W2T2 Simulate Spiking Trials.ipynb

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    "colab": {
      "name": "W1T3 The Psychometric Function.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "<a href=\"https://colab.research.google.com/github/john-s-butler-dit/Basic-Introduction-to-Python/blob/master/W2T2%20Simulate%20Spiking%20Trials.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XFQ4m10G9ZbO"
      },
      "source": [
        "# Simulate Spiking Trials, Week 2 Tutorial 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lK8n73qF9ZbU"
      },
      "source": [
        "In this notebook we will illustrate simple spike train analysis for repeated trials."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "INuPpdSX9ZbV"
      },
      "source": [
        "### Libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mi0jlUXN9ZbV"
      },
      "source": [
        "# LIBRARY\n",
        "\n",
        "import numpy as np # vector manipulation\n",
        "from scipy.stats import norm # Psychometric Function\n",
        "from scipy.stats import poisson\n",
        "\n",
        "# THIS IS FOR PLOTTING\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt # side-stepping mpl backend\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8sltgvNI9ZbW"
      },
      "source": [
        "## Multiple Trials\n",
        "\n",
        "To simulate a single 1000ms trial we generate a matrix of 1000 time 100 trials random numbers between 0 and 1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "804W1Ijzr5c8"
      },
      "source": [
        "Samples=1000\n",
        "Trials=100\n",
        "Random_numbers=np.random.uniform(0,1,[Samples,Trials])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AznR66U2r5c9"
      },
      "source": [
        "The neuron we wish to simulate spikes at 30Hz. We assume that neurons spike in a Poisson fashion. \n",
        "We use the function __poisson.pmf__ from the __scipy.stats__ library to calculate the probability the neuron will fire."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UO2mTSzQr5c9"
      },
      "source": [
        "Spike_Rate=30\n",
        "Spike_Probability_Threshold=poisson.pmf(1, Spike_Rate/1000)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PQ1wiMVtr5c9"
      },
      "source": [
        "## Spikes\n",
        "A neuron will only fire if the probability is below the threshold.\n",
        "We set the neuron to have 0 spikes at all 1000 time points and 100 trials."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zQTRHlGK9ZbW"
      },
      "source": [
        "Spikes=np.zeros((1000,100))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ps1bO_Q8r5c-"
      },
      "source": [
        "Then check the threshold, and if it is less than the threshold the value is set to 1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JY7e7i_ur5c-"
      },
      "source": [
        "Spikes[Random_numbers<Spike_Probability_Threshold]=1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aw30pGZ0r5c-"
      },
      "source": [
        "## Raster Plot\n",
        "The raster plot shows the spike trains for each trial."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "Y9GM0bOnr5c-",
        "outputId": "2846cf49-7a1a-4697-be8c-00ae2a438d49"
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      "source": [
        "fig = plt.figure(figsize=(6,4)) # This setups the size of the figure\n",
        "plt.pcolor(Spikes.transpose(),cmap='gray')\n",
        "plt.xlabel('Time (ms)')\n",
        "plt.ylabel('Trials')\n",
        "plt.show() # This plots the figure"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MTA-98719ZbY"
      },
      "source": [
        "## Spikes per Trial\n",
        "To calculate the number of spikes per trial like before we just sum up the number of spikes. But do note we have to say which dimension we want to sum, 0 is the time dimension and 1 is the trial dimension.\n",
        "The plot below is a historgram of Spikes per trial."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "3FBc7dlu9ZbY",
        "outputId": "377645df-0052-44ca-be71-60a297f471f9"
