tutorials/W2D3_DecisionMaking/student/W2D3_Tutorial1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/NeuromatchAcademy/course-content/blob/master/tutorials/W2D3_DecisionMaking/student/W2D3_Tutorial1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GrV7z42bgQfe"
   },
   "source": [
    "\n",
    "# Tutorial 1 Part 1 - Sequential Probability Ratio Test\n",
    "\n",
    "Please execute the cell below to initialize the notebook environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "both",
    "colab": {},
    "colab_type": "code",
    "id": "XgRvfxSAgHVT"
   },
   "outputs": [],
   "source": [
    "import numpy as np                 # import numpy\n",
    "import scipy as sp                 # import scipy\n",
    "from scipy import stats\n",
    "\n",
    "import matplotlib.pyplot as plt    # import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "Z7M9SWqPHBo_"
   },
   "outputs": [],
   "source": [
    "#@title Figure Settings\n",
    "#@ Figure Settings\n",
    "%matplotlib inline\n",
    "fig_w, fig_h = (8, 6)\n",
    "plt.rcParams.update({'figure.figsize': (fig_w, fig_h)})\n",
    "# %config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "jcxtwRMyHnZ_"
   },
   "outputs": [],
   "source": [
    "#@title Helper functions\n",
    "def simulate_and_plot_SPRT_fixedtime(sigma, stop_time, num_samples):\n",
    "  \"\"\"Helper function for Exercise 1\"\"\"\n",
    "\n",
    "  evidence_history_list = []\n",
    "  print(\"#Trial\\tTotal_Evidence\\tDecision\")\n",
    "  for i in range(num_sample):\n",
    "    evidence_history, decision, data = simulate_SPRT_fixedtime(sigma, stop_time)\n",
    "    print(\"{}\\t{:f}\\t{}\".format(i,evidence_history[-1], decision))\n",
    "    evidence_history_list.append(evidence_history)\n",
    "\n",
    "  fig, ax = plt.subplots()\n",
    "  maxlen_evidence = np.max(list(map(len,evidence_history_list)))\n",
    "  ax.plot(np.zeros(maxlen_evidence),'--',c='red',alpha=1.0)\n",
    "  for evidences in evidence_history_list:\n",
    "    ax.plot(np.arange(len(evidences)), evidences)\n",
    "    ax.set_xlabel(\"Time\")\n",
    "    ax.set_ylabel(\"Cumulated log likelihood ratio\")\n",
    "    ax.set_title(\"Log likelihood ratio trajectories under the fixed-time stopping rule\")\n",
    "  \n",
    "  plt.show(fig)\n",
    "\n",
    "def simulate_and_plot_accuracy_vs_stoptime(sigma, stop_time_list, num_sample):\n",
    "  \"\"\"Helper function for Exercise 2\"\"\"\n",
    "  accuracy_list, _ = simulate_accuracy_vs_stoptime(sigma, stop_time_list, num_sample=num_sample)\n",
    "  \n",
    "  fig, ax = plt.subplots()\n",
    "  ax.plot(stop_time_list,accuracy_list)\n",
    "  ax.set_xlabel('Stop Time')\n",
    "  ax.set_ylabel('Average Accuracy')\n",
    "\n",
    "  plt.show(fig)\n",
    "\n",
    "def simulate_and_plot_SPRT_fixedthreshold(sigma, num_sample, alpha):\n",
    "  \"\"\"Helper function for Exercise 3\"\"\"\n",
    "  # calculate evidence threshold from error rate\n",
    "  threshold = threshold_from_errorrate(alpha)\n",
    "\n",
    "  # run simulation\n",
    "  evidence_history_list = []\n",
    "\n",
    "  print(\"#Trial\\tTime\\tCumulated Evidence\\tDecision\")\n",
    "  for i in range(num_sample):\n",
    "    evidence_history, decision, data = simulate_SPRT_threshold(sigma, threshold, batch_size=10)\n",
    "    print(\"{}\\t{}\\t{:f}\\t{}\".format(i,len(data), evidence_history[-1], decision))\n",
    "    evidence_history_list.append(evidence_history)\n",
    "\n",
    "  fig, ax = plt.subplots()\n",
    "  maxlen_evidence = np.max(list(map(len,evidence_history_list)))\n",
    "  ax.plot(np.repeat(threshold,maxlen_evidence + 1),c=\"red\")\n",
    "  ax.plot(-np.repeat(threshold,maxlen_evidence + 1),c=\"red\")\n",
    "  ax.plot(np.zeros(maxlen_evidence + 1),'--',c='red',alpha=0.5)\n",
    "\n",
    "  for evidences in evidence_history_list:\n",
    "      ax.plot(np.arange(len(evidences) + 1), np.concatenate([[0],evidences]))\n",
    "  \n",
    "  ax.set_xlabel(\"Time\")\n",
    "  ax.set_ylabel(\"Cumulated log likelihood ratio\")\n",
    "  ax.set_title(\"Log likelihood ratio trajectories under the threshold rule\")\n",
    "  \n",
    "  plt.show(fig)\n",
    "\n",
    "def simulate_and_plot_speed_vs_accuracy(sigma, threshold_list, num_sample):\n",
    "  \"\"\"Helper function for Exercise 4\"\"\"\n",
    "  accuracy_list, decision_speed_list = simulate_accuracy_vs_speed(sigma, threshold_list, num_sample=num_sample)\n",
    "\n",
    "  fig, ax = plt.subplots()\n",
    "  ax.plot(decision_speed_list, accuracy_list, linestyle=\"--\", marker=\"o\")\n",
    "  ax.plot([0.0, 1.0], [0.5, 0.5], c='red')  # plot baseline for random choice\n",
    "  ax.set_xlabel(\"Average Decision Speed\")\n",
    "  ax.set_ylabel('Average Accuracy')\n",
    "  ax.set_title(\"Speed/Accuracy Tradeoff\")\n",
    "  ax.set_ylim(bottom=0.45)\n",
    "  \n",
    "  plt.show(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2EGQY_5oE775"
   },
   "source": [
    "# Introduction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 519
    },
    "colab_type": "code",
    "id": "gbBj2DOtAy9E",
    "outputId": "06339e0b-84b1-4595-8be6-551af209f017"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/3CG92WsTk4Q\n"
     ]
    },
    {
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/3CG92WsTk4Q?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f5f7c52a0d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 1 \n",
    "# Insert the ID of the corresponding youtube video\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"3CG92WsTk4Q\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0mXrodKpjhoj"
   },
   "source": [
    "### Tutorial objectives\n",
    "In this tutorial, we will consider a simplified random dot motion task. On each trial $i$, we are shown a dot moving at velocity $v_i$, either in either a leftward ($v<0$) or rightward ($v>0$) direction. Although the dots' velocity varies from trial to trial, the set of all $v_i$ are  generated by a fixed probability distribution, which we know to be either:\n",
    "$$\n",
    "\\\\\n",
    "\\begin{eqnarray}\n",
    "p_L &=& \\mathcal{N}(-1,\\; \\sigma^2) \\\\\n",
    "&&\\textrm{or} \\\\\n",
    "p_R &=& \\mathcal{N}(+1,\\; \\sigma^2) \\\\\n",
    "\\end{eqnarray} \n",
    "\\\\\n",
    "$$\n",
    "We want to determine which of these two possibilities is the true data generating distribution. \n",
    "\n",
    "In W2D1, we learned how to choose between possibilities based on the relative weight of the evidence. Depending on the sensory evidence and our prior experience, we learned to choose between these *two* options: accepting hypothesis $H_L$, that the data comes from the $p_L$ distribution, or accepting $H_R$, that it comes from $p_R$. \n",
    "\n",
    "Here, we add a *third* option: choose to collect more evidence before making a decision.\n",
    "\n",
    "---\n",
    "\n",
    "In this notebook we will perform a *Sequential Probability Ratio Test* between two hypotheses $H_L$ and $H_R$ by running simulations of a *Drift Diffusion Model (DDM)*. \n",
    "\n",
    "As independent and identically distributed(*i.i.d*) samples from the true data-generating distribution coming in, we accumulate our evidence linearly until a certain criterion is met before deciding which hypothesis to accept.  Two types of stopping criterion/stopping rule will be implemented: after seeing a fixed amount of data, and after the likelihood ratio passes a pre-defined threshold. Due to the noisy nature of observations, there will be a *drifting* term governed by expected mean output and a *diffusion* term governed by observation noise.\n",
    "\n",
    "In this tutorial, you will\n",
    "\n",
    "* Simulate Drift-Diffusion Model with different stopping rules.\n",
    "* Observe the relation between accuracy and reaction time, get an intuition about the speed/accuracy tradeoff.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JVUdtpPflovM"
   },
   "source": [
    "---\n",
    "\n",
    "### Sequential Probability Ratio Test(SPRT)\n",
    "\n",
    "\n",
    "<img src=\"https://drive.google.com/uc?export=view&id=1byiUWthtmDAEcevZXOobHgvpZOvVnSDX\" alt=\"drawing\" width=\"400\"/>\n",
    "\n",
    "\n",
    "Suppose we receive a sequence of independent samples from distribution $p$. We know that $p$ is from $\\{p_0,p_1\\}$ determined by a binary latent variable $x$ and need to test between the two hyptheses:\n",
    "\n",
    "$H_L: p=p_L \\text{ or } x=0$\n",
    "\n",
    "$H_R: p=p_R \\text{ or } x=1$\n",
    "\n",
    "When we see $n$ samples $\\{x_{1}...x_n\\}$, we want to calculate the total log likelihood ratio as our evidence for decision:\n",
    "\n",
    "$$S_n = \\log \\frac{\\prod_{i=1}^n p_R(x_i)}{\\prod_{i=1}^n p_L(x_i)} = \\sum_{i=1}^n \\log p_R(x_i) - \\sum_{i=}^n \\log p_L(x_i) \\tag{1}$$\n",
    "\n",
    "Due to the independence of samples, this can be calculated in a incremental way when new data points come in sequentially:\n",
    "\n",
