tutorials/W2D2_LinearSystems/W2D2_Tutorial2.ipynb

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    "<a href=\"https://colab.research.google.com/github/NeuromatchAcademy/course-content/blob/master/tutorials/W2D2_LinearSystems/W2D2_Tutorial2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    "# Neuromatch Academy 2020, Week 2, Day 2, Tutorial 2\n",
    "\n",
    "# Markov Processes\n",
    "\n",
    "**Content Creators**: Bing Wen Brunton, Ellie Stradquist\n",
    "\n",
    "**Content Reviewers**: Norma Kuhn, Karolina Stosio, John Butler, Matthew Krause, Ella Batty, Richard Gao, Michael Waskom"
   ]
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   "source": [
    "---\n",
    "# Tutorial Objectives\n",
    "\n",
    "In this tutorial, we will look at the dynamical systems introduced in the first tutorial through a different lens. \n",
    "\n",
    "In Tutorial 1, we studied dynamical systems as a deterministic process. For Tutorial 2, we will look at **probabilistic** dynamical systems. You may sometimes hear these systems called _stochastic_. In a probabilistic process, elements of randomness are involved. Every time you observe some probabilistic dynamical system, started from the same initial conditions, the outcome will likely be different. Put another way, dynamical systems that involve probability will incorporate random variations in their behavior. \n",
    "\n",
    "For some probabilistic dynamical systems, the differential equations express a relationship between $\\dot{x}$ and $x$ at every time $t$, so that the direction of $x$ at _every_ time depends entirely on the value of $x$. Said a different way, knowledge of the value of the state variables $x$ at time t is _all_ the information needed to determine $\\dot{x}$ and therefore $x$ at the next time.\n",
    "\n",
    "This property --- that the present state entirely determines the transition to the next state --- is what defines a **Markov process** and systems obeying this property can be described as **Markovian**.\n",
    "\n",
    "The goal of Tutorial 2 is to consider this type of Markov process in a simple example where the state transitions are probabilistic. In particular, we will:\n",
    "\n",
    "* Understand Markov processes and history dependence.\n",
    "* Explore the behavior of a two-state telegraph process and understand how its equilibrium distribution is dependent on its parameters.\n",
    "\n"
   ]
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   "source": [
    "---\n",
    "# Setup"
   ]
  },
  {
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
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   "source": [
    "#@title Figure settings\n",
    "import ipywidgets as widgets       # interactive display\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/nma.mplstyle\")"
   ]
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   "execution_count": 3,
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   "source": [
    "#@title Helper Functions\n",
    "\n",
    "def plot_switch_simulation(t, x):\n",
    "  fig = plt.figure()\n",
    "  plt.plot(t, x)\n",
    "  plt.title('State-switch simulation')\n",
    "  plt.xlabel('Time')\n",
    "  plt.xlim((0, 300)) # zoom in time\n",
    "  plt.ylabel('State of ion channel 0/1', labelpad=-60)\n",
    "  plt.yticks([0, 1], ['Closed (0)', 'Open (1)'])\n",
    "  plt.show()\n",
    "  return\n",
    "\n",
    "def plot_interswitch_interval_histogram(inter_switch_intervals):\n",
    "  fig = plt.figure()\n",
    "  plt.hist(inter_switch_intervals)\n",
    "  plt.title('Inter-switch Intervals Distribution')\n",
    "  plt.ylabel('Interval Count')\n",
    "  plt.xlabel('time')\n",
    "  plt.show()\n",
    "\n",
    "def plot_state_probabilities(time, states):\n",
    "  fig = plt.figure()\n",
    "  plt.plot(time, states[:,0], label='Closed to open')   \n",
    "  plt.plot(time, states[:,1], label='Open to closed')   \n",
    "  plt.legend()  \n",
    "  plt.xlabel('time')\n",
    "  plt.ylabel('prob(open OR closed)')"
   ]
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   "source": [
    "---\n",
    "# Section 1:  Telegraph Process"
   ]
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     "text": [
