nb/2022-02-07__N_to_1_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "57ab3994",
   "metadata": {},
   "source": [
    "# 2022-02-07 • N-to-1 simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c99fa4fd",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e8899c91",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pkg.resolve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "87685370",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39musing Revise\n",
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mimport Distributions\n",
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mimport MyToolbox\n",
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mPrecompiling MyToolbox [54cd1024-cafd-4d62-948d-ced4874502bf]\n",
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39musing VoltageToMap\n",
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mPrecompiling VoltageToMap [b3b8fdc5-3c26-4000-a0c8-f17415fdf48e]\n"
     ]
    }
   ],
   "source": [
    "include(\"nb_init.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f91aa092",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Parameters, ComponentArrays\n",
    "@alias CVec = ComponentVector;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9de0f05e",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd8add07",
   "metadata": {},
   "source": [
    "### Simulation duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25409882",
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_duration = 1.2 * seconds;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe9b00fd",
   "metadata": {},
   "source": [
    "### Input spike trains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "55a40ebc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_unconn = 100\n",
    "N_exc    = 800\n",
    "# N_exc    = 5200\n",
    "N_inh    = N_exc ÷ 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d20af118",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_conn = N_inh + N_exc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f4ef6c40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1100"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = N_conn + N_unconn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7abaf6cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogNormal{Float64}(μ=1.0862943611198905, σ=0.7745966692414834)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_spike_rate = LogNormal_with_mean(4Hz, √0.6)  # See the previous notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32e10fe4",
   "metadata": {},
   "source": [
    "### Synapses"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "388fa39a",
   "metadata": {},
   "source": [
    "Reversal potential at excitatory and inhibitory synapses,\n",
    "as in the report [`2021-11-11__synaptic_conductance_ratio.pdf`](https://github.com/tfiers/phd-thesis/blob/main/reports/2021-11-11__synaptic_conductance_ratio.pdf):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "642d4520",
   "metadata": {},
   "outputs": [],
   "source": [
    "E_exc =   0 * mV\n",
    "E_inh = -65 * mV;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe1bb8a3",
   "metadata": {},
   "source": [
    "Synaptic conductances `g` at `t = 0`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0e74fd47",
   "metadata": {},
   "outputs": [],
   "source": [
    "g_t0 = 0 * nS;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36f1bbd3",
   "metadata": {},
   "source": [
    "Exponential decay time constant of synaptic conductance, $τ_{s}$ (`s` for \"synaptic\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "09eea508",
   "metadata": {},
   "outputs": [],
   "source": [
    "τ_s = 7 * ms;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e767fb0",
   "metadata": {},
   "source": [
    "Increase in synaptic conductance on a presynaptic spike"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ac83741d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Δg_exc = 0.1 * nS\n",
    "Δg_inh = 0.4 * nS;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e135c5c",
   "metadata": {},
   "source": [
    "### Izhikevich neuron"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e02dc031",
   "metadata": {},
   "source": [
    "Initial membrane potential `v` and adaptation variable `u` values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ffc8771e",
   "metadata": {},
   "outputs": [],
   "source": [
    "v_t0  = -80 * mV\n",
    "u_t0  =   0 * pA;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "608dfd37",
   "metadata": {},
   "source": [
    "Izhikevich's neuron model parameters for a cortical regular spiking neuron:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "704fe985",
   "metadata": {},
   "outputs": [],
   "source": [
    "cortical_RS = CVec(\n",
    "    C      = 100 * pF,\n",
    "    k      = 0.7 * (nS/mV),  # steepness of dv/dt's parabola\n",
    "    vr     = -60 * mV,\n",
    "    vt     = -40 * mV,\n",
    "    a      = 0.03 / ms,      # 1 / time constant of `u`\n",
    "    b      = -2 * nS,        # how strongly `v` deviations from `vr` increase `u`.\n",
    "    v_peak =  35 * mV,\n",
    "    c      = -50 * mV,       # reset voltage.\n",
    "    d      = 100 * pA,       # `u` increase on spike. Free parameter.\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7dc3944",
   "metadata": {},
   "source": [
    "### Numerics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1d73960",
   "metadata": {},
   "source": [
    "Whether to use a fixed (`false`) or [adaptive](https://www.wikiwand.com/en/Adaptive_step_size) timestep (`true`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "23e0637c",
   "metadata": {},
   "outputs": [],
   "source": [
    "adaptive = true;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd48f06a",
   "metadata": {},
   "source": [
    "Timestep. If `adaptive`, size of first time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "237c9025",
   "metadata": {},
   "outputs": [],
   "source": [
    "dt    = 0.1 * ms;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "817524d3",
   "metadata": {},
   "source": [
    "Minimum and maximum step sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1ffa425d",
   "metadata": {},
   "outputs": [],
   "source": [
    "dtmax = 0.5  * ms  # solution unstable if not set\n",
    "dtmin = 0.01 * ms;  # don't spend too much time finding thr crossing or spike arrival"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a4999f5",
   "metadata": {},
   "source": [
    "Error tolerances used for determining step size, if `adaptive`.\n",
    "\n",
    "The solver guarantees that the (estimated) difference between\n",
    "the numerical solution and the true solution at any time step\n",
    "is not larger than `abstol + reltol * |y|`\n",
    "(where `y` ≈ the numerical solution at that time step)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "75c6af60",
   "metadata": {},
   "outputs": [],
   "source": [
    "abstol_v = 0.1 * mV\n",
    "abstol_u = 0.1 * pA\n",
    "abstol_g = 0.01 * nS;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b19c23fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "reltol = 1e-3;  # e.g. if true sol is -80 mV, then max error of 0.08 mV\n",
    "reltol = 1;     # only use abstol"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b946e87",
   "metadata": {},
   "source": [
    "From the manual: \"These tolerances are local tolerances and thus are not global guarantees. However, a good rule of thumb is that the total solution accuracy is 1-2 digits less than the relative tolerances.\" [[1]](https://diffeq.sciml.ai/stable/basics/faq/#What-does-tolerance-mean-and-how-much-error-should-I-expect)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "28153750",
   "metadata": {},
   "outputs": [],
   "source": [
    "tol_correction = 0.1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9f143aeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0e-5, 1.0000000000000002e-14, 1.0000000000000002e-12)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(abstol_v, abstol_u, abstol_g) .* tol_correction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bbb2f31",
   "metadata": {},
   "source": [
    "For comparison, the default tolerances for ODEs in DifferentialEquations.jl are\n",
    "- `reltol = 1e-2`\n",
    "- `abstol = 1e-6`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62ad293e",
   "metadata": {},
   "source": [
    "## IDs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "955eded5",
   "metadata": {},
   "source": [
    "Neuron, synapse & simulated variable IDs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0ccb8c1",
   "metadata": {},
   "source": [
    "IDs and connections are simple here for the N-to-1 case: only input 'neurons' get an ID, and there is only one synapse for every (connected) neuron."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd36d1a3",
   "metadata": {},
   "source": [
    "A utility function. See below for its usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "158714be",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "    idvec(A = 4, B = 2, …)\n",
    "\n",
    "Build a `ComponentVector` (CVec) with the given group names and\n",
    "as many elements per group as specified. Each element gets a\n",
    "unique ID within the CVec, which is also its index in the CVec.\n",
    "I.e. the above call yields `CVec(A = [1,2,3,4], B = [5,6])`.\n",
    "\"\"\"\n",
    "function idvec(; kw...)\n",
    "    cvec = CVec(; (name => _expand(val) for (name, val) in kw)...)\n",
    "    cvec .= 1:length(cvec)\n",
    "    return cvec\n",
    "end;\n",
    "\n",
    "temp = -1  # value does not matter; they get overwritten by UnitRange\n",
    "_expand(val::Nothing) = temp\n",
    "_expand(val::Integer) = fill(temp, val)\n",
    "_expand(val::CVec)    = val              # allow nested idvecs\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "6ad76f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0mComponentVector{Int64}(conn = (exc = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  791, 792, 793, 794, 795, 796, 797, 798, 799, 800], inh = [801, 802, 803, 804, 805, 806, 807, 808, 809, 810  …  991, 992, 993, 994, 995, 996, 997, 998, 999, 1000]), unconn = [1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010  …  1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_neurons = idvec(conn = idvec(exc = N_exc, inh = N_inh), unconn = N_unconn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6a126c71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0mComponentVector{Int64}(exc = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10  …  791, 792, 793, 794, 795, 796, 797, 798, 799, 800], inh = [801, 802, 803, 804, 805, 806, 807, 808, 809, 810  …  991, 992, 993, 994, 995, 996, 997, 998, 999, 1000])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "synapses = idvec(exc = N_exc, inh = N_inh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d646bc50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0mComponentVector{Int64}(v = 1, u = 2, g = (exc = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12  …  793, 794, 795, 796, 797, 798, 799, 800, 801, 802], inh = [803, 804, 805, 806, 807, 808, 809, 810, 811, 812  …  993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulated_vars = idvec(v = nothing, u = nothing, g = synapses)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24778f43",
