{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(ABC_introduction)=\n",
"# Approximate Bayesian Computation\n",
":::{post} May 31, 2022\n",
":tags: SMC, ABC \n",
":category: beginner, explanation\n",
":::"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running on PyMC v4.0.0b6\n"
]
}
],
"source": [
"import arviz as az\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pymc as pm\n",
"\n",
"print(f\"Running on PyMC v{pm.__version__}\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%load_ext watermark\n",
"az.style.use(\"arviz-darkgrid\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sequential Monte Carlo - Approximate Bayesian Computation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Approximate Bayesian Computation methods (also called likelihood free inference methods), are a group of techniques developed for inferring posterior distributions in cases where the likelihood function is intractable or costly to evaluate. This does not mean that the likelihood function is not part of the analysis, it just the we are approximating the likelihood, and hence the name of the ABC methods.\n",
"\n",
"ABC comes useful when modeling complex phenomena in certain fields of study, like systems biology. Such models often contain unobservable random quantities, which make the likelihood function hard to specify, but data can be simulated from the model. \n",
"\n",
"These methods follow a general form:\n",
"\n",
"1- Sample a parameter $\\theta^*$ from a prior/proposal distribution $\\pi(\\theta)$.\n",
"\n",
"2- Simulate a data set $y^*$ using a function that takes $\\theta$ and returns a data set of the same dimensions as the observed data set $y_0$ (simulator).\n",
"\n",
"3- Compare the simulated dataset $y^*$ with the experimental data set $y_0$ using a distance function $d$ and a tolerance threshold $\\epsilon$. \n",
"\n",
"In some cases a distance function is computed between two summary statistics $d(S(y_0), S(y^*))$, avoiding the issue of computing distances for entire datasets.\n",
"\n",
"As a result we obtain a sample of parameters from a distribution $\\pi(\\theta | d(y_0, y^*)) \\leqslant \\epsilon$. \n",
"\n",
"If $\\epsilon$ is sufficiently small this distribution will be a good approximation of the posterior distribution $\\pi(\\theta | y_0)$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Sequential monte carlo](https://docs.pymc.io/notebooks/SMC2_gaussians.html?highlight=smc) ABC is a method that iteratively morphs the prior into a posterior by propagating the sampled parameters through a series of proposal distributions $\\phi(\\theta^{(i)})$, weighting the accepted parameters $\\theta^{(i)}$ like:\n",
"\n",
"$$ w^{(i)} \\propto \\frac{\\pi(\\theta^{(i)})}{\\phi(\\theta^{(i)})} $$\n",
"\n",
"It combines the advantages of traditional SMC, i.e. ability to sample from distributions with multiple peaks, but without the need for evaluating the likelihood function. \n",
"\n",
"\n",
"_(Lintusaari, 2016), (Toni, T., 2008), (Nuñez, Prangle, 2015)_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Old good Gaussian fit\n",
"\n",
"To illustrate how to use ABC within PyMC3 we are going to start with a very simple example estimating the mean and standard deviation of Gaussian data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"data = np.random.normal(loc=0, scale=1, size=1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Clearly under normal circumstances using a Gaussian likelihood will do the job very well. But that would defeat the purpose of this example, the notebook would end here and everything would be very boring. So, instead of that we are going to define a simulator. A very straightforward simulator for normal data is a pseudo random number generator, in real life our simulator will be most likely something fancier."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def normal_sim(rng, a, b, size=1000):\n",
" return rng.normal(a, b, size=size)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Defining an ABC model in PyMC3 is in general, very similar to defining other PyMC3 models. The two important differences are: we need to define a `Simulator` _distribution_ and we need to use `sample_smc` with `kernel=\"ABC\"`. The `Simulator` works as a generic interface to pass the synthetic data generating function (_normal_sim_ in this example), its parameters, the observed data and optionally a distance function and a summary statistics. In the following code we are using the default distance, `gaussian_kernel`, and the `sort` summary_statistic. As the name suggests `sort` sorts the data before computing the distance.\n",
"\n",
"Finally, SMC-ABC offers the option to store the simulated data. This can he handy as simulators can be expensive to evaluate and we may want to use the simulated data for example for posterior predictive checks."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Initializing SMC sampler...\n",
