examples/00_FluctuationDrivenInitialization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fluctuation-driven Initialization for SNNs\n",
    "\n",
    "This notebook provides a brief interactive tutorial for initialization of SNNs in the fluctuation-driven regime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports\n",
    "import sys\n",
    "sys.path.append(\"../../\")\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import stork.utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for reproducibility\n",
    "np.random.seed(2020)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first define some general simulation and plotting paramters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulation parameters\n",
    "dt = timestep = 1e-3                    # timestep in s\n",
    "duration = 10                           # Duration in seconds\n",
    "epsilon_calc_method = 'numerical'       # Choose between numerical or analytical way of computing epsilon \n",
    "\n",
    "# Cosmetics and plotting\n",
    "spike_amp = 2.0\n",
    "plot_maxtime = 2.0                      # seconds\n",
    "plot_maxneurons = 100                   # neurons\n",
    "\n",
    "color_membrane = '#CCB380'\n",
    "color_theta = '#454545'\n",
    "line_colors = ['#969696', '#525252', 'black']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson distributed input spikes\n",
    "\n",
    "As an example input, we generate homogenous Poisson spike trains and visualize them in a spike raster. We first set parameters of the input, i.e. the number of input neurons and their firing rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input parameters\n",
    "\n",
    "N = 5000                                # Nb. presynaptic neurons\n",
    "nu = 3                                  # presynaptic firing rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we define functions for spike generation and plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_poisson_spikes(N, nu, duration, dt):\n",
    "    \"\"\"Generates a set of Poisson-distributed spikes for $N$ neurons that fire at frequency $\\nu$.\n",
    "\n",
    "    Args:\n",
    "        N (int): Number of input neurons\n",
    "        nu (float): Firing rate of input neurons in Hz\n",
    "        duration (float): Duration of simulation in seconds\n",
    "        dt (float): Simulation time step in seconds\n",
    "\n",
    "    Returns:\n",
    "        np.array: Array containing Poisson distributed spikes\n",
    "    \"\"\"\n",
    "    timesteps = int(duration/dt)\n",
    "    spikes = np.zeros((timesteps, N))\n",
    "    spikeprob_per_timestep = nu * dt\n",
    "    \n",
    "    for t in range(timesteps):\n",
    "        spikes[t] = (np.random.rand(N) < spikeprob_per_timestep)\n",
    "\n",
    "    return spikes\n",
    "\n",
    "def plot_spikeraster(spikes, timestep, axis, max_time = 1, max_neurons = 500):\n",
    "    \"\"\"Generates a spike raster plot\n",
    "\n",
    "    Args:\n",
    "        spikes: Binary array containing spikes\n",
    "        timestep (float): Simulation time step.\n",
    "        axis: Axis to plot on.\n",
    "        max_time (int, optional): Maximal number of time steps to display. Defaults to 1.\n",
    "        max_neurons (int, optional): Maximal number of neurons to display. Defaults to 500.\n",
    "\n",
    "    Returns:\n",
    "        _type_: _description_\n",
    "    \"\"\"\n",
    "    max_timesteps = int(max_time / timestep)                # max timestep calculation\n",
    "    \n",
    "    spiketimes = []                                         # convert to spike times\n",
    "    for t in range(max_timesteps):\n",
    "        spiking_neurons = np.where(spikes[t]==1)[0]\n",
    "        for idx in spiking_neurons:\n",
    "            if idx <= max_neurons:\n",
    "                spiketimes.append((t, idx))\n",
    "    spiketimes = np.array(spiketimes)\n",
    "    \n",
    "    time_axis = spiketimes[:,0] * timestep                  # get x and y axis: multiply by timestep to get seconds\n",
    "    neuron_axis = spiketimes[:,1]\n",
    "    \n",
    "    axis.scatter(time_axis, neuron_axis, s=1.5, c='k')      # plot\n",
    "    axis.set_ylabel('neuron idx')\n",
    "    axis.set_xlabel('time [s]')\n",
    "    \n",
    "    axis.spines['top'].set_visible(False)\n",
    "    axis.spines['right'].set_visible(False)\n",
    "    \n",
    "    return axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we generate example inputs and plot a spike raster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aMHZ+DpLsb4rNvEyrC1mTFEKtCbJVbwXVBcZ4YnI8MVZASY29oBvPG5Lsb4rNvEyrC1lHgYc6GjzGB84p0PHE5HhiDGjHqHOdyLJ/rA7YdV2aNuEgfUprq9U6x36SbSvoXqzcXjPGE4AYA9ox6lwnsuwf624FruvStAkHO3fu3NoFAQDW1ta2vj+yn2Tb1uFepOMJQIwB7Rh1rhNZ9t+/f//Yd2IJVruuS9MmHFx//fW44YYbcMstt4wdFZ78neSdIGpxL5p0lyRdCDDUluyO93o93ev1MrvmkrvtxB2uy13QWL8oitpl0vdo20LIifEAeB6AXwbwuwBuzbl+34Fc744nXTlZiUkS1+XOB5psitpl0vdo20JUbq+VHjTaxiilngTgXRicLqqmfF1rrWesCD4r/+Tc3NzcyZMnbSY7kT179oyNtSbZvXs3lpeXM7+X/IzUF5Y7qTnT2vlcTE4gTfMmDI47uBfAdQB+HMDzc66rLcq1SpkTLScF9TY2NrZ+y5MQ68uk+sJyz6bKqbEST5oNqZNEe5TCpLuUvAB8YXhtt5VmSflWhtrKDI+kYzxXXHFF5m/Zba8vk+oLyz2bKkOQEoerQ+okxB7hYzwA1gC8w1Z6FeRbcTzpOfLpOf6TGhMJ8+vr3NhJzJuEMo+NKjazaWdb9Shk2Qupd5Xba5vTqU8B2GYxvSCk58in5/hPmt8vYX695PUHpkjMm4Qyj40qNrNpZ1v1KGTZR1/vTLxW8gJwAMA6gGfYSrOkfCs9ntHTUHp18+iJYtKThoQnciFPQk6QmDcJZR4bVWwm8SiMkGUvpN6FH2rTg8b/TQD+GcDLADzNZtoFZFudTp03hpq16WCy8ENXCCFjv06oU95815M8eaGdgE9GerfbbS/1yIWdhNk+