nemo-demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "81c9440b",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "rng = np.random.default_rng(729)\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": 2,
   "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": 3,
   "id": "95daec17",
   "metadata": {},
   "outputs": [],
   "source": [
    "brain_area = RecurrentArea(n_inputs, n_neurons, cap_size, density, plasticity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "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": 140,
   "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": 147,
   "id": "e19cea7d",
   "metadata": {},
   "outputs": [
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       "\n",
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       "\n",
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       "    }\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=\"400\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "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": {
      "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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\" 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": 4,
   "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": 5,
   "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": 6,
   "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": 7,
   "id": "077c8f02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ab942d8d8675484e99c85cc7acb35369",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "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": 2,
   "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": 3,
   "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": 4,
   "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": 5,
   "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": 6,
   "id": "ae12c2ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d4a7fe8953cd4f4095131c1f6261eb0f",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "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": "code",
   "execution_count": 7,
   "id": "1ac01c0e-4722-4015-b8ec-20802f2a661c",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.savefig('fsm_example_simple.tiff', format='tiff')"
   ]
  },
  {
   "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": 2,
   "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": 3,
   "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": 4,
   "id": "bff3b7fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_states = 7\n",
    "n_symbols = len(lexicon)\n",
    "n_arcs = len(transition_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "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": 9,
   "id": "bc54a1ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "output_symbols = lexicon[symbol_overlaps.argmax(axis=-1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "66b1d99f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([['the', 'boy', 'throws', 'a', 'stick'],\n",
