nemo-demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "81c9440b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#matplotlib widget\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "#load_ext autoreload\n",
    "#autoreload 2\n",
    "\n",
    "from brain import k_cap, idx_to_vec, FFArea, RecurrentArea, RandomChoiceArea, ScaffoldNetwork, FSMNetwork, PFANetwork"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d28a24eb",
   "metadata": {},
   "source": [
    "## Forming an assembly"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b6688d6",
   "metadata": {},
   "source": [
    "### Initialize a brain area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "39a2305b",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = 1000\n",
    "n_neurons = 1000\n",
    "cap_size = 30\n",
    "density = 0.25\n",
    "plasticity = 1e-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "95daec17",
   "metadata": {},
   "outputs": [],
   "source": [
    "brain_area = RecurrentArea(n_inputs, n_neurons, cap_size, density, plasticity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e43ad0d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "stimulus = np.arange(cap_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a42611b",
   "metadata": {},
   "source": [
    "### Form an assembly by presenting the stimulus several times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7430cfa0",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_rounds = 10\n",
    "\n",
    "activations = np.zeros((n_rounds, n_neurons))\n",
    "\n",
    "brain_area.inhibit()\n",
    "for i in range(n_rounds):\n",
    "    brain_area.forward(stimulus)\n",
    "    activations[i] = brain_area.read(dense=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "637a82da",
   "metadata": {},
   "source": [
    "### Plot activations during formation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e19cea7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x600 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = activations.sum(axis=0).argsort()[::-1]\n",
    "\n",
    "fig, axes = plt.subplots(n_rounds, figsize=(4, 6), sharex=True, sharey=True)\n",
    "\n",
    "for i in range(n_rounds):\n",
    "    axes[i].bar(np.arange(5*cap_size), activations[i, idx[:5 * cap_size]])\n",
    "    axes[i].set_xticks([])\n",
    "    axes[i].set_yticks([])\n",
    "    axes[i].spines['top'].set_visible(False)\n",
    "    axes[i].spines['right'].set_visible(False)\n",
    "    axes[i].spines['left'].set_visible(False)\n",
    "\n",
    "axes[n_rounds // 2].set_ylabel('Round')\n",
    "axes[-1].set_xlabel('Firing neurons')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeb0897e",
   "metadata": {},
   "source": [
    "## Classifying stimulus classes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2562d7ff",
   "metadata": {},
   "source": [
    "### Generate some samples from each stimulus class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "59b3627b",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_classes = 3\n",
    "n_samples_train = 10\n",
    "n_samples_test = 200\n",
    "\n",
    "class_vecs = np.full((n_classes, n_neurons), 0.5 * cap_size / n_neurons)\n",
    "class_vecs[np.arange(n_classes)[:, np.newaxis], np.arange(n_classes * cap_size).reshape(n_classes, -1)] = 0.75\n",
    "\n",
    "samples_train = rng.random((n_classes, n_samples_train, n_neurons)) < class_vecs[:, np.newaxis, :]\n",
    "samples_test = rng.random((n_classes, n_samples_test, n_neurons)) < class_vecs[:, np.newaxis, :]\n",
    "\n",
    "brain_area.reset()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ad2a717",
   "metadata": {},
   "source": [
    "### Visualize sample means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "b97d9436",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Fraction of firing')"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 2), sharex=True, sharey=True)\n",
    "for i in range(n_classes):\n",
    "    ax.bar(np.arange(5 * cap_size), samples_test[i].mean(axis=0)[:5*cap_size], label='Class {}'.format(i))\n",
    "ax.legend()\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.set_xticks([])\n",
    "ax.set_xlabel('Input neuron')\n",