    "$$ S_n =  S_{n-1} + \\log \\frac{p_R(x_n)}{p_L(x_n)} = S_{n-1} + \\log \\Lambda_n \\tag{2}$$\n",
    "\n",
    "The stopping rule can be implemented in two ways:\n",
    "\n",
    "\n",
    "\n",
    "1. Fixed time \n",
    "\n",
    "Make a decision based on $S_n$ immediately when we have collected $n$ samples. That is, accept $H_R$ if $S_n > 0$, accept $H_L$ if $S_n < 0$, and accept $H_R$ with probability $\\frac{1}{2}$ if $S_n = 0$. The significance level or desired error rate $\\alpha$ can then be determined as \n",
    "\n",
    "$$\\alpha = \\frac{1}{1+\\exp(|S_n|)} \\tag{4}$$\n",
    "\n",
    "2. Thresholding \n",
    "\n",
    "We assume equal probability to make a false positive decision and to make a false negative decision, and denote it with $\\alpha$. Then we accept hypothesis $H_R$ if $S_n \\ge b$ or accept hypothesis $H_L$ if $S_n \\le a$ where the thresholds are determined by \n",
    "\n",
    "$$a=\\log \\frac{\\alpha}{1-\\alpha},b=\\log \\frac{1-\\alpha}{\\alpha} \\tag{3}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "i-aX6JIXGUlS"
   },
   "source": [
    "# SPRT as a Drift Diffusion Model (DDM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 519
    },
    "colab_type": "code",
    "id": "riQ1o2VTGeJA",
    "outputId": "a1942d2a-e5a8-4c85-c1d7-1b6d75c5e8ed"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/a-O5n_d5tOA\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/a-O5n_d5tOA?fs=1&start=0&end=40\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f5fa81957d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 2\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"a-O5n_d5tOA\", width=854, height=480, fs=1, start=0, end=40)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "eCAtJdCfuUeG"
   },
   "source": [
    "\n",
    "\n",
    "SPRT as a Drift Diffusion Model (DDM)\n",
    "\n",
    "Let's assume two different Gaussian observation models conditioned on discrete latent variable $z$ \n",
    "\n",
    "$$p_L(x|z=0) = \\mathcal{N}(\\mu_L,\\sigma_L^2)$$\n",
    "\n",
    "$$p_R(x|z=1) = \\mathcal{N}(\\mu_R,\\sigma_R^2)$$\n",
    "\n",
    "Then the log likelihood ratio for a single data point $x_i$ is \n",
    "\n",
    "$$ \\log \\Lambda_i = \\log \\frac{\\sigma_L}{\\sigma_R} -0.5 \\biggr[\\frac{(x_i-\\mu_1)^2}{\\sigma_R^2} - \\frac{(x_i-\\mu_L)^2}{\\sigma_L^2}\\biggl] \\tag{5}$$\n",
    "\n",
    "Without loss of generality, let's further assume the true data generating distribution is $p_R$. In this case $x_i$ can be expressed as $x_i = \\mu_R + \\sigma_R \\epsilon$ where $\\epsilon$ comes from a standard Gaussian. The foregoing formula can then be rewritten as \n",
    "\n",
    "$$\n",
    "\\log \\Lambda_i = \\bigg( \\log \\frac{\\sigma_L}{\\sigma_R} + 0.5 \\frac{(\\mu_R-\\mu_L)^2}{\\sigma_L^2} \\bigg) + \\bigg( \\frac{\\mu_R-\\mu_L}{\\sigma_L^2}\\epsilon -0.5\\big[1-(\\frac{\\sigma_R}{\\sigma_L})^2\\big]\\epsilon^2  \\bigg) \\tag{6}\n",
    "$$\n",
    "\n",
    "where the first two constant terms serve as the *drifting* part and the last terms are the *diffusion* part. If we further let $\\sigma_L=\\sigma_R$, we can get rid of the quadratic term and this reduces to the classical discrete drift-diffusion equation where we have analytical solutions for mean and expected auto-covariance:\n",
    "\n",
    "$$\n",
    "\\log \\Lambda_i = 0.5 \\frac{(\\mu_R-\\mu_L)^2}{\\sigma_L^2}  + \\frac{\\mu_R-\\mu_L}{\\sigma_L^2}\\epsilon, \\text{where } \\epsilon \\sim \\mathcal{N}(0,1)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dJiZBF5BCbvQ"
   },
   "source": [
    "# 1. Simulating DDM with fixed-time stopping rule\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 519
    },
    "colab_type": "code",
    "id": "sCoR-HU4CjlO",
    "outputId": "b5a93a35-2063-48b4-aeda-0d714e4ca682"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/TpqMzI0iZJ8\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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rzcVX+plT/RWTq1MdTpzp4BQyM8+Nc5CsaM8usHrBxirE6YNlGbUtLSULGEI3Tp4gjjrBzxzk8B6arSevGRzyRkn0cgK7cMvNNuHkx8l8rPbOydOlHUrJA6gc8h6KkFQm3JKtIGRjPy+MDw9FSy3OlSU558jnnlPA57DkGrysbHqpSlWVKUpQKUpQKUpQKUpQeO9fan/7pz+E1XNWNevtT/8AdOfwmq5oFKUoFZ3o+2gNqnW2enV/0CdFkkIOFLSw8hxxA4jIWhKkkE4IUQeBrBUoP2BdszEiRCuHluxYkxlhQPi7u4rhOuqA6ye8mQD2KV21+YndLbT/AAve73KB1IE1cdkg5SWYITDaUjqCVpYC8DrcNXxsn3YLMG1xYJtspydEtSIqJJdaLa32I24YeXq+MIKkoUrr5861BoP1b6MpjW0Vs2dnyAHVhiFMyMEJmMsLZeIJ815Tw7eFaY/VBNqe/byiGhZLdohMtFPUJEod9vKB6yWnIiT2FrtzWV7nPuoY+zNtZtk23SJZjSJKmXI7jSUhmQ5v9JDnHWHnHzw4YUPTWvXSDtEu7zbjcHMhU+bIkaVHUW0vOqW23nzUIKUD0IFBgqnHQv0YT9qpaYdvRpSnSqTJWDuYTJJGt0jylnBCWxxWQeQClJg9bIdy/wB0VD2RgyIMm2PynHp7knfR1soylbEdkIWHOJKSyo5yfL6usNjr/Ot3Rla0RLRBdnznklTbTba3XZj+NKplxcZGWo4PAJ4Z06EclKToXtsLvc35dxuceY6/IWp5952O8lICU/6IS0yhtKUhIwlKUADAFbffZu23/Mk7/wBaNXmundsW9xt5CLJM1LZcSnU9HCdSkKSnURkhOSMkA+o0GkFba/U1v+uX3/UIv+8KrUqrm7lbpiY2PfnvSob0xE2O00BHW2hTZbcK8kOcFA5xzFA7tr/KS+/+Wf8AB7fWK6Iegm9bRvMoZgvQ4ilJL0+W0tqO02clSmt5pMxzAwG2snKk6ihJKhtB9m1Z8fcm557P+hY/Tvf5VDdte7ckOJWiz2VuOo8Evz3lSCAeZEVhKAFjjjLihnGQeVBa3dM7Vw9jLAm0wl6X5UH4MgtahvQyWgzKlOFOCClpSjrHN11HaSPzqrNbabVTb0+5MuktyZJdwFOO4GEjOlDbaAEMtDJwhASkZOBxrC0GesextxnMyJcK3SpcaKtKH3YzLjyWVLSpYC92CQNKck8k6k5xqGcXare9LcbYisOyXnlaW2Y7a3nXVYJ0ttNgqWrAPADqq+e5o7pHwSYXb37SiXFckrkF6O4WJSXHEoQtTgcCm5I0tNJA+LwE8zV3vd2nYkhSmrRcy6RxCm4DaVHsU6l9SsenSaCe9IbS7XshKYvCwX2Nl0RHitQXmYuEiI0necd4vvlbaQrJyRnrr80KuDugun647XlDLraIEBlwONw2Vqd1OBOA5KkKCe+HBlYThCEgK8nOVGn6BSlKBSlKC0jShpQKUpQKUpQKUpQKUpQRXadlsuEjOrKArVyPAcR8n7q2U6EoIahQwRglpKyPSs6q1quCSp13WSAVAA8M+SOQ6zw4VsC1fzCQzFjDK2mmwvHlAhCcAJHHHzV5PtCZZYzF63s+44ZXKrqtzGcEDnUkYjHT5P8AzrXVjba8MFGWghJ5KWU8u3SSM1cWyW3G/QgSAkO6eOgHB4c/8GvPnBOPvXqzmufSRKY8fKhwxj5K9LjWOusPLvG7SVpGr0cefVVWbbbTXJeVJkojtk4ACXM+gYTzNazCVGdyi5VrA5K5dtY27ugjnzxxqmdnbncVAlTzcgHhp1KbV6/jMYqR2e/Po0sykYyrgoKC9IPLxhwKa1vFqdKxmfXqqvp7iSdW8kOJW3qJaSQnhjlnhk1RN4StauIA5EhI4DPLl/jhW0vTfaO+2m1jOUEgDtJxxPorXW9xw0tLaiSoKTq4HgCMmu3wme8dPO8bx6y28luWhKRxGoK4/wBkgHiPQeB+WsrYl6knjx1ZPrNRlSSCs9pJAHZ1fJwFSXZ0hSCocMnHzV2Rw1k6UpV2RSlKBSlKBSlKBSlKDx3r7U//AHTn8Jquasa9fan/AO6c/hNVzQTs9Dm0e7D3g7dC2QCCIclSsKxg7pKd5jjnOmoO+0ptSkOJUhaFKSpKwUqQpJwpKknilQIIIPZWyHdh7Uz7beYTlvnyYa2rLa1pMd51oBWHSSUpOlQOBkEEEcDkV4e66tRnXDZp0Mtxrlf7BZ3ZzIG7AmylrY1u4HA5AbPojig16pW58vudLSl1+0qtjrKW4R0bSu3mAFGeGg6A5Yd7qRDLh3eNGvh2Heihu582Cg3QXq43lTxtuz0AS5DERQQ/MccKxHjoWoYbQvcuAqyD5IBTkqSFU1ldpdnJlsU03cIb8Jx+O3IbRJbWypxh3UG3UpWASglCxntQocwazPSNe7TN72Nmsa7Jo3wfQq4P3NL+ot7hSVyEJU0pOHQQMg6h2VOO62sqYMy0IRIlyA7s3a3iqdKkTloLq5WUNOSVKU0wNOQ2khKSpWAMmgpmso1s7MXGcuCIjyoTUhMdyUltZYbfUlKw0t0DSlelaDj/ALxPnDN990D0bWyzwEu2iwvTojjMEx9p2boqU0644tvfiXbW07uMleVtpPijUtGCSdIilosyTslcJm/lBaNqW4+4TKkJhqSYMVzWuAFbhcjJxvSnVhKRnAFBTdKu7ZLZOzWmyxb/AH2A9enbrcHosKC1LctzLbUYrS++/IZSXC5raWAkZHFPDiSMN3ROwcK0rtEyzl4W6/2tmfHZlKC34al4L0daxwWlAW1hWSeKhlWkKUFVUrb+59GeyMe727ZxdonLevEFt7v5NwdT8HOOxXVNJjxykpkAqYUoqdKgkuDgoDSNUtqbUYEmbEKw4YcuTHKwNIcMd5bJUE5OkHRnGTzoGzNilXN5qJAjOS5L+vdssp1OObttbzmlPXhttaj6EmjVhlKkd4JjOmYZJi97BB33fAc3JZ3fMOhwFOO0VcPcPp03rfgDMG03SQkniAUx91k+j44j5auK52SPDu1w23bbSbeNlmb5FCyENqutzYVBjRVnH2xbgcWSckOPp4Z5Bp3tHZJNtediz47kWSwUhxl5OhxsrQlxGpJ5ZQtKvUoVjqu/u0YSjtLdAltTnfXwWptDWSt0LtsJrSgYJ1qWhYGAeJHA8qsDaPoWt71uvzqtnnNmptot5nxS7embrKlstJU4sXC2oOYWtCRjAGFL5+JhYa27ObIzri1cJMOMXmLUwl+Y4FsoEdpWsJWUuKCnPIXwQFHhyrBVsp3GOzjt3h7bW+OpCHZ9sgx0KcJCGy67LSVrIydKQSogAnxeGTVZ90HaLXa5htloiyWzawY8yVNU6l24SkhAcdRGX4saOCCUaR4wczxGmghm0uzky2KabuEN+E4/HbkNoktrZU4w7qDbqUrAJQShYz2oUOYNYqrm7raypgzLQhEiXIDuzdreKp0qROWgurlZQ05JUpTTA05DaSEpKlYAyatm59GeyMe727ZxdonLevEFt7v5NwdT8HOOxXVNJjxykpkAqYUoqdKgkuDgoDSA1ApVr9DvRU3dr47Z5clSY0B64GY8yAhxbFuU4hZZSoKCVuLS2OOdIWT4xTgzW2WHZa/WzaudbLHLtb9hiNrj724PS0SESFuJYfdQv7XIG4XqaBUgaxgq5gNc6UpQKUpQWkaUNKBSlKBSlKBSlKBSlKD1bJ7Ki4ylpKsFMCXIaTkDfPx0ZQ2R19RIHE4qY7LXB5tiRJf+Okl8tJSUhGMacnSAOWeWKw+yM7vMsSwgLcjT4+7B5HegtrSrH3qknFXNI2eSS4cIWVOqcQpvHihzTpBxw1gYBHbXleO5ZjLvvuPW8Dw3Kyz4VBdpkyEd5K0l8PhJd3bKHdB8fUkFShpIO55kZ3ijw04rJbOSnWnFJUrUltaUpCQpZSVHijJPkaiBzJ4Gpi9sxlAwAMcM5/f1CvLbbC20pASreFC9RUCClK+wEcCrByeoVw5c+OU15Y9THw+UvTK3skcm5utqAcBWhTClp0pSE5bGVhR5ggZx24NRZc5t55S3lfE8AhtI8gEYHjccKJ8YnGcYAPOrCFs37ZaCtB4KSs8cKSMDJ80gqGOxRqKN7MMIUtpWct4T4wUkkacpKT98MHGc8cZq+vLhKtnNZ2eiCbLWeYt2YVPqZSNamXFPF9C1aEJbb3JAIQXApZPAgLx1CpVa1LcSDNbSHmSMFBPxicdQHA+k8OrhmpTb7ElvGMkDqOR++s2u0AAFKBjjzHEcPT1VM5rl6aZXhxx9bUB2jnpS0VvMuaUBRJO78nTjrVwIwOqtXNopYcedcb8ZOokEnBwVAJzjkAP31t7tvaky2g0pIKAvUtHIOaEqKEqA5jWE8PRWqW30BTMrQlPFatJTp0jmRhKOpNdPgsptyeOxy8k+Dns70fXG6NF6LGCWwBmRJWI7TnUAypfl8eGcYrwWWOuPv476C09HfU2tCuaSkYPrGeOevNbcbE29mTa2kyA2sCKhtSAUrQnQkg+T5B1DNa2dI8IMz16QcvQIDrhJKsuFndqyT99htJ+Wuvi5fNlpyeI8NMOLzTvuS/lti6UpXW84pSlApSlApSlApSlB4719qf8A7pz+E1XNWNevtT/905/Carmgv3afp9ttwfYnytjIkq4xo7LLT8y4TZEcCOlQaLttSlDLyQVE6VfpyARVG3e3U+9TXLpOkFUtbiFpU38WmOGiNw3GQPtTbeBjrzlRKlFSjGaUF0bZdL9ovaly7vsi3JujsYNPTY91mQmXnkMhlqSuA02RvEhKDp3mDoAORUW6F+kxzZxyZqhtXKDc4i4k+DIUptEplQVjS8gEsup1LAVhQw4vhkgiAUoJZ0iX21TTH+BrCbIloPb4KuMm6KklakFvKpCEBkNhKwAkcdfEnArI9MvSL4SSIElcMRBCtcOAW0vF7epiKdJc3hQndlW9I04OMczUCpQXFeumGC3b7rarDs4LMi9LjGYty5yronRGXvEpisSG0pjqUcgryo6VY5pQUxeF0hFuyybB3oCJF4Rcu+t6QUFMZqPue99GFD4rVr1jysY66gtKC1NhelhiPbzZb5ZUX23tS++4iRMetr8