      "Video available at https://youtu.be/xZO6GbU48ns\n"
     ]
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/xZO6GbU48ns?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fe110d3c450>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 1: Markov Process\n",
    "# Insert the ID of the corresponding youtube video\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"xZO6GbU48ns\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GobuuufnekwX"
   },
   "source": [
    "Let's consider a Markov process with two states, where switches between each two states are probabilistic (known as a telegraph process). To be concrete, let's say we are modeling an **ion channel in a neuron that can be in one of two states: Closed (0) or Open (1)**. \n",
    "\n",
    "If the ion channel is Closed, it may transition to the Open state with probability $P(0 \\rightarrow 1 | x = 0) = \\mu_{c2o}$. Likewise, If the ion channel is Open, it transitions to Closed with probability $P(1 \\rightarrow 0 | x=1) = \\mu_{o2c}$.\n",
    "\n",
    "We simulate the process of changing states as a **Poisson process**. The Poisson process is a way to model discrete events where the average time between event occurrences is known but the exact time of some event is not known. Importantly, the Poisson process dictates the following points: \n",
    "1. The probability of some event occurring is _independent from all other events_.\n",
    "2. The average rate of events within a given time period is constant.\n",
    "3. Two events cannot occur at the same moment. Our ion channel can either be in an open or closed state, but not both simultaneously. \n",
    "\n",
    "In the simulation below, we will use the Poisson process to model the state of our ion channel at all points $t$ within the total simulation time $T$. \n",
    "\n",
    "As we simulate the state change process, we also track at which times thoughout the simulation the state makes a switch. We can use those times to measure the distribution of the time _intervals_ between state switches."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "d9k5q7kzvkWG"
   },
   "source": [
    "**Run the cell below** to show the state-change simulation process. Note that a random seed was set in the code block, so re-running the code will produce the same plot. Commenting out that line will produce a different simulation each run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "colab_type": "code",
    "id": "-BgBZ4drPSEx",
    "outputId": "940ffcc0-7536-4d5f-a29d-9bfe08714694"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 558
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title State-change simulation process\n",
    "\n",
    "# parameters\n",
    "T = 5000     # total Time duration\n",
    "dt = 0.001   # timestep of our simulation\n",
    "\n",
    "# simulate state of our ion channel in time\n",
    "# the two parameters that govern transitions are\n",
    "# c2o: closed to open rate\n",
    "# o2c: open to closed rate\n",
    "def ion_channel_opening(c2o, o2c, T, dt):\n",
    "    # initialize variables\n",
    "    t = np.arange(0, T, dt)\n",
    "    x = np.zeros_like(t)\n",
    "    switch_times = []\n",
    "\n",
    "    # assume we always start in Closed state\n",
    "    x[0] = 0 \n",
    "\n",
    "    # generate a bunch of random uniformly distributed numbers \n",
    "    # between zero and unity: [0, 1),\n",
    "    # one for each dt in our simulation.\n",
    "    # we will use these random numbers to model the \n",
    "    # closed/open transitions\n",
    "    myrand = np.random.random_sample(size=len(t))\n",
    "    \n",
    "\n",
    "    # walk through time steps of the simulation\n",
    "    for k in range(len(t)-1):\n",
    "        # switching between closed/open states are\n",
    "        # Poisson processes\n",
    "        if x[k] == 0 and myrand[k] < c2o*dt: # remember to scale by dt!\n",
    "            x[k+1:] = 1\n",
    "            switch_times.append(k*dt)\n",
    "        elif x[k] == 1 and myrand[k] < o2c*dt:\n",
    "            x[k+1:] = 0\n",
    "            switch_times.append(k*dt)\n",
    "\n",
    "    return t, x, switch_times\n",
    "\n",
    "\n",
    "c2o = 0.02\n",
    "o2c = 0.1\n",
    "np.random.seed(0) # set random seed\n",
    "t, x, switch_times = ion_channel_opening(c2o, o2c, T, .1)\n",
    "plot_switch_simulation(t,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FbzzET_IFZSy"
   },
   "source": [
    "## Exercise 1 (2A): Computing intervals between switches\n",
    "We now have `switch_times`, which is a list consisting of times when the state switched. Using this, calculate the time intervals between each state switch and store these in a list called `inter_switch_intervals`.\n",
    "\n",
    "We will then plot the distribution of these intervals. How would you describe the shape of the distribution?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "flFLMctbGLr5"
   },
   "outputs": [],
   "source": [
    "##############################################################################\n",
    "## TODO: Insert your code here to calculate between-state-switch intervals,\n",
    "##       and uncomment the last line to plot the histogram \n",
    "##############################################################################\n",
    "\n",
    "# hint: see np.diff()\n",
    "# inter_switch_intervals = ...\n",
    "\n",
    "\n",
    "# plot_interswitch_interval_histogram(inter_switch_intervals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 433
    },
    "colab_type": "code",
    "id": "r_VmeNS8Gcel",
    "outputId": "6e292a89-1785-41ba-bed1-9bd0c7708da8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 416,
       "width": 560
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "\n",
    "# hint: see np.diff()\n",
    "inter_switch_intervals = np.diff(switch_times)\n",
    "\n",
    "# plot inter-switch intervals\n",
    "with plt.xkcd():\n",
    "  plot_interswitch_interval_histogram(inter_switch_intervals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uvO80KYIICGP"
   },
   "source": [
    "We can also generate a bar graph to visualize the distribution of the number of time-steps spent in each of the two possible system states during the simulation. **Run the cell below** to visualize the distribution. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "colab_type": "code",
    "id": "WMNwYyQfXCgg",
    "outputId": "c0edd9b3-ef6a-4a3e-d907-f6436fd243bb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 558
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title Distribution of time spent in each state.\n",
    "\n",
    "states = ['Closed', 'Open']\n",
    "(unique, counts) = np.unique(x, return_counts=True)\n",
    "plt.bar(states, counts)\n",
    "plt.ylabel('Number of time steps')\n",
    "plt.xlabel('State of ion channel');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1--Cj2SeSJsE"
   },
   "source": [
    "<!-- Though the system started initially in the Closed ($x=0$) state, over time, it settles into a equilibrium distribution where we can predict on what fraction of time it is Open as a function of the $\\mu$ parameters. \n",
    "\n",
    "Before we continue exploring these distributions further, let's first take a look at the this fraction of Open states as a cumulative mean of the state $x$: -->\n",
    "\n",
    "Even though the state is _discrete_--the ion channel can only be either Closed or Open--we can still look at the **mean state** of the system, averaged over some window of time. \n",
    "\n",
    "Since we've coded Closed as $x=0$ and Open as $x=1$, conveniently, the mean of $x$ over some window of time has the interpretation of **fraction of time channel is Open**.\n",
    "\n",
    "Let's also take a look at the fraction of Open states as a cumulative mean of the state $x$. The cumulative mean tells us the average number of state-changes that the system will have undergone after a certain amount of time. **Run the cell below**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 431
    },
    "colab_type": "code",
    "id": "6IsMk8TxXmDS",
    "outputId": "a365488f-9d6f-4124-ad57-52ffcbda2a66"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 558
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# @title Cumulative mean of state\n",
    "plt.plot(t, np.cumsum(x) / np.arange(1, len(t)+1))\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Cumulative mean of state');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "O5r0KcclQkSc"