    "ax.set_ylabel('Fraction of firing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "805032cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "assembly_support = np.zeros((n_classes, n_neurons))\n",
    "\n",
    "for i in range(n_classes):\n",
    "    brain_area.inhibit()\n",
    "    for j in range(n_samples_train):\n",
    "        brain_area.forward(np.nonzero(samples_train[i, j]))\n",
    "    assembly_support[i] = brain_area.read(dense=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "8b0bee82",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_overlaps = np.zeros((n_classes, n_samples_test, n_classes))\n",
    "\n",
    "for i in range(n_classes):\n",
    "    for j in range(n_samples_test):\n",
    "        brain_area.inhibit()\n",
    "        brain_area.forward(np.nonzero(samples_test[i, j]), update=False)\n",
    "        test_overlaps[i, j] = brain_area.read(dense=True) @ assembly_support.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "9e14a131",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class 0 accuracy: 100.000000%\n",
      "Class 1 accuracy: 100.000000%\n",
      "Class 2 accuracy: 100.000000%\n"
     ]
    }
   ],
   "source": [
    "accuracy = np.mean(test_overlaps.argmax(axis=-1) == np.arange(n_classes)[:, np.newaxis], axis=-1)\n",
    "for i in range(n_classes):\n",
    "    print('Class {:d} accuracy: {:%}'.format(i, accuracy[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "914ec23e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "<img 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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.bar(np.arange(n_classes)-0.25, test_overlaps[0].mean(axis=0) / cap_size, width=0.25, label='Class 0')\n",
    "ax.bar(np.arange(n_classes), test_overlaps[1].mean(axis=0) / cap_size, width=0.25, label='Class 1')\n",
    "ax.bar(np.arange(n_classes)+0.25, test_overlaps[2].mean(axis=0) / cap_size, width=0.25, label='Class 2')\n",
    "ax.set_xticks(np.arange(n_classes))\n",
    "ax.legend(loc=(1., 0.05))\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.set_xlabel('Class')\n",
    "ax.set_ylabel('Overlap with assembly')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fcb1920",
   "metadata": {},
   "source": [
    "## Memorizing sequences of inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ee1e8ab",
   "metadata": {},
   "source": [
    "### Initialize simple and scaffolded networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "37241008",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = 1000\n",
    "n_neurons = 1000\n",
    "cap_size = 30\n",
    "density = 0.4\n",
    "plasticity = 1e-1\n",
    "\n",
    "simple_seq_area = RecurrentArea(n_inputs, n_neurons, cap_size, density, plasticity)\n",
    "scaff_seq_net = ScaffoldNetwork(n_inputs, n_neurons, cap_size, density, plasticity)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c0b1bfd",
   "metadata": {},
   "source": [
    "### Define a sequence of inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cd2f9bca",
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_len = 25\n",
    "sequence = np.arange(seq_len * cap_size).reshape(seq_len, cap_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5f156da",
   "metadata": {},
   "source": [
    "### Train the models by repeatedly presenting the sequence, testing recall after each presentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a660d3ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_presentations = 10\n",
    "\n",
    "simple_seq_assemblies = np.zeros((seq_len, n_neurons))\n",
    "scaff_seq_assemblies = np.zeros((seq_len, n_neurons))\n",
    "simple_seq_recall = np.zeros((n_presentations, seq_len))\n",
    "scaff_seq_recall = np.zeros((n_presentations, seq_len))\n",
    "\n",
    "for j in range(n_presentations):\n",
    "    simple_seq_area.inhibit()\n",
    "    scaff_seq_net.inhibit()\n",
    "    for i in range(seq_len):\n",
    "        simple_seq_area.forward(sequence[i])\n",
    "        scaff_seq_net.forward(sequence[i])\n",
    "        if j == 0:\n",
    "            simple_seq_assemblies[i] = simple_seq_area.read(dense=True)\n",
    "            scaff_seq_assemblies[i] = scaff_seq_net.read(dense=True)\n",
    "    \n",
    "    simple_seq_area.inhibit()\n",
    "    scaff_seq_net.inhibit()\n",
    "#     simple_seq_area.normalize()\n",
    "#     scaff_seq_net.normalize()\n",
