julia_nb.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `~/Projects/Postdoc/nature_temp_paper/temporal_criticality/julia_temp_criticality`\n"
     ]
    }
   ],
   "source": [
    "using Pkg;\n",
    "Pkg.activate(\"./julia_temp_criticality/\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Temporal criticality\n",
    "\n",
    "The goal of this notebook is to show how to use some of the functions in the `julia_temp_criticality` package used to reproduce the \"Temporal Criticality\" paper. \n",
    "\n",
    "## Equations\n",
    "\n",
    "We are trying to simulate the equation\n",
    "\n",
    "$$\n",
    "\\tau_{i,t} = \\max_{j \\in \\mathcal{N}_i} \\left( \\tau_{j,t-1} - B \\right) + \\varepsilon_{i,t}.\n",
    "$$\n",
    "\n",
    "\n",
    "We know that, setting $\\tau_{i,0}=0,\\quad \\forall i$ we will have $\\mathbb{E}[\\tau_{i,t}] = Vt$ with $V=(B_c-B)^+$, where $B_c$ is determined by simulation for finite $N$.\n",
    "\n",
    "## Simulations\n",
    "\n",
    "All of the required code is in the `julia_temp_criticality` package. We will run a short simulation to show that we do indeed have $V=(B_c-B)^+$.  We will run our simulation with $N=10 000$ nodes with each $k=7$ neighbours (this means that $\\mathcal{N}_i$ is a set of $7$ randomly chosen nodes at each time point). We will run the simulation for $T=10000$ time steps, sweeping over values of $B$ ranging from $2.5$ to $4$. \n",
    "\n",
    "As we will see, this will give a value of $B_c$ close to $4$. \n",
    "\n",
    "We will run this using a parallel implementation of the algorithm, using $4$ threads (this can be augmented). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "run_simulation (generic function with 1 method)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this code will run on a personal computer, assuming you have 4 cores available for computations.\n",
    "# if you have more cores, you can change the number of workers below to increase the parallel performance, and then you can also increase\n",
    "# the values of n and T to get better statistics\n",
    "\n",
    "using Distributed;\n",
    "# add 4 workers for better parallel performance\n",
    "addprocs(4);\n",
    "\n",
    "@everywhere using julia_temp_criticality;\n",
    "\n",
    "\n",
    "function run_simulation(n, k, T, Bs)\n",
    "    results = pmap(B->order_parameter_lstsq(meanfield_simulation(n, k, T, B)), Bs)\n",
    "    return results\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first reproduce a crude version of the order parameter plot. A more refined version can be given by running with more datapoints in e.g. a cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Bs = 2.5:0.05:4.5\n",
    "k = 7\n",
    "n = 10_000\n",
    "T = 1000 \n",
    "\n",
    "simulations = run_simulation(n, k, T, Bs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the plotting package \n",
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we approximate Bc as 4 for simplicity\n",
    "\n",
    "pseudo_theory = [positive_part.(4-B) for B in Bs];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(Bs, simulations, label=\"simulation data\", xlabel=\"B\", ylabel=\"order parameter V\", title=\"mean field simulation\", legend=:topleft)\n",
    "plot!(Bs, pseudo_theory, label=\"approximate theory\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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