{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:49:26.342555Z",
     "start_time": "2020-02-21T12:49:25.621415Z"
    }
   },
   "outputs": [],
   "source": [
    "# Data manipulation\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Options for pandas\n",
    "pd.options.display.max_columns = 50\n",
    "pd.options.display.max_rows = 30\n",
    "\n",
    "from IPython import get_ipython\n",
    "ipython = get_ipython()\n",
    "\n",
    "# autoreload extension\n",
    "if 'autoreload' not in ipython.extension_manager.loaded:\n",
    "    %load_ext autoreload\n",
    "\n",
    "%autoreload 2\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import gridspec\n",
    "%matplotlib inline\n",
    "\n",
    "import time\n",
    "np.random.seed(int(time.time()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Specific imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:49:27.402149Z",
     "start_time": "2020-02-21T12:49:26.388787Z"
    }
   },
   "outputs": [],
   "source": [
    "from noise_parameters import NOISE\n",
    "from generate_timeseries import Timeseries, make_params\n",
    "from noise_properties_plotting import PlotTimeseriesComparison #, PlotNoiseColorComparison, PiecewiseNormalize\n",
    "#from scipy.optimize import curve_fit\n",
    "#from neutrality_analysis import KullbackLeibler_neutrality\n",
    "#from neutral_covariance_test import neutral_covariance_test\n",
    "from scipy import stats\n",
    "from noise_analysis import noise_color\n",
    "from matplotlib.colors import Normalize\n",
    "\n",
    "#import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Settings figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:49:27.570668Z",
     "start_time": "2020-02-21T12:49:27.471532Z"
    }
   },
   "outputs": [],
   "source": [
    "from elife_settings import set_elife_settings, ELIFE\n",
    "\n",
    "set_elife_settings()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:49:27.674832Z",
     "start_time": "2020-02-21T12:49:27.640070Z"
    }
   },
   "outputs": [],
   "source": [
    "def ratio(x):\n",
    "    return np.array([x1/x2 for x1, x2 in zip(x[:-1], x[1:]) \n",
    "                     if x1 != 0 and x2 != 0 and ~np.isnan(x1) and ~np.isnan(x2)])\n",
    "    \n",
    "def fit_ratio(x):\n",
    "    # Return the parameters of the fit and the goodness of fit values\n",
    "    x = ratio(x)\n",
    "    x = x[np.isfinite(x)]\n",
    "\n",
    "    if len(x) > 10:\n",
    "        a, b, c = stats.lognorm.fit(x,floc=0)\n",
    "        stat, pval = stats.kstest(x, 'lognorm', args=((a,b,c)))\n",
    "    else:\n",
    "        return np.nan, np.nan, np.nan, np.nan, np.nan\n",
    "    return a, b, c, stat, pval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:53:22.297819Z",
     "start_time": "2020-02-21T12:52:56.151842Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 5\n",
    "\n",
    "ss = np.logspace(-3, 2, N)\n",
    "df = pd.DataFrame({'ss' : ss})\n",
    "\n",
    "df['a'] = np.zeros(len(ss))\n",
    "df['b'] = np.zeros(len(ss))\n",
    "df['c'] = np.zeros(len(ss))\n",
    "\n",
    "for row in df.index:\n",
    "    steadystate = np.array([df.loc[row, 'ss']]).reshape([1,1])\n",
    "    \n",
    "    params = make_params(steadystate, selfint=-0.5, noise=0.1)\n",
    "    \n",
    "    ts = Timeseries(params, noise_implementation = NOISE.LANGEVIN_LINEAR, \n",
    "                            dt = 0.01, tskip=4, T=500.0, seed=int(time.time())).timeseries\n",
    "\n",
    "    x = ts['species_1'].values\n",
    "    x_transf = ratio(x)\n",
    "    a, b, c, stat, pval = fit_ratio(x)\n",
    "    \n",
    "    for key, value in zip(['a', 'b', 'c', 'stat', 'pval'],[a, b, c, stat, pval]):\n",
    "        df.loc[row, key] = value\n",
    "    \n",
    "    fig = plt.figure(figsize=(12,3))\n",
    "    ax1 = fig.add_subplot(121)\n",
    "    ax2 = fig.add_subplot(122)\n",
    "    \n",
    "    PlotTimeseriesComparison([ts], composition=['ts'], fig=ax1)\n",
    "\n",
    "    x = ts['species_1'].values\n",
    "\n",
    "    x_fit = np.linspace(0.01,5,1000)\n",
    "    pdf_fitted = stats.lognorm.pdf(x_fit,a,b,c) #Gives the PDF\n",
    "        \n",
    "    ax2.hist(x_transf[np.isfinite(x_transf)], alpha=0.4, density=True, bins = 50)\n",
    "    cmap = plt.cm.get_cmap('coolwarm')\n",
    "    c = cmap(pval)\n",
    "    ax2.plot(x_fit, pdf_fitted, c=c)\n",
    "\n",
    "    ax2.set_xlim([(0.1*min(x_transf)),min(1.2*max(x_transf), 3)])\n",
    "    #ax2.legend()\n",
    "    ax2.set_ylabel('Count')\n",
    "    ax2.set_xlabel('Ratios successive abundances')\n",
    "    ax2.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:49:59.242941Z",
     "start_time": "2020-02-21T12:49:59.196456Z"
    }
   },
   "outputs": [],
   "source": [
    "new = False\n",
    "\n",
    "if new:\n",
    "    ss = np.logspace(-3, 2, 50)\n",
    "\n",
    "    df = pd.DataFrame({'ss' : ss})\n",
    "\n",
    "    sigmas = [0.5, 0.7, 0.8, 1.0] #0.01, 0.1, 0.2, 0.25, 0.3]\n",
    "\n",
    "    for sigma in sigmas:\n",
    "        df['sigma_%.2f_width_mean' % sigma] = np.zeros(len(ss))\n",
    "        df['sigma_%.2f_width_std' % sigma] = np.zeros(len(ss))\n",
    "        df['sigma_%.2f_pval' % sigma] = np.zeros(len(ss))\n",
    "\n",
    "        for row in df.index:\n",
    "            if row % 10 == 0:\n",
    "                print(row)\n",
    "\n",
    "            params = {}\n",
    "\n",
    "            N = 50\n",
    "\n",
    "            steadystate = np.repeat(df.loc[row, 'ss'], N).reshape([N,1])\n",
    "\n",
    "            # no interaction\n",
    "            #omega = np.zeros([N,N]); np.fill_diagonal(omega, -1)\n",
    "            omega = np.random.normal(0,0.15,[N,N]); np.fill_diagonal(omega, -1)\n",
    "\n",
    "            params['interaction_matrix'] = omega\n",
    "\n",
    "            # no immigration\n",
    "            params['immigration_rate'] = np.zeros([N, 1])\n",
    "\n",
    "            # different growthrates determined by the steady state\n",
    "            params['growth_rate'] = - (omega).dot(steadystate)\n",
    "\n",
    "            params['noise_linear'] = sigma\n",
    "\n",
    "            multi_a = np.zeros(10)\n",
    "            multi_pval = np.zeros(10)\n",
    "\n",
    "            params['initial_condition'] = np.copy(steadystate) * np.random.normal(1,0.1,steadystate.shape)\n",