J5QUHQiSyhZWyrWs6NI4urOT4unB9MnSM7tG/HdMZuBFgw2YUGDHUpTUOKxnQgKVjW5x4rwnISkYASBUHpQXJeOnRUi92vaD4MSg22PHZETvkkPbhl5rV3xugW877ONBxp681V21d17/kzpZRujNlyZJbCte774eW9oC8DVp14zgZxyFYylBOehvpCOzj0+QmIJaptpm29ILpZ3Bllr48EIVvCndeRwzq5ispdOmOW/YomzRaCWY0suqk7wqW+wHHn2oq2inAbQ88FhWr/sWxgAcaypQWX0ldLbt3usK+NQ0RH4ItykNLcVKbW7bVpcbW4dLZKFFCcoHUOdTe+90PCdTtEqLsumJK2mhPx50pVzfkq1OslpC2WnGQhppJUtZaTjUSnxgEgVr7Sgn/AEYdJS7FFv8AEajb1V8htRw+l5TC4RZU6pLqAlBLisu5A1JxpHGuzpi6SxtMLc/Kt6WbnFiojS7g09wuqWgA04/DDYS1JHHx0q4hRGNKUBFeUoJ3009Ih2lfhSFRBD7ztUOBoDpf3giF070qKEaSre+Tg408zUpvHToqRe7XtB8GJQbbHjsiJ3ySHtwy81q743QLed9nGg409eapulBaXRHtbcDf2rhaUx2pc6fNdSxMeDUVaZm/cejPvq0goKFqSknB1hBAzir32weYsNj2pRK2fgbLP3oR2Y0KPckXSXcXVPHfujQtSI0BlDhKG0YSMucBqRr02pQKUpQKUpQWkaUNKBSlKBSlKBSlKBSlKCU9HrQkKejcAt1KHGiryQ5GUHMKPMakgjhWxFhZSUjUAc9XZgD0/wCMVq9s3cDFfjvA43TqCf8ARzhXzE1stClY4pxhQCxp5FKxlJHorwvauGspk+g9kZy42X0/dmZiWkA6UJz6QKxNua3jqUakjgDxUBgA6uPZX2U/q51CFbKFyW5KQ9I3pRgbtwhvdpGAlaPvsE5GK8/isyr18/dnRZ1zmtRigKktt7wpGVKAGVHABJ6+HKvS1I0qKXdJJIKVYByD6arC/wDRsLq2hMxS9bTgcQ62opWhXEDAOeHL9HOp5staHAlAecCy2kJzxzw4cc9denlryxhlet3pMIqUqxlIOO2u+e8ACMdX8q8DLwQOJ9FeO5Sz29VZYWSMs+7G3RYGeGTwqCbM7INyJsmTIaDmfi2dQ4BGnx1f6WeBPZmpdJJWa7LLGDhVqKvFwcIUUE56jp4lHDiKcd1vTLknm1KjlqiCEbqy0sGGjeq14KQgeWUj0Aa+Xm1r3tLdjOeefUNIcWdCeWhocGUn0hGmrz6fNoUQ4zsRrSl+e2pKEowN00o6X3VY69J0p7So9la9D09g+YYr0fB4f9nne0uXthPrfq+0pSu55RSlKBSlKBSlKBSlKDx3r7U//dOfwmq5qzZcNyQlbMdpb7ryFIbaZQp1x1agQlLbaAVLWT1AZqPfWzvv5P3b9nT/AOnQROlSz62d9/J+7fs6f/Tp9bO+/k/dv2dP/p0ETpUs+tnffyfu37On/wBOn1s77+T92/Z0/wDp0ETpUs+tnffyfu37On/06fWzvv5P3b9nT/6dBE6VLPrZ338n7t+zp/8ATp9bO+/k/dv2dP8A6dBE6VLPrZ338n7t+zp/9On1s77+T92/Z0/+nQROlSz62d9/J+7fs6f/AE6fWzvv5P3b9nT/AOnQROlSz62d9/J+7fs6f/Tp9bO+/k/dv2dP/p0ETpUs+tnffyfu37On/wBOn1s77+T92/Z0/wDp0ETpUs+tnffyfu37On/06fWzvv5P3b9nT/6dBE6VLPrZ338n7t+zp/8ATp9bO+/k/dv2dP8A6dBE6VLPrZ338n7t+zp/9On1s77+T92/Z0/+nQROlSz62d9/J+7fs6f/AE6fWzvv5P3b9nT/AOnQROlSz62d9/J+7fs6f/Tp9bO+/k/dv2dP/p0EmNKzp2Luv+Zbp+zrh/Sp4F3X/Mt0/Z1w/pUGCpWd8C7r/mW6fs64f0qeBd1/zLdP2dcP6VBgqVnfAu6/5lun7OuH9KvLc9nZ0VO8lW6bFb1BO8lRJUdvUrOlO8eQlOo4OBnPA0GMpSlApSlAq8ejW7qkxm1L8qOQyo+cEBOk+vSRVHVZHQ3dgkSYp4KXh5Hp0hKVgdh4JNcHtLi8/Ddd51d/s7k8nNN9r/IsWdcEo8twIAxnJ4kV3W7aqMycZVpWMa8Dr68c8V45sZt5J1pB7c44cOGK8UY25oBMtKMpzhWPK9fWDXieHkvR9PxeXL+7SWt7Wxc41KX1akjAHyE5zWTi3aO7kx5AJ60qOD+jtqHWtNqc+1pbGB1DUVdgwa739lYbpCkgp45+LUpB+Qp5V34anqpz48d7XqnDUsHn9NeZa94ojPAD+dYm2xkx06UFWnGMrWpZ55ySo16o0wJ1E4yTwrDW65evq9UohI5VUfTftRKtbUd+C8WXO+C2cJSsKSULWrUlXA8E1Y9xuAOST/zqtunG2b2JHUsHAlpJA5gLadSedb8GPvRzeIzvlulLIuj89a5cuUuQ68EpUpZ6k+SnSPJA44A7TXqFdTLKU4wkDHKu2vaxmng5ZXK7pSlKlUpSlApSlApSlApSlBM+gv7r2L85xv46/ROvzs6C/uvYvznG/jr9E6CKbUdJNmtbve1xvEKE/oSvdSZDTTgQvOhRSo5AODzqV1o99Uj2a3cqzXJKTiVEehukDxQuG7v2So+epMtwepj0Vtl0K7RfC1qss1Sgtcm3RVOlPLfpbDcoDnyeQ6PkoPZtft3a7OWk3S5xbep9KlNJlPNslxKCAsoCzxAKgPlrNWue1KbZfjOofZkNIdadbUFodbcSFtrQocFJUkgg+mvzt7u3aQ3C+yGUEqRaokaInBJSVBCpkhQSOSguSpBP/cdgFbV9w5tH8IWCChSyty2vSoLhPMBpzfx08ByTGkR0j/R7c0FrbW7WQLQhDt0nR4Dbrm7QuU6hlK16VL0JUsjKtKVHHor17PXqNcWWpUGS1Ljvat2/HWl1pzQtTS9C0ZB0rQtJ7CkjqrSv6o9tGX5tmtjepXesR2UtKSSFuznQy0koHlOJREJHDlI4czW3nRRsyLNbrVb+GqFBjtOFIwFvBsGQsDjjW8XFcz5VBJ6UqL3LpGssZwx5F9tjD6VBJZenwmnUqPJKmluBSVegiglFK4MupWEqQoLSoBSVJIUlQIyClQ4EEdYrnQU90290La9kpLMG4RZ77r8NuWlUJuKtsNuPSGEhSn321bzVGcOAMYKePHhbsV4OJQtOdLiErGeBwoBQyOo4NaC/VHPuzA/8Pxf+I3Wt8bD9oi/6uz/7aaD20pXhvl5jQUF6bKYhtJ5uynmo7Y9bjxCR+mg91KjVh6QLPPWGoN6tsx08mos6I+4erg20sqP6KktApSozfOkKzQXCxNvdthvJ8pqVOhsOpzkDU26sKSOB5jqoJNSvNbLgzKQh2M+1IacGUOsOIebWO1DjZKVD1GvTQKV0T5rUdJcfdbYbSQCt5aW0AqISkFayACSQPlrxS9ooTLJluzorUVOcyXJDCI4wSDl9Sg2MEEc+o0GUpWG2Z2st90CzbblDuAbICzCkx5W7J5a9wpWj5a+bTbW2616PhK5w7fvPI79lR4u8xz0b9SdfyUGapXjs91jzW0Pw5LMtlwZQ9GdbfaWO1DrRKVD1GvZQKUqP7R7cWq2qDdxu8CA4oZDcyZFjLI4cQh5aVFPEccddBIKV5LPdGJjaH4chmUy4MoejONvtLHah1olKh6jXroFUf3a/3IT+c4f8D9XhVH92v9yE/nOH/A/QaU0pSgUpSgV6bXNXGWh1s4U2rI7COsH0EcK81KiyWaqZdXcX/s9ORMbbdb5LTxHWFffJV6QcV7rZbWHXFB1tCsecM59FUzsDtMYCylZO5cPjDzFcgoejqNWUjadDZCtXpynHZmvnefwmXFnqdvT+fJ9D4bxc5MZvv6/7TJWzsTyg1u1fe6MjHz8BXCDCVzBOkDl2+k1gIe2jbmAleAOYOAez5ayStpmW0EJUCccST+jlVpx3XVfLmkvSslLCUDirierNYidcEpA48P3msDc9pQvglWezFc7Fb3JSgpecZHPlj0Vp+Hpn+JcukSDZ6EZS9ThwhJzjt+msb3QZDUB9aE53C2l4zjhq3Z49QAXVg2eGGk8gAPn+mo30kwkyY0ptYBS4y4lWewoOT8nA/JVscvLZTLCXGxqra7giQMoyCMaknmM17KhVqdUwQoHr49WpPp9B4Gpkw6FgKScg/wCP0172WFkmXpXz172fBzpSlUClKUClKUClKUClKUEz6C/uvYvznG/jr9E6/OzoL+69i/Ocb+Ov0ToKG7u7Zrv+xSXUpKnLXKizE6eenWYj+f7AalLWf7rPVWC7gbaxC7FJafWEJssyXkk+RGdQJ+s9g3jkv2Kv/bSxoucSfBd4Inw5MZR80SGVtah2Ea8g9WK/NPos25XYYe2lvdG6eulsbihC+B3zc0QpDXD78RZ05f8A/SaCb9zjsq7thM20nOtp1yLTdSjOV7qfe1vGLp4DKUhuSOo8BU7+pr7SYXfLatfltxpzKOzdqMWWr053kIfJ6asb6n5sx3lZVS1ga7tOfeBxghiNiG0k9vxjMlYPY78p10t978Bdqb4o4bZZ+G0pQB5TUqG9cLW0nqBU73gns4mgy0Nvwt24Wrxlx413KyR4yO9rCgJb4HIDLy4bY9cnqJzX6AVpZ9Td2XLjt6u7qSShtqAysknUp5QlzM5+/Abh8efxh7TndOg1G7ubpVnIfibNWVxxt6YhlUxUYlDzxlObuJBbcSQpsLxqWBjWHWk50lxKvtg7iWEYiBPu8tNxU1la4qY5hsuqTnSll1G+kNoJxq3jZXpzhGcCmO6bt78na6Yw2/3o9KuNlaZkKUtsR1PQ7c3Hf3jfjIS2ShWpPEaDjiKtT7GfbH8sv/z717tBh+5G2tn7M3uRsrcnSuO7IlR0IKlKbjy2Ureaeja+KGJCEKGkAai80o4IOd46086PO5WvUG6W26z71ElmJPjyX1bya7IfSwpJKd48346ilIT4yuVbh0GgP1Rz7swP/D8X/iN1rfGw/aIv+rs/+2mtDvqjn3Zgf+H4v/EbrW+Nh+0Rf9XZ/wDbTQRvpo26b2bt065uo3pjNgMtZxv5DqktR2yRxCC4tJURxCUqPHFaQdFnRxeek+TLuV1ua2orDu7XIWkvBKyEu9526LqS2yhKFIJOQE71BIWVGr9+qKNuKssQthRSi+RFO6c4CDDuCElePvN6pocesprK9wNJZXYGEslO8Znz0SAOYdU6HUavTuHGPkxQQ1fcTwEORHGbxJU21IZXIZlMMuiSyhxKnWkLZU2WVKSCNRC8Z5VthSlBqX3d/TPKthZslqfXFdkRxInSGVaHUsuKWhmM04k6mlL0KWtQwdJbAOFLFYro27i5l6Iy9fLjJjzH20uGPCDARD1pBS08t5KzIeTnxtOlIOUgqAC1Vx3T6xH2xW9N8WOmdYHiXPI72bjW8PEZ4bsFt8H0pVX6ICg/OV1279FF4SymSqVEcDTy0J1Nx7tCWsoUoxypQjzEFDiQrJKFJ5qQohf6IWe4tTGo8mOsOsymGn2Vp4hxp9tLrS0nrBQpJ+WtLvqlktkyNnmkqTv24twccSCNYZediojlQ5hJWxKAPahXYa2j6AGVt2XZxLoIWLLbchXApBiNFKSDyISQMdWKCAd3igHZ+aT97Lt5HoPfSE/uUf01rB3NvQzN23aHftyeiWezKcYYSkB0l+Qoy5DcVokNtK+OQtx5YJOtpICgPi9oe7t/yen/AOtW7/fGqwn1O8f/AKJI9N6mfL/0WCKDWjpe2Gn9Gl0gP26et1K0GRDk6d0XA25okRJbSVYcABbCx5K0vJ5HKU2T0adzRL2vjG+7Q3t9uXeEmQwEtIfUG153D0gqUE7tSQkoYa0BDegApzoR7vqmPl7M/wChd/4rZWzfQJ9xdmvzDaP9wj0GlHc73mdsVtJ8CynSWJNwTbZTSSotPrfIbt8tpGcIUVuR1hRGoNvLScZOP0Mr8+emkf8A77a/P+y/zsWg1+g1BQvdo9Lb2zMFlm3r3dwuy3W2XRzisMpQZT6DggPZdZQnOOLqlDi3iql6Fu5LavMNm57Q3Ga3IuaBKQ1FUyFoRI+NQ5LelIdU8+4FBwjCSNeCSc4xn1SZLnf1kJzujbnwjs3gkkvY9OlTHzV7tnu522slMRJEXbMFiTGYeYKJ940ll5pDjOnSMadCk4xwxQQ+I7N6K9oGoxmrftknvdx9JylEu3yXFs712OMhMuOtt4pUniSwRkJcUk/oSK0cvncf7RzlBybtDDmOJRoSuU9cn1pQCpQQFutqKUalKOBwyo9tbuwWS2htBOoobQkntKUhJPzUHdVH92v9yE/nOH/A/V4VR/dr/chP5zh/wP0GlNKUoFKUoFKUoFWVsNAj3CLodSN7HcLetCiFpB8dvJTxxg4weyqtuEkNJKjz5JHaTy+Ss/0AXrTKlxlK1CQ1vOP4RpWDj1pXjH9muXxkt47rvOrs8Hj73mvbt92WvOysplRDKlOpznKcBWM8Mnrrna9lpqiCvUB/aVnHHsFWumJnjjj/AIxWYt0ZHi5SArtNedhz3T0L4eXqiWzeyQa0lz4w55KzVh2yIE4GMY512womo+Kkq9NZyHbOWrj+4VOV31a4Y+V54ydXDqxVcd0BtCi3RVthXx8wKZZSMagSCHnCPMQjUfSSkddWtdH2YLTr76w22yhS1qVwASkEnnzPDl6a0k6SNsnb1IkTXcpbQFNRWuplrPD1uK8pR7fVWvBwXl6+k1+d7GHJjM5je2rb9J1t/afNBpXDgOIzgeoYT/KstZpGheknxVAfIcDB+cD5axKUaynPV/PhXpcPFXrV+jOB82K+ox4pfc9Nfr/6+b5OTeN5PW5fpd3/AEl1KiUK5OMnyitOeKVceHoJ5GpDCuLbvBJwrzVcD8medcOfDlinHOV7KUpWSxSlKBSlKBSlKCZ9Bf3XsX5zjfx1+idfnZ0F/dexfnON/HX6J0CvzX7pzouuDF7vXeNqmyY8mX3205GiyX21GchEp4IW0kpGl511Gnq0dmK/SilBgejrZ5Npg2yAjiIEGNHJ89TLSUOLOOGVLClH0qNaad3v0dTXrrGnW+3SJaJ1uaDyokd+QRIiOLaUXdyk6csGKBk8dB7K3ppQVF3IGxyrLY7c08yWZEvezZKVJLaw5KVloOoUApLiYyIyCDxBbx1VbtKUGsPdp9AsnaAs3Wyth6dGZDEmLlKFTGEKKmnGFrIR3w1rcBSo+OggA5QlK6y2b7p/amzIbhXeyGY80lKEOTo86FMXpyP+k8MPrxpGrQlRwSoqJJreulBrr3NvSvtNtDOeF3sneFr7zdU06iHLjITIDrRaBky1nvglovAhA56DhPXsVSlBoz9UC2VuE27wXYVtmS2hY4zZcixZEhsOJn3NSkFbSSkLCXGyU5zhae0Vu3ZUFLMcKBSUsMggjBBDaQQQeRBr10oIz0pbGR9oYM22SyUtTGtIWnipl1CkusPIGRlSHUIVpzhWkg8Ca0StULa/ozlSTGhrejO4C1hh6bbJqUag04pTOlTDoySAVNuAEg5B4/onSg0tsPdObV3d6G3b9m0qaMmP3x3pDnSnFtb1G+Sl1agzHSUagVLHi89QwTW6VKUGuHdl9BD20qWLjaUpVcoTJZWwpQb7+jBSnEJQtZCEyG1rcI1EBQcUCfFSKpzY/uj9qNnWG7ZcrIqU9HbDMZc9ibHkpCAUtpfSAO+0pAQAQEqITxUonNb5UoNCej7ofv8At5cvhbalp6HCU4hTxkIciLeZa4tw7dFVhxqPjCd6cABS1anHCc76NNhASlKQlKQAlKQAEgDACQOAAHDFcqUFK92vbH5lhnNRI70p0yIBDcdtx9whMtoqIbaBUQBzOKxHcE2eTCszzc2K/DcN3lrDcpl2OtSDHhpCwh0AlBKVDPLKSOo1sDSg1D+qK7OzZ6tnDBgSpgaTdQ4Ykd+QGys24oDhZSdBVoXjPPSew1sZ0IxXGLRs8082tl1qyWpDjbqVNuNrRBYStDiFYUhaVAgpIyCKmFKDRPpg2TuLu2rUpq2TXI3w3s253w3FkLY3bLNrDq9+lO70ILbgKs4GhWcYNb2UpQU93VfQ/wCF0JtEdSG7hb1rdhrc4Ic3iUpfjOKwdCHQhs6upTKM8M1rHsL0w7W7DNi2XKzOSI0YqQyiezJSpkZJ0RZ7JLb8YEqx9sAyAlQSAK39pQam9F3T9tVfrjbGk7N7m2OSW0S3GYk1e7ZcCkLccnPqDLaG8hzASFHdkDVkCtsqUoFUf3a/3IT+c4f8D9XhVH92v9yE/nOH/A/QaU0pSgUpSgUpWPusrgW2yCtfDt0g8yccuFTJtMlt1GGvcsrKlfeJ8VHpPEKV/jsr3dEUkouMHj9sUtB9bjSh+/H6Kw91wNKU+SgY9BOfG4euuGzjimZUNaeGiUwof+qnNOThv4Vt9Z/46uTKY8s48esx6fW/9v16fZubb1ZAJGccCPVWdiPt4ASjj6c/zryQYhBSccHAOfUcZH6RWREEp4lP/OvmL0r2sezNWZwq6v0cBWd3qUAlWAAM5rB2tWMeJgdfoFVz06dIXwewvQrxlfFtjlrcIJCR/ZA8YnsrXi3nZjj1t6KctmM3e07q87qbpG78WLbFUd02UqfI+/UcFKDjnjrB7aoq5HSEIHMYUr18xmu+OpT7i3HVElSlOLUfvlHiSfX9FYyW6VqJHWSfkr6rg4Zx2cfpj1vzyvZ5XJnf6fLlvS8l8uP/AMY9cr97qfZ9aUE5NfUrB66Ro5WCUgKKeaQRqIxzCTxUO3FcUnHV/jlXo45yPHz81mvQRxJ49ddmj08u0cvUe3hSC2FElfBCeKyPXwSP7SjgerJ6q+KeJ6sAnl2dgpMt3XdncdTfZkId1cRwVhxPrwoeqs3Gloc8lQz2HgR8nXUVIriklP7+f7j1Vhy+Fxy6zo0w5bPmmdKj0O9KTgLGodvWPV2/LWcjSEuDKDn949Y6q4eTiyw7unHOV20pSslilKUEz6C/uvYvznG/jr9E6/OzoL+69i/Ocb+Ov0ToFKUoFKUoKRi9O0qR8KvQdk58+FZ58yFKkxpVvLgchYL25grWH3vEUhQCQfLA55qzejnbCLf4cS5W9SlR5iCpAdTu3G1IWpp1p1GSEuocQtBwSklOQVAgnW7oMk7RFva6Ps9DtxS9tdfB39cZTzferyxHQrENlpZeSlG7UFavKUQUkDBuDY/ZSJsdYFwps50R4MGYuXMYLkd4GSp119cRTJ3jTgU9pbKDrBSg+VxoLSpWl6Zq4EzY26WS13qzQ7terfEXIut177F7jXJSUkyLcuQ8ttZa1uJX4qPHCgCQgi9+6lst1nQI6LMh5/dXKK9PiQ5BhSbhb2w53zGYkjihSiWzgcSE8NRGlQWzSqm7ma7WeTGnIsjc+IY85SJlvu7sp2VbZCUJbLRTLccU22d0pQAUfG1g4IKU1/0RbNo24dv9zv8ALmvojXuZboVvYmS4Ue3sxEtKQsNxFoKpKg8kFR5lsk5zwDZmlV/0oy7fYrNJFwkzWoMSEzGLsV974QcHxcdlLMkKDipTitCStSgPGUVEJ1EURsi4/ab9sqINqumz8G+t3Jt6LdLmbh8IpYiB9DzkVb7zsGQ2t1okLUk5wAANYUF69LHSE5ZZOzcZuMh8X27IgrUtakGOlZb+MQEghasLPA45CrCqiO6f+6HR9/4oZ/exV70EE2m6RkwLtZrM9DWRemJS2JgcQG0Ow23XXWVtEaidKGsKB5vpGOGaxd46ZYsa+wtmjHWt6ZG3pkhxAbYcLMmQhlxojUVKRHRgg85CeHXUW7sVnvNnZ++oHjbO7QQn3ljOpMKS4lqWgY4kLWiKkjrBNUztS1vm7rtukZMTb6A4y8g6t/ZrSoWxrdFJ8h1bzaVDkrc44jFBtMx0iIcvLtgaiqcXHtSZ8iUHEhtjW6GkMFrTlTqgtlY8YcFnh4tTiqK7l9AuUvbDaDVvE3a9KiRFjBS5BtCO94zzSutLiVpB44zHGOXGB9M70K7ObUO2e23u5zbS3ID10bur1vgWWVEjHUiE09IQiQGlsFbjSGlHKlaThSDQbU3SQWW3nAAotNOLAPIlCCoA+jhUO6BtuV7SWyBdHY6Iq5hlZZbWpxKO95kiKMLUATkMhXL76sf0RXp+47P26VLcLz79ly64rip1aWVoK1nrWrTknrJNYDuI/wDJuyeu5/8AF59BI+526RXNqbc3cnoqIilyJDW6bWp1IDCgkHWoAknPZWd6PNqX7omcqRaZdpMS4SIraZydBlts6dMpjgNTC9RwRlJ0nClVVPcDfcCP/r8//wB0VkO5EnvSGdpy++4+Wtsbw02XnFulttDcPQ2grJ0NjJwkcBk0F3UrUvaRsWm73GRtuxdjFmXhC7Ne4U6Wm3W6LvCuNEksRHEJh4SEIVrQpSylwgYCnVWb3We0k2JFtMO3S1W9y/XyDbHZreQ5EYlbzerZWCC07kI8cHISF4wSFALnqvovSC4u/PWDvZAaasQuYk61ayoy2o26LeNIThwq1Z6q59H/AES22xupkwlTVP7hTLq5U+bLEnWUKLr7Lyy1v8o5oSkDWrhx4VHtfsi3etsnY0iRJYjp2TbdfRDfeiKmNpnobEd55hSXBHK3W3CEkZLCaDZqlUF3NaXrdddsrGJkiVAtT9segomOqkLiJnx3X3Wm3XMrLXFsYJx8VnylrJv2gUpSgVR/dr/chP5zh/wP1eFUf3a/3IT+c4f8D9BpTSlfFKAyScADJPZQfa8dyuKGB4xyo8kjmfoFYm47Qg5DIP8Apkfwg/vNR91wrJKiSTzJrTHDfdFrKy7665nT4iT1Dn+muNrT98VAKcONSjwQM8VKV1AfKcCsTq58eVdLL6kcQfkPLt5VpuS6s6J488sLcp39L8Ep2iZjNbtuM6ZCgFb54EFpxRxjcDytA8bKjz1VMOjLYty4IUpplThZLElDoAKEuMvhLzC1DiglkhQB5lHCq1Q5nifvgP8AHoq3O5h2kVDmuM7woTJZA0g8FqbVniDz4L+atPFYf8F67Z8OX/JG1tptqyGAtPklGevlzx6KmEuE2lPAccVjYLqiE4xjhjAzjh2Z4Vw2ivbUFl2TLc0NsIUtSl4QCEDOAT1nl6c183j4XL83t5eKlnwR3bnaWNZmHH5SsAhWhI8t0pBJCAfRzPV11pd0lbaO3t/fOI3LaMpZYBJDaSclSifKdVwJPyDhWQ6WOkR6+SHXVDQ0fEZbJJS00k5ASnzieJJ41DozQWQnHEnJI6h1173gvAcfhcfxMuuUne+nyjzObxHL4rknDjO9kk+P1ehQ3TWc4U7w+Trz81YwV33KYlxRSDwR4o7D2/PXVpxXZ4OXy3K98ru/tL9lva3NjeWcWH9vHJjPnr+6/e7r0RSg4SSW1g5C8nSrzc44tkdoNeuQUqyJSClRBw80AVKwOG8T5L45eOkg+usag9gr1xZrjQKQQpKgcocSFp9ac8UK9Iwa3z4tzff4el+1/a9HmY8np2/nw/d5iSkBHI8FK9KsEcfSK61GuLQwBx58f08efbXxasc6tJccdq3rk+qV1Dn+6uxJ7BXnQMesjFdqB21XDzW7Xy1pyr62tTZyhRSfQf5ddfBX1Z5dta3CWMplZ2SO0XIPeKrgsD5FDtHZ6qyNQxlZSQQcEcR66ldvkh1KVDgeRHYRwNeX4ng8l3Ozs4uTzd3opSlcrVM+gv7r2L85xv46/ROvzs6C/uvYvznG/jr9E6BSlKBSlKCIdGGwLFgTckRnnnhc7tLubpf3ZLb0wNBxDe7Sn4obpOM5PE8TWV252aj3mJMt8wKLE5hbLhbIStIV5K21EEBxCglQJBGUjII4VmqUFJR+57bUbKqbtDdZw2ekw3rc06YSGWEQloW20tttnL5O6aSXFHVpbABAqx9v9mX7kmMIl4m2d2M+XQ5B73UHstLa3cpmShaJDICyoIVw1BKsEpSRJqUEI6KOjhiwCetMqTcJd1ld8zZk1TZdkOAFKEhLKUoaZRqXpQBw3hGcYAjc7oSQ1LnT7Je7jYV3RZcmsQjFdjSHVElbyWJTaw0+oqWdQ5FZxpyRVt0oITtx0bxr1bPgW4SJMhvcRmzLWtBlrci7styHHNOhb5U2FKJThWpXDjUYtXQgEzrVdZ+0F0uky0a0x++jDSxultFooLDLQwshSipzVrWdOonSKt2lBDukHo/YvT1lkvvvNLsdwROYSzu9LziCghD+8So7vxMeLg8TxqY0pQR7pI2Rj36FNtszUGJrQQtTenW2UrQ6243rBTvEONoWMg8Uio/F6JYDdmOzaVO95GK4xvCWy/l15UhT+dOjfb9RcHi4yBwqwaUEZ6Ltio+zsGJbISnFsw0uBK3ilTjinnnH3FuFIAKit1XIAAYA4Cq+unc/sOLvAj3y6QIN/kOSbhb4i4yWn3nsl/Q860p1llwkhaEkakkoJ06QLnpQRnYjY5q1W+PamXnXWY0VcdDru73pQrXgq0JCNQC8cB1Cuvom2IY2cgxLXEddfZiF/Q5I0F1XfEl6UrWW0pTwU8oDAHACpVSghnQ30eR9l4aLdDfekNIeedC5JbLmXlBSgS0lKcAjhwrn0W7AMbPouLcV554XK6yrk6X92Sh6WlpLiG92lOGhuU4zk8TxNTClBUO1nQibuXGbntHdplsdnqmLtri4iW1KL6pAjmUhoSBBSpWlLQUNCUpCSkpSRM+lTo/g7SxHLfc21KZWpLja2ilD0Z5AUlt6OtQIQ6kLWniCCFqBBBIqV0oID0e7AS7W4hyTtNdLu2zHUw3HnGLu8KLZDj622w7JkJDYAcWonxlc9Rr3MbAMIuzt+Dzxku2oW0snd7gMiQ3J1gade91NgeVjBPCphSgh+y+wDFvuF6uzTzy374IQfbc3e6a7xZLLW4CUhYyk5OonjyxUwpSgUpSgVR/dr/chP5zh/wAD9XhVH92v9yE/nOH/AAP0GlNYXaqXoSEA8V8/9EfSeFZqobtLI1uK/sYSOzgOPzk1bCboxhNcQa+k19SM866FHU8rhgcv3n0V1ITmu1Sc1zAqlx3eqdu1kkDHZxrPbIyHGX2H2ThTSgr1jIyPVisA2cEVkbHPDCzq8kpPz/8AMCui2ZcdxUk96N+dnNp2Uw0zJDiGmkR9444sgBKQnKio4wBWpPTt0uv39xTbSlsW1lwFljOC+pPAPvjnq60o5J4dfLAbVdIUiXFYtyFFLDR1uAEjfLB+LSv/ALtOM46zjsqFNNZ4q+QVx8HB13e/p8m3JyejkiWrqQD+mvSmQ4AcYTkY4c+Pp6q60jFcs16X4fu6yu58HLOW45ebHpfi60tgdXOiUqSeHEcznjgDmf3VzFd+dKT/AG8j/ZB4/Pj9FW/DmunSq+e3v1dbUlJ5+KfTXYXAeXGvMpjVk9lfGm8VbHkznu3V+at453dw/d/KuJ45PZyr6cDkOdcCccKtf0RAGu1R4D0mulBycV2SXMD1Coxy6W+hlOsgyeJ7K5LP7664wwnJ5muZI661w64fVXLu7EDlWT2ekaVlB5L5esDh8w+asNrrsYe0qSQeKSCPSQRWfLJnhcVuPcu02pSleI7nv2eu70B+PLjKCH4rqHWlKSFhK0HKSUK4KHoNWb9kdtH+Osfqkb6KqInHE8MfNU/6GNmLfdlXRie7JRIatz78BuLoy87GbedkBWtJCnEpbb0tkp1BTnHKRgM99kdtH+Osfqkb6KfZHbR/jrH6pG+iqz2asUu5HTb4UicoY1d6MuvpRqGobxbYKWgR1rIFZe+9Hd4gpLkuzzWWwCVOd7uONoAGSXHGgpLSfSoigmv2R20f46x+qRvop9kdtH+Osfqkb6KqJJzxHEHsr7QW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqjpQW59kdtH+Osfqkb6KfZHbR/jrH6pG+iqus1sfmuNx4jDkl94kNtMpK1rKUqWrSkdQSlSieQCSTwFdEphbSnG3UKbcaWttxDgKFtuNqKHELQrihaVJIIPEEEUFsfZHbR/jrH6pG+in2R20f46x+qRvoqo6UFufZHbR/jrH6pG+in2R20f46x+qRvoqo6UFufZHbR/jrH6pG+in2R20f46x+qRvoqo6UFufZHbR/jrH6pG+isBt70vXe+Md6XGQ06wHUO6UR2WTrbCgk60DOPGPCoFSg6Zr+7StZ+9STx7er56gchRJJPM8T66lG1r+EJQOa1ZPqTx/fioqut+KdNq1112mutAzXYqtdIcaUpUaAdVJOUkGgr7P5D11bthdfJTfvR9jI8rjnrz216Eorqi8OrmkV3Zrfinuxnn3fKUpWqj6E5xjrPCubqxnA4hOAPk/wCZNfY5xqV2J4etRwP5n5K4oyogDrIH6Tj+dR5ut36J9BY4DHAnjj0VwbNdj6snI9XyDgK68VWelLfR9Jrzur4n0V3k15BxPrpyVbB2tnHGuCVFw46hxrlI4AADiTXOMAgdp7azk6zH071a9t/k9JUEjjXlSoqySa+Pu6uHZXWVYB7eFb8nJ+SnHjp2o556h/jhQHJ+WvieAr6wP5fvrPH5pqwKUpXlOp67LcFxHo0loIU5EksSGw6nW2pcd1DyA4jI1tlSACMjIzxHOto+ifatEx5+/bSWi2WdOGxCu7qFQjIVIQpgoDkx098q73bUkSEgYb1JyEk1qjVlbWw7hMsNpmS7wy9DjS3LfEgbttD0YoS+0nU6gAvuhmPqDa+KWVJVniRQXX0n3OJOnKs8XaxzZcREnvmO3FEOO88tHfS3EXJDjGHFJea1NqXpXpJTk5zrxbdvrvbHnFQ75MXunXEJWZD0iPIShwpS53tKK21oWEhQ1JyArqr0dMW2rF+fjyWLcm3rREZZkEOb5UpxpIQlbi9KdQQ2lDaVKyopQMngkCFtNqWUpQkrUtSUpSkFSlqUQlKUpHFSiSAAOZNBbF/jxdqIcy5xIzcG8WpsP3SLFTojXGKSd5cIrRPxTzZClOJBJxnUVFTZNS1bPQ1EXs7eY7d/Um0IVClpkJm6N29Hkx3A22t9Ci222p1CFaySNUcoOFHhVtwYbacebYe74ZaedbZfxp74abcUhl7T97vEJSvHVqxQSywdF91uEWPOhRBJZlS1RWkNuN75S0FwKWW1kJQwFNOJK1KGNJJAT41Z3afoGvtvYclOx2H22UKW6mI/vnWkIGpxSmlJTrCQCSGys8M4wDU5tl3fhbGhcV5cdx2a8wXGiULS29dnA8ELHFBUgFBI44WcYPGsb3EUpabhPjJVhh+1uvuNfeLdZmQWkLKORXu5Dyc9YV6KCn9kNmZl3eTFt0Zcp5QKtKClKW0AgKcddWQhpoah4yiOJAGSQDNtpugq9wGXZCmI8tEcFTyYEgSHWEpBUorZUlKlYAOQjUevGASJ/wBBENiLYdp5AnG1rcnORHJ7cd+W7DjtMw0NaWoxD61Dv18hSCCkv6vvTUe6H5Ni2dmszmtsC6gIdbkR0WG8RxLbcbWEoW5lYGh0tug6TxaxwyaCt9mdiZtxjXKdFQ2qNaWt7JUtxKFad2t1W5R/2hS22pR5cMYyeFeHZDZ9+6yY0GGEqflLWlsOK3aPi2nH1la8HSkNtOK5E+LwBOBV69F7rC7V0kLh8Iq/hVUYaS3iMqLPVF+LUAW/iS34pAxy6qrvuZRm+WT+8n/NabhQYrZ7o1uM+bMtUdprvyCmQp5LjyUNgRnW2VlDvEL1LeaCe3WCcAHHrX0RXdEBy7PxkRYjTAkESXUtSFMq0kLEfBKCQoHQ4UK9HEZunoZGdrNp/wDVrj/xG1VT2y1wdv17t5ury5KZF4bUpDy1LaSlDxcbYbbV4rbHiJa0JA8VRHXQerZToHvtxaRIRGaituhKmu/ntw46lQBSpLKErWgHPDeBBPPGCCYft3sdOsboYucZUdakqW2rKXGn0JOFKYebJS4ASnKfKTrTqCdQzNe6vuz0u8TmZC1KagCI1HaUVFDSXIUeStaWz4odW5IWSsDJAQCSECpXtRIXctjo8mctT8iBO0R3nSVOKSmauGAXDxXhh5SOOc7hJOSM0ENidBV9dXGbREbxJipk70vthmO2rGEynPvHuI8RAXniRkJUU+faHoUvsJ+LFVA75XNUpLK4jiXWVKQkrcS46vR3uUoBVl0IBAOCcHFjd2Fc3hH2biBxQjvw3XnmgcIecZbgoYLo+/CA46QDwyvPMDHKBfZLGxupqQ6hffSoiXAtW8bjrupQppCycoRuipoAeShWkYAGArvbfoSvVoYXMksMusNDLyoj2+VHTnBW62pKVbsHAKkagnmcAEiNbAbDz766pi2Rt8WwlTri1JaZjpVkILzq+AKilWEjKlaVYBCSRbXcjnXG2tiq4xzbmlbk/awp5m5NPKCOQK0JQlR6w2nPIVysEty3bHLkQVqYfuFwWiQ80dLgSqcYisLHFGpiM23kcQHjjBOaCI3XoEvsd2IyYzLoluqaS+w9vI7K0trdIlLKQthOhtfjFGkkBIJUpKTI+gboemquLb9xgx34NtmzostLy476FPsxHkN4jqzvmw+7HUCoY5HHCsD3Jd1ei3eHHYUpLE9EtuS0kqDaw1CfktuKQPF3iXI7YCyMgLUkHxzmU7GEjbJ4AkA3G8ZAJwcWubjI66CKdN/RPOtLlyuHejMe2KuL243LrIDTMh9ZjJTHBBbbwUpCUjxRjgAOHTsp0EX24tIkIjNRWnQlTXf73e63UqAKVJZQla0A54bwIJ5gYIJ9Ytzc3alxiSNbK9ppRUhfFK91KedCCDwKFlsII6wsjrrr7rG7vy7vOjyFKUxAEVuO0oktoDkJiS44Gz4u9W5IcysDJSEJ5JFBm+gzY6dZNoLbHucZUda2Lips6kONvoEGSkrZebJSsA4yMhScjUBkV13/AKE71eJt7lRo7TDDt6uxZXNdMcyEifJGtltKVOFvhwUoJChxSSONebubL9Lm3myomS35SYke5NsCQ4t3coXBkKUlClkkJJSnr5ISOSQBEOni9SJd1u7rzzhXCuMxiMQtYMRuE+thnvYg5jq+JSvKMHWSrmc0GD2x2Zl2h9cS4MGO+hKVacpWlxtZUG3WnEEpcaVpVgjrSoHBSQMPV/8AdkK3h2aeVxcetskrV1qx3i4M+gKecP8AtmqAoFKUoFKUoFKV1yHQhKlK5ISVH5Bmgi21T2pwAfeJCT6zxI9f0VhnTXZLeKjqVzUcn5TmuhznXTj0mmfd2NVy51wSOFdgrT0VtcTXyvqq+UWjsit61ISOalpH6VAfzr7diNSgnyd4vHqCjiu+y/bEKP3mpf8A6aSsfOB+mvC+SSkf455qnm62fKf5TZ2v1ehvgf8AZH7q5g1wSc19Arsnwc9jnQCuFc205wB1kD9JxUy6v0RpzWcBPafGPq4gfzr7HVgKV5owPQVZSPmKq63/AClY4gHA9Q4D/HprtWcISB9+dZ9IHBP/AMqz3bj9Vtdfo6gaVwVXyr/JGumxZ4H1V0M1yknhSJw5+usuS7zkXx7Pr54j0Dh8tcjkc66mE5JUeo8K5vUxu95fNa9OjiKMpySeoVwUeocTXoACQAP/ALqcfevyndFunF4/vruY6vWK8yOJ+WvWjqrbj63bPPpE6pSleO6yrQ6HnGrpFuezr7qGHLg61OtbzhCW03OMgNllxZzpEhlCGwQM4S4BlSkA1fQHGCDggggjgQQcggjkQeug9V3tz8N12PLYcjPsKKHWXhpW2odo5KSRxCkkpUCCkkEEzbZfY23y4LcobSwrddBKWBFuDwhNNNtKJQsyUguMuEBLiXsaASEcFAqHqh9Ljj7bbF/tUPaNDCNDL0zVGntJJ4pFyZBWU8uJTqJGVKUa5xeki1w/HtexsGM+khTb1xnTb2GljiFoZlJRpUk8QQoYIzQXltn0cLaVC2huanLvNs9njJkW+Oyl1NynREKSl1LjgJQzvXlOqQlonLWpIzlCtXukCe5MlSZjsD4N7+c3yI6W1tNpTgNkta0p3gKkKUpYABWpZwM4Fy23be9XyyXmSu8mNKs9wYlh1hbcB16