    "    \n",
    "    \n",
    "    simple_seq_area.set_input(sequence[0])\n",
    "    scaff_seq_net.set_input(sequence[0])\n",
    "    for i in range(seq_len):\n",
    "        simple_seq_area.step(update=False)\n",
    "        scaff_seq_net.step(update=False)\n",
    "        \n",
    "        simple_seq_recall[j, i] = simple_seq_area.read(dense=True) @ simple_seq_assemblies[i]\n",
    "        scaff_seq_recall[j, i] = scaff_seq_net.read(dense=True) @ scaff_seq_assemblies[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "899fdbc6",
   "metadata": {},
   "source": [
    "### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "077c8f02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(10, 4), sharey=True)\n",
    "axes[0].plot(np.arange(seq_len), simple_seq_recall[2] / cap_size)\n",
    "axes[0].plot(np.arange(seq_len), scaff_seq_recall[2] / cap_size)\n",
    "axes[0].set_title('Recall after 3 presentations')\n",
    "axes[0].set_ylabel('Recall fraction')\n",
    "axes[0].set_xlabel('Sequence item')\n",
    "\n",
    "axes[1].plot(np.arange(seq_len), simple_seq_recall[5] / cap_size)\n",
    "axes[1].plot(np.arange(seq_len), scaff_seq_recall[5] / cap_size)\n",
    "axes[1].set_title('Recall after 6 presentations')\n",
    "axes[1].set_xlabel('Sequence item')\n",
    "\n",
    "axes[2].plot(np.arange(n_presentations)+1, simple_seq_recall[:, -1] / cap_size, label='Simple')\n",
    "axes[2].plot(np.arange(n_presentations)+1, scaff_seq_recall[:, -1] / cap_size, label='Scaffold')\n",
    "axes[2].set_title('Recall of last element during training')\n",
    "axes[2].set_xlabel('Presentation')\n",
    "axes[2].legend()\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f94aa5d2",
   "metadata": {},
   "source": [
    "## Simulate a FSM (DFA) to recognize numbers divisible by 3"
   ]
  },
  {
   "attachments": {
    "fsm_0modthree.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "166dd153",
   "metadata": {},
   "source": [
    "We will simulate the following FSM, which recognizes numbers divisible by 3. It does this by tracking the sum of the digits mod 3 and accepting if the result is 0.\n",
    "\n",
    "![fsm_0modthree.png](attachment:fsm_0modthree.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d7f0798",
   "metadata": {},
   "source": [
    "### Define a network to simulate the FSM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4fb46a1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_symbol_neurons = 1000\n",
    "n_state_neurons = 500\n",
    "n_arc_neurons = 5000\n",
    "cap_size = 70\n",
    "density = 0.2\n",
    "plasticity = 1e-1\n",
    "\n",
    "fsm_net = FSMNetwork(n_symbol_neurons, n_state_neurons, n_arc_neurons, cap_size, density, plasticity)\n",
    "\n",
    "n_symbols = 10 + 1\n",
    "n_states = 3 + 2\n",
    "\n",
    "symbols = np.arange(n_symbols * cap_size).reshape(n_symbols, cap_size)\n",
    "states = np.arange(n_states * cap_size).reshape(n_states, cap_size)\n",
    "\n",
    "n_arcs = 11 * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd229cb3",
   "metadata": {},
   "source": [
    "### Define the FSM (via its transitions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dc49392f",
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_list = []\n",
    "\n",
    "for mod in range(3):\n",
    "    for digit in range(10):\n",
    "        transition_list += [[mod, digit, (mod + digit) % 3]]\n",
    "\n",
    "transition_list += [[0, 10, 3], [1, 10, 4], [2, 10, 4]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5df001bd",
   "metadata": {},
   "source": [
    "### Train the model by repeatedly presenting each transition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "58f25e7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_presentations = 15\n",
    "\n",
    "arcs = np.zeros((len(transition_list), cap_size), dtype=int)\n",
    "\n",
    "for i in range(n_presentations):\n",
    "    for j, transition in enumerate(transition_list):\n",
    "        fsm_net.train(symbols[transition[1]], states[transition[0]], states[transition[2]])\n",
    "        arcs[j] = fsm_net.arc_area.read()\n",
    "\n",
    "state_overlaps = np.zeros((len(transition_list), n_states))\n",
    "for i, transition in enumerate(transition_list):\n",
    "    fsm_net.inhibit()\n",