      },
      "source": [
        "plt.hist(Spikes.sum(0))\n",
        "plt.xlabel('Spikes per Trial')\n",
        "plt.ylabel('Frequency')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2hqjY9lsr5dA"
      },
      "source": [
        "## Peri-Stimulus Time Histogram (PSTH)\n",
        "Another way to look at spiking is by time. Similar to above we sum the number of spikes at each time point and divide by the number or trials."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LxaFhh1Jr5dA",
        "outputId": "f80415ca-1f3b-40eb-939f-0ca59473f98b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "plt.plot(Spikes.sum(1)/Trials)\n",
        "plt.ylabel('Spikes per Trial per milisecond')\n",
        "plt.xlabel('times (ms)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UxQzLwCHr5dA"
      },
      "source": [
        "Another way of doing this is to use a moving average window to smooth the spike rate over a 100 ms."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LwCGdIRRr5dA",
        "outputId": "117babe5-9950-49a5-c376-57297bed08ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "plt.plot(np.convolve(Spikes.sum(1), np.ones(100)/10, mode='valid'))\n",
        "plt.xlabel('time (ms)')\n",
        "plt.ylabel('Spike Rate Hz')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FafDelkNw2MgQvESEK0+daAj+MXUezJ3RYukYZrY2JC0Tph5XguC32QiXz24FAHxySqx0REuGCkoloEw9ipwYCEWwfGcXatzOlI2yE/E6NT2jPxjWBH+VEvzDgTV7upNi4+UkKaejOGJEmHrcUoy+zcT/cO60UQBKw1RVKijBr8iJ3Z1amdybzz86422EE67bF8JAKIo6j0MJ/hInGmX4ghF866wj4pbLD/tCZ8qKHr3C1DPYg+e2i7QM8pAK6TRQgl+RE6Io1qSRmVfWFIJf+AbqvU4jK1MJ/tKkT7fvj6xO7X9xFVjjF/H5InpnsKxcp0N7MCU2f69klI1fkRMdfVrizqjazO2mon76Hr2pRp1k4+9Rgr8kEb12zSK3iABmwGErrOD/36tPxN+W7DIeAIM9eESil8oQj6E0fkVOrNrdBSB1HRUzhPDYqc8W6r1OeJxaSKcS/KWJ0WnL5DyLCB7hZC0Uo2o9uOGcKYa5aVDBbxNJgsrUI1CCX5E14UgUj36wEwBQm0VKvsdpg9NOhpnIrLGHorQQvXXrvMnnWWjcTdWZRXVZhTL1ZI8y9SiyRm6YbhZFkQoiQr3XaWj8dUrwlzyiXEO1K1lU/H3eadjfM4Cpo1N3XysEytSTPVa2XvQQ0RIiWklEa4nop/rySUS0mIg2E9Hfiai46oIia4bSML3O6zRKACiNv/QR56rarMVilRNHjanNOJzXKgbT+EXUkYrqiWGlqScAYA4zzwQwC8BcIjoVwC8B3MPMkwF0Avi6hWNQWIAQBseMTd9y0QyhOTpshAZd8Fe7HUadfkVpITR+r4nGXyoMpvETEZx2Uhq/hGWCnzX69LdO/Y8BzAHwD335XwBcYtUYhiu+YLik7ZFCGNxwzpSst3XojsBxjd64lPtASAn+UsQo0DbELlpWkkk4qdNuM23QUqlY6twlIjsRrQDQDuB1AFsAdDGz6L+3G8C4VNtXKtNvew3zHllW7GGkJLFaYzb06c7ChqqYhc/jtKvqnCWKr4QKtKVCmHJOStNsxWEjVQhQwtL5GzNHAMwiogYA/wcg4zRPIpoHYB4ATJgwwZoBljBvbWgv9hBSMiTBH9AE//kzxhjLlMZfuviDEdhtFFcIrdQgIvzzu2dibIM35TpyuWZFgcI5mbkLwHwApwFoICLxwBkPYE+KbR5g5tnMPLu5udlslbJENvH4TBqTlwKiYbqovZMNrM+220bEMn49ThsGlDZWkviCEVQ57UV34A7G1NG1RqVXMxw2m+rCJWFlVE+zrumDiLwAPg1gPbQHwBf01b4C4DmrxjAckUMl39t8qIgjSc2A3tTC48z+8onqkl+2y7oddqXxlyi+YLikzTyZ4nXZ4+6tSsdKU08LgL8QkR3aA+ZJZn6RiNYB+BsR/QLARwAesnAMww45VHJXp6+II0mNmDI7BwmjS4e8rcdpUzb+EkU0zBnu1HkcKjtcwsqonlXMfDwzH8fMM5j5Z/ryrcx8MjNPZubLmTm5W3MF0x+ImXd2HfYXcSSpiejREY4cUvXFZFuOvXY77AhHuaQjmSoVTfCXbihnptR5nVjwcQfabn6p2EPJiI37e9F280tYsavLkv2XrsemQvFJGn9foDQ1lJAQ/DkU52ITU48wGSmtv/Twh8JlofHLReaGg4Lx7iatkf3zK/Zasn8l+EsMv2SHLFVBGDZMPbk7/JwJGj8ALN/ZCQDY0tGHlRZpOors6A9EysLGLwv+4WDrF1FUDy/ahp2H8m/yVYK/xJA1/oESvUBFdIQjBxu/iOqRwwOFYBG9Uc+5ewEu/sOiIY5SkQ/8ZWLjlwvJDaXkSKFwSwlzWw/2pVkzN5TgLzF8uo3f5Shdh2coqo0rl85LZlE9dZ7MSzsrCosvFC4LG39zbayRjOxHK1Xke0vuG5wvlOAvMYTG31jlLH2Nfwgt92RTj1nJXyDmD1AUh12Hfdh12F8Wph45xt83DDR+OcvYbkFrSyX4Swxhf2yscpWsxi9s/LlckEZUj6Txy/bXqFRPReQLKIrDun09AICZ4+uLPJKh89mZY3HKpCYA8X60UkUofX/92smW7F8J/hJDZMU2VrlKVvCFowynnXLK5oxGk2cLsqmnvTcW3VtOpZq7/SFsO9hf7GFkhYh7P+2IkUUeydBx2m344dyjAAwPjV8ofbPT1B8aCkrwlxiGqafaiUC4NC/QcJRz7rN62YnjAWiF2QQNVTHB/+TSXcbr3oHyEfyX3rsIZ9/1drGHkRXiwWvWb3c4Uq2be4aDjV8ofSLiLd8owV9i+IIReJw2eJ0OBEpU4w9Fojnb92+9cDpW335enOCv9Tix6vbzAAD7ewaM5cFhEG+dKVs6NG0/OoxKA/f4QyACaj3D37kLxGaWwyGDNxCOwGknS+z7QAaCn4haTZaNMVtXMXR8QS2Kwu20lbRzN5esXUDzC9SaRPHUeZwYWePC/u6Y4C/Hjkl9JVp4z4xufwi1bkdW7TVLGdHqcziYEAdCUcu0fSAzjX8bET1BRFXSspetGlCl4wtG4HXa0VTlQpc/VJKlZMPRaE4x/INR53VinyT4h0OGZbZ0+0pf6Ai6/SFDWJYD1S477DZCzzAwIfYHrM2YzuTuXQ3gXQALiehIfVl5qAAliEiYaW3yIhJl7OsaGHyjAhOKMJwWaIH1Xif2d8fqE5WTqUcwHLRNQbc/VDb2fUCr2z9c+jtb/dtnIviZme8F8O8AXiCizyIWlafIM/3BCKrcDrQ2ahOs3V2lV6EzEmXYh1CuIRX1Xic6JY24HE09w0HbFPQMhMtK8APQBX/pm9tKQfATADDzIgDnAPghsuikpcgOfzCMKqcdjXqKeVcJmgZCkSicOUb1pKM6IUO0nEw9whnuC5Sm38aMctP4Ac2cOBw0/p6B4gv+C8QLZt4H4GwAcy0bUYUj6p/Xl7AjaijO3XQkZoiWon8jV2x6zsPjS3ZaVmo3FTsP+fDQwm1Zb1eOgl+ZejRSxmkR0fek12arvGPFgCodf1CrhljKgr/bHzKNzBkqiaGOwTIy9dhsACJaL+W3NrRj+x0XFuzYl973Hg72BfAvJ7UaseyZ4AuUR50emXqvE7sOl575NJG+QBg1FobRptP4a6W/7ye8r7VsRBVOf1Dz5leJCIQSFPw7D/vQ2pi6sXWuhBMEfzmZeuxF7Fl7sE/Lhg5mWQIkFOG40hrlwHDpxDUQ0qL7rCLlI4WZfypeE9El8vtM0OP//wpgNDRn8APM/FsimgngfwHUANgO4Epm7slh7GWJX+94VKoRCJEoY1+3H+Mbx+V934mmnbIy9SREQYlOUIXU/LOp/cTMCEWjcFlg0ismpXhPJRKNMgZC0bgkx3yT6eM8lzl3GMBNzDwdwKkAriOi6QAeBHAzMx8L4P8A/CCHfZctwUjU0LJK8SL1hyKIsjVp/ImCvlxMPcycMgu7kLOabDT+SJTBnFvPhVLG4yz9Np/iAV0Kgj9rmHkfMy/XX/cCWA9gHICpiPkHXgdwmVVjGI6EI2xEgBQyAuHdTR14fuVeLN/ZiY8P9KZcL6BnE7ud+b90EgW92c0ZiTL+sWx3Sd+4iQyEoilzEgrZDSqb2k8ilNZZZoJfKFWlHCosMva9FtxjgnTO3dWIafqTiWiV+AhabP9xmR6EiNoAHA9gMYC1AC4G8CyAywEklYTQt5kHYB4ATJgwIdNDDWuYWSuAZi+8xi+6XwlSmSAGwqJ4VP4vyms/MRHvfNyBWo8DvQNhU1PPY4t34Lbn1mIgFMFVp07M+xisIN059AUiljaikR3m2Zh6RLOdobTXLEVc+r0VDEdLts+AKBtt5fjSuY0vyscBiKgGwNMAbmTmHiL6GoDfEdF/AngeQNBsO2Z+AMADADB79uzSfTznkUhCyeJCRSBkowkKjd+Kaeico0dj+x0XIhCO4KhbXzXVysRsZDjZ/4Xg/8OXT8C9b2/G2r0xl5bP4to9cm2grAR/WAj+8tL4nbrCEohEAJRmqKrfwntMkPKsMvOOdH+Z7JyInNCE/mPM/Iy+3w3MfB4znwjgCQBb8vFFhhurd3fj1P9+E6+u2W8sE1EtIka+3uvAtoP9uPLBDywdy55O/+Ar6cTKxVonEERymJlN+lCfpifUZBGWmCuH+gJou/kltN38En716gZ86s75xsM5G4Tgr/M6kgrvWV0bXq4NlI2NX1yL5Sb43fbU11apMFBMwT9USAv+fwjAemb+tbR8lP7fBuBWaBE+Fcf6/T3Y3zOAV9fsM5YJLVYIPpHJumjzIUvbEB7qN510mSJmB24rL0oboanaFdeURSAE0kABbtwl2w4br+99ewu2H/LlFArYI9W1P5zwW1vdDUouepfNzC4YLlNTz7Cy8Q9DwQ/gdABXA5hDRCv0vwsAfImIPgawAcBeAH+ycAwli5h2ywqk0ctWv9lkrdqqgmVbOvqwrSPzzlCF0PgBoLWpCv9cux8b9vfE2chFVOSKndZnv5rFsOfic5EbmnQmlODIVeM/2BfAlo6+QdfbKZkKs9FyDSWkzDR+cU5LW+O3Pqono/kyEXkBTGDmjZnumJkXInUVz99mup9yRdjKI5ImLxxqwrkra9X+YMSS+tzn3L0gq/UNjd/CWuGAJiRX9gcx9zfv4qS2Rjz17U8AiJU+eHr5btz9xZmWjsGsoNpQBf/lJ47HU8t2G5/5c7Txn37HWwiEo4PmAciCPxsbf7maepzDwNTjD5aAxq9X41wB4FX9/Swiet6yEVUIhsYvqfxC4xclj+Vpdr8FtuBcGr3EtBFrBcI3PznJeL1yV7fxupBOXbPa+UMR/LUeJ3552XFY/7O5ePybpwDIThjLZLrd7hw1frGuFTWZiomh8UdKt1heLKrHunsskz3fDuBkAF0AwMwrAExKt4EiPf9Ythv3zt8MAHhlzX5DAAvBL9qtkTRhylUzTMfuzuwjhgql8Tfp1UkBYERN7LUs8Kz0e7y35SBuf2EdAGBcQ6w8hdksYNvBftzwxEcpbehabSMH7DaCzUbwuuxG2e3v/G0FtnT04YYnPsKOQ9k3Y393U0fKz3zBMJ75aA8mjawGkN1D5qXVmu/JVWYav/g+Pf4wrv3TEjyxZCfW7e3BD55amZPj3gqEPCh2B64QM3cnLCuNX2iY8v2nVsZp8MKJGI6mtqtaEf0ha6/Nte6MthkoQIwxEJ8ZLPd8lWcpVjZq+fIfFxuvxzZ4jNdmGv+Nf1+B51fuxZo95pVH+gNh1CZEIcn+g3PuXoDnV+7Fr17NzJIqP/AS8y9ktrRrD5LpY+sAAMEsnLv3va0F25Wfxq99n5W7u/D2xg789IW1+NajS/HUst05KUJWUIh7LBPBv5aIvgzATkRTiOh/ALxn2YjKmB2H+k3NB+IEJ4ZzyvRbUMddjmz41plHZLSNGEeVhfZHAHEt/+QHoay1WhmZ0VgVO77QzgEt9LUvED/7Wr9PE/ipZiA+veKqjJkmXV+VWVx5ppq7eEhddsK4rLaTKcV+EEPBZdfOwxY9oCEcYbT3aNFjuZrd8k1R4/gl/h3AMQACAB4H0A3gO5aNqEzpC4Rx1p1v44oH3k/6TDhzhP3aYdLkxB/Kv6lHtpePz7DaZiGyCgHEachyvRi55o2VDrrRdTEtf3xTTPDf+/YWnPJfbxjv+wNhYxyp7P++YHJ5Y6dJxNAIybyVjsTZ37q95jMNMZ5Rtdp3yeX3GlmT2UxwuCBKjWzVI6LCUTYEfqnUxTL8aBZGzmWy5wuZ+cfMfJL+dyuAz1k2ojKlV7cNb9ifXAdH3MiGc9dE409V5GsoyIK/sSpToROG3UaWh3PKPSAi0dg4ByRzhZWCXzZ9jayJ/21kM92OQzHzQGrBn5nGn6nLoj9hxrG/xzwBT/gjmqpdsFF2Gm3biCpMa6nDaUeOyHib4YAwG8r5DQKz2Xgx8IcicNltlhbIy2TPt2S4TJGGdIJ7/oZ2rfBYQjgnI7c6K5kim0oSzQyJTVEEvmAEVU57quY8liC3KwyEokZJCysFvzzNTlWJdF+3H997coXxPp3gr0oQ/GYP99/rDv/BSEz6+t8FW03Xk8NIXQ5bVj6Rbn8IJ0xoyHj94YI4l4mJdEDMoV1s/MGIJUUQZVLunYjO1+3544jod6hY14UAACAASURBVNLfn6GVXFZkwUAax9rfl+7C959aaQhiIdguPWG8oXnmEno5GLLGX+91xtn5D/vMs3l9gWTt1Sr+36XHAgB6dQ03GmV0+oKG+cFK5654qNz5heMw5+hROGPySIxKcIDf9OTKuBlc34D5beELhpP6Cad6cGZibkg09cgZxjLtPQF4nVpTH7fDbuSOZEJ/IGJpB6hi4XXaU2Yj5xJVZQWdviAaMvT35Eq6x8peAEsBDABYJv09D+Azlo6qDMnEVCNS+4XgH1njxms3nqltb4F2G5Y1fq8Tt1wwDQ9eMxsAUhaHO+wLJmmvVvGlkydg3plHGL9LR18AgXAUk0fVALBW4x8IRXDypCZcPrsVtR4nHv3GKbj9c8ckrSNjVmKZmbG/eyDjh2UmD3hR2O3Rr59iLDOboe087MOEpioQEVwOGw5naMqIRBnBSNTSBKJiIRocAcARepiroKtEbPzivFlJuiJtK5n5LwAmM/NfpL9nmLnT0lGVIWY39OmT4+2n23WNQ7btCVv6UDT+r/35Q6PYmOwIlDVmcZNPGKFdcLv0wm3d/hDabn4Jf160DaFIFK+vO2DkGRSCeq8TgXAUA6GIEW53RLN2w37r0aU57/eqBxcbXbDMCISTOyDJN+M/lu2OO0/1Xid8gWSN/543NqE/mHnp5UzCdsXMos4b08h7TY69p8tvOO07egN4YeVevLHuwKD7L0StmGIiIsYSH8ZbO/rx6AcZ1Z+0lF2H/RjfUCTBL9FGRP8gonVEtFX8WTqqMsRMY7/3yhNRLV18wuFUJ02xheAfisb/1oZ24/XibYeM18LU879XnWiYHkTootD493VrD4DHl+w0hNKs1sacx5It4ibt8YfQp9v6G/Rluw5nXlU0kYWbD6b9fCAUSXJgzxhXb7x+adXeOAdtlctuKrTFw+pbZ2UWLptJmWZxnYyp9+CqU7VeFWbF43zBcFwOBBBTLtJRqMitYiHMblUuO17/7pn4xSUzMGOcluvw5NJdxRwamDVz5oiazIItciUTwf8nAPdBs+ufDa2P7qNWDmq4MH9juxEWNhiJgrul3mM43QQdejVK2ZnosNvgsFFWlRUzRZh6Tp7UZCzzuuwYWePGTj1aRQTU2IgM08rM1noUCvFbPPPRHmzSa/Gbabf5Jmii8QPA6DrNzj+ixh1nK/a67KamnnCEccTI6rjw0HT8bcnggmfnYR88Thuaa9z45JRmAOa+gUAomlRoLpPqokZZYIuzs4uFeKB5XQ5MGV0b19DH6mi1dATDUTy0cBsiUbaktalMJt/Sy8xvAiC9Fv/tAArXIbqE+eqfPsScDIucJZpqvn/eUQAQV61RlCGuSzjpHqfdiO3NJ7EKjPGmm3ENHuzrGYhbx24j43Uh0/hFbPsdr2zAL15aDwA4a2qz5cf1BSOmre9+8JmjAQBjG7xGbP4XThyPapfD1NQTikRTZr+e3NaEC44dg8Yqp/HwfeSDHegcpEx2R28Ao+s8cfZqM8EfjESNtP9zjh6Vcr1EDMFfthq/9r1q3LHvd/3ZUwAg4we0FTz6wQ7jGi8FwR/Qa+dvIqLriejzAGosHVUZImv8v//y8bjsxPFJ67T3DMDlsCVpmm6HzRKNP1VfVbnXrzBf2G0xjd+sXLFVyFmzgiOba3D92ZMt9TV0+0OmN9+lx2tZsDbSBOvRY2px1+UzNY3fxNQTinDKCpdPfvs03HvlifjotvNw+2djjmOzekDx+4waD990gj8Qihjn6qFrT8KEpqqMBL8/qJ3ncrXxiwe2fH7nzhiDKaNqilqvJ8rxwRZWkskd/B0AVQBuAHAitBr711g5qOGAnJ7/hwzir2WNXy76JbP9kC/O5i9w2AmPfrAzh1EmI1/XqWqu13udhklA2JxX7e42oh4KKfhbGpI1MLfTBqfdhkiUU+YbZMrn711kvL7gt++i7eaXcNdrG+EPmTtkbTaCQ5/9+KXErCqXHYu3HcZVDy6OW1/T+Af/veSOYoMJ51AkapwzISD+7bHlAIAr7n8fv3x1AwCh8ceOXeN24NkVeweNhhKhx1ZXYC0W4pwlzqzrvc6ilqiQkyiLLviZ+UNm7mPm3cz8VWgN0idbOqphgKzB3/na4MW1RH2X/7xoOma1xhJjfn7JjLj1rjZpID5Wf1DkWo1SfpjID6BwJAobIUlzrjfR+AFgS7vmzyikqcdptyVpnh6n3TCfhKJDM4F9JDV0WafX3BGJVKlq57gcNgTDUfQOhFCrPxxG62UREp3GmnY++MyktcmLc6dlZo7RZhGxvsyCQDiCxdsO4763tyAaZYQiHPeQPrqlFoDWxCUdhagHX0zslPzbAcDoeo8RzFAMwtK1nPhQyjfpErjqiOgWIvo9EZ1HGtcD2Azgi5aOahjgT5jWt/ckp4DLdPtDcNgIXzu9LS55JzE78hLdlCAj7LO5FiWzSceTxx2MsKk2KgQ/M8etb8wQCuwAu/C4lrj3bofNePjkq1CbWbhsKq3LadcEv2wOam0yn8WF05h6ZIjI8B9ko/HLORVy72TRZF0u7XvutNEZ7b8QRcKKiVAWEs/vhKYq7OnyF8XcE4pE8fSyPcb7Ymr8jwA4CsBqAN8AMB+atv95Zr54sB0TUSsRzdfDQNcS0Xf05bOI6AO9FeNSIjo5D9+j4CSmzX/yV/PTri+ERGLGZuLNZXaziWXpsn9TEYpE0S+FCMo3fSAcMZpPy9R6nIhEGf5QJC68UJh6zLaxks/NHBv3Xqtjomv8eUjiYmbTaJdUSTSi/IF2TjUTzdgU5rtghqYeIL29XiYcYeP7y9fTDinp7q317cZYE/c/WGRPIZp9F5NjxmpRaROb4hO4xjZ4EYowDg0yI7KC97ccwpLtsQzsomn8AI5g5muZ+X4AXwIwHcBn9EYsmRAGcBMzTwdwKoDriGg6gF8B+CkzzwJwm/5+2JGoIQ4WZ5/KWZgYPmYWTmbE8ucQ2bOvawBRBu649FhMa6mLqzne7Q+ZXmBuqS+pXJCsuwg2fgA4c2ozvnZ6rPcPERka71BNPYB27hKFrdthw/ETzPMVXHYbAuEoegbCxjmtdpuXN8jU1ANkLviDksYPAO/dPAcAjHBXANirmyzk60n4LAbbf6F6LhSLr53ehhW3fRpnTBkZt1xE+VjR7W4wEgvvJfZvyDfp7mDj6mDmCIDdzJzeniHBzPuYebn+uhfAegDjoDVxqdNXq4dWGmLYITT+TMrWLt/ZiZdW7TMVsplo/KL3bi6RPaLn6oQRVZjYVBWnFfakEPxOoz1dNM7U06XX7ym04Dc7Zj5NPV/+4wf49qPL4palK5HsdtjQ5QvFxVsn1uIRhCNsWmbbDI/TBqedMjL1yH6WMXUeOO0U18hFvDbT+O/650Zc8/CSlG0s/+Pp1dp4ihjTbiVEhAaTarQi2idRCBeCxLpTNouz49M9VmYSkcjvJwBe/T0BYGauS71pPETUBuB4AIsB3AjgNSK6C9qD5xMptpkHYB4ATJgwIdNDFYwBQ/C7BnWWva1nzpo5brPR+HOJ5e/yB/VxujGqzo33tsScjz3+sGGqiDue1JDaFyf4NYFUjAbcolKpSKDKp6lnueTgFbjTmDmcdptR3bHGnZz+H4my4TAPRaIZ+0REXH6PP73gkU09gCYkRtV6sKcr2TEpX0/Vukb78YE+fHygDx29gSQTVa8USlquGn8qhL8k0YxbCORIq59ffEyaNfNDulo9dmau0/9qmdkhvc5G6NcAeBrAjczcA+BfAXyXmVsBfBfAQymO/wAzz2bm2c3N1ifsZIsQwokp8YmEIlG8vGY/xjd6TWP3EzV8M3uwJ0eNv3cgZEStuB021Hud6A2EjRDIVOYnl2TqkRvACMFfDI1fIB6e4uETjkZxqC8QJ7Aywe2wYWx9fKjoXZfPxM3naw7WaJoIKpfDZtQ8qpLCOQWLtx7Cmj1at1LNLJO59lYnhdKmIpRg6gFgem0B8YI/8WFmZp5cuj1WhqtcM3dTIc6hFW1OB0PW+K8+rc3y41l6BxORE5rQf4yZn9EXfwWAeP0UtEbuww5hAqkdpPjWU0t3Y3N7H9pGVJt+7shgSperxj/n7gV4aOE2ANrDo97rBDPQqxf5OuwLosGbPOV1SmYUXzBiND4XM5tiOP2O10Ngj9Hr5QhhGgwzTvzFGzjrzrcz3lc4EkUwEsX4hOSwCU1Vhh08nT+l2x8yblShFcumni8/uBgX/c9CbOno06J6MjT1AFost1mteJlQNFnwm+V/APFRPYmmm0RFgpnx1T9/aLy32txQanid2jk0y8C2GisrzZphmeAnLdzgIQDrmfnX0kd7AZylv54DYJNVY7ASEWFTN4jGL4TlPVfMMv2ciLDkR+ek3UeuGr+o/QPENH5AywwdCEXQ0Rswbbkoa/z9gYhRh35Tex/sNsLoDBuz55O5M1rw7g/PxtlHaaGtsYeTdsMMJixl9nUPgBm49IRxePybsdLGrU1e4zdKF0Elnwch8M3MIgd6BnRTT+YCdFyDF7u70jf9DoU5aRaRqlS2PDtz2G1xORuJikSp9JwtFsIUVhSNX//t3/nB2QU5npUa/+nQsnzn6KGbK4joAgDfBHA3Ea0E8N/Q7fjFJBJl/PLVDXERL+l48N2tuP7xjwDEa/yyoBX4globteY0wnLUIPVBhMb/m9dzf0YKjR8A3t7YbnzXVpOQRSEs/KEI3lh/ANVuh2HSGtvgsbQlXDrkscqmHkF7b2axB7skh/dpR8RKY4+u9cQEfxo7r6xFC4FvluXao88MsvGJtDZ5sbdrAM8s341bn11tGlMeNtH4vSmcy4lmOVnrT2zMkpibUmmIc2lWbM9qhOA3y1S3goyuSCKaSETn6q+9RFQ72DbMvJCZiZmPY+ZZ+t/L+vITmXkmM5/CzMsG25fVLN/