{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# [Chapter 6](https://github.com/Ziaeemehr/spikes/blob/main/docs/examples/chap_06.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **Nonlinear neurodynamics and bifurcations**\n", "\n", "Code by : Abolfazl Ziaeemehr \n", "- https://github.com/Ziaeemehr\n", "\n", "\"Open" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# uncomment and run this line to install the package on colab\n", "# !pip install \"git+https://github.com/Ziaeemehr/spikes.git\" -q" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sympy\n", "import sympy as sp\n", "import numpy as np\n", "import matplotlib as mpl\n", "from scipy.linalg import eig\n", "import matplotlib.pyplot as plt\n", "from IPython.display import display, Math\n", "from spikes.solver import solve_system_of_equations\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "sympy.init_printing()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "\n", "LABELSIZE = 13\n", "plt.rc('axes', labelsize=LABELSIZE)\n", "plt.rc('axes', titlesize=LABELSIZE)\n", "plt.rc('figure', titlesize=LABELSIZE)\n", "plt.rc('legend', fontsize=LABELSIZE)\n", "plt.rc('xtick', labelsize=LABELSIZE)\n", "plt.rc('ytick', labelsize=LABELSIZE)\n", "mpl.rcParams['image.cmap'] = 'jet'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot the nullclines of a two-dimensional system of differential equations, you can use Python along with libraries like `NumPy`, `Matplotlib`, and `SymPy`. Here's a brief overview of how to do it:\n", "\n", "#### Step 1: Define the System of Differential Equations\n", "\n", "A two-dimensional system of differential equations can be written as:\n", "\n", "$$\n", "\\begin{cases}\n", "\\frac{dx}{dt} = f(x, y) \\\\\n", "\\frac{dy}{dt} = g(x, y)\n", "\\end{cases}\n", "$$\n", "\n", "#### Step 2: Find the Nullclines\n", "\n", "- Nullcline for $\\frac{dx}{dt} = 0$ : Set $f(x, y) = 0$ .\n", "- Nullcline for $\\frac{dy}{dt} = 0$ : Set $g(x, y) = 0$ .\n", "\n", "\n", "#### Step 3: Use SymPy to Solve for Nullclines\n", "\n", "You can use `SymPy` to symbolically solve for $y$ in terms of $x$ (or vice versa) where these equations are zero.\n", "\n", "#### Step 4: Plot the Nullclines Using Matplotlib\n", "\n", "After finding the expressions for the nullclines, you can use `Matplotlib` to plot them over a grid of values for $x$ and $y$.\n", "\n", "#### Example\n", "\n", "Consider the following system of differential equations:\n", "\n", "$$\n", "\\begin{cases}\n", "\\frac{dx}{dt} = x^2 - y \\\\\n", "\\frac{dy}{dt} = y - x\n", "\\end{cases}\n", "$$\n", "\n", "#### Explanation\n", "\n", "1. **Defining the system**: The functions $f(x, y)$ and $g(x, y)$ represent the right-hand side of the system of differential equations.\n", "\n", "2. **Finding nullclines**: We solve $f(x, y) = 0$ and $g(x, y) = 0$ for $y$.\n", "\n", "3. **Plotting**: The nullclines are plotted using `Matplotlib`, with one set for $\\frac{dx}{dt} = 0$ and another for $\\frac{dy}{dt} = 0$.\n", "\n", "#### Tools Used\n", "\n", "- **SymPy**: For symbolic computation, solving the equations for nullclines.\n", "- **NumPy**: For numerical operations and creating arrays of values.\n", "- **Matplotlib**: For plotting the nullclines on a 2D plane.\n", "\n", "This approach helps visualize where the system's derivatives are zero, giving insight into the system's behavior, such as identifying equilibrium points and possible phase portrait structures." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import sympy as sp\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact\n", "from scipy.integrate import odeint\n", "from spikes.plot import plot_nullclines\n", "\n", "# Example usage:\n", "x, y = sp.symbols('x y')\n", "f = x**2 - y\n", "g = y - x\n", "\n", "fig, ax = plt.subplots(figsize=(4,4))\n", "plot_nullclines(f, g, symbols=['x', 'y'], ax=ax);" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# adding direction fields\n", "def fp(x, y):\n", " return x**2 - y\n", "\n", "def gp(x, y):\n", " return y - x\n", "\n", "\n", "def plot_vector_field(\n", " f, g, ax, \n", " xrange=(-2, 2), \n", " yrange=(-2, 2), \n", " num_points=20,\n", " rotatexy=False):\n", " x = np.linspace(xrange[0], xrange[1], num_points)\n", " y = np.linspace(yrange[0], yrange[1], num_points)\n", " X, Y = np.meshgrid(x, y)\n", "\n", " u = f(X, Y)\n", " v = g(X, Y)\n", "\n", " norm = np.sqrt(u**2 + v**2)\n", " u_norm = np.real(u / norm)\n", " v_norm = np.real(v / norm)\n", " if rotatexy:\n", " ax.quiver(Y, X, v_norm, u_norm);\n", " # ax.streamplot(Y, X, v_norm, u_norm, color='k', linewidth=0.5, cmap=plt.cm.autumn)\n", " else:\n", " ax.quiver(X, Y, u_norm, v_norm)\n", " # ax.streamplot(X, Y, u_norm, v_norm, color='k', linewidth=0.5, cmap=plt.cm.autumn)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZwAAAGRCAYAAABR3wXnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAADSb0lEQVR4nOydZXQUSRuFbxIiBLdgMQgegpOF4O6ui8Pi+mG7OAR3XzwQ3G0Xl+Du7gkuIcSIz0zf70fvJAQi0zUBAvRzzhzCTL/VNd09dbuqq95rQpJQUVFRUVH5yph+7wqoqKioqPwaqIKjoqKiovJNUAVHRUVFReWboAqOioqKiso3QRUcFRUVFZVvgio4KioqKirfBFVwVFRUVFS+CargqKioqKh8E1TBUVFRUVH5JqiCo/Jd8fT0hImJCY4fPx793vHjx2FiYgJPT0/F5cUV+/TpU5iYmGDcuHFG1ze58eLFCzRr1gxZs2aFiYkJGjduLFSOMcdcRcVQVMFRiRd9I2RiYoIlS5bEuY2JiQlq1679jWumoqdjx47w8vLCkCFDsHbtWgwcODDebQMDAzFu3LhY4v6rcfz4cYwbNw6BgYHfuyq/JCm+dwVUfgzc3d3Rvn17pEqV6ntXRTEODg4IDw9HihQ/1+UeGRmJ48ePo1+/fhg6dGii2wcGBsLd3R0AULly5a9cu+TJ8ePH4e7ujk6dOiF9+vTfuzq/HGoPRyVRSpUqhbdv32LOnDnfuypCmJiYwMrK6qcTnHfv3oEkMmTI8L2roqJiEKrgqCRKs2bN4OrqihkzZsDPzy/R7U1MTNCpU6cv3o/reY0SSGL58uX47bffkDp1aqROnRouLi4YM2ZMgnFxPcP59L1du3ahZMmSsLKyQvbs2TF06FBotdovynn06BHat2+P7Nmzw8LCAo6Ojhg6dChCQ0NjbffixQv88ccfcHBwgKWlJTJlyoTSpUtj+fLlBn3P58+fo1OnTrH2M2jQIAQFBUVv06lTJzg4OACQe5/6oc/4jq2npydy5cr1xfZx9XRWrFiBQoUKwdLSEg4ODpg+fXqcZV6+fBlNmjRB5syZYWlpifz582PSpElxHru42Lt3LypVqoQsWbLAysoKOXLkQMOGDXHnzh0AwIABA2BiYoKHDx9+Eevr6wsLCwu0bdvW4PIqV64c3cPLlStX9DH49LnVmzdv0KtXL9jb28PCwgI5cuRA9+7d4evrG2v/48aNg4mJCe7evYv//e9/yJ49O1KlSoVq1arhwYMHAIAdO3agRIkSSJkyJRwcHOIdlv6V+Llu+VS+GtOmTUOVKlUwceJEzJ0797vUoX379li/fj3Kli2LkSNHIn369Lh//z62bduG8ePHC5W5b98+LFq0CD179kTXrl2xe/duzJw5ExkyZMCIESOit7ty5QqqVq2K9OnTo0ePHsiZMydu3ryJ+fPn48yZMzhx4gTMzc2h1WpRo0YNvHr1Cr169UL+/PkRHByM27dv4+TJk+jWrVuC9Xnx4gVcXV3h7++Pnj17okCBAjh37hzmzJkDLy8vnDt3DilTpkSPHj1QrFgxDBw4EE2aNEHTpk0BAAULFoyz3IoVK2LOnDlfbJ81a9ZY2y1evBi+vr7o2rUr0qVLh3Xr1uGvv/6Cra0t2rRpE+u4NWnSBHny5MHgwYORMWNGnDt3DmPGjMH169exdevWBL/niRMn0LBhQ7i4uGDYsGFInz493rx5g2PHjuHhw4dwdnZG9+7dMX/+fKxcuRJTp06NFb9mzRpoNBp07drV4PJGjhyJjBkzYufOnZgzZw4yZ84MAHBzcwMgC33ZsmURFRWFP/74A05OTnjy5AkWLVqEY8eO4fLly0iXLl2senTo0AHp0qXDiBEj4Ofnh1mzZqFmzZqYOHEi/vrrL/Ts2RNdunSBh4cHevXqhUKFCqFixYoJHpufGqqoxMOxY8cIgFOmTCFJ1q5dmxYWFvTx8YneBgBr1aoVKw4AO3bs+EV5q1atIgAeO3Yswff0+121alX0e5s3byYAtm/fnjqdLla5n/4/rlgfHx8C4NixY794z9raOtb3kSSJzs7OzJYtW6x9FClShPny5WNwcHCs93fs2BFrfzdu3CAATp8+/Yvvbwht27YlAO7atSvW+xMnTiQATpo0KcHvlRAJba8/btmzZ2dAQED0+6GhocycOTPLlCkT/V54eDhtbGxYoUIFajSaWOXMnj37i/MZFwMHDiQA+vr6Jridm5sbs2XL9sV+ChYsSCcnJ0qSpKi8sWPHEkCsc66nQYMGzJw5M1+8eBHr/UuXLtHMzCzWcdOX06hRo+g6kOSCBQsIgGnSpIlVjq+vLy0tLdmqVasE6/ezow6pqRjMtGnToNVqMWrUqG++7/Xr10fXwdQ09mX7+f+V0LhxYzg6Okb/38TEBFWqVMHbt28REhICALh16xZu3ryJ1q1bIzIyEn5+ftGv8uXLI1WqVDh06BAARN8Be3l54d27d4rqIkkS/vnnH7i4uKBRo0axPhs0aBBSp06NHTt2CH9XQ+jcuXOsh+nW1tYoU6YMHj16FP3e4cOH4evriw4dOiAwMDDW8ahbty4ARB+P+NDvY+vWrQkOwXXv3h1v377F3r17o987e/Ys7t27hz/++AMmJiaKyouPwMBA7N27F/Xr14eVlVWs7+To6Ig8efLE+Z369u0bXQcAKFeuHACgUaNGsLW1jX4/S5YsyJ8/Px4/fqy4bj8TquCoGEyRIkXQpk0bbNiwAdevX/+m+3706BFsbGyQPXv2JC03d+7cX7yXKVMmAMCHDx8AAPfu3QMAjB8/HlmyZIn1srGxQWhoaLS4ODg4YMyYMTh06BBy5MiBEiVKYOjQoTh//nyidXn//j0+fvwIZ2fnLz5LmTIlnJyc4O3tLfxdDSG+46E/FkDM8ejWrdsXx6NAgQIAkKjY9u3bFyVLlkSfPn2QMWNG1KlTB/PmzfsirmXLlsiQIQM8PDyi3/Pw8ECKFCliPSc0tLz4ePjwISRJgqen5xffKUuWLHjw4EGcZemfi+nRT+D49Cbm088+PY6/IuozHBVFTJw4EVu3bsWwYcNw4MABRbEid556+JWc0M3MzBLdp/7f//3vf6hXr16c2346U0w/7Xbfvn04deoUVq1ahZkzZ6Jfv36YP39+ovsT/TwpSOh4fF6PqVOnomTJknFukyNHjgTLyJgxIy5evIjTp0/j8OHDOHnyJAYPHowxY8Zg9+7d0ZMZUqZMiXbt2mHRokV4/fo10qZNiy1btqBu3bqxbj4MLS+x7/T777+jS5cucW6TMmXKL96L73jF9/63OIfJGVVwVBTh4OCAXr16Ye7cufDy8opzm4wZM8Lf3/+L9425O8+fPz92796NN2/eJHkvJzHy5csHQB66q169ukExuXLlQp8+fdCnTx9ERkaiUaNGWLBgAQYOHPjFXbEeGxsbpEmTJnpW1adERETA29s7ugchwqdDP8agPx7W1tYGH4+4MDU1RcWKFaMfot+7dw8lS5bE2LFjceLEiejtevTogQULFmD16tWwsbFBSEhI9GQBpeXFdwzy5MkDExMTREZGGvWdVBJGHVJTUcyoUaOQNm1aDBs2LM7P8+XLh3PnziEsLCz6vYCAAKxatUp4n/rpr3/99RckSYr12de+ayxWrBhcXFywbNmyOMfgtVpttMAGBQVBo9HE+tzS0jJ6mCwuIdZjamqKhg0b4tatW9izZ0+sz+bOnYuQkJDo2WUipE6dGoB8LoyhVq1asLGxwfTp0+OcJh8eHo6PHz8mWEZccfny5UOaNGm+OEbOzs4oW7YsVq5ciRUrViBHjhzRz4qUlhffMciUKRPq1q2L3bt348yZM1+URRLv379P8DupJI7aw1FRTKZMmfDnn3/GO3mgb9++aNeuHapWrYr27dsjMDAQy5cvh4ODA96+fSu0zxYtWqBVq1ZYu3YtHj9+jIYNGyJDhgx4+PAhDh48iNu3bxvzlRLExMQEa9asQdWqVVGsWDF06dIFzs7OCAsLw+PHj7Fjxw5MmTIFnTp1wrFjx9C9e3c0a9YsusG7fv06li5diiJFiqBYsWIJ7mvKlCk4cuQImjVrFj0t+vz581izZg2KFi2KAQMGCH+PTJkywcnJCZs2bUKePHmin0FVrVpVUTnW1tZYs2YNGjdujAIFCqBLly7ImzcvAgMDcf/+fezYsQM7d+5McBirW7duePnyJWrWrAkHBwdERkZi69at8PX1jTNrQo8ePdCpUyc8fvwYI0aM+GLIytDyfvvtNwDA8OHD8fvvv8PS0hK//fYbcuXKhcWLF6N8+fKoUqUK2rdvjxIlSkCSJHh7e2P37t3o0KHDT5mP75vyvabHqSR/Pp8W/SmhoaHMnj17nNOiSXL69Om0t7enhYUFCxQoQA8PD6OmRZPy9OeFCxeyePHiTJkyJVOnTk0XFxeOGzcuwdiEpkXHNUU4vqmzT58+ZY8ePejg4EBzc3NmzJiRJUqU4LBhw/j8+XOSpLe3N3v06MGCBQsyTZo0tLa2Zv78+Tls2DB++PDhy4McB0+fPmWHDh2YNWtWmpub097engMHDmRgYGCs7ZROiybJs2fP8rfffqOVlRUBsFKlSiTjP+Yk2bFjR8bVVNy6dYtt27Zljhw5aG5uThsbG5YtW5bjx49P9Ltu376dDRo0YM6cOWlhYcHMmTOzfPny3LBhQ5zbh4WFMX369DQxMeGTJ0+MKm/SpEm0t7enmZnZF9/5/fv3HDJkCPPmzUtLS0umS5eOhQsXZv/+/Xnnzp3o7eK7RhI6J5UqVaKDg0OCx+Vnx4T8xZ9iqaioJHsiIyORM2dOFC1aFEePHv3e1VERRH2Go6KikuxZv349Pnz4gJ49e37vqqgYwU8jOA8fPsSYMWNQpkwZZMmSBWnSpEGxYsUwadKkL3JdJcSVK1dQu3ZtpEuXDmnSpEHlypVx8uTJr1hzFRWV+Pj333+xcOFC/PnnnyhYsKBRkyZUvj8/zZDasGHDsHDhQjRo0ABly5aFhYUFjh07hi1btqBIkSI4f/58nPPoP+XSpUuoVKkSbGxs0LdvX1haWmLZsmW4f/8+9u/fr06XVFH5xjg6OuL169coWbIkVqxYEeeiWJUfh59GcC5fvow8efJ84XExatQoTJo0CQsXLkSfPn0SLKNs2bK4desW7t69C3t7ewDyNFdnZ2dYW1vjwYMHSbaWQUVFReVX46cZUitVqlSchkotW7YEIOfDSghvb2+cP38eLVq0iBYbQM6N1bVrVzx69AgXLlxI0jqrqKio/Er8NIITH69evQIgr+JOiIsXLwKISVX+Kfr39NuoqKioqCjnp174qdPpMH78eKRIkSKWUVNc6IXp0wyvevTvvXz5Mt74yMhIREZGRv9fkiT4+/sjU6ZM6jCciorKTwFJfPz4ETly5BDK0v5TC07//v1x/vx5TJw4Efnz509wW30aFktLyy8+s7KyirVNXEyZMiXaTVBFRUXlZ+bFixdx3pwnxk8rOKNGjcKiRYvQtWvXWM6N8WFtbQ0AsXopesLDw2NtExfDhw/HoEGDov8fFBQEe3t7vHjxAmnTplVa/e+DTgcUKgS8fQusWwc0aPC9a6Si8vPx8SOQJw8QEQEcPQqUKvW9a5Qg168DjRoBgYFAsWLBuH7dDmnSpBEq66cUnHHjxmHSpEno0KEDli5datCQVs6cOQHEPWyW0HCbHktLyzh7R2nTpv1xBAcA2rUDZs4Etm8HEhmGVFFREWDnTlls8uUDqlQBkvGQ+9WrQOPGstiUKQNs2QLY24tnHv/pJg24u7vD3d0d7dq1w6pVqwweZyxdujQA2U3wc/Tv6bf5qWnfXv53zx4ggczGKioqgqxdK//bvn2yFpsrV4Bq1YCAAKBsWeDgQeA/Q1txvmMetyTH3d2dANi2bVtqtdp4t3v9+jXv3bvH0NDQWO+7uroyVapU0YkYSTIoKIi2trax/NMNISgoiAAYFBSk/It8b4oUIQFy8eLvXRMVlZ+Lly9JExP59+Xt/b1rEy8XL5Lp08vVdHMj9c2Yse3aTzOk9vfff2Ps2LGwt7dHjRo1sHHjxlifZ82aFTVq1AAgP29ZvXo1jh07FiuF+vz581G5cmVUqFAB/fv3h4WFBZYuXYo3b95g3759v85ss/btgaFD5TsxNXeVikrSsWEDQALlywPxGPF9by5eBGrWBIKCgHLlgP37AcFHNl/w0wjOpUuXAADPnz+P5XWup1KlStGCEx+//fYbTp48iZEjR2LcuHHQ6XQoVaoUjhw5kqhF7U9FmzbAX38BZ88CT54ATk7fu0YqKj8Hnw6nJUMuXJDFJjhY1sR9+5JObICfKLVNciM4OBjp0qVDUFBQkkwaICncw/Lz80PmzJmVBdWqBRw6BP/+/ZFx3jyh/b569Sp6MoZSoqKiYGFhIRSropIsuXEDKFYMtLCAydu3QIYM37tGsTh/Xv7ZBwcDFSrIYvOfQWo0xrZrP92kgeQKyejZbkoJDw+Hp6enUGxAQAAmTZqkPPC/OzDNqlXyEIBCQkNDDZqOHh8TJ04UjjUmu7d+CrzKrw3JpLcuX7cOAHA5WzYwjjRc35Nz52J6NhUrxi02SYEqON8ASZLQt29fPHr0SHEsSfTu3RsvXrwQ2veUKVNw//595YFNmkBjaYmsHz9CimPmXmJ4e3tj/fr1ePr0qfJ9A1ixYgX2798vFPvPP/9gzpw5QrG+vr4YMGAAtFqtUPzRo0cRGBgoFAsAHz58EI5VSTpIYvTo0Ul3A6LTyc9vAEx6/tyoaySpOXtW7tl8/AhUrvz1xAZQBeero9Fo0KFDByxfvjzaT10JS5cuhaenJ7JkyaI49vnz55g/fz58fX0VxyJVKpzIlAkA4C8wpPb48WPodDrMnDlT+b4BWFhYoEuXLkINsLOzMwYNGoRVq1YpjnVwcMCxY8fQsGFDBAcHK47PkCEDXFxccPjwYcWxALBq1Sr8+eefQvsG5IkvR44cEb4737t3r/BNAgDcuHFDuCcPyAumjak/ABw4cAAeHh7QaDTCZZiamiIkJARubm7w9vYWLicaLy/g9WsEm5tjH4A3b94YX2YScOZMjNhUqSKvhkiV6ivu0Oj5cypxop8+2LdvXwJguXLlFJfx7t07urq6EgC3bdumOH7dunXMnDkzXVxcFMcGBwdzaLFiJMCIVKnIiAhF8XPmzGGWLFnYuHHjL6afG0LBggWZOnXqWH7zhnLhwgUCoJ2dHe/evas4ftiwYQTA3377jf7+/orjS5cuHX3ulX73oKAgZsiQgVmzZuXKlSup0+kUxfv4+NDS0pLly5fn0aNHFU3lJ8knT54wTZo0bNWqFS9duqQoliQDAgLo4ODAli1b8vTp04r3T5I9evSgs7Mzly5dKnTtaDQaFi5cmLly5aKHhwejoqIUl0GSZ86cIQCmT5+eXl5eQmVE064dCXB71qzMmDEjjxw5Ylx5ScCpU2SqVPLU56pVSUMOtbHTolXB+UroT8yCBQvo5uZGd3d3oXKaNGnCWbNm8c6dO4pjo6KimClTJr57905o3wf27uWHlCnlK3LHDkWxYWFh7N27N9esWSO072vXrtHR0ZEvX75UHPvx40f269ePefPmpUajURx/+vRpFixYkE2bNlUcS5IeHh60tLRkly5dhBrcCRMmEACbNGnCsLAwxfEjR44kALq6uvLDhw+K46dOnUoAzJ49Ox8/fqw4fs+ePQRAU1NT7tu3T3G8fu0bAHbv3l2x6JLkkSNHosXixo0biuNJUqfT0cXFhTly5OCrV6+EyiBJBgaS//2OpjZuzLVr1zIwMFC8vCTg5MkYsalWzTCxIVXBSbboT0zOnDn56NEjRkZGKi7jzZs3zJkzp1AsKTfaIj0rPbt37+YeZ2f5qmzcWHH8vHnzOHLkSOH9Dxw4kPPnzxeOb9asGVevXq04TqvVMiAggGXLluXWrVsVx4eEhPD06dN0cXERig8MDOTUqVNZoEABrl27VnH8x48f2apVKzo7Owsdv6ioKFaoUIGlS5fmkCFDhBr89u3bs3Tp0qxbt65Q47Rv3z6WLFmSjo6OQj0tkuzUqRNbtGjBVq1aCf+Gnj17xr///ps1atQQOg4kyWXL5N9QgQIsVbKkUK87LiRJ4qxZszh06NDo1+XLlxONO348Rmxq1CCV3NOogpNM0Z+YgQMHCpcxZcoU/vnnn8Lxy5Yt4//+9z/h+K1bt3JMs2bylZkiBamwp3TgwAE2b95ceP9nzpxhxYoVheOvXbvG/PnzJ5h1IiHu3r1LOzs7+vn5CcU/fvyYtra2vHnzplD88+fP6eTkxN27dyuOjYyM5Pv371miRAlOmjRJcby/vz9DQkLYqFEjtmjRguHh4YriP3z4wLCwMI4dO5aFCxemt8Cq+rdv3/LEiRO0s7MTGlKOjIykVqtlly5dWK9ePaHeIik37PXr1+fs2bOF4lm2LAlQO3kyM2XKJHw9fsqDBw84a9YsOjs7EwBz5MjBf/75J9G4Y8dIa2v5J12zJunnF0ovLy+Dhx1VwUmm6E+MyJCQnjJlyvDhw4fC8UOHDuWGDRuE47du3cohQ4aQrq7yFarwB+fj48MKFSoI71+n0zFfvnxGpQdq1KiRUePlEydO5PDhw4XjDxw4QFdXV6GhNZJ8+PAhHRwcYqVbUkJgYCDLlSsn1NMj5d5e//792aJFC6F4kty0aRMdHBwYEBAgFP/o0SMWLFiQe/bsEYrX6XQcMGAA27dvLxRPys9Tc+fOzffv3ysLvHdP/u2YmfHxqVOsVq2acB1IcvPmzcyXLx8LFy7MYcOGcdmyZezSpYtBx9bLi0yZUiJA5sp1n4MGjeRff/3F9OnTM3369GzdujXXrVuX4O/NWMFRF35+JZJi4adWq0WKFMYlg6ARC0ajWbIE6NULcHYGbt0yOOFgUuxbp9PBzMxMOD4yMjLOLN6GotFoQNKoRajBwcFGLf4NDAyM0z7dUEJDQ2FqaoqUKVMKl/H+/XuhmZJ6fH19E3XdTYjAwEBYW1sLnweS0YaIooSEhCC10vnCw4YB06YB9eoBe/YY/Zt48uQJTE1Nkeu/tDiGthFeXkD9+kB4OODs/By9eh2GubkOJDF8+HDY2dmhQYMGqF+/PlxdXeNNemxsu6YKzlciqTMNfFcCA4Hs2eWU6hcvAr9C1mwVFWPRauVc/m/eANu2Ac2afZdqHD0qi01EBFC3ruw88p+nJMLDw+Hr6wsHBweDylIzDah8fdKnj/mxrFz5XauiovLDcOiQLDaZMn03M8MjR2LEpl49YMeOGLEBgJQpUxosNkmBKjgqhtG5s/zvxo1yv1xFRSVh9AuP27YFvkNewEOHZJ2LiJBFZ/t2wIjR5SRBFRwVw6hSBXBwkHOW79z5vWujopK8+fAB+Ocf+W/9zdo35OBBoGFDWWwaNJBH9L632ACq4KgYiqlpzA9HHVZTUUmYDRuAqCigWDH59Q05cABo1AiIjJT/TS5iA6iCo6KEjh3lf728ACPybamo/PToh9O+ce9m374YsWncGNiy5buM5sWLKji/CJIkCcUFBwfHJFJ0dJRNzklg9epEY4OCgoT2CcjToVVUfkhu3ACuXQPMzWUzw2/E3r1AkyZyx6pJk+QnNoAqOD8M/v7+wqnrT506hdu3bwvFenp6wsfHJ+aNLl3kf1etAhIRsTlz5sDf319ovytWrEBYWJhQ7M2bN4XtBbRabdL7oKj8kHz8+FHsWli+XP63USNAqfGhIHv2AE2bymLTrBmwebOsd8kNVXC+EVFRUVi4cKFQbGhoKBo2bCi0cC8iIgJdu3YVaoBJYvHixbh69WrMm02aAOnSAc+eyUNrCXDq1Cms1VvqKuTevXvCJmze3t4YMGCAUGOh0+kwdOhQYcG6ceMGIiIihGIBCO9XJel5+fIlhg0bpuw6CguLNlpD9+5fp2Kf8e+/MWLTvLk8kTQ5ig2gCs434d27d6hataqQL41Go0GLFi3w6tUrWFtbK46fMGECHj58KDSkdvz4cdy/fz+24KRMGTNMoL+TiwNJknD58mUsW7ZMqOGPjIzEjBkzcOfOHcWxuXLlwqJFi4RM2CwtLXHnzh00bdpUqIdlYmICV1dX3Lp1S3EsACxYsADr168X7mVt2bIFfn5+QrEAcPfuXaN6eAEBAcKxgDwMa6zonjhxwihPHz358+fH8uXL0b9/f8N/P1u3yjM5c+WSh5+/Mrt3yz0ajQZo0UKeq5BcxQaA6ofztdDnHNInHwTAK1euKCpDkiR269aNAFinTh3FdXj48GH0vs+fP684vn///kyRIgUbf54p+to1OT+UuXm8CT3v379Pa2trZsuWjefOnVO8786dOxMAO3XqpDgPmf7YW1pa8sCBA4r3PXPmzGg/HF9fX8XxpUuXpqWlJefOnas4w/CbN29oZWVFNzc3xdcLSZ44cYKpU6fm8OHDlef9Irlz5066uLjQw8NDccJOkjx58iQrVarE9evXM0KhhxJJhoaGsnLlyhw3bpywJcDbt2+ZKVMmdunShY8ePRIqQ0+9evUIgF26dDEs6Wa5cvJvw8CEqZGRkdyzZw/d3d0VZ7TeuVP+CQJkq1akgBOHYtTknckU/Ym5ePEi06dPTycnJ6EEjnv27GHx4sWF/XTatGnDKVOmCP3woqKimDlz5rgbXX1Cz2nT4owNCAigh4cH+/fvL5TW/dixY6xcuTJPnz6tOJYkO3ToQDs7O6FG78aNG8ySJQtr1qwpFL906dJoP5vg4GDF8QMGDCAA1qxZkx8/flQc37JlSwJgmTJlhBJmNmvWjABYsGBBPnv2THH84MGDCYBZs2blyZMnFcefOXOGpqamNDMz4/jx44V+N7NmzSIA2tjY8Pbt24rj9UyaNIlOTk5cunRp4vW4fTs6USdfv05wU39/f3bv3p0ZMmRgypQpFXv27NghJ3AHyNatv43YkKrgJFv0J+b333/nmDFjeP36dcVlSJLEMmXK8OjRo0JGYlqtltmyZRO+OF6+fElnZ+e4P1yxQr7a8+Qh4xGU/fv3s3Xr1kL7JmV7hrFjxwrF6nQ6tmnTRsgxVJIk+vj4sFixYkI9pKCgIHp6etLR0ZFnzpxRHP/q1Su2bduWdnZ2Qr3Dp0+fskiRIrSzsxNq8N+8ecPs2bPTzs6O//77r+L48PBwFixYkBkyZOC8efOEBOOvv/5i2rRp2bBhQ6HrNyoqisWLF2eBAgW4cOFCxfF6/P39effuXTo6OibuPjpggPybaNIk0XKfPHnCggULEgA9PT0V1Wnbthix+f33byc2pCo4yRb9iXFxcRE2fzp69CjLli0rnNr+zJkzrFKlilAsSV68eJHVq1eP+8OPH8k0aeSr/ujRODe5cuUKq1atKrz/y5cv083Nzah4FxcX4eN34cIF5s2bV9hH5ezZs3R0dOSbN28Ux0ZFRfHcuXO0s7PjrVu3FMe/ffuWly9fpp2dHffv3684/saNG7x37x7z5s3LuXPnKj6Gly9f5pMnT1ixYkV26tRJ8fBcREQEz507x7Fjx9LZ2Vmoh/7q1Su+e/eOxYsXF+4p6enTp0/Cowzh4WSGDPLvIRGX07Vr19LW1pbr16/nnDlzFNVj61a5AwWQbduSb968F7oZFUUVnGSK/sScPXtWuIxq1aoJe4CQstXwjBkzhON3797NDh06xL9Br17yld+yZZwfv3jxgoULFxbev06nY9asWY2y461UqRIPHz4sHN+7d2/hXhZJ/v3336xcubJwY3f48GFhq22SvHPnDnPlyiV8Hb1//57lypXj4MGDheKjoqLYp08furq6CjdS27dvp62trVBvkZQ9gSpWrMhhw4YJxZPycciZMydfxzdUtm6d/Fuwtyfjedaj0+nYrl07urm5CRnSbdlCmpnJfjYVKz7jli3bOXnyZKZPn56///47N2zYQH9//wTLCA0N5YkTJ/j8+XNqtVpKksR58+YZ/LxPFZxkirEnhpRd/Yy5K/Pz80v0AkyIkJCQhO/OE5k8oNVq6ePjI7x/Uh56MMYh8enTp0IPv/UEBATwxYsXwvGSJPHq1avC8SR56dIlo46Bt7e3UUaA4eHhRt04kXJv3Zhr+ebNm3yn0HH2U8LCwoStqvXcu3cv/ueRlSrJv4VEnrUePHhQqEeyaVNMzyZPnjPs3Lkr//jjj+jnbZkyZWL79u25Y8eOBJ+ZPnv2jPXr16ezszMzZMjAPHnyMHXq1EyZMiV79uzJ+/fvJ1gPVXA+YfLkyWzevDlz5cpFAHRwcFBcRqVKlQggztfOnTsNLicpBOeHIJHJAyoqPz3378u/AVNT0oibk/jYuDFGbDp2jN2Bun37Nk+dOiV0QyJJEq9cucLcuXOzVq1aHDhwIFesWMGQkJB4Y4xt14yzk0xmjBgxAhkzZkSJEiUQGBgoXE7mzJnjXMNRqlQpI2r3k9K9u2zKtnw5MGSInORTReVXQr8erV49wNY2SYvesAFo315O6tG5s7yrTw1wnZ2dhcs2MTFB8eLF8eTJkySoqWH8VILz5MkT5M6dGwBQuHBhhISECJWTKlUqtGvXLimr9vPSqhUwcCDw+DFw7Ng3WeymopJsiIiIySvYrVuSFr1+PdChgyw2XbrIYpPU93NG288r5Ke6HdWLTVIgSRKCg4OFk17+MqRODejFedmy71sXFZVvzdatgJ8fYGcH1KmTZMWuWxcjNl27fh2x+R78BF8h6Xn16hVSp06NdOnSIVWqVKhbty4uX76cYExkZCSCg4NjvX4Z9Dmjdu4E3r79vnVRUfmW/P23/G+PHkCKpBkwWrMmRmy6dQOWLv05xAZQBecLHB0dMXToUHh4eGD79u0YMmQIzpw5g3LlysErgWSVU6ZMQbp06aJfdnZ237DW35lixYAyZeSETgnkV1NR+am4cgW4cEFOXta1a5IUuXo10KmT7ADSvTuwZMnPIzYAYEL+nLnY9c9wkiKJ34MHD1CiRAnkzJkTDx8+jHObyMhIREZGRv8/ODgYdnZ2CAoKQtq0aY2uw/dEkiSYJnbVr18vD63lzAn4+ERnEIyKioKFoCkHyW8+xqyiEhc6nQ5mnz6tB4A//pDdb9u0ka9/I/H0lJ/VkEDPnnLnKbmJTXBwMNKlSyfcriWzr5M8yZ8/P1q2bIlHjx7h0aNHcW5jaWmJtGnTxnolNcbcG4hkXdbj6emZ+EbNmwM2NsCrV3IKW8j1nT9/vtA+Q0NDsX37duHY58+fC8UC4mZ1Kj8vu3btwuvXr2Pe8PeXp5ABQO/eRpe/cmWM2PTqBSxalPzEJin4Cb/S18HR0REA8P79e+EydDod3r17JxTr7++PBQsWCMV6e3vjr7/+Eoq9efMmZs2alfiGlpYxs3T+G9e+ceMGFi1aJCSU7969w8iRI6HRaBTHWllZoWXLlsK+NFOnTo3VW1XC06dPheqskry5fv16bD8rT095hlrRooCbm1Fle3jInSUS6NNH/vn8rB17VXAMRN+zyZYtm1D88+fPUbNmTSGvj7dv36Jy5cowFzC6iIiIQPPmzRMfEouHsWPH4sWLF4Zt3KOHvEjg+HHg9m3s27cPPj4+Qt4w7969w8OHD7Fy5UrFsWZmZnj8+DEGDBigOBaQbyoaNGiA0NBQxbGSJKFKlSp49uyZ0L5XrlyJK1euCMUCwLVr14zqCf8MYmlM7zY+7t27hyVLlsjXhCTJXRBAVggj1GH58pjHP/36AQsW/LxiA+Dn9cNxdnZOMNPA69evee/evVgZYP39/eNMtHnp0iWam5vHnzk5Dj5dkbtx40amS5eO9evXV/QdSNLHx4d58uQhAKEkjl27do32lVHK5cuXaWpqqmxlcdOm8pLoXr1Yvnx5AuD48eMV73vHjh0EwJw5cyaepTcOChQoQAD08PBQHLtt2zYCYLly5YTS+1eoUIHp06fn9u3bFcc+fvyY5ubm7NGjB/38/BTHL1myhGXKlOG+ffuEUslMmDCBo0aNEk6Fs27dOnp4eAjZMpDkrVu3OHnyZKNS8ezevZsVKlTg3r17jUqn8ykFCxakqakpFyxYQO7fL1/j6dKRCazKT4ylS+ViALJ/fzKJqvpVUVPbfMKaNWs4YcIETpgwgTY2NkyfPn30/xcsWBBr244dOxIAjx07Fv3ezp07aWNjwz59+nDOnDlctGgRu3fvTgsLC1pbWyvKJ6U/Mbdv36azszMBcNeuXYq/082bN5kxY0bmyJFDsa+MTqfj5s2bWbhwYU6ePFnxvgMDA9m8eXO6u7sbnvHYy4sEKKVKxXMHDrBAgQJC+dTOnDnDDh06cNasWUKC06NHD9rY2PDOnTuKY9+8ecOUKVPS2dlZyA9m+fLlBMDy5csLmaC1a9eOAFilShXFDbdWq2WxYsUIgLVq1VKc+PTjx4/MlSsXzczM2LJly/iTVcZDaGgoCxYsyFSpUrFz585CXjS9evWiqakpa9euzd27dyuOJ8mGDRsSAIsXL84nT54IlaFHkiRu2bKFefPmlW8CGjSQVWLAAOEyFy+OEZsBA34MsSFVwYlFQnnQPu/txCU4d+/eZYsWLejk5MTUqVPT3NycDg4O7NKlCx8+fKioLvoTc+DAAebKlYv9+/dnVFSU4u/0999/s0WLFooNmvR07NiRnp6ewskf8+XLp6zRkSSyUCESYPCkScybN6/Qfkm5p9GxY0ehWI1Gw759+3L+/PlC8devX2fRokV5NB7rhYQIDAzk8OHDaWdnx3v37imOv3v3LkuXLs1cuXIJCd6pU6eYPn16Fi5cWMg189ixYzQ1NWWePHn4/PlzxfHXr1+nhYUFU6VKxWvXrimODwsLi75JU5q+X8/Tp0+ZNm1a2tvbC3lRfY4kScyQIQO1jx+TJiayUiSS6DI+Fi2KEZuBA38csSFVwUm26E+MnZ0dz58/L9S1//DhA21tbfn06VOhOgQHBzNbtmwJJuNLiJCQEGbNmlV53f/+mwSozZOHuXPlEto3KTcaSoYxP+fGjRtG+eEcP36cLi4uQtl9JUni7t276eLiItRD8/f357p161iwYEEhm+tLly7Rw8ODefLk4ePHjxXHr1mzhp6ennRwcBCyJ587dy7XrVsX7fuilJs3b3LKlCksUaIE+/btK+S86uXlxaNHj9LOzk7oxuFzChcuzKCePWWliM8nKhEWLowRm8GDSZ3uB1IbqoKTbNGfmFmzZgmX0adPH6O8WFasWMGuXbsKx587dy5+A7aECA6ONmdrmzWr8P4lSWLWrFmFbJb1lC5dmhcuXBCOb968ORcvXiwcP2jQIHbu3Fk4ft68eSxVqpTwM5Ft27bRwcFBuId85swZ2tvbc+3atYri9CLv7e3NEiVKsE+fPoqNCCVJYnh4OHv06MHSpUsL33hdv36djo6O3Lhxo1C8nhZ16zJKbzooMDy+YEGM2PToEcznz1+wf//+bNOmDTdu3GjQ88KIiIhYN1CBgYGKboh0Ot0XIy1KRj9UwUmm6E+MMeZhGzduFLo71nPlyhWhIR09r1694qlTp8SC+/YlAb4uXVp4/yS5d+9eowTn9OnTQmZXenx8fIy6O46KiuLy5cuNenjt4eFhlK/RoUOHhKyq9Tx79oxLly4Vjg8PD+fEiRON8iVas2aNUUNjT58+FbIb/5THQ4bIapE7d7wma/Exb16M2GTO7MHChV3o4uLCHDlyEADNzMxYvXr1RD175s2bx8yZM7NSpUocMGAAJ06cyLx583LDhg0GPeN98OABM2fOzCpVqnDkyJHct28f69ata7CVuio4yZRfxg8nPvQeISYmpMLnXyoqyQ6djixQQL6m581TFDpnTozYDBsW+5mNh4cH169fzw8fPhhcXnh4OK9cuUIPDw/Wq1cv+jl14cKF+e+//yYaHxkZyfPnz3P27Nls0qRJdHzdunUTvUE1tl37aVPbfG+MTQHxU1C/PrB3r7xW4dNFcyoqPxr79wN16wJp0wIvXwJp0hgUNmcOMGiQ/Pfw4cCkSUm7zubIkSMIDQ1Fzpw5YWtrCxsbG0Vr7i5evIidO3ciQ4YMyJAhA2xsbFC3bt141/wZ266pgvOVUAUHwNGjQPXqgLW1/CPNkOF710hFRYxatYBDh2Tvp9mzDQqZPRsYPFj+e+RIYMKEH39Rp5pLTSX5UrUqUKQIEBamZpFW+XG5c0cWG1NTOR2AAcycGSM2o0f/HGKTFKiCo/L1MDEB/vc/+e8FC2T7AhWVHw19AtrGjYFcuRLdfPp0YOhQ+e8xYwB3d1Vs9KiCo/J1adMGyJpVHlLbtu1710ZFRRkfPsiOaEDMzVMCTJsG6PPkjhunis3nqIKj8nWxtAR79ZL/njNHnqyjovKjsHSpnBW6RAmgfPkEN50yBRg2TP7b3R0YO/Yb1O8HQxWcXwidTicURxK3b98Win327BluurnJ9gWXLgFnzxoce+DAAaHs2oBsySCKOo9GBQAQFRVjIT1wYIJdlUmTgBEj5L/Hj5eH0lS+RBWcH4iIiAi8fftWKPbBgwfYoDeMUsjWrVuxb98+odhVq1bh1IMHshsoYPAMHwDYs2cPdv9n5qaUefPm4dq1a0Kx69evF/Yt+vDhw0+R4l8FwObNwOvXQLZsQMuW8W42cSIwalTM36NHf6P6/YCogvMNCQgIwMaNG4ViX7x4gerVq8PS0lIotkaNGsiSJYvi2ICAAPTv31+op6HT6bBq1SpcuHAhZvx71y7AwN7H7du3MWfOHMX71dOuXTshEzYrKytUr14dfn5+imNTpEiBOnXqxHaHVMC///4rfFNBEh8/fhSKVfkMUn76DwD9+wPx2KSPHx8jMJMny9OfVeJHFZxvAEmsXr0a+fPnRwaBtSgnT55EqVKlkDp1asXxfn5+qFmzJl68eIFChQop3vfQoUPx7t07IcE5cuQInj9/LgtO4cJAzZqyeZUBIqIfxjtz5gwuXbqkeN8WFha4e/cuRgq0AMWLF8ft27dRo0YN+Pv7K4pNly4d0qRJg+LFi+PYsWOK9+3o6IgCBQpg/vz5io+5iYkJJk+ejFGjRgmJpSRJWLRoEe7fv684FpDP2cWLF4WHQQHg1atXRg1pSpKE2bNnC/duo9m/H7h9G0idWvZ8joNx42Ke00yZIi/sVEkYVXC+MpGRkWjbti06deqEnDlzolatWorifX19MWTIEPj6+qJZs2aK9//kyRMEBAQgU6ZMsLOzUxSr0WiQP39+5M+fH6lTp1a878yZM8PV1RXNmzeXLZv//FP+wMMDSMSq++PHj2jVqhXKly+PlClTKt53unTpkCtXLmTNmlVxA5g7d25kzJgRz58/x927dxXvu3Xr1vD19UXv3r0Vu0+6uLigUqVKGDBgAGrWrImgoCBF8UOHDsWSJUvg4OCAIUOGKOrxmJqaolixYihcuDAqVaqEDRs2KOohmpiY4Pnz57C1tUXfvn1x+vRpSJKkqP5Pnz5FgQIFMGjQIJw+fVrxc0dTU1O4ubmhVKlSKFOmDFavXo3w8HBFZQCI6d306AGkTx/rI1IWGnd3+f/TpsVMFlBJBKGEOCqJos859OHDB9arV485c+bkpk2bFJfj5+dHBwcH/vHHH0Jp6k+cOMFSpUoJZwseMWIEZ86cKeynU6xYsZgsv5JEliolJ5UaPTrR2GfPntHFxUVovxEREZwzZw6HDBkiFH/mzBm6ublx//79imNDQkLYpk0bYWuJ8+fPM3v27MJZopctW0YArFq1qpAH08iRIwmARYsWFdr/oEGDCIA2NjZCiVOXLl1KADQxMTEoN1hcjBgxggBYqlQphoWFKQs+f16+Rs3NyRcvYn0kSfKlq8+NNmOGUPV+WNTknckU/Ylp164d27dvT29vb8WNtiRJbN68OadOnarY7VNP9erVhZxG9ZQoUULItVFPzpw5Y/vxbN0q/1IzZJBtDBJAo9EwY8aMwpmWnz17xty5cxvlh1OiRAmhY6/Varly5UqWL19eSKwfPXrEUaNGsXr16orT+mu1Wq5atYqdO3dm3bp1FWccj4yMZPv27dm8eXPWrl1bcabqqKgoli9fno0aNWLFihWFTNx69uzJcuXKMX/+/EKZriMjI9m1a1c2bdqU9erVU5a1XW+T/pktuySRo0bFiM3MmYqr9cOjCk4yRX9iqlWrJnSXSZJr164VbrBI2c+mSJEiwmL15s0b2tvbCzfYkiQxffr0seO1WjJvXvkXa4BXkKOjo1Gp+UuXLs2rV68Kx9eqVYtbt24VipUkiS1btuT48eOF47t3787WrVsLnUNJkvjnn3/Szc1NUTZiUhYNSZI4depU5s2blzdv3lQU7+fnR0mSuGLFCtra2io+hpGRkXz37h2PHTtGJycnjhgxQkh4dTodx48fz4IFC/K+IQ6dDx7EOHp+Yk8uSeSIETFiM3u2fIz69evHTZs2GWVD8iOhCk4yRX9iRCx+9YwaNcooP/Z///2Xe/bsEY5/+PChUeZjGo2Go0aN+vKD5cvlX23OnGQijcisWbP47t074Tps3rzZKC+Yy5cvc9myZcLx/v7+7N27t7Boa7Va9urViy8+G9pRwowZM7ht2zbh+AMHDrBfv37C8Q8ePGC9evWETeSCgoL4xx9/8NChQ8J12L17N//888/EN+zWTb42GzSIfkuSZFsBvdikSTOa2bJlY7Zs2WhhYUEATJEiBbt27cr3798nWHzbtm05ZMgQHjt2jFFRUTxx4oSixnvx4sXs3Lkz//nnH4aFhfHFixeKro2HDx+yVq1aXLRoEV++fEmSPHnypMHxquAkU355P5yEiIggs2eXf70rV37v2qioyLx5Q1pYyNflf8aDkkT+9denw2hRDA8PZ3h4OIODg9miRQtOnTqVd+7cMeim4vHjx5w3bx5r1KhBGxsb5s2bl7a2tty7d69BVfT39+fatWvZtGlT2tjYsEqVKkyXLh1Xr15t0P6joqLo5eXF/v3709HRkaVKlWL69OnZuXNng3ppquAkU1TBSYTp0+VfcIECsrmVisr3Rt+NcXMjKYvN0KExYrNgQdLu7unTp0yfPn20AVq7du3o5+dncHxoaCgrVKgQHd+oUSO+ffvW4HhJkjh9+vToeFtb20SdP1UDtmSK6oeTCMHBgL09EBQE7NwpZ+JVUfleBAYCDg7ydblrF9iwEYYOBWbNkj9euFD2EUxKdDodSMLExCTWy1AkSYKvry90Oh20Wi10Oh2sra2RLVs2g8sIDg6GRqOBJEnRr2zZssVbD2PbtRSKI1RUkoK0aYHeveUVc1OnAo0aqWl1Vb4fCxbIYuPsDNZvgCFDYrIw/f23fKkmNWZmZkbFm5qaKhKXuPjWN8Pqwk+V78eAAYCVFXDhguwOqqLyPQgOjs5+wZGjMGiIabTYLF78dcTmV0UVHJXvR9asQPfu8t/u7qp1gcr3YdEiICAAzJcfA8+3xNy58ttLlwI9e37Xmv10/FSCM2XKFLRo0QK5c+eGiYkJHB0dhcq5cuUKateuHZ0Xq3Llyjh58mTSVlZF5q+/ZOuC06eB48e/d21UfjVCQ4FZs0AAAxx2Yd58uUlctizmXkgl6fipBGfEiBHw8vKCk5OTUJJMALh06RIqVKiA+/fvY/To0Zg8eTI+fPiAatWq4ciRI0lc4x8L0bT7Pj4+iIqKivvDHDmArl3lv/XJqT7h4sWLQvsEoDiPmR51Hs0vxJIloJ8f+qVdgwWHC8DEBFixAujW7XtX7CdFaG5bMuXTRZLOzs50cHBQXEaZMmWYKlUqPnv2LPq9wMBA5syZk3nz5jV4AV9ynBYdEBAglI+NJPfu3cuzZ88KxXbq1Ik+Pj7xb/DiRcz6h+PHY33k6uoqlKkhIiKCTZs2VRxHyilx/vnnH6HYqKgofvz4UShW5RsTFkbJJit7YyEBOcGAh8f3rlTyRl2HEw8igvPkyRMCYKfPciiR5NixYwnA4FXr8Z0YSZIYHh6uqF56QkJCuHr1aqHYly9f0tXVVWjfjx49Yrp06fjo0SPFsQ8ePKCpqSlPnz6d8IY9e8qCU7Vq9Fv683Hw4EHF+/X19SUAHj16VHGsRqNhunTpePHiRcWxkiSxWbNmCQtsApw7d05x7jMVMXRz5rEX/v5PbCR1DbIBGCs4P9WQmrHoh2/c3Ny++Ez/njFDPF5eXmjevLmQX8iJEydQpEgRof3eu3cPZcuWRZo0aWBlZaUoNiQkBI0bN0ZQUBCyZs2qeN/jxo2DJEl4+fJlwhsOHw6YmwNeXvLzHACHDx8GAGzbtk3xfvVp/QcMGKD4eKdIkQJZsmRB/fr14ePjoyhW/+ywdOnSOHHihKJYALC0tEThwoWFHFYlSYK7uztO/3f8lBIWFiZsHPejIYVFoPfIDFiM3jAxIVatMkHnzt+7Vj8/quB8wqtXrwAAtra2X3ymfy++hjMyMhLBwcGxXnrOnj2LatWqoVq1aqhTp44ibxmSGDlyJCpXrozg4GC0TMDqNi6CgoLQs2fPaMdQpZw/fx4fPnxAmjRpFHvihIaGwtraGrlz50ZAQEDCG9vbA506yX+PHw9AbryzZs0KGxsbxc9VgoOD4eDggCxZsuDx48eKYgHZE8fX1xe7du1SHNu4cWP4+fmhRYsWuH79uqLY4sWLI0+ePKhXrx6aN2+ODx8+GBxramqKevXqoWLFiqhQoQL27dun6LilTJkSI0eORM2aNbF27VqEhIQoqntwcDDGjh2LPXv2KI4F5OtFJE4pkgT0rOmNpWHtYQIJnsu16Njxq+9WBfi5nuF8isiQ2vjx4+MdhtEP7/Tp0yfOWP2Q2+evoKAgenh4EABdXFyEMj/PnDmTGTNm5LBhwxTHSpLEihUr8vfffxcaInr+/Dnt7Ox4+fJlxbGknHxz7Nixhn1vHx8yRQp5aO2/50UuLi5CiSvDwsJ49uxZVv1kiE4JR44cYZs2beghMKiv1WpZp04d2traRidIVLpvS0tLVqxYkRqNRnF87969CYC1a9dW7AXz8eNH5suXjwBYvXp1xfEnTpyghYUFzc3N2aJFC0UJOzUaDdu1a8d8+fKxVatWnDp1quIs14mh05FdO2kIkKbQcm0H5cO1vzLqM5x4EBGcmTNnEgD37dv3xWe3b98mAA4dOjTO2IiICAYFBUW/Xrx4QQA8dOgQ7ezsOG/ePB4+fFjx9zhw4ADz5MlDHx8fIV8RT09P1qxZk5IkCaW4HzduHEcbYJYWH+3bt+fOnTsND/jjD1lwatQgSZYsWZKPHz8W2ndkZCQzZ86sOK29nmvXrrFQoUJCxy08PJyLFi1inTp1FGeKliSJx48f5++//87u3bsrjvf392fXrl1ZtGhRTpw4UXH89evXmTt3btrZ2XH58uWK4zdu3EgzMzM6OjoqO/eUxbpTp04EQAcHB6OsJT5HpyO7dGG02KzL1F9OJKtiMKrgxIOI4GzcuJEA4kxHf/DgQQLgvHnzDCpLf2Jy5szJCxcuCKWnv3//Pm1tbXnr1i3FsST54cMH2tnZCT3sJ+Ufv4ODg5BrpR4XFxdlD9C9vWWnRYD08qKbmxvvfOJLopQqVaoYZU9QvXp1YYsHnU7HatWqCfWSSPkmpmrVqpwwYYLiWI1Gw8DAQFauXJl9+vRR3LP29vbmixcvWL58ebZp00axtcD69et5/fp1urq6snHjxop6qTqdjt27d+fs2bOZP39+Nm/enHfv3jU4PiwsjHv37o01UUWnIzt3jhGb9fidXLFC0XdSUQUnXkQE5/Hjx4nOUjN0arD+xJz6L825CB07duTu3buF49etWyds/kXKgtehQwfheJ1Oxxo1aigX2z595JahTBn27tWLDx8+FK7DnDlzjHI8PXjwIIcPHy4c//TpU1auXFnYBC8wMJC//fabsOiHh4ezefPm9PT0FIrXaDQcOXIkW7duLRSv1Wq5cOFCOjk5xXZ+TQRJkqjRaKjRaLhixQrmypWLXl5eCW6/c+dONmzYkNbW1gTA8uXLs2HDhmzQoDHt7I7IYmOi40a0kk0AFQ5XBgcH8++//2aEEb2ixYsX8969e8LxBw8e5JYtW6KXCij9bfn6+nLSpEmxRkuUDNuqghMPiQnO69evee/evS+moLq6ujJVqlSxTkhQUBBtbW3p5OT0TdfhiDZSnyJq/PVdefOGTJlSFh0jBDe5YOw5MPY60DtfGoPosKQepc+CPiciIiLR9VharZanTp3in3/+yYIFC3LcuHE8duwka9V6S4A0M5O4KWUn+brasEFxHXx9fdmhQwc6OTlx7dq11Ol0vHHjhqIyFi1aRCcnJzZo0IAnT57khg0bFLmFnj9/nk2aNKGtrS1HjRrFzZs3c4WCnpqvry9HjhxJBwcHVq9enevWrWPDhg0NHq5XBecT1qxZwwkTJnDChAm0sbFh+vTpo/+/4DMzi44dOxIAjx07Fuv98+fP08rKig4ODpw1axYXLFjAwoUL08zMTNF6kOS48POHQu9NUriw6pejIkRQUAjbt+d/YkNuabxe/o+Li1HX1M2bN1m/fn0WKVKEGTNmVDyhRqvVcuvWrXR1daWVlRULFy6s+Pnsy5cv6e7uzsyZMxMAe/furWiBtFar5eHDh1m3bl0CYKZMmeJ8dv05quB8QqVKleKcKaZ/APkp8QkOSV68eJE1atRgmjRpaG1tzYoVK8a5XUKogmMk/v5kunRyA7Fu3feujcoPhlZLtm0bIzZblweQ1tbyG0YMseoJDQ1l6dKlCYDp06fnpUuXFJehnxCUIkUK5siRg9euXVMUHxgYyD/++INVqlRhgQIF2KhRI8WZRNatW8cBAwawQ4cObNSoEffv35/g9qoBWzJFNWBLAiZPBkaOBHLnBu7dAywsvneNVH4AtFqgY0dgwwYgRQpg0yag2an/AfPmAa6uwPnzSeK9FBISguvXr+Py5ct4/PgxRo0aJeRPo9Vq8eLFC/j6+sLV1VWRCdvnSJIEU9Ovt7zS2HZNFZyvhCo4SUBoKODkBLx7JxuTqLniVRJBqwXat5dFJkUKYMsWoEnJ50DevEBUFHD4MCCwAFpFxth2Tc00oJJ8SZUKGDVK/nv8eCAs7PvWRyVZo9UC7drFiM3WrUCTJpCvoagooHJloFq1713NXxpVcFSSN926yV7zb94g2hlLReUzNBqgTRtg82Y5Jd+2bUDjxgCuXQPWrZM3mjFDtTH/zqiCo/JN0Ol0kCRJeaClJfwHD5b/njJFHl4zkMDAQISHhyvfJyBWV5Xvgl5stm6VxWb7dqBRI8gOskOGyP+2aQOUKvW9q/rLowqOisH4+vpGZ2FWysyZM6HT6RTHabVa9Dt7Vm4sQkKAceMMjr1x4wbWrl2reJ8A4OnpidDQUKHYwMBAoTgV5Wg0wO+/yz0aCwtgxw6gQYP/Pty/X84+bmEBTJr0XeupIqMKzg9IvO6ZiaDRaLBmzRqhWF9fXzRq1EhxxmgAuHXrFsaMGYMUKVIojt2/fz92/fMPdNOny28sWwbcvWtQ7N27dzF79myh3srLly/Rr18/xXEAMHfuXBw7dkwo9uHDh0L2Fb8iUVFAq1Zyj0YvNvXr//ehVgv8+af894ABgKDdvErSogrONyYwMBBXr14Vin3+/Dm6dOkiZJ3s4+ODihUrRlswKMHX1xdVq1aFhYUFzMzMFMVGRUWhffv20Ol0QtM9Fy9ejLCwMDzImlUelJckYOhQg2Lv3buHBw8eCHnLpEuXDqtWrRLqIZUqVQq1a9fG1q1bFcdqNBr89ttvQteIRqPBzp07ha3AfyT0YrNzpyw2O3cC9ep9soGnJ3DnDpAxIzBixPeqpspnqILzjbh//z769OmDQoUKIXPmzIpig4KCMHz4cOTLlw9mZmbIkyePovgtW7agWLFiuHDhAtq3b68oNiIiAh06dMCdO3dQSmAMfP/+/Xj9+jXMzc0Vx/r6+iIgIAA5cuTAjRs3gGnT5OlH+/YBR44kGv/+/XtYWFgo9qQBZMEBgKVLlybu5fMZFStWhE6nQ5s2bRSLjrOzM7JkyYLSpUtj6NChCFMwM8/c3Bze3t7IlSsXZsyYoXj489GjR5gzZw4ePXqkKO5bExUFtGwJ7NoFWFoCu3cDdet+skFICDBmjPz36NFA+vTfoZYqcSK0XFQlUT5dkXvu3LnohIJLlixRXNbJkydpaWlJCwsLIYuCo0ePMlWqVKzxX8p/pQwePJi1a9fm5s2bFcdGRkbSxsaGR44cEdr34sWLOWzYsJhcXv36yavFixaVl5MnQGhoKO3s7BTlqtJz5coVjh8/nr169RKoNdm0aVPa2dkJJR7VZyYvVaqU4rprNBoWL16cANi4cWPFiSZHjx5NAMyfPz+nT5+uKA/cwYMHuWjRIh46dIhPnjwR8vJJjIgIskED+RKwtCQPHIhjo+HD5Q2cnEgjc8CpxEZNbZNM0Z8YPz8/9ujRgy4uLqxSpYriJIrh4eGsXr06+/fvL+RLExgYyLx58/Lw4cO8cuWK4vinT5/S1taWQUFBQuZx+/fvZ4MGDRTH6Rk7diznzp0b88b79zEpb5YuTTS+UqVKilOG6PH392f27NmFsgN//PiRq1atYq1atYT8cFavXs0qVapw6tSpivd96dIlFi9enHZ2djx58qSiWJ1Ox2bNmhEAmzRpQj8/P4Njo6Kior1sAHDMmDFKq54gERFk/fryqbeyIuNMbfj4MWlh8dMkfk1uqIKTTNGfmIoVK7JTp06MiIhQ3DuJiIhgnTp12L9/fyEDNUmS2LRpU7q7uyuK+5QOHTpw/vz5wvHdunXjqlWrhOO7d+/OTZs2xX5zzhy5QcmUiUzEEbJTp07cvn278P6bNm3KHTt2CMXqdDqWK1eO27ZtE4r39/dnoUKFhHqW796946VLl+jg4MCNGzcqig0JCeGCBQs4ceJE2tvbKzp+kiRx7NixzJ49O+3s7Pj7778rNlGTJIk3b96M5fYZEUHWqxcjNocOxRPcqJG8Uc2a5I+YKT2ZowpOMkV/YsaPHy+cnr5Hjx7s1auXcPzGjRtZo0YNoZ4JST579ox58+YVTk0vSRKdnJwU3SV/TtOmTXn8+PHYb0ZFkYUKyQ1LPJbfesaPH2+waV5c7Ny5k+3atROOv3HjBgsWLChsD+Dt7U17e3tlJnaf4OPjQ2dnZyHRImWn29KlS3PAgAGK4i5dusSIiAiuXLmShQoVYo0aNRLsKUZERPDgwYPs27cvHR0daWFhQXd3d06cOJFjx05hvnyPCMiuFfGOzh48KF8TKVKQcRi2+fn5Kcqo/DlardYoLxtSPi6iv0eSfPDgAV+/fi0cHxYWxpMnTwq3KargJFOSIlv027dvjfIx0bs+GoOx2a6NMasiGX/P7ujR/+wbTcnr1+ONN+bHTcrH0JhGiqTR5+Ddu3dGxfv7+yt27PwUjUYj7BpLyj298+fPJ7qPkydPcujQoSxQoAAtLCw4bdo0Tpkyh/nze//Xs9Hx6NF4CoiKIgsUkK+JgQPj3GTw4MEcNGiQ8Pd49OgRHRwcOH36dKHrSpIktmnThkWKFIm2OlF6XjZs2MAcOXKwd+/e9PHxobe3Nz9+/Ghw/JMnT1i2bFkWLVqUK1asYFhYmKIefGBgoCo4yRHVnuAb0Ly53MBUqKAOn/xkPHr0iK9f+7NWLUb3bBIw/CRnz5Y3zJKFDAiIc5PQ0FAWKVLEqCHW9+/fs2nTpqxYsSJPnTrFw4cPKy7j5MmTLF26NGvXrs3q1asrfrb68eNHzpw5k3Z2dnR1daWrqyvfv3+vqIxLly6xQ4cOzJEjB83NzTly5EiDbm7VHk4yRRWcb8CzZzHOoOvXf+/aqCQhYWHyYxhAtrFJ0I7q9WsybVp54+XLEyz3wYMHtLW15YULF/jgwQOhukmSRE9PT6ZOnZqZMmUSGu7U6XTs378/ATBjxoyKnUNJ+bukTZs2elahUhtySZLYu3dvmpqaRk8SScwGXBWcZIoqON+ICRPkhiZHDtKIYSOV5ENYGFmjRozYfP4I7wtat5Y3LlUq0anyOp2OU6dOpYWFBYcOHSpcx6tXr7Js2bIEwOLFiyu20JYkiadPn+a0adPYpEkTFilShHfu3FFUhk6n4/Pnz3no0CHOnz+fkydPZnh4uKIySHk48/nz5zxz5gxv376d4LaqAVsyRfXD+UZERACFCwNPngD9+8smWyo/LGFhcuLNI0dkd4p9+4CKFRMIOHQIqFULMDUFLl0CSpRIsHxJkjBv3jz89ddfyJQpE168eCGUcknPy5cvsWPHDlhbW6Nr167C5ZDEx48fk31boRqwJVNUwfmGHD4M1Kwpp56/cAEoXfp710hFgLAwOfGmlxeQOrWce7N8+QQCwsPlmw1vb+B//wPmzDF4X1evXsXvv/+O2bNno16snDgqCaEasKmo1KgBtG0rp6Hv3l1O3KjyQxEaKife1IvNgQOJiA0gZ4D29gZy5pQN+hRQokQJXLlyRSiDuYo4quCo/BAkmvF59mwgQwbg+vUvhtWCg4OF9qk2Rt8GvdgcOwakSQMcPAiUK5dI0L17gD6D+Pz5cqBCUqdOjYYNGyqvsIowquCofDMCAgKEG/9FixYlvIGNjezoCMiJG589AwB4e3sLWzIsXLgQIiPOQUFBwsZvvxohIXLizePHY8TGzS2RIEkCevaUzXDq1//PR1rlR0AVnF8QY9wsd+3aJXTnHxYWhqZNmyJlypSKY2/duoUpU6YkvmGXLvIT5rAwoE8fgMSuXbuwf/9+xfsEgH379mHjxo2K48zMzNCqVSsh36LXr18L+x39aOjF5uRJIG1a+fl/2bIGBC5eLAelSgUsWKDaRv9AqILzA/LgwQOhOK1WiwULFgj5w0RGRqJnz57Yvn27Yk8cjUaDFi1awNfXV7FNAUn069fPsFT7JibA0qWyQcrevcC6ddi5cyeOHTsm1OMICgrCn3/+qdj5M3Xq1Lh79y7atWun2EzNwsICFStWlO0YFBISEvLDmLd9/AjUqQOcOhUjNmXKGBDo4wP89Zf899SpqrHaj4bQZGqVRIlrvnpkZCR3797N6dOnK05Zo9VquXXrVpYpU4YeHh6K63P06FEWLlyYefLkUZw2/tmzZyxdujQB8J9//lEUq9Pp2K5dOwJgs2bNFMWS5K5du5gmTRqamJgYfswmTyYB6tKlY4G0aZkqVSru379f8b4LFChAS0tLzpw5U3FskyZNCICdOnVSfK7bt29Pc3NzTpw4UdG50id7nTBhAt++fau0yt+M4GCyXDl56Uy6dOSFCwYGShJZrZocWLEiaUTaJxUx1IWfyZRPT8ybN2/YrVs3ZsiQgWnTpuXjx48VlfX27dvoBr9y5cqKE+/5+Pgwd+7cBCCUufnmzZtMly4dM2bMqDg3miRJ3Lp1K4sUKcIJEyYo3rckSXRxceGKFSsMTyKq0ZClS5MAnxcpwv8NGCD0Azlw4AAzZ84s5Osyfvx4FipUiGvXrlV8vs6dO0cAdHJy4pMnTxTFXrlyhSlSpKC5uTmHDRtmsNjpLRE2bNjAGzduGJ0DLz6Cgkg3txixuXhRQfDSpTF5bozI7aYijio4n7FhwwaWKFGCVlZWzJQpE1u3bm1wyodKlSpFe3l8/tq5c6eienx6Yh4+fEhHR0cCEMrjdO7cOdrb2zNz5sxChl4bNmxggQIF2LRpU6FElAMHDmTv3r2FTNQkSWKJEiV46tQpoUbs/fv3tLOzU57d9s6daF+UjbVrK96vngoVKvDSpUuK40JCQnjhwgUWLlxYyFZi6tSpLFOmDJca4PnzOWPHjqW1tTXr16+vqGF4+/YtixYtSgC0sLDgqVOnFO87IYKCyLJlZc1In55UdFifPSPTpJGDZ89O0nqpGI4qOJ+wYMECAmC5cuW4ePFiTpgwgZkyZWKOHDn46tWrROMrVarEzJkzc+3atV+8Xrx4oagu+hOzZMkS2tracvPmzUJmWtu2baO9vT3Pnj0rZKC2Z88e5s6dm8+ePRNKe3Hw4EEWKlSIoaGhimNJ2YCtYsWKQrGk/P2F7QGmTCEBhllaki9fChUxYsQIzpkzR2z/JOvVq/eln48BSJLE169f09HRUXHDHxUVRS8vL44bN47Ozs6KMj0HBASwXLlytLW1Zb58+bhq1Sqhm5TPM2QHBpJlysh6kSEDqehS1ulict2ULZto+hqVr4cqOP/h5+fH1KlTs0SJErGGQC5dukQTExP+8ccfiZZRqVIlOjg4JEl99CemdOnSwl4m8+fPZ4ECBRQPwek5c+YM7e3thT08/Pz86ODgoNhAS48kSXRzc+OheN2yEqdv375csWKFWLBGw7eOjnJDVbu2UEbpffv2sWnTpmL7J3n58mUWLFhQ2Cbh4sWLtLe3V3zDo2fbtm20s7PjiRMnDI4JCQnh2bNnefPmTbZo0YJ58uRJ1MRNkiTevXuX06dPZ4UKFViuXDkeOnSIhw4d4s6dXixYMFBMbEhy7twY57X79xUGx6DRaIR9YPSI3LR9ihIrgbgIDg42yrJEp9MxIJ5s2oagCs5/eHh4EAA9PT2/+KxSpUpMkyZNos8A9IKj0+kYFBRk1InVn5gPiThSJsSpU6eMin/37p1QFlo9Wq2W586dE44nZcE35kfu4+NDf39/4fgPp09TsrSUGywBI7bQ0FDeN6KRI40/BmfPnhU2wSNlEzjRmxZSNmHbtWtXgts8fvyYgwcPZr58+QiAuXLlYsuWLdm4cSdmzPiQAJkxI6n43uXmTfK/87emTBnh70CSw4cP57Rp04Tj79y5w3z58vF6Av5LCSFJEl1dXTl48OBEszLHx/Tp01m8eHEeOHCAkiQpfr54+/ZtZs+enX/++SffvHlDkoqsDVQ/nP/o0aMHAcT5jGP48OEEkGjjW6lSJaZIkYIpU6YkAFpZWbFOnToGjeFHREQwKCgo+vXixQs1W3RyYeFCWXAsLEgjBFjFMB48eMANGzbQ319O4Kx3A1fcToeHky4u8rBotWp0LlTIqHr5+/vT2dmZ642wsjh06BDt7Ozo6elJPz8/xVmig4ODOXDgQObOnZt79uyhh4eH4puRY8eO0dXVlVWqVOGwYcO4bt06RfF+fn4cN24cc+TIwR49erBgwYIGT05Rezj/Ub9+fQKI8wL4+++/CYB79+5NsIyOHTty+PDh3LBhA7dv385Ro0Yxbdq0tLCw4NF4rQZlxo4dG+dkA1VwkgGSRNavL7d8hQrJ+e9Vvir+/mTJkkaIDSk7d/5nqhb+9CmzZs1qdL2ePn1KR0dHHj16VNEw46folwmULl2affv2FSrjypUrLFGiBM3MzDh8+HDF8ZIkcdOmTTQ3N6epqSnXrl2ruIyQkBBWqVKFAGhjY2PQM2JVcP6jatWqBBDnMJh+uG3r1q2Ky71//z6tra2ZN2/eBLdTezjJHF9fMls2uQHr3ft71+an5sMHskQJ+VBnzizYqTx0SC4AIP/9lySZPn16o5/BkPIQpbW1NYsWLSpc3tatW6NvKvfs2aM4XqPRcODAgcyQIUP05CKl3Lp1i8OGDWP16tWZOXNmrlmzRnEdjh07xqVLl3LQoEH8/fffEzWlUwXnPxLq4SxcuNCgHk58dOrUKd7huvhQDdiSIQcPxjRiu3d/79r8lHz4QBYvHuP2fOuWQCGvXpE2NnIhvXqRJD09PZkhQwb26dPH6Dru3buXtra2BMCDBw8KlSFJEk+cOMEOHTrQ0dFReKGtVqvlhQsXOHnyZD5//lyoDH19fHx8jHrubAjGtms/TWqbnDlzApANkT7n1atXAABbW1uhsh3/S5/x/v17scqpJA9q1gQGD5b/7tQJePr0e9bmp+PDB6BaNeDaNSBLFtlqoHBhhYVotcDvvwO+voCLCzBzJgDAysoKAQEBCAgIMLqedevWxd27dzFw4EDMmjVLqAwTExNUrFgRq1evxo0bN4TrZWZmBldXVwwfPhx2dnZCZejr4+joCFPT5N2kJ+/aKaD0f6ZbZ8+e/eKzs2fPInXq1ChQoIBQ2Y8ePQIAZMuWTbyCKsmDyZMBV1cgIABo3lx2DFUxGj8/WWyuX5cTdx87JiA2ADB6tJyYM00aYNs2wNoaANC4cWNkzJgRv/32W5LUN02aNJg9ezamTp1qWJ6+BEibNq1w2/LLkcQ9ru/G+/fvaW1tHe86nC5dukS/9/r1a967dy/WYkZ/f/84p55eunSJ5ubmdHZ2VlQfdUgteRFrrP7ZM/lJNkB2755gnFarTZLnBj8z79+TRYrIhzNrVjnJgxD//hsz5LllyxcfDxgwgOfPnzeusipGoT7D+YS5c+dGZxpYsmQJJ06cyEyZMjFbtmx8+clK844dOxIAjx07Fv3ezp07aWNjwz59+nDOnDlctGgRu3fvTgsLC1pbW/Ps2bOK6qIKTtIjSZLwmpxt27bFfuPgQdLERG7c4li7pefixYu8YHB2yRj8/f2FF/z+SPj6Rs9cZtas5N27ggU9fSqvCgXIfv3i3OTu3btfLcebimGogvMZ69atY/HixWllZcWMGTOyVatW9Pb2jrVNXIJz9+5dtmjRgk5OTkydOjXNzc3p4ODALl26COUvUwUnbl69ehVL/JUwadIkobxmgYGBzJ49+5c9FXf3mBXs8czbnT59OgcMGKB4nwEBAXRzc1O8ME+SJOHMEN+ad+/IwoXlQ5gtGylc7ZAQslgxuSBXV9KIRa4qXxdVcJIpyVlwoqKiFC9Y0/P8+XOhKZyknDmhYMGCQrm5Vq9eTQBCPZxhw4YRwBf5vajTkXXqyA2dg4Pcgn5G3bp1mS1bNsWpaSIjIwmA48aNU1zf33//XciC4lvy7h3p7CwfuuzZjcg4o9ORzZvLBdnYyMOdKskWVXCSKQmdGJ1OJ5wMMyQkhJs2bRKahhkUFMRZs2axadOmiu+8w8PDOXHiRFpbW8fqGRqCJEn8+++/mSJFCnbs2FFRLEkePnyYKVKkYKZMmRTHPn/+nFZWVgQQdxLLDx/IPHnkBs/NjfxkyEaj0TBNmjQEoDhTtiRJNDMzo6mpKU+fPq0odvPmzQTAzp07K7pOrl279k18cN6+ldfPAmSOHGQiSzcSZtw4uSBzc1LhcVL59qiCk0z5/MS8efOGq1evZps2bVi7dm1FSfy0Wi337t3Ltm3bMlWqVBw6dKiiumi1Wo4dO5Zp06almZmZ4mScERERbNGiBQGwfPnyih+iv3z5kq6urgTAf/9bxKeE8+fPM3369KxTp47i2A8fPrBz587s0aNH/DnR7t+XzVkAskOH6CSf/v7+nD9/Pps3by70PKZx48bMnTs3X79+rSguNDSUqVOnppWVlaLEp2/evKGdnR0rVqzIefPmCSf8THgfZMGC8qHKmZMUGG2OYdu2mEkCybxHpyKjCk4y5dMTExEREZ0Jwd7e3iCrhE+RJInt27ePbvCVDklpNBp27tyZpqamHDJkiKJYUv4uJUuWZOHChYUWyt25c4f29vacPn260EPfWbNmsU+fPvTz81McS5LFixdPPAHnoUOkmZnc+H1iI3Hy5Ek2aNBAaL86nY5FixblzZs3FcfOmjWLjRo1Umxpcf78eVpYWBAAN2zYoHi/CfHmDVmgQIzYGOWBduUKaW0tF/a//yVZHVW+LqrgJFP0J8bb25sdO3aks7Mz8+XLx9u3bysqJzAwkK1atWL58uXZvn17xQ/cQ0JCWL9+fbZq1Yo7duxQnKU2PDyclStX5rhx4/ju3TvFvZvIyEgWL1480WzDCcU7ODgodr7UExoayixZshi2Avvvv+UG0MREvvsmefXqVVatWlVo3yQ5ZcoUjhw5UnGcJEn08/Ojo6Oj4llyK1asYOvWrWlra8tFixYlybTu169jxMbW1kixefJEntIGyD43Ao6qKt8HVXCSKfoTkyNHDk6cOJGRkZGKU1ecP3+eefLk4dixY6nRaBT3bN68ecOSJUsqshr+FI1Gw0aNGrFfv37CjdaIESMM8iKKj9WrV7NVq1bC8adOnWKtWrUMD+jbNyaztJcXHzx4QFdXV+H9e3t7M0+ePMLH79ixY8ybN6/iH3hISAhfvnzJWrVqsVatWgb1qgMCArhx40a2adOGS5cuZWBgIAMDA3nvXhDz5tURIO3sSCOcDuR51Hnzyse4SBHZmU3lm2LMDYgqOMkU/YkRNS8jyaVLlwpntCXJ69evc9myZcLxHz9+5NSpU43Kz7Ro0SIGBwcLxx8/fpy3hBJyyTx58oReXl6GB2i1ZNOmcoOYJg1DTp3iljgWISrBw8PDKD+