    "\n",
    "\n",
    "            ts = Timeseries(params, noise_implementation = NOISE.LANGEVIN_LINEAR, \n",
    "                                dt = 0.01, tskip=4, T=500.0, seed=int(time.time())).timeseries\n",
    "\n",
    "            multi_a = np.zeros(N)\n",
    "            multi_pval = np.zeros(N)\n",
    "\n",
    "            for i in range(N):\n",
    "                x = ts['species_%d' % (i+1)].values\n",
    "\n",
    "                x_transf = ratio(x)\n",
    "\n",
    "                a, b, c, stat, pval = fit_ratio(x)\n",
    "\n",
    "                multi_a[i] = a\n",
    "                multi_pval[i] = pval\n",
    "\n",
    "            df.loc[row, 'sigma_%.2f_width_mean' % sigma] = np.nanmean(multi_a)\n",
    "            df.loc[row, 'sigma_%.2f_width_std' % sigma] = np.nanstd(multi_a)\n",
    "            df.loc[row, 'sigma_%.2f_pval' % sigma] = np.nanmean(multi_pval)\n",
    "    df.to_csv('results/width_ratios/width_lognormal_fit_1_interaction0.15_b.csv')\n",
    "else:\n",
    "    df = pd.read_csv('results/width_ratios/width_lognormal_fit_1_interaction0.15_b.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:50:00.577381Z",
     "start_time": "2020-02-21T12:49:59.376200Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 396.85x180 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmas = [0.01, 0.1, 0.3, 1.0]\n",
    "\n",
    "cmap = plt.cm.get_cmap('coolwarm') #viridis')\n",
    "\n",
    "norm = Normalize(vmin=0, vmax=0.21, clip=True)\n",
    "mapper = plt.cm.ScalarMappable(norm=norm, cmap='summer')\n",
    "\n",
    "fig = plt.figure(figsize=(ELIFE.TEXTWIDTH,2.5))\n",
    "\n",
    "gs = gridspec.GridSpec(1,2, width_ratios=[5,5], right=0.7, top=0.95, wspace=0.05)\n",
    "gs2 = gridspec.GridSpec(2,2, height_ratios=[1,5], width_ratios = [1,4], \n",
    "                        left=0.75, right=0.95, top=0.95)\n",
    "\n",
    "ax = fig.add_subplot(gs[0])\n",
    "ax2 = fig.add_subplot(gs[1])\n",
    "ax_legend = fig.add_subplot(gs2[0:2])\n",
    "ax_cbar = fig.add_subplot(gs2[2])\n",
    "\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "\n",
    "path = 'results/width_ratios/'\n",
    "df1 = pd.read_csv(path + 'width_lognormal_fit_1.csv')\n",
    "df2 = pd.read_csv(path + 'width_lognormal_fit_1_interaction0.05.csv')\n",
    "df3 = pd.read_csv(path + 'width_lognormal_fit_1_interaction0.1.csv')\n",
    "df4 = pd.read_csv(path + 'width_lognormal_fit_1_interaction0.15.csv')\n",
    "\n",
    "#for i, df, alpha in zip(range(4), [df1, df2, df3, df4], [0, 0.05, 0.1, 0.15]):\n",
    "for i, df, alpha in zip(range(3), [df1, df3, df4], [0, 0.1, 0.15]):\n",
    "    for j, sigma in enumerate(sigmas):\n",
    "        w = df['sigma_%.2f_width_mean' % sigma].values\n",
    "        pval = df['sigma_%.2f_pval' % sigma].values\n",
    "        ss = df['ss'].values\n",
    "        \n",
    "        col = np.array(mapper.to_rgba(alpha))\n",
    "                \n",
    "        #with np.errstate(divide='ignore'):\n",
    "        ax.plot(ss, w, c=col, alpha=0.3, marker='o', markersize=3, label=alpha if j==0 else \"\")\n",
    "        ax2.plot(ss, w, c='lightgrey', alpha=0.3) #, label=alpha if j==0 else \"\")\n",
    "        s_ax2 = ax2.scatter(ss, w, s=3, c = pval, cmap=cmap, vmin=0, vmax=1)\n",
    "        \n",
    "        x = 2e-1 #ss.values[0]\n",
    "        y = w[0]\n",
    "        \n",
    "        if i == 0:\n",
    "            ax.annotate(r\"$\\sigma_\\mathregular{lin} =$ %.2f\" % sigma, xy=(x, y), xytext=(x, 1.5*y))\n",
    "            ax2.annotate(r\"$\\sigma_\\mathregular{lin} =$ %.2f\" % sigma, xy=(x, y), xytext=(x, 1.5*y))\n",
    "\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax_legend.legend(handles, labels, title='Interaction ' + r'strength $\\alpha$', \n",
    "                 loc=2, ncol=3, columnspacing=0.5)\n",
    "ax_legend.axis('off')\n",
    "\n",
    "cbar = plt.colorbar(s_ax2, cax=ax_cbar)\n",
    "cbar.set_label('p-value lognormal fit')\n",
    "\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Width distribution ratios $x(t+\\delta t) / x(t)$')\n",
    "ax.set_xlim([1e-1,2e2])\n",
    "#plt.ylim([-0.01,0.15])\n",
    "ax.set_yscale('log')\n",
    "ax.grid()\n",
    "\n",
    "ax2.tick_params(axis='both', left=True, labelleft=False)\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_xlabel(r'Mean abundance', ha='right', x=1)\n",
    "#ax2.set_ylabel('Scale lognormal fit')\n",
    "ax2.set_xlim([1e-1,2e2])\n",
    "#plt.ylim([-0.01,0.15])\n",
    "ax2.set_yscale('log')\n",
    "ax2.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-21T12:50:00.869968Z",
     "start_time": "2020-02-21T12:50:00.810456Z"
    }
   },
   "outputs": [],
   "source": [
    "new = False\n",
    "\n",
    "if new:\n",
    "    N = 50\n",
    "\n",
    "    def find_ss_selfint(x):\n",
    "        amplitude = 2.10E+00 \n",
    "        x0 = 2.87E+00\n",
    "        k = 1.14E+00\n",
    "        offset = -1.77E+00\n",
    "\n",
    "        return 10**( -1/x0 * np.log(amplitude/(x-offset) - 1) + k)\n",
    "\n",
    "    # stool A\n",
    "    f = '../../Data/Faust/25_timeseries/25_timeseries.txt'\n",
    "\n",
    "    x = np.loadtxt(f).T #pd.read_csv(f, na_values='NAN', delimiter='\\t', header=None)\n",
    "\n",
    "    x = x[150:,:] # do not consider the traveling\n",
    "\n",
    "    experimental_abundance = np.sort(x[0,:])[::-1]\n",
    "\n",
    "    experimental_noise_color = noise_color(x.T)\n",
    "\n",
    "\n",
    "    ss = experimental_abundance[:N]\n",
    "\n",
    "    sigmas = [0.01, 0.1, 1.0, 2.0] #0.01, 0.1, 0.2, 0.25, 0.3]\n",
    "    interaction = 0.03\n",
    "\n",
    "    params = {}\n",
    "\n",
    "    steadystate = (experimental_abundance[:N]).reshape([N, 1])\n",
    "\n",
    "    selfints = -find_ss_selfint(experimental_noise_color['slope_linear'].values[:N]) / steadystate.flatten()\n",
    "\n",
    "    df = pd.DataFrame({'ss' : ss, 'selfints':-selfints})\n",
    "\n",
    "\n",
    "    # no immigration\n",
    "    params['immigration_rate'] = np.zeros([N, 1])\n",
    "\n",
    "    params['initial_condition'] = np.copy(steadystate) * np.random.normal(1,0.1,steadystate.shape)\n",
    "\n",
    "    for sigma in sigmas:    \n",
    "        params['noise'] = sigma\n",
    "\n",
    "        params['noise_linear'] = 0\n",