Zifve3oJbn10z6LrMbBRSAoCvfCLmsF24uSNpfX8wnJGT7J4rZuLfPnWk6WciAmHJ9sMIZ9h1KnHq6LLbcNx4zVzy0c4uHOqLOX0TEdrkxv2aHXtMXUwgWt0gIlMckqlHcMfLGzLaVkQ6tTZqTUqumN2Ka06bCJuNMLJW+60zNatVGQW/HDh2XHzV0m5/KOMELsGEpipEoozvPbkSj36wE9sOJld/DYazMfUkBA9IZrqBhGtEFniZlpEuJ7Q8G+CgiQJnNaFIFESZmX7zwaBXJBF9E8A/ANyvLxoP4FkrB1VoDuhZt+lKsgqTQqJAGF3nwYafzwVgXh/erN+qGZ8/fjx+OPdo08/k2j49Kdr7JZIYmWCzEcbUe3DKpCbs6vQZNmozR634HbZ0aLXbv/7JSYbtu1QEvyvB1AMABwbR+A/3B8HM2HnYB4eN0KI7d3/5hePws4u10hlmReESkXshi3NLRHjh38+IW6+9J6A7YjO/mRNnYGbXlFyyQZBKuUg8v/I17k+o/S+/v+X8aZkNuIxwO+xoqfNgV4Yz/3wS0GeGheplnYkqch00s00PADDzJgCjrBxUoRFP+KZqc3PMK6v3YcqPX8Hm9t6kGGuP0w6P047RdW5TU1Gmgj8d8s2bSXVFAJj7m3dMl7c2VWHXYX+sxLKJ4HfZtfFu0XsNjG/0Go0hUjmpC40Yt2yXXrT5UMp0+7c2HMAJP38dj3ywA3u6/GhJYbISiViZ5GcASNtZ6/53tiIczTyOHwAmJbQDTBRCUb0tollhPcG0lljQnTshMkc0cQGAbz+6PO6z/kBlm3oAYHxTFXYPocFPrgTD0YJmxGeSHhZg5qB4EhGRA0DxapdagKiJn0rjf2XNfgDA6j3dmN4SP50XN2C122HqFPIFw0ZiyFC4+fyjcccrGzIW/PINLlPncaIvEI6VWDa52IRQbe/RH4hVLvzs4hlYvqMTnz5mdC7DzztjdL/I3oTYda3rVLIw3n5QE6Dr9vbAF4wY8fdmvHbjmWisTv05QbsXfvLZ6WhMkeg1vaXOyJ7NJvy1pd6LSSOrse2gNtvqTZjhdfQFEImyMVsRzBzfgD98+QSMrnNjyqhazPzZP7M+trh+CxFHXqo0VbkMhaeQBMPJTXOsJJMjLSCiH0FL4Po0tBDMF6wdVn54ZfU+/OLFdXhm+e606wlhahbV0B8I4/mVWnIxgVLWSnfphbtkmBnzN3bkJRFm9kStfMCiQVoGDkaVy47+YNj4rmYXmzAjdPQFUON2wGG3YdLIalx24viMe8daTXOtG26HzeiAJmLyUzkoxXn724e7EAinL6Nw1JhajKpN7WQTph4RYWTGyZOajN642Zh6AOCCY8cYr+VaSd2+EL77d61iSqJJyGYjXHhcC2a3NcVVFc2mo5Roy3ns+IZB1ixf6r1ObGrvw31vb8m5Gm4umPltrCSTI90MoANasbZvAXiZmX9s6ajyxNIdnfjL+9tx8zOr09ZtF0Ih0eYJAD95fq3xmsFxjh85rd/lsCWlwItMynz4a4QJQCQGZUprkxenSK0Vq9z2uFh+M41fOAAP9wctrxKYK0Saz2K3XpGyXneAp6qzIs+UPth6aEja1Y8vmIYatwNj6pMfDl89vQ1nTm2Gx2lHWL/msjH1AJrWL5BnkW9/3I73tmjCOVVRuEQSv6f8UElEZDCXih+nGIiH5i9f3YDthwpn6+8ZCKFmkNDwfJLJkW5n5tsA/BEAiMhORI8x85XWDm3o/OdF0zFpZDVufXYNDvQOxN1QMj0mtecFH0uFr5hjESEA8NZNnzJeu+y2pHobwhH8pZOHXnJiRI0b01rqDGGSKT+7eEacZlqlC/V0BdfkCBGrqwQOhSqXw/geogF7qmblsuAf6rR67owWzJ3RYvrZT/ROWr9542NjWbZlrBskjd1vUjIDiH3fwUjU+O+98kQAwP+8uQl3v/5x3G+xp9OHuceMMRL2KhFZ0dFqUxXGp7XrsL+gD9xMrshWIroFAIjIBS0Td9gkXYkfc2eap7dZ0xGBrOEHwlFDwwTiIymcJqaefPeoddoJr687gCN/9HLaGczbG9tTfib8DaJ5jJkAlL+XWS2fUqHKZUenXjhOCEszU8/8je14ZvmeuGVWT6vlJibOLKd8sjnNZ1IdFRj8gSx8IKmuPaHZin1Go4zdnX5MGFG52j4Q/7tm6k/LB7s6fabJlFaRydX/NQDH6sL/RQAL9IbrwwLRzixdGGRM8Cevc1DKCPUFIzjUH3sQyEJTdGWSyXePWiGsRK38VNzzekzbTLRTJqbhm9mfXVKGZ6nY9M2octljGr8uyMxMPb99I1lPsbqLWKJSkA3VUhNwX4peCoOVzfi/6z6B+68+MWV4YGIJ6I6+AALhKFoLKHxKkQuPbTH6KhdK8DMzegfCGc/i8kG6DlwnENEJ0Kpq/hbAFdA0/QX68mGBuAFfWrXXNNSvZyCEjw9oDkIzjV8W5v5gOOXF4HLYkpzD6WLlc0EW0unSyg/2xR5Wifleh/vjk1PMxkZEhkmoVG38gCb4hfmjXq85ZOYDMZsbWR1BIRc4y9bUI4dgyud5sOJtMi31XnzmmNT2fKHZvrhKC1wwktoq2L4PAE3VLtx8gZZPk2nOzFARciJdRdh8k+6KvFv6uwNAJ7RmLHcDuMv6oeUHEUP/7Iq9+Mt725M+/8FTK43XiVp0orO2LxBJWTLXzLmbLmQyF2TNMV16vVwm+ugx8UnWJ08aEfc+1diq3MNB8DsMn4cw6S3YmJw9LUwt/yElyFku+F25m3rkJDK5Nrzo25xNpE4qxHn9zRubsKWjzwj/zdRpXM7U6qG+2VZ8zRXhC8zHec2UdGWZz07zN6dgIxwicvLUfpO+uBv2x5y3iVp0Yr2WnoEQuv0hXDJrLLbfcWHcZ2bOXfE+Xz1qZcHvC6XWRsTMY0ydJ0mDm9XagG3/7wLjfSpTgIhEKWXBL5tTxjdqzco7THojRJhxxuSR+NdPHWmkxFtt6pFr4mRr6qmvcmL7HRfiouNa4rTOQDiKGePqsPEX5w95fPJ5DUWiRkXKVJ3EKgm5SGEhEEX/SkLjJ6Kr9P/fM/sr2AiHiCwcHnhna9Lncm2MxHKsiaabxxfvxM7DPvMa9ibO3Xxr/PJYU2VZyuasVBFAmaSFi1XkmPBSo0q6UapcdkweVYttB/sx9dZXcNWDi426Rn4pe1poVVZr/HE2/hyPJZreC4LhaN6uJfka9gcjhtKTquZPJWG3Eew2Kpzg1zX+QnY8S3ckEcdUm+JvWDDYjTJ1tPZVvjh7PHyhSJwzVGj8U0fXoEbShFI1L0kl+PM1hZMFSCpTz77uWNRROE0/2uevPx2/uGRGys+/f95RuPSEcZhzdOlW55CFq9dlN8pHB8NRLNx8EId0x7xcNkM4RS137g4hqkcgBL+4JvOZ5DOi2oUTJmiJWr5gxDBzVlrXrVS47MmmW6sohsafcl6nN1kHM/+0YKOxgETtNhrluMiW3oEwjp/QgLaR1WDWtPxY/XvtxF939mQ8vngnFm87DMA8lM5pt6FT78Mqt90Tn+UDWVjtSVGzXc4zCKfpR3vc+AajWqcZlxw/Dpfo0Q2lihzZUu1yJD2QD/UF0R8IwxcMG2WLxUM4X+a3TMY2FI0/EmX0ByOocTsQjEQH7fiWKUSEn35uBj77+4VYv68Hnf1B2G1k+QNxuGCmyOUbZsbm9j58sFVLyiukjX/Qq4iIjoAW1XMqtACJ96G1Tky2m5QodR6HYSsNRaNw22I3Ze9ACA1VLsNs4AtGYoJfcrrIwttM8IsywQs3H8RZU7VWkfkO55RNPf/30R5ccVJyYtjerpgfI12WZjkg3yhVLnuS4P/R/63Gil1dxudATAhbfZPJgr8xR3NZnRRyWeN2aIW88jhuod2LMuO1bkfBqkOWOi5Hss8u3zy0cFtcifdCdrbL5Cp6HMCTAFoAjIVWq+cJKweVb9646SzjdeJT3B+KwOu0o0o35chx0wPSFEwOpTSrtimycw9IDuS8h3NK+0llxenSE5rmf/9T+K/PH5uX45Yq8tTY67LDndAMRQh9IHbOxPm3Oj9BNplMHpWbZdTomKbb+YOR/BbySryOlZknhuazs7ZWj7