bVatWRXuXKEWSJC5atCjRiR579uxhoUKFohNSZsuWjY6OjrS1dWWKFE8IkPb2cudEBE9PT147fVqe9qyfFahgaDk8PJw9e/YUNrIj5WFK0Z42KQ8Nt2zZUvh6liSJ9erV4759+4TrMHnyZPbv3194PdrNmzdZpkwZHjp0iJIkRb8MRfXDSaYk52nRKokQHk5WrhwzVdeo8aMfi/v373PGjBncvXs3X76M6Yw4OJCfLWdTRM0qVRjg5sZoJzaBRTuNGzfmqlWrhOvw8OFD2tvb8/jx40LxOp2Oo0ePZuHChfnkyRMh8bt69SpdXFzYtWtXBgUFKTbGCwkJ4ahRo2hra8vFixfTy8tL0cxESZJ4+PBhlilThhUqVKCXlxf/97//GSw6ag8nmaIKzg9OYGDMYsRcuRTdjf8MvHgRM1vcwYE0JmmCFBXFXXrX1ZQpSYVZO/TcvXuXjo6OwmvISLnBt7Oz49WrV4V7zps3b6adnR0HDRrEAwcOKI6PiIjgiBEjmDt3bjo6Oip+rkvKQ7XNmjWjtbU1ixQporjHI0kS9+7dy/z58xMAu3fvbtBIhio4yRRVcH4C3rwhc+eWG8p8+X4Z0Xn+nHRykr+2o6OcdUYYrZahjRrFrLUR8I75lK5du3LSpEmK14J9yvHjx5kjRw4WLlxYeLh4+fLlBMCcOXMyICBAcXxoaCgrVKhAAHRychKykvfy8mKOHDkIgGXLllW01IIkw8LCOHjwYLq5uTF16tRs165douvzVMFJpqiC85Pg7S3f4gPy+NJPLjrPnsVobK5cxotNWIsWJECNiQmfLVhgVN10Oh3HjBlDAOzQoYNwOYcPH2b69OkJgDt27BAq4/r16+zevTutra3ZqVMnoTKCgoK4adMmtm7dms2aNVO8GJuUeyqPHz/mqlWruHHjRqF6kPKxffz4Md/FkW3jU1TBSaaogvMT4eMTW3QEc8Eld54+lUUGkEXHqCwzWi3ZqZMsNgCbmZoKT23/lAsXLjBdunQsWLCgUeW8e/eOXbp0YalSpYyatRUQEMC5c+fyrnDWUpmIiAjh7CPfEmPbNROSTFrDAxUACA4ORrp06RAUFIS0adN+7+qoGMvTp0CVKvK/efIAR48C9vbfu1ZJxrNnQOXK8tdzcpL9bIT9wKKigPbtgS1bADMz9EyfHlLTpli2bFmS1PXSpUuoVasWnj17hjRp0hhV1oULF5AtWzY4ODgkSd1+doxt134aAzYVla+KoyNw/Lj87+PHgJsbcPv2d65U0vD0aWyxOX7cCLEJDQUaNJDFxtwc2LQJD4sUwahRo5KsvqVLl8bBgwfh7e1tdFm//fabKjbfEFVwVH4pKA8jC8XeDw8HTp0CChUCXr0CKlQATp9ONG7Pnj2K9xUVFSVSRcX4+MSITd68wIkTgKATu2z7WaMGcOiQ7NS5Zw/QvDnc3d1hn8S9wdKlS6No0aJJWqbK10cVHJUfjvDwcOHYJUuWCMU9ePAAU6dOlVvjU6fkHk5goNzAbt0abxxJDB06VLGN8caNG3Hr1i2huhqKt7csNs+eyWJz7BiQM6dgYQ8eAGXKAOfOARkyAEeOADVrAgAqVKiQZHVW+bFRBUflm/P+/Xu8fPlSKPbkyZOYOHGiUOy0adOwY8cOmJiYKIojiZ49eyI4OFh+I2NG4PBhoH59ICICaNkSGDsWkKQvYh89eoT79+9j7969ivaZKVMm1K1bF69fv1YUZyh6sXn+HMiXTx5GExYbLy9ZbJ48kYccT50CypZNusqq/DSogvMLotPp4OPjIxQbHh6OlStX4siRI0KxU6ZMQY0aNWBjY6MoVqfTYfz48ahSpQqqVaumeN9z5szBsGHDULx4ccWxa9aswfHjxxEZGRnzprU1sGsXMGiQ/P/x42XhCQmJFbtv3z4AwK5duxTtM1euXHj58iXq16+PkM/KNJYnT4BKlYAXL4D8+WWxyZFDoCASWLAAqFVL7u2VLQtcuAA4OydpfVV+HlTB+caEh4fj7NmzuHnzpuLYsLAwHDp0CH/99Rf279+vKFaSJJw6dQr9+vVDvnz5EBgYqCj++fPnGDZsGOzs7LB8+XJUqVJFUfz+/fuRL18+jBgxAoMGDYKFhYWi+FmzZmHs2LHImTMnKleurCjW398fhw8fBgAhwcmcOTPSpk375XMIMzNg1izAw0N+QL59O1C6dKzJBLlz54a9vT2qVKmi6NmRo6MjrKysEBISgkePHimuc3w8fiyLzcuXQIECsthkzy5Q0MePQOvWQP/+gFYLtGkj93QU3kio/GIk1fxsldh8Ol9dkiTOmjWLRYsWpZmZGWvWrMnw8HBF5a1bty7a56RPnz6K1w78+++/NDExIQB6enoqiiXJ06dP09zcnJaWlkJrDk6cOMHUqVOzYMGCQjmoRo8ezYoVK3LUqFGKYzUaDQsUKMBt27bRWyAh2IEDB9iwYcOEF+adPi3bX+rTt6xYEW3k5uzsrNgDiZQTLdrb2wuZv8XFw4eyjw0gm6gJ5gMlr18n8+eXC0qRgpw3L/q7qvzcqAs/kymfnpirV6+ySpUqBMAaNWoozgV19epV/vbbb8yYMSObNWumuMG+evUqCxUqxHLlyrFXr16KYkny8uXLdHR05Lhx4xQbgpHk2bNnaWdnxwsXLgglTjx48CDz58/PoKAgocVxK1euZLNmzRTH6Rk8eDAXLlyY+Ia+vmStWjEuls2bk76+LFKkCJ8JrqKcOnUqBw4cKBT7KQ8exOhhoUKyTbRiNBpy8mQ5RY3eGEcwL5rKj4kqOMkU/Ylp0aIF8+bNy82bN3PmzJmKxCYoKIj9+/dn7ty5uXv3bp48eVJRz0ir1XLatGl0cHDgwYMH6evrq9hxc8uWLbSzs+Px48cpSZJisbt48SLt7Ox4/vx5RXF6Xr16RTs7O167dk0oPiIigrlz5+adO3eE4knSxcWFDx48MGxjnU5ulPXuoZkzc6ijo1DPipRtrrNnz85AA3xjtFotz5w5w2HDhsUy6rt/n8yeXa6OszOZSPaSuLl/nyxbNkZMmzSRBVbll0IVnGSK/sTMnDlTsXGanmHDhnHYsGGKXTr1nDhxgk2bNuX79++F4kNCQlizZk2jUpL07duXp0+fFo7fsmWLUZ4+jx494ujRo4XjNRoNe/furTz9yZUrpItLdAMdUbu2sJnMjBkzeOPGjXg/Dw8P5/jx45k5c2YCoKmpKfPly8d8+fLR0bE2zczeESALFxYQm9BQcsQI6vQCmjYtuXq14iG0hw8fCtsCkGRUVBQXLlxolDfTjh07EjyOifH8+XPOmTNHOBWOJEkcPXq0YtfeT1m3bh23bdsmXAdvb28OGjRI2K5d9cNJpiRFLrWksAZW+Y5ERpKjR8f0diwt5f9/hZxZkiTx3r17nD59OqtUqcJr167x9OkPtLHR/ic2OmUdEkmSbbb1OeQARtWoIZxg7dKlSyxevLhRjXX9+vU5Z84coXhSTtrp4ODAR4L+RgEBAaxWrRo7deokZKgnSRKXLFlCW1vb6KShSsu5desWy5Urx7p169Lb25vPnj1TdEyDg4M5evRo5siRg1OmTGFgYKAik0dVcJIpavJOlWju3CGrVYsZjsqWTX7QrnDiiBJu35aYNWuMk7PBnVxJIg8dIkuViqmvnR27ZMzIEIXp7z+nVKlSvHDhgnD827dvaWdnZ9Tw6M6dO+nk5MTnz58rMi7TExUVxW7durFSpUrcvXs3X7x4obiMu3fvslixYuzWrRtbtmypWHR0Oh09PDxoa2tLV1dXjhkzRnEdXr9+ze7du9PW1papUqXiyZMnDYpTh9Q+Y8OGDSxRogStrKyYKVMmtm7dmk8V5Fi/fPkya9WqxbRp0zJ16tSsVKmSkM2zKjgqsdD3GBwdYxrynDnJuXPJJL5G7tyRjUoBsmhRA8VGqyV37iTLl4+pX6pUco8sJISZM2cWSp//KStWrGDnzp0Vz9D8lJ07d7JEiRJcvny5cBlr1qxhgQIFWLFiRaEelyRJHD9+PE1NTVm/fn2hMj5+/MjChQsTAAcMGKA4npRtu/GfJbjIsHNgYCDLli1LAEyVKhVPnTqVaIwqOJ+wYMECAmC5cuW4ePFiTpgwgZkyZWKOHDkMmpZ68eJFpkyZkg4ODpwxYwbnz5/PwoULM0WKFDx8+LCiuqiCoxInkZHkkiXyDC99w546Ndmvn5Dt8ufcukVmySIXW6wYmehQva+vLHp6e0+AtLAgBwyIfuBz69YtZsiQQbEd8ufcvXs3+iZQlFu3btHe3p4AhKeLnzp1iqlTpyYAIcdOkly2bBlz5sxJAEI+NCEhIVy3bh3r169Pc3NzoTIiIyN54sQJjho1iuXLl+f+/fsVlyFJEp8+fcotW7Zw/PjxiTqHqoLzH35+fkydOjVLlCgR607s0qVLNDEx4R9//JFoGWXKlGGqVKliTWENDAxkzpw5mTdvXkV3MqrgqCRIRAS5eDFZoEBMQw+QxYuT06cLOZ99KjbFi5PxmkgGBJCbNpENG8rraPT7Tp+eHDbsC7+fLl26EAA7duyouE6fsmvXLgJg9uzZhcuIiopiv379oifkiHL9+nVWqlSJZcqUEX6uFBUVxQ0bNrBevXrCE3NIeSbi5s2bhZ4LfYoxPUdD+S6C4+DgQHd3dz5//lxop18DDw+PeBc1VqpUiWnSpEnwhD558oQA4nTvGzt2LAHw3LlzBtdHFRwVg9A/M/m88QfkxZV9+5I7dsgClEDDePMmmTmzHFaixGdi4+8v72PCBLJChZhJDPpXqVLk33+T8Tyj2bhxIwHw33//Nfrruru708zMTGjx76d4enqySpUqRpUhSRK3bdtmtHmaJEmK19b9qHwXwSlSpAhNTEyYIkUK1qlTh9u3bzd6fNdYevToQQB8+PDhF58NHz6cABKcEqn/UcU1Fnrw4EEC4Lx58wyujyo4Kop5/14ebqtYkTQ1jS0KAJkhg/xZ+/ZyT2TePHLFCl6ftIeZ0kQQIEvavaP/yJlk9+5kjRoxftGfvwoVkssw4AG8r68v06dPr3gNV1zodDo2btxY6IH951y5cuWb3NWrxGBsu5ZCJB3OjRs3cPnyZXh4eGDTpk04ePAgMmfOjI4dO+KPP/5A/vz5RYo1ilevXgEAbOMw89C/9/LlSxQpUsSo+PiIjIyMldwxOrOwioqhZM4M9OghvwIDZb+Aw4eBs2eBO3eAgADg5MlYITdQBNVwFB9giVK4hMMvaiD9pDisEJyc5DxvFSoAdevKWZ0NJEuWLBg7diwsLS2N+34ATE1NsWbNmtiJUAUpUaKE0WWofFuEBAcASpUqhVKlSmHOnDnYunUrPDw8MGvWLMyaNQtubm7o1q0bWrRogZQpUyZlfeMlLCwMAOL8UVhZWcXa5mvET5kyBe7u7oZXWEUlIdKnB5o0kV8AEBkJ3LsH3L0rZ958+RLX71mi2onR8NekRek093DIdRrSZ6wJpE4t+/bkzg3kygUULgxkymRUdfr27Wv8d/qPNGnSGG0NrfJjIiw4eqysrNC+fXu0b98eT548wdixY7FhwwacPXsW/fv3R4cOHTB48OCvbuNqbW0NQO5pfC5yesMu/TaJxX+OIfHDhw/HIH2qesg9HDthn16Vr40kSdDpdDA3NxeKv3v3LvLmzSscDwB+fn7InDmzYRtbWgLFiskvAFevAtWrAwEa4LffgIMHCyJdum3CdUmMFCmMbipUVJLGnkCr1WLbtm3o27cvNm3aBBMTE9SoUQMVKlTAokWLUKhQIezevTspdhUvOf9zj4pr2Cuh4bKkire0tETatGljvVTiR6PRCPu8REZGYtOmTYpdNAHZTG3v3r3o1KkTTE2VX/7BwcEYNGgQpkyZIiw2Dx48QOPGjXHnzh2h+GixCZB9zw4eBNKlEypKReXbYswDpDt37nDQoEHMkiULTUxMmD17do4YMSLW/PhHjx6xePHizJcvnzG7SpQVK1YkOEstderUCc5Se/z4caKz1M4qyIz7tScNaLVa4bxSoaGhPHHihNAD17CwMO7bt49jx441KKHkp+h0Op46dYq9evVi3bp1FT+EfvPmDceNG8esWbNy2LBhimJJ8tixY3RzcxNafyFJEtevX89s2bIlOgElPnx9fdmnT59oiwoRLl+WZy8Dci5NdU6Kyrfku8xSW7FiBcuWLUtTU1OamZmxdu3a3LFjR7xTHVetWkUzMzOhChrK+/fvaW1tHe86nC5dukS/9/r1a967d++LVPeurq5MlSpVrOneQUFBtLW1pZOTk1HrcLy9vbl3717OnTuXffv25YYNGxR9v4cPH3LBggXs1q0bXV1d6e7urqg+b9684YABA1iqVCmam5srXpn88eNHtmnThlZWVjQ3N6eXl5ei+KioKLZu3ZoAmCFDBsWL9nQ6Hbt27UoAzJ8/v2KxlCSJo0aNIgDhxt7T05OmpqZs0KCBUPy7d+/o4OBAALx48aLi+IsXY8TGzU0VG5Vvz3cRHBMTE+bIkYMjR440KG3MhQsX4uw5JDVz586NzjSwZMkSTpw4kZkyZWK2bNliZWjt2LEjAfDYsWOx4s+fP08rKys6ODhw1qxZXLBgAQsXLkwzMzMePHhQUV0+PzH6ugHgyJEjFS82279/P83NzQmA48ePVxzv5eUVfXc+d+5cRbEkeeTIEebJk4empqZCBm4HDhygvb09s2XLJrSeY//+/bS1tWW1atWEsk8fPHiQ9vb2dHd3F+qd6G0Wjhw5IpQPLCoqio0aNWLPnj25ePFixfEXLpDp0sliU64cGRysuAgVFaP5LoKzc+dOoxdufS3WrVvH4sWL08rKihkzZmSrVq2+8CKJT3BIuWGpUaMG06RJQ2tra1asWDHO7RJDf2I2bNhANzc3lixZksWLF+eSJUsUlXP27FlWr16dxYsXZ+fOnTlr1ixF8Y8ePWLjxo1ZtGhRrl69mpMmTVIU/+HDB3bu3JkuLi48d+4cV69erSg+MjKSQ4YMYcGCBXnt2jVev35dUbwkSZw3bx7z5MnD27dvC13oe/fupYODA2/fvi20qvzBgwe0t7c3KNdUXGg0GjZv3pxdunQRGgY9f152BQDkVGdBQRI3bNgglDhSRcUY1NQ2yRT9ialevTq9vLwoSZJiHwx3d3cWKVKEO3fupCRJin1xzp49S3t7e65YsYJarVZxYxsREcH8+fNzwoQJwmk3/vjjD3bp0kXY02f79u0sX748fQXNvt6/f898+fLx/v37QvEkWatWLe7evVs4fvHixWzXrp3QTdq5c2TatBIB0sbmHlu1+oPt2rWjnZ0dAbBYsWIcPXp0glk/JEni1atXhetPypk4go3oVoWGhhq9ol9Jpo+4uH37tlEpaEJCQgzOqhwf//77r7A/FimPwhiT0y4gIMAoPx1VcJIpSTFpwN/f3yjDKY1GY1QjQdLoSQ8fjUxpr9VqjV7hbmy8sTmutFqtUCaOs2fJNGn4n5+NH7du3c89e/Zwz549LFKkCCtUqMBp06bx7t27CTYgWq2WhQoVMqrB7t+/P6dMmSIcf+nSJebJk0c4BYxGo6GrqyvXrFkjXIdFixaxRIkSiie76Hn8+DFz587NFStWCMXrdDp27NiRZcuWFbYc3759O21tbTlr1ixqtVrF4vX06VNWrlyZFStW5NWrVxkVFcUP8Sbd+5KAgABVcJIjamobFWM4cyZGbCpXJj/tIEqSpKiRIMl//vmH5cqVE76zffHiBXPmzCncUyXl9FPjxo0Tjn/69Cnt7Ox48+ZN4TImTZpENzc3hoSECM3SfPXqFYsXL87Ro0fzwYMHQjczq1atoq2tLXfv3i1kK/D27Vu2aNGCrq6u7NGjh6LZs6R8/ezYsYN58uRhy5Yt6erqavCNqdrDSaaogqMiyunTsmMBQFapEltsRJEkiZUrV+b27dsTTUEfHz169ODs2bOFe3wfPnygra0tHzx4YJBdSFzs37+fBQoU4KpVq4SHpoYPH86qVauyXbt2QvHBwcGsXbs2c+TIQXd3d6Ey7ty5w9y5c9PExETIVoAkZ8+eTQDMkiXLF8+pDeHdu3fRVg+VKlUyqPepCk4yRRUcFRFOnZJ9zwCyatWkdaP28vKinZ0dO3fuLBTv7e1NOzs7du3aVSheo9FwwoQJzJIli+LJL3r8/PxYqVIlAuCuXbuEyjh37hzTpElDADx//rzieEmSOGHCBAKghYWF0PPBt2/fsnXr1rS0tGTmzJmFBPjEiRPs378/nZycWKhQIcVDhZGRkTx37hxnzJjBRo0asUOHDoneTKiCk0xRBUdFKSdPxohNtWpJKzYkOX36dAJgnjx5hOL1U/tz5MghFK/T6di3b18CYL169YTK0Gq1nDBhAs3MzNioUSOhMiRJ4saNG2lnZ8datWoJlUGSV69eZdu2bVmjRg3hocrAwECuWLGC48aNM+p57YMHD4yeGCJJUqK9RlVwkimq4Kgo4fjxGLGpUYP8WvYqc+bMIQD6JWoFGjcjR44kAOEH75IkcdKkSUyTJo1Rs7XOnj3LvHnz8s2bN8JlhIWFccKECYqn6n/Os2fPjJr99iNhbLtmQpJJni9HBcHBwUiXLh2CgoLUvGoqCXL8OFCvHhAWBtSsCezaBXzNJOt///03cufOjTp16iiOJYlevXqhU6dOKFOmjHAdPDw8UKRIEZQuXVq4jKCgILx+/RoFCxYULgOQv5OJiYlRZfwqGNuuqYLzlVAFR8UQjh0D6teXxaZWLWDnzq8rNnqCg4OFr0udTodXr17B3t7eqDpoNBqjsm2rfHuMbdeSJFu0ioqKcry8Yno2tWt//Z7NpxhzE2RmZma02ABQxeYXRBUcFZXvwNGjstiEh8sGnDt3Av/5/Kmo/LSogqOi8o05ckQeRouIkEVnxw5VbFR+DVTBUVH5hhw6BDRoIItN/frA9u2ymaeKyq+A6hv7nQgNDYWVlRXMzMwUxUmShPfv3+PVq1dwcnJCOgVWjyTh5+cHb29v+Pj4oESJEsiXL5/B8VFRUXj06BHu37+Pe/fuoXTp0qhVq5bB8aGhobh9+zZu3LiBmzdvInfu3Bg4cKDBM4QiIyNx69YtXLt2DdeuXYNGo8GsWbMUPY/4+PEj7t27hzt37uDu3bto3LgxypUrZ3C8MRw8CDRqBERGyqKzdasqNiq/GEk1P1slNp/PVz937hxLlixJOzs7pk2blnPnzlW0WOzdu3fR5mkmJiacPn26oniNRsO6detGe/KIeOroDcwAcMiQIYoXqh0+fJimpqYEwDZt2iheh/Hu3bvoLMlFixZVnEFakiT26tUr+jvMmzdPUTwZY9dQv359VqpUie3btzdoDcb+/aSlpbzOplEj0sh8oCoq3wV14WcyRX9iXr16xZUrV9LNzY3m5ubMli2bohTnGo2G27dvZ5UqVZghQwamTZuWe/fuNThekiQeO3aM9evXp5OTE83NzRVn3L1z5w7btm1Le3t72tracvr06YrifX19OXjwYObIkYPlypVj165dFaXqj4yM5KJFi2hvb88mTZqwVKlSipNXXr58mY0aNWK+fPloa2ur+BhIksRz586xb9++TJs2LQGwW7duX7jGxsXevaSFhSw2jRuTr169V2xVoaKSHFAFJ5miPzE2Njbs1KkTT58+zRUrVvD169cGl7Fu3To6ODiwYcOGPHjwIC9evKjIU+TOnTssWbIky5Qpw61btzIyMlKRNbTeOMzJyYlLly5lRESE4lXZ8+fPZ44cOThu3DgGBgbSx8dHUc/q4sWLdHJyYrt27fj48WN+/PhR0Sr38PBw1qtXjwULFuT69eup0WgU+7IsWbKEefLkYdmyZblw4UIuXbqUmzZtMih2zx7S3Fz2sylS5DHnzFnIadOm0dTUlCVKlODYsWN5+fLlRHuLxnigkHJaeWMICwszKjOAJEnC2Qn0KL3J+Bx/f3+jv4MxmQ1ICtsS6Hn16pVQlms9UVFRfPLkiXC8KjjJFP2JScgYKzGuXbtGHx8f4fiAgACeOXNGOJ6UEz6KeLnouXbtmnB2YlI2ULt165ZwPEkePXrUKIfa06dPx/qRGiqY//4b07MpWPA2R44cxzFjxnDYsGE0MTGhg4MD+/btywMHDiSYNNHPz49OTk4cPHiwQT2qz5EkiSVLluShQ4cUx+r5888/OX78eOH4S5cusWjRosLeRFqtloULF1Z0w/Q5Y8eOZatWrYSvhZs3b9LBwYGXL18WitfpdPztt984cOBAYeGbM2cOnZ2deenSJaH427dv087OjqNGjWJoaCh1Op2iG0DVDyeZouZS+7X55x/S3FwWm+bNyU/bl7dv3/LmzZuKfugfP37kgAEDmDdvXh4+fFixGdr169dpZ2cnfIf94cMH2tvbGyX+3bt359ChQ4Xjr169Sjs7O+E7dK1Wy1atWrFTp06KG1o9J0+epJ2dHffv38+AgADFZYSGhrJTp04sV64cX758yStXriiuw+HDh5k7d26OGjWKGzZsUHxD5+/vzz59+jB37txcvHgxhw8fbnCs2sNJpqiC8+uya1eM2LRoEVtsjOX8+fN0cHAgAK5du1ZRrKenJ11dXXnu3DmhXuvOnTtZqlQpvn//Xig+JCSE+fPnp5eXl3DPfdOmTXRxceGBAweE3EOjoqLYqFEj9urVy2gvmypVqnDnzp2K4yVJ4vLly2lvb88sWbIIPc8LCgpix44daWpqylq1agmdj6tXrzJr1qwEwDlz5hi8X1VwkiGq4Pya7NwZIzatWpFGjEbGia+vL7t06cKsWbPSwsJC0QQUnU7Hxo0bM2XKlPz333+F9t+qVSs6OTnxxIkTQvFnz55ltmzZhO0JNBoNW7VqRTMzM3p6egqVcf36daZNm5ZmZmZ8+PCh4nhJkjho0CACoK2trZCN+vPnz1mgQAECYNWqVYWsCZYsWUJHR0cC4KBBgxTHv3z5kiNGjKCbmxstLCy4bt26RGOMbdfUhZ8qKknEzp1AixaARgO0bg2sWwekSOKVblmyZIGHhwdev36Ns2fP4vbt24iMjDQoNiQkBKlSpUJ4eDg8PDwU7zswMBDPnj3DkydP8O+//yqOB4B79+7hw4cPOHToEAIDAxXHa7Va2NnZQZIkLFq0SKgOuXLlQq9evWBmZgZ3d3fF8SYmJhg3bhxmzpwJkhg3bpziMuzs7HDjxg1s27YNVlZWmDNnjuIyevToAW9vb9y4cQPp0qXDlStXFMXnzJkTkyZNwpkzZ/Dhwwdkz54dUVFRiuuhCCGZUkkUtYfza7F9O5kihdyzadMm6Xs2Scm6deuYKVMmvn37VnFsaGgomzVrxgIFCgjv/9y5c8yRI4dwD4UkT506RScnJ+GH56TsYNq6dWveuXNHuIzIyEiuXbvW6FmA79+/FzZx+5aofjjJFNWe4Ndh2za5R6PTAW3bAp6eSd+zSWqePn2Kly9fonz58opjJUnC2LFj0alTJzg5OQnt/927d1izZg2GDh0qFA/ImSuuX79udKaI0NBQpEqVyqgyfhVUP5xkiio4vwZbtwK//y6LTfv2wKpVgMJsRT8skZGRsDQiNw9V47MfDtUPR0XlO7FlS4zYdOjwa4kNAKPEBoAqNr8gP53gHDp0CBUqVEDq1KmRPn161K9fH7du3TI4vlOnTjAxMYnzNXfu3K9XcZUfik2bgDZtZLHp2BFYufLXEhsVFRGS+UizMv755x80adIEhQoVwpQpUxAZGYkFCxagXLlyOHPmDFxcXAwua+3atV+8V6pUqaSsrsoPysaNQLt2gCQBnTsDy5erYqOiYgg/zTMcrVaL3LlzgyTu3LkTPb74/PlzFCpUCGXKlMGRI0cSLadTp05YvXo1jD0s6jOcn5MNG+RnNZIEdOkii43pTzdOoKISN+oznP84efIkXrx4ga5du8Y6EPb29mjevDm8vLzw+vVrg8sjieDgYOh0uq9RXZUfkHXrYsSma1dVbFRUlPLTDKldvHgRAODm5vbFZ25ubli9ejUuX76Mhg0bGlRe+vTpERwcjBQpUqBs2bIYPXo0atSoEe/2kZGRsRbgBQcHx/r8+fPnuHDhAqKiohAVFQUTExO0bNkS1tbWBtUnMjISmzdvRmhoKMLDwxEREYHWrVsjd+7cBsUDwJ49e/D48WOEhoYiJCQElSpVQu3atQ2Ov3XrFry8vBASEoKQkBDY2Nigb9++MDc3Nyg+NDQU27ZtQ1hYGMLDwxEVFYW2bdvCzs7O4DrcvXsXISEh0c/VUqZMCWdnZ4PjRVm7Vn5WQwLdugFLlqhio6KimCRZDZQM6Nu3LwHEmXp+7969BMC///470XL+/PNP9u/fn2vXruWuXbs4ZcoUZs2alSYmJgl6qIwdOzba2OvTV1BQED9+/Mh169bR0tKSAOjs7Mxr164Z/N00Gg0PHjzIggULRlseKPXEuXLlClu0aEEAtLCw4Jw5cxSl03j16hWnTJlCExMTAmDr1q0VpZuPjIzk3r17mTt3bgJgzpw5efToUYPjSTlrcp8+faKPrZubG+/du6eojA8fPrBKlSqsU6cOu3TpQnd390QN1Dw9SRMTeVFnjx5kaKh4engVlR+Zn27hZ1RUFCZPnmzw9p06dYKjoyP++OMPrFy5Ek+ePPnirt/LywvVqlXDjBkzMGTIEMV1ev/+PVxcXBAZGYmXL1/GuUgsrh6OnZ0d6tWrh0uXLqFatWrw8/ODi4sLJk2aBCsrq0T3e+nSJXh4eOCff/5BsWLFkD9/fjx69AgrV66EjY1NovHv3r3DkiVLsHHjRqRJkwa///47NmzYgOXLl6N48eKJxkuShFWrVmHDhg149OgRWrZsiUePHqFx48bRs/kS4+zZs/Dw8MC+fftQunRp2NnZ4d27d1i2bBkyZsyYaPzr16+xZs0a7N27F97e3qhVqxZ2796NsWPHok+fPoladEuShN27d+PKlSu4evUqrl27huDgYISHh6NNmzZwd3dPcPGipyfQpQtBmqBJk3cYOvQpdu/eiaNHj6J+/fpo0KABihcvnuCxCA8Ph6mpqVHTiLVaLVIYsZqURq550TcTxpbxPeMlSYKpkd1SnU6n2Bb+U4w9jxqNxuARhbggCY1GAwsLC6F4o59NJ5XyJRUfP36Ms6cQ3+vYsWMkE+7h7Nmzx+AeTnyMGzeOAAz2FNHfCWzevDnaMMkQK+JP2b59O1esWEE/P7/oMpWkv/D29qa7u3t0gkJJkhgSEqKoDmPHjuXx48eje0NK49evX09PT8/o1B+BgYGKvsPt27c5ZswYXrx4kTqdjhqNRlF6er2t9Ny5c3ny5EkGBQXx77//5s2bNxON9fCI6dnY2//DWrVqs3bt2ixZsiQBMGXKlGzYsCH379+fYDn79+9n1qxZ2aFDB+7Zs4d+fn5ctWqVwcfh7du3LFiwoFAqe1I+BtWrV1dsnvcpEydO5PLly4Xjr127xkaNGgklqSRla4EKFSrwwYMHwnUYM2YMp06dKhx/48YNlilTRvHvWI/eD2fbtm3CdRg1ahTbtWsnnErn6tWrzJcvn7A3kuqH8x9TpkyJVxCWLl1KANy9e7dw+Z6engTA9evXG7S9mkvtx2bFihix6dOH/FQbDh8+zD179ihKjx8cHMz169ezUaNG0SnhmzdvbrCLpZeXF+3t7bly5UqGh4czODhY0fc5cuQIc+XKxVevXimK0/PixQva2dkJ++FIksRGjRpxwoQJQvEkuXv3bubPnz/6BkwpAQEBLF68OOfOnStch3nz5rFAgQL08fEREs9Hjx7RxcWFf/75JzUajWIX06ioKI4bN465c+fmsWPHeO3aNcU52M6dO8ciRYrw999/582bNxWJj2pP8B9HjhwhAI4bN+6Lzzp27EgTExOjfORHjhxJAAY/d1AF58dl2TJZaACyX7/YYmMskiTxr7/+op2dHbNkycKCBQsabDHw4sUL/vbbb6xRowa7dOmieN/Lly9nyZIleefOHSG7571797JQoUIMCgoSusMOCAhgnjx5ePToUaHEoSQ5c+ZMVqpUibdv3xayWn7//j1dXFy4dOlSbtmyRagOmzZtooODAwcMGCAkwCEhIWzdujWrVavGcuXKCbl/nj9/nvnz56etrS2nTZumOD4qKoozZsxgxowZmSZNGoN7v6rg/IdGo2HOnDlpa2sb62A8e/aMqVKlYtWqVWNt//79e967dy/WDy8kJCROb4unT58yQ4YMzJw5s8F3targ/JgsXRojNgMGJK3YJAVHjx5lihQpCIDbt29XHD9o0CCmS5fOYMOtzxk6dCgLFSokHH/lyhXa29uzQoUKQvGSJLFLly5Mnz49V61aJVSGj48PM2bMyFSpUvHdu3eK43U6HQcPHkwArFixolCW58ePH0f3dMeMGaM4XpKk6GF+U1NToSEyb29vli1blgCYI0cOg9xgVcH5hB07dtDExISFCxfmggULOHPmTDo4ODB16tS8ceNGrG31s8o+vWivXbvGtGnT8o8//uCMGTO4dOlS/u9//2OaNGmYIkUKRT9wVXB+PJYsiRGb//0v+YkNKT/LOHDgAJs3b85s2bIpGiLTaDTs3bs3ATBXrlzUarWK9q3T6dirVy8CYIkSJZRWnaQ8HJkqVSoCUDRTU094eDjbtWtHACxWrJhQY3/79m3WqFGDADhw4EDF8SR55swZ1q9fnwASnL0aH5Ik8cKFC/zjjz+YLl06njt3Tqged+7c4fjx41mlShV6e3sLleHr68uNGzdy1qxZiV4TquB8xoEDB+jm5kZra2umTZuWdevWjbO7GJfgvHnzhu3atWOBAgWYNm1apkiRgtmzZ2fLli15+fJlRfVQBefHYtGiGLEZODB5is3nvHv3TsgP5vDhw8yVKxd37NihOFan03Hy5Mk0MzMT9pG5du0a8+fPz/79+wvFk7Lddfbs2Xn8+HGheEmSuG/fPpYoUcKoofabN29y4MCBQq6feoKCgnjkyBHheD0ilttKUQUnmaIKzo/DwoUxYjN48I8hNsYSEhIiNCSn59SpU0bN+gwJCeFff/3FyMhI4TL8/f25a9cu4XhS7vW9ePHCqDJI/hDmaUnBT7cO52dBzaX2Y7BwIdCvn/z30KHAtGmAmjXfMIxdUwIkzdoYlW+HmktNRUWQ+fNjxObPP1WxUYqxYgNAFZtfDPVsq/ySzJsHDBgg/z1sGDB1qio2KipfG1VwVH455swB/vc/+e8RI4DJk1WxUVH5FqiCo/JLMXs2MGiQ/PfIkcDEiarYqKh8K1TBUfllmDkTGDxY/nv0aGDCBFVsVFS+JargqPwSzJghz0IDgLFjgfHjVbFRUfnW/DQGbMkdX19fVK9eHREREbCyskLp0qUxffp0ZMqUyaB4kujcuTNOnjwJKysrZM2aFTNmzECpUqUMrsO2bdswcuRIpEyZEilTpkTnzp3RtWtXg2cKvX//Hu3atYMkSUibNi1y5cqFESNGGGQzoGfWrFl48eIFsmXLhqxZs6JYsWIGWSXoefz4MZ4+fQpnZ2dky5bNoHT106bJEwMAYNw4WXBUVFS+A0m5KEglBv0CqQULFrB169bMnj07M2XKRGtra86YMcOghH3BwcH8559/2L9/fxYsWJDZsmUjALZp04Zv3rxJNF6j0fD8+fOcPHkyq1WrxsyZM9PCwoJ58+Y1OPfSs2fPuHbtWnbr1o358uWjlZUVTU1N2bt3b4Oy9n78+JEnT57k7Nmz2bZtW9rZ2REA06VLx8mTJydqd6DVavn8+XOeOHGCnp6eHDp0aLQ1RYYMGTh58uQEFw9OnhyzqHPcOB11Oh379etHd3d3Xr16VWjBntKUMCoqPwtqpoFkiv7EdO3alTt27GBAQAC3b99uUII8PVOnTmWLFi24dOlSent789atWzx8+LDB8VeuXGHFihXp7u7O06dPMzIykrNnz2ZERIRB8ZIksXLlyuzevTvXrVvHZ8+ecdmyZV/kpUuIUaNGsU6dOhw9ejR3797NDRs2cMiQIQanmD9+/DgLFSrEevXqsV+/fpw1axYzZcrEHj16JOr2OWlSjNikTDmJGTNmZMaMGaOdVwGwQYMGifrrdO/ena6uruzTpw89PT05e/Zs9u3b1+DEjzt27GDr1q2jvZqUipw+5ZLoj1ySJPbp04evX78WiifJlStXCnuokOT9+/fjzORuKFqtlj169FCczv9TFi5cqMgp93Pu3LnDvn37UqPRCMXrdDq2bduW9+/fF67DjBkzuGjRIuHMBjdu3GCLFi2ErwXVDyeZoqa2iRtjU4CEh4cbZIA1YUKM2EycGPuzESNGcPHixXz+/LlB+9Rqtbx9+zZXrVrF3r17M1euXATA1KlT093dPdE8WpGRkVy2bBlz5crFNm3a8J9//lFkZiZJEt3d3eni4kIfHx+hY7h8+XIWK1ZM+Hq8du0abW1thRNEhoeHs3Tp0sIZnkly+vTprFixosE3TJ9z79492tvbC+cti4qKYtu2bdmoUSPhvGW7d++mra0t//33X5LKe8uvXr1i9erV2bBhQ/r6+tLf319RvFar5Zw5c2hra8sVK1YwICBAUS45tYeTTFEF5/vh7h4jNpMnJ23ZkiRxxowZdHd35+LFi7l9+/ZEe1p6IiMjuXTpUtrY2BAAZ8+erWjfGzdupL29PefOnct9+/YprvuYMWNYo0YN+vr6KjZwI2X31uLFizM0NFSx8ysp+/nY29vz4sWLQskuJUliz5492aZNG/r6+gr1NG7evEl7e3ueOHFCyEFVp9Pxf//7HytUqMANGzYImcHdvXuXBQoUoLu7OwcMGCBUB30m/EqVKvHEiROKy/Dx8WGtWrXo7OzM4sWLG3w+VMFJpqiC830YNy5GbIxwE/5qvH//nh07dmThwoWZIkUKuru7K+qxbN++nQBoZ2en+NrSe8nkzp2bM2fOVFp1kuTAgQNZqVIlIQ8Xkjx58iRz5crFOnXqCPXUNBoN69aty/z583Pjxo1Cdbh69SptbW1pa2vL0NBQxfGSJHHQoEEEwO7duwvVwcfHh5kyZSIAoWE+SZLYt29fAmC2bNkMeqb7Offv32e6dOmih5YN6W0Z266p06JVfgpIefbZuHHy/6dNA/7667tWKU4yZ84MT09P3Lp1C6GhoWjSpAk+fvxocLyNjQ2aNGmCV69eYZh+6p2BkETGjBnh7e2NOXPmICoqSmn1kS1bNpw4cQIrVqyAVqtVHJ8yZUoEBQVh//79OHnypOJ4ksiUKRMePHiAmTNnggK5h0nCxMQEL1++xN9//y0UnzNnTtjY2GD58uW4dOmS4jJSpkyJQYMGwcHBAV27dsWHDx8UxZuYmOCvv/7C7NmzYW9vj9atWys+H/nz58eDBw/g6ekJa2trTJo0SVG8EEIypZIoag/n2yFJ5OjRMT2bGTO+d42+Pt7e3hwyZIjB1sB6JEni5s2bmS1bNq5cuVLxfrVaLSdPnsz/t3fmYVGV7R//sisgyqKIskmaJu5Lam64Z+aeZu6pr1n6kra4pOUe2mLmkpny6hvmlpmiaW+oaRkuIIIgIoggAgKC7NswM9/fH/ObSWSbczA2n891zXXBOed+zn3OmXm+59nu29jYmMePH5dsT/7dypk0aZIs+6KiIn711Ve0sLCQnQ8nNzeXa9eupYuLi+zfaF5eHrdu3crx48dTpVLJKkOpVPLkyZOykrg9TnR0tN5jkmVRVFRUYatTdKnVUITgVA1qNblixd9iI7OnqNYidxJGRkZGpWY7BQUFcfHixbJsSc2U//nz5zMlJUV2GbGxsfz2229l25OaGYBhYWGVKqOwsJD5+fmVKqO2IPLh1FBEPpx/HhJYsUITfBPQxElbtKh6fXqWUCgUMDU1rVQZRUVFMDExeUoeCf5pKluviUgDgloJqYn0vGGD5v/HI0ALqobKig0AITbPGEJwBLUOEli2TDMxANDktvH0rF6fBAJBxQjBEdQqSM3ss88/1/y/dSuwYEH1+iQQCPRDCI6g1kBqIj5/+aXm/23bgPnzq9cngUCgP0JwBLUCEvjgA83EAADYvh14553q9UkgEEhDCI6gxkNqsnRu3qz5f8cOYN68anVJIBDIQAhOFZGbm4udO3fC2toajRs3RuPGjdGyZUu98+EAwNGjR5Gfnw97e3vY29vDwcEBdnZ2ettHREQgKioKjo6OcHR0hJ2dnV75ZLQoFAqEhoaiVatWsqd6K5VKGBvr/7UjNVOdv/5a8//OncDcubJOLRAIqpunuiqomvn22285efJktm7dmgYGBpR7eVFRURw/fjxtbGxYv359vvjii/zpp58klaFdIHX79m0eO3aMH330Ee3t7QmAVlZW3LBhg14RZ/Py8njp0iVu3bqVffv21YXVHz58uF6rzNVqNWNjY3n8+HEuWbJEZ29lZUUvL69yc8loKSgoYHh4OH/++We6uroSAJs0acKJEyfqnW5BpVIxOTmZixcvpru7O2fMmMEtW7YwICCgHN/Jf//770Wd331HpqSkcO3atbx+/brsRYv6XLNAICiJiDTwGC4uLrS0tGTfvn3p6OgoS3BiYmJoZ2dHW1tbrl27ljt27GDv3r0JQFJode2D0Yak37x5M6dNm8aFCxfqFV6fJL28vNi4cWMOHjyYS5cu5bp169ijRw+9w3kEBQXRzs6O7dq14+TJk7lx40a6uLhw2bJleucV6datG+3s7NijRw9Onz6dPXr0YMuWLblr1y69wsSvWbOGDg4OtLa2ZqtWrdixY0cCoIuLC9etW1dmXg61mpw/Xys2Krq4rGHXrl3ZtWtXGhsbEwAdHR35ySefVBiAcdSoUZw7dy4///xz/vzzz3zttdf4wQcf6B2W/auvvuLmzZuZkJBAkkxOTpYkdv7+/vT29pYd/iQrK4vbt2+XLbBqtZq7d++WHVKfJH///Xe9o2KXRlJSEo8ePSrbXqVScdeuXXolLiyL06dPV+oaEhMTKxWCRq1W86uvvpIVqVvLzz//zMuXL8u2j4uL46ZNm2QnEczIyBCCoyUmJkb3ox4xYoQswZk0aRINDAyKvXkrFAp27tyZ1tbWen9ZSnsTkPqDz83NLVbJZGdnS6p0FApFMVHQtjKkkJGRUeycwcHBkr6s6enpxQThypUrPHXqVLllqNXkO+9oxMbAQM0NG1IYHR3N6OhoXrlyhV26dOGyZcvo7+9foS9qtZqBgYE8cOAA165dyxkzZuii9JqYmPDNN9/UCUlZBAUF8b333qOzszM9PDz4xhtvcNSoUXq/OERHR/OVV15hr169eP36dSYnJ0sKhZKVlcVhw4ZxxowZslpnarWanp6eHDNmjOzkYb6+vmzdurXsBGhJSUl0c3Pj2bNnZdmr1WpOnz6ds2bNki28J0+epKurK6OiomTZJyUlsXPnzly3bp0sH1QqFVesWMH27dvLzit04cIFurq68rPPPqNKpZL8EpOSksIJEyawR48evHnzJvPz8yWJuEjAVgZyBCcnJ4f16tWjh4dHiX179uwhAL1DootYavJQqci339aKDflkfEm5rQQteXl59PLy4oEDBxgUFCQpr4tKpeKFCxfo4OBAAHRwcNA7mZdareaxY8fo5uZGDw8Pjh8/XpJwKxQKzpo1i4MHD+bVq1d5//59vW21vr/xxhucM2eO7NhfGzdu5KBBg6hQKGQJ1/Xr1+nk5MSoqChZ9oWFhRwyZAhXrVrFvLw8WZX+zz//TDc3N8bExMjKepmRkcF+/fpx4cKFDAoKktXiOnjwIJ2cnHju3Dnu27dPsv3Dhw/56quvctiwYXzvvfdkpSY4cuQInZycOGvWLM6bN0/veym61MpAjuBcunSJAPjRRx+V2Hf79m0C4KJFi/QqSwiOdFQq8q23/habvXur26OSZGRk8NixY9y/fz93797Nbdu2MSkpSW/7y5cv61JcS/mhkxrRWrVqFevXr8+xY8dK9r2wsJBDhw6lh4cHv/nmG8n2arWa06ZN45QpU7hmzRrJ9qQmn0/btm05e/ZsWYKRmZnJTp06cfjw4bLTRR8+fJgtW7Zk9+7dZXUt5eXlcdSoUbS2tuaXX34py4fAwEDa2trS3Ny8whTnpaFWqzl37lwC4IABA2RdR0hICC0sLAiAW7Zs0ctGCE4ZyBGcI0eOEECpP8bc3FwC4IQJE0q1LSgoYGZmpu5z//59ITgSUKnIf/3rb7H573+r26N/BqVSyYCAAG7cuJHDhg2TXGHt3r2bVlZWBMBjx45JslWr1VyxYoVuDE3O27m2pd+kSRNZqZ5v3rypG1+V072mVCo5Z84cAmC/fv0k25PktWvXaGNjQwD08fGR5YM2AVuDBg1ktZTCwsI4ePBg3XVIbbmrVCru37+fw4cPp5GRET/++GPJPqSlpfGHH37gpEmTaGtry9OnT1doU+cEp7CwkCtXrtT7ExMTU2o5cgTn+++/JwB6e3uX2KdSqQiAI0aMKNV25cqVuhlgj3+E4FSMSkXOmaMRG0NDUkYdUGtRKBSS3/QzMjL4+eefs1evXpIHoAsKCvjpp5/S3Nyce2U0IXNzc7lo0SIaGBjI6g7S5uOxs7PjmDFjJNuTmnGEefPm0cDAgJcuXZJVxu3btzlmzBi6ubnJnogQHBzMiRMncsaMGbLsSU3WTU9PT0kTkp4kOTmZ27dv13sSTGkoFAoGBQU9e/lwsrOzS624y/r8/vvvpZbztFs4OTk5ooXzD6BSkbNm/S02MuqwZ5bCwkK9Jy48yb1797hixQrZY2J//vknp02bJsuW1FSSkyZNYmxsrOwyLl26xNWrV8u2JzWD8FeuXKlUGREREZXOhyN3MkdVU1nBqXELPy0tLWWljX0aNG/eHAAQHx9fYl9CQgIAwNHRsVRbMzMzmJmZ/XPO1UHUamDOHGDPHsDQEPDxASZPrm6vag+mpqaSFv4+jrOzM9auXSv7t9anTx906dJF8kJeLU2aNMGBAweQk5Mj6/wA0LNnT3Tv3l22PQD069evUvaAJlVzZZFzD2sjz8ZV6kn79u1hZmYGf3//Evu02yr7BRdoUKk0YrN3r0ZsfvgBmDSpur169pASaeJJzM3NK31+S0vLStkbGRlV2gdB1WFY3Q5UF6mpqYiIiEBmZqZum4WFBUaPHo0LFy7g2rVruu1KpRJbt25Fo0aNMGLEiOpwt06hUgGzZmnExsgI2L9fiI1A8CxQp1o4J06cQEhICADgzp07AIB169bp9q9YsUL397Zt27B69Wrs2bMHM2fO1G338vLC2bNnMWzYMCxatAh2dnbw8fFBUFAQdu/eLdJFVxKVCnjzTU33mZERcOAAMGFCdXslEAiqgjolOD/99BP++9//Ftv28ccf6/5+XHDKws3NDf7+/li2bBm++OILFBQUoF27dvjxxx/x2muvPXWfnyVUKmDGDE33mZERcPAgIG6pQPDsYMDqGqGv42RlZaFhw4bIzMwUrSIASqVGbPbvB4yNNWIzfnx1eyUQCKRQ2XqtTrVwBDUTpRKYNk0jMsbGwOHDwNix1e2VQCCoap7ZSQNVjVKpRFZWVqXLqG0olcDUqX+LzY8/CrERCJ5VhOBUASqVCjExMejevTvs7OzQvXt3zJw5E3fv3tW7jLy8PCxZsgSurq4YOnQoFixYgF9++UWSH7du3ULPnj0xa9YsbN68GefOnUN+fr7e9iSxfPlybN68GVevXoVCoSj3+KIizbqaQ4cAExPgyBHAyekaQkJCZK//UKlU1bZOSyAQVJKntQJVUBztitx27drRxsaGXbp0obu7Oy0sLPjhhx/qFfDxhx9+oIeHB5s3b057e3t26tSJANilSxceOnSowoB9kZGRHD9+PLt3786mTZuycePGNDU1paGhIceMGcNz585VGMpCG9a+X79+bNeuHRs0aEAANDAw4KuvvsrIyMhS7RQK8rXXtBEEijh8+Dd8++23OXLkSAKgs7Mz33nnHZ45c6ZcH27fvs0VK1bwm2++4fHjx/nnn3+yZ8+e3LFjh95hXTZv3swLFy7oYn8FBgZKCifz22+/yQ5pT2pW9d+8eVO2vUqlqvRqeH3ClpRHXFyc7NQEpCZ0SmXuAamJNl0ZoqKimJ6eLtu+oKCg0j5cvHixUs/hxo0bsqNLkJpILhcvXpRtX+dC29QVtA8mJCREFz7k7NmzTE1N1buMiIgIBgYGMiMjg6Qm4J+fn5/eX9j09HT6+fkxIiKCubm5VCgU/OSTTyTl4vj111/5+++/MyQkhPfv3+fixYu5du3ackOSKBTk+PEasTExUfHDDy/wwIEDPHDgABctWkQbGxtOnTqVhw4d0l1bWdy/f59btmzh0qVLOX36dA4aNEgX1qhBgwZcu3ZtuUEklUolvby8OGzYMNrZ2dHDw4Nt27blSy+9xKCgIL3ugbe3N1u0aMFRo0bx999/55kzZyTFrbpw4QKdnJy4YcMGFhUVSa5wEhMTdUnv5KBWqzl8+PBSo6Dry5YtW+jh4SE7W+qtW7fo5OTEiIgIWfZKpZIvvfQSN23aJMueJL/++mv27NlTdmWpvYZTp07JslcqlXz55Zc5efJk2cnwdu/ezRYtWvDPP/+UZR8REcHWrVtz4cKFJfJt6cOjR4+E4NREntX0BAoFOW6cRmxMTcmTJ4vvf/DgQaXiRkVERHDt2rU8efIkExISJCekO3PmDOvVq6drpc2fP1+vZ1RUVMQff/yRL730Ehs2bMjmzZvrLVikJvHVxIkT2aNHD27cuJEXLlzQ25bUiE6nTp24Zs0aJiUlSY7UnJ2dzR49evDLL7+kWq2WHM5erVZzzpw5fPPNN6lWq2W9pR8/fpytWrXiw4cPZdk/fPiQL7zwAg8cOCA7BtyqVavYp08fZmdny4p/Fh4ezhYtWnD//v1MSkqSfB1FRUX09PRkjx49mJiYyGvXrkn24dKlS3zuuefo5eXFw4cPSw4+mpubS09PT7Zu3ZrfffedpIjZooVTQ3kWBaewkBw79m+xkZmu5B/l0aNHjIqKYlJSEnNyciRXGOHh4WzZsiUNDAxoYWFBX19fSfZ79+4lANrZ2ZUZ6bwsMjMzOXDgQLZt25Zr166VZEuSqampbNeuHefPn8/9+/dLtlcoFBw0aBA/+eQTWfl0SHLTpk3s06cPN2zYIEt0YmJi6OLiwvfff59//fWXZHu1Ws2PPvpIl7lVDrGxsWzTpg07d+4s+flr2blzJ5s3b043NzdJSQC1pKWl8ZVXXqGxsTGXLFkiywc/Pz/Wq1ePZmZmvHr1ql42QnBqKM+a4BQWkqNHa8TGzIzUI7VGraawsJDR0dE8f/68pG6m8+fPc/LkyWzYsCHbt28vOb3A559/TgCsV6+e5DTFarWaXl5eBMC2bdvKaiX4+vrS0NCQTZs2ldW9du/ePbZs2ZIA+Mcff0i2V6lU9PT0JACOHDlSsj2pGQuytrYmAL0ztj7O4zl53NzcZLWUgoODdZljPT09Zfnw0Ucf6XIj/frrr7J8ePPNN2lra8tmzZrplddHCE4N5VkSnMJCctSov8VGxnf/mUPbvffbb79JslOr1fzf//5HDw8PjhgxQtZ40LRp0wiAP/74oyRbrf24ceMIgN9//71ke4VCwXXr1tHU1JTjxo2TbE9qxjL79etHAAwNDZVsr1ar+eOPP9LNzY09evSQ1dIqKCjgjh076OzszHXr1km2JzXdnDt27GC7du1kiS+pyT564MABzpgxgykpKbLKKCoq4oULF3jo0KEKj61svSYiDfxDPCuRBgoLNbHQTpwA6tUDjh8Hhg6tbq9KR61WVziVuzYRHByM5s2bo3HjxpJtg4KCcOTIEaxbtw6GhtJXR/z222/46aef8O2338qKOH337l2sXLkSXl5eZab80GJiYlIiKjRJ+Pj4IDg4GJs2bZJ8fgAoLCzEjh070K1bN/Tp00dWGQqFAkePHsXYsWNlpychidjYWLRo0UKW/ePlVCb6tz5Utl4TgvMP8SwITmGhJjzNL79oxMbXFxgypLq9Kh2FQoGYmBio1erqdqXGoP3py62ktPdSjmBpz69Wq/VKMdCoUSM0bdq0hK/Z2dmwtLSsVEVbFRV1XUGEthFUCwUFGrE5dQqoX1/Twhk0qLq9Kh2SePDgAYyMjODk5CS7ghRUPSSRl5eHlJQUAICDg0Ox/Q0aNKj0OYTYVB1CcASSKSgAxo0DTp/WiM3Jk8DAgdXtVdkolUrk5eWhWbNmTyVpmKBqqV+/PgAgJSUFTZo0EUnXajHiVU8giYICYMyYv8Xml19qttgAmnA4gCYls6B2on1RKCoqqmZPBJVBCI5Ab/LzgdGjgf/9DzA313SnDRhQ3V7pj+g6qb2IZ1c3EF1qAr3Qio2f399i079/dXslEAhqE6KFI6iQvDxg1CiN2FhYaLrThNgIBAKpiBaOoFzy8oCRI4Fz5wBLS43YyFyyIBAInnFEC6eKUKvVWLZsGdatWwdfX19Za0JOnTqF7du348qVKygoKJDsQ0pKCo4ePYqHDx/qdXxuLvDqq3+Lza+/As2a3RX5aGoAGzZsQK9evWp8mQLB44gWzj/Mxx9/jOTkZMTFxSE8PByZmZmoV68epk6dig8//BDPP/98mbb+/v64cOECkpKSkJycjKioKAQFBQEAnJycsGnTJowfP77MAdXk5GQcOXIEWVlZyM7ORmZmJnbv3g2FQoEXXngB48aNw9KlS2FpaVnCVis2588D9eop4Onph6ioh1i8eBcSEhLw6quvYuTIkfDw8Ch3hfW1a9eQlJQEOzs72NraIjg4GH5+fpg9eza6d+9e4WBwamoqwsPD0bFjRzRs2BAKhQKXL19Gv379yrV7nJs3b+qm1sqhsLAQpqamsgeutbPkKjOdV6lUwtj4759rSEgIOnbsKMmH2bNno2nTptiwYUOpxzxZ5sKFCxEbG4tjx45BrVbDwMCgUoP3KpVKdw+++eYbfP7553jw4AHc3d2xefNm9O3bt1z7yi7azcnJQf369WU/B5LIzMxEo0aNZPuQlpYGW1tb2faPHj1Cw4YNZV+DWq1GamoqmjRpItuHyiBaOP8wbm5umDlzJnbv3o1FixbBy8sL8fHx2LVrV7liA2hWURsZGaFLly548803MW/ePAwePBhHjhxBdHQ0XnvttXIrgMLCQt2CR2dnZ/Tq1QvW1taYOHEiNm7ciJUrV5YpNiNGaMTG1LQQo0fvQH7+Wdy4cQM5OTmIj49HaGgoQkNDkZiYWO41REZG4sCBA1i5ciUmTZoET09PfPfdd+jRowc6duyIEydOlGufmJiIzz77DO3atUOLFi3w+uuvY/jw4Rg6dCiuXLlSri2gmUb71VdfISEhAQkJCcjKykJiYqKkTKcpKSm4efMmHj16BJKSU31nZmbi1q1byM3NlWSnRaFQIDw8vJh9SEgIOnXqpJc9Sdy+fRsnT57E6NGjyzzuyTIDAgLw4osvAtC8vNy7d0926zY/Px+3bt2CUqnEoUOHsHDhQixfvhzXr19H3759MXz4cMTFxZV7DcnJyfjzzz9lnR8APv/8c/zrX/+SLVw3btxAt27dcOfOHVn2KpUKgwcPxtatW2XZA8C2bdswdOhQJCcny7LXXsORI0dk2WtfnmQjKwKboEJKC3JXmUx/JCuVR4Yk8/PzK0x4lp1N9uunCcRpZUVeulR8v5+fX6UyPx48eJDLly+nr68vk5OTJdk+fPiQW7duJQCam5uzdevW/Oqrryq8L/n5+QwNDWVCQgJv377NgKtXef3iRSbfvUt1djaZk1PhJyc5mVHBwbx59SqjgoOZfPeuXnbaT2ZiIm9cusQHiYnMycmRlI8mPDycffr0oZmZGdu3b88rV67QyMiI/v7+3L9/P83MzIolhJs9ezbbt29f7FmfOXOGNjY2fPToka7M/v37s169euzUqRMDAgJ0ZSoUCpqYmOgS3QHgiy++yIiICL0iCpfFgwcPeOvWLb744oucN29esX1t2rTh0qVLy7TNz89nSEgIe/bsycuXL8s6v0Kh4JgxYzh37lyqVCpZv8eff/6ZLi4uDAkJkRUtOyUlhb179+Y777zDoqIiyQE31Wo1t2zZQldXV/7xxx+8ceOGZB8iIiLYvXt3TpkyhUFBQQwJCdHbVkSLrqHUxmjRWVlknz5/i43M3/U/SnJyMtPT0yVVFvn5+QwPD2d+fj5zcnJ4JyREc5HV8LkTEsKgoCDeuXNHr2u4desWGzRowPfff59hYWHctGkT7e3taWhoqMvn06FDB86fP5+kJsGYo6NjiYykH3zwAWfMmMGQkBD+9ddfujLv3LnDo0ePslmzZroytSmtATA4OJgPHjxgeno6i4qKGBYWxtTUVK5YsYIWFhblfp6MgKxWqxkZGUkjI6MSSb88PT3Zr1+/Cp+hv78/nZyc6OPjw/DwcH2/AjoKCwv56quvcv78+bKjPJ85c4ZOTk6cNGmSrAo/Pz+fU6dOZd++fTlkyBBZwnf58mW6ubmxWbNmPHLkiGR7hULBVatWsUGDBmzRooXeL5FCcGootU1wsrLI3r019WLDhuSVK9Xt0dPjccEhqWl1VJPgPIyNZWBgIAMCApiUlFSh7wMHDuTUqVNJairshIQEDh06lC4uLrpW0okTJ2hmZsb169fT2tqaYWFhJcp5/vnnda3Kbt26ceTIkcUqukmTJvH555/X/f/zzz/T1ta2RDnZ2dkMDAzkH3/8wcjISEZFRZX5KS2NclxcHAFw9+7dxRKPrV+/vtj5n0T7DHNzc7ly5UoC4PTp0yu8f6Vx69Yt2tjY0MDAoNR7VRFKpZKzZs0iAHp4eMgSjMDAQFpaWhIAvb29JdsXFRVx5syZBMBGjRrx3r17ksvQihYADh06VK9WtxCcGkptEpzMTPKll/4WGz2T/9UaSgiOWi2pO6y8jzo7W+9uOebkkP+f3jk1NZVRUVHlZnuMjY0lgGKprBUKBcePH8/BgwcXa8V07tyZpqamPH/+fIlywsPDaW5uzry8PIaFhREA9+3bV+y7OW3aNE6YMEH3/yeffMKBAweWKCsnJ4dhYWEMCAiQ1bWqvSZvb29GR0frtq9bt46tW7cu0077DPPy8nj48GE2b96cRkZGkrOmkmR6ejoXL15MMzMzjh07VrI9qemWmjp1Kg0NDXn48GFZZVy6dImTJk2inZ0dExISJNur1Wr++eefnDVrFocPHy6ry12tVjMwMJDLli3TS/iE4DzGt99+y8mTJ7N169Y0MDCgnCGqGTNmFOu7fvzz1Vdf6V1ObRGczEyyVy+N2DRqRAYEVLdHT58SglODKO/t+NixYzQ2Ni5Rkbi7u3Pt2rVMTExkUVERf/31V9avX59GRka8detWiXI2bNjA0aNHFyszMTGxWLeeu7s7169fr7MZNWoUFy1aVKpfKpWKS5cupbm5uaQuNVLTpaXtUgsNDdWNg+jbpaZ9htnZ2Vy8eDHffffdMm0qIjY2llOnTmVAJb70kZGR/OSTT2SN52iJj4+XnYBNS05OTpXUNZWt1+rUtGgvLy+kpaWhc+fOyM3NRXx8vOyyfHx8Smzr1q1bZdyrcWRmAi+/DFy+DFhbA2fOAF26VLdXzxblzTI0NDTUJY3TTok+deoUbt68iS5dusDBwQFBQUGYMGECdu7ciYMHD+Ljjz/Gjz/+WKyc48ePY86cOcXKbNiwIRo3bgySOH36NG7evFlshlpoaCjGjh1bpl8ffvghpk2bBkNDw2LTtR+nefPmJbaZmpqia9eu8Pf3xxtvvKFLiOfn51fuDLonsbS0xMaNGxETEyM7n42Liwt8fHyQl5cn2VZLq1atsHr1atn2gOY+lXavpGBhYVEp+yrjqcpfNRMTE6PL0z5ixIhKtXAqS01v4WRkkD16aFo21tbktWvV7dE/R01u4ZRHQkICzczM+PbbbzM6OprHjx9ns2bNCIDx8fGMiYlh06ZNdS2TwMBAGhgYMDAwUFdGcnIyjY2NdTMCKypTi4uLCxctWsSEhIQKZzZK5eDBgzQxMaG3tzfDw8O5cOFCWlhYMDY2tkyb2voM6xqiS60MKis4arWamZmZkqavPk5NFpz0dPLFFzViY2NDPjZEUCepzZWVj48PHR0daW1tzYEDB3LZsmW0s7NjWloa27Rpw7lz5xY7ftSoURw2bJju/927d7N37956lfnkMVoheu+99576dW3fvp0uLi40NTVlly5deOHChXKPr83PsC4hBKcMKis4VlZWBEBjY2P27duXv/32W7l2BQUFzMzM1H3u379fIwUnPZ3s3l0jNra2ZHBwdXv0z/MsV1YjR47kxo0bq9uNSvMsP8OaRGUFR0QaeAJ7e3t4enpi+/btOHbsGNauXYvIyEgMGzas1HEdLV5eXmjYsKHu4+TkVIVe60d6OjBkCBAQANjaAmfPAhKiowhqIX369MEbb7xR3W4IBAAAA7JmRWJUKBT49NNP9T5+5syZcHV1LbH91VdfxS+//PJUAk0+fPgQ7du3R2FhIeLj40sdoCssLERhYaHu/6ysLDg5OSEzMxNWVlaV9qGyPHqkEZugIMDOTiM2HTpUt1dVQ0FBAWJiYtCiRQvUq1evut0RyEA8w5pBVlYWGjZsKLteq3Gz1BQKhaRZHx4eHqUKztOkcePGePvtt7Fq1Sr4+/tjyJAhJY4xMzMrN4hldfLoETB4MHD9OtC4sSb6c7t21e2VQCB41qhxgmNpaVkjw99rRU3f0P41hbQ0jdgEBwuxEQgE1YsYw9GTqKgoAEDTpk1l2ZPExYsXkZ6eLtuHxMRE3boFfUhNBQYN0ohNkyaAn58S7u41T8wFAsGzQY1r4VQVqampSE1NhYODAxo2bAgAyM3NBckSIfvv3buHb775BnZ2dpITVJ07dw75+flIS0vDnj17EBQUhDZt2qBXr154//334e7uXqbtgwcPEBcXh9zcXOTm5uKPP/7A9u3b0bt3bwwYMAADBgxAz549S130lpoKDBigRliYIWxtldi1KxYKRTo6dJiFAQMGYOTIkejXr1+F3YCxsbGwsLBAw4YNYWpqik2bNqFp06YYM2YMzM3NK7z+9PR0mJub684TGRmJBg0awMHBoUJbQNPFSlJnr239SlnoJ0WkS4MyFxY+bg9I8/mf8KE67Z9WGdV9/uq+j2q1GoaGlWsnPI0y5FKnBOfEiRMICQkBAF3OinXr1un2r1ixQvf3tm3bsHr1auzZswczZ84EoGnF9O/fHxMmTECbNm1gZWWFW7duwdvbG/n5+Th06JDkRF579+6Fg4MDbG1t0bBhQzg6OuK1117Dm2++CTc3t3JtfX198fPPP8PCwgIWFhbIz89Hfn4+UlJSYGhoCAcHh1K/vA8falo2YWGGMDFJg7OzJz777J7uvoSFheHEiROYMmUKlixZggYNGpTpw1tvvYWYmBhkZGRAoVCgqKgIeXl5sLS0xIQJE7B06dJy8/ps27YNW7ZsgaWlJVq1agVzc3OcPn0a06dPrzABHQBcvXoV48aNQ8eOHTFgwAD069cPmzZtwsaNG9GqVatybQGN2Lzyyivw8vJCkyZNYGZmhoKCAknPMSYmBkZGRmjWrBlMTEz0ttPy6NEjZGRkwNXVVVbiLIVCgbt37+K5556TdX6SuHPnDpo1ayZ7RXpycjIMDQ1lJ+7Kz89HQkIC3NzcZFV2/P98OCTRtm1bWT6sW7cO1tbWWLBggSz74OBgLFmyBD/99FOpeaQqQqVSYcCAAfj000/RR2ae9o8//hhqtRpr164tM8JDeVy7dg3vvPMO9u3bp9fv50lEPpzHKC8O2pOXqo04u2fPHt22Bw8ecOrUqWzTpg2trKxobGxMBwcHTpw4sdjqbX0obb56eHi47IWkWvuKotsmJ5Pt2mnW2TRtSj4eWiszM5MbN25kWFiYrAi3arWac+fO5YIFC3jo0KESIfDLIzU1lZcuXeIbb7xBAGzevDkHDRpU4fomUhN/6+LFi1y7di179+5NADQ1NeXy5cuZm5tboX1aWhqvXr3KsLAwhoaG8saNG4yLi9P7HqhUKiYkJOhC9aekpFChUOhlS2ruW3x8PENDQ5mbmyvJVktycjJDQ0NZUFAg69llZWUxJCSk1AjO+qBQKBgaGqrLpyMVtVrNu3fv8u7du7L8z8/P57Vr19inTx/ev39flg8pKSls164dv/32W1n2arWaK1asYI8ePZiWlibrOq5evUoXFxfu27ePpPQcV9nZ2Zw0aRIHDBjApKQkWc/j0KFDdHR05K5du5icnCypjMquw6lx06LrCpWdPiiHlBRg4EDg5k3AwQH4/XegdesqObXeREdHw97eXtYbIqBp9f3222+wsLCAubk53N3dy02zDRSfUpuVlaXLLNmgQQO4ubnp3WpQKBRISEhAWloa6tevj9atW0t6y8zKykJsbCxMTU1hZ2cHOzs7vW0BTUspPj4eTZo0gZWVlV5dmo+TmZmJe/fu6VoZUu0LCgoQGRkp216tVuPOnTuwtLREo0aNJNlrn2FISAjWrVuH//73v3BwcECzZs0k+ZCcnIyBAwfivffeg42NTZnx4srjiy++wPfff49p06Zh+vTpsLe3l2QfFxeHV199FS+//DKUSiU2bdokyZ4ktm3bhk2bNqF58+bYuXNnuV3zpREfH48ZM2YgOTkZrq6u8PX11avlWel6TZZMCSqkqkPbJCWRbdtqWjbNmpG3b1fJaWsFj69SLyoqYl5eHjMzM5mWliY5mVtaWhrDw8MZGBjImzdvSn5DTUhIYEBAAK9duyZ51bxarWZiYiIDAgIYEREh6w374cOHDAwMZFRUlGRbUhOV+Pr167JbyUqlkmFhYQwKCpJ0/Y8/w/Xr17N+/fqyQ+7ExcXRzs6O5ubmfPDggWR7tVrNefPmEQBnz54ty4dr167R3NycBgYG9Pf3l2yvUCg4btw4AmCHDh1kRWD4448/aGxsTABcvXq1XjYi0oAASUnAgAFAeDjQvDlw/jxQwdDIM4uxsTHq168PKysr2NjYoFGjRpIGcW1sbPDCCy+gc+fOcHJyQn5+vqTz29vbo0WLFrC0tMTdu3ehVqsl2Zubm8PCwgLZ2dmyZjyShJGRETIyMmRFSVYqlQA0YzKZmZmS7VUqFQwNDaFSqZCcnCzZniTUajVUKhW+/fZbpKamSi4jKysLHTp0QF5eXrExXn1Rq9V46aWX0KpVK/znP//BtWvXJJfRokULrFq1Co6OjpgzZ06xReP6YGJigs2bN2PNmjXIysrCRx99JNmHvn37IiIiAhs2bMCJEydw+vRpyWVIRpZMCSqkqlo4Dx6QbdpoWjaOjqTMF9c6TU2Nw1VYWMiCggLJdmq1mitXrmTnzp1ljQkWFRXx3r17vHPnTrHtXl5e7Nmzp172MTExpebe0Qe1Ws2kpCRev35d7/GsJ59hZGQkhw8fzuXLl8v24ZdffmGnTp149+5dWWUUFRXRx8eHs2bNktXaIzUtlYMHD/LkyZOy7EnNGOPZs2crXdc8fPiwwmNE8M4aSlUITmJicbF5ov4Q/D81VXAqw6RJkzh37lxdOg59mDFjBpcsWaL7Py8vr5j9pEmT+NZbb+n+f/fdd3WJ20ojKytL1gQI8u9o0WZmZuzSpUuFCchKe4ZqtZrnz5+XdA+eRCu+lUGpVMrKtlkbEV1qzyiJiYCHBxARATg5abrRnnuuur0SVBUhISHo3Lmz3lOM1Wo1fvnll2JJzurXr1/MPiQkpFgStoCAALz44otlltmgQQNZ07QPHTqEhQsXYsWKFbh+/Tr69u2L4cOH6yZz6IuBgQH69+9fqTUlxsbGcHZ2lm0PAEZGRrKmKD+LCMGphSQmasZsIiMBZ2chNlIhgdzc6vnImRN669YteHh4oH79+ujcuTMCAwMRGRmJjh07wtHREd98802x4/39/WFubo579+7ptv31118wNDREjx49KiyzqKgIpqam8Pf3x/Lly2FgYKCzexps2rQJs2fPxpw5c/DCCy9g8+bNcHJywo4dO57aOQQ1EyHLtYyEBI3YREUBLi6aqc8tWlS3V7WLvDxA5qzsSpOTA0hZexkREYEePXpg7ty58Pb2xo0bNzB69GiQRIcOHdCzZ08EBATojieJhQsXYuHChXBxcdFt9/X1xciRI2FoaFhhmUZGRrh48SJ69OiB4OBg2Nvbl4jQ/Omnn1YY1f306dPo27dvsW0KhQLXrl3D0qVLi20fOnQo/P399b8xglqJEJxaRHy8Rmzu3NGIzfnzwD8cKFtQzcyfPx+jR4/GF198AQB47rnncPjwYQQFBcHCwgI9e/bE3r17dcf7+PggLi4Oy5YtK1aOr6+vroyKygQ0cftsbW3RsYyESfPmzcPEiRPL9b158+YltqWmpkKlUpVYu2Jvb4+kpKRyyxPUfoTg1BLu39eITXS0RmTOn9eIjkA65uaalkZ1nVtf7t27h3PnziEoKKjYdhMTE50Q9OzZE0uWLEFOTg4MDQ3x0UcfYd26dcXCFd26dQvx8fEYPHiwXmUCwPXr18sUG0AzPdzGxkb/i3mCJ6eis5rjrAmqBiE4tYC4OI3Y3L2r6T47f14zdiOQh4GBtG6t6iI4OBjGxsZo3759se1BQUGYPHkyAKBbt24wMjJCUFAQzpw5A1tbW8yaNavY8b6+vhgyZAjq16+vV5nac5cnOHK71Ozs7GBkZFSiNZOSkiJ5xb6g9iEEp4Zz755GbGJiADc3zZiNEJtnA0NDQ6jVaigUCt0sqFOnTuHmzZu62WT16tVDx44dcfToUXz33Xc4ceJEiVlbx48fx5w5c/QuEwBCQ0PLDfsit0vN1NQUXbt2hZ+fX7Hy/fz8is2gE9RRnuIUbcFjlDZfXerisNhY0tVVs87muefIuLin7eWzQW1dh5OQkEAzMzO+/fbbjI6O5vHjx9msWTMCKBY4dcGCBTQwMODIkSNLlJGcnExjY2MmJydLKtPFxYWLFi1iQkICMzIynup1HTx4kCYmJvT29mZ4eDgXLlxICwsLxsbGlmlTW59hXUMs/KyhaB9Meno6c3Jy+PDhQ86YMYOvv/46v/vuO0ZHR5drHxPzt9i0bEnev0+eOXOGnp6e9PPzY2FhoWSfcnNz+fXXXzMhIUHmVZGhoaGVWmhXGVu51ObKysfHh46OjrS2tubAgQO5bNky2tnZFTtm9+7dNDExYURERAn73bt3s3fv3pLL9PHx0QmR3Jhl5aFd+GlqasouXbrwwoUL5R5fm59hXUIITg1F+2Csra3ZvHlztmzZkvb29gRAKysrzpgxg6GhoaXa3r1LurhoxMbQMIoNG7altbU1raysdKkWHBwceODAgXJbTQEBAbS1taWrqyvbtWvHXr166QIGDhw4kN7e3szOzi73Ojp06MCuXbtyzJgx/Pe//82XXnqJLVu25ObNm/X60i1ZsoQeHh58//33eeDAAXp7e/Odd97RO2jiuXPnOHDgQG7ZsoX37t1jUVERz507p5ctqamopkyZwoCAAF1ofqktzfv378sOR0+S6enpTEpKqlT4k7i4uDLFesCAAXz33XdL3Tdy5Ehu2LCB9+/flx0VgNSkl6hM1IyCggImJibKts/Ly+Nff/3FpKQk2WXs3r1b0nfnSSIiIrhixQrZz1GpVPLtt9+u1Avf1q1befToUdn2oaGhnD9/vl5pPUrj0aNHQnBqIqW9CezevZvHjx8vN35WdDTp7KwRm+efJx9POePn58e3336bp06d0vtNr6ioiOnp6YyLi+Nff/1FNzc3Tp48mTt37tQr4nB+fj6joqJ47tw57t27l88//zwB0NnZmW+88UaFLbX8/HxevXqVO3bs4OzZs+nm5kYANDc354oVKyrsrlEqlfzjjz/43nvv0c3NjV27dqWpqSkXLFjAnJwcve6Bv78/L1y4wJCQECYlJfHu3buSYpjl5eUxIiKCt2/fZn5+PnNzcyVVOgqFghEREbxz5w6VSqXkCkubSyYyMlInOiqViklJSVy/fj2bNWtW5n3cuHEj4+LimJKSwrCwMNkhWHJzcxkSEiK7olKpVLx165as6Myk5nt06dIljh07VrYPwcHBdHJyqrA1VRZ5eXl85ZVXOGfOHNl5rby9vdmiRQuGhITIsr99+zbd3d25dOlSKpVKyX7k5+dz4cKFbNu2LYODg5mbmyup10G0cGooch5MdDTp5PS32FTiRahUFAqF7LczUlP5X7x4kenp6bLL2Lx5M5ctW8bNmzfz4MGDvHHjht62arWaCxcu1LXyWrZsyYsXL1Zop+2OycjIYHR0NAMCAhgcHKy3YGnPnZqaypCQEIaEhEh+W1er1bx//z7DwsJ47949yYnQ1Go14+LiGBERwczMTPr5+dHAwIAvvPACL1++rFcZDx48YHh4OBUKhawuWW0St4KCAln2RUVFDA0NZVpamuTWlvYZrl69mq+88gqTk5NlVXrXrl2jk5MTL168KKvSLyws5MSJE/n666/Tz89PVhefn58fnZyceOzYMf7nP/+RbJ+dnc0JEyZw8ODBfOedd2T9Hk+fPk1nZ2dOmTJF79QEpBCcGovUB3PnjiYAJ0C2bq0JzCkoSX5+PnNycpiZmclHjx4xNTVVLxtt/39aWhpjYmIYERHBsLAwyQPi2nw2AQEBekXXfZL4+HgGBATw5s2bkseztKIVGBhY7gB7eWgzl8q1T0tL440bN0odL9KHgoIChoSEMDQ0VJJoaZ9hXl4eZ82aRVdXV3p5ecny4erVq3R0dKSTk5Oklw4tSqWS06ZNo6mpKT/99FNZPgQFBdHc3JwNGjSQlDlXi0ql4pgxYwiAkydPluXD//73PxoZGdHAwIC//vqrXjYieGcd4M4doH9/TSSBNm0062wcHKrbq5pJvXr1YGFhASsrK1hbW8PW1laSvY2NDVxdXdG6dWu4u7tLzlro4OAAd3d3ODs7IzMzEzkSVpCSRIMGDWBjY4P8/HwkJiZKOjegCTZpYGCAhw8fyspnY2xsjKKiIqSmpkrOwfK4fXZ2NrKzsyXbGxoawsjICAUFBUhJSZFsDwBNmzZFbGwsvvzyS+Tm5kq21wYcvX//PrZu3SrZnqRuzdD69etlPUeSGDRoELKzs7FgwQLJ9iqVCq+//joGDhyI/fv3Y//+/ZLL6N69O7777jsMHjwY06dPLxZ77x9DlkwJKkTfN4HISLJ5c03L5oUXNJk7BU+Xf3KGk9wuyqKiIiYnJ8vumoqPj2dkZKSs8+fk5PDWrVuMiYmRbEtqxnPCw8MZGRkpy16bTycoKEjvMaXHn6Faraavry9btGjBL7/8UpYP2dnZXLlyJR0dHfno0SNZZcTFxfGdd97hv/71L1n2pGYiwrx583j69GnZZURFRXHjxo2yWmtakpOT9eqarWwLx4CUE79WUBH65P6OjNQs6kxMBNq2Bc6dA8Ri66dPQUEBYmJi0KJFixJBKGszSqUSBgYGMDIykmxLEhkZGbCyspJtn5aWBisrK5iamkq2B4CcnByoVCo0bNiwwmNLe4YFBQXYt28fZs2aJTtFwYMHD5CSklJuVIWKSEhIQJMmTWSlatCiVCprRYoDfeq18qj5V1hHuX1bIzYPHgDu7hqxadKkur2q29S1d6vKVFAGBgawtraulL2dnZ1sewCwlBCyu7RnV69ePV0EBbk4ODjAoZL916VFVJBKbRCbp4EYw6kGIiL+Fpt27TThaoTY/HNo3+AVCkU1eyKQi3a8qjKtCEH182zIag3i1i1g4EAgKQlo3x44exZo3Li6varbGBsbw9zcHA8fPoSJiUmlMkQKqhaSyMvLQ0pKCho1aiSr+09QcxCCU4WEh2vEJjkZ6NBBIzaV7JUQ6IGBgQEcHBwQExNTNTNxBE+dRo0aoWnTptXthqCS1BnBSUhIwPfff49ff/0VkZGRyMrKgqurK1555RUsXbpU0vTZO3fuYOnSpfj999+Rn5+P9u3bY8mSJRg3bpxs/8LDNd1oKSlAx44asZE4o1dQCUxNTdGqVSvRrVYLMTExES2bOkKdmaX27bff4t1338XLL7+Mfv36wcrKClevXsXevXvh4OCAq1ev6vWGFBsbi+7du+tS9drZ2WHfvn3466+/sGfPHsycOVMvfx6fzREXZ4WBA4GHD4FOnYAzZ4TYCASC2kdlZ6nVmXU4YWFhpYYb2bVrFwHwgw8+0KucSZMm0cDAgAEBAbptCoWCnTt3prW1NbOysvQqRztf/dKlTDZurFln07kzmZam3/UIBAJBTUNEGvh/3N3dS53eqE0SFRoaWmEZubm5OHbsGPr3749u3brptpuYmMDT0xPp6en45ZdfJPk1YoSmZdOli6ZlU4msvAKBQFCrqTOCUxYJCQkAgCZ6zDsODQ1FQUEBXnrppRL7tNuuXr0q6fyPHgFdu2rE5uTJ73Hu3DkUFRVJKkNLeHg4wsPDZdkCmmnBaWlpsu2BureWRSAQVB11ZtJAWXzyyScAgBkzZlR4rFacHB0dS+zTbouPjy/VtrCwsFhsqszMTACAhUUQTEw2YPToPNy7dw9xcXFo0KABhgwZgg8++ADu7u5l+vP999/jxIkTMDc3h7m5OfLy8nDs2DG4u7tj/PjxGDduHFq0aFGmfVRUFFatWgV7e3s0adIETZo0wYYNG+Dh4YFZs2ahR48eMDAwKPeeeHp6wtbWFm3atEHr1q1x4sQJNG/eHFOmTIGZmVm5tgDg4+ODxMRE9OvXD127dsWdO3dgYmKCVq1aVWgLaET2+PHjeP311+Hm5gaVSgWVSqX36naVSoXPPvsM06dPl71A79ChQ+jWrRuee+45WfahoaHIzs4u9UVGH/Ly8nDq1Cm89tprsuwB4OjRoxgxYoRez6w0AgMDYW1tLfseZGRk4MqVKxg2bJgse5L46aefMGbMGNmLJP39/dGsWTO4urrKsn/06BEuXbqEESNGyLIniR9++AETJkyQ/RzOnj0LZ2dnvX8/T5KcnIzz589j4sSJFf72S0Nbr8l98axxkwYUCgU+/fRTvY+fOXNmmV+gzz//HIsXL8acOXOwa9euCsvy8fHB9OnT4e3tjVmzZhXbp1arYWRkhBEjRuDkyZMlbFetWoXVq1fr7bdAIBDUVqKjo+Hm5ibZrsa1cBQKhaSK28PDo1TB2bVrF5YsWYLhw4dj+/btepVlbm4OAKVG0c3Pzy92zJMsW7YM7733nu7/jIwMuLi4IC4uTq9YUQINWVlZcHJywv379+XNgnkGEfdMHuK+SSczMxPOzs6wkTkYXeMEx9LSstLjBP/5z3/w1ltvYdCgQTh69Kje3S/aLpfSus3K624DADMzs1KbyQ0bNhRfZhlYWVmJ+yYRcc/kIe6bdORG66hzkwb27NmDf/3rXxgwYAB8fX0lRQdu3749zMzM4O/vX2Kfdlv37t2fmq8CgUDwLFGnBGfv3r2YM2cOPDw8cPLkSdSvX7/MY1NTUxEREaEbBAMACwsLjB49GhcuXMC1a9d025VKJbZu3YpGjRrJHjAUCASCZ50a16UmF19fX8yePRtWVlaYNGkSfvrpp2L7LS0tMWbMGN3/27Ztw+rVq0tED/Dy8sLZs2cxbNgwLFq0CHZ2dvDx8UFQUBB2796td9PbzMwMK1eulD0b5VlF3DfpiHsmD3HfpFPpe/a0VqBWNytXriSAMj8uLi6lHr9nz54SZd2+fZvjxo1jo0aNWK9ePXbr1o0//vhj1VyIQCAQ1FFq3LRogUAgENRN6tQYjkAgEAhqLkJwBAKBQFAlCMERCAQCQZUgBKeKSEhIgJeXF/r37w8HBwdYWFjA3d0dH374YaUDatZldu7ciSlTpqBNmzYwNDSUFf+pLnPgwAF07doV9evXh52dHd544w2R1bQcvLy8MGHCBLi5ucHAwEB2XLVnicjISHzyySfo2bMnGjdujAYNGqBTp05Yv349cnNzJZUlJg1UEU8rQdyzhqurK9LS0tC5c2fExMQgPj5eRKz+f7Zt24Z///vf6N27N6ZOnYrU1FRs3rwZZmZmCAgIQLNmzarbxRqHgYEBbGxs0KVLF1y7dg1WVlaIjY2tbrdqNEuXLsW2bdswcuRI9OrVC6ampvj9999x+PBhdOjQAZcvXy53zWMxqnWO3DPE00oQ96wRExNDlUpFkhwxYgTFV1ZDamoqLS0t2aVLFxYVFem2BwQE0MDAgLNnz65G72ou0dHRur/d3d1LLJcQlCQgIIDp6eklti9fvpwAuG3bNr3LEl1qVcTTSBD3LOLq6io7blNd5vjx48jJyYGnp2excP3dunVDv379cPjwYSgUimr0sGYiJ8Lxs063bt3QqFGjEtvl1F3il1zNSEkQJxBo0SYCLCtZYHZ2NiIiIqraLcEzhJy6SwhONSMlQZxAoKUyyQIFgsqiUqmwZs0aGBsbY8qUKXrb1ZlYalXF004Qd+TIEcyZMweDBg16Sh7WPJ7mPRNoyMvLA4BSY1ppI6RrjxEInjaenp64fPky1q1bh9atW+ttJwRHItWZIK628rTumeBvHk8W+OQMoYqSBQoElWHFihX45ptvMGfOHHz00UeSbIXgSKQ6E8TVVp7GPRMU5/FkgU/mt68oWaBAIJdVq1Zh/fr1mD59Onbu3Cl5XZwYw6liKpMgTiDQok0EWFayQEtLS7Rp06aq3RLUYVavXo3Vq1dj6tSp2LNnj6zZo0JwqhApCeIEgvIYPXo0zM3NsWXLFiiVSt32wMBA/PHHH5g4cWKdbzkLqo41a9Zg1apVmDJlCvbu3St7qYKINFBF+Pr6YuzYsbCyssJnn31WQmyeTBAn0HDixAmEhIQAAPbt24fbt29j7dq1uv0rVqyoLteqna+//hoLFy5E7969MW3aNKSmpuKrr76CiYkJAgMDdd1ugr/x8fHRhf7ZunUrFAoF3n//fQBAo0aNsGDBgup0r0ayfft2LFiwAM7OzlizZg2MjIyK7be3t8eQIUP0K+wpLUYVVIDUBHECDTNmzCj3vj3r7Nu3j507d2a9evVoY2PD119/nXfv3q1ut2os/fv3F79BiVT0G+zfv7/eZYkWjkAgEAiqBDGGIxAIBIIqQQiOQCAQCKoEITgCgUAgqBKE4AgEAoGgShCCIxAIBIIqQQiOQCAQCKoEITgCgUAgqBKE4AgEAoGgShCCIxAIBIIqQQiOQCAQCKoEITgCgUAgqBKE4AgEAoGgShCCIxAIBIIqQQiOQFDLUCqV6N27N8zNzXHz5s1i+77//nsYGBhgyZIl1eSdQFA2Ij2BQFALiYuLQ6dOndC8eXNcvXoV9evXx+3bt9GtWze0bdsWFy9ehImJSXW7KRAUQ7RwBIJaiLOzM7y9vREWFoZFixahsLAQr7/+OoyMjHDw4EEhNoIaiXF1OyAQCOQxduxYLFiwANu2bUNYWBhCQkJw6NAhtGjRorpdEwhKRXSpCQS1mMLCQnTo0AGRkZGYOXMm9uzZU90uCQRlIrrUBIJaTGhoKGJjYwEA4eHhKCoqql6HBIJyEIIjENRSsrOzMWnSJFhbW2PDhg24evUqli9fXt1uCQRlIsZwBIJayltvvYW7d+/i119/xdChQ3Hjxg188cUXGDx4MIYOHVrd7gkEJRBjOAJBLcTb2xtz5szB4sWLsXHjRgCaFk/nzp2Rk5ODkJAQ2NvbV7OXAkFxhOAIBLWMiIgIdO3aFe3bt8eff/5ZbAp0YGAgevfujQEDBuD06dMwMDCoRk8FguIIwREIBAJBlSAmDQgEAoGgShCCIxAIBIIqQQiOQCAQCKoEITgCgUAgqBKE4AgEAoGgShCCIxAIBIIqQQiOQCAQCKoEITgCgUAgqBKE4AgEAoGgShCCIxAIBIIqQQiOQCAQCKoEITgCgUAgqBL+DwOcWisxBe0gAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = sp.symbols('x y')\n", "f = x**2 - y\n", "g = y - x\n", "\n", "fig, ax = plt.subplots(figsize=(4,4))\n", "plot_nullclines(f, g, symbols=['x', 'y'], ax=ax);\n", "plot_vector_field(fp, gp, ax);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### adding an interactive trajectory solution\n", "If you are getting messy output just comment the line iteract()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ode(x, t):\n", " return np.array([fp(x[0], x[1]), gp(x[0], x[1])])\n", "\n", "def plot_trajectory(x0=-1., y0=0, tspan=2):\n", " \n", " fig, ax = plt.subplots(figsize=(5, 5));\n", " plot_nullclines(f, g, symbols=['x', 'y'], ax=ax);\n", " plot_vector_field(fp, gp, ax)\n", " t_range = np.arange(0, tspan, 0.1)\n", "\n", " sol = odeint(ode, y0=np.array([x0,y0]), t=t_range)\n", " ax.plot(sol[:,0], sol[:, 1] , c='g', alpha=.5);\n", " ax.plot([x0], [y0], 'go', ms=10, alpha=0.5);\n", " ax.set_title(f'Phase Portrait (x0={x0:.2f}, y0={y0:.2f})')\n", " # plt.show()\n", "\n", "# comment the following line if you don't want to use interactive mode:\n", "# interact(plot_trajectory, x0=(-1.99,1.99,.1), y0=(-1.99,1.99,.1), tspan=(1,5,0.5))\n", "\n", "# uncomment the following for using without interactive mode\n", "plot_trajectory()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Equation 6.3\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{dA}{dt} &= \\frac{1}{\\tau_A}\\big( -A + 2B \\big) \\\\\n", "\\frac{dB}{dt} &= \\frac{1}{\\tau_B}\\big( -B + \\frac{L}{1+A} \\big) \\\\\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def fp(A, B):\n", " return -A + 2 * B\n", "\n", "def gp(A, B):\n", " return -B + L / (A+1)\n", "\n", "def ode(x, t):\n", " return np.array([fp(x[0], x[1]), gp(x[0], x[1])])\n", "\n", "A, B = sp.symbols('A B')\n", "L = 10\n", "f = -A + 2 * B\n", "g = -B + L / (A+1)\n", "\n", "def plot_trajectory(A0=4, B0=6, tspan=3):\n", " \n", " fig, ax = plt.subplots(figsize=(5, 5));\n", " plot_nullclines(g, f, symbols=['B', 'A'], x_range=(0,10), y_range=(0,10), ax=ax);\n", " plot_vector_field(fp, gp, ax, xrange=(0,10), yrange=(0,10), rotatexy=True)\n", " t_range = np.arange(0, tspan, 0.1)\n", " \n", " sol = odeint(ode, y0=np.array([A0,B0]), t=t_range)\n", " ax.plot(sol[:,1], sol[:, 0] , c='k', alpha=.5);\n", " ax.plot([B0], [A0], 'ko', ms=10, alpha=0.5);\n", " ax.set_title(f'Phase Portrait (A0={A0:.2f}, B0={B0:.2f})')\n", " \n", "\n", "# comment the following line if you don't want to use interactive mode:\n", "# interact(plot_trajectory, A0=(0.1,9.99,.1), B0=(0.1,9.99,.1), tspan=(1,10,0.5))\n", "\n", "# uncomment the following for using without interactive mode\n", "plot_trajectory()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Related tool\n", "#### pplane\n", "There is also a java/matlab tool available for visualization of the nullclines and vector fields [here](https://www.cs.unm.edu/~joel/dfield/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Stabiliby of steady states" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The process includes the calculation of the Jacobian matrix, finding the eigenvalues of the Jacobian matrix at the equilibrium point, and classifying the equilibrium point based on the nature of the eigenvalues.\n", "\n", "We'll use the `sympy` library for symbolic differentiation (to compute the Jacobian) and `numpy` for numerical linear algebra (to find eigenvalues).\n", "\n", "Here’s a step-by-step Python code that implements the process:\n", "\n", "### Explanation:\n", "\n", "1. **Step 1 (Equilibrium Points):** \n", " - We define a system of equations $\\frac{dX}{dt} = F(X)$. \n", " - The equilibrium points are found by solving $F(X) = 0$.\n", "\n", "2. **Step 2 (Jacobian Matrix):**\n", " - The Jacobian matrix is calculated symbolically using `sympy.jacobian`.\n", "\n", "3. **Step 3 (Eigenvalue Analysis and Classification):**\n", " - The Jacobian matrix at each equilibrium point is substituted into and evaluated numerically.\n", " - The eigenvalues are calculated using `numpy.linalg.eigvals`.\n", " - The type of equilibrium point is classified based on the eigenvalues:\n", " - **Node (Stable/Unstable):** All real and either positive (unstable) or negative (stable).\n", " - **Saddle Point:** Mixed signs among real eigenvalues.\n", " - **Spiral (Stable/Unstable):** Complex eigenvalues with negative or positive real parts.\n", " - **Center:** Purely imaginary eigenvalues (neutral stability).\n", "\n", "### Customizing the Code:\n", "\n", "1. **System of Equations:** Modify `F` for your system.\n", "2. **Variables:** If your system has more variables, extend the variables `x1`, `x2`, etc.\n", "3. **Jacobian Calculation:** The Jacobian calculation automatically scales with the number of variables in the system." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "import sympy as sp\n", "import numpy as np\n", "from IPython.display import display, Math\n", "sp.init_printing()\n", "\n", "def find_jacobian(F, X):\n", " \"\"\" \n", " Compute the Jacobian matrix for a system of equations F(X). \n", " \n", " Parameters\n", " ----------\n", " F: sympy.Matrix\n", " The system of equations represented as a sympy Matrix.\n", " X: sympy.Symbol or iterable of sympy.Symbol\n", " The independent variables of the system of equations.\n", " \n", " Returns\n", " -------\n", " J: sympy.Matrix\n", " The Jacobian matrix of the system of equations.\n", " \n", " \"\"\"\n", " J = F.jacobian(X)\n", " return J\n", "\n", "def equilibrium_points(F, X):\n", " \"\"\" \n", " Solve for the equilibrium points by setting F(X) = 0. \n", " \n", " Parameters\n", " ----------\n", " F: sympy.Matrix\n", " The system of equations represented as a sympy Matrix.\n", " X: sympy.Symbol or iterable of sympy\n", " The independent variables of the system of equations.\n", " \n", " Returns\n", " -------\n", " eq_points: sympy.Eq\n", " List of equilibrium points in the system.\n", " \n", " \"\"\"\n", " eq_points = sp.solve(F, X)\n", " return eq_points\n", "\n", "def has_complex_elements(matrix:sympy.Matrix):\n", " return matrix.has(sympy.I)\n", "\n", "\n", "def classify_equilibrium(Jacobian, X_eq, X):\n", " \"\"\"\n", " Classify the equilibrium point by calculating eigenvalues of the Jacobian at X_eq.\n", " \n", " Parameters\n", " ----------\n", " Jacobian: sympy.Matrix\n", " The Jacobian matrix of the system of equations.\n", " X_eq: sympy.Matrix\n", " The equilibrium point.\n", " X: sympy.Symbol or iterable of sympy\n", " The independent variables of the system of equations.\n", " \n", " Returns\n", " -------\n", " classification: str\n", " The classification of the equilibrium point.\n", " \"\"\"\n", " # Substitute the equilibrium point into the Jacobian\n", " J_at_eq = Jacobian.subs([(x, x_eq) for x, x_eq in zip(X, X_eq)])\n", " # Evaluate symbolic Jacobian numerically\n", " J_at_eq = J_at_eq.evalf() \n", " # check if there is any complex value in the Jacobian \n", " if has_complex_elements(J_at_eq):\n", " J_at_eq_np = np.array(J_at_eq.tolist(), dtype=complex)\n", " else:\n", " J_at_eq_np = np.array(J_at_eq.tolist(), dtype=float)\n", " \n", " # Compute eigenvalues \n", " # J_at_eq_np = np.array(J_at_eq).astype(np.float64) # Convert to numpy array\n", " eigenvalues = np.linalg.eigvals(J_at_eq_np) # Compute eigenvalues\n", "\n", " # Classify based on eigenvalues\n", " real_parts = [ev.real for ev in eigenvalues]\n", " imag_parts = [ev.imag for ev in eigenvalues]\n", "\n", " if all(np.isreal(eigenvalues)): # If all eigenvalues are real\n", " if all(ev > 0 for ev in real_parts):\n", " stability = \"Unstable Node\"\n", " elif all(ev < 0 for ev in real_parts):\n", " stability = \"Stable Node\"\n", " else:\n", " stability = \"Saddle Point\"\n", " else: # Complex eigenvalues\n", " if all(ev < 0 for ev in real_parts):\n", " stability = \"Stable Spiral\"\n", " elif all(ev > 0 for ev in real_parts):\n", " stability = \"Unstable Spiral\"\n", " else:\n", " stability = \"Center (Neutral Stability)\"\n", " \n", " return {\"eigenvalues\": eigenvalues, \"stability\": stability}" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Jacobian:'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}2 x & -1\\\\-1 & 1\\end{matrix}\\right]$" ], "text/plain": [ "⎡2⋅x -1⎤\n", "⎢ ⎥\n", "⎣-1 1 ⎦" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Equilibrium point (0, 0) is classified as: Saddle Point, eigenvalues: [-0.61803399 1.61803399]\n", "Equilibrium point (1, 1) is classified as: Unstable Node, eigenvalues: [2.61803399 0.38196601]\n" ] } ], "source": [ "# Define the variables (states)\n", "x, y = sp.symbols('x y')\n", "f = x**2 - y\n", "g = y - x\n", "F = sp.Matrix([f, g])\n", "X = sp.Matrix([x, y])\n", "\n", "# Step 1: Find equilibrium points\n", "eq_points = equilibrium_points(F, X)\n", "\n", "# Step 2: Calculate the Jacobian matrix\n", "Jacobian = find_jacobian(F, X)\n", "display(\"Jacobian:\", Jacobian)\n", "\n", "# Step 3: Classify each equilibrium point\n", "for X_eq in eq_points:\n", " # display(Math(f'x_{\"{eq}\"} = {sp.latex(X_eq)}'))\n", " D = classify_equilibrium(Jacobian, X_eq, X)\n", " classification = D['stability']\n", " eigenvalues = D['eigenvalues']\n", " print(f\"Equilibrium point {X_eq} is classified as: {classification:>20s}, eigenvalues: {eigenvalues}\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Equilibrium point:'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ \\left( -5, \\ - \\frac{5}{2}\\right), \\ \\left( 4, \\ 2\\right)\\right]$" ], "text/plain": [ "[(-5, -5/2), (4, 2)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'Jacobian:'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIcAAAA2CAYAAADtcYraAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGGklEQVR4Ae2d7VHcMBCGDyYFJKED0kGADi4dAKkgSQfJ8Av+MUkHJBUQ6ABSQQIdJKmAQAfkfYx1o7Nl38lfd5K1M0L2WpJ3V69317LPbBwfHz+fOOjk5OTBwU6sCC2guXZiYFO63qjcF8rnCG2QVKq2wEVh/sHDxYY8x29tfBB6rqv7hnFEOrxGKZWdsXg+6bktfT/lM7Sr+h/74t/mPO9Kfd+r08Ez755r1kGK4BK/qWAUjIOxRkE5MM5UvzEKaxuvfwNPpdUFT1gJmmSAB5UDlQ9S5DxoZfyFBwjoPSPZAS9CvogHbUXBg6OV9uF3nkqF3wJEMaHEYzwXv5UXTeAIGyCA4I9AgKdwURE0rjaVvOBzjkrNRnBAoDioUJPEfKLjjZNS+ifPgRUiIgECYBBOzB1MY+0SOBqbbm07koheCiRf2kq48rAiJYiLP1R84iN3J61cZlvDrWN/2eRMcpGDVIUbL7HXARwkUzteUqfGJQsIECxcvVQ9W/MoNfJkpLDiabB1bC5A7EuuV7bH0PY2pY28CRxtrLcGfQUAEtA91cUEFMCwatyYVh5WGkvu7riVs1+qJlxFTblnIAG91jb5hk1T8VolpVGAQ0YwS8XT3DoX4v3R9pXqr7bFItu+kj6EDvKNIrVO2GMBRyfZedG6674v4L/qU8aUc/Rp3cDHTuAIfAL7FD+Bo0/rBj52AkfgE9in+AkcfVo38LETOAKfwD7FD/ZWVrdxPKg7VOHl6NKzGfHMG/R3arOl/eIKYp92jWLsID2HJpolYxZ+AAhljnScY3cAQoVVQhbDWDBK5GGBUMFxm086q6AuwmvM3rxWW7ZZTt52NU48twWCBIdblSduDgC8SRE4D+LhcRItaYFgc44a/UphJm/LE0oeyI2SdNFwYfAMaukffMUIjqrJBxhVwKnqEzRfgEDfxj/4ihEchA8XYahiqHG1i4YncGCL7KGktj9q2yusxphzAACM4ko+Wz/G1rijoejAkc/cqeqpmUVdNWzzRvaoPIfRv2kdZFjRJOMV+I0ok867kty6sq6RvflEDc/wdYz3Ht6pJPKwQKjgwAPUrngKGLXHPWw02qaxhpXRTmiXitd6Dl19ZPjpB0ddWtxjrFXbfxE4yPpLD7U89MuaSslH3z6htJduG33JqrE7sX9T+WrB0XTQYr8+DVg8V9f7kn2qMfGgJMEktrzZPntuo/1oaRBwBG49wPACHVQDEj6m1pu34DzrQitJSGXkfRWuxFrKJ6O2TRcHdR5WD6vIDqvIjKsPkewffC0l/+Dg0ETwrgXf8apdkMqB8Ve115JvldaMp/JehU9rzpF4rIsUfzGWtRHflpP1lKB+IyP58Xw8cDM/fMr2xTP7c7awdwYNKxIIt8xX7pYx8JHamlhfu+yt8fii3tyH02wldQyAkTtAjOkijMbCmXN9RHzA0+oTjq6T9s2T3MvY2inG0J6DK895hdrSSSEm8lwFF74w/Cxqo/EWvRw0URvzQlAJPDqG3BkwtF0XgtQsHhoaHLyNtUym/1rt8Ba49L0BzZ0BxD6f5CAMAYh7bXNLXumh7H4xbA8WVmRYPACeoJbU7qOK+XX4LzXmw7ND0U+diI+fXJoTShY7ITXsUdRDeg7AwdtYlaSJIJzYnoVPb9NvKFo2jA0lz0rPM5jnkJbE8kWeg+SJO5m3uVUABncZlKyvanKWImB2xS++XU6C6fv5hVrw5jKNphoSHOQPAMRJmkjCyVw81z4g4As11NkdS7ENg4nHTw+6+BYW57FvXRl+tLQ5lOaaPCYX45dIxwgnJa8ivpkoZ7/SQO0ZnIdQlkgWMJ6DF2bmrmrtlyarA4vxGUTOZSZ9om3CxKEKucYsDIiPPNxCQkfaJ9zY+cjTkSX+qh+TXvlykDUE3mfOe1nHot3MbW3rl2HBgIMJstcfmKQ+jMRkM+5soUmCsV86l/iA03lMfC/SWIBxdk5XZ2OgvK2rScw8VlDx3jZdTx4fHwct+uc/ZyrbXZ6XMduO14dcbWVadf8NBBiadHXiQU5V9xG6vNWRHDxnIOQ1ClveJwykw+Yq5NQk1Lr4Fcj0PQGjbPX/J2hbH4mZLlwAAAAASUVORK5CYII=", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}-1 & 2\\\\- \\frac{10}{\\left(A + 1\\right)^{2}} & -1\\end{matrix}\\right]$" ], "text/plain": [ "⎡ -1 2 ⎤\n", "⎢ ⎥\n", "⎢ -10 ⎥\n", "⎢──────── -1⎥\n", "⎢ 2 ⎥\n", "⎣(A + 1) ⎦" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Equilibrium point: (-5, -5/2)\n", "Eigenvalues: [-1.+1.11803399j -1.-1.11803399j]\n", "Classification: Stable Spiral\n", "--------------------------------------------------\n", "Equilibrium point: (4, 2)\n", "Eigenvalues: [-1.+0.89442719j -1.-0.89442719j]\n", "Classification: Stable Spiral\n", "--------------------------------------------------\n" ] } ], "source": [ "A, B = sp.symbols('A B')\n", "\n", "L = 10\n", "f = -A + 2 * B\n", "g = -B + L / (A+1)\n", "F = sp.Matrix([f, g])\n", "X = sp.Matrix([A, B])\n", "\n", "eq_points = equilibrium_points(F, X)\n", "display(\"Equilibrium point:\", eq_points)\n", "Jacobian = find_jacobian(F, X)\n", "\n", "display(\"Jacobian:\", Jacobian)\n", "for X_eq in eq_points:\n", " D = classify_equilibrium(Jacobian, X_eq, X)\n", " classification = D['stability']\n", " eigenvalues = D['eigenvalues']\n", " print(f\"{'Equilibrium point: ':<30s} {X_eq}\")\n", " print(f\"{'Eigenvalues: ':<30s} {eigenvalues}\")\n", " print(f\"{'Classification: ':<30s} {classification}\")\n", " print(\"-\"*50)\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### A short-term memory circuit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", "\\frac{dE_1}{dt} &= \\frac{1}{\\tau} \\big( -E_1 + \\frac{100(3E_2)^2}{120^2 + (3E_2)^2} \\big) \\\\\n", "\\frac{dE_2}{dt} &= \\frac{1}{\\tau} \\big( -E_2 + \\frac{100(3E_1)^2}{120^2 + (3E_1)^2} \\big) \n", "\\end{align*}\n", "$$\n", "\n", "where $\\tau=20$ ms.\n", "\n", "- find fixed points,\n", "- plot isoclines,\n", "- find stability characteristics of the fixed points,\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Jacobian:'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}-0.05 & - \\frac{810.0 E_{2}^{3}}{\\left(9 E_{2}^{2} + 14400\\right)^{2}} + \\frac{90.0 E_{2}}{9 E_{2}^{2} + 14400}\\\\- \\frac{810.0 E_{1}^{3}}{\\left(9 E_{1}^{2} + 14400\\right)^{2}} + \\frac{90.0 E_{1}}{9 E_{1}^{2} + 14400} & -0.05\\end{matrix}\\right]$" ], "text/plain": [ "⎡ 3 ⎤\n", "⎢ 810.0⋅E₂ 90.0⋅E₂ ⎥\n", "⎢ -0.05 - ──────────────── + ─────────────⎥\n", "⎢ 2 2 ⎥\n", "⎢ ⎛ 2 ⎞ 9⋅E₂ + 14400⎥\n", "⎢ ⎝9⋅E₂ + 14400⎠ ⎥\n", "⎢ ⎥\n", "⎢ 3 ⎥\n", "⎢ 810.0⋅E₁ 90.0⋅E₁ ⎥\n", "⎢- ──────────────── + ───────────── -0.05 ⎥\n", "⎢ 2 2 ⎥\n", "⎢ ⎛ 2 ⎞ 9⋅E₁ + 14400 ⎥\n", "⎣ ⎝9⋅E₁ + 14400⎠ ⎦" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Equilibrium point: (0.0, 0.0)\n", "Eigenvalues: [-0.05 -0.05]\n", "Classification: Stable Node\n", "--------------------------------------------------\n", "Equilibrium point: (20.0000000000000, 20.0000000000000)\n", "Eigenvalues: [ 0.03 -0.13]\n", "Classification: Saddle Point\n", "--------------------------------------------------\n", "Equilibrium point: (80.0000000000000, 80.0000000000000)\n", "Eigenvalues: [-0.03 -0.07]\n", "Classification: Stable Node\n", "--------------------------------------------------\n", "Equilibrium point: (-6.89655172413793 - 13.1577820885096*I, -6.89655172413793 + 13.1577820885096*I)\n", "Eigenvalues: [ 0.0577033+0.j -0.1577033+0.j]\n", "Classification: Saddle Point\n", "--------------------------------------------------\n", "Equilibrium point: (-6.89655172413793 + 13.1577820885096*I, -6.89655172413793 - 13.1577820885096*I)\n", "Eigenvalues: [ 0.0577033+0.j -0.1577033+0.j]\n", "Classification: Saddle Point\n", "--------------------------------------------------\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tau = 20\n", "E1, E2 = sp.symbols('E1 E2')\n", "X = sp.Matrix([E1, E2])\n", "F1 = 1/tau *(-E1 + (100 * (3*E2)**2)/ (120**2 + (3*E2)**2))\n", "F2 = 1/tau * (-E2 + (100 * (3*E1)**2)/ (120**2 + (3*E1)**2))\n", "F = sp.Matrix([F1, F2])\n", "\n", "fig, ax = plt.subplots(1, figsize=(4,4))\n", "plot_nullclines(F1, F2, symbols=['E1', 'E2'], \n", " x_range=(-10,100), y_range=(-10,100), \n", " num_points=100, ax=ax, loc='best')\n", "\n", "eq_points = equilibrium_points(F, X)\n", "\n", "Jacobian = find_jacobian(F, X)\n", "\n", "display(\"Jacobian:\", Jacobian)\n", "for X_eq in eq_points:\n", " D = classify_equilibrium(Jacobian, X_eq, X)\n", " classification = D['stability']\n", " eigenvalues = D['eigenvalues']\n", " print(f\"{'Equilibrium point: ':<30s} {X_eq}\")\n", " print(f\"{'Eigenvalues: ':<30s} {eigenvalues}\")\n", " print(f\"{'Classification: ':<30s} {classification}\")\n", " print(\"-\"*50)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Hysteresis, bifurcation, and memory\n", "- [TODO!](https://pydstool.github.io/PyDSTool/PyCont.html#head-80e716dddbabca5f9aabaacdbdefd5d2eeeb6f47)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Adaptation, forgetting, and catastrophe theory\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{dE_1}{dt} &= \\frac{1}{\\tau} \\big( -E_1 + \\frac{100(3E_2)_{+}^2}{(120+A_1)^2+(3E_2)_{+}^2} \\big) \\\\\n", "\\frac{dE_2}{dt} &= \\frac{1}{\\tau} \\big( -E_2 + \\frac{100(3E_1)_{+}^2}{(120+A_1)^2+(3E_1)_{+}^2} \\big) \\\\\n", "\\frac{dA_1}{dt} &= \\frac{1}{\\tau_a} (-A_1 + 0.7 E_1) \\\\\n", "\\frac{dA_2}{dt} &= \\frac{1}{\\tau_a} (-A_2 + 0.7 E_2)\n", "\\end{align*}\n", "$$\n", "\n", "where $\\tau = 20$ ms, $\\tau_a = 4000$ ms.\n", "\n", "for plotting the isoclines, we consider the first two equations and consider $A_1$ as a parameter." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0.0, 0.0), (36.0000000000000, 36.0000000000000), (64.0000000000000, 64.0000000000000), (-9.3628088426528 - 18.5411985061749*I, -9.3628088426528 + 18.5411985061749*I), (-9.3628088426528 + 18.5411985061749*I, -9.3628088426528 - 18.5411985061749*I)]\n", "[(0.0, 0.0), (-10.6423173803526 - 21.500641960307*I, -10.6423173803526 + 21.500641960307*I), (-10.6423173803526 + 21.500641960307*I, -10.6423173803526 - 21.500641960307*I), (50.0 - 14.2828568570857*I, 50.0 - 14.2828568570857*I), (50.0 + 14.2828568570857*I, 50.0 + 14.2828568570857*I)]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "def adaptation_isoclines(A1:float, ax:plt.Axes, title:str=\"\"):\n", " tau = 20\n", " E1, E2 = sp.symbols('E1 E2')\n", " X = sp.Matrix([E1, E2])\n", " F1 = 1/tau *(-E1 + (100 * (3*E2)**2)/ ((120+A1)**2 + (3*E2)**2))\n", " F2 = 1/tau * (-E2 + (100 * (3*E1)**2)/ ((120+A1)**2 + (3*E1)**2))\n", " F = sp.Matrix([F1, F2])\n", "\n", " plot_nullclines(F1, F2, symbols=['E1', 'E2'], \n", " x_range=(-10,100), y_range=(-10,100), \n", " num_points=100, ax=ax, loc='best', title=title)\n", " eq_points = equilibrium_points(F, X)\n", " print(eq_points)\n", "\n", "\n", "\n", "fig, ax = plt.subplots(1,2, figsize=(10,4))\n", "adaptation_isoclines(24.0, ax[0], title=r'$A_1=24$')\n", "adaptation_isoclines(36.0, ax[1], title=r'$A_1=36$')" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def ode(x, t, tau, tau_a, stm):\n", " E1, E2, A1, A2 = x\n", " dE1dt = 1/tau *(-E1 + (100 * (3*E2+stm*(t>=200)*(t<=400))**2)/ ((120+A1)**2 + (3*E2+stm*(t>=200)*(t<=400))**2))\n", " dE2dt = 1/tau * (-E2 + (100 * (3*E1)**2)/ ((120+A1)**2 + (3*E1)**2))\n", " dA1dt = 1/tau_a * (-A1 + 0.7 * E1)\n", " dA2dt = 1/tau_a * (-A2 + 0.7 * E2)\n", " return np.array([dE1dt, dE2dt, dA1dt, dA2dt])\n", "\n", "t_range = np.arange(0,8000,1)\n", "values = odeint(ode, y0=np.array([1,1,0,0]), \n", " t=t_range, args=(20, 4000, 50))\n", "\n", "\n", "fig, ax = plt.subplots(1, figsize=(6,4))\n", "ax.plot(t_range, values[:,0], label=\"E(t)\", c='k', lw=2)\n", "ax.plot(t_range, values[:,2], label='A(t)', c='k', lw=2, ls='--')\n", "ax.legend()\n", "ax.set_xlabel('Time (ms)')\n", "ax.set_ylabel('Spike Rate')\n", "ax.margins(x=0.01)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Competition and neural decisions\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{dE_1}{dt} &= \\frac{1}{\\tau}(-E_1 + S(K_1 - 3E_2)) \\\\\n", "\\frac{dE_2}{dt} &= \\frac{1}{\\tau}(-E_2 + S(K_2 - 3E_1)) \\\\\n", "S(x) &= \n", "\\begin{cases}\n", "\\frac{100(x)^2}{120^2+(x)^2} & x \\geq 0 \\\\\n", "0 & x<0\n", "\\end{cases}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def neuron_system(X, t, K1, K2, Tau):\n", " E1, E2 = X # Unpack the state vector (E1 and E2 represent the neuron states)\n", " \n", " # Post-synaptic potentials\n", " PSP1 = (K1 - 3 * E2) * (E2 < K1 / 3)\n", " PSP2 = (K2 - 3 * E1) * (E1 < K2 / 3)\n", " \n", " # Define the differential equations for each neuron\n", " dE1_dt = (-E1 + 100 * (PSP1) ** 2 / (120 ** 2 + (PSP1) ** 2)) / Tau\n", " dE2_dt = (-E2 + 100 * (PSP2) ** 2 / (120 ** 2 + (PSP2) ** 2)) / Tau\n", " \n", " return np.array([dE1_dt, dE2_dt])\n", "\n", "\n", "def plot_competition(K1, K2, ax, tau=20, y0=[1,0], t_range=np.arange(0,400,5)):\n", " values = odeint(neuron_system, y0=y0, \n", " t=t_range, args=(K1, K2, tau))\n", " E1, E2 = values[:,0], values[:,1]\n", " ax[0].plot(t_range, E1, label=r'$E_1(t)$', c='r', alpha=.7)\n", " ax[0].plot(t_range, E2, label=r'$E_2(t)$', c='b', alpha=.7)\n", " ax[0].legend()\n", " ax[0].set_xlabel('Time (ms)')\n", " ax[0].set_ylabel('Spike Rate')\n", " ax[0].margins(x=0.01)\n", " ax[0].set_title(f'$K_1=${K1}, $K_2=${K2}', fontsize=12)\n", "\n", " Xiso = np.arange(0, 101) # X for Isoclines\n", " Isocline1 = 100 * (K2 - 3 * Xiso)**2 / (120**2 + (K2 - 3 * Xiso)**2) * (3 * Xiso < K2)\n", " Isocline2 = 100 * (K1 - 3 * Xiso)**2 / (120**2 + (K1 - 3 * Xiso)**2) * (3 * Xiso < K1)\n", "\n", " ax[1].plot(Xiso, Isocline1, label=r'$dE_1/dt$', c='k', alpha=.7)\n", " ax[1].plot(Isocline2, Xiso, label=r'$dE_2/dt$', c='k', alpha=.7, ls='--')\n", " ax[1].plot(E1, E2, label=r'$E_1, E_2$', c='r', alpha=.7)\n", " ax[1].legend()\n", " ax[1].set_xlabel('E1')\n", " ax[1].set_ylabel('E2')\n", " ax[1].margins(x=0.01)\n", " return ax\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(10,4))\n", "plot_competition(120, 120, ax)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 4 }