    "        params['noise_sqrt'] = 0\n",
    "\n",
    "        for repeat in range(20):\n",
    "            # interaction\n",
    "            if interaction == 0:\n",
    "                omega = np.zeros([N,N])\n",
    "            else:\n",
    "                omega = np.random.normal(0,interaction, [N, N]); \n",
    "                omega *=  np.random.choice([0,1], omega.shape, p=[0.9, 0.1])\n",
    "            np.fill_diagonal(omega, selfints)\n",
    "\n",
    "            params['interaction_matrix'] = omega\n",
    "\n",
    "            # different growthrates determined by the steady state\n",
    "            params['growth_rate'] = - (omega).dot(steadystate)\n",
    "\n",
    "            ts = Timeseries(params, noise_implementation = NOISE.LANGEVIN_LINEAR, \n",
    "                dt = 0.01, tskip=19, T=50.0, seed=int(time.time())).timeseries\n",
    "\n",
    "            PlotTimeseriesComparison([ts], composition=['ts'])\n",
    "            plt.show()\n",
    "\n",
    "            multi_a = np.zeros(N)\n",
    "            multi_pval = np.zeros(N)\n",
    "\n",
    "            for i in range(N):\n",
    "                x = ts['species_%d' % (i+1)].values\n",
    "\n",
    "                x_transf = ratio(x)\n",
    "\n",
    "                a, b, c, stat, pval = fit_ratio(x)\n",
    "\n",
    "                multi_a[i] = a\n",
    "                multi_pval[i] = pval\n",
    "\n",
    "            df['sigma_%.2f_width_mean_%d' % (sigma, repeat)] = multi_a\n",
    "            df['sigma_%.2f_pval_%d' % (sigma, repeat)] = multi_pval\n",
    "\n",
    "    #df.to_csv('results/width_ratios/width_lognormal_fit_experimental_interaction2.csv')\n",
    "else:\n",
    "    df = pd.read_csv('results/width_ratios/width_lognormal_fit_experimental_interaction2.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T22:01:10.410810Z",
     "start_time": "2020-02-19T22:01:09.228490Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2Gp70+NPmdSiKQFdULltwDDnbZnd2G1E9SG2olqzdRYUxE1c6SM+j4PaQd3qRuoaqxMCzsb08IHFkHsUxcOSGYuCWVjXp7PblHLy1umlUffjTg58HlPZwm297DgBSSlzXHXwP0Pfrn+J1tpNevYK6T39lcDCQnkdu1ctoVTUYLXOoOOd8Cttb0WvqMGfNRab7EN2dSFNn+plnk6ubidf2Jnge0s2g5hIohRyWGaUQDiI8D9c1yT72K4y5x1FxzvkIZepvFu6JlPLO/rqt4+F36kkp/2scnltWSp3RLxRC/B/ABp4F/gBkyybVOBEPhg96E1ZVFKJmgKgZwFQ1NnV34kpJZU2Q05vmoKkKqzp20J5JEA+E6Uh18fA6wabe3QRUl4qgwnvmQ2emlmRBQ8olwEsgCqhCRWoZPBnC659sSEDiYLlJEBJPuuTdBInCNoJa1aDvfqmlEceLieJJJYQYTIWwN1JKcoZO3iqgVNVgWdbgSiC/8m+kn3gQ4TjU/sNXsXftpOfZpxGepGLpuwge+zbqb74NJRhGahp9zz+N29GJURlDAoFIDNnQQmbbNuzOPszqCmQmQ2JrB+KV11DMALEzzkVKecRs1C5ZsuQ2plhx7vGmVPfKXwC/6HexfA/wNSGELqX8TFmlm6SMtDo4sVFlc89bA8DxDS04nqQqGOLFHVv456cfpSubYnuil5iR54J5eZqiglhAAUsww1iIEGmkZ5Gyd6GgoSshVBGgO7eekFZFurCDoF6LJkw8bDQliK6EJt1MfyIhhKD66hux27ejT2tGqMU/GyklrpAI20IqKghBrmMXxCqQwTCZ7k5y/3s/zrrl6NNnYe3chl0RR+gGYu1KxDlXErj4SnLLHsBzXNRIEM+2UdIJKio1zHmLUDJd7PzeraRfeZ66az9DZM4MvFQv+tEnI4bJw+PjMxyjyV55JpCjGDDVACSFELOOpOyVo2G41cHeAwDAq+3b6MllqQqE0IRCVzZFRzrJDi9DfRQKDphqlm09Git7dnH+3BhBfRppuxNN0XGlTViN4mERNaeTKGzDlRbd2fUoQkNXQ9SEjvIDrQ4RoWkYzbOGtglB9NRzMOI1qBVVRXPN2e9A6etBrapBD0fp2rweqYewt29BZDPgeWiZBKJ5LsIsVi+ThkEkHiXveIh8lkA0hNQ0rHAFgXQnqVXL0Rcfi/3K7yi01eGpxXw6xqLTD/vv4DM5KTl7pZRyyPq6f1P2sGavnArsPQAMKH5NUXh43Wus2t0GSHKOyp+3uKzpLJ7XkXaoNN+gIz2HsNHJydPDxEMxopqCoUbI2rvpzW/GdjMYIoojs6iY2FaSgjndT4lcJoQQBI4+dvCzohvUXv5BAKTronsSr7sdGatEzJyFUHRSrZJA6yacaUfR+Ys7iZx0MurWLYBKMN+Hed5V5N9cDdk0xtuWUlV/DM5fHyWvRdFVA88MEYz6gVY+pVOq6eZVIcQ/7pGmeL6Ucj2HOXvlVGRPxX/NktM5rr6J+1a9xJ+3rKc9lWBjj4uCQEWSU2x+s24teDm2JSRVoQQtFRWcM7OZeKCJvsIWglpVMT+LEgEEiqJSFZiHroYHUyxMZJv9VEKoKi23fh9r1066fnI7Su8uHAdymQzurJmoZpCev72I9eZyNNciUBWDmQtQYzXYG1bhRKtIPv9HzDMvwnlWwUpm6C1Y1Fz7j2h1xQInXi6DMIOIMsR5+EwdSk1T/D3g6P40xauAa4GPlFm2fZgs4fIHSzwY5tzZCzi+sYUV7dt4btsmfv3GcvryWbyCTVUkwo50krQNf9gCMdNGyC66Mq9yxgwdQ8kR0EM0RuIIoSLxBlMxWE6a1sQyNDU4ocoYTvU+BTAapjHty99Feh72ji3kvvol3FUrcWYuQk314VVOo8/RCCcT2E89hfW/v6P+5EWIVB/ZVAr9vu9jzDgKu3UDIhJFjVQgpST/t6fJPHE/WkMzFR//8hGzWeszeg6o6KWUfcBHhBDnA53AsYxTmuKJ4qFRbgYU/rmzF/Ch405hRft2tq5/k/nHLOCmp35Dxi6QtlyylkAXgmVb0tiupCIAUXMzVcEUxzfMpj5SS8FOkrZ2krXbsbw0YaMO281NGJv9kdKnAEJRMJrnMO+u+wHYtWwZTTd/jZ4f/gumo+I1NZPK6qCksFMplFAE6VoojkXk2BNwu9sQWMjOHbjTZ5HftpFCXQt0tIHngupvzvoMT6mbsTcDfwRupuhWeXjiyX2YFa9lVryWZbuTLJ1/HNNjcX624nkeWPsKaauAlJKunKA7B4mCR1D3eLVdkrF3MS9uURVKY8sMAbUSFZ2804cmAr7NfoIQnHMUDf/2I/oevo/s8r+ibO9Gr67Grm1CD2romRR2Wx/pNa+jZZPFmfzzfyCVTRN8+/mYrRsIn33RoCeQj89wlPq/owqYKaX8gBBiDsW8N+MSNHWks6Sxhf9obOGa40/nD5vWkncd/rL1TVZ2tIPM40iTxkiAX6zoZnF9gpZKyaVHzaMiFkSgoqtBKsyWwdm8b7cff9RoJdUf/hTRs86nJpsBRSF1/w+xLBvFNOnNKriPP4G7q4PKk08ivPF1ZCSOsmkNgbedgxGrHHI/z8qBUFF0Y5y+kc9Eo1RFL4AzhBDPSSk3CSH8BEPjzJLGFpY0tgDwoWM7ebZ1I53ZJDtSCbrSKR7f1I61S8f28jyxYTmXHH0MmmKTdxwiZjvNsUXoSpj29ArA833tJwDGjLlvvf/s18i9sQphmKTuvAMZMIlecBaBnp1gg+FaiECQxH3/j5xrU/MP30CoGk66l9TGlSAEFQtORjFGzp/vc+RQqtfN5wGEEJ8VQpwGPF9WqXxGxYB5B4q5dB5dv5Ll7a2kbZsXtiv05ixyTjuNsQIBTVATXIPjpghqxTw6EbMRiZwwdnsfUCtriZz2DgDmfm8Ju799M07fbtxYFcSiqOke8m++jsimKEQq6P3DIzhvvk7kkiuw0VCkVwy+OkIVvRBiNvAloEJKefke7YuAL/R//IaUcvV4yHe4GZVhT0r5nxQTmvlMUOLBMJfMP443uzv4w+Z15GyTabEZpG3Jpp4dzKgI4Ho2htZLhZnEkx5pq5dp0eMw1IhvypmAqJEI9V+4ncRvfopMJ5DJLpxInEzGxbNV5Jp1OD0JUBW0Pz2MesYFaJU1aOEYANK2QVWPKBdMKeVm4FohxIN7Hfos8CmKWUS+xRFigvZ3cKYg8WCYm05/F+fOOpo/bl5HdShMdzbNm111JK0sEd3DkX0EtB48r5mQniRkuFTb3ezOrKL4NyD89McTCCUQIv7BGwAorHoRt30rmb/8jXT7bsg51M8KoAUETiiI+cxDiAs/it22BTeVoPPO29Cr66j/wu0IXR/fLzL+VPR7EiKEiI63MIeLUSl6IUStlLKzXML4jB17+uS/FXm7kk09nWxPmMSDYSw3gxCdNEXz/K3tJfL2DuKBCnJONy4OADMrz/Fn9hMM89hT4dhTiZs1JL/9TYyFCxE1VUgrC65NIZXFe+AHZM0gsmE2TkMLWkWQ3GP/hXnqRaiNsw78kHHgRDUsk7L07b8ELgPnF5BrpJSLSrlMCFFBcTaTOihBJyGjndH/G3B9OQQphSMhuGasGRp5exqbejp5dttGPCl5YXueeDBF1rIouAq218eJDSoOFgEtgKYYvt1+AhNfeh6xk09HaCqJH3wJ23HJvrmFtKsTnzsNJZ0iEAiiBoMEqqJYrkRd+cyEVfQp4fGDyoPLwX9Bz9r8np+FENXA14HjhRBfAI6RUn6Youn5+xQdTL51aBJPHkr1o28C5gDTBurFSikPeynBIym4phzEg2FOmh5mTlUtXdk075g1n/9e9RcMdSshQydnC369Nsvcqjyq6nLyNJumWHn97f3B+9BQQ8VKVBXX/TNu9y4qK2rY/KXPkVqzEVFbh9ObwO3uRHWSBKc3oBz9jnGWeD8ooAbHZh9BStkNfGKY9tXA1WPykElEqTP6SmAmEO3/F6ZYzdgjiT1n+RWBC/if158lakpSBUE8qPPKrp2kCn30ZAvMikO8jI4b/uA9NijRCpRoBQDzf3g3XQ/9GjedIlAXJ7HWJu1FKazbQiSyAn3mMeMs7fAIRYyZovcZSqnulauB1UKIU/tz0/tMEWbFa/nk284ftOP/96qXyNkKtaHpmFqErmz6oIux+IwPQghqL7sCAOl5GI1NJH79EzzDxNndPs7SjYxQQA8dWdW0DhejtdF/vyxS+Iwre87wP3TsKfz3qpcI6QZRIzCYN99nciIUhdBxJ6NXVZNft4rQKUvHW6SREQJF9xV9ORitH/0b5RLEZ2IwK17LDSefs9/auT6TD715DnrzxC42LgSoum+6KQclK/oR8tH7TEEOpXauj8/BIoRAC/ihPeVgNPno5493PnofH58pjBD+jL5MjDYffRfjmI/ex8dn6iIEKJpvoy8HpfrRB6SUT/Z/XL5Xe36Ey3x8fHxKx5/Rl41SDWLfFEJ4wFqgD5jV/7oPeK5Msvn4+BxBCAVUw7fRl4NS/ehvFELUAQspFiF5Qkr5elkl8/HxOcIQKJo/oy8Hoxk+/x34jJQyO5AGwcfHx2esKLpX+jb6cjAaRf8vwN1CCAd4DT8Fgo+Pz1gihL8ZWyZGo+i/BqwHZgO/Ko840L9auF5K+YFyPcPHx2fiIYTwbfRlYjS/6s1Syi4hRJhiqs+PHeiCvct59V97B2ABy6SU9+19jZTyGSHE6aOQy8fHZyrgz+jLRsmKXkrZ1f9vRghRUvmtYcp5XQY8KKV8VAjxgBAiA7yn/9hTUspfjkJ2Hx+fKYQQIFR/M7YcHNQ6ScpRlIEZShMw4K3jSikfBh7e8wQhxHHAmUKI16SUT+x5rK2tjfnz5w9+vvjii0vOYZ5Op1m2bNl+z5HCQqoFhGsipFHSfQ8Xpcg/GSl3n3r5PIphwASslzpV+/SgEQLVOOJLHZaF0eS60aWUthBiDtA9UHdxlLRRVPavAcP+5UkpVwIXDXesqamJV1555SAeC8uWLWPp0qUjHrfdDNsSz6AoAVRMGqMnTqjKSgeSf7JSzj7d9v3v0vWnP2JEIiy6r2zbSgfNVO3Tg6UYGTvxBuSpwGh+1X8XQkwHbgV+UMoFQohqIcSdvFXO67fA+4QQPwIeHa2wA9WIHn101JceEMtNoyga0vPIOz3kneSYP8NnX8rZp3ZXF4RCOJVxHMcZ8/v7jDUCoaoH9drnTkKEhRA/F0LcJYT44B7t7xZCPCiE+JUQ4l3DSiHE9Xu8v7EsX/UwMxrTTQz4O+AbwIdKuWCEcl4HnQytnNWIDDWCiolUJBKPrNOJrgYIaPGyPM+nSDn7dMY/3UL3U78ncvyJWJaFbduYpokyAc04Poz1ZuyQ/UCKUfwAp1N0EEkCNwJPDRVBfBs4XQgxk2Jd2bnAf4yVUOPFaBT9MmC6lHKVEGJDmeQZN3Q1TGP0RCw3XVT6SoCMtYuc3UPUnI6mBMZbRJ9RosVi1F9+5eBnx3HI5XJomoZhGAghxlE6n70RQqDopdvof/byWn7x8mCJjJq9Dg/ZD9yj/SHgZxStGdcNc9sfUDQtPwtIYFfJAk1gRjO1yQAnCyHuB3aXSZ79Us5lPhSVfdioR1fDKEIlak4nYkwjVWgjZe3E22MPOpPJcPXVV3Pddddx331veYlu3ryZa6+9lssvv/yA5/qUv0/3RNM0Qv3FtLPZ7D7mHL9PxxkBQlNLfn3ktMU8/ZkrePozV0Axs+6eDOwHwlA99wXgbOBM4JZhpHgvsAS4Afg08PWx/IrjxWgU/cVSyiv6A5kuKJdA+2NgmV+qV8YA2WyW22+/nZtuuomGhgZ++cvSvTh1NUhlYA6aMOnNbyLvJAD47W9/y+WXX85dd93FI488Mnj+7Nmzufvuu4fcY6RzfQ5/nwohME2TYDCIZVnkcjk8zwP8Ph13xNjZ6NlrP1AIce8e7XcBPwGeGOa6vwG/AX64x2vSMxrTTVAIMYPicmbiuKOUwB133MHZZ5/N5z73OVpbW9m2bRu///3vufDCC/c5d+PGjfzgB0P3mr/yla9QVVWNqVWQttrJOd1s276VxYuLykkd/j/aIG1tbSxevLikc31KY2z6tDku2xAAACAASURBVGqIOWf79u0l95Pfp2NP0XQzNpGxUsoMQ/cD7+tv/yWwv1nBx4AsxcDOKcNoZvT/ylvLma+WRZoDcLDL/NWrV7No0SJyuRzBYBCAlStXAnDrrbfy4x//mNtvvx0AKSWO4wx5DaAIjZjZTESvp6o+yIYtryOlNzgjHImmpiba2toADnjukcZ49+me5py6ujpaW1uBA/eT36flYTSmmz1fY8iTFLP0Xg68v//fSU+phUfeDlRQ3JAFOArYWCaZRuRgPTQuu+wyvve97/HII4/w5S9/mYceemjwmKqqXHfdddx2220AzJs3b5/Z397oapgPX/kJPvmp6/jd737HBe9+By+88AIrVqzgyiuv5Etf+hIrVqzgG9/4Bl/4whe47LLLuOGGG3j88cdLNlHYbmZwY3gi+fOPNROhTwfMOVdeeSXXX389jz32GBdddNGY96nPARACxnl1JKV8QAjxWP+KYMpQ6jqpqv81gCyDLGXj0ksvJRaLDRucIoQ4KO+LSCTCvT//H1xpk7bakdLl5FM+hqoY3HnnnUPODYfD3HPPPSXf23YztKeWI5EIBI3RE0ct31SnHH0ajUa59957cRyHQqGApmmceuqpCCEOuU+llHQ/eC+F1s3UX/tptHj1qOWb8ghGsrcfVqaakofSC488KoR4t5TydwBCiEvLK1Z5ueWWW/Z5v2fbaFCFToXZguWmSRRaMdUYIb0Wx8sNOyMvZaZuuWksN4PtpQholVhu+qBkO5IYyz7VNA1VVbEsi2w2i2maaNqh2Y6tXTvpeepRZCiC+eSj1HzgmkO635RECMQo3Ct9SqdU081FwFX9syQB/D1w2F0NBuy5l1xyyYRbLhtqhHhgDlmnm87salKFXSiKikChMXIShhrGdrPsSr86ZKY+nLIXKPQVNmO7GYJaNfXh44ccn0pmnYnapwPmHF3XKRQK9P7l9xSeeJDYuRcTu/D9g+c53bvp/PHt6PXTqb7mBoQy/IxUyfeiTm/CERqhYxbtc9zatgm3t5PA4pMRR2xAlxj3Gb0Q4tcULRYDS0IppbxiHEUaE0qdptQAuf5/PcbJt7ScUZRjgRAKYb0W17Poy21GiDAFp4/u3DqCWpyc003abidqNOFJB8tND6uoJR5hvQFXKxDSapG8tdlnuxl2pl7GctOYamzC5eQZLRO9TxVFIRgM0vvi07iV1SQ2rUfNvLWyT7/6IlnLRn39FWI7t2M0zRz+PoZJ9dLTcVEIHrVgyDE30UP3nf+O1A0qUknCZwwbmT/1mRg2+vcf+KzJR6mmm58LIdYDHwZCwLnAR8sp2GQmqFUS0KqQSEJ6LbWhY9DVMBG3EdvNkbJ2ENbrMdTIsNcbagRNMXHdHJpiDjnPctN40sLDRSJHHCx8xpb43/09qT88THTphQTDb/3e+oJjsZb9DhYsQa+fPuL1yrS5aKqJohmIwF79pajISAV2RRXCNMv1FSY8YoLY6IUQ1wJXUNSPqpRy6fhKdOiMxvD4MYrhwLcBV5dHnKnB3ukUBhSxroaZFn0bvbnNBPWa/SroqDkd1Tb2mbELFCwvS97pI6jGRxwsfMaW4KKTCC46aZ92o2kmzV+/k2w2i6cojKSm7LZWXAlKeN8+V6MVVH70JvLJBMF5C4a5+khBgDYhbPRLgBeklP8qhLh5vIUZC0ZjDOwAAhRNN3XlEWf/HM5w+UNlz3QKe7dXh+bjeMNv7A+YZpL5VrJ2F7abJWN1IIWF7Wboyr6BiobnOVQEZmK5aWx38joJTKY+3R+GYWBZ1rDH8m+uYec3P0/3T/8Tp6sDKSVSvuW41rV7Nx3ZPG68Fpnqxdn0OtI9ArNtDphuDuY1tvQBphDiQ8AJY33z8WA0M/r7gAJwM/Dn8oizfya6PbdUVMVAETq2m9nHIyeRbyVjd+B4OXJOH5t6nySs1+AG20jkm8m7CVyZR1VUdmdWoSgaughNWlv9VOlTTdMoFAp4njckO6ZnWdhdu/Eqq5DBEPntW0n+750ITYMF52Ft30yy4OJ6Htl0isCj9+KhEGjfinnGxNmcPmyMsJl9mPl3ihuyFzJ8PpxJR6leNwI4T0r5feAz5RXpyCCk15C1u6joV84DvvNpaze706/hSg9PWmTUDpJqJY4maM+8iuUkydk9mHolUcPA8Qp4quvb6icAhmEMpkIG8Ap5tn/hE1QunE1wzizsVIbksj8gGipRPAc30UvPXd9EP/EsxKLTCEeiSKFghSs5InOligljunlP/0sBrqJor5/UlLoZK4UQbxNCXAUk+tt+V1bJxoHeXIaubJqaUIR4sLxKU1fDeNYuXM9CVQwsN03G2k3S2oaHRFFVhGfiunky3i5kAJJ5B0Uxcb18UeFbvdjkCKPieLl9VghHOtk317Hjv35A/B3voubd5Q/90DSNbDY7mALZzaRRGuqwG5pRdneg9nUi3QC2KwgGg6h42PFavDfX4K1bS37GbCJnvhdXgjbzqLLLO+GYAF43/bxTSnnlgU+bPIzGdPNHwABqmWSRsaXQm8vww789ieWmgCDvmns8NaEohqpiqhrG4EvFUDXUA/g6lzJoBPUakoXtGGqErN2Fi42uBAlocVwvT0GmEQhUxcB1dAQaBacPx8tRcNMgPTQtgq6E6Mu3kshvm7QmnHLwxh0/4eVkM7MfXsaZ57xzMGJ2f6+R8CyLwpYNmLPmFWvQDoMQAk3TsG0bXddxgmFCJ56Bvv4FlGgFVvNM8j1p3IKNWxlDqBrR6S2k31iFF61Cdu8kcf+dBD71VRKP/AJl1zaiH/gUanV9uX6iCYaYKKabl4UQF1MsToKU8plxlueQKVnRSyl/Xk5BSqGcwTUd6U5mVu4iFjDpzvZgqi5VwRCW61JwHZKFPJbrYLkuluvgyrd82wcGAbN/IMjZNk9uWoOmqoQ0nSsWnjSo7PccAMK6Snv6VVShI4RCc+zt7M6sQphQcDOkrV3k7E4cLwdCENbrUBzISRfXTWF5KVzbxlBCGGoIBZNEvpWKwAx0NTwpAqvK2af3eReyxVZRbI9z+yMuBzZCPc8bfL/35iiwzwDQccftFDasITBzLs03D83pJ10XFAUhBLKnm80//iFaKEzTJz9D9TsuRZ57MSCwfvRv6AEdV2hIM4ynqsQu/RD2G/+Im0sjwjWIaBTZ3UF+dzs4HspfHiPy7qtQAsXEa04ygZtOY04b2ZVzsiIFyIkxo18KPEdxTxLgyFH0E4FybtzFAqCgkshLglqOykA3UaMWQ4uhipHthlJKbM+l4DiDA8GOZB8Z2yKmBFjX1cGTG9eysG4aAH/a/Aa6qqIrKhfPb8H1dDKOQsQIoCkmMyvPwXLTOF6Oncnl5JwuXOmAKtHVEAFtHm5uHZabxPFspJA4bp601Y7t5XG8fNH2H5hJR2YlChpGv7vnRFT2ZS0luHgGby5rZ/aMMIVCAUVR0DQNXdf3O3vfewCQUuKmk3hGAFsoZDKZYkpdRUH07cZ9/mGEESBw/jUkn3uGwsYNWIC3bSscswghiqs/mU6SXN1KYNECkqvfwJl3LEogTOy9V8P/3ocbCUNAx9vwKkrTbJyONnKrl2O3vkn8hq+SWvUc27/1XXA9mm/6IhWnnVGW3238EEh1Qtjo1/XvR04ZSlb0QogvAosohgZLKeXfl02qcaA2VMsJ0+aQsnNE9Zk0xxbiYZPMbwMkhhrD1CrQlKEBLUKIwRn9AAFN483uDlwpWVDTwLmzjkZVBK91bGd3NknUCJIo5Hh1Z4DufCcKRf/4mtDxhI0wuhqmM9NJTz6B67kEtBjZvIPEoz56PGGzno09f8Jy0iA0hBDk7F486ZKiDcfL0JVbT97uwlCjVIeOOiI3az997RzOP6eelukhQkEV13VxHIdsNjtoZtE0bZ8assOZcZo+eRPpl58j8ra3o4fDeF4xPXWheye2HkAKA6+vG3PBMai/vActYBKYMXPweum5RN79Pry//itKVwekUzC3mM/ePPZ0opFqEn/+DQXbxVn9Guqp5+O1bsKqqsezcuR3bKGQSCCnNSNyWaxdO8v98x1+xIQx3ZwthHiCt0w3R8ZmbD9iqin3PdHVMHOqTtvH1BHSa/GkQ8FJkrba8aRVVPpqFE0JDTszjAfDvH/hifvY6E9oaGFTdyeulIR1A8czWNcZoSFqIGWA1r4MrX0Z1nft4qF1K6gPW5zZImiMaiBsTDVKWK/FdsPsTP4VTU0iCKCpaZB5JJJUoY2s3Ysrs2hKiIy9m6g7/YgMrFIUwdFzo4OfVVVFVVVM08TzPBzHIZ/PI6UcVPojFRHRa+qIX/jePe6toCgK6tzjsNM9EKlCiddSWPMa0ZOOBSmxOnagV9WSeuinuJ6N1DXqL3g70qzGiIVoq37L/NKqzeFF41LO5ClItJH8zf2YzY0Y6W76nDDeX57CWLSI6pOPQ1Y0Uv3OfQusTH7EmJluhBBhisVDLGCZlPK+/vZGiuUEBXC/lPK5va4TwK1Syj+OiSAThNEo+jlCiPdTrB07Jb1udDU87KxXERpBvYqgXoWUHpabIuf0YHs70JUQplaBoYQHl+hQVPZ7b8LuPQAA7M4kydgFWhM9vNn9HOu7OljRvo20XSCgGjy7TeNdc6NEcyHmNSwmbcFruzppS0SZFkugKiE8TyIUD7yBfDvVpKw8Aa0Cy1GoCh59xM3mD4SiKBiGgWEYg4VJLMvC8zxUVR1U+gdKdyzMIMYp7x78XLHkFOzlf0VU1+PGa+j92XfI7diNDIdx0dC72wlVd+DNXYzsD7DyMglqCt3UKbvpDs+gYbogntyGHQ2hSwvn+ZV4xy0A2yI6bybKgjNR9OE3hCc1AqQyZtbky4AH+zPvPkB/hSngn4AUEKFYV3YI/R6GJwkh/iylnDIVZUbzq/6FYp6bUJlkmRQIoWBqFZhaRb99PlOc7XvtaCKAqcUw1GjRBXKYjdC9B4ABxZ/I5/jV2uWDATcqgrSd5/VOWNOZxlRUlnX/iiXTWqgwFTzaSRSgKqARC9RguwJdD+PhomsRNCeAoUQxA5VEjCPFa+PgEEKg6zq6rhft8f0mnj3t+mvWp7n/4R184D1NLFlUOeK91Moq6m8q5vxzk32kk70I6VDY3IpREcSYNYN02kI8/wzOqQFSLyyD1U8jsjmONopBVTWnnIyzvBfbVAjWzyH4jveTbN2AZ4YwGppxKO4jHEzO/YmNQKqlq6R7Hvo9P3tosOxrzV6Hm4DX+9+7e7QvBD4L7Aa+TTG1y968HXhECJHjCMteOSG8biYaRft8ZNAsYns5Ck6CZGE7PbkNBLRKFLT9boQOKP7eXIbGSIxoIICpqmQVBby3/n9ansvqrp3szqaZHpPMrbLoygS5bEEDLRXH0pvbhKYYIAVRswmkh6lV4HkOrjd8aL7PvuxpuwcGlf4vHthAR5fF17+X5td3n1rSvdRYJZWXfYRg6yZcNUzioZ+hqRLpecjqOrRgiJ0P/Jzw3JnYCRsl0AP5NGpNA8aFV+NsWol+3FkEK2vwtCyW41Ho2oFe2TC48phKSCGQo7DRX/O+i7nmfRcDUHHSBV17HW6jqOxfY2iqlzagF0jD8HFpUspLhBAL+9+vKVmgCUzJuW6EEJcIIX4lhLhfCPF35RRqJCZ6XhRdCRIxGgjrdWii+H9oIMPkgYgHw1yz5HS+ctbF3PHuv+cLb7+AeVV1GP3mIAFoikJvPsNLO3axJdHLjuROfv7ai/xpUye9uTl0pGuImEsI6lXEzBYqAjPQlAB5tw8oRt9mrI4JlRtnovfpgE2/pTlOJit559L4qK4PLHobFRd9gKoLLqHp376PFowTKiTQdm3HtiykZZF9fS3SDCBdiZPO0fa1mymk0mgnvQulsjhRDdTPxFQFZsMMFEUpuoc6DvaGVXjJnnJ89XFBCvWgXsPwW+B9QogfAY8KIe7tb/8u8C3gx8CPhrtQCPGfFE0/lwkhpoT3zWhMN5cMLGH6f7z/LY9IIzNZ8qIMzPKzdieGFit5IzQeDHPS9DAnTZ/J3y04nkvmH8u3nnuKrlyKfF+K5sZpvLhjMz05lee2ucQDgkyhwJ+2PMrceC2aqnJcQzOfetupGKogb/f1DzQpMoUOOrKvowgVBXXIKmM8/e0nS5/e+PF5fPKa2Th2Htd1D2o2rTdMp+bjnx/83PrnP1F1+lLSf+03Pzg2TjKHjNey8/99E1HIEV18LNXXfBazrgWzrgWA5HNPYXdsxwyFsLe/ieraRD/+1SEFS6RtIT0PxZxEyRSEwBsj98r+coAf2aPpvv72tcA1B7jckVJ+rSiS+NaYCDTOjEbRB4UQLf3v/Z29/TCQpjjn9JJ3etCU4EHdZ0ljCz+86Cq6smnWvbqS5kVHc9NTD5K2CnRn02QtiBg6tlVg1e6dqIqgLdlLzra4atFi8m43VcE8lruBrsxawCNqNlFwsyTyrYT0WrJOF93ZdehKCE0JTlh/+4mAaahoaoB8Pk8oNLzH1ahQVOo+dB1S1bFf+QPSdjDzDpbtQm0d2oL5kE/Qd9fXCF3wQfTpLQhFo/CXR7HjdciaWtxAhECmD3vVMpz2rTiWht4yj74H70Z6LrWf+gp606wx+f7lRjI6000Z0YQQ/0IxA8DB/fFOMEaj6P8V+HT/+6/u5zwf3vLg0ZQAaXsXUWPaQd1nwIa/QzdY0tjCTy79MM+2bmTFrlaWbd1AQNPY0lc0T+Zsl75CjuW7tvJM6wYW1Yc5qsriioVnENQydOfWkXOTFJxeMk4HBTeJlC6WmyKoVREPHkVntpNkvpNYoBhb4Cv9oQx45FiWNZi87FCpv+oauOqawc9OJsOW669CMz1kvIqULbD/9FtEoYCiqOjxakRnG6J+Bj2vLseMV1LVs5vM9g68rk7MN1dgx6pA08ht38qzrVHmBLtodFrRjjkVJVIxJnKPPQJveDPMYUVK+dmpZqMvNXvl24EKYFl/01HAxjLJNKUIatX05Tdju1l09dAdlmbFa5kVr+X/cBpbejtZ0b6d57dv4tX2bWxL9hBUdVShsjvTw86USlhP8rcdazlleiOm2kjGzqKJYuWrvJNAoKAIAyldevM7+POWFCFtJ6qA4xsXMqfqNF/Z74VhGGSz2f363R8KWjjM3HseJvn07yDdg/O3v+LEYvR25AkVegmEg8Q/eB2JF19EZFJY+RxmzTTcN9dhWTmIVWOmUmhNc3imZzptLz3NcbM2kA2YBPo6CbzrQ2Mu85ggmBAzeiHE1cD5xbdiSgSHljqjrwKaKe5UC4pK36cEhCh6wSQL24gH5gzxtT9UBpT+ObPms6mnkx3JXl7asZWeXJodiV429iTZ1FOgJ9dLb66GaKAXsKkIpImaNkiDvOtgqhVUBKaRdxpRxJOEdBfbC5IsJI/IiNoDIYQgEBhDE85wz1AUKt5R9CgJn3khXff/FLF8GWLeTNSWRnJPP4RZ3UIopGLUxAksOoPA4jOxWjfgbl6NEq3EPOkcmh98nONOtnCsGvRsD0rNwa0sDwcSgatMiBQIR08F5b4npSp6Dzgd+CVFRX8hMCV2ow8HmmJiapVk7N1EjIYxv/+em7hnzTyKTT2dqELh5Z2tuFIiqeCZ1t0kCr3MqYriyjCeG6YnP52g5qIqgouPOoPObBdZK4gQBSoMj6AujsiI2lIohwlnJLSqWhqu/zzRcy8h/eSDaMkevGglViFL8MwzUK0CmTfWYO/ehhZ0UetqCSw6E4C5x04jt3IrQnqEL/ooSmVtWWU9NCaG6QbQhRBv463g0LXjLM8hU6qirwFyFFMUexQrsPiMgpBWQ19+E1m7GymdQ/ZwGSkN8oDSrw6FuWv5s7zZsxtT0aiLxGjtU8naKit3tVFwWunKZrhg7gKytk1rX4aC63HWzMVs7N7B/Opq5sTP8Gfz+2HAhCNRMHQNRTm0mf2K1/vIF1xOPbFq2FVC+OhjCB/9FZy2zbhd7eR6klgv/I5ctI7WH3yfmnNOwZjRjP3iS1h9LhVvPxua5hOvnU5O6KjxqkOSr9xIwBvDFe8hkKI4mRUUxZr0e5KlFh75OeAHTB0CQggCWhWtfU8T0KtRUA7aw6U3l+GBNa/gulmCussl80+hNjx0pjYrXsvn3n4+m3o6AagOhXl43Wts6e3imLoGjm9o5sUdW3ho3WvUhqL05DK8a84xnDz9LLLWOmZUziFkjBwB6lPs041bCvznXStJpBTu/eHbCAUPbka6bmOKW259HUWRfPzDc3nvu0c2sWhNs9GaZmMCnHshnmWx+32X0Pt4ivgJi0hsaaP3j8/gRWJEjlmEGq5HZDITP5pWTBjTzSsUFbwAUkIITUo5qYv4jiZg6n+EEL8UQjwihPhLOYWaqnjSRlEMVEU/YCDV/oKburJperLdeGxEV3eyNfHSsOcVZ/czOWn6TGbFa7lmyen8n+NO48yWo6gIhDimpoEl9c04nsfqjp28uGMLaQtqw02k7TH96iMy0QOmDsRra1Jkcx62Y9PRmd/vuYmkTT7vDntMUwWNdQpNjRo//OlG/vrS3oGeI6MYBgvv/gUzbvgHKs+6ELmjDa+qlraf3om9eQNQNDW57vDPnijIftPNwbzGmGuBBcDRwE0Uk6NNakaTAuGqgfdCiBvLI87+KWeRisNBMZAqRKbQQUivGdH+PVA/ViLxPIuq0DykeCuNQU0ogq5Y5OwM1UGDiG6UtGk6YNaZU1VLVzaNpij896qXaE8nqAwEqTSDdGXTCCFY0b6NoKaXvaTiZAmYGon3vnsauzqzzG4JMLN5ZK+ql1f0cMvXV2MaKsccFUMIuPDMt47PnRXhug/N4sFHW6mtUtjdVRjxXsNh1NVj1BVzGjV96h/Yfsd/gKpQ2NZK+OiFFDa8QffKV6h958UY9Y0H9V0PBxPEdLNeSvkdACFEDUVz9aRmNPnoB1L06cAJ5RFn/0x2paCrYaZHT2V3djW1wYXDKmbbzZDIt5K2dxFQ4/QVNpNze3GDycGasPFgmKWzlrC+u49jaisI64FRbZrumVjtQ8eeAkBIN4gaATRF4YmNa9nY3cGOZB/vX3hi2ZX9ZCYW1bn5U0cP5rjfm41b0tz0r69j6ArzZ+t0dDps2ZZAFZDODrUGHL+4El316OyRnH/uwSvjyrPPxenrwU2lqDznnQDs+s7X8Kpr8LZupvnL3zjoe5cXgScnxGasFEL8hKL5phN4eZzlOWRGEzBVS9FmlQNuLo84Ux9dDRMxGhHDLDdtN8O2xHN40iJVaMNSU7jSLioQ4Q2ZtceDVVSYx9AQiVAdmr/PoFFqWoNZ8VpuOPmcwY3drmzRnLSksYW0VaArm/YV/QEYKFQykHl0T555oQtddUilJBecU0O8IsjzL3cjhCQU3Nc+dtTcCMcGAmja0PtIKXnu5W5CAZUTjt1/vh0hBLXvef+QawPNM8ht3UzwtLMO4ZuWFwm4jL+il1J+UQjx/9s78zC5qjLh/87dau3qvTud7nT2hEAChLCI7IgKsinCiCiKD4PfiKijjLgy6ogbMuOMwzio33wqLqOIoqwqLiibSICEJQnZl04v6aWquva6y/n+uFWd6k4nqe50p6ua+3ueevr2ufeeeu89VW+99z3ved9IYXt4puWZCiai6FuBU3DHoxM3xafHJDDUGvJ2Al0dvbo6byexZQ6/VkfQaCGgNmDJHJaTAqmMstrdGqc6fr1hXCXfnViLxD5s9kwYbeHHsmkG0gnSZo4awz+SN9/j0GiahmVZGGMKh7/lgjns2BWlrtbPlZe04/MZXHh+K47jsHbt2gP6GVu7tsgTzwzylf/YiO3Af9x2IscsrRn3uLE8/2KUmz/3Egs63sm3/nURgZax2XwrCYEjZ951I4T4LDC/sL1HSvnaiLop0CylvApACHHHNMnzmsBQwgybuwnRMrpdDQMOWSuGKnxE/J0Yaph4bhf9mdw4ynp8pZC3k5hOBkMJjEz6lhPdE82kuOeV5wBIm3muWLHas+bLRFVVcrncAYp+ToufT31kOZqmkc0eerL2UPh9CjVhBcuS6Hr5kTNPPTtEa7NCd1+WOOGKTtwiAaf8+JDppEFKeQOAEGJWGLTlpkC4GGgTQlyLOx5Tv+rnNYQbdeMgpTNqpayuhmgMLMN2TBCgKQa6GsKv1SFkdJyeHMZT9oYaRgBZK4Zfqy/bfz+QTpLK51hU30TGsrCcqp+DOmqoqjpSSHysr77YPrZtPA7WfsrqBm69+RgMXWHxgvKfst7x1g4ymQxzWsPMaan0TJaVYdEDdYU0CACNMyrJFDGRBVOPsj8c89HpEee1g66EyNtJfFpkVLsiDDQthC1zmE6GfK6LRG4vtpYbmYx1/e+DuNMl4/SthmgOrSJjDtAQWFJ2rH5TMIwEuhJxWoJhz20zQRRFwbbtkaIlRUoV/ZN/G+Sh3/eQzZpc8Pr9PvrefVkGBlPMbT24j3rpwomPR3Ojjxvft3DaV+9OBVKCVRmTsf8HeFPJdtVTrqLfBkQOe5RH2RhaDXkrcYCid6QFQmA5OfalXiKV7yNrDmLW+OkarqU1dAID6Y2krTiCPiynY9z+dSWA1GontCCrPhDi3AXLEEKwes48z20zQTRNO6Si7+3P8r2f7SQcEAgBg0NuCGU0luc9H3yWBfNU3n3lXE496eBhmgez+A/FeE8UlcnMW/QFV01xsRTAOcyC4JNyFX194VW8+Gr41FQ0hhIi5fQeuEMIpLSJZ2NEM1EEJoqiIVAwnQxpsx+bPJY9DDjkCwulxouyceTEF8gEdIOWUI2n5CeBpmmk0+lR1rPjONg2bNwS5+57tuPTQSiAdEMzAfKmQ12dQme7Ri5nIaVkT3ea59bHOP+sZiLh/atFq0NhTw4JM67ogTtnWoDpoFxF/yDwISmll8hsihBCQaBgOyZqYdm3aafcXPG5PL/dvo5aX5SwnqHWryDR0JUAQb2ZeL4L20kDtqwmJQAAIABJREFUoKvBQpTNs4BAIGirWQOAZOKK3rRtbM83PymKvvminz5vOtzwsbU4jsnCeQE62zX6B