vOMBsDm8Hkv8n3c9aktuQr5Vx1PkRs3abDB04yisYlqlTnnzXU+KPkjFGugvQlrvdrvttB65sJMw24twPPcD+GzRy5bchHzvC0izuuwSh4MkEsKJSHJcvutJnrzQgX6f+J6gkDVRadIOJ77zYIHK7bW1yQVa60ttpRULeQG+qIN+nggxUUDS5ATfweE8eaED/T7xPUEha6LSTTfdtPW6Sh2M1fbnYOK1JF0IvFeblBhPLIR4cpP0tMgYj398T1DIm6hkUgeF2T78UFtm4sBFAC5yKSMhK5rzeIowqmDdbld3Oh3d7XYlVDRrhBirdinTdH8wXw2KsIbLmFD5KVOX0t/1Xe8dIsfxAHgRgPcDeAhnJxM8BOB9AF5kW15Cbq0cT15ljbyiblG3GE/RhshmkN+lnrEQKj9l6lLRXewjRIbjAfDbODuz7TEAXwVwJvF6E8CbbcpMyK7keKQ+Aaa78i6Gh6Tm3Qe28150GM9mkD8P6btr2CR9umi32w2tUpOo3F5bm1yglPppAIcArAD4NQB/oLX++vCzJwL4TwB+CcAhpdTHtNZ/Yku2CZICzknSQcTk+7aQmncf2M570aCvzSB/HtJ317DJ5ubmxNdEJja3zOkB+BaA/VrrzyQ/0Fp/A8CNSqkPArhn+F0RjkfqSYOjUwWPHj2Kzc1NzMzMYN++fVZPG5Sadx/YznvRUyHzvmfzVMlJeavF6ZUJZmZmJr4mQjHpLiUvAF8D8N4C33svgK/ZkptIt9JQW93GvMvgK+8Sh/Ty8u5S1yJp25Bftlxt5tl3WTf5/s3DYxmEj/FgsDv1Hxf43h8DWLMlN5FurWI8PvCVd4mNQ17eXepaJG0b8suWq808+y7rJt+/eXgsAxGO55MAvghg24TvtIbf+aQtuYm0azWrrU7EFNB2qWuRtGNf3xRTWdcVj2VQub22eQLpnwBoA7hDKbUz/aFS6jIAfw7gYgx6PaKI/kQ/R5jaZX19HRsbG2PvuQ5om+js8tTQImnv3bt34msX2MwzT10NTxRlYOK1kheAWQDHMJg2vQHg4xg4mD8G8LHhe48BuBvArC25CflGPR6Jw0ESMLVL+vedTkf0uH/oGE+v1xvTvdfrWZNvoleItEg1GhXj0YPG/0IAvwPgYZxduzO6Hh5+dqFNmQnZRo6nSve0CTeZabc99qEj38SsO2kcIobaoLV+SGv9KgyG064C8DPD6yoAF2utX6W1fsimTFtU6Z6O1kscO3YMhw8fRr/fd6VeMEy77SG6/VEMNeQQs+6EFMXmAtIzGEwauEprvQbgr22l7YMq6xuasA7GdN1HiHUjMa9ViVl3Qoqi9GCYyjwhpb4B4D1a65+zkmB5+Sfn5ubmTp486U3moUOHtlaIA8DCwkIjVv6vr6+j3++PNY6zs7Oh1SKkUQi4D1XVH9rcueAkgO+xmJ54mvp02uStdgiRQsz3oc0Yz+8A2KeU2mcxTa+UnYY7OzuLpaUlLC8vY2lpyfnTxpkzZ7Br1y5s27YNu3btwpkzZ5zImWaH9JDi7bffbjz9nNPZZcPyCUuW/asO9YsoS5OZCckLwCUAfg+D2WtLAP41gMuH759z2ZKbkG+8gFT6lOpOp3PO1GQXTLND1pENpraSbvumw/IJS5b9q5aJxbKs3F7bHGq7f5gRBeC/DK88NOwO81lB+mSBU6dOTXxti2l2WFxcxO23346VlZXc79iWScLC8glLlv2PHDmy9X+ZoX4JZWlzqO3I8Loz8X/eJXLGm62prOvr6zh48CB27NiBHTt24ODBg1a6szt37pz42hbT7DA7O4trr7124ndsyBQxJOARyfnlNO9q2CrTLPtXHeoXUZYm3SVJFywMtdlaEOpiKEprrVdXV3Wn09GtVkt3Oh29urpqnGYWvnZRnpZe04Z3JOe3CYulXWCrTIXuLlG5vbY2nTo0IaZT57Fnz55zDnHbvXs3lpeXA2kUJ2k71t2GTctvE6h5mVaeTm115wIymHl2//33n/N+nYYmfA0JiRgS8MDInqdPnx57P5lf1zb3VaY25Ugemhxhc/heel5LYdJdSl4AfrnE9QZbchPyRRyLkJ55dt555+ler1eroYkmHyDngrQ92+32Ofl1bXNfZRrz2T9VcDV8LySv1dtrkx+PJTTYCHQT524O+ljis9Hnm7bkJuQbOZ68ClK24rRarbEK0mq1rOghCW5kaRcJ5/T4KtMsOaM63+12dafT0d1ut1Ddt6FzDPeb1mLvucrttc0pzS/Lef9xAL4XwL8B8FwAN2JwfIIo8lYBl10dvHPnTpw4cWLstQ09JDE/Pz82bl3XITBfFLGna5v7KtMsOck6P+L48eMAJtd9GzrHcL8BNbznTLxW2QvAawE8BOAKB2k7ORah7JOG6cwzoU82Y8TylBgLIWYR+k5/kpx0nS9a923oHMP9prXYe05Ej2cqWuvfUEq9HMD/APBin7KnkfdEUfZJY/v27bjnnnus6yGJ0fqBSQjYwNAqLvNTxJ5FvuNaB1ek63zy/UnY0DmG+w0IWz5OMPFaVS4Afwrgqw7SFRHjMUXok01phAZDK1O3/IQiy45VYzw2qMv9Fojq7bXJjysJBI4D+KaDdEXMamsK027YWIYwilK3/FShKUNbrpxRDZ2cfMcD4CIAv4XBrLYPOUifjscjZTcSjb2HULf8VMGGDWKwoysdY8h7SSq31zZPIL1vwscXAngyBitd1wG83pZcEoYiG4mO3q/DWUV1y08VbGwuGYMdXW2iKWFzTinYnFxw6YTPNgA8iMEGom/SWn/KolwSgGlBWVvBUCmTFGIK7rqymY1AvBQ7TrKRqwkH09KVUte9YNJdknSBQ21e8TVeXcPhCee4slmdYhSTbBQqxhNhXZcf43F9mTieZIXo9Xq61+sFvbmE7kQbhBiC0T4pUp4mNou9vhTFtF6tra3pXq+n2+22brfbRttijWye3vUkgrouz/EAuADAUwBsdyUjJa+y48k6xiDkU0fT9rOaROz626aIPUxs1hR7m+Yzq82oaqu89icC21dur60vIFVK/SKAVwK4AoPJBG8D8PLhZz8J4OcBvFZr/U+2ZVdlUpAvRADQZhAy9oBmDMFonxQpTxObxV5fimJar7LsUtVW6d+1Wi0cOHCg1nXd2rEISqkZpdQ7AfwugGcC+Aece17DCQAvAfDTtuTaYFLwMO+zstuUJ79/8OBBHDx4MPe3No8DiP1ogaqnLCbJK6uqW8373qI+KW9jY2Pss6zyNLFZ7PWlKKb1Kssup0+frlQf0mkdOHCgcl2PBpPuUvICcAiDNTrvBbBj+N5jAG5Nfe8zAI7akptI12uMp2xXvcxwHmM8dskrq6rDLb6Ho9LyOp1O9Hu2xU4yxjM7O2tUHyK2efgYD4BPAPgCgG2J97Iczx0AHrQlN5Gu11ltZYOTeRshFvktMcPWBrDT0nMFJ1jIpsHlU7m9tnkC6Q8A+LjW+uEp33sYwMUW5Qah7JBEleE8Mp0iw155ZTWpDCel63s4qinDX7HC8qmAiddKXgC+DuB9qfeyejx/DeDLtuQm0vXa4ynbPZY2ZbsuFBn2qrIBbIh1HnlEPBTTCBpcPiKG2u4C8GUAT0i8N+Z4ALQBfBPAB23JTaQdzQJSlwvUbKwt8HkjmeqcHuZot9tW9J10UqbkBiZLxxj0rjMm9hdediIczyuHjuYPATxepxwPgBkMjkTYBPDztuQm5EfjeHxtQlg1bZ/Bc1Odba6nmJTuwsJCFGtcYtW7ztR4XVXl9trmOp63APgpAD8DYF4p9f7h+x2l1BKAHwPwfQA+gIFzaiy+NiGsmrbPtRymOi8uLuL222/HyspKpd9PSneU1midx/79+yvr6YsiZSdR7zpjcj/VdV2VtckFWutNAC/CYB3PUwH84vCjHwLwKgCXALgZwEu0HnRRYsZkLYerYGRWOlXS9hksNdV5dnYW1157beXfT0o3vc7Dpl1crQXK0jF08Ns0r77XTdnGxP579+6d+DpaTLpLeRcGs9Z+CsBrALwOwM8BeKoLWQmZXofaTLrAjPGMyzLV2Ze+NuW4GkKRGOOxvT2NsOGmqZjYv9frjeW91+s51LQ04WM8oS/fjsf13P3QjYVk6mCbvPrjI2++7TfpXiniKLvdrpd1MhJnngpfI0THE1OPR0L6MVMH29jeTcGGbFdMkldkMkSn0/Gib5ndRXwhvK5Xbq9dbBL6PAD7MdiZ+oKcr2mt9Stsy/aJ680r6xpUtEEdbJNXf3zkzbf9Jt0rRXSZmZnBwsKC841ipW0WDNR4k1wTr5W8ADwJwEcwmC792JRr05bchPxoplMXGeqw9aRjOqziO95TRJbwp0Aj6tjjKatLqLiGxB7PNNL3zOrqqs9h1PBDbQB+b+hUPgPg1RhMn74q77IlNyE/GsdT5Ma31eDHFNgtKqsOMZ486hjjKatLKMcjMcYzjVDDkkNEOJ4vDC8vB79lyA/meMreyD4DhqaybOha1D42ToX03aBKasRDYnM2XdF6QNufayvPp5iKcDxrAN5hK70K8oM5nrK9Aom9CFe/L5OGBF3LImnYKiRFJgkUtY2v+lIHYu3x2JxccArANovpRUPZYK3PgKGpLBu6FrWP7VMhfQSE6zDRwQY2d0woWg9o+3Ntdf311+OGG26QPxnBxGslLwAHAKwDeIatNEvKj6bH0zR82aduPZ6YhpLSdmi3286fvptw30lcEJwg/FCbHjT+bwLwzwBeBuBpNtMuIDuaGE/TiHFnAQkyY2pYR3Zot9vnDP3wtNTq2BzCdEDl9lrpQaNtjFJqc/Tv0CCT0Fprq2uIlFIn5+bm5k6ePGkzWUKCsWfPHhw7dmzr9e7du7G8vBxQo+nEqLNksuwJQIqNVdUf2jyB9EEApwE8MPw76XrQolziiNg3Z3SFL7vY3tyzqN4SN8AtgqtyCXkfZNkzvVHoAw88EN/9adJdknQhonU8sSCoSy8KX3axPZTkY7ZYyOEvV+US8j4oss4p4P1Zub222eOpJb6fdorIq6pT2d8VmTXUxF6Rr9lUyaMZFhcX0e/3jexcVG/fs8Vs1aEqeqdlnzlz5hxdQs6ey6oDt912W+Z3o5rVZ+K1JF1w1OPx/bRTRJ7r9RE+dImZWGfP+ejxVPmtLXvakJ01E09KHU/rkb5i6vFY3yS0bvh+2qmyHqKoTi7WGzVxLUWIjRtt2Lmo3ib5q6KnrTpURe+0rFOnTp3z+ZEjR0qn64K0rrOzs7j88ssxMzODffv2yV2zk4WJ15J0wWOPx+cU2na7fY6Msk9geVNdbTwhCT+oqjZIs3PePVDkfklvZJnOm88n98Ar/0shpeeVoHp7bfJjSZcrx5N1g/lYNDjJSZR1fEWcWVWkNYh1RZqd8+6BIvdLunHv9XrBJiQE3t25FALXLdHxuHI8WWRtzGe7ItjcSNTlpqTCT0isDa7s7Hojz6zvltnIUmBjS85Sub3mrLYKpOfWr62t4fDhw+j3+85kmKyHcLm2IuS6jSbhys79fh