgYZroDAFqDmmtuZaVx1Nb8HfN1ztvn1JrYmtRrkt78/pv628l/0+jOo0lsAUAzkOnM1M9H/VwvnPaCBrYdmFC/qXSTfvKfn+jOeXdqT9WeNEQIAAAAAADQcEhuASlQ4YufljAd620FraAeW/yYLv/gcu2q3JVQf2SHI/X8ac/rgRMfUP+2/VMeHwDg0B1ecLheOv0lXT/ierlMV0L9m2ve1BlvnqGXV76soJU4ZS4AAAAAAEBzQHILSIHKGsmtTFdqk1vl/nLd8MkN+vuSv8dNVyVJOa4c3XHMHXpm8jMa3mF4SuMCADQ8l+nSlcOu1GtnvJb0ul7iK9Ef//dHXTDzAn1T+E0aIgQAAAAAADg0JLeAFKj010huuVOX3NpRvkOXvHeJZm+ZnVB3bNdj9e8z/63zBp0n0+ByAAAtSd82ffXM957Rr8b8SlnOrIT6FXtW6MJZF+q3n/+WqQoBAAAAAECzwt1sIAVqTkuYqpFb64rX6cKZF2rV3lVx5Q7DoRuOukGPTXxMHbM6piQWAEDqOUyHLhxyod6Z9o4m95mctM3rq1/XlDem6KllT8kb9KY4QgAAAAAAgANHcgtIgUpfIO44KwUjt1btWaUf/+fHCetrtfG00ROnPKHLh17OaC0AaCU6ZnXUfSfcpydPeVJ98/sm1Jf5y/Tg1w/qjDfP0Mx1MxOmsAUAAAAAAGhKuLMNpEDitITORn2/b3d/q5/85ycJ00z1zuutf532L43qPKpR3x8A0DSN6TJGr53xmm4eebMynZkJ9dvLt+tXc3+lH878oebvmJ+GCAEAAAAAAPaP5BaQAonTEjbej97a4rW66sOrVOIriSsf3mG4nj/tefXM69lo7w0AaPpcDpcuPeJSvX3m25rSd0rSNpGHJH764U+1tHBpiiMEAAAAAACoG8ktIAWqaozcymqkkVvbyrbpyg+v1D7vvrjykZ1G6h+T/qF8T36jvC8AoPnpnN1Z9x5/r16a8pJGdhqZtM28bfP0w1k/1HUfX6flu5enOEIAAAAAAIDkSG4BKZAwcqsR1tzaU7VHV314lXZVxK+xdUyXY/TYxMeU7cpu8PcEADR/hxccrqdPfVqPTHhEvfN6J20ze8ts/eDdH+iG/96gFbtXpDZAAAAAAACAGkhuASmQOC1hwya3/JZfN31ykzaUbIgrH95huB6e8HDSdVUAAIgwDEMTek7QG1Pf0O1H3672Ge2Ttvvv5v/qvHfP05UfXKkvtn0h27ZTHCkAAAAAAADJLSAlEqclbNjk1oNfP6iFuxbGlfVv019/O/lvynJlNeh7AQBaLpfp0gWDL9B7Z7+nX4z6hdpltEva7ovtX+jKD6/UD979gd5f/74CViDFkQIAAAAAgNaM5BaQAo05LeH7G97Xc8ufiyvrkt1F0ydOZ40tAMBByXRm6pLDL9F7Z72nG4+6sdZ/T1bsWaFb5tyiKW9M0ZNLn9Teqr0pjhQAAAAAALRGJLeAFKhspGkJ1xWv053z7owrc5tuPTjhQXXK7tQg7wEAaL2yXFm6bOhlev+s9/WzET+rdSTXtvJtemjhQ5r46kT9+rNfa2nh0hRHCgAAAAAAWhOSW0AKVDbCtITl/nLd+OmNqgxUxpXffvTtOrz94YfcPwAAETnuHF0x7Ap9cM4HuuOYO9Qzt2fSdj7Lp7fXvq0fzvqhzn/3fL2y6hWV+EpSHC0AAAAAAGjpSG4BKVDhi1+LJOMQR27Ztq07592p9fvWx5VP6z9NZw88+5D6BgCgNh6HR+cNOk9vn/m27h9/f50PU3y7+1v94cs/aMLLE3Tr7Fs1b+s8Ba1gre0BAAAAAADqy5nuAIDWoOa0hFnuQ/vRe275c/pg4wdxZUPaDdHtR99+SP0CAFAfDtOhU3qfokm9JmlJ4RK9tOolfbDhA/ktf0Jbn+XTexve03sb3lPHzI6a0neKTu19qg5rf5gMw0hD9AAAAAAAoLkjuQWkQENOS/j1zq/1wNcPxJXlufP0wIkPKMOZcdD9AgBwoAzD0JEdj9SRHY/ULaNu0Ztr3tQrq17R9vLtSdvvqtylp799Wk9/+7S65XTTKb1P0am9SHQBAAAAAIADQ3ILaGT+oCV/0I4rO9hpCQsrCvWL2b9Q0K5Olhky9Kfj/6Tuud0PKU4AAA5F+8z2unzo5br08Es1b+s8/Xvtv/XJ5k8UsAJJ228t26qnlz2tp5eFEl0n9TxJ47uP11Edj5LL4Upx9AAAAAAAoDkhuQU0spqjtqSDG7nlt/z6xexfqKiyKK78quFX6YTuJxx0fAAANCSn6dT4HuM1vsd4FVcVa9b6Wfr32n9r+e7ltZ6ztWyrnlv+nJ5b/pxyXDka23Wsxncfr+O6Haf2me1TGD0AAAAAAGgOSG4BjazmelvSwSW3Hvr6IS3ctTCubFzXcfrpsJ8edGwAADSmNhlt9MMhP9QPh/xQ3+39Tu+tf0//2fAfbS7dXOs5Zf4yfbjxQ3248UMZMjSk/RAd3eVoHd35aI3oOEJZrqwUfgIAAAAAANAUkdwCGlmy5NaBTkv4nw3/0bPLn40r65rdVfcef68c5sGv3wUAQKoMbDtQA9sO1M9G/Ewr96zUfzb8Rx9s/KDORJctW8t3L9fy3cv19LKn5TSdGlYwTGO6jNGYzmN0RMERynRmpvBTAAAAAACApoDkFtDIKmokt0xD8jjNep+/bt863Tnvzrgyl+nSAyc+oDYZbRoiRAAAUsYwQqOxhrQfohuOukEr96zUJ5s/0Zwtc/Tt7m/rPDdgBbRw10It3LVQ05dMl9NwalC7QTqy45Ea3mG4juxwpDpnd5ZhGCn6NAAAAAAAIB1IbrVQmzZt0iOPPKKZM2dq06ZN8ng86t+/v8477zxdc801yspiSp9UqbnmVqbLUe+bbmW+Mt34yY2qCFTEld9+9O06vODwBosRAIB0iE10XXPkNSqsKNRnWz/T7C2z9cW2LxL+/aspYAf07e5v9e3ub/WvFf+SJHXM7KhhHYaF+m0X6rsgsyAVHwcAAAAAAKQIya0WaObMmbrwwgu1b9++aFlFRYXmz5+v+fPn64knntCsWbPUt2/fNEbZetScljDTXb8fO8u2dNtnt2n9vvVx5Wf2P1NnDzi7weIDAKCp6JDVQdMGTNO0AdPkC/q0eNdifbXjK/1v+/+0rGiZAnZgv33sqtyljzZ9pI82fVTdb2YHDW43OJrwGtB2gLrndGdqXwAAAAAAmimSWy3MkiVLdN5556miokI5OTm67bbbNGHCBFVWVuqll17SP//5T61atUpTpkzR/PnzlZOTk+6QW7zYkVvtVKITHdukbQVSl+FSHSO4/rHkH/p086dxZUPaDdGvj/410y0BAFo8t8MdWluryxhdN+I6lfvLtXDnwmiya9XeVbJsq159FVYWqnBroeZunVvdv+lWn/w+6tumr/rl91P/Nv3Vt01f9cjtIafJV+QWzbYlKyhZAcnyh7bBQPg4UhaUgv6YssgrKNnB8NZKPLaDkmXFlMVsI+9bs71thc+JOY572UnKYuoUqVd4P3wcLY89tpNsVUt5jbo4Rvh7rCEZZsx++Dtq3PHBbGu+R23vVdv2EGM45PjrG8N+Po9hSqZTMh2S4Qhva5Y5JTNcFm1TV9vw1uEKn2NWxwsAAAA0I/zm3sLceOONqqiokNPp1AcffKCxY8dG60466SQNGDBAt956q1auXKkHHnhAd955Zx29oSFU+EJPmU8yF+gh19+U7fVKj/9eGnCKdO4MyZ2dcM47a9/R35f8Pa6sjaeNHpzwoDKcGakIGwCAJiXbla3jux+v47sfL0mq8FdoWdEyLS5crCWFS7SkcIn2efftp5dqPsunVXtXadXeVXHlLtOl7rnd1SO3h3rm9gxt83qqZ25PdcnpIpfpatDP1SJYQSlQJQW8MVuvFPRW78ceB30xL3+S/ZiyQEzb2CRTMJyAsmISUMEayalou5oJqv2PAARaFdMVTna5JIcz5tgRs++MaVNXnTOcRKutzhWfXIvr0yk53KGXM7x1uKrLIvuR9k6P5PCE+gUAAECrY9i2XfMxPDRT8+fP15gxYyRJV111laZPn57QxrIsHXHEEVqxYoXatm2rnTt3yuVqmJs0W7ZsUY8ePSRJmzdvVvfu3Ruk3+bupa826W9vfqQP3bcqw/DHVx42VTrv2biiuVvm6mf//Vnc1EumYerxSY/r6C5HpyJkAACaHdu2taFkg5YULtGK3Su0Ys8KrdyzUpWBygZ7D4fhUNecruqR20NdsruEXjmhbefszuqc1VkuRxNKflmW5K8IvXzl4W2F5C8Pbyskf2X4VVFjW6MsUBV6+aukQKQ+vE+yCEA6GY5wosstOTNCiTFnRqjMmVFjP7x11GyTbBu7nxnaujKr+3RlhMpJrgEAANSpsfIGfAtrQd56663o/o9//OOkbUzT1MUXX6zbbrtNe/fu1aeffqpJkyalKMLWqdIf1JWOmYmJLUla/m9p9YfSgND/g483fqxb5tySsKbIL0b9gsQWAAB1MAxDffL7qE9+H53Z/0xJUtAKalPpJq3YHUp0Ld+zXN/t+U57vXsP6j2CdlCbSzdrc+nm5DHIUEFmQXWyK7uzOmR2UPvM9uqQ1UEFGQXqkNVBee68uqcY9ldJVftCL2+p5N0nVZWE90uq932lkrcsvF8WennLQoksX3koiQUALZ0drE7kp4PpTEx+uTJj9rNCiTBXVpK6yH5mYpvYc50x55hmej5nK2DbtmzZCtpBWbYly7Z0oM+DH8gSAoYMmYYpwzDkMBwyZLAEAQ5M7NTFCVMeB2Pqg0na2LWcY9Wjz2AtbWrpM3aq5GSfofogSXmysnqUN3jbGqI/q0aSshrl0bqY6Ydr9rG//VrPr2N65DrrapxvmKFX7LTJ0eNk00Yn6b/m+Yrp16il36Tvmeyz1dFnsmmlk75Hzc9Z488DzRLJrRZk7tzQOhLZ2dkaOXJkre3Gjx8f3f/ss89IbjWy3RU7dWLm/7QvaCrPsmr+8yZ9eJeCfSfoqW+f1v8t/r+E9UMuPuxi/eiwH6UsXgAAWgqH6YgmvE7re1q0fE/VHq0tXqt1xeu0pniN1u1bp7XFa7W7avchvZ8tO7S+V2Whvin6ptZ2LpkqMN3qIIfaW4Y6BINqH/Cpra9Kbb3lauP3qq1lqU3QUhsrKA/zLKSPGTONmllzPSNH6CazYSZf68gwE9sbRpI+wuWGo/ocGTH9xP6iXrMs2c0H1f5L/0GtcxVzE0VS8rW7aqz5ddBb1V1f59phdgPGYB3CuQfQPuHz1Ig/Mr1mXWu5WVb1dJuRG4lILSsQetjAV5qa93N49pMgqyVZFlseSZbF7SdJqDlcB3zjL2AF5A16VRWokjfojb6SHfuCPvksn/xBvwJ2ILoNWIGEMn/QHyq3at9G9iOJKcu2FLSDsu2YhJUsWVa4XLaCVkx5E/j5MRROdBmhxFfCS0nKkrSJJMwiZQ7TIafhjNt3mA45DIecZrg8vO8wHNG6yH5s+9i+arZP7MuUQ6acMmTKlsOWnDLkkOSQLadty5TksG05w9vqlxXeBuWwFT4OvyzJtCPXyNh1KxsgYVOz/qD6tGppX0uMB3NOJGkE4NDUmdiLHNf13bu2JJykfidJZzycvs/WCpDcakFWrFghSerfv7+cztr/1w4ePDjhnPrYsmVLnfXbt2+vd1+tyY6iN/Tj7m0ltVWmZamf36+BPr8G+nzq4Q9oR+VGvfTGFK2u2JZw7ul9T9fNo25OfdAAALRg7TLaqV3ndhrdeXRceXFVsdaXrNfm0s3aVLJJm0o3aXPJZm0q3aQSX0mDvb9flrZbVYp+c3KEXx6XlNsmoX2WZaltONHVJmiFE19B5VmWci1buZYVfeVF9oOWssM3jNLGdFVPEebw1Ni6q9fKcXhqX1snbutKTDbFlSU5jl3bJ/JyxCarYtf9iTmO1PM0J5qbSNIsLjEWiE+CJaxfF7vvT1JWsy4Ys+8Pr3cXaRdIUheIb5f0PSN1sWvtxay/ZwfT/SfbdATDaxhWFdfZzJbkl+Q1DHlNQ1WGEdoPv0LHpryG5DXNhHqvYajKNOUznapyOOQ1HaFjw1SVGW4jhc6XrSrZ8soS/6cOjS07NJMLOYv9Mmw79BUqug0lzKLbcJ3TViiBpsh+JMlmy7RDX8FqJtnMcJ+R9vFlkbaxfVT37Qz3acYk7EyF2jrCsTgTYrfD54T6MsL7odvnoTpDkmlIphGqd5gOGQr1bdqheodsGeHzoudG+wnFZ8bVAy2bXcvLMoyYY1u2HZRlhL9G2dV1liQZkiUjvg8jVBc6jmkf/qGKtM8u3aquqfu4rRLJrRaiqqpKRUVFkrTfOSvbtm2r7OxslZeXa/Pm5NPqJBOZFxMHxq5YHv1JqzRNLfN4tMzjiW+UJLF19oCzdccxd8g00npbCgCAls+2pfJCtdm3RSNKtmpEyQ6ptEgqLZFKK6TSgPaVlWhzsEIbXU5tczq13enQdqdTO8Lb8kacJqrCNFVhmtp6gF/dTdtWTjgBFkl65chUjkxlGk5lmy5lmW5lO9zKcniU5chQljNTWa4sZbtylOXKDm09ucp058qIHSUQ93R/7Cu8jo3Dw9RZQDpERviZDknudEfTcKxgTMLLH0ruBLzhZFjsNlwefVUl2VbVaJusTWTrC60tGPCG1ho8yCSbJanKMOQzEpNMXrM62ZSsvsqs5bzYc2r0Edm3GyVBn/7RTYAk2YahgKQAD6IcEjOcfDMUSrKFkmCRhFlMYi2cvAu1i0mWSTJiknIKtzfCbWqO/zbC7WLbSLFt7fj2NfoxavSjWvuJvIcdLU9Wr3CbZLFK8XnmmjnnuLo6/h7Wu4862sWdE/Ne9e0vchxJzESSMlJskiZUFyqrTthEzrVqnBdJ/kT6qy4zqo+NmHYx58Umh6pjM6LJobhEVOQ8I77c3s95jfNv4IGZGNyuB9MdRAtHcquFKC2tngIhJydnv+0jya2ysrLGDAuSfP4tB/STZhqmrj3yWl0x9Arm2wYAoCHYtlS6Q9qzTireKBVvlvZtCm+3hF5Bb51d5IdfR/h8SetLDSMu2bXN6VChw6lCp6kih0NFDoeKHY6G/2x1sAxDJQ6HShzS1qQt/OFXeei3Syt8WJnY0pChTGemsl3ZynJlKdOZKY/DowxnhjIcGcpwZsjj8MSV16dNhiNU5na4Qy/TLafp5DsQgHimQzLDU+cdANu25bf80envfEFfaPq6oD96HKkLWIG446RtA1Xy+svl9VfKG6iQN1Alb6AytLW88gZ9qgp65bP8qrL88loBea2A/CSEADRRlmFEr1B+vn8BDYpBuI2P5FYLUVVVFd13u/f/hJ4nPHKosjLJ3Yta7G+U1/bt2zVmzJh699cqWJb2ObJk2CX1emJgQNsB+vXRv9bITrWvmQYAAJIIj77S7rXSnrUx23WhpJa/vFHfPte2lev3a6Dfn1jpcEtZ7eXLaqM9mXkq9GSp0OVRkdOpIlMqlKW9tl97LZ+Kg5Uq9per2FcqqwndDLVlqyJQoYpARdLkV0Nzma5ossvlcMltuhMSYLHHsW0i50a2TtMpl+mS03RG1wxxms7ocXQ/vG5IpH1kP1nbaB8xZYy2R3Nn23bcOkWx28g6RrHlQSuooB1UwArErX0UWTMp9pWsLmgFQ2spRepqvuwa5yarCyeeIgmsuERUOGGF9HPYtjy2rYzw1mOFt7Ytt23LKVsuOzRVmys8lZsrPJ2cK7wukys8BZwrvO+qeV54OrjYKeMio0oiI04cMfuRNtGRKZGp5GKmqjNlJ4ziiLW/m5b7rzeiIxqs8LRXQVWPaLDCoxFi921JwfCxbYT2bUlBo7qv2H3LkIIKJS8CRqj/YHQbqguEt7HHVrS8un3i+TXLE/tJ7Dd0XqDG+Yy+AtASWe37pTuEFo/kVguRkZER3ffV8kRxLK839HRyZmb9n3zb33SHSMI09cSPP1NJZYW2b5irbev/ozVdB2tb1WZ9t+G/2uIvUZtgUId7fZps5uvEi16Rw8GPJQAAtQoGQkmrwpXSrpVS0Spp95pQEstXuv/zG4LDI+V0knI6hl5Z7aXsgtA2q72UFdlvFyp350iGIbekzuHX/li2pVJfqfZU7VGxt1h7q/YmbMv8ZSr1larUV6oSX0l0324Bzwj6Lb/8ll/latykZEMyDVMOwyGH4Yjum2Zoa8iIO47WG2bcfs02SevraO8wHNFYDBkyDKPObaSdDMmUud/20XPCNyGj71OjbSTRFz2WWetoPNtO/Pta29/hWssPoI/aRBI7oXUXbNmKP47blxUtk0I/r5YsyVa0XVzdAfabrF3NZFMksVRXAqpmEipZcqpmGVo+p+mMjprNcGbI7XBHjz2mSx7DIY/pVIbhlMcw5ZEpj2EqQ0Zo37blkSGPpAxL8iiSsLKUYdly20FlBIPyWEFlWAF5AgE5o+uphaeQtL37WYctvI2sGWc3nYc9Gl742miEJ0SLrgnplAyzet90Vk85GruOZNxxHfVGzXZ1nGM4QmtiRteldNbos+bLoYS1LBPWvXSE+3XV2o9lKHq9ir6sWrY162vbjyTh7YAsy6rXeQE7EHedrW/bhPNqi3s/7xf59yByHbdsK64MQDOS0SbdEbR43EVvIXJzc6P79ZlqsLw8dKOgPlMY4tC4naYKcnNUMHSyhg6drFMjFT2/lJ46NablbmnbIqnH6CS9AADQClXskXYsrX7t/DaUzAru/0Geg2I4pNwuUl5XKa+LlBve5nSWcsOvnE5SRn74JlTjMQ1T+Z585XvyD+g8y7ZU4a9ISHiV+sNJMG+JKgIVKveXh0Zi+cOvJGUBmxEPByJyA8qvJKP3ACCJDEeGPE6PPKYntHVUv2ITT3Hb8BSv0XMj7WscR/qIPfY4PHKYqZ0it0HYdijBZQVC669ZgXDiywqV20HFJ4mkhKRRXJ3qqKvrvAaoY4RSrUxJpsOUS650h9Kk1Ux4Ba1g9IGISHnQrqUsSeIs9qGMmmUH0nfNBzQiD2dI1Q+cROtiypO1j2sb06a2PurTvmab0H/x7ZM9LCMp7gEdo8Z4ztrqaraLPUzoI/a8er5XQoz17CPhAaQax5EHmSL9xD0MVaMsaRtD8Q9ExZTFPnwVec+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"text/plain": [
"<Figure size 1000x1000 with 5 Axes>"
]
},
"metadata": {
"image/png": {
"height": 833,
"width": 859
}
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 10))\n",
"\n",
"plt.subplot(5, 1 ,1)\n",
"plt.plot(timesteps, T, label='T')\n",
"plt.plot(timesteps, x, label='x')\n",
"plt.legend()\n",
"\n",
"plt.subplot(5, 1, 2)\n",
"plt.plot(timesteps, mu_0, label=r'$\\mu_0$')\n",
"plt.plot(timesteps, mu_1, label=r'$\\mu_1$')\n",
"plt.plot(timesteps, mu_2, label=r'$\\mu_2$')\n",
"plt.legend()\n",
"\n",
"plt.subplot(5, 1, 3) \n",
"plt.plot(timesteps, rho_0, label=r'$\\rho_0$')\n",
"plt.plot(timesteps, rho_1, label=r'$\\rho_1$')\n",
"plt.legend()\n",
"\n",
"\n",
"plt.subplot(5, 1, 4)\n",
"plt.plot(timesteps, a, label='a')\n",
"plt.ylabel('a')\n",
" \n",
"plt.subplot(5, 1, 5)\n",
"plt.plot(timesteps, vfe)\n",
"plt.xlabel('time')\n",
"plt.ylabel('VFE')"
]
},
{
"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": "3.10.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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