    "    fsm_net.arc_area.forward([symbols[transition[1]], states[transition[0]]], update=False)\n",
    "    fsm_net.state_area.forward(fsm_net.arc_area.read(), update=False)\n",
    "    state_overlaps[i] = idx_to_vec(states, n_state_neurons) @ fsm_net.read(dense=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1983d4bf",
   "metadata": {},
   "source": [
    "### Test the model by presenting a string of digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c2ea2b34",
   "metadata": {},
   "outputs": [],
   "source": [
    "# positive example\n",
    "sequence = [3, 0, 4, 7, 1, 10]\n",
    "# negative example\n",
    "# sequence = [6, 7, 3, 10]\n",
    "\n",
    "outputs = np.zeros((len(sequence)+1, n_state_neurons))\n",
    "fsm_net.state_area.fire(states[0], update=False)\n",
    "outputs[0] = fsm_net.read(dense=True)\n",
    "for i in range(len(sequence)):\n",
    "    fsm_net.forward(symbols[sequence[i]], update=False)\n",
    "    outputs[i+1] = fsm_net.read(dense=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ee6d921",
   "metadata": {},
   "source": [
    "### Plot the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ae12c2ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "window.mpl = {};\n",
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       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
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       "\n",
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       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
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       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
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       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
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       "    titletext.classList = 'ui-dialog-title';\n",
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       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"1000\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "symbol_overlaps = np.zeros((len(sequence)+1, n_symbols))\n",
    "symbol_overlaps[np.arange(len(sequence)), sequence] = 1.\n",
    "\n",
    "state_overlaps = outputs @ idx_to_vec(states, n_state_neurons).T / cap_size\n",
    "\n",
    "fig, axes = plt.subplots(len(sequence)+1, 2, figsize=(10, 4), sharey=True)\n",
    "for i in range(len(sequence) + 1):\n",
    "    axes[i, 0].bar(np.arange(n_symbols), symbol_overlaps[i])\n",
    "    axes[i, 1].bar(np.arange(n_states), state_overlaps[i])\n",
    "    axes[i, 0].set_xticks(np.arange(n_symbols))\n",
    "    axes[i, 1].set_xticks(np.arange(n_states))\n",
    "    \n",
    "axes[-1, 0].set_xticklabels([i for i in range(n_symbols-1)] + ['□'])\n",
    "axes[-1, 1].set_xticklabels(['mod 0', 'mod 1', 'mod 2', 'Accept', 'Reject'])\n",
    "\n",
    "axes[len(sequence) // 2, 0].set_ylabel('Round')\n",
    "axes[0, 0].set_title('Symbol Area')\n",
    "axes[0, 1].set_title('State Area')\n",
    "    \n",
    "for ax in axes.flatten():\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37163c7d",
   "metadata": {},
   "source": [
    "## Simulate a PFA to generate simple sentences"
   ]
  },
  {
   "attachments": {
    "simple_sentence_pfa.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "edad1a49",
   "metadata": {},
   "source": [
    "We will train a NEMO network to simulate the following PFA, which generates sentences like \"the boy throws a ball\", \"a dog catches the ball\", ....\n",
    "\n",
    "![simple_sentence_pfa.png](attachment:simple_sentence_pfa.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f89a5a8c",
   "metadata": {},
   "source": [
    "### Define a network of brain areas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d65a9005",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_symbol_neurons = 1000\n",
    "n_state_neurons = 500\n",
    "n_arc_neurons = 5000\n",
    "n_random_neurons = 1000\n",
    "cap_size = 70\n",
    "density = 0.25\n",
    "plasticity = 0.1\n",
    "\n",
    "pfa_net = PFANetwork(n_symbol_neurons, n_state_neurons, n_arc_neurons, n_random_neurons, cap_size, density, plasticity)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "536da047",
   "metadata": {},
   "source": [
    "### Define the PFA (via its transitions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "98db3565",