+HDx/GsWPHStXhMvqkP9u5c2fh31bVjwjHxGslLwCXoMCRCAAuAnCJLbmJdL31eEZPYS63ILf5pOfyqZFPpH5wZeeqPaky+pgMZ7FHLZrwQ20YnDz6+wW+dzOAR23JTaTrfQGpwGCfMXQkAyTZYaRLt9vVnU5Hd7vdTJ2q6Cy9DtvUL6bTeCNBhON5DMCtBb53M2py9HUdK6L0hsgXkuyQt34jrVMVnaXXYZv6mZappDohhKgczzsBPGRLbiJdbpljgSJDG014cpQ0xJPWJU+nMjrHvmN4lXQlnMZbMyq310YLSJVS+1NvfXfGeyPOA/ADAH4UALeQFsr8/PzYzrdZgd9RwBc4u0vu0tJSYRmmv/dBETuE0iX5/qTvFQnaA27LwJWcKumalqmkOhE7pjsXfAQD7z/iR4dXHqMjE37LUC5xhI/dCmLY7SDE7gTTdDl69Cg2NzdzV6qX0dlXGbiSUyVdCafxkgGmjuftOOt4fgHAvQA+mvPdbwP4PID3aK2PG8qtBevr6+j3+2MVeXZ2NqhOo00JJ2Hy5Le+vo6NjY1z0ivyO5+2KmIHX4x0Sdrg0UcfxXXXXYe77757zB5Fdfb19O5KTpV0TctUUp2IHpNxuuSFgjEeVxcijPHEGqw0GbfPWsVeh9lXPpi0SWRZezQxxkOsEybGk3JgXIxakhiGnLIwefJL5/H8888v1HOJ1VY2mZTnsvbw9fTuSg57H3FDZxGQoqu/XZ7R45uqK/C5Q0K53QHqVGdI/bDW41FK3Vri61pr/QpbsmOlaLCyyAyeGGaKAdUDtAzsjttgdPxxMsaTpE51htQQk3G65IVBjGfatTn6a0tuQn50MZ6iFFk/kPcdjoU3E5M6EztZdT72mJapHEd6hY/xAHh+zvuPA/C9AF4A4FoAvw3gPRbl1p4iM3jyvsOn2mZiUmdiJ6vOA4h63ZKpHGntgM3JBXdO+crblVJ/AeBtAN5tS24TKDLMlPcdBuWbiUmdiZ0qp/j6lB1CjrR2wOvkAq31H2Gwa8EbfcqNndEMnuXlZSwtLWXOApudncXi4iLm5+dx1113od/vY319nUH5CmQF3WMLxBetM9O+EyNZdT7vPhiV65VXXoldu3bhyiuvnDoZY9J3Te+3vHq2vr6OgwcPYseOHdixYwceeeSRiflJ/15cO2AyTlflAvAnAL7hIN3axniKUuTYYcZ4ppNlR64jiocyMZ6iG7AW/a7p/ZZXz7JkdzqdQkeP29Arh+rttcmPSwsb9LD+EcDXHKTdeMfjK1hsoxJLdohZdixrW8n5I2eZtgFrshwvvvjiQpu12tRnlHaWngImjIiYXJCLUqoF4HIArwewE8B7fchtGr6CxTYCldKCnUny7FjGtpLzR84ybQPWZDlOSsOVPqO0s/SMecKIzXU8m0W+BuDLAF5jSy45i69gsY1ApbRgZ5JJdixqW8n5I2eZtgHrpHJrtVo4cOCA1fssr+4tLi7i0UcfxTve8Q4AwDXXXBP3hBGT7lLyAnA/gM/mXJ/GYCfrGwC0bclMyRc31FbX4Zas/dbK5tFHzMSH/YvGDmKOCa2treler6fb7bZut9u61+vVpi5Pw+b+eDUkjhiPy0ui46lT45Mk2dh2Op1KefThFHzY33MwNwhZjW9d6vI0kuXY6/V0r9erRZlago7HhuOx3VjUdWV4Esl59KGbCxnperi6uhrUiRUNbBO3FGmfPD/wyHM8AHYA+KHhtcOVnIQ8Y8dj+wm5rj2eJJLzGLLHYzPNqr1KWzS5xyOJInXN8/0ow/FgMHlgAcBnMNiXLXmdAnAIwONsykzINnY8tp9e6zTckofkPIaM8ZiQroetVitob6PJMR5JCNx/L7zjAXABgA/g7EagqwCOD6+v4OwmoR8EcIEtuQn54no8sSBlHDuvETdp3CU7xjyk9Xh8ULWcJJavK53Y48lu+G8YOpe/A/CjGZ+/AMCJofO5wZbcRPriYjyxIGXmTtFV22V0ivFhQlqMxwdVy0li+brSiTGe7Ib/XgBnADx5wne+a/id+2zJTaQtblZbLOSt3vY9rFN01XYZnSRPfiBnqVpOEstXok6OqNxe29wk9KkAPqS1Xs37gtb6KwA+DOApFuUSQ8qcbOlTj+Sq7ao6pb97+vRp55t8xrahqG+y7FOkjKv+zjc2TxauLSZeK3kB+CcA7yrwvXcBuNeW3ES67PFUpAkxnna77W1IRuLwjySy7FOkjKv+zjdFdapBPREx1HYDgIcAPH3Cd54+/M6v2pKbSDsKx+PyRpF4E2YRQs8iwx+2Tq5s0FBLJdL26Xa7hWxcN7uGyo/F+0+E4zkfgwPeHgDwcgDbEp9tA/AyDLbVeReA823JTciIwvG4fMqJ5QkqhJ5VZwRV0TWWcghF1Vl7dbNrqPxYlFu5vba5O/WnMVjH8zQANwO4WSn11eFnFyW+pwF8WimV/K3WWl9mURexuNw8MpaNKUPoWWTzRFsnV0azUWMg0vY5evTo2Od5Nq6bXUPlR0I7YdPxXJrx3vaM955uUWZ0mG5bvr6+jn6/P1ZZRydHxrIlehU9J+W7CKPTNkfp7N+/v7D9yuo6kkWySdvn0KFDOH78+NbrPBvXza6h8iOinTDpLkm6EMlQm6sTCm2k7YsqetoaHihrv1hsGjO0sV9qFeMJfUlwPD5uINcBSamNgK18V51kQNxiumg2VJmFrCsC6ikdjwTH4yNY6FqG1ACujx6PbVmkOFUnHOT9PsJAfVSyh1Rur60ffT085no3BotEL8j7ntb67bZlh8ZH0M51QFJC4DELW/m2NcmA2CVt41OnTk38fNrvfZVZyLoScz21uXMBlFK/AuBLAP4KwP8B8NaM67bh39owWoF8+vTpsfddBO1GAcnl5WUsLS1lBthNVkRXXUFuk3T6Z86cMZpYkEyv3+9jcXFxov0krobPI+bV70ndNzY2xj7buXPn2OtpZeCyzCbZOERd8dneOMOku5S8ALwWg01CNzBYz/ObAK7Pu2zJTcgPNtSW7vK22+2gsQGTLnjVFeQ2MR12MdVXwNh5YQQMt1Qmq5wlxnikTegR1N6Ej/FgcN7OwwC6ttIsKd+L48k6m6Tb7ToJ+Fet1EUD8a7Tr4rt82jqtuI9SWx5S9a59DZGVXV33finbdxutzNl2dCjSBqCylyE4/kWgL+0lV4F+V4cT/ppw8YTeVFZRdMt+jvX6VcldI8nJmLLW9b9Y6q77/qYJ8uGHpFNfhHheO4H8Ke20qsg34vjyTpCoOheU6ayij7ZFH3ycp1+VWyfRxPT0FlZYstb0d6DSZoulxhM6qXZ0COy6f4iHM8igC8jsUebzytkj8fVE0dTp04Td4Q+zdVFnZsUK7IdG5qkv68eTxE8OScRjuc7ABwB8CEAz7CVbgn5wWI8rp44fPcspD8tE3NMGjYbjaKLOpdM0/X6n0n6+4rxFMHTQ2Xl9lrpQaNtjFLqwwAeD+A5GMxuewDA54b/p9Fa6x+xIvis/JNzc3NzJ0+etJksIbViz549Y/t07d69G8vLy85/64uyOsaQpyp4ypea/pVsbK7jeR6AeQyUmQHw/QD2D9/PusQT8xoJFxSxhyubxVYWUvW1eZqrxHUjZXWMIU9VEJ8vk+5S8sJg1+nCly25CfnWh9oYAxkn5Iyb2MpCqr6hYzyuKatjDHmqQmNiPKEvF45H0Hz5Qvhez5BlD1cz5fLSldpwSKg7praxbVuJZRVaJ9OYcWD96XjY45ExC87V2qC8z6WWkQS9THWwnQcJNpGmk+ks2cD6V26vrW8SWidiO/HQ9aaBRexR1WbTdM9LV+pGiRLqjqltbNtWYlmF1qnqKbd535Vg00JU9VgANg2uR028ZY4+Vno807quRbvGEvZwkvBEmUWWbVz1lCTjuo7E2uPxee+4qj9F89DUHo9JQ/+YyWWidI4+VhxP2SGfvMIOUSFCj1cXJcs2VXWPJc9ZuK4jscZ4fN47rupPGSfLGE/Ely3HkxUUTlaO88477xzHUyTI7mpbHalMuiEkBN4lEMIOMTjqOtQPn3koMkrjqMzpeFz2eLJ6OWV7PK42EpXKpCe+mIfHbBLCDjHYPgYdp+EzD1Un5ligcnvNyQUpsoLC+/fvP+d75513HrZv345rrrmmUJD96NGjY59HEwSsyKSgp4TAuwRC2CGGYHQd6ofPPEwrU5FlbuK1JF1wuFdbXlynTBc2tqc40+657fzGMERkg7x8RraHlyjqXndi7PEEdxi2LpeOJy8AWKZAY6v8ppXVdn6b0mDm5dNW/mOrhzaoe91hjKfGjier4OoQBM2jbN4k7JrgQq8yv7dhg7x8pk+57Xa7pdMuS12cVJ3v08DQ8fgcarP9FCqRsnlzbYuq6ZvqVeb3NmyQl0Z6ckqn0ymdti1dYqMu+RBI5faakwsKkBecq0MQNI+yeZOwa4ILvcr83oYN8vI5MzMz9r30axeIDEpXoM73aazQ8RRgfn5+7GyL0Rbjs7OzWFpaCqLT+vo6+v3+2M00OzsbRBfgXBttbGxgz5491nSrauu8snPxe1NZQH4+9+3bh+PHj4+9do2N/Egg5H1KcjDpLkm6ECDGExJpQ1smp0C6JLYYT4i0JckkUVG5vbZ2AmlomnYCqesTBut+UiUhxBgRJ5ASj7g+YTAr/aKnaoo//bAGSD3hNDZ4Ym4gTLpLki44HGqTiOthEJMdpDlE4x7O1LKDKzs2pHyqt9cmP5Z0Nc3xpPHR2FdZD0En5AauTbFD2o6tVstKPZ1UPq53p/AIHU/THY+PJ6wqMhry5Ocd2tUOaTvasuek8qnRusDK7TWnU9cEH2suqqyHqMtaEGlwbYodRna75ZZbsLa2tvW+aT2dVD5590ST7hU6nprgY81FlfUQNvWStnYpJK7WpsRs4yq6J+14+PDhrfdN759J5ZN3T9Rl3VQhTLpLki40fKhN6viwTb0iHIqIjphtbKK7z/uHMR7GeEhFQtwkkk519EGImYsxT1qQrruEOmUZOh46Hr+EeDL2KVPCk3+I3Skk5Lsq0nWXrl8FKrfXjPGQSoQIhEo61dEHrnXISv/IkSNb/8c2aUH6hAsJdUoK3LkAXGVchRC7E4wCtqPGcf/+/Th48CAOHjxovewk7L6wd+/eia9NycrjyMbLy8tYWlqKZmIBACPdfbQBoeuUqHbOpLsk6YLBUFsNu8DOCTlenbf2wmbZSRiP7/V6Y3nr9XpW05eQRyn4aANC29tBHhnjMXE80oOSefiqyKFvmDTp8oqx7LJI2zl96mjMeZNOrG1AGRzkkTEeE2KdP9/v97fWHoz0d7G2w5ecoqTLK/1ZrKTt3Ol0xj6POW/SibUNKIOkPNLxQH5QMg9fwUppQdFkeY3iHnfffXdUZZdF2q4zMzNYWFiIrl7GSKxtQBlE5dGkuyTpQgOnU/uKTfmSI21IzzdNjzX6KH8bMngo3xaM8TTR8dQtxsOGV2Tj4g2pG92G0FOCzAIwxtNEfJ0l70uOtCE93/iys1R8lL8NGSHqad3uDa7jiRRRc/ItYXLqaRXqaENbhLBNmXUuVfWzsZambBpnzpzBrl27sG3bNuzatQtnzpxxLlM8Jt0lSRcaNtQmtOtthMmpp1Woow1tEcI2ZYYaq+oXIsbT6XTGdO10Os5leoIxnqY5niasO9D63Hy2221rN11TbJikaANmyzauGsyYyq7Vao3p2mq1jNIT5IQqt9ccaouU2nW9c0jna2VlBf1+30nadbVhktFaoWPHjuHw4cO5trRlm6LyyhJT2e3cuXPi67K4sqlXTLyWpAsN6/EIeupxytramm63206ebptiwyRFewq2bOOqZxJT2a2urupOp6NbrZbudDp6dXXVKD1BvT0OtUl2PDHdJGUINc260+nUzpa+KBIb4eF91fFxT9iIb/V6Pd3r9Uz1pOOR7HjqevOFWFiaDtTWxZa+KNIw2izXuj505SF5s1EHm+vS8VR1PEUKMf2d1dXVUr9xMVRUtPK5vPFDdPmzJhvU4AhhUZiWq4S6GYq07Vqtlpi8Odhcl46nquMp8oSSNdRT9je2n4KKPlnVbTpyEbvWtYfpC1P7SaibocirnxLyJqnH0/idC4qsCE6/d+rUqdK/abfbuOSSS6xtzld0JbPLFc8hNh1Myjx9+jRWVla2PhvlrW6rvH1jWq4S6mYoRra65ZZbsLa2tvW+hLyJ2lzXxGtJuiC8x2P7iUfqU6XP4ZO8vNXxSdoVLspLat2chG07SMqbQzjUVtXx+IjxuGiApY6j+7zh8vJWx9iBK1yUl9S6OQnbdpCUN4fQ8VR1PGkaUmGcIWiNgRPqVj9iLi+bZRGzHQJSub1ufIwnjbTTNmND0imHLqhb/Yi5vGyWRcx2iBE6nhR1DHj6RNQphw6oW/2IubxslkXMdogSk+6SpAuWhtpCjnn7pIxOEvUfUecYVggkl3WaupeFKR7KkjEeW44n5Cwfn5TRSaL+I+o8ay8Ekss6Td3LwhQPZckYjy1cnAIpcXimjE4S9R/hW7e6nxIquazT1L0sTJFcljwWwQMSt3Avo5NE/UdI1i1GqtiTJ7nKRPS9YdJdknRB8CahEocEGOMhWVSxZ0zDc02CMZ4GO55QDWNTG2Ta2z3pvHa73aBrYEKXebfb1Z1OR3e73VLya1Bn6HikOp5QT4NNfQqlvd2TzmvooyqklHlZ+TWoM5Xba04ucEyoAJ/kwKJLaG/3pPM2MzODhYWFYGtgpJR5WflNqjNpOLnAMaECfKIDiw6hvd2Tztu+ffuwtLSE5eVlLC0tYXZ2Nqg+ocq8rPwm1Zk07PE4JtSK6KauxKa93SMtr6HL/OjRo9jc3MTMzAz27dtXWL40O/pE6UF8JHqUUifn5ubmTp48GVoVQghpAqrqDznURgghxCt0PIQQQrxCx0MIIcQrdDyEEEK8QsdDCCHEK3Q8hBBCvELHQwghxCt0PIQQQrxSpwWk37jggguecNlll4VWhRBCas+nPvWp92itf7zKb+vkeL4IoAXgwQo/H3mre+1pREhhWP9ISKrWv3sb73hMUEqdBACt9b8IrQtpHqx/JCQh6h9jPIQQQrxCx0MIIcQrdDyEEEK8QsdDCCHEK3Q8hBBCvMJZbYQQQrzCHg8hhBCv0PEQQgjxCh0PIYQQr9DxEEII8QodDyGEEK/Q8RBCCPEKHQ8hhBCvNNrxKKVmlVK/opT6jFLqW0qpzyulblVKfU9o3Ui9UUpdqZTqK6X+XCn1OaWUVkpxUR1xjlKqpZR6iVLq95VSnx62fQ8rpU4opX5ZKXWhcx2auoBUKfUdAP4KwA8D+AKAvwZwKYC9AL4M4Ie11vcFU5DUGqXUHQD+ffp9rbXyrw1pEkqpAwBuHr78BwB/D+CJAOYBPAHAPwK4Smu94kqHJvd4fgkDp/M3AC7XWv+01vrZAP4bgIsB3BpSOVJ7/gbArwL4cQBPAfBIWHVIg9gA8BYAc1rrOa31f9RavxDADwD4BIAfBPA/XSrQyB6PUurxAFYAPAlAV2v9idTnJwA8C8BurfXfBlCRNAyl1LcAXMAeDwmJUuo5AO7C4EHoiVrrb7uQ09Qez3MxcDr3pp3OkHcM/77Yn0qEEBKcE8O/FwB4sishTXU8neHf4zmfj95/lgddCCFECt8//LsB4IwrIU11PJcM/34u5/PR+0/3oAshhEjh0PDv+7TWzuKOTXU8o+mCazmfPzz8+wQPuhBCSHCUUi8C8AoMejtvcCmrqY6HEELIEKXUDwL43wAUgNdorU9M+YkRTXU8Dw3/tnI+3zb8+00PuhBCSDCGC+bfB+AiAG/WWi+5ltlUx3N6+PdpOZ+P3n/Agy6EEBIEpdR2AB/AIJ79VgDX+ZDbVMcz6kZ2cz4fvf93HnQhhBDvDLfG+b8A5gD8OYD/rD0t7Gyq4/kogK8DuEwptSvj82uGf9/jTSNCCPGEUuoCAO/CYIuw9wP4Ga31pi/5jXQ8w9W4/2v48kal1CimA6XUqzFYv3Mndy0ghNQNpdQMgD8CcDUGe1T+pKsdCnJ1aOKWOcDWJqEfAfBsnN0k9OnD19wklDhFKfXvMD5ldS8GM4o+nnjvV7XWf+FVMVJ7lFKHcHYvtncC+EbOV6/TWn/FhQ7nuUg0BrTW31JKPR/A6wH8LICXYLBS9zYAb9Ba5y0uJcQGF2PwkJPm2anvEGKbixL//8SE770RgBPH09geDyGEkDA0MsZDCCEkHHQ8hBBCvELHQwghxCt0PIQQQrxCx0MIIcQrdDyEEEK8QsdDCCHEK3Q8hBBCvELHQwghxCt0PIQQQrxCx0MIIcQrdDyEDFFK3a+UimrzQqXUG5VSOnH9vUFau1JpaaXUpRbVJQRAg3enJs1i2IB+FoNzlp4XVhsnfBTAPwEw2VX9DIC3Df9/IYAdpkoRkgUdDyFn+REA54dWoiK3aK1vM0lAa30awEsBQCn1EdDxEEfQ8RAyRGt9b2gdCGkCjPGQ2qOUeiMGw2wAcFUqhnFb4nvnxHiUUpcOv/cRpdQ2pdSblVIPKqXWlVLHlVIvTnz3p5RSH1dKPayU+pJS6rBSajZHp5ZS6vVKqU8opR4aXh9TSv2Cg/zPK6XuUEo9oJR6RCn1RaXU3UqpRaXUhbblETIN9nhIE7gHwJ8B+A8AvgTgfYnPjhZM4/EAPgTg+wAcAfBdAPYDeKdS6oUArgDwGwDuBPD+4WevAvBkAD+XTEgp1QbwQQDPAvDF4W8UgHkAtymldmutX1U2k1kMHeMdw/TvBnAXgO8EsBPA6wD8HoCHbMgipCh0PKT2aK3vUErdg4Hj+Uet9UsrJPMcAB8G8P1a64cBQCn1UgBvBfC7GDiY52itjw0/eyqATwD4WaXUG7TW9yXSeisGTmcJwOu01o8Mf7MDwHsB/Bel1F9orZMOsirXYTCycY3W+s+SHyil9gBYtSCDkFJwqI2QYjwG4JUjpzPk7RicSf8MADeOnA4AaK0/D+APhy/3j95XSu0C8CIAywBePXI6w998CcAvDl++0pLeFw///r/0B1rrZa31Ny3JIaQwdDyEFON+rfVnkm9orR8D8MDw5QcyfjPq5Twl8d4Lhn/vGP5+DK31JzAY+tprpu4Wfzv8+wdKqT1KKd7zJDishIQU459z3n9owuejzy5IvHfp8O+vZyzW1MPJDRdiEEOywX8HcALAizGI8XxFKfVupdQBpdR3WJJBSCkY4yGkGOf0Tkp+PmL0sHcUgPPp21rrB5VSuwFcDeDHAFyFgRN6MYDXKqWeo7VmnId4hY6HEL+Mdha4Q2v9Wz4Eaq0fxWAo8AMAoJR6OoBbMXBGrwPwWh96EDKCQ22kKXx7+Df0w9YHh39/IpQCWusHALxp+PJfhtKDNBc6HtIUvgJgA8BlSqmZUEporT+OgfN5rlLqRqXUE9PfUUp1hmuDjFFK/Vel1HdnfPSi4d8HbcghpAyhn/4I8YLW+ttKqfdhENs4oZQ6jkEv6KNa67d6VufnMVjE2sNgnc89AD4P4EkYrO/5XgzW+NhYx3M9gN9USp0AcAqDhaQdAJdjsCnob1qQQUgp2OMhTeIAgD/AYLHnzwJ4BQbBdq9orVcw2KVgAcCnAPwQgGswcDr3AXgN7DmEVwG4HUALwL/FYNfpRwG8GcCztNanLMkhpDBK66iOHyGEJBjuQ3c9gJeZ7k6dSvcjGDjl79Na328rXUIADrURUhcOKKWeB+BzWutfqpKAUuoSAL8yfPmDlvQi5BzoeAipB88dXicBVHI8ALYDsL47NiFpONRGCCHEK5xcQAghxCt0PIQQQrxCx0MIIcQrdDyEEEK8QsdDCCHEK3Q8hBBCvELHQwghxCt0PIQQQrxCx0MIIcQrdDyEEEK8QsdDCCHEK3Q8hBBCvELHQwghxCt0PIQQQrxCx0MIIcQr/x94oj9DZnvUUAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 450x375 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate Poisson Spike Trains\n",
    "spikes = get_poisson_spikes(N, nu, duration, timestep)\n",
    "\n",
    "# and plot them (at least the first 100 neurons and first 2 seconds)\n",
    "plot_maxtime = 2.0                      # seconds\n",
    "plot_maxneurons = 100                   # neurons\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(3, 2.5), dpi=150)\n",
    "plot_spikeraster(spikes, timestep, ax, \n",
    "                 max_time=plot_maxtime, max_neurons=plot_maxneurons)\n",
    "ax.set_xticks(np.arange(0, plot_maxtime+1, 1))\n",
    "ax.set_yticks([])\n",
    "ax.set_ylabel('Input neuron #')\n",
    "\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neuronal dynamics\n",
    "\n",
    "To successfully initialize postsynaptic neurons in the fluctuation-driven regime, we take into account input parameters and neuronal dynamics to define the synaptic weight distribution.\n",
    "\n",
    "We first set the parameters of the LIF neuron model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LIF parameters\n",