"Sampling 4 chains in 4 jobs\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"
"
],
"text/plain": [
" mean sd hdi_3% hdi_97%\n",
"a 0.001 0.044 -0.078 0.086\n",
"b 0.956 0.038 0.885 1.026"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"az.summary(idata, kind=\"stats\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The posterior predictive check shows that we have an overall good fit, but the synthetic data has heavier tails than the observed one. You may want to decrease the value of epsilon, and see if you can get a tighter fit."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"az.plot_ppc(idata, num_pp_samples=500);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lotka–Volterra\n",
"\n",
"The Lotka-Volterra is well-know biological model describing how the number of individuals of two species change when there is a predator/prey interaction (A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution,Otto and Day, 2007). For example, rabbits and foxes. Given an initial population number for each species, the integration of this ordinary differential equations (ODE) describes curves for the progression of both populations. This ODE's takes four parameters:\n",
"\n",
"* a is the natural growing rate of rabbits, when there's no fox.\n",
"* b is the natural dying rate of rabbits, due to predation.\n",
"* c is the natural dying rate of fox, when there is no rabbit.\n",
"* d is the factor describing how many caught rabbits let create a new fox.\n",
"\n",
"Notice that there is nothing intrinsically especial about SMC-ABC and ODEs. In principle a simulator can be any piece of code able to generate fake data given a set of parameters."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"from scipy.integrate import odeint\n",
"\n",
"# Definition of parameters\n",
"a = 1.0\n",
"b = 0.1\n",
"c = 1.5\n",
"d = 0.75\n",
"\n",
"# initial population of rabbits and foxes\n",
"X0 = [10.0, 5.0]\n",
"# size of data\n",
"size = 100\n",
"# time lapse\n",
"time = 15\n",
"t = np.linspace(0, time, size)\n",
"\n",
"# Lotka - Volterra equation\n",
"def dX_dt(X, t, a, b, c, d):\n",
" \"\"\"Return the growth rate of fox and rabbit populations.\"\"\"\n",
"\n",
" return np.array([a * X[0] - b * X[0] * X[1], -c * X[1] + d * b * X[0] * X[1]])\n",
"\n",
"\n",
"# simulator function\n",
"def competition_model(rng, a, b, size=None):\n",
" return odeint(dX_dt, y0=X0, t=t, rtol=0.01, args=(a, b, c, d))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the simulator function we will obtain a dataset with some noise added, for using it as observed data."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# function for generating noisy data to be used as observed data.\n",
"def add_noise(a, b):\n",
" noise = np.random.normal(size=(size, 2))\n",
" simulated = competition_model(None, a, b) + noise\n",
" return simulated"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ZQ70DXkwbBoD4wsAHACDa5swz3IEup1N+B2GAcGEZIwLWrVs3ZWdnR+WzBwwYoAEDBkTls62OacMAEN/IlwIAiKby9xzXzxIzvBA5BLuAOJAxxOYOdMXLtGHylQHAKWYf+KDNBoDY5GtwxdcgDBBuPDUAcSAepw2zbAcAvJk5XwptNgDEppIS37OIXelWSkpiv1+C6GBmFxDj4nXaMMt2AMCbr4EPs7SFtNkAEJsqm5Vb1rbTviMyCHYBMSzepw2bfdkOANQUKwx80GYDQOBY/g1Ujr9+IIYxbdjcy3YAoCb4G/gov1uvGdBmA0BgWP4NVI6ZXUAMY9qwuZftAEBNqGzgw3XeLPcD2mwACAzLv4HKEewCELOssGwHACLNKgMfgbbZLN0BgDIs/wb8I9gFICbFe74yALCSYNps19Idz2Pl3wMA4kXGEJs70MXyb+AUgl0AYpKVlu0AQLwLps1m6Q4AnMLyb8A3m2EY5slKGiX5+fnRLkJYpaamxtx3qkp6erq6dOmil19+OdpFQQyIxzoEhAv1BzXFFeBydfBiJdBFHQJCE091yN/y71hpD1HzrFJ/UlNTq7yGmV3AL66++mpJ0rvvvhvVcgAAgKqxdAdAPCNlB1A5gl0AAACwHJbuAIhnpOwAKkewyyQSV2XJSEiQM31khXOO7MmylZaquNfoKJQMAADAXNhtF0C8s8pOu8Fgt12EE8EukzASEpS0aqIkeQW8HNmTlbRqok70GhOtormtX79eo0aN0rBhw9S9e3dNmzZNubm5cjgcSk9P1+jRo9W4cWP39a5lgfPnz9e0adO0fPlyHThwQOPGjdOAAQMkSd99953mzp2rjRs3qqCgQA0bNlSfPn105513ql69ehXK8N577+nNN9/Ujh07dMYZZ+iSSy7RXXfd5bO8ubm5+vDDD7Vhwwbt2bNHJ0+eVIsWLXTZZZfp5ptvVq1aZX/+P//8s6699lr369LT093/PWzYMN15553un//1r39p0aJF+uGHHyRJZ599tq699lpdddVVfn9X6enpmjFjhr755hsVFhYqOzs7mF87AADwwNIdAIhN7LaLcCLYZRKuAJdnwMsz0OVrxle0fPPNN5o3b5569eqlG264QVu2bNHixYv13//+V7NmzVKDBg3c1zqdTo0aNUpFRUXq06ePHA6H6tevL0lasWKFHn30USUkJOg3v/mNGjdurLy8PC1cuFCrV6/WzJkzdfrpp7vfa9asWZo2bZrq16+vQYMGqVatWvrss8+Ul5fns5zvvfeeVq5cqc6dO+vCCy/UiRMntGHDBk2ePFnffvutnnzySUlS3bp1NWzYML355puSpD/84Q/u9+jatav7v1988UW98cYbatSokQYOHCibzaZly5bp73//u7777jvdd999Fcrw1Vdfae7cuerWrZsGDx6sPXv2VPv3DgAAWLoDALGK3XYRTuzGKHPtxugKcBl2h2wlzmoFuiK1g4JrtpIkPfLIIxo0aJD73MyZMzV9+nQNHDhQ48ePl1Q2s2v37t3q2bOnnnrqKdWuXdt9fUFBga699lqddtppmjZtms4880z3ucWLF+vPf/6zrrvuOo0dO1aS9NNPP+nGG29U/fr1NXfuXHfA7OjRoxo6dKi2bdtWYTfGXbt2qXHjxrLb7e5jhmHon//8pz744ANNnTpV559/vvtcZQnqN23apOHDh6t169aaMWOGUlJSJEmFhYUaNmyYtm3bpilTpqhz584Vflfjx4/XwIEDg/tlI6qssgsJYEbUHyA01CEgNNQh64vV3