   },
   "source": [
    "Notice in the plot above that, although the channel started in the Closed ($x=0$) state, gradually adopted some mean value after some time. This mean value is related to the transition probabilities $\\mu_{c2o}$\n",
    "and $\\mu_{o2c}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TXTpLfObJgeY"
   },
   "source": [
    "## Interactive Demo: Varying transition probability values & T\n",
    "\n",
    "Using the interactive demo below, explore the state-switch simulation for different transition probability values of states $\\mu_{c2o}$ and $\\mu_{o2c}$. Also, try different values for total simulation time length *T*. \n",
    "\n",
    "Does the general shape of the inter-switch interval distribution change or does it stay relatively the same? How does the bar graph of system states change based on these values?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 526,
     "referenced_widgets": [
      "afdac5bff7a043ab811b0c4c9580eb24",
      "54de5aa92b3545169fc69c49b2b1391a",
      "89b0fc8d8442487792eb18114342dbf5",
      "3630c1e47b684f39b3d8e82d17747257",
      "202908dad632446ca2c968ad29eb6137",
      "b706fe2ada4b4e55903cfabc29899d92",
      "e30b2f9c9ed340ffa016b55bd3950c3c",
      "7850ae15c9994afb88e5129930926199",
      "26873fd7a7ad427ca9bed5b623291664",
      "5f2737b5917d4695a246aedad0988652",
      "6eb7fe8220ab46428bbe65d25df8c1d4",
      "c932be7edc814ac590329a2ba671c7e3",
      "f09313c542fc4901b0dbe8b7166b5832"
     ]
    },
    "colab_type": "code",
    "id": "cjm7IJ-IZ95X",
    "outputId": "8fad518e-6bc7-4515-9059-53e9b484ec36"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 558
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title \n",
    "\n",
    "#@markdown Make sure you execute this cell to enable the widget!\n",
    "\n",
    "@widgets.interact\n",
    "def plot_inter_switch_intervals(c2o = (0,1, .01), o2c = (0, 1, .01), T=(1000,10000, 1000)):\n",
    "\n",
    "  t, x, switch_times = ion_channel_opening(c2o, o2c, T, .1)\n",
    "\n",
    "  inter_switch_intervals = np.diff(switch_times)\n",
    "\n",
    "  #plot inter-switch intervals\n",
    "  plt.hist(inter_switch_intervals)\n",
    "  plt.title('Inter-switch Intervals Distribution')\n",
    "  plt.ylabel('Interval Count')\n",
    "  plt.xlabel('time')\n",
    "  plt.show()\n",
    "  plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "yh_YtuUZZ1o7"
   },
   "outputs": [],
   "source": [
    "# to_remove explanation\n",
    "\"\"\"\n",
    "Discussion: \n",
    "(1) Does the general shape of the inter-switch interval distribution \n",
    "change or does it stay relatively the same? \n",
    "(2) How does the bar graph of system states change based on these values?\n",
    "\n",
    "Answers: \n",
    "(1) The shape of the distribution remains the same, but larger values of either \n",
    "c2o or o2c shifts the distribution towards shorter intervals.\n",
    "(2) If c2o is larger than o2c, then the channel tends to be open a larger\n",
    "fraction of the time.\n",
    "\n",
    "\"\"\";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "N60UwFIPFEWj"
   },
   "source": [
    "---\n",
    "# Section 2: Distributional Perspective\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 518
    },
    "colab_type": "code",
    "id": "X7SnoyIFSzDy",
    "outputId": "8bd6f84f-53a4-405a-be21-19583e9dd9ba"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/U6YRhLuRhHg\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/U6YRhLuRhHg?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fe10e53fcd0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 2: State Transitions\n",
    "# Insert the ID of the corresponding youtube video\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"U6YRhLuRhHg\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kv_ujmfkSvAY"
   },
   "source": [
    "We can run this simulation many times and gather empirical distributions of open/closed states. Alternatively, we can formulate the exact same system probabilistically, keeping track of the probability of being in each state.\n",
    "\n",
    "<!-- Although the system started initially in the Closed ($x=0$) state, over time, it settles into a equilibrium distribution where we can predict on what fraction of time it is Open as a function of the $\\mu$ parameters.  -->\n",
