Finite_automata.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ca38c1e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans\n",
    "import scipy\n",
    "import math\n",
    "from datetime import datetime\n",
    "import matplotlib.animation as animation\n",
    "from PIL import Image\n",
    "import random\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d33d45f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = math.ulp(1.0)\n",
    "\n",
    "def softmax(x):\n",
    "    return np.nan_to_num((np.exp(x)+epsilon))/np.nan_to_num((sum(np.exp(x))+epsilon))\n",
    "\n",
    "def simulate_allstarts(eta,simlen,beta,a,h,noise,H):\n",
    "    m_log=np.zeros([simlen,P,P])\n",
    "    x_log=np.zeros([simlen,P,N])\n",
    "    x_last=np.zeros([N,P])\n",
    "    projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "    for start_node in range(P):\n",
    "        x=xi[:,start_node]+noise*(np.random.rand(N)-0.5)\n",
    "        for t in range(simlen):\n",
    "            r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "            r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "            x+=eta*(r[0]-x)\n",
    "            m=np.zeros(P)\n",
    "            for i in range(P):\n",
    "                m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "            x_log[t,start_node,:]=x\n",
    "            m_log[t,start_node,:]=m\n",
    "        x_last[:,start_node]=x\n",
    "    autocorr = np.corrcoef(x_last.T) #correlation between attractors\n",
    "\n",
    "    return (autocorr, m_log, x_log)\n",
    "\n",
    "def simulate_allstarts_freq(eta,simlen,beta,a,h,freq,noise,H):\n",
    "    m_log=np.zeros([simlen,P,P])\n",
    "    x_last=np.zeros([N,P])\n",
    "    projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "    for start_node in range(P):\n",
    "        x=xi[:,start_node]+noise*(np.random.rand(N)-0.5)\n",
    "        stim_node=start_node-freq\n",
    "        for t in range(simlen):\n",
    "            if (t>1) & (t%freq==0):\n",
    "                x+=xi[:,stim_node%P]+0.0\n",
    "                stim_node-=freq\n",
    "            r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "            x+=eta*(r[0]-x)\n",
    "            m=np.zeros(P)\n",
    "            for i in range(P):\n",
    "                m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "            m_log[t,:,:]=m\n",
    "        x_last[:,start_node]=x\n",
    "    cor_activity=np.corrcoef(x_last.T) #correlation between attractors\n",
    "    return (m_log, cor_activity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5cc027b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv('family-tree-adjacency-matrix.csv')\n",
    "df = df.set_index(df.columns[0])\n",
    "\n",
    "G_automata = nx.DiGraph()\n",
    "G_automata.add_nodes_from(list(df.keys()))\n",
    "\n",
    "for i in G_automata.nodes():\n",
    "    for j in df[df[i].notnull()].index.tolist():\n",
    "        G_automata.add_edge(i,j)\n",
    "        \n",
    "plt.figure(3,figsize=(3,5)) \n",
    "nx.draw(G_automata, pos=nx.bipartite_layout(G_automata, ['H','M','B','L']), with_labels=True, \n",
    "        node_size=550, node_color='lightgray')#, font_weight='normal')\n",
    "# plt.savefig(\"family_tree_graph.pdf\", format=\"pdf\", bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "20c04511",
   "metadata": {},
   "outputs": [],
   "source": [
    "P = len(G_automata.nodes()) # number of patterns\n",
    "N = 1000 # number of neurons\n",
    "H = nx.adjacency_matrix(G_automata).T # adjacency matrix\n",
    "\n",
    "char_ratio = 0.25\n",
    "char_N = round(char_ratio*N)\n",
    "rel_N = 1-char_N\n",
    "\n",
    "homer = np.random.rand(N)\n",
    "marge = np.random.rand(N)\n",
    "bart = np.random.rand(N)\n",
    "lisa = np.random.rand(N)\n",