XatwCr1J5DdGFnwajLO9JHuQJdhd5hqRpdLq1atKgRvbrnlFqWmpmrx4sVyOp1e50aPHu0V6JKkjz76SEePHtWIESO8Al2SdOmll6pt27ZasmSJ+9jixYtVUlKim266yR3okqTTTjtNGRkZPsvZtGlTr0CXJNlsNv3+97+XJK1duzawL6yy5YuSlJmZ6Q50SVJKSooyMzO9rvGUlpZGoAsAAAAAApQxxOYOdLHbLqqLZYwm48ie7A502UqccmRPNl3Aq1OnTrLZvBuc2rVrq23btsrOztb27dt1zjnnSJKSkpJ07rnnVniPr7/+WlLZksgdO3ZUOF9cXKxDhw7p0KFDOuOMM/Tdd99JknvmlCdfx6SyJZQLFizQkiVLlJeXp2PHjslzIuP+/fsD+r6StGXLFkneyxpdXMdcZfTUsWPHgD8DAAAAAOIdu+0iHAh2mUj5HF2unyWZKuDlb8qga8ZVYWGh17XlA2OSdPjwYUnSwoULK/2sY8eO6YwzznC/p6/P9pzp5WncuHFauXKlzjrrLPXv31+pqamqVauWCgsL9eabb6q4uLjSz/ZUVFSkhIQEv5+fkJDg9b2rKhsAAAAAwBu77SJcCHaZhK9k9L6S1puBvzW8Bw8elCSvZX7+nHbaaZKkV1991T0LrDKu98zPz1fTpk19fq6nb7/9VitXrlR6erqee+45r+WMX3/9tTsZfaCSk5NVWlqq/Pz8CgGsgwcPqrS01P2dAAAAAADBYbddhBM5u0zCVlrqMxm9M32kTvQaI1tpaZRKVtHmzZtVfl+D48ePa8uWLUpKStJZZ51V5Xu4lvd99dVXAX1mmzZtJJUlii/P17GdO3dKknr16lUhb5ev6yXJbrer1M/vuW3btpKkDRs2VDi3ceNGSWX5uQAAAAAAwatst93MobZfdtsFAkOwyySKe432O3PLmT5Sxb1G13CJ/Nu2bZs++OADr2Ovvvqq8vPzdemll8rhcFT5HgMGDFBycrKmTp2qH374ocL548ePu/N6SWVJ6+12u15//XWvmVxHjx7VnDlzKrzelfT+v//9r9fxH374QfPmzfNZptNPP10FBQU6ceJEhXNXXnmlpLJdJ48ePer1+TNnzvS6BgAAAACqY+bsUs2Z5zuoM2eeoZmzzTMJItyG3ZHgd+ZWxhCbht1B+AKBYxkjgtazZ08988wz+uKLL9S6dWtt2bJF2dnZatKkiYYPHx7Qe6Smpurvf/+7HnnkEd12221KT09Xq1atVFxcrF27dmnjxo3q1KmTXnzxRUlSy5YtNXToUE2fPl233nqrLr74Ytntdv3nP//ROeeco23btnm9f4cOHdShQwd99tlnOnDggDp27Kg9e/bo888/V+/evbV06dIKZerWrZtycnI0duxYde7cWQ6HQ506dVLnzp3VpUsXXX/99VqwYIFuvvlm9e3bV4Zh6D//+Y/27NmjG264QV26dAn5dwsAAAAgftntNp9L9jyX+AGoGsEuBO28885TRkaGpk6dqjfffFMOh0OXXHKJRo8erQYNGgT8Pr1799a8efP0yiuvaO3atVqzZo3q1KmjRo0aacCAAbr88su9rh82bJgaNmyoN954Q++++65SU1N1ySWX6M4779Tvfvc7r2vtdruee+45TZ48WdnZ2crJyVGLFi00ZswY9erVy2ewa+jQoTpy5Ii++OILrV+/XqWlpRo2bJh7t8cHHnhAbdu21aJFi/Tuu+9Kks4++2zdeeedGjBgQFC/QwAAAAAoz1eOKl+5rABUzmaUT74Uh/wlXLeq1NTUiHyn9evXa9SoURo2bJjuvPPOsL8/YBaRqkNAPKD+AKGhDgGhiZU65ApwORyS0ykCXagRVqk/qampVV7DolcAAAAAAEwkY4jNHehyONiFEAgWwS4AAACLiecExgAQD+bMM9yBLqdTftt8AL4R7AIAALAYVwLj8p0f17IXu50ZAABgVZ45upZ9mqDMob7bfAD+kaAeAevWrZuys7OjXQwAAOIeCYwBIDb5ast9tfkAKkewCwAAwII8Oz9z5xskMAaAGFBS4nvQwvVzSYkhiXYeqArBLgAAAIvKGGJzB7pIYAwA1jfsDv+ZhsraeNp5IBDk7AIAALAoEhgDAABURLALsCB24QIAkMAYAADAN5YxAhbk2oVL8l6y4tnxAQDELhIYAwAA+EewC7AgduECgPhGAmMAAAD/CHYBFsUuXAAQv0hgDAAA4B85uwALyxhicyclZhcuAAAAAAAIdgGWxi5cAAAAAOIJm3UhEAS7AItiFy4AAAAA8ca1WVf5fo+rf2S3s9oF5OwCLIlduAAgNs2cXSq73Xf+xTnzDJWUGJXm6wIAINaxWRcCQbALsCB24QovOpcAzMI1Wi15D1p4PsQDABDv2KwLVSHYBVgQu3CFF51LAGbBaDUAxB4GViMjY4jNHehisy6UR7ALQNwr37m8/17fS0UBoCYwWh0edC4BmAUDq5Hha7Mu7pVwIdgFACrfuTxA5xJAVDFaHTo6lwDMglm74Vf+9+f6WeKeiTIEuwDgF3QuAZgFo9Who3MJwEyYtRs+bNaFQBDsAoBf0LkEYAaMVocPnUsAZsLAaniwWRcCYcpg1+HDhzVhwgR99dVX2rFjhwoKCpSamqpf/epXuuWWW3TppZfKZvP+4y0sLNTEiRO1ePFi7du3T40aNdKll16qMWPGKCUlJUrfBIBVeHYu77+3vl546SCdSwA1jtHq8KNzCcAsGFgNDzbrQiBMGezKz8/X22+/rfPPP18XX3yxzjjjDB04cEDLli3TPffcoxtuuEF///vf3dcXFRXp1ltvVU5Ojnr37q2rrrpKubm5mjNnjlavXq3XXntNycnJUfxGAMyMziUAs2C0OvzoXAIwA2btAjXLlMGuFi1aaO3atapVy7t4hYWF+sMf/qC33npLQ4YMUZs2bSRJM2bMUE5OjjIzM/Xggw+6r58wYYImTZqkGTNm6J577qnR7wDAOuhcAjALRqvDi84lADNgYBWoeaYMdtntdp/HU1JS1KdPH33//ffatm2b2rRpI8MwtGDBAiUnJ2vUqFFe199999165ZVXtHDhQo0ZM6bC0kcAkOhcAkAsonMJwCwYWAVqnimDXf6cOHFC2dnZstlsOvfccyVJeXl52rt3r/r06VNhqWJSUpK6d++uzz77TNu2bVPr1q2jUGoAAADUNDqXAMyCgVWg5pk62HX48GHNnTtXpaWlOnDggFasWKFdu3Zp9OjR7sDVtm3bJMlvIKtVq1bu6wh2AQAAxAc6lwAAxC/TB7uysrLcPzscDv3pT3/S0KFD3ceOHDkiSX53XHQdd13nS7169ZSQ4P+ByIpSU1OjXQTA0qhDQPVRf4DQUIeA0NRUHZr0cpESEqQRd1fcDO3lqUUqLZVGjWCjNFhLrNyDTB3satGihbZs2aKSkhLt2rVLH330kV544QVt3LhRL774YoUE9tVVUFAQlvcxi9TUVOXn50e7GIBlUYeA6qP+AKGhDgGhqck6VFxclhvw+PHjXkumPXMG5uefqJGyAOFglXtQIAE5Uwe7XOx2u1q0aKG77rpLCQkJeuaZZ/TWW2/p5ptvVt26dSWV7dToi+u46zoAAICaNHN2qez2irmjpLIOUUmJUemSOwCAOfna9MLX5hgAap7lnqz69OkjSVqzZo2kUzm58vLyfF7vyunlug4AAKAm2e02zZhlaM48w+u4q0Nkt9MZAgCryhhiU+bQsna+7yWlBLoAk7BcsGvPnj2SymZ7SWWJ6Rs3bqwNGzaoqKjI69oTJ05o3bp1aty4McEuAAAQFZ4dIVfAi5F/AIgdGUNscjgkp1NyOES7bhIzZ5dWGGhymTPP0MzZpTVcItQkUwa7cnJyfCaUP3TokF544QVJ0kUXXSRJstlsuv7661VUVKRJkyZ5XT916lQVFBTo+uuvl81GgwPzo0EGgNjEyD8AxK458wx3oMvplN/nedQsZlbHN1Pm7Fq0aJEWLlyonj17qlmzZqpTp45+/vln/ec//1FRUZEuu+wyDRw40H19Zmamli5dqhkzZignJ0cdO3ZUbm6uVqxYofbt2yszMzOK3wYInKtBluQ3ySUAwJoyhtg0d77ByD8AxJDyM3VdP0u089FGTrX4Zspg12WXXabCwkJt2rRJa9eu1fHjx1WvXj1169ZNV199ta666iqvmVrJycmaP3++srKy9Mknn2jNmjVq2LChMjIyNHr0aCUns90rrIEGGQBil6+Rf9p1ALAuX8/pvp7nET2e/x6uASf6VfHBZhhG3M+xtMLWmsGwynah8M9143R1iGiQaxZ1CKg+6o9v/kb+ad9RHnUICE1N1iF227WOvpeUugecln3Kv4k/VrkHpaamVnmNKWd2AfGOpS4AEDsY+QeA2FRZIKusXadtNwNmVscnQpqACZHkEgBiR0mJ7xlcrqT1JSW08QAARILngNOyTxMq7I6M2MXMLsBkSHIJALGFkX8AAGoeM6vjG8EuwERokAEAAAAgdJXNrHadZ8ApdhHsAkyEBhkAAAAAQsfM6vhGsAswERpkAAAAAABCQ4J6AAAAAAAAxAyCXQAAAAAAAIgZYVvGePLkSR06dEjFxcV+r2nWrFm4Pg4AAAAAAACoIORg16pVq/Tyyy9r06ZNOnnypN/rbDabvv3221A/DgAAAAAAAPArpGDXsmXLNHr0aJWUlKhevXpq0aKFkpOTw1U2AAAAAAAAICghBbuysrJUWlqqRx55RLfccovsdnu4ygUAAADUiJmzS2W3237Z+djbnHmGSkqMSndMBgAA5hLSXfv7779X586dNWTIEAJdAAAAsCS73aYZswzNmWd4HZ8zz9CMWYbs9opBMAAAYF4hzexKTk5Ww4YNw1UWAAAAoMa5ZnTNmGW4f3YFujKH+p7xBQAAzCukYFevXr20ceNGlZaWKiGBqd0AYhvLXAAgdnkGvObON+R0ikAXAAAWFVKvbOzYsTpx4oSefPJJlZSUhKtMAGBKLHMBgNiWMcQmh0NyOiWHQwS6gDg1c3Zphec9lznzDM2cXVrDJQIQrJBmdr399tu66KKLNH/+fP3nP//RBRdcoDPPPNPntTabTaNGjQrl4wAgqljmAsQ+ZnDGtznzDHegy+ks+5m2HYg/rgFOyTvo7fncB8DcQt6N0WazyTAMbd++Xdu3b/d7LcEuALGAZS5AbKODE7/KD164fpaY4QXEGwY4AesLKdj1xBNPhKscAGAZGUNs7kAXy1yA2EIHJz75+jf29bcAIH4wwAlYW0jBrmuuuSZc5QAAy2CZCxDb6ODEn5IS38FM188lJYYk/v2BeMMAJ2BdJJ0AgCB4jv4v+zRBmUN9J60HYG2BJCongXHsGHZHgt9ObMYQG3nagDjla4ATgDWENLPL0+bNm7Vu3Trt3btXNptNjRo1Uvfu3dWpU6dwfQRgSSQ7jh0scwHiRyAzOMnvBQCxizx+gLWFHOz68ccf9dBDD+mrr76SJBlGWQNgs5U1AJ06ddJTTz2l1q1bh/pRgCXRGYodLHMB4kOgHRzyewFAbGKAE7C+kIJde/fu1W233ab9+/ercePGuvzyy9W8eXNJ0s8//6x///vf+u9//6vbbrtNb7/9tho3bhyWQgNWQmcodlQ2A6/s35F/S8Dqgu3gkN8LAGIPA5yA9dkM11Ssanjsscf0+uuvKyMjQ3/84x+VmJjodd7pdOr555/X7Nmzdcstt+j//u//Qi5wJOTn50e7CGGVmpoac98pFrg6UK4lMXSGzIs6BFSf1etPdZee972k1L3scdmnLE1H9Vm9DgHRRh0Cqs8q9Sc1NbXKa0IKdvXr109JSUn6+OOP/V5jGIauvPJKnThxQkuXLq3uR0WUFf4xg2GVP1Crq06HiM6QNVCHgOqLx/rDYAbCKR7rEBBO1CGg+qxSfwIJdoXU2963b586dOhQ6TU2m00dOnTQvn37QvkowHRcubjK78ri6vTY7bYKx9nNBQBiCzu0AoA1sIMuEF9CytmVkpKi3bt3V3nd7t27lZKSEspHAaYTTC4udnMBgNhDAmMAsA42jQLiS0jBrs6dO2v58uVavny5fvvb3/q8Zvny5dqwYYP69u0bykcBphRIYmI6QwAQm0hgDADWwaZRQHwJKWfXxo0bdeutt8pms2ngwIEaMGCAmjdvLpvNph07duiDDz7Qhx9+KEl65ZVX1Llz53CVO6yssCY1GFZZZxtLKsvFVd1kx4ge6hBQfdQfIDTUISA0VdUh8iwC/lnlHhTxBPWS9N577+kvf/mLjh8/LpvNu5EwDEO1a9fW3/72Nw0aNCiUj4koK/xjBsMqf6Cxghtm7KEOAdVH/QFCQx0CQhNIHWLTKMA3q9yDAgl2hbSMUZIGDx6snj176q233tL69eu1d+9eSVLjxo3VvXt3XXfddWratGmoHwOYErm4AAAAAOvwtWkUz+1A7Ak52CVJZ555pu65555wvBVgGeTiAgAAAKyDgWogfoQl2AXEIxITAwAAANbAQDUQXwh2AdVUWVL5shslN0sAAADADBioBuJLUMGudu3aKSEhQf/617/0q1/9Su3btw/4tTabTd9++23QBQQASImrsmQkJMiZPrLCOUf2ZNlKS1Xca3QUSgYA8IV2GzAXBqqB+BJUsKtZs2ZlL6pV9jISzwNAzTASEpS0aqIkeXWcHNmTlbRqok70GhOtogEAfKDdBgAgeoIKdi1durTSnwEAkeHqKHl2nDw7TL5mDgAAood2GwCA6CFnFwBYhGfHKXH1FNlKnHSYAMDEaLcBIH6xnD26/C9cDsC4ceO0cOHCKq9btGiRxo0bF8pHAQBU1nEy7A7ZSpwy7A46TABgcrTbABCfXMvZHdmTvY67ZvkaCSGFY1CFkH6777zzjtavX1/ldRs2bNC7774bykcBAPTLKNAvHSZbibPCzRMAYC602wAQn5zpI3Wi1xivgBfL2WtOjSxjdDqdstvtNfFRABCzyt8cXT9L4mYJACZEuw0A8Y3l7NET8WCXYRj69ttvlZqaGumPAoCY5WsUyFfyYwC+zZxdKrvd9sv28t7mzDNUUmJUui09IElfT54oJdh13vCK7e3XUyZLpSU6b2TZLou02wAAqaytdwW6WM5ec4IOdg0ZMsTr588//7zCMZeSkhJt375d+/fv1+DBg6tXQgCAbKWlPkeBXD/bSkujUSzAMux2m2bMMiTJK+A1Z56hGbMMZQ6tGAQDKkiwK71oorKnyCvg9fWUyWXHk8e4j9FuAwAk38vZCXhFXtDBrjVr1rj/22azaf/+/dq/f7//D6hVS7/73e/0pz/9qXolBACLicQMksp2auFmCVTNVR89A16egS5f9RXxI9Ads84bPlLZU+QV8PIMdHkGwGi3AQAsZ4+eoINdn332maSy5Yn9+/fXZZdd5jeQ5XA4lJqaKofDEVopAcBCLjw+SWs3JmiORlaYQWJbOVkXdimVNMb/GwCICM+A19z5hpxOEeiCpFM7ZknenQ/PToqLZ8Cr+NkpSk9wVgh0AQCsJdBl6oEOjrh+Zjl79AQd7GrevLn7v0ePHq327dt7HQOAeHd+F7suODZRk1bKHfByBbpGtcvSiS5j5Ix2IYE4lTHE5g50ORwi0AVJvjsfle2Ydd7wkSp+dooSE5wqLnUQ6AKiiJyMCIsAl6kHMzjCcvboCilB/ejR/qdnA0C8ct3ARqks4NV3/ghl/OrlskAXu68AUTVn3qlAl9NZ9jMBL0jB7Zj19ZTJSv8l0JWY4NSGKZMJeAFRQk5GhEOgy9SDGRxhOXt0hXU3xsOHD+vo0aMyDMPn+WbNmoXz4wCgRgUzbdkz4HVnm6lKtPvuNAXzngBCUz5Hl+tniRleKBPIjlnlOz8bXD+Xmw0AoGaUz8l4/70V23sgEIEuUw9mcATRE3Kwa9++fXrxxRf12WefqaCgwO91NptN3377bagfBwBRE8y0ZUmavnWE7iqZokS7U8UlDk3fOkIZ6aG9J4Dq8dXx8ZW0HvGtqh2zfI3y+5oNEAwGPYDQeedkPEBORlRboMvUAxkcQXSFtHh57969+v3vf6+3335bSUlJql+/vgzD0Pnnn68GDRq4Z3h17txZ3bp1C0uBASBanOkjdaLXGCWtmihH9mRJvhNPSqeS0Sfay26AiXanbCsna848o9rvCaD6Skp8j/BnDLEpc6hNJSW+Z6Ujfni2vUfv3VyhbZYklZb4HOU/b/jIsnwupSVBf65r0MPrczzKYySUPa4nrsqqcI3ntYmrsoL+bCCWZAyxuZeok5MR1fX1lMnuQFdigrMsOb0PvgZHYC4hzex6+eWXtXfvXt1zzz0aOXKkxo0bp3fffVdvvPGGJGnt2rX661//KpvNphkzZoSlwAAQTYFMW/ZKRu+xzbArh1f5XRqZCg1EXmXJicvqI52ieBbojlnnjfQ/27a6SxjLf46uGO+zPMwEBipHTkaEKtBl6uXbaNfPErm4zCSkYNfnn3+uFi1aaORI3/+gPXr00KxZs3T55Zdr8uTJuv/++0P5OAAwhaqmLXcrnKwLyyWj98zh9WVh2X8F854AgMiJ9o5ZngEv5+qpSioprlCeYHeMBOKJ51L1+++trxdeOsgSdQQl0GXqgQ6OIPpCCnbt2bNHv/vd79w/J/wyzbq4uFiJiYmSpCZNmqhnz576+OOPCXYBiAlV5XTp1tnQiQT/naZupaUqDvI9AQCRY4Yds04NehT7HfRgJjBQETkZ4U9QORErW6Y+Re5l6tEeHEHgQgp2paSkeO28ePrpp0sqC4K1bNnSfTwxMVF79uwJ5aMAwBQCmbYcbKeJqdAAEH5WS/zuGvSQPVG2kmK/gx7MBAa8VZaT0XWeperxKZjl34EuUzfD4AgCE1Kwq2nTptq5c6f75zZt2kiSli9frltvvVWSdOzYMW3YsEGNGjUK5aMAIOoiMW05Eu9ptQ4eAESClXJceZYp5YrxKvz4cb/3AGYCA97IyQh/WP4d30IKdqWnp2vevHnav3+/GjZsqH79+qlOnTp66qmntGvXLp155pl6//33deDAAd10003hKjMAREUkpi1H4j2t1MEDgEixSicnmEEPZgIDQHBY/h2/Qgp2DRo0SLt379b//vc/NWzYUGeccYb+9re/ady4cZo5c6ZsNpsMw1CbNm3I1wXA8iIxbTkS72mVDh4ARJoVOjmBDnqQFBnxZObsUtntFZcmSmU5ukpKjEpndAGeWP4dn0IKdrVr107PP/+817EBAwaoa9euWr58uQ4fPqzWrVurX79+cjgcIRUUABA4K3TwAKAmmL2TE+igB0mREU/sdpvP5PKeyeiBQLH8Oz6FFOzyp1mzZiEtW9yzZ48+/vhjrVixQj/88IP279+vevXqqWvXrsrMzNT5559f4TWFhYWaOHGiFi9erH379qlRo0a69NJLNWbMGKWkpITydQDAkszewQOAmhArnRySIiOe+NpN0deui0BVWP4dvyIS7ArV/PnzNX36dJ111lnq1auXGjRooG3btmnJkiVasmSJnnvuOV155ZXu64uKinTrrbcqJydHvXv31lVXXaXc3FzNmTNHq1ev1muvvabk5OQofiMAqHmx0sEDgOqikwNYl2fAa+58Q06nCHQhKCz/jm9BBbvWrl0b0of16NEjoOs6