    "\n",
    "(see diagram in lecture)\n",
    "\n",
    "The same system of transitions can then be formulated using a vector of 2 elements as the state vector and a dynamics matrix $\\mathbf{A}$. The result of this formulation is a *state transition matrix*:\n",
    "\n",
    "$\\left[ \\begin{array}{c} C \\\\ O \\end{array} \\right]_{k+1} = \\mathbf{A} \\left[ \\begin{array}{c} C \\\\ O \\end{array} \\right]_k = \\left[ \\begin{array} & 1-\\mu_{\\text{c2o}} & \\mu_{\\text{o2c}} \\\\ \\mu_{\\text{c2o}} & 1-\\mu_{\\text{o2c}} \\end{array} \\right] \\left[ \\begin{array}{c} C \\\\ O \\end{array} \\right]_k$.\n",
    "\n",
    "\n",
    "Each transition probability shown in the matrix is as follows:\n",
    "1. $1-\\mu_{\\text{c2o}}$, the probability that the closed state remains closed. \n",
    "2. $\\mu_{\\text{c2o}}$, the probability that the closed state transitions to the open state.\n",
    "3.  $\\mu_{\\text{o2c}}$, the probability that the open state transitions to the closed state. \n",
    "4. $1-\\mu_{\\text{o2c}}$, the probability that the open state remains open. \n",
    "\n",
    "\n",
    "_Notice_ that this system is written as a discrete step in time, and $\\mathbf{A}$ describes the transition, mapping the state from step $k$ to step $k+1$. This is different from what we did in the exercises above where $\\mathbf{A}$ had described the function from the state to the time derivative of the state.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LyqBMGfgb_nW"
   },
   "source": [
    "## Exercise 2 (2B): Probability Propagation\n",
    "\n",
    "Complete the code below to simulate the propagation of probabilities of closed/open of the ion channel through time. A variable called `x_kp1` (short for, $x$ at timestep $k$ plus 1) should be calculated per each step *k* in the loop. However, you should plot $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ObBQCkKQReF1"
   },
   "outputs": [],
   "source": [
    "def simulate_prob_prop(A, x0, dt, T):\n",
    "  \"\"\" Simulate the propagation of probabilities given the transition matrix A,\n",
    "  with initial state x0, for a duration of T at timestep dt.\n",
    "\n",
    "  Args:\n",
    "    A (ndarray): state transition matrix\n",
    "    x0 (ndarray): state probabilities at time 0\n",
    "    dt (scalar): timestep of the simulation\n",
    "    T (scalar): total duration of the simulation\n",
    "\n",
    "  Returns:\n",
    "    ndarray, ndarray: `x` for all simulation steps and the time `t` at each step\n",
    "  \"\"\"\n",
    "\n",
    "  # Initialize variables\n",
    "  t = np.arange(0, T, dt)\n",
    "  x = x0 # x at time t_0\n",
    "\n",
    "  # Step through the system in time\n",
    "  for k in range(len(t)-1):\n",
    "      ###################################################################\n",
    "      ## TODO: Insert your code here to compute x_kp1 (x at k plus 1)\n",
    "      raise NotImplementedError(\"Student exercise: need to implement simulation\")\n",
    "      ## hint: use np.dot(a, b) function to compute the dot product\n",
    "      ##       of the transition matrix A and the last state in x\n",
    "      ## hint 2: use np.vstack to append the latest state to x\n",
    "      ###################################################################   \n",
    "\n",
    "      # Compute the state of x at time k+1\n",
    "      x_kp1 = ...\n",
    "      # Stack (append) this new state onto x to keep track of x through time steps\n",
    "      x = ...\n",
    "\n",
    "  return x, t\n",
    "\n",
    "# parameters\n",
    "T = 500     # total Time duration\n",
    "dt = 0.1   # timestep of our simulation\n",
    "\n",
    "# same parameters as above\n",
    "# c2o: closed to open rate\n",
    "# o2c: open to closed rate\n",
    "c2o = 0.02\n",
    "o2c = 0.1\n",
    "A = np.array([[1 - c2o*dt, o2c*dt],\n",
    "              [c2o*dt,     1 - o2c*dt]])\n",
    "\n",
    "# initial condition: start as Closed\n",
    "x0 = np.array([[1, 0]]) \n",
    "\n",
    "# Uncomment this to plot the probabilities\n",
    "# x, t = simulate_prob_prop(A, x0, dt, T)\n",