NunFqinvRKVaN4pJb/CKaDaiRqzU3SD0gz78IIubqHjb2XGmlobDa3N9ud64+QcOPK3DWSAlPi8EjJyEjc6QIp2ebsm7f77TPLpXpb3G6MtcvUF6terxwjTp5gnOK6e5227jbPTnpc5t5xpy3SI4EZKFrDi5EOQglLikDQRFUnOeBWnqyRXFKCxuiPpNFnM+PNhi4Wu6hYlxMp1grSpBWyV4SsltRQpKinUAghSSjjn27zsRDIkR7Vdbk4OLcSc42mM2rBwH1Fw7xHV42/wDUedU1SgtLod6T49oeu7c6BvbZewtL8SNpV3slanwltlt1SUuR9zJcaKSpJKUoIOU4Mn2R6Qdltn5TL1nttweLii3IlTFpWqJGWlWpMFhTmXHStLQUV6To1YUonSaGpQXN0d9K0KBfLxeH2ZJi3BqahpDSGlvpLsqJIZ3iCsIGUxVA4UcKcTzGVCoY01xp1EhlRadafQ+0tOCWnW3Q80pOoYJStKSMj72vPSgvS89IOzW0W5k7Q26fEuDTKG3XbYpKmZSUFWkeMvUOZOFI1JCgneLCQainS70kMXONCtVnhLttpgeM206oKffc0rSlcjSpYwN66rBWsrW4VqUTjFbUoLO6eekKLfxZBEafbNvguNP98JbSN66IwKWihStaU97nxjjOscOeOP1wIvg/8Cbt/vv4Q32vS3uN13131q16ter7zTp58eVVnXusdnkznAxCivS3lAkNxmnHl6QQCpSWwSlsFScqOAMjJoLA6CekGLYU3xMtp9w3GA20xuEtqAdaEoBLpWpOhKu+QdQzjQeHLP3og6So1vizLPe4a7haZx1KSyQHozh3YUpoKWjKCW23AUrQptbetOSqq/u9klQ3RGlxJEaQSgJYfZdadXvFaG922sBTgUoFKSnIUeAzXftDszOt27NwgSoQeGWzKYeYC+GSEqcABWBzTzHWBQXFsf0h7MbPymXbRbrg/vSW5UuaptTkaMtKiUQWNYC3C6ljUpYSdCVAFROKgT3SBub07fIbJUn4RkSG2XyEKWy+hxhxtwo1BtxbDrgyNQSVA+NjjgLtsfcobSZMu1zY0deMPPxZDTY1EJRrWtIDeokAasasjGa9OyWxM64GM6iBMVCdmR2HZbMd5xppLkhDLyw6ElBDepRUryUlPjYoJp0m7W2GapV1tDN0gXpU2PJAd72MVLzTqHHHlDW4c+JqGjGV4JSAVVnr50h7M7RbmRtBbZ0S4NMobcctqklqSlBUQASsHGSSAtAUkK061AZqqntkJTsy4QbbFk3BUGZMY+IZW8vdxpLzCHHt0NLWoNczgZOBWMRZJanHY6YUpUhgFT0dMeQp9hKSgKU8wlO8aSC42CVAD4xPaKC07D0kWWFdLRLt9mct1vtzEtlwp0OzZZlR1tJekgrIcU2ojm6tWlazk+KgVltxc0z5dzlNJUhE6fOkNpcxrQiVJdebDgSSAsJWMgEjOcE86yP1vrxvEsfAtw3ymt6G+9JOd3558XATnhx6yBz4VhH7XIbS4tyLIbQy+Y7q3GHkIZkAFRjurUkJak6QTulEKwCccKCw+nfpCi35NjERp9s26Atp/fpbSC66IoKWihStaU97HxjjOscOeKxrvfhOtpaccZdbbkBZZccbcQ3IDatDimHFAJeSlfikoJweBwa6KBSlKBSlKBWH2tkaGsfhFBPyDxj+nAHy1mKiO2r+VpRnyE/Osg/uA/TVsZujCL6uOeVfFc6+n6KDn+mt4o7OuuZNdSD5R/xxrmTV9q6fDSlKlaMhZGiorAGSUpR/6riEHl/ZKqxj58dWOQUfk41ndm/FBcx5ClrPqjx3Ffxut/NUfHNWe3j/ADrOet+c/Sf7Tf2elPZ6q7K6h1191GumVjY5ZrujHGVeaCR6+AHzmuhPGu8DCP8ATV8yefzmpl6IcRxwBzOB8p4V2zljUQOSAED1IGP36j8tICglQUeIQFKPpIB0D2sforxk4plfe6ek/wApk6O2ldYUaajUbNOqWfJH6a+rOE+uutfjEV2niQOpNY3Lrb9mmtRzRwAFda1V2KNefTqOOznV8vdmorOrtjpx4x6+X+OqvrivTX1R5DsrqcNMukJ1rsYr1INdDaa7k10cHZjyJ3SlK8h2FKUoFKUoOKkA4JAJHIkDIzzwequVKUClKUClKUClKUClKUClKUCrC6MrUXYV+eUqdIYR8GsyLdadymRODzzymjJecZeXHgIW2dW7QdZVg8E8a9r0224PRlbyNIejOaSneRnXWFlKsak62iFaTgZGccKDYmzxCy7sdmA9bHhZtpGoDEx12SuNOcU+u2tOyX0N6H1NqKkNLSgtlxKAkFIFVrsLYLsW2GX3Ta4kzaG0oCro0tD5uOtxSZENiWjLr7aSrelRSFlTaFFXECv3J7ykhtT7ym0ureDanXFIS84Spx5LZOkPqJJKwNRzxNcrncn5RSqVJflKQkpQqS87IUhJwSlCnlKKE8BwHDgKC74lqXp21LVqvAdXabkh643Z4qXcZIlslKUQGIrLJWd264ChTpaQkAaQ4M9F1t81+67Kv2lqSuC3DsPeL7CXe940VsNC5JdeHxbJBblb5CiFEcFA5SDTzl/mKUhxU+WpxttbSHFSpKnG2nAA42hwr1IaUEpBQDg4GRXTGukhpBZalSG2SsLLLbzyGStJCkrLKVBBWCkEKxnIFBdd8ixZEK9Nqi3OZp22vCpzNmdZbd4uPCAua29Hf3sHAcCfFCQ6D99XofnuMyJpQ3KhSoXRvMQVSpSJFwToW0uKuc6y21uLillbeRpC0jdk4OMUZCukhhanmJT7Dy9Wp1h55l1es6l63W1BatR4nJ4nnXUJTgLig65qeCw6rWvU8HDlwOqzlxKjxIVnPXQTnaWW4nZ60NpcWlv4Zu69CVKCdTLcZ1pWAfKS464sdilk8+NT3a5Kp112wsyRqcu0SG/DQpWnXc7XbIc+MhJV4qS8330hSjjPDPooZTyylLZWotpKlJQVKKEqWAFqSgnSlRAGSBxwOypLsPtSm3PrnutPTJzKcwnHJADTT5ZeYL01C0LdlhsLZUhCVt8WcEkEaQ93TTMQZnecdeuPZIsa1MqBJCzBQUy3SOWtctckkjmEp9GITRSiclSiokklSiVKUTxKlKPFSickk880oFKUoFKUoFV/fHtbjiu1asepJ0j5gKnUx3QlavNST83D56rl9WedXx7Wor6r99fUdfo/nTGa5JQRxP8A9jlnPIit4q+M8QfXXZXzNcNVW1odlKJNfCcVayaV2z0TCGF9u5/Tv3lKP/8AiOmo2eZ9dSWb4jRB7UJ9YZYYH8T66jLYya58bbJ87v8APr+7S93pTQ0zXyuti5iu+QrTu09iAflVlR+YiukDPzD5TwFc7irKnMdRwP8AZGn+VLdWEnRzaWAheRxUpKR6gdR/dXnVXY4cJQO3Ur9JwPk4V01GN/ym9H0V9Nca4uHAp5tQcGuZNdrI6z110tV6Eq/dWPF161bJweXXNpOkek8660Jyc9QrsUa1w77vope2nxRzXDFfFKrk0Oulu7CdI7uWK7Emuiuxs8q6ZdVnnOif0qGeFb/mNeyv3qeFb/mNeyv3q8d1pnSoZ4Vv+Y17K/ep4Vv+Y17K/eoJnSoZ4Vv+Y17K/ep4Vv8AmNeyv3qCZ0qGeFb/AJjXsr96nhW/5jXsr96gmdKhnhW/5jXsr96nhW/5jXsr96gmdKhnhW/5jXsr96nhW/5jXsr96gmdKhnhW/5jXsr96nhW/wCY17K/eoJnSoZ4Vv8AmNeyv3qeFb/mNeyv3qCZ0qGeFb/mNeyv3qeFb/mNeyv3qCZ0qGeFb/mNeyv3qeFb/mNeyv3qCZ0qGeFb/mNeyv3qeFb/AJjXsr96gmdKhnhW/wCY17K/ep4Vv+Y17K/eoJnSoZ4Vv+Y17K/ep4Vv+Y17K/eoJnSoZ4Vv+Y17K/ep4Vv+Y17K/eoJnSoZ4Vv+Y17K/ep4Vv8AmNeyv3qCZ0qGeFb/AJjXsr96nhW/5jXsr96gmdKhnhW/5jXsr96nhW/5jXsr96gzu1b2hojrWoJ/mf3VB1mvddLy5I0hYQNOcaAoc+Bzknq/fWOJq8y1NI09tuklpSFpSlRRnAWNQzggEjtGcj0iu65XJ2QUl1erQCEjAASCckAD01jkuY7KFw1MuO9+pd607VKxXxuutTmaJcx/g1e8kRp6RXOO3rUhPnLSn2jj+fzV5d8ewfPXZEmKbUlaQklByMgkfLg1bLlnl6d0THqzu0DvigecVK+Rbrq0/JobaP8AtVgGeZrslT1OABQTgBI4Z5JbS2OZ7E59ZNedLhHZ89Z45Sfz6T9lsur0k0Qa85ePYPnoHj2D561nNjtTy1k7ekKW2Dy1pJ9STqPzCvMV5JPaSf08TXUxMUgkgDOlSeOeGpJSSOPPjXWXj2D56j8Webf89TydNPZJVxAPDQhKfm1f/Kus10OyCokkDJ7M9mO30V8Lx7B89RjyxNxd4Ndb5rrDx7B89fFuZ7KZcssJi5tV2rPz150uY7K+749g+eoxzxhY9aRgYrio10d8HsHz18Lx7B89a3mx1pWYXbmrqruTXk3nqrlvz2D56rhy4y7qbjXpzXa3Xh357B89c0yiOofP9NazxGO1MuO156UpXA3KUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQKUpQf/9k=\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/TpqMzI0iZJ8?fs=1&start=0&end=40\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f5f7af70e50>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 3a\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"TpqMzI0iZJ8\", width=854, height=480, fs=1, start=0, end=40)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7Ewvvt2N28Ei"
   },
   "source": [
    "Exercise 1\n",
    "---\n",
    "\n",
    "Assume we are performing a random dot motion task and at each time we see a moving dot with velocity $x_t$. All data points are sampled from the same distribution $p$, which is either $p_L=\\mathcal{N}(-\\mu,\\sigma^2)$ or $p_R=\\mathcal{N}(\\mu,\\sigma^2)$. Let's now generate some simulated data under this setting and perform SPRT using the fixed time stopping rule. \n",
    "\n",
    "In this exercise, without loss of generality, we assume the true data-generating model is $p_R$.\n",
    "\n",
    "* Complete the code in function `simulate_SPRT_fixedtime` to create two Gaussian random variables to represent our observation models.\n",
    "* Complete the function `log_likelihood_ratio` to calculate log likelihood ratio for a sequence of data points\n",
    "* Complete the code in function `simulate_SPRT_fixedtime` to calculate cumulated evidence given a list of individual evidences\n",
    "* Run 10 simulations and plot the DDM traces by commenting out our provided code\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vIYN6vH9hMxT"
   },
   "outputs": [],
   "source": [
    "def log_likelihood_ratio(xvec,p0,p1):\n",
    "    \"\"\"\n",
    "    Given a sequence(vector) of observed data, calculate the log of likelihood ratio of p1 and p0\n",
    "\n",
    "    Args:\n",
    "        xvec (numpy vector): a vector of scalar measurements \n",
    "        p0 (Gaussian random variable): a normal random variable with `logpdf` method \n",
    "        p1 (Gaussian random variable): a normal random variable with `logpdf` method \n",
    "\n",
    "    Returns:\n",
    "        llvec: a vector of log likelihood ratios for each input data point\n",
    "    \"\"\"\n",
    "    ################################################################################\n",
    "    ## Insert your code here to:\n",
    "    ##      Calculate the log of likelihood ratios of `p1` and `p0` given a vector of measurements\n",
    "    ##      Hint: using `p1.logpdf`\n",
    "    ################################################################################\n",
    "    raise NotImplementedError(\"Function `log_likelihood_ratio` incomplete\")\n",
    "\n",
    "\n",
    "def simulate_SPRT_fixedtime(sigma, stop_time, true_dist=1):\n",
    "    \"\"\"\n",
    "    Simulate a Sequential Probability Ratio Test with fixed time stopping rule.\n",
    "    Two observation models are 1D Gaussian distributions N(1,sigma^2) and N(-1,sigma^2).\n",
    "\n",
    "    Args:\n",
    "        sigma (float): standard deviation \n",
    "        stop_time (int): number of samples to take before stopping\n",
    "\n",
    "    Returns:\n",
    "        evidence_history (numpy vector): the history of cumulated evidence given generated data\n",
    "        decision (int): 1 for pR, 0 for pL\n",
    "        data (numpy vector): the generated sequences of data in this trial \n",
    "    \"\"\"\n",
    "    muL = -1.0\n",
    "    muR = 1.0 \n",
    "    ################################################################################\n",
    "    ## Insert your code here to:\n",
    "    ##      Create two Gaussian variables `pL` and `pR` with mean `muL` and `muR` respectively and same std. `sigma`\n",
    "    ##      Hint: using `stats.norm(...)` to construct an instance of 1D Gaussian distribution\n",
    "    ################################################################################\n",
    "\n",
    "\n",
    "    if 'pL' not in locals() or 'pR' not in locals():\n",
    "        raise NotImplementedError(\"Function `simulate_SPRT_fixedtime` incomplete\")\n",
    "\n",
    "    # Generate a random sequence of data \n",
    "    if true_dist == 1:\n",
    "        data = pR.rvs(size=stop_time)\n",
    "    else: \n",
    "        data = pL.rvs(size=stop_time)\n",
    "    \n",
    "    # Calculate cumulated evidence\n",
    "    ll_vec = log_likelihood_ratio(data, pL, pR)\n",