       "       ['a', 'boy', 'throws', 'the', 'ball'],\n",
       "       ['the', 'boy', 'throws', 'the', 'stick'],\n",
       "       ['a', 'dog', 'chases', 'the', 'ball'],\n",
       "       ['the', 'boy', 'throws', 'a', 'stick'],\n",
       "       ['the', 'boy', 'throws', 'the', 'stick'],\n",
       "       ['the', 'boy', 'throws', 'a', 'ball'],\n",
       "       ['a', 'boy', 'throws', 'the', 'ball'],\n",
       "       ['a', 'boy', 'throws', 'the', 'ball'],\n",
       "       ['a', 'boy', 'throws', 'the', 'ball']], dtype='<U6')"
      ]
     },
     "execution_count": 10,
     "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": 12,
   "id": "95e19a70",
   "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": {
      "text/html": [
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2/Q7qzqJoafD6v77UgFdf6vJgE4o6IF2+juVWRMWuapO0f3t0W+o6wE4mlwovOsEiO6ZI6CHeMRRJwQQQKA6gUrGawVg/fKJxhidbI9+B1171tJwhWiFWYV3PQVdJ5A1vhYGdI1LCr/65ZYvvvjCjl/R76BrjFawV9jV3yq86zkzO+20k507aDwr3vQ3GqN1BV0PnW1v0yo9BXdduddtYOUCuv5e46R+0UUn9XWBQX+rh9gq5GsVgTadZNDJcq1q01isz9ZFiOjkOPegV9cf+at8CxDQ893+1N5BAV1J1hV0nXnXEjg2BBBAAAEEEEAAAQQQyIcAAT0f7UwtPRDQ2WctCdOyMv2jp6mzIYAAAggggAACCCCAQH4ECOj5aWtq6riAlq7rZ8C0PE3LyvQTLGwIIIAAAggggAACCCCQHwECen7ampoigAACCCCAAAIIIIAAAgg4LEBAd7hxKBoCCCCAAAIIIIAAAggggEB+BAjo+WlraooAAggggAACCCCAAAIIIOCwAAHd4cahaAgggAACCCCAAAIIIIAAAvkRIKDnp62pKQIIIIAAAggggAACCCCAgMMCBHSHG4eiIYAAAggggAACCCCAAAII5EeAgJ6ftqamCCCAAAIIIIAAAggggAACDgsQ0B1uHIqGAAIIIIBACAK9hk8KoRpm+piBQdSDSiCAAAIIuCtAQHe3bSgZAggggAACQQgQ0INoRiqBAAIIIJCBAAE9A2R2gQACCCCAQJ4FCOh5bn3qjgACCCBQiQABvRIt3osAAggggAACFQsQ0Csm4w8QQAABBHIqQEDPacNTbQQQQAABBLISIKBnJc1+EEAAAQR8FyCg+96ClB8BBBBAAAHHBQjojjcQxUMAAQQQcEaAgO5MU1AQBBBAAAEEwhQgoIfZrtQKAQQQQCB9AQJ6+qZ8IgIIIIAAAggUCBDQ6Q4IIIAAAggkEyCgJ3PiXQgggAACCCBQpQABvUo4/gwBBBBAIHcCBPTcNTkVRgABBBBAIFsBAnq23uwNAQQQQMBfAQK6v21HyRFAAAEEEPBCgIDuRTNRSAQQQAABBwQI6A40AkVAAAEEEEAgZAECesitS90QQAABBNIUIKCnqclnIYAAAggggMAiAgR0OgUCCCCAAALJBAjoyZx4FwIIIIAAAghUKUBArxKOP0MAAQQQyJ0AAT13TU6FEUAAAQQQyFaAgJ6tN3tDAAEEEPBXgIDub9tRcgQQQAABBLwQIKB70UwUEgEEEEDAAQECugONQBEQQAABBBAIWYCAHnLrUjcEEEAAgTQFCOhpavJZCCCAAAIIILCIAAGdToEAAggggEAyAQJ6MifehQACCCCAAAJVChDQq4TjzxBAAAEEcidAQM9dk1NhBBBAAAEEshUgoGfrzd4QQAABBPwVIKD723aUHAEEEEAAAS8ECOheNBOFRAABBBBwQICA7kAjUAQEEEAAAQRCFiCgh9y61A0BBBBAIE0BAnqamnwWAggggAACCCwiQECnUyCAAAIIIJBMgICezIl3IYAAAggggECVAgT0KuH4MwQQQACB3AkQ0HPX5FQYAQQQQACBbAUI6Nl6szcEEEAAAX8FCOj+th0lRwABBBBAwAsBAroXzUQhEUAAAQQcECCgO9AIFAEBBBBAAIGQBQjoIbcudUMAAQQQSFOAgJ6mJp+FAAIIIIAAAosIENDpFAgggAACCCQTIKAnc+JdCCCAAAIIIFClAAG9Sjj+DAEEEEAgdwIE9Nw1ORVGAAEEEEAgWwECerbe7A0BBBBAwF8BArq/bUfJEUAAAQQQ8EKAgO5FM1FIBBBAAAEHBAjoDjQCRUAAAQQQQCBkAQJ6yK1L3RBAAAEE0hRwJqAvXLjQzJs3L8268VkIIIAAAgjkUqBr166mqamporrXcxzuM/K+isri6punjurvatEoFwIIIICAYwLVjMWqgjMBvaWlxTQ3NzvGSnEQQAABBBDwT2Du3LmmW7duFRWccbgiLt6MAAIIIIBAWYFqxmKnAno9z9yn3Xc0ienZs6eZOXNmxROgtMuS5ueFWi8ZhVq3UOtFm6V5ZGf3WaH2Rx/rVc1Ze5/G4eJe7WMbpXFk5rXeIY8Rcf2CNg9v/k2blxbwvb9XMxY7FdDjOqdLr0dXGao9K+JSXQrLEmq9ooFcKzRoM1d736LlCrU/hlovjjN/jq0QSxrycVWuvfJa75C/b+KOT9o8vLkcbV4+oIc4f49rc2eWuMcV1KXXQ/1yDLVeIQ/ktJlL3wzJykKbJXNy6V0ht5lLzrWUJa9tlNd6hzyuxx0HtDkBPa6PhPR6Xvs7Ab2KXhxqZwm1XiEP5LRZFQdwg/+ENmtwA1Sx+5DbrAoOJ/8kr22U13qHPK7HHWC0OQE9ro+E9Hpe+zsBvYpePH/+fDN69GgzYsQI07lz5yo+wc0/CbVe0g61bqHWizZz8zsirlSh9sdQ6xXXnj69ntc2ymu9Qx4j4o472jy8+TdtXlogr/2dgB53VPA6AggggAACCCCAAAIIIIAAAhkIENAzQGYXCCCAAAIIIIAAAggggAACCMQJENDjhHgdAQQQQAABBBBAAAEEEEAAgQwECOgZILMLBBBAAAEEEEAAAQQQQAABBOIECOhxQryOAAIIIIAAAggggAACCCCAQAYCBPQMkNkFAggggAACCCCAAAIIIIAAAnECBPQ4IV5HAAEEEEAAAQQQQAABBBBAIAMBAnoGyOwCAQQQQAABBBBAAAEEEEAAgTgBAnqcEK8jgAACCCCAAAIIIIAAAgggkIEAAT0DZHaBAAIIIIAAAggggAACCCCAQJwAAT1OiNcRQAABBBBAAAEEEEAAAQQQyECAgJ4BMrtAAAEEEEAAAQQQQAABBBBAIE6AgB4nxOsIIIAAAggggAACCCCAAAIIZCBAQM8AmV0ggAACCCCAAAIIIIAAAgggECdAQI8T4nUEEEAAAQQQQAABBBBAAAEEMhAgoGeAzC4QQAABBBBAAAEEEEAAAQQQiBMIPqD3Gj4pzsCZ16ePGehMWSgIAggggAACCNQm4NMcpFxNmZ/U1g/4awQQQKASAQJ6JVp1fi8DYJ2B+XgEEEAAAQQyFCCgZ4jNrhBAAIFABAjoDjUkAd2hxqAoCCCAAAII1ChAQK8RkD9HAAEEcihAQHeo0QnoDjUGRUEAAQQQQKBGAQJ6jYD8OQIIIJBDAQK6Q41OQHeoMSgKAggggAACNQoQ0GsE5M8RQACBHAoQ0B1qdAK6Q41BURBAAAEEEKhRgIBeIyB/jgACCORQgIDuUKMT0B1qDIqCAAIIIIBAjQIE9BoB+XMEEEAghwIEdIcanYDuUGNQFAQQQAABBGoUIKDXCMifI4AAAjkUIKA71OgEdIcag6IggAACCCBQowABvUZA/hwBBBDIoQAB3aFGJ6A71BgUBQEEEEAAgRoFCOg1AvLnCCCAQA4FCOgONToB3aHGoCgIIIAAAgjUKEBArxGQP0cAAQRyKEBAd6jRCegONQZFQQABBBBAoEYBAnqNgPw5AgggkEMBArpDjU5Ad6gxKAoCCCCAAAI1ChDQawTkzxFAAIEcChDQHWp0ArpDjUFREEAAAQQQqFGAgF4jIH+OAAII5FCAgO5QoxPQHWoMioIAAggggECNAgT0GgH5cwQQQCCHAgR0hxqdgO5QY1AUBBBAAAEEahQgoNcIyJ8jgAACORQgoDvU6AR0hxqDoiCAAAIIIFCjAAG9RkD+HAEEEMihAAHdoUYnoDvUGBQFAQQQQACBGgUI6DUC8ucIIIBADgUI6A41OgHdocagKAgggAACCNQoQECvEZA/RwABBHIoQEB3qNEJ6A41BkVBAAEEEECgRgECeo2A/DkCCCCQQwECukONTkB3qDEoCgIIIIAAAjUKENBrBOTPEUAAgRwKENAdanQCukONQVEQQAABBBCoUYCAXiMgf44AAgjkUICA7lCjE9AdagyKggACCCCAQI0CBPQaAflzBBBAIIcCBHSHGp2A7lBjUBQEEEAAAQRqFCCg1wjInyOAAAI5FCCgO9ToBHSHGoOiIIAAAgggUKMAAb1GQP4cAQQQyKEAAd2hRiegO9QYFAUBBBBAAIEaBQjoNQLy5wgggEAOBQjoDjU6Ad2hxqAoCCCAAAII1ChAQK8RkD9HAAEEcihAQHeo0QnoDjUGRUEAAQQQQKBGAQJ6jYD8OQIIIJBDAQK6Q41OQHeoMSgKAggggAACNQoQ0GsE5M8RQACBHAoQ0B1qdAK6Q41BURBAAAEEEKhRgIBeIyB/jgACCORQgIDuUKMT0B1qDIqCAAIIIIBAjQIE9BoB+XMEEEAghwIEdIcanYDuUGNQFAQQQAABBGoUIKDXCMifI4AAAjkUcCagL1y40MybNy/1Jugz8r7UP7NeHzh1VP96fTSfiwACCCCQI4GuXbuapqamimpcr3G4okIE9maf5iDl6JmfBNYxqQ4CCGQiUM1YrII5E9BbWlpMc3NzJljsBAEEEEAAgZAF5s6da7p161ZRFRmHK+LizQgggAACCJQVqGYsdiqg+3TmXpOYnj17mpkzZ1Y8AXK5H4daL5mHWrdQ60WbufxNUbpsofZHH+tVzVl7n8bh4l7oYxulcZTntd4hjxFx/YI2D2/+TZuHO6+oZix2KqDHdU6XXo+uMlR7VsSluhSWJdR6RQO5VmjQZq72vkXLFWp/DLVeHGf+HFshljTk46pce+W13iF/38Qdn7R5eHM52rx8QA9x/h7X5s4scY8rqEuvh/rlGGq9Qh7IaTOXvhmSlYU2S+bk0rtCbjOXnGspS17bKK/1DnlcjzsOaHMCelwfCen1vPZ3AnoVvTjUzhJqvUIeyGmzKg7gBv8JbdbgBqhi9yG3WRUcTv5JXtsor/UOeVyPO8BocwJ6XB8J6fW89ncCehW9eP78+Wb06NFmxIgRpnPnzlV8gpt/Emq9pB1q3UKtF23m5ndEXKlC7Y+h1iuuPX16Pa9tlNd6hzxGxB13tHl482/avLRAXvs7AT3uqOB1BBBAAAEEEEAAAQQQQAABBDIQIKBngMwuEEAAAQQQQAABBBBAAAEEEIgTIKDHCfE6AggggAACCCCAAAIIIIAAAhkIENAzQGYXCCCAAAIIIIAAAggggAACCMQJENDjhHgdAQQQQAABBBBAAAEEEEAAgQwECOgZILMLBBBAAAEEEEAAAQQQQAABBOIECOhxQryOAAIIIIAAAggggAACCCCAQAYCBPQMkNkFAggggAACCCCAAAIIIIAAAnECBPQ4IV5HAAEEEEAAAQQQQAABBBBAIAMBAnoGyOwCAQQQQAABBBBAAAEEEEAAgTgBAnqcEK8jgAACCCCAAAIIIIAAAgggkIEAAT0DZHaBAAIIIIAAAggggAACCCCAQJwAAT1OiNcRQAABBBBAAAEEEEAAAQQQyECAgJ4BMrtAAAEEEEAAAQQQQAABBBBAIE6AgB4nxOsIIIAAAggggAACCCCAAAIIZCBAQM8AmV0ggAACCCCAAAIIIIAAAgggECdAQI8T4vXMBXoNn5T5Pqvd4fQxA6v9U/4OAQQQQACBYAV8GsvLNQLjfLBdlIoh4KwAAd3ZpslvwXwa1Bm489tPqTkCCCCAQGkBn8ZyAjo9GQEEXBIgoLvUGpTFCvg0qBPQ6bQIIIAAAggsKuDTWE5ApwcjgIBLAgR0l1qDshDQ6QMIIIAAAggEIEBAD6ARqQICCDREgIDeEHZ2Wk7Ap0GdK+j0ZQQQQAABBLiCTh9AAAEE0hIgoKclyeekJkBAT42SD0IAAQQQQKAhAj6N5eWAOBHfkO7DThHItQABPdfN72blfRrUGbjd7EOUCgEEEECgsQI+jeUE9Mb2FfaOAAJtBQjo9AjnBHwa1AnoznUfCoQAAggg4ICAT2M5Ad2BDkMREECgVYCATmdwTsCnQZ2A7lz3oUAIIIAAAg4I+DSWE9Ad6DAUAQEECOj0AXcFfBrUCeju9iNKhgACCCDQOAGfxnICeuP6CXtGAIFFBbiCTg13WPIAACAASURBVK9wTsCnQZ2A7lz3oUAIIIAAAg4I+DSWE9Ad6DAUAQEEuIJOH3BXwKdBnYDubj+iZAgggAACjRPwaSwnoDeun7BnBBDgCjp9wAMBnwZ1AroHHYoiIoAAAghkLuDTWE5Az7x7sEMEECgjwBJ3uodzAj4N6gR057oPBUIAAQQQcEDAp7GcgO5Ah6EICCDQKkBApzM4J+DToE5Ad677UCAEEEAAAQcEfBrLCegOdBiKgAACBHT6gLsCPg3qBHR3+xElQwABBBBonIBPYzkBvXH9hD0jgMCiAlxBp1c4J+DToE5Ad677UCAEEEAAAQcEfBrLCegOdBiKgAACXEGnD7gr4NOgTkB3tx9RMgQQQACBxgn4NJYT0BvXT9gzAghwBZ0+4IGAT4M6Ad2DDkUREUAAAQQyF/BpLCegZ9492CECCJQRYIk73cM5AZ8GdQK6c92HAiGAAAIIOCDg01hOQHegw1AEBBBoFSCg0xmcE/BpUCegO9d9KBACCCCAgAMCPo3lBHQHOgxFQAABAjp9wF0BnwZ1Arq7/YiSIYAAAgg0TsCnsZyA3rh+wp4RQGBRAa6g0yucE/BpUCegO9d9KBACCCCAgAMCPo3lBHQHOgxFQAABrqDTB9wV8GlQJ6C7248oGQIIIIBA4wR8GssJ6I3rJ+wZAQS4gk4f8EDAp0GdgO5Bh6KICCCAAAKZC/g0lhPQM+8e7BABBMoIsMSd7uGcgE+DOgHdue5DgRBAAAEEHBDwaSwnoDvQYSgCAgi0ChDQ6QzOCfg0qBPQnes+FAgBBBBAwAEBn8ZyAroDHYYiIIAAAZ0+4K6AT4M6Ad3dfkTJEEAAAQQaJ+DTWE5Ab1w/Yc8IILCoAFfQ6RXOCfg0qBPQnes+FAgBBBBAwAEBn8ZyAroDHYYiIIAAV9DpA+4K+DSoE9Dd7UeUDAEEEECgcQI+jeUE9Mb1E/aMAAJcQacPeCDg06BOQPegQ1FEBBBAAIHMBXwaywnomXcPdogAAmUEWOJO93BOwKdBnYDuXPehQAgggAACDgj4NJYT0B3oMBQBAQRaBZwJ6AsXLjTz5s2jaRAwfUbe543C1FH9vSkrBUUAgfwIdO3a1TQ1NVVUYcbhirh4c4yAT2N5uaowztPVEUCgWoFqxmLty5mA3tLSYpqbm6utP3+HAAIIIIAAAv8nMHfuXNOtW7eKPBiHK+LizQgggAACCJQVqGYsdiqg+3TmXpOYnj17mpkzZ1Y8AXK5H4daL5mHWrdQ60WbufxNUbpsofZHH+tVzVl7n8bh4l7oYxulcZTntd4hjxFx/YI2D2/+TZuHO6+oZix2KqDHdU6XXo+uMlR7VsSluhSWJdR6RQO5VmjQZq72vkXLFWp/DLVeHGf+HFshljTk46pce+W13iF/38Qdn7R5eHM52rx8QA9x/h7X5s4scY8rqEuvh/rlGGq9Qh7IaTOXvhmSlYU2S+bk0rtCbjOXnGspS17bKK/1DnlcjzsOaHMCelwfCen1vPZ3AnoVvTjUzhJqvUIeyGmzKg7gBv8JbdbgBqhi9yG3WRUcTv5JXtsor/UOeVyPO8BocwJ6XB8J6fW89ncCehW9eP78+Wb06NFmxIgRpnPnzlV8gpt/Emq9pB1q3UKtF23m5ndEXKlC7Y+h1iuuPX16Pa9tlNd6hzxGxB13tHl482/avLRAXvs7AT3uqOB1BBBAAAEEEEAAAQQQQAABBDIQIKBngMwuEEAAAQQQQAABBBBAAAEEEIgTIKDHCfE6AggggAACCCCAAAIIIIAAAhkIENAzQGYXCCCAAAIIIIAAAggggAACCMQJENDjhHgdAQQQQAABBBBAAAEEEEAAgQwECOgZILMLBBBAAAEEEEAAAQQQQAABBOIECOhxQryOAAIIIIAAAggggAACCCCAQAYCBPQMkNkFAggggAACCCCAAAIIIIAAAnECBPQ4IV5HAAEEEEAAAQQQQAABBBBAIAMBAnoGyOwCAQQQQAABBBBAAAEEEEAAgTgBAnqcEK8jgAACCCCAAAIIIIAAAgggkIEAAT0DZHaBAAIIIIAAAggggAACCCCAQJwAAT1OiNcRQAABBBBAAAEEEEAAAQQQyECAgJ4BMrtAAAEEEEAAAQQQQAABBBBAIE6gpoC+5557xn1+6+u333574vfyRgQQQAABBBBAAAEEEEAAAQTyJlBTQB80aFCr18KFC80dd9xhmpubzYYbbmj/+zPPPGPmzJljFOQnTpyYN1vqiwACCCCAAAIIIIAAAggggEBigZoCeuFeTjzxRDN79mxz2WWXmY4dO9