deqkV199Vd27d/c6vm7dOmVkZOixxx5T//79lZiYKEmaMWOGcnJylJmZqQcffNB9/YQJEzRp0iTNmDFD99xzT0hlR3wgPwBiBR08APGOTg5gfRlDbO5Al8MhAl0ICsu/41tQwa7bbrtNNlv1G5icnJyArrv00kt9Hu/evbt69uyplStXasuWLfr1r38twzC0YMECJScna9SoUV7X33333XrllVe0cOFCjRkzJqSyIz6QHwCxgA4eANDJAWLBnHmnAl1OZ9nPBLwQKJZ/x7eggl1XX3111ANGtWrV8vr/vLw87d27V3369KmwVDEpKUndu3fXZ599pm3btql169Y1XVxEUCRmYZEfALGADh4A0MkBrK78M7jrZ4kZXogtiauyZCQk+Lw3ObIny1ZaWuk9Db4FFex68sknI1WOgPz8889atWqVGjVqpLS0NEnStm3bJMlvIKtVq1bu6wh2xZZIzcIiPwCsjg4eAACwMl+Dzb4GpYFYYCQk+Fx94blaA8EzZYJ6X5xOp/70pz+puLhYY8eOld1ulyQdOXJEkvzuuOg67rrOl3r16ikhIbbyMKWmpka7CBF3/71S7dpFypp8TLVr19aIu5P18tQizZh1TKNH1tGIu6u/KcH990pz5x9wT5u+/976YSw5rCAe6hAQKdQfIDTUIcS7xMQijR6pCs/zruf/0lIpNdX/sz51CJZyxXiV1K6jpKVPq07tOrL3/aNKlj2v0lUTldDvT0rp+8caLU6s1B9LBLtKS0v1yCOPaO3atbrhhht09dVXh/X9CwoKwvp+0Zaamqr8/PxoF6NG3HiDdPy4TVmTj2nq9GPuWVg33nBC+fkn3NcFu+SxfH6AF146yOhRHImXOsSUaURCvNQfIFKoQ4B0841l/+/5PO9y4w3+z0nUIVhU5zvkOH5MSUufVsnyF2QrcZalJel8h1SDf89WqT+BBORCCnZlZWUFfK3NZquQQD4QhmHo0Ucf1fvvv69Bgwbpscce8zpft25dSVJhYaHP17uOu65D7Alkl5ZgljySHwDxginTAAAAgDk400cqcfUU2UqcMuwO0o+EKORgl81mk2EYPs+7ktkbhlGtYFdpaanGjx+vRYsWacCAAXryyScrLDd05eTKy8vz+R6unF6u6xB7AtmlJdDE8+QHQDzxtUOjr50cAQAAAERmkzQXR/Zkd6DLVuKUI3syz+MhCCnY9cQTT/g8Xlpaql27dmnlypXatGmTbrnlFp133nlBvbdnoOvKK6/U008/7c7T5al169Zq3LixNmzYoKKiIq8dGU+cOKF169apcePGBLtiVDCzsAJJPF9S4nvXRdfPJSWGJIJdiB2eAS/XSBKBLgAAANQ0K6TYiNQmaeUHnF0/S94rMKzwOzKLkIJd11xzTaXnR48eralTp2rKlCm64YYbAn5fz0DX5ZdfrmeeecZnoEsqmz12/fXXa9KkSZo0aZIefPBB97mpU6eqoKBAo0aNcs8yQ+yoziysqpY8VhaFL7uWvyPEHqZMAwAAINqskGIj0BVDwfC1ssLXCgzJGr8js4h4gvq7775b77zzjl544QVNmTIloNdMmjRJixYtUnJyslq3bq2XX365wjX9+/dX+/btJUmZmZlaunSpZsyYoZycHHXs2FG5ublasWKF2rdvr8zMzLB+J5hDdWZhBbLkEYg3TJkGgPCL5FIXAIhFgabYiPbspkBWDAXDVlrqc2WF62dbaWmFY6QhqVqN7MaYlpamL7/8MuDrd+7cKUkqKiryGyBr3ry5O9iVnJys+fPnKysrS5988onWrFmjhg0bKiMjQ6NHj/Za2ojYEewsLBLPAxUFOmUaMCsCCjCrSC11AYBYFkiKDTPMbgpkk7RAVRaY8/U8ThqSwNRIsOunn37SyZMnA77+ySef1JNPPhnUZ9StW1fjxo3TuHHjgi0e4gCJ54GKgpkyDZgVAQWYVSSWugQq2rMeACAUVaXYMMPspmivGCINSdUiGuw6fPiwJk+erJycHPXs2TOSHwVUisTzQEXBTJkGzCqaAQVEh5UCOeFe6hIoM8x6AIDqCiTFRjRnN5lhxRBpSKoWUrDr4osv9nuuqKhIhw4dkmEYql27th544IFQPgoICYnnURkrdZzCKdgp04BZRSuggOiwWiAnnEtdAmWGWQ8AUB3BpNiIxuwmM6wYIg1JYEIKdrlya/l841q11LRpU/Xo0UN33nmnzj333FA+CgAixmodJwAVRSOggOiwWiAnWktdyOkCwGqCTbERjdlN0V4xRBqSwIUU7MrNzQ1XOQAgasrfIHTFeFN3nABUFO3cGahZVgnkRHupCzldAFhJMCk2ojW7KdorhkhDErgaSVAPAGbn2XFyrp6qpJJiU3acAFQU7YACosPsgRyzLHUhpwsAqwg0xUY8z24iDUngwh7sKiwslCSlpKSE+60BIKJOdZyKTdlxAlCRGQIKiA6zB3LMttSFnC4AYgWzmxCIsAS7li1bpldffVUbN25UUVGRJKlOnTrq2rWrbr75ZvXr1y8cHwMAEeXqOMmeKFtJsek6TgAqinZAAdFhhUBONJe6xPOsBwCxj9lNCERIwS7DMDR+/Hi98847Moyy0dPTTz9dhmHoyJEjWrlypb744gsNHjxYTzzxhGw2HjYBmJNnxyDlivEq/PhxOgSABUQ7dwZqHoGcqjHrAQAQ70IKds2dO1eLFi1S48aNNXLkSA0YMMC9fLGwsFAffvihJk+erPfee0/t2rVTRkZGOMoMAGFFxwkArINATtWY9QAAiHc2wzUlqxquvPJK7dq1S++//75atmzp85qffvpJgwYNUtOmTfXRRx9Vu6CRlJ+fH+0ihFVqamrMfScgkhJXZclISHB3ADzrkCN7smylpZV2HEIxc3ap7PaKS7CkslxEJSVGpTNXALMJxz2IeoF4xnMcYllNtO/UIaD6rFJ/UlNTq7wmpJZkx44dSk9P9xvokqSWLVsqPT1dO3bsCOWjACBiinuN9jvS7UwfGbFAlyTZ7TbNmGVozjzvcQdX0m27nSVYiB0zZ5dW+Ft3mTPP0MzZZTNyqBcAEJto3xFPAn3uQWSEtIyxfv36cjgcVV7ncDgCirwBQLzxtWucr93lgFjg6uRI3jskev7Ne56jXgBAbKF9RzwJ9LkHkRFSsKt///764IMPVFBQoHr16vm85tChQ1q9erUGDBgQykcBQFDKL030FOmlicHyfPCbO9+Q0yke+BCTgunkUC8AIDbRviNeENyNrpBydhUWFur2229XSUmJHnroIV144YVe57/88ks988wzstlsmjt3rjt5vdlYYU1qMKyyzhaIJF9J5ys77iladajvJaVyOiWHQ1r2KfmIYE2B1B/Xg57DoSo7OdQLxJuavAdZaWAIsSdS7Tt9IZhNMM890WaV+hPIysGQZnaNHDlSDodD33zzjYYOHap69eqpWbNmkqRdu3bp0KFDkqTzzz9fI0d630RdATAAiARfuykGEuiKljnzDPcDn9NZ9rNZb4JAqDKG2Nyj+Q6H/P6tUy+AyDISEnzuOux5vwQigfYd8STQ5x6EV0jBrjVr1rj/2zAMHTp0yB3g8rRp06YKx2w2/oHhG7twIVw8A16Jq6fIVuI0baDLczqz62eJmyFiUyCdHOoFEHlWGxhCbKB9R7whuBsdIQW7Pvvss3CVA3AjkR/CyZk+0h3oMuwO0z24+1q372t9PxArAunkUC+AmmOVgSHEBtp3xBuCu9ETUrCrefPm4SoH4EYiP4STI3uyO9BlK3HKkT3ZVA/wJSW+/65dP5eUGJKi/zdPXheEQ6CdHKvUCyBWmH1gCLGD9h3xhOBudIUU7AIihV1aEA7ll2K4fpZkmgf5ypbklv29m+NvnrwuCIdAOzlWqRdArDD7wBBiB+074gnB3egKS7Dr4MGDevvtt7V+/Xrt3btXktS4cWN1795d11xzjRo0aBCOj0GcIZEfQuEr54iv3CRWEe1cduR1QTjQyQHMxwoDQwBgRTz3RFfIwa5PPvlE48eP19GjR2UYhvv4t99+q+XLl2vKlCn65z//qUsvvTTUj0KcIZEfQmErLfUZhHH9bCstjUaxqs0MuezI6wIAsSXWBoYQHdEekAMAX0IKdn311Vd64IEHVFpaqksuuUSDBg1SixYtJEk7d+7Ue++9pyVLluiPf/yjXn/9df36178OS6ER+0jkh1BVlj/Kig/uZsllR14XAIgdsTYwhOgww4AcAG/k2w0x2DVt2jSVlJTopZdeqjBzq127drr44ou1ZMkSjR49WtOnT9eECRNCKiziA4n8AN/MkMuOvC4AEDtibWAI0WGWATkAp5BvN8Rg1/r169WlS5dKlyj2799fXbt21bp160L5KMQREvmhMvE+ShHNXHbkdQEAAL6YYUAOwCnk2w0x2HXkyBE1bdq0yuuaNm2qr776KpSPQhwhkR8qE++jFNHKZUdeFwAAUBk2lwLMJd7z7YaUKbBRo0bKzc2t8rrc3Fw1atQolI8CAElljfaJXmOUtGqiHNmTJfkOxMQizyUByz5NUObQshwZc+YZVb84RJXldTnRawx5XQAAiHO+BuQARJczfaQ7/Ui85dsNaWZXnz59tGDBAr344ou69957ZbN5R+8Nw9CLL76oH374Qddff31IBQUAl3gcpYh2LjvyugAAAH/YXAowp3jOtxtSsGvkyJFavHixpk6dqo8++khXXHGFmjdvLpvNph07duijjz7Sjh07dMYZZ2jkyPj4hQKoGfG2KyC57AAAgBlFe0AOgG/xnm83pGDXmWeeqblz52rs2LH67rvvNHXqVPfsLsMoa9jS0tL07LPP