    "    ################################################################################\n",
    "    ## Insert your code here to:\n",
    "    ##      Calculate cumulated evidence given a vector of individual evidences \n",
    "    ##      Hint: use `np.cumsum`\n",
    "    ################################################################################\n",
    "    evidence_history = None\n",
    "\n",
    "    if evidence_history is None:\n",
    "        raise NotImplementedError(\"Function `simulate_SPRT_fixedtime` incomplete\")\n",
    "\n",
    "    # Make decision\n",
    "    if evidence_history[-1] > 0:\n",
    "        decision = 1\n",
    "    elif evidence_history[-1] < 0:\n",
    "        decision = 0 \n",
    "    else: \n",
    "        decision = np.random.randint(2)\n",
    "    \n",
    "    return evidence_history, decision, data \n",
    "\n",
    "sigma = 3.5  # standard deviation for pL and pR\n",
    "num_sample = 10  # number of simulations to run for each stopping time\n",
    "stop_time = 150 # stopping time\n",
    "\n",
    "\n",
    "#######p#########################################################################\n",
    "## Un-comment the following code block after completing this exercise\n",
    "################################################################################\n",
    "#plot_and_simulate_SPRT_fixedtime(sigma, stop_time, num_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cellView": "code",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 602
    },
    "colab_type": "text",
    "id": "MajRz2MA7MEJ",
    "outputId": "c4d06c28-0d34-42e8-90f6-7340dc9f5060"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W2D3_DecisionMaking/solutions/W2D3_Tutorial1_Solution_a06a0721.py)\n",
    "\n",
    "*Example output:*\n",
    "\n",
    "<img alt='Solution hint' align='left' width=547 height=406 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/tutorials/W2D3_DecisionMaking/static/W2D3_Tutorial1_Solution_a06a0721_1.png>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Lm53ptaYM3U6"
   },
   "source": [
    "Now let's look at how the dynamics change if you change the noise level and stopping time. \n",
    "\n",
    "\n",
    "\n",
    "* Play with different noise levels and stopping times and observe the corresponding trajectories. Once you have completed exercise 1, check the box to enable the demo.\n",
    "\n",
    "*Hint*: you can click `...`>`Form`>`Hide code` to hide the code section if the slider is too far from the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 595
    },
    "colab_type": "code",
    "id": "qod-OfREMUFW",
    "outputId": "a1a56e51-47ff-48e1-8947-6436a9ea7e6e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Trial\tTotal_Evidence\tDecision\n",
      "0\t49.539465\t1\n",
      "1\t49.014654\t1\n",
      "2\t42.317223\t1\n",
      "3\t35.553389\t1\n",
      "4\t52.393774\t1\n",
      "5\t54.418002\t1\n",
      "6\t61.205527\t1\n",
      "7\t47.963342\t1\n",
      "8\t53.231520\t1\n",
      "9\t56.579111\t1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title # Interactive Demo: Noise level and stopping time { run : \"auto\" }\n",
    "\n",
    "sigma = 4  #@param {type:\"slider\", min:0.05, max:10.0, step:0.05}\n",
    "num_sample = 10  # number of simulations to run for each stopping time\n",
    "stop_time = 394 #@param {type:\"slider\", min:5, max:500, step:1}\n",
    "################################################################################\n",
    "## Un-comment the following code block after complete the exercise above\n",
    "################################################################################\n",
    "try:\n",
    "  simulate_and_plot_SPRT_fixedtime(sigma, stop_time, num_sample)\n",
    "except:\n",
    "  print(\"Complete Exercise 1 first\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "VVexVf_jD3sD"
   },
   "source": [
    "# 2. Accuracy vs. Stopping time\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 519
    },
    "colab_type": "code",
    "id": "AN676cMKEKct",
    "outputId": "853b6fa6-c2a0-4b93-9f73-ac797de5d895"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/TpqMzI0iZJ8\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/TpqMzI0iZJ8?fs=1&start=41\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f5f786c1d50>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 3b\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"TpqMzI0iZJ8\", width=854, height=480, fs=1, start=41)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "70waeNwo_9bo"
   },
   "source": [
    "Exercise 2\n",
    "---\n",
    "\n",
    "If you stop taking samples too early, e.g., make a decision after only seeing 5 samples, or there's a huge amount of observation noise that buries the signal, you are likely to be driven by observation noise to a negative cumulated log likelihood ratio and thus make a wrong decision. You could get a sense of this by increasing noise level or decreasing stopping time in the last exercise.\n",
    "\n",
    "Now let's look at how decision accuracy varies with the number of samples we see quantitatively. First we'll fix our observation noise level. In this exercise you will run several repeated simulations for a certain stopping time to calculate the average decision accuracy. Do this for a range of stopping times and plot the relation between average decision accuracy and stopping time. You should get a positive correlation between these two quantities.\n",
    "\n",
    "* Choose a noise level. For example, $\\sigma=3$  \n",
    "* Complete the function `simulate_accuracy_vs_stoptime` to simulate and compute corresponding average accuracies for a list of stopping times.\n",
    "* Plot accuracy versus stopping time using the pre-written codes \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fveZyW1yjp54"
   },
   "outputs": [],
   "source": [
    "sigma = 4.65  # standard deviation for observation noise\n",
    "num_sample = 200  # number of simulations to run for each stopping time\n",
    "# list of stopping times to play with\n",
    "stop_time_list = list(range(1,150,10))\n",
    "\n",
    "def simulate_accuracy_vs_stoptime(sigma, stop_time_list, num_sample=100):\n",
    "    \"\"\"\n",
    "    Calculate the average decision accuracy vs. stopping time by running repeated SPRT simulations\n",
    "    for each stop time \n",
    "\n",
    "    Args:\n",
    "        sigma (float): standard deviation for observation model \n",
    "        stop_list_list (list-like object): a list of stopping times to run over\n",
    "        num_sample (int): number of simulations to run per stopping time \n",
    "\n",
    "    Returns:\n",
    "        accuracy_list: a list of average accuracies corresponding to input `stop_time_list`\n",
    "        decisions_list: a list of decisions made in all trials\n",
    "    \"\"\"\n",
    "    accuracy_list = []\n",
    "    decisions_list = []\n",
    "    for stop_time in stop_time_list:\n",
    "        decision_list = []\n",
    "        ################################################################################\n",
    "        ## Insert your code here to:\n",
    "        ##      * Run `num_sample` repeated simulations, collect decision into `decision_list`\n",
    "        ##      * Calculate average decision accuracy as `accuracy`\n",
    "        ################################################################################\n",
    "        for i in range(num_sample):\n",
    "            # _, decision,_= ...\n",
    "            # append to container\n",
    "            pass \n",
    "        # accuracy = ...\n",
    "\n",
    "        if not 'accuracy' in locals():\n",
    "            raise NotImplementedError(\"function `simulate_accuracy_vs_stoptime` incomplete\")\n",
    "\n",
    "        accuracy_list.append(accuracy)\n",
    "        decisions_list.append(decision_list)\n",
    "\n",
    "    return accuracy_list, decisions_list\n",
    "\n",
    "################################################################################\n",
    "## Un-comment the following code  after completing this exercise\n",
    "################################################################################\n",
    "# simulate_and_plot_accuracy_vs_stoptime(sigma, stop_time_list, num_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cellView": "both",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 394
    },
    "colab_type": "text",
    "id": "cYzFe6HY8Zrd",
    "outputId": "34cd4e16-0b8e-4144-9c32-46eeef48bdd5"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W2D3_DecisionMaking/solutions/W2D3_Tutorial1_Solution_a5a89cc2.py)\n",
    "\n",
    "*Example output:*\n",
    "\n",
    "<img alt='Solution hint' align='left' width=520 height=386 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/tutorials/W2D3_DecisionMaking/static/W2D3_Tutorial1_Solution_a5a89cc2_0.png>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2B8sIcy7QfMo"
   },
   "source": [
    "\n",
