derived_single_cell_oscillator_w_readout (1) (1).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from math import sqrt\n",
    "import time \n",
    "import numpy as np\n",
    "import matplotlib.animation as animation\n",
    "%matplotlib inline\n",
    "from scipy import signal\n",
    "import pprint\n",
    "import math\n",
    "from sklearn.metrics import mean_squared_error\n",
    "import scipy.optimize as optimize\n",
    "import scipy.io as sio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* include more cells modify source so that it works for more cells  \"done\"\n",
    "* how to characterise spatial patterns \n",
    "* find readout \"done\"\n",
    "* auto correlation power spectral density quality factor \n",
    "* statistics for characterizing patterns\n",
    "* power spectral density applications in . biology patterns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [],
   "source": [
    "def listRightIndex(alist, value):\n",
    "    return len(alist) - alist[-1::-1].index(value) -1\n",
    "\n",
    "def return_heaviside(n_c, n_t, dx, dt, v_0):\n",
    "    ha2d = np.ones((n_c, n_t))\n",
    "    for i in range(n_t):\n",
    "        for j in range(n_c):\n",
    "            ha2d[j][i] = int((j*dx - v_0*i*dt)>0)\n",
    "    return ha2d\n",
    "\n",
    "def closest_time(u, u_0, t):\n",
    "    vals = list((u-u_0)**2)\n",
    "    val = min(vals)\n",
    "    return int(listRightIndex(vals, val)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = 8\n",
    "n_t = c*200\n",
    "dt = 0.05\n",
    "gamma1 = 18\n",
    "n = 8\n",
    "m = 8\n",
    "tau_2 = 5\n",
    "k = 5\n",
    "gamma2 = 1\n",
    "n_c = 100\n",
    "dx = 1.5\n",
    "v_0 = 2.5\n",
    "tau_d = 7\n",
    "P_u = 1/tau_2\n",
    "beta = 0.05\n",
    "u_0 = 0.99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [],
   "source": [
    "u2d = np.ones((n_c, n_t))\n",
    "w2d = np.zeros((n_c, n_t))\n",
    "r2d = np.zeros(n_c)\n",
    "t = np.asarray([i*dt for i in range(n_t)])\n",
    "x_ = np.asarray([i*dx for i in range(n_c)])\n",
    "ha2d = return_heaviside(n_c, n_t, dx, dt, v_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(n_t-1):\n",
    "    for cell in range(1, n_c-1):\n",
    "        u2d[cell][i+1] = u2d[cell][i] + dt*(-u2d[cell][i]*(1/tau_2)+ P_u*ha2d[cell][i])\n",
    "        c = beta*(w2d[cell-1][i]+w2d[cell+1][i])\n",
    "        if (i - tau_d >= 0):\n",
    "            w2d[cell][i+1] = w2d[cell][i] + dt*(-w2d[cell][i] + gamma1*(u2d[cell][i]**n/(u2d[cell][i]**n+1))*(1/(1+w2d[cell][i-tau_d]**m))+c   )\n",
    "        else:\n",
    "            w2d[cell][i+1] = w2d[cell][i] + dt*(-w2d[cell][i] + gamma1*(u2d[cell][i]**n/(u2d[cell][i]**n+1))*(1) + c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [],
   "source": [
    "for cell in range(1, n_c-1):\n",
    "    r2d[cell]  = w2d[cell][closest_time(u2d[cell], u_0, t)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [],
   "source": [
    "loc = 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c7ab8fda0>]"
      ]
     },
     "execution_count": 429,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_, r2d)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c7ad34438>]"
      ]
     },
     "execution_count": 430,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pfRMY9lyTNgFfqqrvdNvDnus3gG9U1URV/RD4DPAaFvg5dqxE/15gXfeu9zJ6P8JtH/JMU20HLu2uX0rvnPpRkyTA3wJ7qurPF9FcI0mWd9d/jt5/hD3AncBvD2uuqrqqqlZX1Vp6z6d/r6q3DHsugCQnJHnB5HV656l3M+THsqr+C9if5CXd0q8DXxn2XH0285NTOzD8ub4NnJPk+O7/5+TXa2GfY8N6Q2UB3hS5EHiI3vng9w15lhvpnaP7Ib1XP2+jdz54B/C17t+TjvJMv0rvx8RdwP3d5cJFMNcZwH3dXLuBP+7WXwx8EdhH78fx5w7x8TwPuGWxzNXN8EB3eXDy+T7sx7Kb4UxgrHs8PwecuEjmOh74b+Dn+9YWw1zvB77aPfc/ATx3oZ9j/kWuJDXkWDm9I0maBaMvSQ0x+pLUEKMvSQ0x+pLUEKMvSQ0x+pLUEKMvSQ35f6QQbJ5i9jIxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, u2d[loc, :])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c7ad945c0>]"
      ]
     },
     "execution_count": 431,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, w2d[loc, :])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "def save_animation(filename, animation_object):# supported format is mp4\n",
    "    Writer = animation.writers['ffmpeg']\n",
    "    writer = Writer(fps=15, metadata=dict(artist='Me'), bitrate=1800)\n",
    "    animation_object.save(filename, writer=writer)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(xlim=(0, 2*x_[-1]), ylim=(np.amin(w2d),1.2*np.amax(w2d)))\n",
    "ax.set_ylabel(\"w\")\n",
    "ax.set_xlabel(\"cell_index_i\")\n",
    "fig.tight_layout()\n",
    "line, = ax.plot([], [], color='steelblue', lw=2)\n",
    "\n",
    "def update(num, u, line):\n",
    "    line.set_data(x_, u[:, num])\n",
    "    return line,\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, n_c, fargs=[ w2d, line],\n",
    "                              interval=40, blit=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "#save_animation(\"w2d.mp4\", ani)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "u = np.zeros((n_t))\n",
    "ha = np.zeros((n_t))\n",
    "\n",
    "w = np.zeros(( n_t))\n",
    "cell_pos = 5\n",
    "\n",
    "\n",
    "for i in range (n_t-1):\n",
    "    u[i+1] = u[i] + dt*(-u[i]/tau_2 + gamma2)\n",
    "    if (i - tau_d >= 0):\n",
    "        w[i+1] = w[i] + dt*(-w[i] + gamma1*(u[i]**n/(u[i]**n+1))*(1/(1+w[i-tau_d]**m))    )\n",
    "    else:\n",
    "        w[i+1] = w[i] + dt*(-w[i] + gamma1*(u[i]**n/(u[i]**n+1))*(1)    )\n",
    "\n",
    "for i in range(n_t):\n",
    "    ha[i] = int((cell_pos - v_0*i*dt)>0)\n",
    "        \n",
    "plt.plot(t, u)\n",
    "\"\"\""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}