AgCApVix/ITPBXMfMjzBzW/x4FMGibGCJqJaL5RLSOiNYS0Xf05X+XOnJtJ6IVQ/0SgyEX3EoU/IFwFG6nzbTRciqN3yyGXpQt/uE/VuFVvZqnOJYVpp5U+QQ9/hCIgIlNVQUt+lQM4jX+2OR1nElIovhc+G2sjlbKh6MuMckq34W8qhOqxqqInhiF0PgTkUtyWE0mV9ErRHQzEbXpnbh+COBlImoioqY024UB3MTM06GZia4jounMfIXoyAWt/MMzafaRN4QwSDyZgVAUHofdVPAbGr/DHnfDnT8j2YRSI91E//2yNn073B+Ew0ZxjuGhIGsEqQR/tz+EOo+zIhply4LfbiOcPKkJl8waiweuOTFp3Rp3vN/GasGfD+05UfCHIvmL6gHiM4TN3lcymsZvbX8COal+ZI0bnzqq2dLjyWQikb6o//9WwvJ/gWbzN+3Rxsz7AOzTX/cS0XoA4wCsA4xm7F+E1nDdcr736am46amVCEnTt0A4gv5AGG6nDV5nsqnHCLNy2gxTz6+/ONO03rssaIWA3nnYh3GN3rgG10NBNvWkE/ylHHufT4RNVPy8bocdv/mX4wFoGZhyA3ZhLzcEv8Vhqh5H/gV/vmu2JzaiqZTrJhOcDsLOw34ws2V+j2AkilmtDXj2utMt2X86Br2KmHlSmr+MGnMSURu00g+LpcWfBHBA7+hlOUJoBiOxp/hRt76K3kAYHqfd0HbkMEm/niTlcdpxzFitAcvoNI3RRcNtUd1wT5c/r4WX4jJ3QxHTqIOegTDqSriwWj4RGr9Z7fzExDUh1I4br53HERZXoBSKQGLmdDbUJdr4LW7WoQR/jDV7erB+Xw/+tGi7ZccIhiMFbb4ik1JCENFJAHYx8379/TUALgOwA1qp5sOptk3YTw00k86NzNwjffQlpHESE9E8APMAYMKEoZc1FlNks2YrbkfMxi8X+RIRMmPrvfj6GZNwwsQGnDgxtXXruevOwGX3vYeIPofzBSJGbHk+qNVNRnYbIRJldPtDaE7Yf38gnGS7LVfETTO6Lvk3bm30YqXk3BVC9N4rT8DHB/pwRHON5eN77cYzTWv2Z4q4JoUyEsizczcRJfiTkcOj800gHM2bGThb0l1F9wMIAgARnQmtXs9fAXQDeCCTnRORE5rQf4yZn5GWOwBcCuDvqbZl5geYeTYzz25uHrrtS2iHd7yyIalmj8dpN+K8d3f68OdF2/DEkp2487WNGFnjhtdlh81GaYU+oHVuOvWIEYaJaCAcyWuIVuKNaWbuyUeP3+FCt+4MazbR+BN75tr16XpLvdcIt7Wao8bUDkmYOvUqqQNhLbEwn5m7ZpiZMCudP7+3PW0J9KGQ7/DcbEh3VLuk1V8B4AFmfpqZ/xPA5MF2rNvwHwKwnpl/nfDxuQA2MHP6noh5RGhK7246iJ88vzYuQ9ftsBlx/L96dSNuf2EdbnlmNQBkrbG7nTbDKRwI5ffEzpk2Ci31Hnzv01MBwLQNZL56/A4HTp7UhFG1btx47pSkz86ZNgrjGry44ZwpaKn3YPIo6zV8K/A67fAHo7EKjnkWFN84Y1LcsRQa1519pPF6yfaMjBtZEwhH4yqxFpJ0EsJORA5mDgM4B7rZJYPtBKcDuBrAailk80fM/DI0x3BBcwESp8hydI/bYUuKARd8VxeymeJx2C3T+EfWuPH+Ledg2Y5OAOYav7+CNP4RNW4s+fG5pp99ckozFt2sxQ18L8tzWEp4nDb4QxHD3JPvh/qtF01HfzCMJ5bswsiayu28lcgPPnM0/jB/C4D46Jt8UugG6zLprqInoNXePwjAD+BdACCiydDMPWlh5oUATN3hzHxt1iMdIolT5PsXxBKP3U57yidva1N2zlm302bU3si3xi8woj1M4n77GvihkwAAEr1JREFUK0jwVwIepx2BUKyImhXnVph4Jo4oTJvB4YZV5ZkD4UjRSmSkq9XzX0T0JrSM3X9yzDZiA/DvhRhcPhmV4AD8tdSlqtbtgN1GcNoJoYT6Nom24sEQGj8zI5BnjV/QojsMRTN3GX8wYvgrFMMfr9MOfyhihBlbkV373XOn4pixdfjklJF53/dw5sFrZuMbf11qWSeuoJ48WgzSSghm/sBk2cdm65Y6o00cgAKhQZuVMc42tV/T+KNYubsbUbamJky124GRNS7sSog4WL+vB8FIVGn8ZYTHacdAnMaf/4e612XHxbNKuyBfMTipTQvmsErwByx21qejvHP6JdJlsopQPzNbXrY2OFFF8ZI/LAJgXeGllnpvUmOZ83/7LgCtKJ2iPIhp/KpefqGp9TjgsJFR3jvfFFPjrxjBn458xi8nJmxZFa5V7bbDl6IZy/jGyu6bWk54XHb4Q1HDuasKqRUOm40wrtGbNLPOB5EoIxxluOzFOZ9K8AN5TaJIzBi1qrlClcsR135RbhM5QkVnlA0ehw2BUAT9uo2/UkJ1S4UJTVV4cdU+vLpmX173azRpUhq/9bz+3TNx7rRYR6kXrj8DP/nsdDSmSN+/YnZr1sdorIrfl1XJQl5XvMa/u1Nz9E4eVYOZaRqsKIYXXle8qUf5bwqLUAq//ejyvO5XRP4pG38BmDK6Ftd+Ipawcuz4enz19Ekp15+bQyMTj/QEv2HO5LS1fYZCldOObYf6sWZPN9p7B7CrU5uO/vKyYyuiMmeloCVwyXH8SvAXEqv60hRb46+4eaPcUCWRKpc9riyz05b9SZHzAawMq6x2O8AMXPQ/CwEA//V5rX/uWJNa9IrhSyGiehSFR9QMUxp/gUgXpbPs1k/HvXekeUikQtb4raxvnujk6w9oNuBiFX1SWIMm+KPwB8Mgir++FMOXgKHxl17JhrJECH6zsLhEYZpudpCKOI2/gCdVZCIrjbC88Di1TlC/e2szAKieuAXGnsOsPxOUjb/AHDGyBudNH43/vtS8H+3dl880XjtyOOly0xUrte/ELmCH+oNwO2x5a/qiKA1U4bTi8uMLpgHIf/5EsW38FSf4vS47HrhmdspMxctOHI9pLXUAMGQhamV98+PGN8RVEASU468cUXH7xWVMvQc/nHsU+oMR9AXCg2+QIYapR2n8pYM4F9EhluWrs7ixReKDxawjl2J4o5qjFB+RELnXpDZWroh7tVjVOZXgN0HY9cxq92SD1TdtYh2hxEbyiuHPXMmkJ5shFYVD9OqQkySHiqHxF6kevxL8Jgif7lA771jd0FvMKISDKLGyqGL443bYcfwELSFvXB77NysyR/TrDuVRsVIafwny4wunYeKIKsPWny1fOW0iTpnUhBqLI2xEaF+xHESKwnD7Z4/B0WNqMWNcfbGHUpGI6L58KlbBiB7VU4KNWCqWEyc2YcEPzs55+59ePCOPo0mNR58muh129CKs7MFlyszWBrx645nFHkbF4rTnX+MXDxFHkaLwLHvcEFErEc0nonVEtJaIviN99u9EtEFf/iurxlDuNOnF2Ka11AIATpzYWMzhKBRliRWCP6KbkXNJEs0HVmr8YQA3MfNyIqoFsIyIXgcwGsDFAGYyc4CIRqXdiyIlR4+pw4PXzMZpR47AB1sP4eRJTcUekkJRdlhh6gnrD5FccoXygWWCn5n3Adinv+4lovUAxgH4JoA7mDmgf9Zu1RgqgXOnjwYAnDNtdJFHolCUJ1aaenKpDpAPCvK4IaI2AMcDWAxgKoBPEtFiIlpARCel2GYeES0loqUdHR2FGKZCoVAkYYXgD0d1jb9cE7iIqAbA0wBuZOYeaLOMJgCnAvgBgCfJpAAJMz/AzLOZeXZzszU17RUKhWIwrDD1lK1zFwCIyAlN6D/GzM/oi3cDeIY1lgCIAhhp5TgUCoUiV/Kl8S/b0YkzfvkW3t7YjrBh6ikzjV/X4h8CsJ6Zfy199CyAs/V1pgJwATho1TgUCoViKAjhHB6ixr92bzd2d/rxwsp9iOimnmLVVLTycXM6gKsBzCGiFfrfBQAeBnAEEa0B8DcAX2EeYlEchUKhsAhh6nllzT5sO9if836EeWfBxx1YvacbQPHKbFsZ1bMQQKpvdZVVx1UoFIp8IjT+D7Yextl3vY3td1yY035EmYaDfQHM31jcgBWV669QKBRpyJcdvpSq5yrBr1AoFGkw