    "tau_syn = 10e-3\n",
    "tau_mem = 20e-3\n",
    "theta = 1.0                             # threshold\n",
    "refractory_period = 2e-3                # refractory period in s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The neuronal dynamics are captured by a kernel describing the shape of the post-synaptic potential (PSP) evoked by each spike. For weight initialization, we require the integral of the PSP-kernel $\\epsilon$ and the squared PSP-kernel $\\epsilon^2$, which we refer to as $\\bar\\epsilon$ and $\\hat\\epsilon$ respectively. \n",
    "\n",
    "The values of $\\bar\\epsilon$ and $\\hat\\epsilon$ can be computed numerically or analytically. For practical purposes, numerical estimation with the same time step used for SNN training leads to more accurate results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$\\bar\\epsilon$: 0.010507353352192265\n",
      "$\\hat\\epsilon$: 0.001841948059032449\n"
     ]
    }
   ],
   "source": [
    "def epsilon_analytical(tau_mem, tau_syn):\n",
    "    epsilon_bar = tau_syn\n",
    "    epsilon_hat = (tau_syn ** 2) / (2 * (tau_syn + tau_mem))\n",
    "\n",
    "    return epsilon_bar, epsilon_hat\n",
    "\n",
    "def epsilon_numerical(tau_mem, tau_syn):\n",
    "    kernel = stork.utils.get_lif_kernel(tau_mem, tau_syn, timestep)\n",
    "    epsilon_bar = kernel.sum() * timestep\n",
    "    epsilon_hat = (kernel**2).sum() * timestep\n",
    "    \n",
    "    return epsilon_bar, epsilon_hat\n",
    "\n",
    "def get_epsilon(tau_mem, tau_syn, calc_mode=\"numerical\"):\n",
    "    if calc_mode == 'analytical':\n",
    "        return epsilon_analytical(tau_mem, tau_syn)\n",
    "    elif calc_mode == 'numerical':\n",
    "        return epsilon_numerical(tau_mem, tau_syn)\n",
    "    else:\n",
    "        raise ValueError('invalid calc mode for epsilon')\n",
    "\n",
    "print(r'$\\bar\\epsilon$', end=\": \")\n",
    "print(get_epsilon(tau_mem, tau_syn)[0])\n",
    "print(r'$\\hat\\epsilon$', end=\": \")\n",
    "print(get_epsilon(tau_mem, tau_syn)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weight initialization\n",
    "\n",
    "We can now initialize the synaptic weights given a target membrane potential distribution that ensures sparse, fluctuation-driven firing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialization target parameters\n",
    "mu_U = 0.0      # Target mean of membrane potential distribution\n",
    "xi = 2.0        # Target distance between membrane potential mean (mu_U) and firing threshold (1.0) \n",
    "                # in units of standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sigma_w(theta, xi, N, nu, mu_U, epsilon_hat, mu_w):\n",
    "    \"\"\"Calculate standard deviation of the weight distribution, that can be used for initialization.\n",
    "\n",
    "    Args:\n",
    "        theta (float): Threshold.\n",
    "        xi (float): Initialization parameter, usually 1<xi<3.\n",
    "        N (int): Number of inputs.\n",
    "        nu (float): Input firing rate.\n",
    "        mu_U (float): Target mean membrane potential.\n",
    "        epsilon_hat (float): Integral of the squared PSP-kernel.\n",
    "        mu_w (float): Mean of the weight distribution.\n",
    "\n",
    "    Returns:\n",
    "        float: Standard deviation of the weight distribution.\n",
    "    \"\"\"\n",
    "\n",
    "    sigma2_w = 1 / (N*nu*epsilon_hat) * ((theta - mu_U) / xi) ** 2 - mu_w ** 2\n",
    "    sigma_w = np.sqrt(sigma2_w)\n",
    "    return sigma_w\n",
    "\n",
    "def get_mu_w(N, nu, mu_U, epsilon_bar):\n",
    "    \"\"\"Calculate the mean of the weight distribution, that can be used for initialization.\n",
    "\n",
    "    Args:\n",
    "        N (int): Number of input neurons.\n",
    "        nu (float): Input firing rate.\n",
    "        mu_U (float): Target mean membrane potential.\n",
    "        epsilon_bar (float): Integral of the PSP-Kernel.\n",
    "\n",
    "    Returns:\n",
    "        float: Mean of the weight distribution.\n",
    "    \"\"\"\n",
    "    mu_w = mu_U/(N*nu*epsilon_bar)\n",
    "    return mu_w\n",
    "\n",
    "def sample_normal(N, mu, sigma):    \n",
    "    return mu + np.random.randn(N) * sigma\n",
    "\n",
    "def get_w_params(N, nu, theta, mu_U, xi, tau_mem, tau_syn, eps_calc_mode=\"numerical\"):        \n",
    "    \"\"\" \n",
    "    Get mean and standard deviation for the synaptic weight distribution based on \n",
    "    a target in the fluctuation-driven reigme (defined by mu_U and xi) \n",
    "\n",
    "    Args:\n",
    "        N (int): Number of inputs.\n",
    "        nu (float, optional): Input firing rate. Defaults to None.\n",
    "        theta (float, optional): Threshold. Defaults to None.\n",
    "        mu_U (float, optional): Target mean membrane potential. Defaults to None.\n",
    "        xi (float, optional): Initialization parameter, usually 1<xi<3. Defaults to None.\n",
    "        tau_mem (float, optional): Membrane time constant. Defaults to None.\n",
    "        tau_syn (float, optional): Synaptic time constant. Defaults to None.\n",
    "        eps_calc_mode (str, optional): Calculation mode of epsilons. Defaults to \"numerical\".\n",
    "\n",
    "    Returns:\n",
    "        weights\n",
    "    \"\"\"\n",
    "    epsilon_bar, epsilon_hat = get_epsilon(calc_mode=eps_calc_mode, tau_mem=tau_mem, tau_syn=tau_syn)\n",
    "    mu_w = get_mu_w(N, nu, mu_U, epsilon_bar)\n",