    "# plot_state_probabilities(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 430
    },
    "colab_type": "code",
    "id": "jy6Duo05QhgQ",
    "outputId": "e9e119d6-5170-4f29-e5a1-604fa96633e9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 558
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "\n",
    "def simulate_prob_prop(A, x0, dt, T):\n",
    "  \"\"\" Simulate the propagation of probabilities given the transition matrix A,\n",
    "  with initial state x0, for a duration of T at timestep dt.\n",
    "\n",
    "  Args:\n",
    "    A (ndarray): state transition matrix\n",
    "    x0 (ndarray): state probabilities at time 0\n",
    "    dt (scalar): timestep of the simulation\n",
    "    T (scalar): total duration of the simulation\n",
    "\n",
    "  Returns:\n",
    "    ndarray, ndarray: `x` for all simulation steps and the time `t` at each step\n",
    "  \"\"\"\n",
    "\n",
    "  # Initialize variables\n",
    "  t = np.arange(0, T, dt)\n",
    "  x = x0 # x at time t_0\n",
    "\n",
    "  # Step through the system in time\n",
    "  for k in range(len(t)-1):\n",
    "      # Compute the state of x at time k+1\n",
    "      x_kp1 = np.dot(A, x[-1,:])\n",
    "      # Stack (append) this new state onto x to keep track of x through time steps\n",
    "      x = np.vstack((x, x_kp1))\n",
    "\n",
    "  return x, t\n",
    "\n",
    "# parameters\n",
    "T = 500     # total Time duration\n",
    "dt = 0.1   # timestep of our simulation\n",
    "\n",
    "# same parameters as above\n",
    "# c2o: closed to open rate\n",
    "# o2c: open to closed rate\n",
    "c2o = 0.02\n",
    "o2c = 0.1\n",
    "A = np.array([[1 - c2o*dt, o2c*dt],\n",
    "              [c2o*dt,     1 - o2c*dt]])\n",
    "\n",
    "# initial condition: start as Closed\n",
    "x0 = np.array([[1, 0]]) \n",
    "\n",
    "# Uncomment this to plot the probabilities\n",
    "x, t = simulate_prob_prop(A, x0, dt, T)\n",
    "with plt.xkcd():\n",
    "  plot_state_probabilities(t,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YYrEN_vAbfGF"
   },
   "source": [
    "Here, we simulated the propagation of probabilities of the ion channel's state changing through time. Using this method is useful in that we can **run the simulation once** and see **how the probabilities propagate throughout time**, rather than re-running and empirically observing the telegraph simulation over and over again. \n",
    "\n",
    "Although the system started initially in the Closed ($x=0$) state, over time, it settles into a equilibrium distribution where we can predict what fraction of time it is Open as a function of the $\\mu$ parameters. We can say that the plot above show this _relaxation towards equilibrium_.\n",
    "\n",
    "Re-calculating our value of the probability of $c2o$ again with this method, we see that this matches the simulation output from the telegraph process! \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "XaAtBpyRXyuP",
    "outputId": "ae7bfde1-9cde-4cc6-fdff-20d717f199da"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of state c2o: 0.167\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.83333333, 0.16666667])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Probability of state c2o: %.3f\"%(c2o / (c2o + o2c)))\n",
    "x[-1,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fi_wtMHRHGkq"
   },
   "source": [
    "---\n",
    "# Section 3: Equilibrium of the telegraph process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 518
    },
    "colab_type": "code",
    "id": "ut5ABlcTUKCZ",
    "outputId": "49ae835f-d5bf-456e-e274-ffe081291f85"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtu.be/csetTTauIh8\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/csetTTauIh8?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fe10e3bf810>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 3: Continous vs. Discrete Time Formulation\n",
    "# Insert the ID of the corresponding youtube video\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id=\"csetTTauIh8\", width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtu.be/\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ioX4_e3JUM_s"
   },
   "source": [