   "metadata": {},
   "outputs": [],
   "source": [
    "lexicon = np.array(['the', 'a', 'boy', 'dog', 'throws', 'chases', 'ball', 'stick'])\n",
    "\n",
    "transition_list = [[0, 0, 1, 0], [0, 1, 1, 1], # subject article\n",
    "                   [1, 0, 2, 2], [1, 1, 3, 3], # subject\n",
    "                   [2, 0, 4, 4], [2, 1, 4, 4], # verb throws\n",
    "                   [3, 0, 4, 5], [3, 1, 4, 5], # verb chases\n",
    "                   [4, 0, 5, 0], [4, 1, 5, 1], # object article\n",
    "                   [5, 0, 6, 6], [5, 1, 6, 7]] # object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "bff3b7fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_states = 7\n",
    "n_symbols = len(lexicon)\n",
    "n_arcs = len(transition_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a5514242",
   "metadata": {},
   "outputs": [],
   "source": [
    "states = np.arange(n_states * cap_size).reshape(n_states, cap_size)\n",
    "symbols = np.arange(n_symbols * cap_size).reshape(n_symbols, cap_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c82c797c",
   "metadata": {},
   "source": [
    "### Train the model by repeatedly presenting each transition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f8307a17",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_presentations = 15\n",
    "\n",
    "for i in range(n_presentations):\n",
    "    for j, transition in enumerate(transition_list):\n",
    "        pfa_net.train(states[transition[0]], transition[1], states[transition[2]], symbols[transition[3]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "759ff22c",
   "metadata": {},
   "source": [
    "### Sample from the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d9ba11e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_trials = 10\n",
    "\n",
    "symbol_outputs = np.zeros((n_trials, 5, n_symbol_neurons))\n",
    "state_outputs = np.zeros((n_trials, 5, n_state_neurons))\n",
    "\n",
    "for i in range(n_trials):\n",
    "    pfa_net.state_area.fire(states[0])\n",
    "    for j in range(5):\n",
    "        pfa_net.step()\n",
    "        symbol_outputs[i, j] = pfa_net.read(dense=True)\n",
    "        state_outputs[i, j] = pfa_net.state_area.read(dense=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c2935395",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbol_overlaps = symbol_outputs[:, :, :cap_size*n_symbols].reshape(n_trials, 5, n_symbols, cap_size).sum(axis=-1)\n",
    "state_overlaps = state_outputs[:, :, :cap_size*n_states].reshape(n_trials, 5, n_states, cap_size).sum(axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bc54a1ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "output_symbols = lexicon[symbol_overlaps.argmax(axis=-1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "66b1d99f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([['the', 'dog', 'chases', 'a', 'ball'],\n",
       "       ['a', 'dog', 'chases', 'a', 'ball'],\n",
       "       ['the', 'dog', 'chases', 'a', 'stick'],\n",
       "       ['a', 'dog', 'chases', 'the', 'stick'],\n",
       "       ['the', 'boy', 'throws', 'the', 'stick'],\n",
       "       ['a', 'dog', 'chases', 'the', 'stick'],\n",
       "       ['a', 'boy', 'throws', 'the', 'ball'],\n",
       "       ['a', 'boy', 'throws', 'the', 'stick'],\n",
       "       ['the', 'dog', 'chases', 'a', 'stick'],\n",
       "       ['the', 'boy', 'throws', 'the', 'ball']], dtype='<U6')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output_symbols"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9df25d7",
   "metadata": {},
   "source": [
    "### Plot the activations for one sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "95e19a70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trial = 0\n",
    "\n",
    "fig, axes = plt.subplots(6, 2, figsize=(10, 4), sharey=True)\n",
    "axes[0, 0].bar(np.arange(n_symbols), np.zeros(n_symbols))\n",
    "axes[0, 1].bar(np.arange(n_states), [cap_size, 0, 0, 0, 0, 0, 0])\n",
    "axes[0, 0].set_xticks(np.arange(n_symbols))\n",
    "axes[0, 1].set_xticks(np.arange(n_states))\n",
    "\n",
    "for i in range(5):\n",
    "    axes[i+1, 0].bar(np.arange(n_symbols), symbol_overlaps[trial, i])\n",
    "    axes[i+1, 1].bar(np.arange(n_states), state_overlaps[trial, i])\n",