    "    sigma_w = get_sigma_w(theta, xi, N, nu, mu_U, epsilon_hat, mu_w)\n",
    "\n",
    "    return mu_w, sigma_w\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For illustrative purposes, let's define a nice plotting function for distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_histogram_with_gaussian(data, mu, sigma, axis, color, linecolor, bins=40, orientation='vertical',\n",
    "                                 minmax = None, valrange=None, linewidth=1.0, edgecolor=\"white\"):\n",
    "    \n",
    "    if minmax is None:\n",
    "        minmax = (np.round(-4*sigma, 1), np.around(4*sigma, 1))\n",
    "        \n",
    "    xax = np.arange(minmax[0], minmax[1], 0.01)\n",
    "    axis.hist(data, bins=bins, color=color, density=True, orientation=orientation, \n",
    "              range=valrange, label='Simulation', edgecolor=edgecolor)\n",
    "    \n",
    "    if orientation=='horizontal':    \n",
    "        pdf = gaussian_pdf(xax, mu, sigma)\n",
    "        axis.plot(pdf, xax, color=linecolor, lw=linewidth, label='Theory')\n",
    "        \n",
    "        # remove bottom axis\n",
    "        axis.get_xaxis().set_visible(False)\n",
    "        axis.spines['bottom'].set_visible(False)\n",
    "        axis.set_ylim(minmax[0], minmax[1])\n",
    "        axis.set_yticks([minmax[0], mu, minmax[1]])\n",
    "\n",
    "    else:\n",
    "        pdf = gaussian_pdf(xax, mu, sigma)\n",
    "        axis.plot(xax, pdf, color=linecolor, lw=linewidth, label='Theory')\n",
    "    \n",
    "        # remove left axis\n",
    "        axis.get_yaxis().set_visible(False)\n",
    "        axis.spines['left'].set_visible(False)\n",
    "        \n",
    "        axis.set_xlim(minmax[0], minmax[1])\n",
    "        axis.set_xticks([minmax[0], mu, minmax[1]])\n",
    "\n",
    "    axis.spines['top'].set_visible(False)\n",
    "    axis.spines['right'].set_visible(False)\n",
    "    return axis\n",
    "\n",
    "\n",
    "def gaussian_pdf(x, mu, sigma):\n",
    "    return (1/(sigma * np.sqrt(2*np.pi))) * np.exp(-0.5 * ((x-mu)/sigma)**2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can sample the synaptic weights taking into account the input parameters and neuronal dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 450x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get synaptic weights\n",
    "eps_calc_mode = \"numerical\"\n",
    "mu_w, sigma_w = get_w_params(N=N, nu=nu, theta=theta, mu_U=mu_U, xi=xi, tau_mem=tau_mem, tau_syn=tau_syn, \n",
    "                             eps_calc_mode=eps_calc_mode)\n",
    "weights = sample_normal(N, mu_w, sigma_w)\n",
    "\n",
    "# Plot synaptic weights\n",
    "fig, ax = plt.subplots(figsize=(3,2), dpi=150)\n",
    "plot_histogram_with_gaussian(weights, mu_w, sigma_w, ax, 'grey', 'black', bins=20)\n",
    "\n",
    "ax.set_title(r'$W \\sim \\mathcal{N}(\\mu_W,\\,\\sigma_W^{2})$', \n",
    "        color='black', fontsize=8, verticalalignment='center', horizontalalignment='center')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Membrane Potential follows a Gaussian\n",
    "\n",
    "Before we can have a look at the membrane potential, let us define some functions, that compute it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_membrane(I, tau_mem, theta, dt, refractory_period=0, spike_amp=2):\n",
    "    \"\"\"Compute the membrane potential.\n",
    "\n",
    "    Args:\n",
    "        I: Input current.\n",
    "        tau_mem (float): Membrane time constant.\n",
    "        theta (float): Threshold.\n",
    "        dt (float): Simulation time step.\n",
    "        refractory_period (float, optional): Refractory period. Defaults to 0.\n",
    "        spike_amp (float, optional): Height of a spike. Defaults to 2.\n",
    "\n",
    "    Returns:\n",
    "        Membrane potential.\n",
    "    \"\"\"\n",
    "    u = np.zeros(I.shape)\n",
    "    decay = np.exp(-dt / tau_mem)\n",
    "    refrac = 0\n",
    "    \n",
    "    for t in range(1, u.shape[0]):\n",
    "        if refrac > 0:                                  # Implement refractory period\n",
    "            u[t] = 0\n",
    "        else:\n",
    "            u[t] = u[t-1] * decay + (1-decay) * I[t]    # update\n",
    "            if u[t] >= theta:                           # spikes\n",
    "                u[t] = spike_amp\n",
    "                refrac = refractory_period\n",
    "        refrac -= dt                                    # decay refrac\n",
    "    return u\n",
    "\n",
    "def get_current(spikes, weights, tau_syn, dt):\n",
    "    \"\"\"Compute synaptic currents.\n",
    "\n",
    "    Args:\n",
    "        spikes: Incoming spike trains.\n",
    "        weights: Synaptic weights.\n",
    "        tau_syn (float): Synaptic time constant.\n",
    "        dt (float): Simulation time step.\n",
    "\n",
    "    Returns:\n",
    "        Synaptic current.\n",
    "    \"\"\"\n",
    "    currents = np.zeros(spikes.shape)\n",
    "    decay = np.exp(-dt / tau_syn)\n",
    "    \n",
    "    for t in range(1, currents.shape[0]):\n",
    "        currents[t] = currents[t-1] * decay + spikes[t]\n",
    "\n",
    "    currents *= weights.T\n",
    "    return currents.sum(1) # Sum over all input neurons to get total input current"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore we want to compute the theoretical mean and variance of the membrane potential,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mu_U(N, nu, epsilon_bar, mu_w):\n",