    "Since we have now modeled the propagation of probabilities by the transition matrix $\\mathbf{A}$ in Section 2, let's connect the behavior of the system at equilibrium with the eigendecomposition of $\\mathbf{A}$.\n",
    "\n",
    "As introduced in the lecture video, the eigenvalues of $\\mathbf{A}$ tell us about the stability of the system, specifically in the directions of the corresponding eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "sogUMI55carF",
    "outputId": "c1cccde5-14d4-4018-af7d-da8c84114703"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues: [1.    0.988]\n",
      "Eigenvector 1: [0.98058068 0.19611614]\n",
      "Eigenvector 2: [-0.70710678  0.70710678]\n"
     ]
    }
   ],
   "source": [
    "# compute the eigendecomposition of A\n",
    "lam, v = np.linalg.eig(A)\n",
    "\n",
    "# print the 2 eigenvalues\n",
    "print(\"Eigenvalues:\",lam)\n",
    "\n",
    "# print the 2 eigenvectors\n",
    "eigenvector1 = v[:,0]\n",
    "eigenvector2 = v[:,1]\n",
    "print(\"Eigenvector 1:\", eigenvector1)\n",
    "print(\"Eigenvector 2:\", eigenvector2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "G1uBx-SHU3yx"
   },
   "source": [
    "## Exercise 3 (2C): Finding a stable state\n",
    "\n",
    "Which of these eigenvalues corresponds to the **stable** (equilibrium) solution? What is the eigenvector of this eigenvalue? How does that explain \n",
    "the equilibrium solutions in simulation in Section 2 of this tutorial?\n",
    "\n",
    "_hint_: our simulation is written in terms of probabilities, so they must sum to 1. Therefore, you may also want to rescale the elements of the eigenvector such that they also sum to 1. These can then be directly compared with the probabilities of the states in the simulation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "azaDtAkPckFS"
   },
   "outputs": [],
   "source": [
    "###################################################################\n",
    "## Insert your thoughts here\n",
    "###################################################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
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      "[0.83333333 0.16666667]\n",
      "[-1.06150861e+15  1.06150861e+15]\n"
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    "# to_remove explanation\n",
    "\"\"\"\n",
    "Discussion: \n",
    "Which of the eigenvalues corresponds to the stable solution?\n",
    "What is the eigenvector of this eigenvalue?\n",
    "How does that explain the equilibrium solutions in Section 2?\n",
    "\n",
    "Recommendation: \n",
    "Ask the students to work in small groups (of 2 or 3) to discuss these questions.\n",
    "\n",
    "\n",
    "Answers:\n",
    "Whichever eigenvalue is 1 is the stable solution. There should be another\n",
    "eigenvalue that is <1, which means it is decaying and goes away after the\n",
    "transient period.\n",
    "\n",
    "The eigenvector corresponding to this eigenvalue is the stable solution. \n",
    "To see this, we need to normalize this eigenvector so that its 2 elements\n",
    "sum to one, then we would see that the two numbers correspond to\n",
    "[P(open), P(closed)] at equilibrium -- hopefully these are exactly the\n",
    "equilibrium solutions observed in Section 2.\n",
    "\n",
    "\n",
    "\"\"\";\n",
    "\n",
    "\n",
    "# whichever eigenvalue is 1, the other one makes no sense\n",
    "print(eigenvector1 / eigenvector1.sum())\n",
    "print(eigenvector2 / eigenvector2.sum())"
   ]
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    "---\n",
    "# Summary\n",
    "\n",
    "In this tutorial, we learned:\n",
    "\n",
    "* The definition of a Markov process with history dependence.\n",
    "* The behavior of a simple 2-state Markov proces--the telegraph process--can be simulated either as a state-change simulation or as a propagation of probability distributions.\n",
    "* The relationship between the stability analysis of a dynamical system express either in continuous or discrete time.\n",
    "* The equilibrium behavior of a telegraph process is predictable and can be understood using the same strategy as for deterministic systems in Tutorial 1: by taking the eigendecomposition of the A matrix."
   ]
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