    "    axes[i+1, 0].set_xticks(np.arange(n_symbols))\n",
    "    axes[i+1, 1].set_xticks(np.arange(n_states))\n",
    "    \n",
    "\n",
    "for ax in axes:\n",
    "    ax[0].set_xticklabels([])\n",
    "    ax[1].set_xticklabels([])\n",
    "    \n",
    "axes[-1, 0].set_xticklabels(lexicon)\n",
    "axes[-1, 1].set_xticklabels(['subj\\nart', 'subj', 'verb\\nchase', 'verb\\nthrow', 'obj\\nart', 'obj', 'end'])\n",
    "\n",
    "axes[6 // 2, 0].set_ylabel('Round')\n",
    "axes[0, 0].set_title('Symbol Area')\n",
    "axes[0, 1].set_title('State Area')\n",
    "    \n",
    "for ax in axes.flatten():\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.set_yticks([])\n",
    "    \n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1b6f8a29-7ab1-4205-a4e0-a3c0b4890a47",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse import csc_array, csr_array\n",
    "from nemo import k_cap, idx_to_vec, random_sparse_array, random_block_array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b7ec13-9b29-486b-8228-a849b9d66bf8",
   "metadata": {},
   "source": [
    "## Estimate & simulate a Markov chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "09dee3cb-9c39-4832-81be-963306efdce2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\svemp\\AppData\\Local\\Temp\\ipykernel_23728\\3049401489.py:76: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_xticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n",
      "C:\\Users\\svemp\\AppData\\Local\\Temp\\ipykernel_23728\\3049401489.py:78: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  axes[0].set_yticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cap_size = 500\n",
    "input_cap_size = cap_size\n",
    "n_inputs = 3000\n",
    "n_neurons = 20 * cap_size\n",
    "density = 0.1\n",
    "norm_m = int(2 * input_cap_size * density)\n",
    "\n",
    "n_states = 3\n",
    "distribution = rng.exponential(scale = 1., size=(n_states, n_states))\n",
    "distribution /= distribution.sum(axis=-1, keepdims=True)\n",
    "\n",
    "arc_inp_w = random_sparse_array(n_inputs, n_neurons, density)\n",
    "arc_rec_w = random_block_array(np.eye(n_neurons // cap_size) > 0, cap_size, cap_size, density)\n",
    "\n",
    "state_assm_idx = np.arange(n_states * input_cap_size).reshape(n_states, -1)\n",
    "arc_assm_idx = np.arange(n_states * cap_size).reshape(n_states, -1)\n",
    "\n",
    "for i in range(n_states):\n",
    "    idx = np.ix_(arc_assm_idx[i], arc_assm_idx[i])\n",
    "    arc_rec_w[idx] *= 10\n",
    "\n",
    "lam = 24\n",
    "beta = 1000\n",
    "def get_weight(n_rounds, exact=True):\n",
    "    if exact:\n",
    "        if n_rounds == 0:\n",
    "            return 1\n",
    "        w = 1 + np.log(beta * lam) / lam\n",
    "        for i in range(n_rounds-1):\n",
    "            w += beta * np.exp(-lam * (w-1))\n",
    "        return w\n",
    "    else:\n",
    "        return 1 + np.maximum(np.log(beta * lam * n_rounds) / lam, 0)\n",
    "\n",
    "empirical_count = np.round(distribution * 100).astype(int)\n",
    "\n",
    "for i in range(n_states):\n",
    "    for j in range(n_states):\n",
    "        idx = np.ix_(state_assm_idx[i], arc_assm_idx[j])\n",
    "        arc_inp_w[idx] *= get_weight(empirical_count[i,j])\n",
    "\n",
    "n_rounds = 10\n",
    "n_samples = 500\n",
    "\n",
    "actual_counts = np.zeros((n_states, n_states))\n",
    "\n",
    "noise = 5.\n",
    "for i in range(n_states):\n",
    "    activated = np.zeros((n_samples, n_rounds, cap_size), dtype=int)\n",
    "\n",
    "    randomness = noise * np.sqrt(cap_size * density) * rng.standard_normal((n_samples, n_neurons))\n",
    "    \n",
    "    activated[:, 0] = k_cap(arc_inp_w[state_assm_idx[i]].sum(axis=0) + randomness, cap_size)\n",
    "    for j in range(n_rounds-1):\n",
    "        act_array = csr_array((np.ones(cap_size * n_samples), activated[:, j, :].reshape(-1), np.arange(0, n_samples*cap_size+1, cap_size)), shape=(n_samples, n_neurons))\n",
    "        activated[:, j+1] = k_cap((act_array @ arc_rec_w).toarray(), cap_size)\n",
    "        \n",
    "    dense_act = idx_to_vec(activated, n_neurons)\n",
    "\n",
    "    overlaps = dense_act[:, :, arc_assm_idx.reshape(-1)].reshape(n_samples, n_rounds, n_states, cap_size).sum(axis=-1)\n",