    "\n",
    "brother = np.random.rand(N)\n",
    "sister = np.random.rand(N)\n",
    "mother = np.random.rand(N)\n",
    "father = np.random.rand(N)\n",
    "son = np.random.rand(N)\n",
    "daughter = np.random.rand(N)\n",
    "husband = np.random.rand(N)\n",
    "wife = np.random.rand(N)\n",
    "\n",
    "homer_wife = np.concatenate([homer[:char_N-1],wife[:rel_N]])\n",
    "homer_son = np.concatenate([homer[:char_N-1],son[:rel_N]])\n",
    "homer_daughter = np.concatenate([homer[:char_N-1],daughter[:rel_N]])\n",
    "\n",
    "marge_husband = np.concatenate([marge[:char_N-1],husband[:rel_N]])\n",
    "marge_son = np.concatenate([marge[:char_N-1],son[:rel_N]])\n",
    "marge_daughter = np.concatenate([marge[:char_N-1],daughter[:rel_N]])\n",
    "\n",
    "lisa_father = np.concatenate([lisa[:char_N-1],father[:rel_N]])\n",
    "lisa_mother = np.concatenate([lisa[:char_N-1],mother[:rel_N]])\n",
    "lisa_brother = np.concatenate([lisa[:char_N-1],brother[:rel_N]])\n",
    "\n",
    "bart_father = np.concatenate([bart[:char_N-1],father[:rel_N]])\n",
    "bart_mother = np.concatenate([bart[:char_N-1],mother[:rel_N]])\n",
    "bart_sister = np.concatenate([bart[:char_N-1],sister[:rel_N]])\n",
    "\n",
    "# 'H', 'H-W', 'H-So', 'H-D', 'M', 'M-Hu', 'M-So', 'M-D', 'L', 'L-Mo', 'L-F', 'L-Br', 'B', 'B-Mo', 'B-F', 'B-Si'\n",
    "xi = np.vstack((homer, homer_wife, homer_son, homer_daughter,\n",
    "          marge, marge_husband, marge_son, marge_daughter,\n",
    "          lisa, lisa_mother, lisa_father, lisa_brother,\n",
    "          bart, bart_mother, bart_father, bart_sister)).T\n",
    "\n",
    "xi_mean=np.sum(xi, axis=1, keepdims=True)/P\n",
    "xi_bias=xi-xi_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c66271d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "simlen = 100\n",
    "start_node = 1\n",
    "a=0\n",
    "h=1\n",
    "\n",
    "beta = 1\n",
    "eta = 0.1\n",
    "noise = 0\n",
    "\n",
    "m_log=np.zeros([simlen,P,P])\n",
    "x_log=np.zeros([simlen,P,N])\n",
    "x_last=np.zeros([N,P])\n",
    "\n",
    "projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "for start_node in range(P):\n",
    "    x=np.copy(xi[:,start_node])\n",
    "    for t in range(simlen):\n",
    "        r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "        r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "        x+=eta*(r[0]-x)\n",
    "        m=np.zeros(P)\n",
    "        for i in range(P):\n",
    "            m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "        x_log[t,start_node,:]=x\n",
    "        m_log[t,start_node,:]=m\n",
    "    x_last[:,start_node]=x\n",
    "\n",
    "autocorr = np.corrcoef(x_last.T) #correlation between attractors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c59721cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "node_labels = np.array(['H', 'H-W', 'H-So', 'H-D', 'M', 'M-Hu', 'M-So', 'M-D', 'L', \n",
    "                        'L-Mo', 'L-F', 'L-Br', 'B', 'B-Mo', 'B-F', 'B-Si'])\n",
    "fig, axes = plt.subplots(nrows=math.ceil(P/4), ncols=4, figsize=(9,9))\n",
    "\n",
    "axes = axes.flatten()\n",
    "for i in range(0,P):\n",
    "    axes[i].plot(m_log[:,i,:], label=node_labels)\n",
    "    if (i % 4 == 0):\n",
    "        axes[i].set_ylabel('Pattern overlap')\n",
    "    if (i >= 12):\n",
    "        axes[i].set_xlabel('$t$')\n",
    "\n",
    "plt.tight_layout()\n",
    "axes[7].legend(bbox_to_anchor=(1.1, 0.85),loc='upper left', borderaxespad=0.)\n",
    "# plt.savefig(\"automata_a0_h1.pdf\", format=\"pdf\", bbox_inches=\"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "064eeb68",
   "metadata": {},
   "outputs": [],
   "source": [
    "simlen=400\n",
    "\n",
    "a=0\n",
    "h=1\n",
    "\n",
    "beta = 0.5\n",
    "eta = 0.1\n",
    "noise = 0\n",