6swzzwy9tADwi3gbpSCXHQAAMCMG5ADzId9uiMEuSWrbtq0++OADZWdna/369dq7d68kqXHjxurevbt69uwZciEBwFO8j1IAAACYBQNygPlUlm/XdT7WhRzscklPT1d6eroKCwslSSkpKeF6awBwY5QCMJeZs0tlt/veXn7OPEMlJUalHSEAsSVxVZaMhASf92JH9mTZSksrzQMJILbQJkQH+XZD3I3RZdmyZcrMzFS3bt3Uo0cP9ejRQ127dlVmZqaWLl0ajo9ADJg5u9Tvrixz5hmaOTv2o8sIHbsCAuZit/veFdSVw8VuZ0QfqIxVno8SV2W5d0Euz5E9WYmrsiRJRkKC147JntckrZooI4HgNxBPaBMQLSHN7DIMQ+PHj9c777zjztF1+umnyzAMHTlyRCtXrtQXX3yhwYMH64knnqiwWyPii6tDJHknqfRMaglUhVEKc2P0Lv6UT0J8/72+kxUD8M0qz0euDqvkfb/1nHHtec7zWl+zsgHEB9oEREtIwa65c+dq0aJFaty4sUaOHKkBAwa4ly8WFhbqww8/1OTJk/Xee++pXbt2ysjICEeZYVG+dmWhQwTElkA7Q4gtnu373PkH5HSKdh0IkFUCxsF0WD2vde2cTKcWiF+0CYgGm+GaklUNV155pXbt2qX3339fLVu29HnNTz/9pEGDBqlp06b66KOPql3QSMrPz492EcIqNTXV1N/J9QDncIgOEUzJ7HXI7PxtIMBDTezre0mpnE7J4ZCWfcqyBCAYVnk+ci89+mU35Mra9tNe6uTeOfnovZtruKSIVzzHmRdtgvlZpf6kpqZWeU1IT6I7duxQenq630CXJLVs2VLp6enasWNHKB+FGhbJ/BEZQ2zuBzmHQ6Z8kANQfa78aUmrJuq0lzoR6IoTc+YZ7nbd6ZTfewgA36zyfORMH+kOdBl2h9+23ZE92X2NrcTpN98XgPhAm4CaFlKwq379+nI4HFVe53A4Aoq8wTwimXCYDhEQ+wLtDCE2eC652rSugTKH+r6HAP4Emvw8llnl+SiQDqvnjN6j9252D4DQuQXiE20CoiGknF39+/fXBx98oIKCAtWrV8/nNYcOHdLq1as1YMCAUD4KNSxS+bXKv4frZ8/PBGB9vjpDBLxik697g697CFCZeM/351mP7r+3vl546aAp64+/ZerSqX83X0vXfeX7AhAfaBMQLSEFu+677z5t3LhRt99+ux566CFdeOGFXue//PJLPfPMM2rRooXuv//+kAqKmuedcNjwmT9i5uxS2e2+g19z5hkqKTE07I4E9890iIDYF0hnCLGjpMT3IIjr55ISQxJtOyoXz7t1WeX5KNAOq6201Oe/metnW2n1U2EAsB7aBERLSAnqhwwZouLiYm3atEk2m0316tVTs2bNJEm7du3SoUOHJEnnn3++EhMTvT/YZtPcuXOrX/IwskICtmCEO6lcZQmH/c328nU8mMAYEE1WScxoRv46p/HSaQX1B6EJJvl5rCj/fORZh8z0fJS4KktGQoLPfw9H9mTZSktV3Gt0FEqGYAX6TG7VZ3fuQ0D1WaX+BJImK6SZXWvWrHH/t2EYOnTokDvA5WnTpk0Vjtls0R+hQtV85Y/wvOEFs9yxspth2XX8TQBWx+gdgFA400e6t6WPl3x/Vnk+qiyQFQ//TrHElZtXkt/B6mCuAwAzCinY9dlnn4WrHDChQPNrBbLcEUB8oDMEIBTk+wMiL9DB6kjl8AWAmhBSsKt58+bhKgdMJtj8ERlDbO5Al5m3ywaAWGTVpSaAJ/L9ATUn0MFqBrUBWBVPvvCpsoTDmUNtvyQcPsUq22UD8WDm7FK/dXDOPEMzZ7OUMNa4lpqU/3d3DVzY7cF3Svg7Qk3yl/yc7emByMkYYnM/u1c2WB3odQBgJgS74NOwOxIqveF5zhDwnAW27NMEZQ713ekCUDMiEfiAubkGIjz/3UNdasLfEWpSZfn+TvQaQ74/IAICHaxmUBuAFYW0jBGwynbZQDwhx0Z8CvdSE/6OUJPI9wfUrEBz8wZ6HQCYDcEuhKSy5Y6u82bZRQjmxXbm4UeOjfgU7vyJ/B0B1kQeP1QmlGT0DGoD4UebHRn8xhCSYJY7Av4YCQk+c7K4crgYCfwdVQc5NuJPJJaa8HcEWI9VliEnrsrym4/NkT1ZiauyarhE8SHQ3LzB5vAFUD1WabOthpldAKLONaPLc9ctX8mKERxfgQ8CFbErUktN+DsCrMcqy5Bdg12S93JVz2cAhF9lg9Flfxu2oK4DEBqrtNlWQ7ALgCl4BrwSV0+RrcRJoCsE5NiIL5FaasLfEWBdVliGzGBX+LAMCrA2K7TZVkOwC4BpONNHugNdht3BQ241RSLwwUO0uUUifyK5WgDrC3cev0hgsCs8XMugJP8J5gGYmxXabCsh2AUgYoJNPO/InuwOdNlKnHJkT+ZhtxoiEfjgIdrcIrHUhA1IAOuzyjJkBrtCxzIowPqs0mZbBcEuABETTC6O8ssWXD+Xfy2qFonARzQfotmtMzrI1QKYS7AzbK20DJnBrvBgGRRqEs9n4WWlNtsqCHYBiJhAc3H4OubrtYiuaD1Ek8AYAIKbYWulZcgMdoUXy6BQU3g+Cx8rtdlWQrALQEQFkovDVlrqMz+H62dbaWnNFRiVisZDNAmMASC4GbZWWYbMYFf4sQwKNYXns/CxSpttNTbDMIxoFyLa8vPzo12EsEpNTY257wTrO+2lTu4lCkfv3Rzt4lSKOuSfq2Pleoiu7syu6kx9dz1AuZa58CBlTtQfIDRV1aFwtcNmwDKo8PK3DMrKfyPVwX2oZvF8FlusUn9SU1OrvIatswBEnK9cHLAez4fmZZ8mKHNo2ZKaOfOCHzNxTX0v/7fgfmBKqHh7cqaPdP8NkcAYQLzKGGJzB7qsvkytuNdov225M30kga4g+FsGFcq9GggEz2cwK5YxxoBgE5YCNYlcHLEh3LkEqjP1nQTGoeN+gZrGzJ3wY5kafGEZFKKF5zOYFcGuGBBMwlKgJpGLI3ZE4iE6kHxuLvEaNA13cIr7BWoaCYzDi926YkMkBh7YQRfREK/PZ7AG0wa73nvvPa1fv15ff/21tm7dKqfTqSeeeELXXnutz+sLCws1ceJELV68WPv27VOjRo106aWXasyYMUpJSanh0tes8rMr7r/X9ywMRvRR00g8Hzsi9RDtTB/pDnT5m/oez0HTcAengklwDYQDCYzDh926YkcwbTvP7zCreH4+gzWYNtj10ksvaefOnUpNTVXjxo21c+dOv9cWFRXp1ltvVU5Ojnr37q2rrrpKubm5mjNnjlavXq3XXntNycnJNVj6muf5sDN3/gGfCUsZ0UdNq2xpCjc/SIFNfY/noGkkglPe9wvD8gmuER3BLE8MZhYn/GOZWuwIpm3n+R1mFc/PZ9FEADxwpg12/eMf/1CrVq3UvHlzTZs2Tc8995zfa2fMmKGcnBxlZmbqwQcfdB+fMGGCJk2apBkzZuiee+6piWJHVcYQm7vj4ithKSP6AMwk0Knv8R40jURwqqr7BVCVYJcnBjKLE5VjmVpsCbRt5/kdZhXvz2fRQgA8cKYN+fXq1UvNmzev8jrDMLRgwQIlJydr1KhRXufuvvtu1atXTwsXLpRhxP4OJL4SlpbnuStL30tKuVECiAp/U99P9Brjc5fGeBfu3dcCuV8AlfFVXytbnsiuvEBFgbbtPL8DcPG1yyoBcN9MG+wKVF5envbu3auuXbtWWKqYlJSk7t27a8+ePdq2bVuUSlgzPP/AN61rUOk2w7G0ZTUAa6ps6vuJXmOY+l5OOINTnveLZZ8msC09qs0z4HXaS50qDXS5zh29dzNBbeAXwbTtPL+jJiSuyvLbNjuyJytxVVYNlwi+EAAPjOWDXa4gVuvWrX2eb9Wqldd1schfwlJ/HRhG9AFEW3Gv0X6nuDvTR1Y6NT7ehDM4Fez9AqiKM32ke7aWr+WJzOIEfAu2bef5HTXBtUS9fNvsasuNBMuHD2IGAfCqmTZnV6COHDkiSX53XHQdd13nS7169ZRg4YqbmFik0SOlEXefmtmWmpqq+++VatcuUmmplJpadu7lqUWaMeuYRo+soxF3J+vlqUXKmnxMtWvX9no9EO9SU1OjXQTEqEkvFykhQT7b3JenlrXZo0b4brMludv26rTdvu4Xnu/peb8IBfUnfpQse16lJU7JnihbSbFO3zRb9r5/PHU+KVHq9yeleByTJF0xXiW166iOUaIU/l4qoA7FtmDbdp7fg0cdqqZf2uakpU+rTu06svf9Y1k7v2qiEny15Yial6cWyek85g54vfFWUtjag1ipP5YPdoVDQUFBtIsQkptvLPv//PwTksr+OPPz8yVJN95w6pznCNKNN5xQfv4J3XiDdPy4TVmTj+n48eNEhAF51yFEn1V2nQl0d7ri4rK2uHyb69lGu9rzo0dLvdpsF1fbffToMa/jVSl/v/Dkeb8IBfUnfvjcZGLp0zp2/NipetAls+z/ff1NdL7D/7k4Rh2KfcG07Ty/B486FKLOd8hx/JiSlj6tkuUvnNpBt/MdtNcmUX6m/px5RoX2oLrPz1apP4EE5Cwf7Kpbt64kqbCw0Od513HXdfGMLasBeLJKEMkqu84EujtdMDtrsfsazMrf8kRJPusBzMkq94FYE0zbzvM7ooEddM3LX0oKyfvZ0irPz5Fk+WCXKydXXl6ez/OuXF2u6+IZnSYAnqxyEww0OBTozKpgBPOevjr6/nanC3TLecCsKttkwnUe5meV+0A84/kd0eBrB10CXuYQaAA8mMHVWGX5YFfr1q3VuHFjbdiwQUVFRV47Mp44cULr1q1T48aNCXYBQDmRuAlGapZAIMGhQGdWSYEHsYJ5T89rklZNdI+I+goIuL6T67uQWBRWU1ngmA6RdcRaZygSgx5AvPG5RJ0Zu6YRTAA83gdXLT8v2Waz6frrr1dRUZEmTZrkdW7q1KkqKCjQ9ddfL5stPv5BASAY4d662DVLwNcusDNmGbLbq98WV7XrjK8d3vzNrAp0t6Fg3tOzHJXtTuf5O2FnLQDRFktb2LOTHBAadtCNPfG8a6NpZ3YtWLBA69evlyRt3brVfWzNmjWSpP79+6t///6SpMzMTC1dulQzZsxQTk6OOnbsqNzcXK1YsULt27dXZmZmdL4EAFhAOGcYBTpLoDozwHwFh3wFvKSqZ1ZNyRmunslSuo8lh9nJY7Q6Z7iGpQf3ni6BTP33lVjU11IiAKgJsTLTNJjl5AAqYol67Ank+TlWmTbYtX79er3zzjtexzZs2KANGzZIkpo3b+4OdiUnJ2v+/PnKysrSJ598ojVr1qhhw4bKyMjQ6NGjvZY2AgC8hfsmGMiU6WDzxAQTHAokqardbtPwN4Zryo1lAS/X9dnJYzT8jeEVPj/QRK2BTP0PNLEoANSUWOoMBTtAEU4k/IfVsUQ9tsT74Kppg11PPvmknnzyyYCvr1u3rsaNG6dx48ZFsFQAEFsidROsapZAMHligg0OBTKzynX98FnDtX7QFNlLnCqRwx3oKl/eQN4z0N3p2FkLgJlYoTMUbBApkAGKSASmSPgPwCwYXDVxsAuAOZH8NXZE8iYYyCyBQJNmBhMcCiapasYQm7oXvSx7kVPFpQ4lJjg15cYpOm/Iqetmzi5VzxNTlF5U8T03bpJWJw13d4YCnfrPzloAzMIqnaELj0/S2o0JmqORFYJItpWTdWGXUkmnNgwJZIAiEoGpWEv4D8C6GFwl2AUgSMHuTgfzitRNMJhZAoHkiQk0OBTozCoXR/ZkpRdN1JStozUld4SGt3tZw9Mm6kT2qetcga7s5DE6z+M9N26S0osm/vJOZceZ+g/AaqzSGTq/i10XHJuoSSvlDni5Al2j2mXpRJcxcv5ybaCDHpEKTMX77mcAzIHBVYJdAIJE8tfYEYmbYLCzBMKZJyaYpKqeyein5A6XwyFNyR2hzp1tXknru3YqVfbmX/J4JRunOkO/5Pvq2qlUxb+8J7laAFiNVTpDrnZ8lMoCXn3nj1DGr14uC3R5tPvBDnpEKjAVKwn/AcDKCHYBCFo0k7/C3IKZJRDuPDHBzKyylZZ6JaN3ff7wWb8EsX4JjBX3Gq3zekmZyUaFztB5Q0a6A10SuVoAIJI8A153tpmqRHvFZ4/q7CQXicBULCX8BwCrItgFoFoC3Z0O8SXQWQLRzhMz7ftRmvGG788fPmu4MpNtyujlXfaqOkPkagGAyJq+dYTuKpmiRLtTxSUOTd86Qhnpp84HM+jhykE6feuICoGpO9NernYOUisk/AeAeECwC0C1BJL8FfAn2nligv38QEfpydUCAJHhytGV2K7s2SNRTtlWTq6QtD5QrhyktlxDmUO984Al7c+qVg7SaA/kAABOIdgFIGjB7HgH+BLtPDHBfH6wo/TkagGA8PJKRu/x7OHK4VWdgNf0rSNkyzXK3jPNJqdG6s60l5W0P0uTckfLaOg9aywQ0R7IAQCcQrALQFCCTf4KWFl1RunJ1QIA4dWtcLIuLJeM3jOH15eFZf8VjJISQ/Y+I3UizVYhB6nRcES1AlPRHsgBAJxCsAtAUKqT/BWwquosdyRXC4BYFM0dZ7t1NnQiwf+zR7fSUq8NQwLhKqtTFXOQls3oKvue7LQLANZEsAtAUIJJ/gpYXSjLHU9dQ64WANYXzR1nI/nsUVUOUnbahVm5NlnwVQcc2ZOrvckCECsIdgEAEAbkagEQyyKx42y0Z00FkoOUnXZhVq5NFiTvoK/n37ULgTHEI4JdACRxE4T1RbvTRK4WALEu3DvORnPWVDA5SNlpF2bk6+/V19+1FFxgDIgVBLsASOImCOtjqQkARF44d5yN5qypYHOQhvN7BzPAyGAkKuMZ8PLcZMHf33UggTEgVhDsAiCJmyCszypLTei4ALCycO84G61ZU8HmAQvn9w5mgJHBSFTFmV5xkwV/10lVB8aAWEGwC4AbN0FYnRWWmtBxAWBVkdpxNpyzpiIh3N87mAFGBiNRlao2WfAUaGAMiAUEuwB44SYIqzN7p4mOCwArCnTH2erkTwz3bLFwitROu8EMMDIYCX8C2WSh/PWBBsYAq4tcpl4AluTrJghYia9Ok9k400fqRK8xSlo1Uae91IlAFwDTq2zH2cyhtl92nD2VP7F82+sKGtntNp/HM4fatOzTBGUO9f36QMycXer3dXPmGZo5u9TnucoE+r2rw5k+0v28VdUAYzDXIj7422TB9XxR/hne8/qj9272ex0QK5jZBcAt2NEhwGwitcQmEphFCcBKAt1xNpj8ieGeNRWJjUoiudNuMLNsmJGD8oLZZCGY3UeBWEGwC4hhwSTC5iYIq4vUUpNIoeMCX9jAALEg0PyJlc2acp0PJphklY1KpOAGGBmMhC/BbLIQ7O6jQCwg2AXEsGASYXMThNWFu9MUSXRc4A8bGCBWBJI/MRKzpqywUUkwA4wMRiIcgt19FIgFBLuAGBZMImxugrC6SC41CSc6LqgMGxggVkQz6Xw4NyqJxGzLYAYYGYwEgOoh2AXEOHbwAcyFjguqQrsNq4t2/sRwBtoiMdsymAFGBiMBoHoIdsWRYEamyBkSW0iEDZgHHRcEIhrtNvd+hEO08yeGO9BmldmW1F8A8OZ/zQdijmtkyt82tEZCQrWuhfn5SoQNwPwSV2X5ra+O7MlKXJVVwyWqGfH6vT1Fo93m3o9wqCx/YuZQ2y/5EyPDX6Atc2jZLo1z5lXvs53pI3Wi1xglrZqo017q5DfQFc22i/oLAN6Y2RVHghmZssooFqpGImzAuuI1WXm8fm+XaLXb3PsRDtHMnxjJjUoCmW0ZzbaL+gsA3gh2xZlg8oCQMyQ8ojmtnETYgLXFa+clXr+3FP12m3s/rCySgTZfsy395V6MVttF/QWAUwh2xaFg8oCQ68m/QINY0RzlIxE2YH3x2nmJ1+9thnabez/gLZjZltFuu6i/AFCGxdtxKJg8IOR68i/Q3AieeR5c19bUKF9xr9F+39+ZPpJEpYBFONNHutths3VeIpmjxszfO1ICbbcj+Xvn3g+c4m+2ZflnO0/RbLuovwBQhmBXnPG8YR+9d3OlN+pgro0VwXQeggliBZrYFAB8MXPnJZJJkc38vaMtUr/3eLz3A5WpbLbliV5jfM62jFbbRf0FgFNYxhhHgskDEu2cIdES7JLDYHOgMa0cQLDMvslE+XuDrhgfltmrZv/e0RaJ3EDxeu8HKlPZLHh/qSyi0XZRf2NHNPP9ArGEYFccCSYPiBlyhkRDdToPgQaxAklsCgCerNJ58SyTc/VUJZUUhzXQVf4zPH+OZ+HODRSv934gXKLZdsVz/Y214FC870gMhAvBrjgSzMhUsKNYsSTYzkMgQSxmKACoDit1Xk4F/ov9Bv4D7ZBE83tbrdMUzlnD8XzvB8Ihmm1XPNffWAsORXtXTyBWEOwCfAhmtlZVQSxmKACoLit1XlyBf9kTZSsp9hn4D7RDEs3vbbVOUyADLlYL4AFWZaU2O5ZEajl9NEV7V08gFhDsAnyozmwtyXcQy0ozMwBYU7SDGZ7tYcoV41X48eM+A0ZWGK22QhldAp01bLUAHgAEK9zL6cN9X63O+5HvFwgNwS6gnEA7D4EGsRjlAxBp0QxmBDt71Qqj1VYoYzC/dysF8ACgugJZTh+ocN9Xq/N+5PsFQkOwCyGJ9myCcAum80AQC4BZBBrMiESbXZ3Zq1YYrTZ7GYP9vVshgAfAXKz2nB/IcvpAhXuQINj3I98vEDqCXQhJJGYTRPPGypJDAFYVSDAjEm12dQL/VhitNnsZq/N7N3sAD4C5RPM5P9j+QKDL6YMR7kGCQN+PfL9AeBDsQkgisTQimstxmK0FwMqqCmaYYTlbtEarg+k4xeqIutkDeADMJRKzhgN9zg+mPxDJ4FC4BwkCeT8G34HwINiFkEVy1MP1M7lFAKBqgQQzormcLZqj1YF2nGJ1RD1WA3gAghdMcCrcs4YDfc4Ppj8QyeBQuAcJAnk/Bt+B8CDYhbCIxKiHRG4RAAhUMMGMaC1ni+ZodaAdp1gcUY/VAB6A6gl2FUW4Zw0H+pwf6HWRCg6Fe5CAQQegZhHsQlhEYmlEODtjVkmwaZVyAjCXYIMZgbTZkWiPoj1aHUjHKdpljIRYDOABqL5gg1ORmDUc6HN+tAZnwj1IwKADUPMSol0AWJ9n43303s060WuMklZNlCN7csjvW/7GWl2uEazy7+Equ5FgjqoQaDkTV2X5/X04sicrcVVWxMsKwDwqC2ac6DXGK5gRaJttlXYzWM70ke77SrwkaS/uNbrSjiSDKED8cd0fklZN1GkvdQpoV8CqnvODaV8Dfc4PZ38gGMHcV6PxfgCqxswuhCRSoxThnuZrlTxggZYzmkn8AZhPoLORgmmzrdJuBosk7QBQpqpZU5GYNezrff0950dz2V+4Z/nG4qxhwOwIdiEkwSyNCHRJTKA31mCX2FglD1gg5YzVTiiAyAp2OZtV2s1AhbvjFOh9iCXqAMyoquBUMPeM6gawPM9XJ2k9APhDsAshCWaUItDZSIHeWKszuyla6/6DFUg5Y60TCiDyqjOybJV2syqR6DgFeh9iNi4AswkkOBWJWcOBPueTaxBAqAh2ocYEOmoT6I21OrObrLJ8JdByxkonFIB5WaXdrEokOk6hzEZgNi6AaAl38D+Y9jXQ53yrLPtj5i5gXgS7UKPCPRspmPezyna/wZQzVjqhAMzJKu1mICLVcQr0PsRsXABmEe7gv1UCU5HAzF3AvAh2ocaFezZSIO9nlXX/wZQzljqhAMzHKu2mGQR6X2M2LgAziOfgVLgxcxcwL4JdqHHhno0UyPtZZd1/oOWkEwog0qzSbppBMDuQMRsXAGILM3cBcyLYhRoV7tlIgb6fVUawAi0nnVAAkWaVdjPaqrsDGbNxAaBmRTK/FjN3AfMh2BUDrJIYMdyzkeJ5dhOdUAAoE817YCjJ6OPlfgUAZhHJ/FrM3AXMh2BXDLBKYsRwz0ZidhMAIJr3wEDvQ9yvACD6IpVfi5m7gDnZDMMwol2IaMvPz492EULm2cimXDFehR8/TmJEoJpSU1Njol0AoiEa9cdfR4N7IKyIexAQmqrqkOse4ZqFFc5AV1XHAbOzyj0oNTW1ymuY2RUjPEcqnKunKqmkmMYVABAXSA4MAAhUOPNrMXMXMK+EaBcA4eNMHynD7pBKikmMCACIK657IMmBAQCV8ZVfq7qKe432e79xpo80Rd5kIF4R7IohroZb9sSQG24AAKwknJ0XAEBs8lxeePTezTrRa4ySVk3kngHEIJYxxgh/ObskEiMCAGIbyYEBAFVhZ1wgvhDsigE03ACAeMU9EAAQCPJrAfElpoJdmzdv1sSJE7Vp0yY5nU6de+65uv322zVw4MBoFy2iaLgBAPGKeyAAIBCV5c9iUASIPTET7Fq9erWGDRsmh8Ohq666SnXr1tXixYs1duxY7dy5U8OHD492ESOGhhsAEK+4BwIAAKC8mAh2nTx5Uo8++qhsNpteffVVdejQQZI0atQo3XjjjZo4caIuv/xytW7dOroFBQAAAAAAQETFxG6M2dnZ2r59uwYMGOAOdElSSkqKRo4cqZMnT2rRokVRLCEAAAAAAABqQkwEu9asWSNJ6tOnT4VzvXv39roGAAAAAAAAsSsmgl15eXmSpFatWlU4V69ePaWmpmrbtm01XCoAAAAAAADUtJjI2VVYWChJqlu3rs/zKSkp2r17t9/X16tXTwkJMRH3c0tNTY12EQBLow4B1Uf9AUJDHQJCQx0Cqi9W6k9MBLtCVVBQEO0ihFVqaqry8/OjXQzAsqhDQPVRf4DQUIeA0FCHgOqzSv0JJCAXE9OZUlJSJElHjhzxeb6wsNDvrC8AAAAAAADEjpgIdrVu3VqSfOblKigoUH5+vs98XgAAAAAAAIgtMRHs6tGjhyRp5cqVFc598cUXkqQLLrigRssEAAAAAACAmmczDMOIdiFCdfLkSV1++eXas2eP3nrrLbVv315S2fLFG2+8UT/++KM+/PBD/epXv4pySQEAAAAAABBJMRHskqTs7GxlZmbK4XBowIABSklJ0eLFi7Vjxw7dd999GjFiRLSLCAAAAAAAgAiLmWCXJG3evFkTJkzQpk2b5HQ6de655+r222/XoEGDol00AAAAAAAA1ICYCnYBAAAAAAAgvsVEgnoAAAAAAABAItgFAAAAAACAGFIr2gVAeGzevFkTJ06skK9s4MCB0S4aYAp79uzRxx9/rBUrVuiHH37Q/v37Va9ePXXt2lWZmZk6//zzK7ymsLBQEydO1OLFi7Vv3z41atRIl156qcaMGaOUlJQofAvAPKZPn65nn31WkvTmm2+qc+fOFa6hDgEVffrpp3rttdf07bff6tixY2rYsKE6d+6sBx98UE2bNnVfR/0BvBmGoU8//VTz58/Xjz/+qCNHjujMM89Uz549deedd6ply5Ze11OHEI/ee+89rV+/Xl9//bW2bt0qp9OpJ554Qtdee63P66tTTz744APNnTtX33//vRwOhzp37qx77rlHv/71ryP51YJGzq4YsHr1ag0bNkwOh0NXXXWV6tat696J8v7779fw4cOjXUQg6p599llNnz5dZ511lnr06KEGDRpo27ZtWrJkiQzD0HPPPacrr7zSfX1RUZFuvvlm5eTkqHfv3urQoYNyc3P1+eefq3379nrttdeUnJwcxW8ERM///vc/XX311apVq5aKiop8BruoQ4A3wzD0l7/8RW+++abOOuss9enTR6eddpr27t2rtWvX6plnnlH37t0lUX8AX5588knNnj1bjRo10sUXX6yUlBTl5ubqiy++UHJyst544w2lpaVJog4hfvXr1087d+5UamqqkpOTtXPnTr/BrurUkylTpuiFF15Qs2bNdNlll6moqEj/+te/dOLECc2cOVM9e/asqa9aNQOW5nQ6jf79+xvnnXee8c0337iPHzlyxLjqqquMDh06GD/++GP0CgiYxCeffGKsXbu2wvG1a9caHTt2NC644ALjxIkT7uMvvfSSkZaWZjz99NNe17uOv/TSSxEvM2BGJ0+eNH7/+98b1113nTF27FgjLS3N2LhxY4XrqEOAt7lz5xppaWnGY489Zpw8ebLCeafT6f5v6g/gbe/evUa7du2Mvn37GkeOHPE6N3v2bCMtLc14+OGH3ceoQ4hXX3zxhbFjxw7DMAxj6tSpRlpamvH222/7vDbYevLjjz8aHTp0MC699FLj8OHD7uNbt241zj//fKN///5e97JoI2eXxWVnZ2v79u0aMGCAOnTo4D6ekpKikSNH6uTJk1q0aFEUSwiYw6WXXuoeMffUvXt39ezZU4cOHdKWLVsklY2+L1iwQMnJyRo1apTX9Xfffbfq1aunhQsXymBiLOLQ9OnTlZubq3/+85+y2+0+r6EOAd6OHz+uSZMmqWXLlnrkkUd81p1atcqyi1B/gIp27typ0tJSde3atcLSqt/97neSpIMHD0qiDiG+9erVS82bN6/yuurUk0WLFunkyZMaMWKE6tat6z7epk0bDR48WNu3b1d2dnb4vkyICHZZ3Jo1ayRJffr0qXCud+/eXtcA8M3VwXD9f15envbu3auuXbtWmLqblJSk7t27a8+ePdq2bVuNlxWIpq1btyorK0sjRoxQmzZt/F5HHQK8ffHFFzp06JD69++v0tJSLV68WNOmTdPrr79eoR5Qf4CKWrVqJYfDoQ0bNqiwsNDr3PLlyyVJ6enpkqhDQCCqU09ccQVXnMHTb37zG0nS2rVrI1jq4JCg3uLy8vIkld0AyqtXr55SU1NpyIFK/Pzzz1q1apUaNWrkzvPgqjOtW7f2+RpXfdu2bZvfa4BYc/LkST388MM655xzdNddd1V6LXUI8Pb1119Lkux2uwYNGqQff/zRfS4hIUEZGRl66KGHJFF/AF9SU1N1//336+mnn9aVV16pfv366bTTTtPWrVv15Zdf6g9/+INuvfVWSdQhIBDVqSd5eXlKTk5Wo0aN/F7vik+YAcEui3ONbHhOI/SUkpKi3bt312SRAMtwOp3605/+pOLiYo0dO9a9rOTIkSOS5HcHEtdx13VAPJgyZYq2bNmit956Sw6Ho9JrqUOAtwMHDkiSZs+erQ4dOmjBggU655xzlJOTo//7v//TrFmz1LJlS918883UH8CPYcOGqXHjxvrzn/+s119/3X28S5cuGjRokPveRB0CqladelJYWKj69etXen35mZfRxDJGAHGptLRUjzzyiNauXasbbrhBV199dbSLBJhWbm6upkyZoqFDh6pjx47RLg5gOa6cJw6HQ5MmTVKnTp102mmnqXv37powYYISEhI0e/bsKJcSMLfJkydr3Lhxuvvuu7V8+XJt3LhRr732mkpKSjRkyBAtXrw42kUEYCIEuyyuqpGJwsJCv7O+gHhlGIYeffRRvf/++xo0aJAee+wxr/OuOuNvZKKqGZVArHnooYfUsmVLjRkzJqDrqUOAN9fz2nnnnacmTZp4nWvTpo1atmyp7du36/Dhw9QfwIcvv/xSL730km655RYNHz5cZ555ppKTk9WtWzdNnTpVSUlJeuKJJyRxDwICUZ16kpKSUmncwXWNWbCM0eJc62e3bdum8847z+tcQUGB8vPz1aVLlyiUDDCn0tJSjR8/XosWLdKAAQP05JNPKiHBO+5f1Zpz1xp3X7nygFi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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plotting observed data.\n",
"observed = add_noise(a, b)\n",
"_, ax = plt.subplots(figsize=(12, 4))\n",
"ax.plot(observed[:, 0], \"x\", label=\"prey\")\n",
"ax.plot(observed[:, 1], \"x\", label=\"predator\")\n",
"ax.set_xlabel(\"time\")\n",
"ax.set_ylabel(\"population\")\n",
"ax.set_title(\"Observed data\")\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As with the first example, instead of specifying a likelihood function, we use `pm.Simulator()`."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Initializing SMC sampler...\n",
"Sampling 4 chains in 4 jobs\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"