    "\n",
    "    actual_counts[i] = (overlaps[:, -1] > 0.8 * cap_size).sum(axis=0)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(6, 3), sharey=True)\n",
    "axes[0].matshow(distribution, vmin=0, vmax=max(distribution.max(), actual_counts.max()/ n_samples))\n",
    "axes[0].set_title('Target Proportion')\n",
    "for i in range(n_states):\n",
    "    for j in range(n_states):\n",
    "        axes[0].text(j, i, np.round(distribution[i, j], 3), ha='center', va='center', color='w')\n",
    "axes[1].matshow(actual_counts / n_samples, vmin=0, vmax=max(distribution.max(), actual_counts.max()/ n_samples))\n",
    "axes[1].set_title('Estimated Sample Proportion')\n",
    "for i in range(n_states):\n",
    "    for j in range(n_states):\n",
    "        axes[1].text(j, i, actual_counts[i,j]/n_samples, ha='center', va='center', color='w')\n",
    "for ax in axes:\n",
    "    ax.set_xticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n",
    "    ax.set_xlabel('Next State')\n",
    "axes[0].set_yticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n",
    "axes[0].set_ylabel('Initial State')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aac3d3bd-46f7-4c61-ab22-c07529445aff",
   "metadata": {},
   "source": [
    "## Estimate & simulate a trigram model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af93a670-2b80-4ad8-94f0-cc9b99a9fac6",
   "metadata": {},
   "source": [
    "### Define the corpus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "045155ed-4092-4789-9df1-c08a5fd5c80f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['the owl and the pussycat went to sea in a beautiful pea green boat . they took some honey and plenty of money wrapped up in a five pound note . the owl looked up to the stars above and sang to a small guitar you elegant fowl . how charmingly sweet you sing . o let us be married . too long we have tarried but what shall we do for a ring . they sailed away for a year and a day to the land where the bong tree grows and there in a wood a piggy wig stood with a ring at the end of his nose . dear pig are you willing to sell for one shilling your ring . said the piggy i will . so they took it away and were married next day by the turkey who lives on the hill . they dined on mince and slices of quince which they ate with a runcible spoon . and hand in hand on the edge of the sand they danced by the moon . □ □ □']"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = 'The Owl and the Pussycat went to sea In a beautiful pea-green boat. They took some honey, and plenty of money, Wrapped up in a five-pound note. The Owl looked up to the stars above, And sang to a small guitar,'\n",
    "v2 = 'You elegant fowl! How charmingly sweet you sing! O let us be married! too long we have tarried: But what shall we do for a ring? They sailed away, for a year and a day, To the land where the Bong-Tree grows And there in a wood a Piggy-wig stood With a ring at the end of his nose.'\n",
    "v3 = 'Dear Pig, are you willing to sell for one shilling Your ring? Said the Piggy, I will. So they took it away, and were married next day By the Turkey who lives on the hill. They dined on mince, and slices of quince, Which they ate with a runcible spoon; And hand in hand, on the edge of the sand, They danced by the moon. □ □ □'\n",
    "\n",
    "def clean(s):\n",
    "    return ' '.join(s.split()).lower().translate({ord(c) : ' .' for c in '.?!;'} | {ord(c) : None for c in ',:\"'} | {ord('-') : ' ', ord('\\n') : ''})\n",
    "\n",
    "corpus = [clean(s) for s in [v1 + ' ' + v2 + ' ' + v3]]\n",
    "corpus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1875b8df-caa8-4203-80af-e585cf69d1cb",
   "metadata": {},
   "source": [
    "### Define the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "36a52bef-c450-4205-907e-b723f8a350f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "cap_size = 500\n",
    "density = 0.1\n",
    "\n",
    "lexicon = list(set([token for s in corpus for token in s.split()]))\n",
    "sequences = [[lexicon.index(token) for token in s.split()] for s in corpus]\n",
    "trigram_seq = [(seq[i], seq[i+1], seq[i+2]) for seq in sequences for i in range(len(seq)-2)]\n",
    "trigrams = list(set(trigram_seq))\n",
    "trigram_count = [trigram_seq.count(gram) for gram in trigrams]\n",