   "metadata": {},
   "source": [
    "Example usage of these objects:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d92181a8",
   "metadata": {},
   "source": [
    "Pick some global input neuron ID"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "65d87a01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "802"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = N_exc + 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70f9a818",
   "metadata": {},
   "source": [
    "We can index globally, or locally: we want the second connected inhibitory neuron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0f670b17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(802, 802)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_neurons[n], input_neurons.conn.inh[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed0b54f5",
   "metadata": {},
   "source": [
    "Some introspection, useful for printing & plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "08e9b3c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"conn.inh[2]\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels(input_neurons)[n]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66502b1e",
   "metadata": {},
   "source": [
    "## Connections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "62a6bdde",
   "metadata": {},
   "outputs": [],
   "source": [
    "postsynapses = Dict{Int, Vector{Int}}()  # input_neuron_ID => [synapse_IDs...]\n",
    "\n",
    "for (n, s) in zip(input_neurons.conn, synapses)\n",
    "    postsynapses[n] = [s]\n",
    "end\n",
    "for n in input_neurons.unconn\n",
    "    postsynapses[n] = []\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c13b13e",
   "metadata": {},
   "source": [
    "## Broadcast parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a857ac6a",
   "metadata": {},
   "source": [
    "A bunch of synaptic parameters are given as scalars, but pertain to multiple synapses at once.\n",
    "Here we broadcast these scalars to vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "26ef609e",
   "metadata": {},
   "outputs": [],
   "source": [
    "Δg = similar(synapses, Float64)\n",
    "Δg.exc .= Δg_exc\n",
    "Δg.inh .= Δg_inh;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5a36b6e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = similar(synapses, Float64)\n",
    "E.exc .= E_exc\n",
    "E.inh .= E_inh;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "424658a3",
   "metadata": {},
   "source": [
    "Initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f734dc87",
   "metadata": {},
   "outputs": [],
   "source": [
    "vars_t0 = similar(simulated_vars, Float64)\n",
    "vars_t0.v = v_t0\n",
    "vars_t0.u = u_t0\n",
    "vars_t0.g .= g_t0;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9e74050",
   "metadata": {},
   "source": [
    "Maximum error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7bf02297",
   "metadata": {},
   "outputs": [],
   "source": [
    "abstol = similar(simulated_vars, Float64)\n",
    "abstol.v = abstol_v\n",
    "abstol.u = abstol_u\n",
    "abstol.g .= abstol_g\n",
    "abstol = abstol .* tol_correction;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c111fa6",
   "metadata": {},
   "source": [
    "## ISI distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "912807c0",
   "metadata": {},
   "source": [
    "Generate firing rates $λ$ by sampling from the input spike rate distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "05b1d316",
   "metadata": {},
   "outputs": [],
   "source": [
    "λ = similar(input_neurons, Float64)\n",
    "λ .= rand(input_spike_rate, length(λ));\n",
    "# showsome(λ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da893593",
   "metadata": {},
   "source": [
    "`Distributions.jl` uses an alternative `Exp` parametrization, namely scale $β$ = 1 / rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "9e8713b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "β = 1 ./ λ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2ff447ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "ISI_distributions = similar(input_neurons, Exponential{Float64})\n",
    "ISI_distributions .= Exponential.(β);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a66cfef7",
   "metadata": {},
   "source": [
    "## Initialize spiking"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "954215e5",
   "metadata": {},
   "source": [
    "Generate the first spike time for every input neuron by sampling once from its ISI distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b21763fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "first_spike_times = rand.(ISI_distributions);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06625d12",
   "metadata": {},
   "source": [
    "Sort these initial spike times by building a priority queue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ea66d7cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "upcoming_input_spikes = PriorityQueue{Int, Float64}()\n",
    "\n",
    "for (neuron, first_spike_time) in enumerate(first_spike_times)\n",
    "    enqueue!(upcoming_input_spikes, neuron => first_spike_time)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c1fae39",