qXFixYYAYPHmy6detmxo4dm7hQvBEBBPwS6DV8kjcFnj5moDdlpaAIIIAAAgj4IuDTXKCcKfMEX3pcuOVMLaD36NHDTJkyxay55ppttF577TWz2WabmU8++SRcRWqGQM4FfBqUGXhz3lmpPgIIIIBAXQR8mgsQ0OvSBfjQlARSC+jdu3e3y9h33333NkW78847jZbCf/rppykVmY9BAAHXBHwalAnorvUeyoMAAgggEIKAT3MBAnoIPS7cOqQW0IcNG2auvvpqc9JJJ5lNNtnEij3++ONmzJgx5qCDDjITJkwIV5GaIZBzAZ8GZQJ6zjsr1UcAAQQQqIuAT3MBAnpdugAfmpJAagH922+/NePGjTMXXnihmTVrli3eCiusYIYOHWqOO+641vvSUyo3H4MAAg4J+DQoE9Ad6jgUBQEEEEAgGAGf5gIE9GC6XZAVSS2gF+q0tLTYf9XD4dgQQCB8AZ8GZQJ6+P2RGiKAAAIIZC/g01yAgJ59/2CPyQXqEtCT7553IoBACAI+DcoE9BB6HHVAAAEEEHBNwKe5AAHdtd5DeQoFUgvoH3zwgTn++OPNgw8+aD788EOj30Uv3PSTa2wIIBCmgE+DMgE9zD5IrRBAAAEEGivg01yAgN7YvsLeywukFtAHDBhgZsyYYYYMGWLvPW9qamqz59122422QACBQAV8GpQJ6IF2QqqFAAIIINBQAZ/mAgT0hnYVdh4jkFpA79q1q3n00UdN3759QUcAgZwJ+DQoE9Bz1jmpLgIIIIBAJgI+zQUI6Jl0CXZSpUBqAb13797muuuuM/369auyKPwZAgj4KuDToExA97WXUW4EEEAAAZcFfJoLENBd7kmULbWAPnnyZDN+/Hhz+eWXm169eiGLAAI5EvBpUCag56hjUlUEEEAAgcwEfJoLENAz6xbsqAqB1AJ69+7dzRdffGG++eYb06VLF9OpU6c2xZk9e3YVxeNPEEDABwGfBmUCug89ijIigAACCPgm4NNcgIDuW+/KV3lTC+jXXHNNWbmDDz44X7LUFoEcCfg0KBPQc9QxqSoCCCCAQGYCPs0FCOiZdQt2VIVAagG9in3zJwggEIiAT4MyAT2QTkc1EEAAAQScEvBpLkBAd6rrUJgigdQCun5irdy28sorg48AAoEK+DQoE9AD7YRUCwEEEECgoQI+zQUI6A3tKuw8RiC1gN6hQ4dFfvu8cN8LFiygMRBAIFABnwZlAnqgnZBqIYAAAgg0VMCnuQABvaFdhZ1nFdBfeOGFNrv6+uuvzXPPPWcmTJhgzj77bLPnnnvSGAggEKiAT4MyAT3QTki1EEAAAQQaKuDTXICA3tCuws6zCuil9jNp0iQzduxY8/DDD9MYCCAQqIBPgzIBPdBOSLUQQAABBBoq4NNcgIDe0K7Czhsd0N944w3Tt29f8/nnn9MYCCAQqIBPgzIBPdBOSLUQQAABBBoq4NNcgIDe0K7CzrMK6C0tLW12tXDhQjNr1ixz+umnm1dffdU8//zzNAYCCAQq4NOgTEAPtBNSLQQQQACBhgr4NBcgoDe0q7DzrAJ6ew+JU0jv2bOnufHGG82mm25KYyCAQKACPg3KBPRAOyHVQgABBBBoqIBPcwECekO7CjvPKqA/8sgjbXalwN6jRw+z+uqrm8UWW4yGQACBgAV8GpQJ6AF3RKqGAAIIINAwAZ/mAgT0hnUTdpxAILWfWUuwL96CAAKBCvg0KBPQA+2EVAsBBBBAoKECPs0FCOgN7SrsPKsr6NrPW2+9ZS644AIzbdo0+5voa6+9thk6dKhZbbXVaAgEEAhYwKdBmYAecEekaggggAACDRPwaS5AQG9YN2HHCQRSu4J+3333mV133dU+sX3zzTc3uv/8scceM/p99LvuusvssMMOCYrDWxBAwEcBnwZlArqPPYwyI4AAAgi4LuDTXICA7npvynf5Ugvo/fr1M/379zdjxoxpIzp8+HAzefJk8+yzz+ZbmtojELCAT4MyAT3gjkjVEEAAAQQaJuDTXICA3rBuwo4TCKQW0BdffHHz0ksvmTXWWKPNbl9//XWz3nrrma+++ipBcXgLAgj4KODToExA97GHUWYEEEAAAdcFfJoLENBd7035Ll9qAV0/pzZhwgSz9957txG9+eabzfHHH29mzJiRb2lqj0DAAj4NygT0gDsiVUMAAQQQaJiAT3MBAnrDugk7TiCQWkA/44wzzPnnn2+0pH2zzTazD4mbMmWKXfKugH7KKackKA5vQQABHwV8GpQJ6D72MMqMAAIIIOC6gE9zAQK6670p3+VLLaDroXB6gvv48ePNe++9Z1VXXHFFc8IJJ5g99tjD6Ao7GwIIhCng06BMQA+zD1IrBBBAAIHGCvg0FyCgN7avsPfyAqkF9MLdzJs3z/7rZ599Zs455xxz5ZVXmi+//JK2QACBQAV8GpQJ6IF2QqqFAAIIINBQAZ/mAgT0hnYVdh4jUHNAnzNnjjnmmGPsk9o7depkl7gPGTLEjBo1yowbN8707t3bDBs2zOy7775li6Ir8FGwp9UQQMAvgT4j7/OmwFNH9femrBQUgWoFunbtam81q2RjHK5Ei/cigECxgE9zgXKtxzyBvp2WQDVjsfZdc0AfPHiw/Z3zffbZx9x7771m2rRp9ufW9NT2kSNHmq233jpRHVtaWkxzc3Oi9/ImBBBAAAEEECgtMHfuXNOtW7eKiBiHK+LizQgggAACCJQVqGYsTiWgr7LKKuaqq64y22+/vXn77bfN6quvbo499lh7P3olm09n7jWJ0T31M2fOrHgCVIlJ1u8NtV5yDLVuodaLNsv66E9nf6H2Rx/rVc1Ze5/G4eIe62MbpXHU5bXeIY8Rcf2CNg9v/k2blxbwvb9XMxanEtC1rP2dd96xD4TT1qVLF/Pkk0+aPn36xPU3b1+PrjJUe1bE1YqHWq9oINcKDdrM1d63aLlC7Y+h1ovjzJ9jK8SShnxclWuvvNY75O+buOOTNg9vLkeblw/oIc7f49q85iXuHTt2NO+//77p0aOH3ZfOFLz44otm1VVXjdu3t6+H+uUYar1CHshpM/++Rmgz2sw/AfdLHPJxRUBvX4A2r/w2FveP5PIlpM1pc9/7cNLy1xzQO3ToYAYMGGA6d+5s96n70bfddluz5JJLtinD7bffnrRMzr8v1C+IUOtFQHf+kGq3gKH2x1DrxXHm53EWSqlDPq4I6AT0QoG89vWQx5i472HaPH+rJmoO6IMGDYrrV/b1iRMnJnqfD2+aP3++GT16tBkxYkTriQkfyh1XxlDrpXqHWrdQ60WbxR2tbr4ean8MtV5u9qLqSpXXNsprvUMeI+KOANo8vPk3bV5aIK/9veaAHtepeB0BBBBAAAEEEEAAAQQQQAABBOIFCOjxRrwDAQQQQAABBBBAAAEEEEAAgboLENDrTswOEEAAAQQQQAABBBBAAAEEEIgXIKDHG/EOBBBAAAEEEEAAAQQQQAABBOouQECvOzE7QAABBBBAAAEEEEAAAQQQQCBegIAeb8Q7EEAAAQQQQAABBBBAAAEEEKi7AAG97sTsAAEEEEAAAQQQQAABBBBAAIF4AQJ6vBHvQAABBBBAAAEEEEAAAQQQQKDuAgT0uhOzAwQQQAABBBBAAAEEEEAAAQTiBQjo8Ua8AwEEEEAAAQQQQAABBBBAAIG6CxDQ607MDhBAAAEEEEAAAQQQQAABBBCIFyCgxxvxDgQQQAABBBBAAAEEEEAAAQTqLkBArzsxO0AAAQQQQAABBBBAAAEEEEAgXoCAHm/EOxBAAAEEEEAAAQQQQAABBBCouwABve7E7AABBBBAAAEEEEAAAQQQQACBeAECerwR70AAAQQQQAABBBBAAAEEEECg7gIE9LoT12cHvYZPqs8H1+lTp48ZWKdP5mMRQAABBBBAAAEEEGiMgG9z8lJKzNUb03/a2ysB3Z22qKgkvn0ZcNBX1Ly8GQEEEEAAAQQQQMADAd/m5AR09zsVAd39Nmq3hL59GRDQPe1oFBsBBBBAAAEEEECgpIBvc3ICuvudmYDufhsR0D1tI4qNAAIIIIAAAgggELYAAT3s9m1E7QjojVBPYZ++fRlwBT2FRucjEEAAAQQQQAABBJwS8G1OzhV0p7pPu4UhoLvfRlxB97SNKDYCCCCAAAIIIIBA2AIE9LDbtxG1I6A3Qj2Fffr2ZcAV9BQanY9AAAEEEEAAAQQQcErAtzk5V9Cd6j5cQXe/OZKX0LcvAwJ68rblnQgggAACCCCAAAJ+CPg2Jyegu9+vuILufhu1W0LfvgwI6J52NIqNAAIIIIAAAgggUFLAtzk5Ad39zkxAd7+NCOiethHFRgABBBBAAAEEEAhbgIAedvs2onYE9Eaop7BP374MuIKeQqPzEQgggAACCCCAAAJOCfg2J+cKulPdp93CENDdbyOuoHvaRhQbAQQQQAABBBBAIGwBAnrY7duI2hHQG6Gewj59+zLgCnoKjc5HIIAAAggggAACCDgl4NucnCvoTnUfrqC73xzJS+jblwEBPXnb8k4EEEAAAQQQQAABPwR8m5MT0N3vV1xBd7+N2i2hb18GBHRPOxrFRgABBBBAAAEEECgp4NucnIDufmcmoLvfRgR0T9uIYiOAAAIIIIAAAgiELUBAD7t9G1E7Anoj1FPYp29fBlxBT6HR+QgEEEAAAQQQQAABpwR8m5NzBd2p7tNuYQjo7rcRV9A9bSOKjQACCCCAAAIIIBC2AAE97PZtRO0I6I1QT2Gfvn0ZcAU9hUbnIxBAAAEEEEAAAQScEvBtTs4VdKe6D1fQ3W+O5CX07cuAgJ68bXknAggggAACCCCAgB8Cvs3JCeju9yuuoLvfRu2W0LcvAwK6px2NYiOAAAIIIIAAAgiUFPBtTk5Ad78zE9DdbyMCuqdtRLERQAABBBBAAAEEwhYgoIfdvo2oHQG9Eeop7NO3LwOuoKfQ6HwEAggggAACCCCAgFMCvs3JuYLuVPdptzAEdPfbiCvonrYRxUYAAQQQQAABBBAIW4CAHnb7NqJ2BPRGqKewT9++DLiCnkKj8xEIIIAAAggggAACTgn4NifnCrpT3Ycr6O43R/IS+vZlQEBP3ra8EwEEEEAAAQQQQMAPAd/m5AR09/sVV9Ddb6N2S+jblwEB3dOORrERQAABBBBAAAEESgr4NicnoLvfmQno7rcRAd3TNqLYCCCAAAIIIIAAAmELENDDbt9G1I6A3gj1FPbp25cBV9BTaHQ+AgEEEEAAAQQQQMApAd/m5FxBd6r7tFsYArr7bcQVdE/biGIjgAACCCCAAAIIhC1AQA+7fRtROwJ6I9RT2KdvXwZcQU+h0fkIBBBAAAEEEEAAAacEfJuTcwXdqe7DFXT3myN5CX37MiCgJ29b3okAAggggAACCCDgh4Bvc3ICuvv9ypkr6AsXLjTz5s1zX8yREvYZeZ8jJUlWjKmj+id7I+9CAAEEEKhZoGvXrqapqamiz2EcroiLNyOAAAJWwLc5ealmY66efoeuZixWKZwJ6C0tLaa5uTl9GT4RAQQQQACBnAnMnTvXdOvWraJaMw5XxMWbEUAAAQQQKCtQzVjsVED36cy9JjE9e/Y0M2fOrHgC5HI/DrVeMg+1bqHWizZz+ZuidNlC7Y8+1quas/Y+jcPFvdDHNkrjKM9rvUMeI+L6BW0e3vybNg93XlHNWOxUQI/rnC69Hl1lqPasiEt1KSxLqPWKBnKt0KDNXO19i5Yr1P4Yar04zvw5tkIsacjHVbn2ymu9Q/6+iTs+afPw5nK0efmAHuL8Pa7NnVniHldQl14P9csx1HqFPJDTZi59MyQrC22WzMmld4XcZi4511KWvLZRXusd8rgedxzQ5gT0uD4S0ut57e8E9Cp6caidJdR6hTyQ02ZVHMAN/hParMENUMXuQ26zKjic/JO8tlFe6x3yuB53gNHmBPS4PhLS63nt7wT0Knrx/PnzzejRo82IESNM586dq/gEN/8k1HpJO9S6hVov2szN74i4UoXaH0OtV1x7+vR6Xtsor/UOeYyIO+5o8/Dm37R5aYG89ncCetxRwesIIIAAAggggAACCCCAAAIIZCBAQM8AmV0ggAACCCCAAAIIIIAAAgggECdAQI8T4nUEEEAAAQQQQAABBBBAAAEEMhAgoGeAzC4QQAABBBBAAAEEEEAAAQQQiBMgoMcJ8ToCCCCAAAIIIIAAAggggAACGQgQ0DNAZhcIIIAAAggggAACCCCAAAIIxAkQ0OOEeB0BBBBAAAEEEEAAAQQQQACBDAQI6BkgswsEEEAAAQQQQAABBBBAAAEE4gQI6HFCvI4AAggggAACCCCAAAIIIIBABgIE9AyQ2QUCCCCAAAIIIIAAAggggAACcQIE9DghXkcAAQQQQAABBBBAAAEEEEAgAwECegbI7AIBBBBAAAEEEEAAAQQQQACBOAECepwQryOAAAIIIIAAAggggAACCCCQgQABPQNkdoEAAggggAACCCCAAAIIIIBAnAABPU6I1xFAAAEEEEAAAQQQQAABBBDIQICAngEyu0AAAQQQQAABBBBAAAEEEEAgToCAHifE6wgggAACCCCAAAIIIIAAAghkIEBAzwCZXSCAAAIIZCPQa/ikbHaU0l6mjxmY0ifxMQgggAACCGQr4NuYW0rHtbGYgJ5tP2ZvCCCAAAJ1FPBtsuDapKCOTcNHI4AAAggEJuDbmEtAD6wDUh0EEEAAAfcFfJssENDd71OUEAEEEECgfQHfxlwCOj0ZAQQQQACBjAV8mywQ0DPuIOwOAQQQQCA1Ad/GXAJ6ak3PByGAAAIIIJBMwLfJAgE9WbvyLgQQQAAB9wR8G3MJ6O71IUqEAAIIIBC4gG+TBQJ64B2S6iGAAAIBC/g25hLQA+6MVA0BBBBAwE0B3yYLBHQ3+xGlQgABBBCIF/BtzCWgx7cp70AAAQQQQCBVAd8mCwT0VJufD0MAAQQQyFDAtzGXgJ5h52BXCCCAAAIISMC3yQIBnX6LAAIIIOCrgG9jLgHd155GuRFAAAEEvBXwbbJAQPe2q1FwBBBAIPcCvo25BPTcd1kAEEAAAQSyFvBtskBAz7qHsD8EEEAAgbQEfBtzCehptTyfgwACCCCAQEIB3yYLBPSEDcvbEEAAAQScE/BtzCWgO9eFKBACCCCAQOgCvk0WCOih90jqhwACCIQr4NuYS0APty9SMwQQQAABRwV8mywQ0B3tSBQLAQQQQCBWwLcxl4Ae26S8AQEEEEAAgXQFfJssENDTbX8+DQEEEEAgOwHfxlwCenZ9gz0hgAACCCBgBXybLBDQ6bgIIIAAAr4K+DbmEtB97WmUGwEEEEDAWwHfJgsEdG+7GgVHAAEEci/g25hLQM99lwUAAQQQQCBrAd8mCwT0rHsI+0MAAQQQSEvAtzGXgJ5Wy/M5CCCAAAIIJBTwbbJAQE/YsLwNAQQQQMA5Ad/GXAK6c12IAiGAAAIIhC7g22SBgB56j6R+CCCAQLgCvo25BPRw+yI1QwABBBBwVMC3yQIB3dGORLEQQAABBGIFfBtzCeixTcobEEAAAQQQSFfAt8kCAT3d9ufTEEAAAQSyE/BtzCWgZ9c32BMCCCCAAAJWwLfJAgGdjosAAggg4KuAb2MuAd3Xnka5EUAAAQS8FfBtskBA97arUXAEEEAg9wK+jbkE9Nx3WQAQQAABBLIW8G2yQEDPuoewPwQQQACBtAR8G3MJ6Gm1PJ+DAAIIIIBAQgHfJgsE9IQNy9sQQAABBJwT8G3MJaA714UoEAIIIIBA6AK+TRYI6KH3SOqHAAIIhCvg25hLQA+3L1IzBBBAAAFHBXybLBDQHe1IFAsBBBBAIFbAtzGXgB7bpLwBAQQQQACBdAV8mywQ0NNtfz4NAQQQQCA7Ad/GXAJ6dn2DPSGAAAIIIGAFfJssENDpuAgggAACvgr4NuYS0H3taZQbAQQQQMBbAd8mCwR0b7saBUcAAQRyL+DbmEtAr7DLLly40MybN6/Cv+LtCCCAAAII/H+BPiPv84pj6qj+dSlv165dTVNTU0WfzThcERdvRgABBHIv4NuYW6rBXBqLVcam/wzIC13oXS0tLaa5udmFolAGBBBAAAEEvBaYO3eu6datW0V1YByuiIs3I4AAAgggUFagmrHYqYDu05l7TWJ69uxpZs6cWfEEyOV+HGq9ZB5q3UKtF23m8jdF6bKF2h99rFferqD72EZpHOV5rXfIY0Rcv6DNw5t/0+bhziuqGYudCuhxndOl16OrDNWeFXGpLoVlCbVe0UCuFRq0mau9b9FyhdofQ60Xx5k/x1aIJQ35uCrXXnmtd8jfN3HHJ20e3lyONi8f0EOcv8e1uTNL3OMK6tLroX45hlqvkAdy2sylb4ZkZaHNkjm59K6Q28wl51rKktc2ymu9Qx7X444D2pyAHtdHQno9r/2dgF5FLw61s4Rar5AHctqsigO4wX9CmzW4AarYfchtVgWHk3+S1zbKa71DHtfjDjDanIAe10dCej2v/Z2AXkUvnj9/vhk9erQZMWKE6dy5cxWf4OafhFovaYdat1DrRZu5+R0RV6pQ+2Oo9YprT59ez2sb5bXeIY8RcccdbR7e/Js2Ly2Q1/5OQI87KngdAQQQQAABBBBAAAEEm2Dk1AAAHX5JREFUEEAAgQwECOgZILMLBBBAAAEEEEAAAQQQQAABBOIECOhxQryOAAIIIIAAAggggAACCCCAQAYCBPQMkNkFAggggAACCCCAAAIIIIAAAnECBPQYoYcffthss8025tNPPzVLLbVUnCevZyjw4x//2PTt29dccMEFGe61cbvyqb6hHzfTp083q666qnnuuedsHwx5q7XfFfeFq6++2vzqV78yc+bMcZ6t0nY+5JBDbL3uvPNO5+sWcgF79epl+5j+KbUleY9vRknqlOQ9vtW7vfKGPgaVa6NQ656kXkne41v/TlKnJO/xrd6Vlvf000+3Y+/zzz9f6Z86+X4CelGzFE9G6fRO9ltbqFqDg7s1a79kLtc3b8dNpcHNt75WWN5a+50vAb29cL1gwQLz0UcfmWWXXdYstthisc1IQI8lyuQNSUKo2nXJJZc0Xbp0yaRMWewkr/UmoLcVCHXemqRe