    "n_words = len(lexicon)\n",
    "n_trigrams = len(trigrams)\n",
    "\n",
    "density = 0.1\n",
    "word_cap_size = 500\n",
    "\n",
    "n_word_neurons = n_words * word_cap_size\n",
    "\n",
    "first_word_graph = np.zeros((n_words, n_words), dtype=bool)\n",
    "second_word_graph = np.zeros((n_words, n_words), dtype=bool)\n",
    "for i, trigram in enumerate(trigrams):\n",
    "    first_word_graph[trigram[0], trigram[2]] = True\n",
    "    second_word_graph[trigram[1], trigram[2]] = True\n",
    "\n",
    "\n",
    "trans_inp_ws = [random_block_array(first_word_graph, word_cap_size, word_cap_size, density), \n",
    "                random_block_array(second_word_graph, word_cap_size, word_cap_size, density)]\n",
    "trans_rec_w = random_block_array(np.eye(n_words) > 0, word_cap_size, word_cap_size, density)\n",
    "\n",
    "word_assm_idx = np.arange(n_word_neurons).reshape(n_words, word_cap_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0992beb-6f44-4fec-bc27-757be18a54d4",
   "metadata": {},
   "source": [
    "### Train the model by presenting the corpus 5 times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "7e49d7bb-57d1-469c-b4f9-e9d7d79befea",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_presentations = 5\n",
    "\n",
    "lam = 60\n",
    "beta = 0.5\n",
    "def get_weight(n_rounds, exact=True):\n",
    "    if exact:\n",
    "        if n_rounds == 0:\n",
    "            return 1\n",
    "        w = 1 + beta + np.log(lam) / lam\n",
    "        for i in range(n_rounds-1):\n",
    "            w += np.exp(lam * (1 + beta - w))\n",
    "        return w\n",
    "    else:\n",
    "        return 1 + np.maximum(beta + np.log(lam * n_rounds) / lam, 0)\n",
    "\n",
    "for i in range(n_trigrams):\n",
    "    for j in range(2):\n",
    "        trans_inp_ws[j][np.ix_(word_assm_idx[trigrams[i][j]], word_assm_idx[trigrams[i][-1]])] *= get_weight(n_presentations * trigram_count[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fae388d5-4eb0-4c06-84f3-ad9ce262e46f",
   "metadata": {},
   "source": [
    "### Sample from the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "63c225fe-c8b5-493b-9710-d7f9fd25b3ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'the owl looked up to the land where the bong tree grows and there in a wood a piggy wig stood with a ring. they took some honey and plenty of money wrapped up in a five pound note. they took it away and a day to the stars above and sang to a small guitar you elegant fowl. they took it away and a day to the land where the bong tree grows and there in a wood a piggy wig stood with a ring. they took some honey and plenty of money wrapped up'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_rounds = 10\n",
    "word1 = 'the'\n",
    "word2 = 'owl'\n",
    "seq_len = 100\n",
    "noise = 10.\n",
    "\n",
    "activated = np.zeros((seq_len, word_cap_size), dtype=int)\n",
    "activated[0] = word_assm_idx[lexicon.index(word1)]\n",
    "activated[1] = word_assm_idx[lexicon.index(word2)]\n",
    "for i in range(seq_len-2):\n",
    "    temp_act = np.zeros((n_rounds, word_cap_size), dtype=int)\n",
    "    \n",
    "    randomness = noise * np.sqrt(word_cap_size * density) * rng.standard_normal(n_word_neurons)\n",
    "    temp_act[0] = k_cap(np.sum([w[activated[i+j]].sum(axis=0) for j, w in enumerate(trans_inp_ws)], axis=0) + randomness, word_cap_size)\n",
    "    for j in range(n_rounds-1):\n",
    "        temp_act[j+1] = k_cap(trans_rec_w[temp_act[j]].sum(axis=0), word_cap_size)\n",
    "\n",
    "    activated[i+2] = temp_act[-1]\n",
    "\n",
    "dense_act = idx_to_vec(activated, n_word_neurons)\n",
    "overlaps = dense_act.reshape(seq_len, n_words, word_cap_size).sum(axis=-1)\n",
    "sampled_seq = overlaps.argmax(axis=-1)\n",
    "' '.join([lexicon[i] for i in sampled_seq]).replace(' .', '.')"
   ]
  }
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",
       "_figure_label": "Figure 1",
       "_model_module_version": "^0.11",
       "_size": [
        600,
        300
       ],
       "_view_module_version": "^0.11",
       "layout": "IPY_MODEL_a4ed89172b3b4a10b40dbc845ff8ce83",
       "toolbar": "IPY_MODEL_289d150ddecc4722bc3cef3bfeff48e1",
       "toolbar_position": "left"
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}