   "metadata": {},
   "source": [
    "## Parameter object"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b7e351c",
   "metadata": {},
   "source": [
    "Encapsulate all 'parameters' used in the differential equation function\n",
    "and the event callback functions in one `NamedTuple`,\n",
    "which is passed through to these functions by DiffEq.jl.\n",
    "\n",
    "This is so that we don't need to read these variables\n",
    "from the global scope (closure), which slows type inference i.e. compilation time.\n",
    "\n",
    "'parameters' in quotes, cause some values are mutated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a51a2d28",
   "metadata": {},
   "outputs": [],
   "source": [
    "params = (;\n",
    "    E, Δg, τ_s,\n",
    "    izh = cortical_RS,\n",
    "    postsynapses,\n",
    "    ISI_distributions,\n",
    "    upcoming_input_spikes,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0abd479a",
   "metadata": {},
   "source": [
    "## Differential equations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf84b46b",
   "metadata": {},
   "source": [
    "The derivative functions that define the differential equations.\n",
    "Note that discontinuities are defined in the next section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4d22c924",
   "metadata": {},
   "outputs": [],
   "source": [
    "function f(D, vars, params, _)\n",
    "    @unpack v, u, g = vars\n",
    "    @unpack izh, E, τ_s = params\n",
    "    @unpack C, k, vr, vt, a, b = izh\n",
    "    I_s = 0.0\n",
    "    for (gi, Ei) in zip(g, E)\n",
    "        I_s += gi * (v - Ei)\n",
    "    end\n",
    "    D.v = (k * (v - vr) * (v - vt) - u - I_s) / C\n",
    "    D.u = a * (b * (v - vr) - u)\n",
    "    D.g .= .-g ./ τ_s\n",
    "    return nothing\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbf18a78",
   "metadata": {},
   "source": [
    "Applied performance optimizations:\n",
    "- Don't use `I_s = sum(g .* (v .- E))`, which allocates a new array. Rather, we use an accumulating loop.\n",
    "- `D.g .= …`: elementwise assignment; instead of overwriting `D.g` with a new array that needs to be allocated.\n",
    "- Parameters via function argument, and not closure of global variables: to speed up type inference (apparently)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b48eda3",
   "metadata": {},
   "source": [
    "About the sign of the synaptic current `I_s`:\n",
    "membrane current is by convention positive\n",
    "if positive charges are flowing _out_ of the cell.\n",
    "\n",
    "For *e.g.* `v = -80 mV` and `Ei = 0 mV` (*i.e.* an excitatory synapse),\n",
    "we get negative `I_si` (namely `gi * -80 mV`), *i.e.* positive charges flowing in ✔."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70eb31c5",
   "metadata": {},
   "source": [
    "## Events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "971f6164",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "An `Event` encapsulates two functions that determine when and\n",
    "how to introduce discontinuities in the differential equations:\n",
    "\n",
    "- `distance` returns some distance to the next event.\n",
    "   An event occurs when this distance hits zero.\n",
    "- `on_event!` is called at each event and may modify\n",
    "   the simulated variables and the parameter object.\n",
    "\n",
    "Both functions take the parameters `(vars, params, t)`: the simulated\n",
    "variables, the parameter object, and the current simulation time.\n",
    "\"\"\"\n",
    "struct Event\n",
    "    distance\n",
    "    on_event!\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "378ad6f7",
   "metadata": {},
   "source": [
    "Input spike generation (== arrival, because no transmission delay):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "2169a8a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "function time_to_next_input_spike(vars, params, t)\n",
    "    _, next_input_spike_time = peek(params.upcoming_input_spikes)\n",
    "        # `peek(pq)` simply returns `pq.xs[1]`; i.e. it's fast.\n",
    "    return t - next_input_spike_time\n",
    "end\n",
    "\n",
    "function on_input_spike!(vars, params, t)\n",
    "    # Process the neuron that just fired.\n",
    "    # Start by removing it from the queue.\n",
    "    fired_neuron = dequeue!(params.upcoming_input_spikes)\n",
    "\n",
    "    # Generate a new spike time, and add it to the queue.\n",
    "    new_spike_time = t + rand(params.ISI_distributions[fired_neuron])\n",
    "    enqueue!(params.upcoming_input_spikes, fired_neuron => new_spike_time)\n",
    "\n",
    "    # Update the downstream synapses\n",
    "    # (number of these synapses in the N-to-1 case: 0 or 1).\n",
    "    for synapse in params.postsynapses[fired_neuron]\n",
    "        vars.g[synapse] += params.Δg[synapse]\n",
    "    end\n",
    "\n",
    "end\n",
    "\n",
    "input_spike = Event(time_to_next_input_spike, on_input_spike!);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38772241",
   "metadata": {},
   "source": [
    "Spiking threshold crossing of Izhikevich neuron:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "ac8cc02c",
   "metadata": {},
   "outputs": [],
   "source": [
    "distance_to_spiking_threshold(vars, params, _) = vars.v - params.izh.v_peak\n",
    "\n",
    "function on_spiking_threshold_crossing!(vars, params, _)\n",
    "    # The discontinuous LIF/Izhikevich/AdEx update\n",
    "    vars.v = params.izh.c\n",
    "    vars.u += params.izh.d\n",