    "    return N * nu * epsilon_bar * mu_w\n",
    "\n",
    "def get_sigma_U(N, nu, epsilon_hat, mu_w, sigma_w):\n",
    "    return np.sqrt(N * (mu_w**2 + sigma_w**2) * nu * epsilon_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "before we finally plot the membrane potential and how it is Gaussian distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 825x375 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(5.5, 2.5), dpi=150, gridspec_kw={'width_ratios': [0.7, 0.3]})\n",
    "\n",
    "# get membrane potential values and parameters\n",
    "currents = get_current(spikes, weights, tau_syn, timestep)\n",
    "out_with_spikes = get_membrane(I=currents, tau_mem=tau_mem, theta=theta, dt=dt, refractory_period=refractory_period, spike_amp=spike_amp)\n",
    "out_without_spikes = out_with_spikes.copy()\n",
    "out_without_spikes[out_without_spikes==spike_amp] = 0\n",
    "epsilon_bar, epsilon_hat = get_epsilon(calc_mode=eps_calc_mode, tau_mem=tau_mem, tau_syn=tau_syn) \n",
    "mu_U = get_mu_U(N=N, nu=nu, epsilon_bar=epsilon_bar, mu_w=mu_w)\n",
    "sigma_U = get_sigma_U(N=N, nu=nu, epsilon_hat=epsilon_hat, mu_w=mu_w, sigma_w=sigma_w)\n",
    "\n",
    "# specify plot parameters   \n",
    "figsize = (3.5, 1.4)\n",
    "time_axis = np.arange(0, plot_maxtime, timestep)\n",
    "minmax = (-2,2)\n",
    "\n",
    "# plot membrane potential\n",
    "ax[0].plot(time_axis, out_with_spikes[:len(time_axis)], color=color_membrane, lw=1)\n",
    "ax[0].hlines(theta, 0, plot_maxtime, color=color_theta, lw=1, ls='dashed', zorder=10)\n",
    "ax[0].hlines(0, 0, plot_maxtime, color='black', lw=1, ls='dashed', zorder=10)\n",
    "\n",
    "ax[0].set_ylim(minmax[0], minmax[1])\n",
    "ax[0].set_xlabel('time [s]')\n",
    "ax[0].set_ylabel(r'mem. pot. $u(t)$')\n",
    "ax[0].set_xticks(np.arange(0, plot_maxtime+1, 1))\n",
    "ax[0].set_yticks([minmax[0], 0, minmax[1]])\n",
    "\n",
    "\n",
    "# plot histogram of membrane potential with corresponding theoretical curve\n",
    "plot_histogram_with_gaussian(out_without_spikes, mu_U, sigma_U, \n",
    "                             ax[-1], color_membrane, 'black', orientation='horizontal',\n",
    "                             minmax=minmax, bins=15)\n",
    "ax[1].hlines(theta, 0, 1, color=color_theta, lw=1, ls='dashed')\n",
    "ax[1].hlines(0, 0, 1, color='black', lw=1, ls='dashed', zorder=10)\n",
    "ax[1].axes.yaxis.set_ticklabels([])\n",
    "ax[1].set_ylim(minmax[0], minmax[1])\n",
    "\n",
    "ax[0].text(plot_maxtime+0.1, theta, r'$\\theta$', color=color_theta,\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "ax[0].text(plot_maxtime+0.1, 0, r'$\\mu_U$', color='black',\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "ax[1].text(0.2, minmax[0]+0.2, r'$U \\sim \\mathcal{N}(\\mu_U,\\,\\sigma_U^{2})$', color='black',\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "ax[1].text(1.0, theta, r'$\\xi \\sigma_U$', color='black',\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "\n",
    "# Remove top and right spines\n",
    "ax[0].spines['top'].set_visible(False)\n",
    "ax[0].spines['right'].set_visible(False)\n",
    "ax[1].spines['top'].set_visible(False)\n",
    "ax[1].spines['right'].set_visible(False)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different values for $\\xi$\n",
    "\n",
    "Now we can have a look at the membrane potential distribution for different values of $\\xi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mempot_range(membrane):\n",
    "    \n",
    "    absmax = np.abs(membrane).max().round(1)\n",
    "    return (-absmax, absmax)\n",
    "\n",
    "def get_membrane_without_spikes(I, tau_mem, dt):\n",
    "    \"\"\"\n",
    "    Only implement leaky membrane, without refractory period or spike reset\n",
    "    \"\"\"    \n",
    "    u = np.zeros(I.shape)\n",
    "    decay = np.exp(-dt / tau_mem)\n",
    "    \n",
    "    for t in range(1, u.shape[0]):\n",
    "        u[t] = u[t-1] * decay + (1-decay) * I[t]\n",
    "        \n",
    "    return u\n",
    "\n",
    "def run_simulation(mu_U, xi, tau_mem, tau_syn, N, nu, duration, dt, theta, spike_amp, calc_mode=\"numerical\"):\n",
    "    # Get initial weights\n",
    "    mu_w, sigma_w = get_w_params(N, nu, theta, mu_U, xi, tau_mem, tau_syn, eps_calc_mode=\"numerical\")\n",
    "    weights = sample_normal(N, mu_w, sigma_w)\n",
    "\n",
    "    # Get spikes, currents and membrane potential\n",
    "    spikes = get_poisson_spikes(N=N, nu=nu, duration=duration, dt=dt)\n",
    "    currents = get_current(spikes=spikes, weights=weights, tau_syn=tau_syn, dt=dt)\n",
    "    membrane = get_membrane_without_spikes(I=currents, tau_mem=tau_mem, dt=dt)\n",
    "\n",
    "    # Get membrane potential considering reset and output firing rate\n",
    "    out_with_spikes = get_membrane(I=currents, tau_mem=tau_mem, theta=theta, dt=dt, refractory_period=refractory_period, spike_amp=spike_amp)\n",
    "    out_without_spikes = out_with_spikes.copy()\n",
    "    out_without_spikes[out_without_spikes==spike_amp] = 0\n",
    "\n",
    "    # Analytical calculation of mu_U and sigma_u\n",
    "    mu_U = get_mu_U(N=N, nu=nu, epsilon_bar=epsilon_bar, mu_w=mu_w)\n",
    "    sigma_U = get_sigma_U(N=N, nu=nu, epsilon_hat=epsilon_hat, mu_w=mu_w, sigma_w=sigma_w)\n",
    "\n",
    "    return membrane, out_without_spikes, mu_U, sigma_U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1003.5x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot membrane potential with different values of xi\n",