    "**Suggestions** \n",
    "\n",
    "* Play with difference values of  noise level `sigma` and observe how that affects the curve. What does that mean?    *Hint*: you can click `...`>`Form`>`Hide code` to hide the code section if the slider is too far from the figure\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 388
    },
    "colab_type": "code",
    "id": "a5RhyLKjQWmk",
    "outputId": "6f68438d-b4da-451b-d371-5287c2bad37d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Interactive Demo: Accuracy vs. Stopping Time { run : \"auto\"}\n",
    "\n",
    "sigma = 5.5  #@param {type:\"slider\", min:0.05, max:10.0, step:0.05}\n",
    "num_sample = 200  # number of simulations to run for each stopping time\n",
    "# list of stopping times to play with\n",
    "stop_time_list = list(range(1,150,10))\n",
    "\n",
    "try:\n",
    "  simulate_and_plot_accuracy_vs_stoptime(sigma, stop_time_list, num_sample)\n",
    "except NotImplementedError:\n",
    "  print(\"Complete Exercise 2 first\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xWCWFOgMEwku"
   },
   "source": [
    "# Simulate DDM with fixed thresholds\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WEaSf2Cf3Pmm"
   },
   "source": [
    "Exercise 3\n",
    "---\n",
    "\n",
    "In this exercise, we will use thresholding as our stopping rule and observe the behavior of the DDM. \n",
    "\n",
    "With thresholding stopping rule, we define a desired error rate and will continue making measurements until that error rate is reached. Experimental evidence suggested that evidence accumulation and thresholding stopping strategy happens at neuronal level (see [this article](https://www.annualreviews.org/doi/full/10.1146/annurev.neuro.29.051605.113038) for further reading).\n",
    "\n",
    "* Complete the function `threshold_from_errorrate` to calculate the evidence threshold from desired error rate $\\alpha$ as described in the formulas below. The evidence thresholds $th_L$ and $th_R$ for $p_L$ and $p_R$ are opposite of each other as shown below, so you can just return the absolute value.\n",
    "$$\n",
    "\\begin{align}\n",
    " th_{L} &= \\log \\frac{\\alpha}{1-\\alpha} &= -th_{R} \\\\\n",
    " th_{R} &= \\log \\frac{1-\\alpha}{\\alpha} &= -th{_L}\\\\\n",
    " \\end{align}\n",
    " $$\n",
    "\n",
    "* Complete the function `simulate_SPRT_threshold` to simulate an SPRT with thresholding stopping rule given noise level and desired threshold \n",
    "\n",
    "* Run repeated simulations for a given noise level and a desired error rate visualize the DDM traces using our provided code \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "908KKBVUnKwk"
   },
   "outputs": [],
   "source": [
    "def threshold_from_errorrate(alpha):\n",
    "    \"\"\"\n",
    "    Calculate log likelihood ratio threshold from desired error rate `alpha`\n",
    "\n",
    "    Args:\n",
    "        alpha (float): in (0,1), the desired error rate\n",
    "\n",
    "    Return:\n",
    "        threshold: corresponding evidence threshold\n",
    "    \"\"\"\n",
    "    ################################################################################\n",
    "    ## Insert your code here to:    \n",
    "    ##      * calculate the evidence threshold from desired error rate\n",
    "    ################################################################################\n",
    "    raise NotImplementedError(\"function `threshold_from_errorrate` incomplete\")\n",
    "\n",
    "\n",
    "def simulate_SPRT_threshold(sigma, threshold , true_dist=1, batch_size=100):\n",
    "    \"\"\"\n",
    "    Simulate a Sequential Probability Ratio Test with thresholding stopping rule.\n",
    "    Two observation models are 1D Gaussian distributions N(1,sigma^2) and N(-1,sigma^2).\n",
    "\n",
    "    Args:\n",
    "        sigma (float): standard deviation \n",
    "        threshold (float): desired log likelihood ratio threshold to achieve before making decision\n",
    "        batch_size (int): generate and process data in batches instead of serially for speed. The size of each batch\n",
    "\n",
    "    Returns:\n",
    "        evidence_history (numpy vector): the history of cumulated evidence given generated data\n",
    "        decision (int): 1 for pR, 0 for pL \n",
    "        data (numpy vector): the generated sequences of data in this trial \n",
    "    \"\"\"\n",
    "    muL = -1.0\n",
    "    muR = 1.0 \n",
    "    \n",
    "    pL = stats.norm(muL, sigma) \n",
    "    pR = stats.norm(muR, sigma)\n",
    "\n",
    "    has_enough_data = False \n",
    "    \n",
    "    data = np.zeros(0)  \n",
    "    evidence_history = np.zeros(0)\n",
    "    current_evidence = 0.0\n",
    "    while not has_enough_data:\n",
    "        # generate a batch of data \n",
    "        if true_dist == 1:\n",
    "            data_batch = pR.rvs(size=batch_size)\n",
    "        else: \n",
    "            data_batch = pL.rvs(size=batch_size)\n",
    "\n",
    "        # individual log likelihood ratios\n",
    "        ll_batch = log_likelihood_ratio(data_batch, pL, pR)\n",
    "        # cumulated evidence for this batch\n",
    "        evidence_history_batch = np.cumsum(ll_batch) + current_evidence\n",
    "        # update the collection of all data\n",
    "        data = np.concatenate([ data, data_batch])\n",
    "        # update the collection of all cumulated evidence history\n",
    "        evidence_history = np.concatenate([evidence_history, evidence_history_batch])\n",
    "        current_evidence = evidence_history[-1]\n",
    "        \n",
    "        # check if we've got enough data\n",
    "        if np.abs(current_evidence) > threshold:\n",
    "            has_enough_data = True \n",
    "\n",
    "    # find earliest time to cross threshold\n",
    "    ################################################################################\n",
    "    ## Insert your code here to:    \n",
    "    ##      * Find the index of first data that crosses one of the thresholds\n",
    "    ##      and assign that to `id_crossing`\n",
    "    ##      Hint: use `np.argmax` on a vector of Bool numbers will give you the index of the \n",
    "    ##          first non-zero value\n",
    "    ################################################################################\n",
    "    \n",
    "    if id_crossing not in locals():\n",
    "        raise NotImplementedError(\"function `simulate_SPRT_threshold` incomplete\")\n",
    "\n",
    "    # discard redundant data because of  batching\n",
    "    if len(data)-1 > id_crossing:\n",
    "        data = data[:id_crossing + 1]\n",
    "        evidence_history = evidence_history[:id_crossing+1]\n",
    "\n",
    "    # Make decision \n",
    "    if evidence_history[-1] >0:\n",
    "        decision = 1\n",
    "    elif evidence_history[-1] <0:\n",
    "        decision = 0 \n",
    "    else: \n",
    "        decision = np.random.randint(2)\n",
    "\n",
    "    return evidence_history, decision, data\n",
    "\n",
    "\n",
    "sigma = 2.8  \n",
    "num_sample = 10\n",
    "log10_alpha = -6.5 #log10(alpha)\n",
    "alpha = np.power(10.0,log10_alpha)\n",
    "\n",
    "\n",
    "# Uncomment the line below to run the simulation and visualize the results\n",
    "# simulate_and_plot_SPRT_fixedthreshold(sigma, num_sample, alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cellView": "both",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 595
    },
    "colab_type": "text",
    "id": "HtTfLBrgje41",
    "outputId": "4823bc9c-b471-40f3-e6a6-36b538f20f06"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W2D3_DecisionMaking/solutions/W2D3_Tutorial1_Solution_490660b2.py)\n",
    "\n",
    "*Example output:*\n",
    "\n",
    "<img alt='Solution hint' align='left' width=513 height=387 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/tutorials/W2D3_DecisionMaking/static/W2D3_Tutorial1_Solution_490660b2_1.png>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4ViDRvaeRUVY"
   },
   "source": [
    "**Suggestion**\n",
    "\n",
    "* Play with difference values of `alpha` and `sigma` and observe how that affects the dynamics of Drift-Diffusion Model. *Hint*: you can click `...`>`Form`>`Hide code` to hide the code section if the slider is too far from the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 595
    },
    "colab_type": "code",
    "id": "ll6l1UVKRNqM",
    "outputId": "344cdc4d-f0bc-407a-c6fe-9b3cbde02b4c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#Trial\tTime\tCumulated Evidence\tDecision\n",
      "0\t103\t13.645931\t1\n",
      "1\t120\t13.908627\t1\n",
      "2\t291\t13.704891\t1\n",
      "3\t153\t13.597201\t1\n",
      "4\t153\t13.694892\t1\n",
      "5\t148\t13.719644\t1\n",
      "6\t183\t13.679953\t1\n",
      "7\t220\t13.633841\t1\n",
      "8\t137\t13.996508\t1\n",
      "9\t118\t13.612481\t1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Interactive Demo: Noise levels and thresholds { run : \"auto\"}\n",