68vx639uxIKPs9PaRX2eUkAJfoVCoRiEb5wxyXgdiTJ+99ZmfOXhJVnto5Sq5yrBr1AoFINw60XTjTaMuzt9Oe1DmXoUCoVimCHaYJ5159s5bR9Qgl+hUCiGF0PtwBUMR1Gk6M0klOBXKBSKDDjYF0xa9sSSnYNux8z4/VubsONQPxpKpGeGEvwKhUKRAVefNjFp2S3PrB50uzV7enDXPz/G0h2dGFHjxhmTtQo1136iLd9DzBjVgUuhUCgyYFyDF7deOA2/eGl93HJmTpuBe6BnwHjtcdrw6DdOsWyMmaI0foVCociQKpM+2vMeWZZ2mwO9McHvKlJRtkRKYxQKhUIxDKjSI3tkXl93IO02nf0x34DXZPtioAS/QqFQZEgugvsv7++Ibe8sDeu6EvwKhUKRIUc2V2e1/vaD/ejoDRjvq91K41coFIphxeRRtVmt3x8Mx703MxUVAyX4FQqFYog8+O5W0+Xd/lDc+2LV309ECX6FQqEYIu9sMm8i2KMLftHM5UD3gOl6hUYJfoVCociCRKX9wmNb8M7HHVi1uwtLth2O+0xo/HddPhOA1oSlFLCy524rEc0nonVEtJaIvqMvv52I9iS0Y1QoFIphgdwo9sLjWjC6zgMA+NzvF+GL97+PQDhW06d3QLPxH9/aCAC46LixhRtoGqyMLQoDuImZlxNRLYBlRPS6/tk9zHyXhcdWKBQKS1n4H2djbL0Xuzp9eHjRNmP53q4BTBqpRf+Iipyj693Y+Iu55Z/Axcz7mHm5/roXwHoA46w6nkKhUBSScQ1e2GyEBq8rbvmuw1q9/pW7unDnaxsBaBm7boe9spy7RNQG4HgAi/VF1xPRKiJ6mIgaU2wzj4iWEtHSjo7iNiZWKBQKwd/nnYrbLppuCPFajyPO7r9TF/zzHllqLCsVgS+wXPATUQ2ApwHcyMw9AO4DcCSAWQD2AbjbbDtmfoCZZzPz7ObmZquHqVAoFBlxyhEj8DWpFaPNRnA7YqJUaPztvaXhyDXDUsFPRE5oQv8xZn4GAJj5ADNHmDkK4I8ATrZyDAqFQmE1Tsl2v6fLj83tfXFO4FLDyqgeAvAQgPXM/GtpeYu02ucBrLFqDAqFQlEImqpjdv5AOIqN+3uLOJrBsTKq53QAVwNYTUQr9GU/AvAlIpoFgAFsB/AtC8egUCgUltNc48aOQ5qJJxSJotOX3K2rlLBM8DPzQgBmHo2XrTqmQqFQFIN/O/tI/PbNzdjT6UM4wiWTqJWK0ggqVSgUimHMnKNH47nrTseRzTUIRqJJNXpKDSX4FQqFIk+4HDaEhoHgL42uAAqFQlEGOGyEcITR4w/B47Th/qtnY9KI7Gr4FwIl+BUKhSJPOO0xjf/41kacNbU0c5CUqUehUCjyhFM39RzsC8aFeJYaSvArFApFnnDaCAOhKPZ0+tHaVFXs4aREmXoUCoUiT/QHI9jT5QcAtDZ5izya1CiNX6FQKPLEXl3oA8DIGncRR5IeJfgVCoUiT/iDsSYs9V5nEUeSHiX4FQqFIk/4lOBXKBSKysIXDBuv65TgVygUivJHLs9c5ynd2JnSHZlCoVAMM/4271T88d2taBtZjVpP6Wr8SvArFApFnpgyuha/+sLMYg9jUJSpR6FQKCoMJfgVCoWiwrCy9WIrEc0nonVEtJaIvpPw+U1ExEQ00qoxKBQKhSIZK238YQA3MfNyIqoFsIyIXmfmdUTUCuA8ADstPL5CoVAoTLBM42fmfcy8XH/dC2A9gHH6x/cA+CG0vrsKhUKhKCAFsfETURuA4wEsJqKLAexh5pWFOLZCoVAo4rE8nJOIagA8DeBGaOafH0Ez8wy23TwA8wBgwoQJVg5RoVAoKgpLNX4ickIT+o8x8zMAjgQwCcBKItoOYDyA5UQ0JnFbZn6AmWcz8+zm5tLsYqNQKBTDEWK2xsxORATgLwAOM/ONKdbZDmA2Mx8cZF8dAHbkOJSRANLuv8JQv0cM9VvEo36PeMrh95jIzEmas5WmntMBXA1gNRGt0Jf9iJlfznZHZgPPFCJaysyzc92+3FC/Rwz1W8Sjfo94yvn3sEzwM/NCADTIOm1WHV+hUCgU5qjMXYVCoagwKkHwP1DsAZQY6veIoX6LeNTvEU/Z/h6WOXcVCoVCUZpUgsavUCgUCgkl+BUKhaLCKGvBT0RziWgjEW0mopuLPR6rSVURlYiaiOh1Itqk/2/UlxMR/U7/fVYR0QnF/QbWQER2IvqIiF7U308iosX69/47Ebn05W79/Wb987ZijjvfEFEDEf2DiDYQ0XoiOq2Srw0i+q5+n6whoieIyFMp10bZCn4isgP4A4DzAUwH8CUiml7cUVmOqIg6HcCpAK7Tv/PNAN5k5ikA3tTfA9pvM0X/mwfgvsIPuSB8B1qRQMEvAdzDzJMBdAL4ur786wA69eX36OuVE78F8CozHw1gJrTfpCKvDSIaB+AGaAmkMwDYAfwLKuXaYOay/ANwGoDXpPe3ALil2OMq8G/wHIBPA9gIoEVf1gJgo/76fgBfktY31iuXP2hlQd4EMAfAi9BySw4CcCReJwBeA3Ca/tqhr0fF/g55+h3qAWxL/D6Vem1AqxS8C0CTfq5fBPCZSrk2ylbjR+zECnYjVha67JErogIYzcz79I/2Axitv66E3+g30EqAR/X3IwB0MXNYfy9/Z+P30D/v1tcvByYB6ADwJ93s9SARVaNCrw1m3gPgLmg9QfZBO9fLUCHXRjkL/opFrojKzD3yZ6ypLBURw0tEFwFoZ+ZlxR5LCeAAcAKA+5j5eAD9iJl1AFTctdEI4GJoD8SxAKoBzC3qoApIOQv+PQBapffj9WVljUlFVAA4QEQt+uctANr15eX+G50O4HN6McC/QTP3/BZAAxGJciXydzZ+D/3zegCHCjlgC9kNYDczL9bf/wPag6BSr41zAWxj5g5mDgF4Btr1UhHXRjkL/g8BTNG99C5ojpvnizwmS9Eroj4EYD0z/1r66HkAX9FffwWa7V8sv0aP4DgVQLc07R/2MPMtzDyetZpQ/wLgLWa+EsB8AF/QV0v8PcTv9AV9/bLQgJl5P4BdRHSUvugcAOtQodcGNBPPqURUpd834veojGuj2E4GK/8AXADgYwBbAPy42OMpwPc9A9pUfRWAFfrfBdBskW8C2ATgDQBN+voELfJpC4DV0CIciv49LPptPgXgRf31EQCWANgM4CkAbn25R3+/Wf/8iGKPO8+/wSwAS/Xr41kAjZV8bQD4KYANANYAeASAu1KuDVWyQaFQKCqMcjb1KBQKhcIEJfgVCoWiwlCCX6FQKCoMJfgVCoWiwlCCX6FQKCoMJfgVZY1ekfLfpPdjiegfFh3rEiK6LQ/7uYuI5uRjTAqFGSqcU1HW6DWLXmStAqPVx3oPwOeY+eAQ9zMRwB+Z+bz8jEyhiEdp/Ipy5w4ARxLRCiK6k4jaiGgNABDRtUT0rF6HfjsRXU9E39OLmH1ARE36ekcS0atEtIyI3iWioxMPQkRTAQSE0CeiPxPRffp+thLRp4joYb0O/p/1dez6emuIaDURfRcAmHkHgBFENKYwP5Gi0nAMvopCMay5GcAMZp4FGDMAmRnQqph6oGVl/gczH09E9wC4Blp1zwcAfJuZNxHRKQDuhVb3R+Z0AMsTljVCK+37OWgp/6cD+AaAD4loFrQa8OPEbISIGqRtl+vrP53b11YoUqMEv6LSmc/MvQB6iagbwAv68tUAjtMrnX4CwFNaSRcAWmp/Ii3Qyh7LvMDMTESrARxg5tUAQERrAbQBWADgCCL6HwAvAfintG07tKqRCkXeUYJfUekEpNdR6X0U2v1hg1ajfdYg+/FDq9hotm95v8a+mbmTiGZCawDybQBfBPA1fR2Pvk+FIu8oG7+i3OkFUJvrxqz1M9hGRJcDRi/amSarrgcwOZt9E9FIADZmfhrArdDKJAumQiseplDkHSX4FWUNMx8CsEh3oN6Z426uBPB1ov/f3h3bIAzEYBR+lqhYIS0LwCYZiDYdBTswBgViAlIwz1GcIgVEgYQ7v28A66pflnWyYwae9AMen+7APlbzoB8MwC0iHsCFfh50uamwo2/SlNL5nVNKEhFn+lz/+medETi01o45L5Pe2fFLeSZgm1BnA5wS6khf2fFLUjF2/JJUjMEvScUY/JJUjMEvScUY/JJUzAsb1pFyzL7pFgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DWTnLxR79Zbb"