    "end\n",
    "\n",
    "spiking_threshold_crossing = Event(distance_to_spiking_threshold, on_spiking_threshold_crossing!);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "286d59e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "events = [input_spike, spiking_threshold_crossing];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b310aa",
   "metadata": {},
   "source": [
    "## diffeq.jl API"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5db9d2a",
   "metadata": {},
   "source": [
    "Set-up problem and solution in DifferentialEquations.jl's API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "8acf93e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39musing OrdinaryDiffEq\n"
     ]
    }
   ],
   "source": [
    "@withfeedback using OrdinaryDiffEq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "7db8d667",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[36mODEProblem\u001b[0m with uType \u001b[36mComponentVector{Float64, Vector{Float64}, Tuple{Axis{(v = 1, u = 2, g = ViewAxis(3:1002, Axis(exc = 1:800, inh = 801:1000)))}}}\u001b[0m and tType \u001b[36mFloat64\u001b[0m. In-place: \u001b[36mtrue\u001b[0m\n",
       "timespan: (0.0, 1.2)\n",
       "u0: \u001b[0mComponentVector{Float64}(v = -0.08, u = 0.0, g = (exc = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], inh = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = ODEProblem(f, vars_t0, float(sim_duration), params)\n",
    "    # Duration must be float, so that `t` variable is float."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "0ad0e4c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "function condition(distance, vars, t, integrator)\n",
    "    for (i, event) in enumerate(events)\n",
    "        distance[i] = event.distance(vars, integrator.p, t)\n",
    "    end\n",
    "end\n",
    "\n",
    "function affect!(integrator, i)\n",
    "    events[i].on_event!(integrator.u, integrator.p, integrator.t)\n",
    "end\n",
    "\n",
    "callback = VectorContinuousCallback(condition, affect!, length(events));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "318323ce",
   "metadata": {},
   "source": [
    "The default and recommended solver. A Runge-Kutta method. Refers to Tsitouras 2011.\n",
    "See http://www.peterstone.name/Maplepgs/Maple/nmthds/RKcoeff/Runge_Kutta_schemes/RK5/RKcoeff5n_1.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "a5241d2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Tsit5(stage_limiter! = trivial_limiter!, step_limiter! = trivial_limiter!, thread = static(false))"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver = Tsit5()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "553dddab",
   "metadata": {},
   "source": [
    "Don't save all the synaptic conductances, only save `v` and `u`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "683155f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "save_idxs = [simulated_vars.v, simulated_vars.u];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc3dfdac",
   "metadata": {},
   "source": [
    "Log progress (only relevant in REPL; not visible in nb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "ba7f617e",
   "metadata": {},
   "outputs": [],
   "source": [
    "progress = true;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "ab44a038",
   "metadata": {},
   "outputs": [],
   "source": [
    "solve_() = solve(\n",
    "    prob, solver;\n",
    "    callback, save_idxs, progress,\n",
    "    adaptive, dt, dtmax, dtmin, abstol, reltol,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c5a5043",
   "metadata": {},
   "source": [
    "## Solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "a3030359",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 12.388856 seconds (23.88 M allocations: 1.152 GiB, 4.50% gc time, 89.20% compilation time)\n"
     ]
    }
   ],
   "source": [
    "sol = @time solve_();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92838062",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "4e69c1a4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mimport PyPlot\n"
     ]
    }
   ],
   "source": [
    "@withfeedback import PyPlot\n",
    "using Sciplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "6d50911c",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\" tzoom = [200ms, 600ms] e.g. \"\"\"\n",
    "function Sciplotlib.plot(sol::ODESolution; tzoom = nothing)\n",
    "    isnothing(tzoom) && (tzoom = sol.t[[1,end]])\n",
    "    izoom = first(tzoom) .< sol.t .< last(tzoom)\n",
    "    plot(\n",
    "        sol.t[izoom] / ms,\n",
    "        sol[1,izoom] / mV,\n",
    "        clip_on = false,\n",
    "        marker = \".\", ms = 1.2, lw = 0.4,\n",
    "        #  xlim = tzoom,  # haha lolwut, adding this causes fig to no longer display.\n",
    "    )\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "80f21910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <Figure size 800x480 with 1 Axes>)"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 400
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sol);"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,jl:light"
  },
  "kernelspec": {
   "display_name": "Julia 1.7.0",
   "language": "julia",
   "name": "julia-1.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.7.0"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": false,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "513.807px",
    "left": "25.3523px",
    "top": "123px",
    "width": "212px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}