    "sigma = 5  #@param {type:\"slider\", min:0.05, max:5.0, step:0.05}\n",
    "num_sample = 10\n",
    "log10_alpha = -5.9 #@param {type:\"slider\", min:-8, max:-0.1, step:0.1}\n",
    "alpha = np.power(10.0, log10_alpha)\n",
    "threshold = threshold_from_errorrate(alpha)\n",
    "# construct a simulation model\n",
    "num_sample = 10\n",
    "\n",
    "################################################################################\n",
    "## Un-comment the following code block after completing the exercise above\n",
    "################################################################################\n",
    "try:\n",
    "  simulate_and_plot_SPRT_fixedthreshold(sigma, num_sample, alpha)\n",
    "except NotImplementedError:\n",
    "  print(\"Finish exercise 3 first\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YsGQ3hmAFf8A"
   },
   "source": [
    "# Speed/Accuracy Tradeoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XXYN2pRKpbpQ"
   },
   "source": [
    "---\n",
    "### EXERCISE 4: \n",
    "\n",
    "The faster you make a decision (by allowing higher error rate $\\alpha$), the lower your accuracy will be. This is known as the speed/accuracy tradeoff. To illustrate the speed/accuracy under thresholding stopping rule, let's run some simulations under differenct thresholds and look at how average decision speed changes with average decision accuracy. \n",
    "\n",
    "* Complete the function `simulate_accuracy_vs_speed` to simulate and compute average accuracies vs. average decision speeds for a list of error rates.\n",
    "\n",
    "* We've set up a list of error rates. Run repeated simulations and collect average accuracy with average speed for each error rate in this list, and use our provided code to visualize the speed/accuracy tradeoff. You should see a negative correlation between speed and accuracy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "in2p3wvJ8B5N"
   },
   "outputs": [],
   "source": [
    "sigma = 3.95  \n",
    "num_repeats = 500  # number of simulations to run for each error rate\n",
    "alpha_list = np.power(10,list(range(-5,0)) + np.linspace(-0.9,-0.1,9).tolist())   # list of error rates\n",
    "\n",
    "threshold_list = list(map(threshold_from_errorrate, alpha_list))\n",
    "\n",
    "def simulate_accuracy_vs_speed(sigma, threshold_list, num_sample=100):\n",
    "    \"\"\"\n",
    "    Calculate the average decision accuracy vs. average decision speed by running repeated SPRT simulations\n",
    "    with thresholding stopping rule for each threshold\n",
    "\n",
    "    Args:\n",
    "        sigma (float): standard deviation for observation model \n",
    "        threshold_list (list-like object): a list of evidence thresholds to run over\n",
    "        num_sample (int): number of simulations to run per stopping time \n",
    "\n",
    "    Returns:\n",
    "        accuracy_list: a list of average accuracies corresponding to input `stop_time_list`\n",
    "        decision_speed_list: a list of average decision speeds\n",
    "    \"\"\"\n",
    "    decision_speed_list = []  # container for average decision speed for each alpha\n",
    "    accuracy_list = [] # container for decision accuracy for each alpha\n",
    "    for threshold in threshold_list:\n",
    "        decision_time_list = [] # container for decision time for each simulation\n",
    "        decision_list = [] # container for decision for every simulation\n",
    "        for i in range(num_repeats):\n",
    "            # run simulation and get decision of current simulation\n",
    "            ################################################################################\n",
    "            ## Insert your code here to:    \n",
    "            ##      * run a simulation of SPRT with thresholding using function `simulate_SPRT_threshold`\n",
    "            ##      * calculate decision time(number of data seen) from return values and assign that to `decision_time`\n",
    "            ################################################################################\n",
    "    \n",
    "            if 'decision_time' not in locals():\n",
    "                raise NotImplementedError(\"function `simulate_accuracy_vs_speed` incomplete\")\n",
    "            decision_list.append(decision)\n",
    "            decision_time_list.append(decision_time)\n",
    "        ################################################################################\n",
    "        ## Insert your code here to:    \n",
    "        ##      * Calculate decision speed given a list of decision times \n",
    "        ##      and assign that to variable `decision_speed`\n",
    "        ################################################################################\n",
    "\n",
    "        if 'decision_speed' not in locals():\n",
    "            raise NotImplementedError(\"function `simulate_accuracy_vs_speed` incomplete\")\n",
    "        decision_accuracy = sum(decision_list) / len(decision_list)\n",
    "        decision_speed_list.append(decision_speed)\n",
    "        accuracy_list.append(decision_accuracy)\n",
    "\n",
    "    return accuracy_list, decision_speed_list\n",
    "\n",
    "\n",
    "################################################################################\n",
    "## Un-comment the following code block after completing this exercise\n",
    "################################################################################\n",
    "# simulate_and_plot_speed_vs_accuracy(sigma, threshold_list, num_sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cellView": "both",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 412
    },
    "colab_type": "text",
    "id": "7LEMZkDhGwfK",
    "outputId": "32965159-1be2-48b1-cf54-c6b5e80bd710"
   },
   "source": [
    "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/master//tutorials/W2D3_DecisionMaking/solutions/W2D3_Tutorial1_Solution_be044152.py)\n",
    "\n",
    "*Example output:*\n",
    "\n",
    "<img alt='Solution hint' align='left' width=512 height=406 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/tutorials/W2D3_DecisionMaking/static/W2D3_Tutorial1_Solution_be044152_0.png>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fLNQFQeAVgM0"
   },
   "source": [
    "**Suggestions**\n",
    "\n",
    "* Play with difference values of  noise level `sigma` and observe how that affects the speed/accuracy tradeoff. *Hint*: you can click `...`>`Form`>`Hide code` to hide the code section if the slider is too far from the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 404
    },
    "colab_type": "code",
    "id": "TADBiJlkVO7Y",
    "outputId": "0d2da8bd-37ed-4a48-c7d4-a014c1f67586"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Interactive Cell { run : \"auto\" }\n",
    "sigma = 3.75  #@param {type:\"slider\", min:0.05, max:5.0, step:0.05}\n",
    "num_repeats = 500  # number of simulations to run for each error rate\n",
    "alpha_list = np.power(10,list(range(-5,0)) + np.linspace(-0.9,-0.1,9).tolist())   # list of error rates\n",
    "\n",
    "################################################################################\n",
    "## Un-comment the following code block after completing the exercise above\n",
    "################################################################################\n",
    "try:\n",
    "  threshold_list = list(map(threshold_from_errorrate, alpha_list))\n",
    "  accuracy_list, decision_speed_list = simulate_accuracy_vs_speed(sigma, threshold_list, num_sample=num_sample)\n",
    "# # Plotting\n",
    "  \n",
    "  fig, ax = plt.subplots()\n",
    "  ax.plot(decision_speed_list, accuracy_list, linestyle=\"--\", marker=\"o\")\n",
    "  ax.plot([0.0, 1.0], [0.5, 0.5], c='red')  # plot baseline for random choice\n",
    "  ax.set_xlabel(\"Average Decision Speed\")\n",
    "  ax.set_ylabel('Average Accuracy')\n",
    "  ax.set_title(\"Speed/Accuracy Tradeoff\")\n",
    "  ax.set_ylim(bottom=0.45)\n",
    "  plt.show()\n",
    "  \n",
    "except NotImplementedError:\n",
    "  print(\"Finish the functions above first.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0x-GVLx8FjIl"
   },
   "source": [
    "# Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mSyJa_35WOKM"
   },
   "source": [
    "Good job! By simulating Drift Diffusion Models to perform decision making, you have learnt how to \n",
    "\n",
    "1. Calculate individual sample evidence as the log likelihood ratio of two candidate models, accumulate evidence from new data points, and make decision based on current evidence in `Exercise 1`\n",
    "2. Run repeated simulations to get an estimate of decision accuraries in `Exercise 2`\n",
    "3. Implement the thresholding stopping rule where we can control our error rate by taking adequate amounts of data, and calculate the evidence threshold from desired error rate in `Exercise 3`\n",
    "4. Explore and gain intuition about the speed/accuracy tradeoff for perceptual decision making in `Exercise 4`"
   ]
  }
 ],
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