      },
      "source": [
        "## Problem 1\n",
        "Plot a Neuron with a spike rate of 50Hz for 1000 ms for 200 trials.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "ll-tN8Nk9Zbb",
        "outputId": "ce74e048-18ad-463f-d5b9-6c217e2b3e54"
      },
      "source": [
        "##############################################################################\n",
        "## INSERT: Plot a Neuron with a spike rate of 50Hz for 1000 ms for 200 trials.\n",
        "##############################################################################\n",
        "#######################ANSWER#################################\n",
        "\n",
        "\n",
        "#######################ANSWER#################################\n",
        "\n",
        "Random_numbers=np.random.uniform(0,1,[Samples,Trials])\n",
        "\n",
        "Spike_Probability_Threshold=poisson.pmf(1, Spike_Rate/1000)\n",
        "Spikes=np.zeros([Samples,Trials])\n",
        "\n",
        "Spikes[Random_numbers<Spike_Probability_Threshold]=1\n",
        "\n",
        "\n",
        "fig = plt.figure(figsize=(6,4)) # This setups the size of the figure\n",
        "plt.pcolor(Spikes.transpose(),cmap='gray')\n",
        "plt.xlabel('Time (ms)')\n",
        "plt.ylabel('Trials')\n",
        "plt.show() # This plots the figure"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LZRS8QDf9Zbc"
      },
      "source": [
        "## Problem 2\n",
        "Plot the histogram of Spikes per Trial of a neuron with a spike rate of 50Hz for 1000 ms for 200 trials."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "E-xSHswd9Zbc",
        "outputId": "885fbd37-6c03-4f51-aa7f-370308290e17"
      },
      "source": [
        "\n",
        "fig = plt.figure(figsize=(6,6))\n",
        "##############################################################################\n",
        "## INSERT: Plot the histogram of Spikes per Trial of a neuron with a spike rate \n",
        "## of 50Hz for 1000 ms for 200 trials.\n",
        "##############################################################################\n",
        "#######################ANSWER#################################\n",
        "\n",
        "\n",
        "\n",
        "#######################ANSWER#################################\n",
        "\n",
        "\n",
        "\n",
        "plt.xlabel('Spikes per Trial')\n",
        "plt.ylabel('Frequency')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Io8PeR-r5dC"
      },
      "source": [
        "## Problem 3\n",
        "Plot the Peri-Stimulus Time Histogram (PSTH) of a neuron with a spike rate of 50Hz for 1000 ms for 200 trials."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TZ8fgmswr5dC",
        "outputId": "add85886-ee4e-4378-ebd8-b01164b872b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        }
      },
      "source": [
        "fig = plt.figure(figsize=(6,6))\n",
        "##############################################################################\n",
        "## INSERT: Plot the Peri-Stimulus Time Histogram (PSTH) of \n",
        "## a neuron with a spike rate of 50Hz for 1000 ms for 200 trials.\n",
        "##############################################################################\n",
        "#######################ANSWER#################################\n",
        "\n",
        "\n",
        "#######################ANSWER#################################\n",
        "\n",
        "\n",
        "plt.xlabel('time (ms)')\n",
        "plt.ylabel('Spike Rate Hz')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6dp5s8jI9Zbe"
      },
      "source": [
        "---\n",
        "# Summary\n",
        "\n",
        "In this tutorial, we learned:\n",
        "\n",
        "* To simulate a raster plot.\n",
        "* To calculate the spikes per trial.\n",
        "* To calculate the spikes per second.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vvhb1tmyr5dC"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}