2ze986FdMwN8vzzzwPQ2uznkx9aSjKZ5Jil7hPejZ9YhyJsnnp2kNv/edXIe8xmi14isKZI0QshQrgrWvPAY1LKH5fsWwX8AVgkpRy1PF1KuWtKBKgwyrqr0v2UnCKEeKcQ4i0li6c8jgBDrSHvuJ8z007RlXiaocwOuoafQjCIKnTS5lyC+vFoiRV0RE4naDTT4F+CpoSRtKIJH3k7SSLfhV+vK0mtICdl0edtC1t6in6yFMMswXXJZDJ5UimHPd0ZDF3hoje00jF3dGrj7btSfOOuLTy9dpB0YRFVOKQxv12ntma0NT9RhV0tSr6II5VJvcbhCuDeQvTMZcVGIYQO/D3wyNG5ospgIj+fvwcM3IVTlRyMWzUU4+kBMlaMjDlEWG/GUBWkVMlYFhCgNbwY1aofmYgdymzGtGMIdpC1YoWoGoVUbh95O4FAQSKRk1D0pmNjO9WjGCqN0pwy9bUK73p7O3lLRVUFjfUGJ650E8WVKvpXNg0jpSSTdfjBPbvZ25vh219fzXVXd3L5hW2kM/vHcTKKfjLnzQRSgi1F2a9f3fM9rr/qLK6/6iw4UCd1AHsK26VfhH8C/pNDuJ+FEG8UQny6sH311F3hzDGROPp+KeXDAEKIyw53sMfh0RQ/WSuGgk4y34Nfq8eRDpqm0xGx0JQAyxuXU+MLAXEA+tP99CX7yVpRIEVfaj1NwWOo8XWQt4bRFIOB9EZq/QuRE0zR4RQsec+inzyqqvLq1iHCYZPmBpXLLlzAm8/r5NE/76GzXRwQeuk4kvt/243tuBNgugY7d6dZvKCeV14d5ke/2EZTo58ff+uUSclT8Rkrx+A45ct68duv5+K3Xw/A+ccHx2aB68JV9usYbdCeiLv481TciJp/HafrtwPdhe2TgZ+WLVSFMpE4+ncWPjACuAa4fzoEKrzXycA2KeWPpuM9KgXLSRPLbGNQbsKnRmgLryHvpMjaUfqV7YQMMHSJIlQQkmgmxYObt6Aru4j4BtFVg6w5RNrsx3XVmPi1tsKCqaSbFE3a7vnsn7B1LX7ngPQIpm3j13TPR38EPP7XQb73k63ouuDzt5xIMCh4aWOcH9/bxeqVBroxxPuuXoSqugotmbLYvjvJCSvchVbSkaxeWYuUkmjMpKNNpa9/f4KzUss8m7X501P9HLcsQndflhdfifGOt86jNjLa3aMoSnVY9AgsZ8omY38J3FnQJw8IIX4opbxWSvkOACHE94FvH+TcTOEYhddgHH0e123TCfxXOScJIRYBnwFqpZRXHmqCpIiU8qFCGuQby5StasnbSTQlQEBtQkoHiYOuBDCUIGBjyxQD6Q1k8xbd2SFqhvrJWSpSbcR24ggMhFCRuE8HtrRImfswlBCaEsK28677RqiYdoo98afI2cNkzH4ivvkYamhUeoS8bRPQdM+iPwJSaYu+IRvHAtN0lasjYSDqeg96+vLc//sBIiEVzbHIm5L3v3shXd0DZLMWC+YFCRRy2l95WTsL5sU5Zvn+giGli7K+9B+bePb5QfKmJFKj4DgQjZt84kPLRx1fNRZ9wXUzJV1JmQLeV9L04zH7rzvE6Q8BHwZ+zSyppFd24REhxEpcP/0dwHLg8TLO2w5cL4S4t9BUnCB5QAjxMyFECnhrYd/vpJQ/KfyKfhz4xgSvpeow1DC6EnRXyLK/bJ+rHgSqUEnlh9g2uJY+JcdQl47p2CSyNj41Qp3fIGS0EdKbydlx6v2L0BQ/df4F5O0UeVvBKaSJSpn97EutA6GRs4YwtAimo7J5cBdza+ZTHwhhOq5Fn7WOUjL6Wcibz2tF1xUa6nTmF9IWn3ZSAzffuJzn1+0lVKOzfmOKbM5hzbI81/7jSyzs9PEv/zgfy7JJlWS0DAc1zjuzaVRaBSHEiPLesSvNwk6NbE6i6xpm3ubFjXEe+F0Pl77JzX5ZXRb9xFw308hm4EOF7cq/cWUwER99BLgc+Aow2TLyHcBLhW1bSvkr4FdjjvkMbsz+64GHS3d0dXWxfPl+a+WSSy4pOy99Mpnksccem5zUU0jCzBM3c9TqPmp0AynySDWHsH1sl242VEeBPmHTEMqiqFl6ojqKIlFzzxERQWw9jZaIMJgwCcWzDGx4Ftu/FwBh+1HMfhJykLSIE7R3UqPWYGuD5GtjCDuA1EwS0a1s6N/GvsGtqIrCmS3NmLZGIgfDVp7ctj2Huowpo9rHNJtz2LM3g64L5ncEEcL9Ug0PQaloAQXOP93HUDxFJmMDEkOD91waRSB48aUYuZzEkbBxk0U4KDAMAykljuOQSOSJJ23qIgaBQiaDqy+2GU46mKbJvPYgsbh7XPfufTz4kB9HQl3E/ZFQFGUkGqiSmSqL/gj5AK6CDwOrgPNmVpwjZyKK/jGgXUr5ohBiyyTf72ATJCNIKb94sJM7OjrGzfhXDo899hjnnnvupM6dKqKZFN9f9zQSP2ndx5mHyPX+wKt1tIS6ydlbySgZEpkktYEWWsIaGRt0JUXWrKOjIczi+jVEc/WoQkcIDYV27l7/G0JGiIQ0OPPYUwjoFtujFpoSREEllpM8E0tw8sp2TOdV5jTpGKpBUD+W7kSMk+e2HnFd23Ko9jH93v/u5A9/7SKTkXzjtpNYNP/g9ysajXLHXVtJDDvMa/dz0rExYtkOnlnbR2OdgqYJsnlJfV09H/uHFaRSKTRNQ0rJxz73Kk11eXr6bb77b69DVVVM08S2bfx+V/P/8fE9PPCH3QRDAe57NIWiwS03Lub1pzTxyB/28ouHBvno/1nC6lWVWSJSSoFlz7yil1J+qrgthPjoTMoyVZQ18yGEOAM37GNDIYZ+b5nnNQoh7gJWCyE+hTtB8nYhxH8DE64dV+1l5wbSSXqScWwpsaUcyf0+Pj5URSfia2NuZAlk6+ioC+LIFGDiOBmgBolDyhwga8WwpYWCSn8qTk+ijxrDQZJ1q0YBbTWn0l5zKvPrzqE1tAjHUelN9qFiEzIMLMdCyjiW8yo9yefpSTw3bonCqaTax/SSN87hpFU1vPWilkNWmAL463NRcjmHTTtMmhp8+AyVSy9oIRp350SCQZVVK+p520Vzed+H1/LFf9s0Umkqm3MwDEFtxBhxw4xNt3DaSQ1888vH84kPLSMUFNSFFcIhDUVRuO/hHkwzy3d/tGOa7sSRI5lYeGXpayoRQnxdCHG7EOIbwMop7XyGKNeibyi8JoSUchD4hzHN7xvv2HKo9gpTtb4gUkoGUkn0sHKYpGF58tYAqi6AKAFNZ07oGPYMrwfHQZIDMjgyyGB6I1l7iEx+gNbwCdT4TDpr95Ex04SNAHV+BdNJE9QaR3Lr1PprOHP+YsK6QYN/JwopHOlDU9wYfAETSnE86XtS5WNaX6fx4RuWF1wsNopy8K/Un5/ah2VJGmp13vqWOWzcMEQgoNNQ555z3LIIZ5w2h03b0ui6TTYn2LglQWtzM7omCQQEqcx+f/vYQifFpGpzWwN844vHk8uZI4uzznl9A39dG+PKS9qn94YcIRUS8FVMg5CTUo6Tp6T6KHcytjrNrQojZ5u847iTkUAynz1MPpksilBpCR9HJvoK6VyciL8ThjchSKKKIHmaMdQgQ9kuTEshoEs3Dl9J0FZTS51/Lo0BjaDukLfTBPX9+e8VoRHQBJ21bdQH6knm95J3Ggj7ahFsIGcn0JXQhEoUvhYxTXNksjSXyx2Q0KyU09Y0sHZdjOuvmY9SqEpl2YJo3ELXVfYN5rjrh7vZ2ZUmFFBwJCzqDKGqKrd+bAlbtvezfEnrSORNcaK1SLHKlZSS1mYftq2NTNxeeUk7V791PoFA5Wakl5IZd92UJDUr/CuklPK1kdRMCPFzIIS7MtbGzYpw4XQKNh6VVBw8lUpx4403YhgG5557Lu9617sO2r59+3a+9KUvsaO3mwfu+xUhw8dTe7aRNvMEdeMg76DgyCx5K44iwth2AlUY6Eo7pmhDE3sR9DCU8dGT2IHlqCjCT0PgeCT96IqgxjBRFAekm/dGKSlfqAody85jOjaa4sNQa7Acg6BegyqWUuc3aQ4eO+0++moe09tuu42hoSF+9av98QS2baOq46farYvorFoR4XVrGnHsFIqiEAzoXHf1fB59rI89ezN098NA1CHkl7Q0Cu7/XS+rV+V5ZdMAbz6njnze4cUNcU5cWX9A2UIYvRK2uF0t4ZUSsGc+6mZsUrNZEXVTbq6bq4C1wJuBC3HDLI86xcf8iSqEdDrNHXfcwc0338ycOXP4yU9+csSy/PKXv+TKK6/ku9/9Lvfff/8h2xctWsRd3/kOjpSEDDez4aL6JrYN9Y/bt2mnEOwBoWE5eQytE9sR+NQGJDpgYslhIE3etsmYPhwZwrINuhPrSZt9uHH4eRShsi/tBjpFMym2DPYRzaRQhIYlTSzHwZEWjrQwbRtdUVGEj4DWOO1KHqp7TL/97W+PUrY+n498Pj9u3z19WX7zpz6eXRfjZ7/uGmWRv/7kBlpb/AxFbSzTpr0tjOVIUimHp5+N8uX/2MILLw3z9NohPv2VDfzbXZv5w+N9ZLKS//7Bdp74m7sotBh6Wfoqba94hS/Bdib3mjIR3KRmc3BDvD8HfH7qep85JhJ1swxoB0xg4fSIMz1861vf4pxzzuHjH/84u3btYvfu3TzyyCNcdNFFBxy7detW7rxz9I/6P//zP9PQMHqKoquri1Wr3KyCpRbcwdp7knH82v4Vi62hCJsH+8jbFoY6ehjcpGSCkD4PQw1i2Rl8moXpCDRlGarShaGqZK1+dAVsaePYWQK6giKGCRsrgW4URcev1mI5WYazGX6zbS2OI9EUhbetWIHtmJi2TTHEOm+b6KqKqlDw0lculTCmlmWNUp7FKlPjFQmvjWiAwuZtOa64JMymrQmyOXtEIV/ztnn84S99rFgW4aQTWvn1w9v5xUO9ZHOSpQvDbNic4F1XBMhlEzQ2Kji2zd337OEvT+/jF/d3cd8PXo/PEAco+VIqXdG7cfQzLQUANwC9wO3Aew9zbFUwkfXGn8NdLXYzblKgo85kIzRefvllVq5cSSaTGfFRrl+/HoDbbruN73znO9xxh1sGV0qJZVmjXuPR0dFBV1cX4E6KHa69OxEjUKLohRAsqGtiR3Rsig53IVXWdhhIJ+hPDdGX2obuS9GTXIvlOKhiDpoSBMI0BhcQ0NdQ61/AsU1n49P85OwEoKMSIG0NkrWGSOQlmwZ6UBVRiPjJoigOpmPjSBtVGDjSRBEKinBXcx4NqnVMiwp9rPI0DIMNrw6xe296VLuuCc59fTMf/cASXngpzv/+cg8Dg1leeDmKlJK6WoO3XdzOMUtrcByHc89s5pI3zuW9Vy/krq+v5rH7zmbVighf/uxKLn1jGz6fYEFnmLlzNOa1+wj43a9yqVVf3C7KW+lICaY1udcU0wf4cWt1thzm2KqgbIteSvkqbua3GWOyERpXXHEF3/jGN7j//vv57Gc/y3333TeyT1VVbrjhBr72ta8BsHTp0gOsv4P1edNNN/HQQw9x6aWX8vTTT/PCCy/w3ve+d1Q7QM++Pr76yc/w0vr1fOUrX+FTn3LDdDsidTy8+WWkhNbw/mIfyTw8sQuagxZ9qR46a7MMx2yOy2UwnSSqaCBoHIdMdVHrW0FLsA9N2U7QMPA782kILmXzQI6IsZy83IglLXSlH0WYbI8Osri+iTpfGJ8qsBy7kELBB7jFq1VFIo9SAYhqHdO+vj5uvfVWXnjhhVFj+uSzMX50zxZ2d1t8/5un0Nbqxrj/+pFu/vJ0H9t2mQwnHY5foZPNWQR8B95ny7LwGTpvfcvckSImxQeJthYft36th7oahbNPn8stNy2jvjaApink89WXlngsFWLR/wg3TcstwB9nWJYpYSKum6rlsssuIxKJjLu4RogDMwqWQygU4nvf+96ottNPPx3ggPa8ofGv3/wmixuaR7XHsxnW9e5mXV8XLcEwVx3nFgxZ272L4ZykNVxPLBdnrsyjKTCcy6IpASQSVQRI5v280NtPgz+Mrq6gKVhbsshpPVI4BLRGBG6RkwsWLiCaNXjL0pUYqoZPVTFtG0e6TxGSaOGeHD2LfrLM9JhGIhHuuuuuAyZe02mLWMIhElYwTYds1uYn9+0hlXZ9936/wvIlETKZFJEajSULQ+Ry+5OWPfHMAOs3DPN3l82nrfXAOq+qKkilIJ22CQZV6msNNE2Me92lFn3x/0pGSiolRfY/AvcAH5HV/KtZQtmKXgjxWdzFAxI36uaaaZNqmvnkJz95wHZp21TTk4xzQuuBtV0H0knCvoBbbk5Ktg3181zPLoZzWV4d7MOyHbK2YMdQPYGMSsS3iozlWoDxbIYndm/Dr+m0R+o4Ze58QkbrqP5VEUBFL8TFC/xaDRnTXaRlOQ66qpK1iq4IBU1xP9PqSCT99DNVUTdHc0yLVvN40TVvPq8VwxA01kFnR5Af3bubXzy4G0XAFRc10zlPcsO7F4PMsX79ulHuH9N0+PkDXZgm/DC/m1s+uPSA/kNBnR/850n07MvR2e7nN3/Yw9IlNZy40nVfpbMOmmajqqOVfjXoKymhQrI03AJcCdwthOiWUn5ipgU6UiZi0bdIKWc0CX8lheKVS84ysR2HwDhhlE3BMEFNZ+NAL8ubXCXdNRzDtC0yVp6klWNN23wkDn4rRN7REG5JEaKZNI50aAqGEcBQNnNA/6oSoK1mDXk7SdpU+NOupxhIJXCkw/mLjkHBwXYGsJwwilDQREHRK+KoPUJX44Ip0zQPGi+vKII3nNVKKpVCSsnCzhBtLSq6Jnhy7RDJpGTrziyGmuOCM8wRRW9ZDq9uS7CoM8TGzUlef/LBs+O2Nvtpbfbzuds3sHN3lMDj+7jz9hbu/203jz/VTW2tj1tuWj7qnEq35otMZQTNEZDAXf2fxc1dX/VMJB99rRDinRQqYBSLkBxNqlEp9CaHaaupHXdffSDEVcet4YndWzm2uY2GQIi8bfGnHZtI5fNYtoMjHTYN9FKXthh4dT1vWHgsPk1FURSGc1m64kMsa2ql3j/+QhhdDaGrIboTfViOTWuoFtOx6UvuQxF7sB3BYFqnIdCAVnAXKwKcCo+6mUksyxrJL3MwipWmzji1kfse8pHN5cmbAkWF3XvSzO9QiMXNkQide+7vYv3LQ6ia4Fu3ryYQ8I1Uqiql1DJfND9Ed2+MSMRAEZKNWxJkcg52NIuUYtTx1WLR23ZFyPlj4HfAx6SUiZkWZiqYSD76P7K/lGBFjEY10J2Isbqt86D76wMhTmlfQCyboT4QYnVbJ9uG9pGxLNJWnoFUkoBu0Or3MWiapMwceVvh4S0v41NVcrbFeQuPwZFuYZKBdHIktYIsGaamYBjLdpDSxJYOQd3BdLSRfPZZK4VacN0oQo4oCo/RFFeejrdYqZRi7VhN0/inG5eycUuMY5bU4fdrPLc+wZ+e7KG5MTui6PNmQamXxLv39Wf56a93cd4ZzZxyYv0B73HtVfM463U1NNa5T4vXvaOThx7t5qRVQTTtwNTE1WDVV4Kil1K+E0AIcTluTvqqZyL56N/ilRKcGDnLRMKo+PnxaAqG2VpYPNUWjtBaU4vtONiOw3tOeB0/feU5hoYHsUIqzaEwu2KDONKhPdJAxsxjOw7DuQz3dG3HkaAKQX0gRd4ewrTdhU+1/gDnLViOqigsqGtEFSbDuQBuJFkDgjCq4pYrVISs+MnYmaKovA+Hqqojk6w1YY01x9ejaRpCCM47s5kzTq3lmWeeGQmDvOgNc2hr1jn+uNqR6lP/8+OdrHtlmN/+sY9bPnoCW3fEsByHj7x3LuD+6MxtDY5sNzUYXHf1QoaHh0eFWRapdKteSok1RYr+YEWOhBCfBBbjLor6gJSy6xDdnMtrSdEfzVKCh6LafPQ9yTht4fHdNqVoiooiBDnLJKAbvGHBMSTNHM3BGk5om0d/JsWAtR3//Lk0BcJ0xYcYzmXJWRZNoRoag2F2x4fYERtkTVsnQ5koUu4llQ/QkximrWYNaVNhbqSOpmCYvG1hO4Km4MmkzL9R51+G5QTQFFfBuHH0Rye8strGtBy3DeyPgHHKmOxIJm2++s1XMTSorzdoa3WfyI5ZWkPvvhRGR4Ann09SF4J1m/fH55cuzCo+aWiaRiZro2rWSGx9qUyVjAScqbPoRxU5olBhSkr5VQAhxNtw88z/8BB93DVVwsw0E3HdZHDdNg7w5WmT6BBUm4++OxHnpEO4bUppDoYZSCcxbZvmUA21dgCfpjOYTpHIZdxCJaEwaTPP0107R9w2p85dQL0/SJ0/QNay2BEdoClooSgN+NQWJBZ5O8lwTifi8xPSDaKZNJqiUOevwVDrydsZclYCTXGjSBThplE+GlTTmJbrtilSdN+U8sqrcX748x7ecfkcwFW+OdMZiXhKJvcff/mFczj7dbU0N0Xo6nP4/ZN5/v7K/S4c27ZHipNYloWUkk1bEvzwnp3s3mvzr/+yippQZSv3UUzQR//8Y/+X5x/7n+K/TWN2jypyVLpDCBEG/g54/3j9CiFuxq1brQkh/ial/HrZQlUoZbtugB9MsyyzimI5vsO5bYq0hCJsj/ZjSwdD1chaJvFsmp+9spaueBR7IMobF7ajkGU4my5E8ZgjfnjTceisrWdZQyundbTxTNej5J1hwrgZKOO5GG3hWkKGj5SZKyRTy2I53cSzPrJWNw2BVresoaiYhStHhHQc8ru2os/pQAkcOlf84XBsi0Q8iu+QGUdHU+q+KbpSfnTvHvJ5k+/9dDfXXArProsRiQQIhVRsW7Kw000r3NOX4WvffIVgQOHjN61k0bwgV7+lgVBo//sXLfriKl2AnV0ZosOSdNZhKJqlJrR/kr7yXTcTU/QnnHU9J5x1PQBfvt4/don5uEWOhBAR3JrXtxxiolUp8dPfUbZAFUxVZa+cbkonMw+dQvjwbOrvJWeZRDOpsvqK+PwM59yVqal8jq7hKKZjs7G/mwV1TfTIQfpTCfyaxubBPmwcbEdy3sJjiGXTPLj5JaR0SOZynNG5GMliaowG2mrmoqshhnO9LG+cg66q5Kxifp0MhhrCpzWSyu9DCAtH2ijCwZwFk7GxX3yfxHNPotY10nLzl8o652DKcGjvTnK5HAG/D/+CZWX1paoqjuNgWvDQY1EUVeH0kxv4y9P7OOOkBvoHt/Obx/ewb8Cms11FSvj23Tv58mdOYMPmBEKBgSGLbbsSNDeN/qEam5my+P+bzmll5644/tUGCztDh7ymSsN9MpkyC+OXwJ0Ft/MDQogfSimvBb4P6MBnhBD3SCnHW/l6nBDiGlz92FY6P1mtlGvRXyWE+BfgC7ium5unVaoZIJpJ8a1nH2M4l0MRggsWHUONz/XFFr8nRet5JGStcO6oCS8gkcvy220bWFzXyJbBfVx1iJKBRYQQ1Pj87IkP8UzXDuK5DEKA6dj0JocxHYcN/d0A5BwLQ3GzTz68+SXq/UFyVp4VTW30poYZSCdJ5qE7AQ0BqA/gZqYsLPBRFYW8beHXGsnZDvH4XhxgvlaHIy0Elb8ythzs+BCoGrZpHtZXXo7/WhXg1q4vn76YyrOvJHluQw5Hwnsvb+Ci85sxDIMHHtpBb7+NIgQ1IY1tu3O0NAo+9rmX+Mf3L2PVMRFypsLK5TVs3ZHk2ed7OXXNHBYviIzyz5fK/rcXojy5doh0WnLeGbW0tQYPyHtTyUxV1I2UMsXoIkdFH/0VZZz+J9wfA3DDLMe6haqO10T2ynIYSCeJGH6WN81h73CMllANSxvdtRLFr1HxCyUoLjln3P+3DO5jWUML82rr6RqOMZBOlmXVG6rKtmg/Pk3jpIZOXtnXzaLmZpqDNaTzKk5tI3V+P3/YvhFNUUnkMvSl4jy2czOmYzOczxUKjyg8sXsbc2sG2djfw8XLjh+V9z6oG/SnEmQthaf3KEjpEM/BMY2+QmIzgS2Pju9mOidjG975D/ie/Qv+ZSvRfQemE5gILZ2LyaWT+A5ZFWw0yazkoedUsAx6h1RCfpjbagBuNExzo8EXPn4c8+cF0NU8v38izl+e6mYgarLulThXv62DYDBIPp/n019+hcY6m98/HuN//v3UA/LeFyd+bVtimW4SNcdxq06VMyFcCbium5mXteCqnlVMRNEXs1cCfHMaZDks06kUmoJhfJpOfypJQNPpiNSX7V8fS0uoBk1R6BqOoQpxmJKBLtFMij/v3Ez3cJzeZJyw4UNRBG3hCM2hCJnAMD1CEMtmWdY4B0NV2WRbNIcjNARCzI3Ucu785fQkY4Uc8w5tNbXkLItd8QEaA/tlCOkGe22LWDaNIvzoWpje5ACJXI7mkIUiFOyjpBymczJWCYWpOfctU9OXqhI4yMK3g6GrIFGxRJhPfTDMyvmCbDY7aoL2lNUNOI5DMmly+YXtxGIptuzIc+ZpjQxGc4TDrg9+6cIQ8XiCxQtcg8FxnFFhnkWFfvbpTfh8gnAQ5s4JjPwAFH35lcwUu248SijXR38GUIv7SANuHOqr0yXUwZhOpVBcpToVPvrJ9DWQTqIIhXMWLGXz4D6Ob22nI1JHLJtBVzSadIMzC33W+f2sntPJbY8/TGdtPWGfj4Cm4dPd4WwKuikNehJxmoNhdEWjtmTlbMjwoauqm4JBN9g21I+iCJpCtTjSOqoW/WzGpwvef5FCKgtNEdd1kktEsbJZ1Mb92W+zeYgmoSMkeMfl7YRCIT59x3aknWPJwhzvuqyWz398BV3dUdrb3B8bx3EOsOgty3XRnHZSI+l0eqS9Wix6AMdT9NNCuRb9N4H/hzt7HZ8+cWaW+kDoiCdhJ9tXUzCMKgRdwzFqDB9LGpr5r2dfIZXPoSkqb9IbqQ+EiGUrXxgkAAANGklEQVTTbBnax2ntC7l0+fF0RhqoMfz899o/YzmSnbEBTmqbz5mdi5lbU8/xre1sHeon4tuv6E3bojc5DMDVK0/h4S0vU+cPUB+oJWfFURW1UrIIVj0BQxAoeM3ye7aR6NpFvrcPVq0GXHfFvU9JAirsjkpOmOda5739OZrrJTu6skAtQkga6w0URfDcizF6+mJccPY8/D4Vx5F89NaXSaazvOfvlnLB2S0jYaBF33x1WPSVsTJ2NlKuor8COB84G4gwA9b8bGfsU8BAOkkylyOZz9KfTrIwJNgR7efWP97PruFBXurrZnXbPM7oWMJQNoUjHToidewZHmRbtJ+w4WdBnZsYa/NgH0samgnqBtFMike2vszmwX3kLYurjlvDkoYW8rZVKC+YQxMajmfRTznJe79NtM8mWB8gtXcHrDoDy5HkbIlfhVjaYnOPwzJN8qkPdLJpS5QzTm1DUWxs20YIQXzY5DNffYW2ZpXefsHfXzOfTNZmw5YktTUKT68d5IKzW0aUfNGir/TFUgBIWRE++tlIuYp+D7ARN5NbK1C5peSrmNKngFg2zcb+HjYM9gCQ8g/TtLsTSzrMCdWyIzZI3rJoDIQ4s3MpinDnBHyqgRBgqBrxbIYHN7/IztggqXxu5IdEoHBax0JimQwD6SSOdOhNxolnW4A8quLDlgcm1PI4MrT6ZvzrnyK0cA2KYyKzaTQFVrSbDCYMfAYksgpbem1WzfMzt7meSMQgm82OKHpDV2hu0Eilbdpa3AnmUFDj5g8sY+26KDe8eyGOI/n5A92kUhbvvXrxiD+/Kix60/vcTQflKvq9wM+Br0opu6dRHo8CluOwvGkO8XwGn6ZjpXMgBZpQSJhZFOCU9gU4EoYySRY3NHPK3PkYqkYslyaoG+yMD7JlqI+Fdc2F8oHJERdRLJNBFQJNUfjzri3Es2mimRQXLA5iKAq741GimbYpc2V5QOQ9H8M4+Xwyj/wQFIHQDYQQnLHCj+3AK10W/XE/c+sEqScfJZMYJvyGixGaMRJl8+ymPJdftpBjF/o5dmlkpO9L39TGpW9qA+CFl2L8+pFeNE3Q0R7h3NPDPP7XQZ55boCrLl/MMUtrZuoWHAbPop8uylX0y4FzgJuEEAFgUEp52/SJNT7VlhflSGgKhplf18C63j04jkNIVTlr/hLOmr+EF3r2sHGgh4ZAmKyV54k929gdGySs+zhnwTKGh7OEdIO/de3g5X099CaHOa190cjE8FgXkV/TaapvxnQcehMJNg308PK+LMlcrqw1AEfCa2lMhaoRWHUy/hUnuObrk0+57UKgqXDCfDfKy+zdS8+jv8aubyShawQvuBwpJUPD8MhTaQzVIRjWOPbAuiQALJgXJG8qDCdtjlseQQjJXXfvpCYkuPP/bePOr5x4tC55QlRKeOVspFxFrxReAWABcGTrySdJNeVFOVLqAyFuPOVcTu9YRCybIberm4X1binChfXNI6t449kMT+3ZRmddI7aUpM08UkqyloWD5Jz5S3Gk5KzOJSMKe+xEcVDTMR0HVQhAw5Ewv9BfuWsAJstraUyLiMOE7ar1DeiqQHTtwHf5uxD5LM5gDzUN82iuteka0FjQdvCvbn2dwa/vPh3Hkei6QjKZ5NTV9fzmT4Pc/IFKrqMhcTxFPy2Uq+j/HXgM+Hcp5a7pE8ejlPpAiPMXrQDgsX3DB+yrD4SIZlI837MbXdVQhSCk++hOxOiMNLA7PsSShhbmhmsPqFdb2k+phZ/I72TTQAKj0F85awA8phbFF2DOF/4LbBuhGwz/4KuYvhDagiVcu6aV0IJVhIKH+bFQxUi6YyEE/3Tjcj754couES0lWGZl1BKcbZSbAuG6aZbDY5KUKmpNUXh