    "\n",
    "m_log=np.zeros([simlen,P,P])\n",
    "x_log=np.zeros([simlen,P,N])\n",
    "x_last=np.zeros([N,P])\n",
    "\n",
    "projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "x=marge\n",
    "for t in range(0,100):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log[t,0,:]=m\n",
    "x = np.concatenate([np.copy(x)[:char_N-1],daughter[:rel_N]])\n",
    "for t in range(100,200):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],daughter[:rel_N]])\n",
    "for t in range(200,300):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],brother[:rel_N]])\n",
    "for t in range(300,400):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log[t,0,:]=m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7283b3f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "simlen=400\n",
    "\n",
    "a=0\n",
    "h=1\n",
    "\n",
    "beta = 0.5\n",
    "eta = 0.1\n",
    "noise = 0\n",
    "\n",
    "m_log2=np.zeros([simlen,P,P])\n",
    "x_log=np.zeros([simlen,P,N])\n",
    "x_last=np.zeros([N,P])\n",
    "\n",
    "projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "x=bart\n",
    "for t in range(0,100):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log2[t,0,:]=m\n",
    "x = np.concatenate([np.copy(x)[:char_N-1],father[:rel_N]])\n",
    "for t in range(100,200):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log2[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],wife[:rel_N]])\n",
    "for t in range(200,300):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log2[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],husband[:rel_N]])\n",
    "for t in range(300,400):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log2[t,0,:]=m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed3b5b9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "simlen=400\n",
    "\n",
    "a=0\n",
    "h=1\n",
    "\n",
    "beta = 0.5\n",
    "eta = 0.1\n",
    "noise = 0\n",
    "\n",
    "m_log3=np.zeros([simlen,P,P])\n",
    "x_log=np.zeros([simlen,P,N])\n",
    "x_last=np.zeros([N,P])\n",
    "\n",
    "projection=((a*xi)+(h*(xi@H))).T # auto+hetero\n",
    "x=homer\n",
    "for t in range(0,100):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log3[t,0,:]=m\n",
    "x = np.concatenate([np.copy(x)[:char_N-1],father[:rel_N]])\n",
    "for t in range(100,200):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log3[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],son[:rel_N]])\n",
    "for t in range(200,300):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log3[t,0,:]=m\n",
    "x=np.concatenate([np.copy(x)[:char_N-1],mother[:rel_N]])\n",
    "for t in range(300,400):\n",
    "    r=softmax(beta*(x@xi))@projection-((1/N)*(xi_mean.T))\n",
    "    r=softmax(beta*(x@xi))@projection-((1)*(xi_mean.T))\n",
    "    x+=eta*(r[0]-x)\n",
    "    m=np.zeros(P)\n",
    "    for i in range(P):\n",
    "        m[i] = np.corrcoef(x,xi[:,i])[0,1]\n",
    "    x_log[t,0,:]=x\n",
    "    m_log3[t,0,:]=m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "052c7f18",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(3, ncols=1, figsize=(5,6))\n",
    "\n",
    "axes = axes.flatten()\n",
    "axes[0].plot(m_log[:,0,:], label=node_labels)\n",
    "axes[1].plot(m_log2[:,0,:], label=node_labels)\n",
    "axes[2].plot(m_log3[:,0,:], label=node_labels)\n",
    "axes[2].set_xlabel(\"$t$\")\n",
    "axes[0].set_ylabel(\"Pattern overlap\")\n",
    "axes[1].set_ylabel(\"Pattern overlap\")\n",
    "axes[2].set_ylabel(\"Pattern overlap\")\n",
    "\n",
    "plt.tight_layout()\n",
    "axes[0].legend(bbox_to_anchor=(1.02, 0.3),loc='upper left', borderaxespad=0.)\n",
    "# plt.savefig(\"automata_a0_h1_over-time.pdf\", format=\"pdf\", bbox_inches=\"tight\")\n",
    "plt.show()"
   ]
  }
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