    "fig, ax = plt.subplots(1, 3, figsize=(6.69, 2.0), dpi=150)\n",
    "\n",
    "# plot parameters\n",
    "xis = (1.0, 2.0, 3.0)\n",
    "umus = (0.0, 0.0, 0.0)\n",
    "ymin, ymax = -2.5, 2.5\n",
    "yticks = [-2, 0, 2]\n",
    "\n",
    "for idx, xi, umu in zip(np.arange(3), xis, umus):\n",
    "    # run simulation\n",
    "    membrane, out_without_spikes, mu_U, sigma_U = run_simulation(mu_U=umu, xi=xi, tau_mem=tau_mem, tau_syn=tau_syn, N=N, nu=nu, duration=duration, dt=dt, theta=theta, spike_amp=spike_amp, calc_mode=\"numerical\")\n",
    "\n",
    "    # plot histogram and theoretical curve\n",
    "    minmax = get_mempot_range(membrane)\n",
    "    plot_histogram_with_gaussian(membrane,\n",
    "                                mu = mu_U,\n",
    "                                sigma = sigma_U,\n",
    "                                axis=ax[idx],\n",
    "                                color=color_membrane,\n",
    "                                linecolor='black',\n",
    "                                bins=20,\n",
    "                                minmax=(ymin, ymax),\n",
    "                                valrange=(ymin, ymax),\n",
    "                                orientation='horizontal',\n",
    "                                linewidth = 1.25)\n",
    "        \n",
    "    xmax = gaussian_pdf(np.arange(ymin, ymax, 0.01), mu_U, sigma_U).max() \n",
    "    \n",
    "    ax[idx].hlines(1.0, 0, xmax, ls='dashed', color=color_theta, lw=1)\n",
    "    ax[idx].set_xlim(0, xmax* 1.2)\n",
    "    ax[idx].set_yticks(yticks)\n",
    "    \n",
    "    if xi == 1.0:\n",
    "        f = lambda float: int(float)\n",
    "    else:\n",
    "        f = lambda float: np.round(float, 2)\n",
    "    ax[idx].text(xmax, ymax, r'$\\xi={}$'.format(int(xi)) + '\\n' + r'$\\sigma_U={}$'.format(f(1/xi)),\n",
    "                   fontsize=7, \n",
    "                   verticalalignment='top', \n",
    "                   horizontalalignment='right')\n",
    "\n",
    "    ax[idx].spines['top'].set_visible(False)\n",
    "    ax[idx].spines['right'].set_visible(False)\n",
    "    \n",
    "ax[-1].text(xmax*1.1, theta, r'$\\theta$', color=color_theta,\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "ax[1].axes.yaxis.set_ticklabels([])\n",
    "ax[2].axes.yaxis.set_ticklabels([])\n",
    "ax[0].set_ylabel(r'Mem. pot. U')\n",
    "ax[-1].legend(fontsize=6, borderpad=0.0, loc='lower right', handlelength=1.0, handleheight=0.5, frameon=False)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run another batch of simulations, this time looking at the membrane potential when considering the spike reset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1003.5x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot membrane potential with different values of xi\n",
    "fig, ax = plt.subplots(1, 3, figsize=(6.69, 2.0), dpi=150)\n",
    "\n",
    "for idx, xi, umu in zip(np.arange(3), xis, umus):\n",
    "    # run simulation\n",
    "    membrane, out_without_spikes, mu_U, sigma_U = run_simulation(mu_U=umu, xi=xi, tau_mem=tau_mem, tau_syn=tau_syn, N=N, nu=nu, duration=duration, dt=dt, theta=theta, spike_amp=spike_amp, calc_mode=\"numerical\")\n",
    "\n",
    "    # plot histogram and theoretical curve\n",
    "    minmax = get_mempot_range(out_without_spikes)\n",
    "    plot_histogram_with_gaussian(out_without_spikes,\n",
    "                                mu = mu_U,\n",
    "                                sigma = sigma_U,\n",
    "                                axis=ax[idx],\n",
    "                                color=color_membrane,\n",
    "                                linecolor='black',\n",
    "                                bins=20,\n",
    "                                minmax=(ymin, ymax),\n",
    "                                valrange=(ymin, ymax),\n",
    "                                orientation='horizontal',\n",
    "                                linewidth = 1.25)\n",
    "        \n",
    "    xmax = gaussian_pdf(np.arange(ymin, ymax, 0.01), mu_U, sigma_U).max() \n",
    "    \n",
    "    ax[idx].hlines(1.0, 0, xmax, ls='dashed', color=color_theta, lw=1)\n",
    "    ax[idx].set_xlim(0, xmax* 1.2)\n",
    "    ax[idx].set_yticks(yticks)\n",
    "    \n",
    "    if xi == 1.0:\n",
    "        f = lambda float: int(float)\n",
    "    else:\n",
    "        f = lambda float: np.round(float, 2)\n",
    "    ax[idx].text(xmax, ymax, r'$\\xi={}$'.format(int(xi)) + '\\n' + r'$\\sigma_U={}$'.format(f(1/xi)),\n",
    "                   fontsize=7, \n",
    "                   verticalalignment='top', \n",
    "                   horizontalalignment='right')\n",
    "\n",
    "    ax[idx].spines['top'].set_visible(False)\n",
    "    ax[idx].spines['right'].set_visible(False)\n",
    "    \n",
    "ax[-1].text(xmax*1.1, theta, r'$\\theta$', color=color_theta,\n",
    "                   fontsize=7, verticalalignment='center')\n",
    "ax[1].axes.yaxis.set_ticklabels([])\n",
    "ax[2].axes.yaxis.set_ticklabels([])\n",
    "ax[0].set_ylabel(r'Mem. pot. U')\n",
    "ax[-1].legend(fontsize=6, borderpad=0.0, loc='lower right', handlelength=1.0, handleheight=0.5, frameon=False)\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "4801fe533c28fcaf57028b73c965aa7a759ac2803d659f55fa41a0b68c770499"
  },
  "kernelspec": {
   "display_name": "Python 3.8.10 ('stork-dev')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}