020ae79nNb7duoNbnRxHwxsUrDmmVl1r4jtQ4f2EHWauW1nCz56OfIYSiQiGbKLk0ergGqQr09CA+M4abSPbwDCUlf90EIb/k7ONkRUffSCm9OPpporJ/4j3Koqiotwz2YUvJqpYOHtv5Kita2qgxAlhlLpgx7RSDmVdRhE5QjxM2ylMmHtNL6MqbsLq2YMo8QtVRQ3Vln7t9HyRzKvGsQioH4cOn0p85JOOWT/Q4cjxFP4soRtSkbQu/pqMKZULul7ydRFN8BLRG8naKvJ1EVz2LfqZRG1pQG1qYTLaeJa3QG/VRH4bQkaX7mXaklJ7rZprwFP0sotSNc8WKE7EcZ0LpHAw1jCYC5O0UAoGhev75aqcuJLhkzUxLUR4SieNZ9NOCp+hnGUeSxkFXQ7TVrCFvJzHUsGfNexxdpJfrZrrwFL3HKHQ15Cl4jxlBSun56KeJo1MBugJ44IEHZlqEI6La5S9wQAGH4oKpyVxftd+Tape/wNQV5ZAS2zQn9fI4NFWl6Lu7u0cphdIvyuG2H3zwwUm/7+G+kAfbP1772LbDyV3t8o/ZHjeM5zvf+c7IqtijMablKFhvTA++Peb4KQvNkhJsy57UayxCiJAQ4gdCiO8KId5V0r5SCPHjwmvlVMle6VSVojdNc9JK4UiooC/VpKggRX8AsVhsSvsrh0pR9EdCtX8mx8edjJ3MaxyuAO6VUt4AXFbS/hHgg8CNwIem6UIqDlHpGe1KEULEgS0lTbXsz49/uO0mYGyl+HIp7W8i+8drH9t2OLmrXf7S7eVSylEZtWZoTA93Pw51jDemo9sOGNPJIoT4DRNzBTWx/4lih5RyxEIXQnwKeERKuU4I8RMp5TWF9nuklH9X2B5pn+1U1WSslHJitdw8Kh5vTD2KSCkvnMLuuoAOYB2jPRdxIUQtIIHEFL5fRVNVFr2Hh4dHOQghQsCdQBZ4ArhQSnltwS//cUAAt0spX55BMY8anqL38PDwmOVU1WSsh4eHh8fEec0peiHE2UKITwghrp1pWSZL4Rp+OtNyTBYhxMVCiM8JId49Rf1V9ZhW+3jC1I+px9RSVZOx5SCEWAR8BqiVUl5Z8NV9C8jj5tRvl1J+TQjxiRkU85Ac7hqklD8WQrx+RoU8BGXK/2fcELcj7o8KH9NqH0+Y+jH1OLrMOoteSrldSnl9SdPB4mkrlmq/hsPJL4RQcCfEyiotNdvvxwyJNSGmekw9ji6zTtGPQwewp7BtA38VQnwSqKYi56OuQQhxAnCWEGIqw9Gmk7Fj8BmgHpisFVvtY1rt4wlTP6Ye08isc92Mw6h4WinlX4C/zKxIE2bsNawHLp5ZkSbEWPm/OMX9VduYVvt4wtSPqcc0MusseiFEoxDiLmB1YXXcL4G3CyH+G6iKLFLVfg1TLb93P2ae2XANr2W8OHoPDw+PWc6ss+g9PDw8PEbjKXoPDw+PWY6n6D08PDxmOZ6i9/Dw8JjleIrew8PDY5bjKXoPDw+PWY6n6D08PDxmOZ6i9/Dw8JjleIrew8PDY5bjKXqPKUUIcZ0QYl1hWxdC7BJCXDIN7zHpPoUQ906lPCX91o63Xea51wkhLhFCLBZC3C+EuKpk32VCiLMOds5h+j3sd7y0n4O9l0d181pIauZx9Hm1kF+9FXgaQAgxH7gZt1bnNuBR4F2FY/4vsBw4B9gOOFLKLxU7E0IcN+ZYgHcKIc4D9hVy0V8HDEgpHywU8fhNaX/AL4AvAJuB8EH6PUCGgty3AfuA+4G3F69BSvnvY677DiHENwv9nYeb0bF4DdcA5+IWpP40MGfM/YgVDv0A7vdyb0m/DYBTuMbSa1oIBIUQAC+N098FwFohxKh7LaV8esx1nQDsK/RTfK8lwOdxa64+gJuZctzx8ah8PEXvMR3ci6sQQ8DvCm03ApnCaxXwIOAH+oBrgb8Bv5FS/kwI8b9j+suNc+zvpJQ/EELcewirtbS/BuCTuKl1izKN1+9YGT4I/IuUcosQ4mtjrmEsNwH3AAPA34/Z1wG8CPxaSpkTQoy9H48XjnsQ2CmlfKqMa/ot+3/cxsr2OPBIoSDIkjHX+fSY67qupJ/rCu/zD8CtUsodQoifAw+Nc288qgRP0XtMB5nC315cyxNcN+EPpZQvAggh/hP4Oq4F+oXCManCXzGmv4+Mc6ws+StxlXbx8xwapz+BWw3JBqxD9DtWBnGwaxiHU3F/SCLAMuDV4g4p5e2FvPNfF0LcOs79uK60IyHEe4CTCvKVUiqfU9I+Xn/xQ1xn6fml/VCyv/Qej31vjyrCU/Qe08UtuAriPYX/7wS+LITowXVf/An4BK6VeTjGO/ZCIcSJwFoppSyUsbtdCLEQqBunj+/iulJ2HKbfsXwL+HxB7geBTxSvQUr5hTHHngZ8GPABN1Ci6IUQ7weW4irVQQ68H7tKO5JS3g3cXTj3YLKtBz4jhNAO099411l6XY8AHyz0U+TbwBeFEGngf4EJzTl4VBZemmIPDw+PWY4XdePh4eExy/EUvYeHh8csx1P0Hh4eHrMcT9F7eHh4zHI8Re/h4eExy/EUvYeHh8csx1P0Hh4eHrMcT9F7eHh4zHL+Px7nshD1E6KqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 396.85x180 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigmas = [0.01, 0.1, 1.0]\n",
    "\n",
    "cmap = plt.cm.get_cmap('coolwarm') #viridis')\n",
    "\n",
    "norm = Normalize(vmin=0, vmax=0.21, clip=True)\n",
    "mapper = plt.cm.ScalarMappable(norm=norm, cmap='summer')\n",
    "\n",
    "fig = plt.figure(figsize=(ELIFE.TEXTWIDTH,2.5))\n",
    "\n",
    "gs = gridspec.GridSpec(1,2, width_ratios=[5,5], right=0.7, top=0.95, wspace=0.05)\n",
    "gs2 = gridspec.GridSpec(2,2, height_ratios=[1,5], width_ratios = [1,4], \n",
    "                        left=0.75, right=0.95, top=0.95)\n",
    "\n",
    "ax = fig.add_subplot(gs[0])\n",
    "ax2 = fig.add_subplot(gs[1])\n",
    "ax_legend = fig.add_subplot(gs2[0:2])\n",
    "ax_cbar = fig.add_subplot(gs2[2])\n",
    "\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "\n",
    "dfs = [pd.read_csv('results/width_ratios/width_lognormal_fit_experimental.csv'),\n",
    "    pd.read_csv('results/width_ratios/width_lognormal_fit_experimental_interaction2.csv')]\n",
    "\n",
    "for i, df, alpha, label in zip(range(2), dfs, [0, 0.15], ['No interaction', 'With interaction']):\n",
    "    for j, sigma in enumerate(sigmas):\n",
    "        w = df[['sigma_%.2f_width_mean_%d' % (sigma, d) for d in range(20)]].median(axis=1).values\n",
    "        pval = df[['sigma_%.2f_pval_%d' % (sigma, d) for d in range(20)]].median(axis=1).values\n",
    "        ss = df['ss'].values\n",
    "        si = df['selfints'].values\n",
    "\n",
    "        x = ss * si\n",
    "\n",
    "        p = x.argsort()\n",
    "\n",
    "        x = x[p]\n",
    "        w = w[p]\n",
    "        pval = pval[p]\n",
    "        ss = ss[p]\n",
    "        si = si[p]\n",
    "\n",
    "        col = mapper.to_rgba(alpha)\n",
    "\n",
    "        ax.plot(x, w, c=col, alpha=0.3, marker='o', markersize=3, label=alpha if j==0 else \"\")\n",
    "        ax2.plot(x, w, c='lightgrey', alpha=0.3) #, label=alpha if j==0 else \"\")\n",
    "        s_ax2 = ax2.scatter(x, w, s=3, c = pval, cmap=cmap, vmin=0, vmax=1)\n",
    "                        #c=col, label=alpha if j==0 else \"\")\n",
    "        x = 9e-1 #ss.values[0]\n",
    "        y = w[0]\n",
    "\n",
    "        if i == 0:\n",
    "            ax.annotate(r\"$\\sigma_\\mathregular{lin} =$ %.2f\" % sigma, xy=(x, y), xytext=(x, 1.5*y))\n",
    "            ax2.annotate(r\"$\\sigma_\\mathregular{lin} =$ %.2f\" % sigma, xy=(x, y), xytext=(x, 1.5*y))\n",
    "\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax_legend.legend(handles, labels, loc=2)\n",
    "ax_legend.axis('off')\n",
    "\n",
    "cbar = plt.colorbar(s_ax2, cax=ax_cbar)\n",
    "cbar.set_label('p-value lognormal fit')\n",
    "\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Width distribution ratios $x(t + \\delta t) / x(t)$')\n",
    "ax.set_xlim([5e-1,1e2])\n",
    "#plt.ylim([-0.01,0.15])\n",
    "ax.set_yscale('log')\n",
    "ax.grid()\n",
    "\n",
    "ax2.tick_params(axis='both', left=True, labelleft=False)\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_xlabel(r'Mean abundance $\\times$ self-interaction', ha='right', x=1)\n",
    "#ax2.set_ylabel('Scale lognormal fit')\n",
    "ax2.set_xlim([5e-1,1e2])\n",
    "#plt.ylim([-0.01,0.15])\n",
    "ax2.set_yscale('log')\n",
    "ax2.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-02-19T22:01:15.285129Z",
     "start_time": "2020-02-19T22:01:14.783420Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.scatter(df['sigma_0.01_width_mean_0'], df['sigma_0.01_width_mean_2'])\n",
    "plt.plot([1e-4,1e-1], [1e-4,1e-1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": true,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}