//73v83s2bPNcsstZ5qamrI47Oq+j7zWu1JYAnqlYp69P29Bw7PmaVPcWoODb3V3ub5pHDdff/216dSpkxfNQkBP3kw+B/TktfzvOwnolYrV5/1Jgmp99tzYT81rvYvVNZb8/e9/z+Xqx5DrniSoNvYIrM/e81rvSjUJ6JWKefR+Ta6uueaaNiWeOHGiGTRokHnggQfMiSeeaF555RW7pFX/fc0112x971133WXUOV5++WWz4oormoMPPticfPLJia66uEB07733mrPOOstMnTrVdOzY0Wy66abmwgsvNKuttpoLxWu3DAqFffr0sa9de+21ttxHH320OfPMM+2ZU92WMHToUKO20e8obr311uaiiy4ya6yxhvn888/NCiusYP7whz+Yvfbaq007/vznPzfvv/++6dq1a8PqrvKpLrfffrstx/HHH2/rES3pL1e3qNBXXHGFOeOMM8wnn3xi+vfvb7bcckv772kvLa72uIm+TI899ljb9xR6dcVy5syZ5pe//KV58MEHTYcOHcxOO+1kLr74YntGfO7cuWbppZc2Tz75pPnhD39oFi5caJZZZhnbT5966ilb9RtuuMEMGzbMzJo1y+hsuv7/bbfdZvvD8ssvb4466igzYsSIRG377bffmrFjxxpZqlwqg/5+//33t0vc9bkq2xNPPGH71WWXXWaPHW1yHzJkiHn00UftGX2V8aSTTjL77rtv675vvfVWM2rUKPPmm2/aK3n9+vUzf/rTn+yVPW36njnvvPPMP//5T6PJt6wGDx5sX6u1bokA/vOmuONMx55uM3nttddsubfddlv779/97nftLlwL6O2Zy33cuHFtSB566CFrXnwrg77jTzjhBNuu6n86JrVsX+1bHNCfeeYZM2DAAPs9pPGALblAqWNj4MCBi9zatPvuu9tb0NQO2tRuhx12mJk2bZr585//bLp162aPeX2vRJurYTZv9b788svtuKTvV33fR9uuu+5qunfvbudkcfMrjfeXXnqpueeee+xcTeOlbk3UP3/5y1/s966+n9Zff31z5ZVXmnXXXTd5R6zjO/Nc91Ksmqv95je/MTfeeKNpaWkxG264oTn//PPNRhtt1DqWlGtTX8Ns3uqtsVNzK82ZNFf7wQ9+YE499VQ7H4/aMC53jRkzxvaNL774wvzsZz8zPXr0MMoyLHGv45dWoz5ak39NphT6NGBo02Rs++23NxtvvLE599xzbQf4xS9+YYOEztBqu++++2znUPhTCHrrrbfMkUceaSdrI0eObFR1KtqvgoYGOQ1cCoennXaaDUzq6IWDZkUfWuc3KzhoAqyJmMLs008/bd0VDo444giz2267mTfeeMNoENQETSdY1DY6yaIrtXrvu+++ayZNmtRa0j333NMG4uITNXWuyiIfrxCmSYlOIChUaoKhLy3VVfWLq5v65lZbbWX7rCY6+qLTl5/6bdoBvdrjRgFdoWiLLbYwo0ePtidY1P8UvBX0VM9vvvnGBlK1ieqvTa/vt99+5rjjjjMvvPCCnYSpz2rJqtpZAVpl0gCvz9dxed1115mVV17ZTgL1T2FILte26jMK5xoEVE4NJK+++qr9TlBwW2uttew+FM4VwHSSQGFby6HVt3SyQO9VudTPfv3rX9vvDX2f6LNUJgXwPfbYw8ybN8+GvoMOOsh85zvfsfvV98cll1xig7vud1e/njBhgj0BWGvdkvbpuONMfVQnu3TC8sMPP7R11MT67rvvtrtwKaCXM9expQmhTopo04mg9957r01AV5uut9569qSFAp/aVe252Wab2foXBnTVW8FRfVvfT2zJBcq1009+8pNEAV0nxfS9qe90jdHqlwpwO+ywgy2IiwE9j/VWO+n7Q98X2223nW2b6GSqxkBN5OPmV5q76ISgjjUdmxpLdFJTY8Paa69tLzZE46guQrz++utOrNbKc91LfRvoZKZOUulEyiqrrGLHR51k07j64osvxraprwE9b/XWfEkXoDTP0/zpb3/7m81W+q7WMa9jt1zuuvnmm82BBx5ofvvb39rc9cc//tHO9b7//e8T0JMPtX69s9RSXQWcaPDQQKKz+F9++aVZfPHFbRBSsC+8KqerSrrKogmej5vCjga8l156qfUqtWv1UFspEOgkSnSv0fDhw+2Xua5C6oxcNHlW2XVFs2fPnjZ877333vYqrCbWM2bMsKsePv74Y/u/999/v73a3qjts88+s1eF//d//9fss88+thgayFdaaSV7UuGYY46JrZtWAehzdKY52g444AD772kHdH1+NceNAvo555xjg6xOfGmTvY4lTa7UVtp0QmWdddax7aWz6ArmmmBp8qaJ15QpU8zbb79tV07svPPONihpMq4ve11xVv/Q8Vvp/WgKzCqXAvLhhx/epjtES9w1iVCwKyynrtopuLe36XtDE0aF62effdaebNBnaSJSvCm86wRL4ckErTTQ989jjz1WU90q6dvljjO1TfGmkxQ/+tGP7AkHnWhwKaCXM29veXrxrQwKfDrxo6tx7d2OEX2GVl1p8qCTg0lPBlXSJqG/t1w7tXerT3tX0HWcKZBHm74TdQImOnHkYkDPa711wlnPebjqqqtsc/3+97+3Jyf/9a9/2Yl63PxK3+16IKBOpEZb9L2j47V4HNVKC4V+F7Y8173YXyfadXJX7aOT8Nq0ZD86VjX+qz+Ua1MfA3re6q366nj/61//2rriUG2teZauhmueq3Yul7s0d9eKGK2cibZNNtnEfPXVVwR0F77Y6lGGUkFDQTAKEbqStcEGG5h33nnHXgHT1T4thdVZ22jTlUp1FHVEHx5CoyvLusL6+OOP26Cq+qjsuuqn0OPiprbS2TJdwYs2BXMtkdEZWP2v2qCwXXQlUlcrtUJAmw5wTaAV7DW462ycrrpXGubS9NFVYS2bjfpX9Nkqu04caAnxT3/607J1K66nPkNnF1XvLAN6ueNGAV1XtuUdbSqj2kEBvXDToK0wrqvLCuYKPzppoTbWiTMFdF21VjDX1RgFR03QNeHVFTOd8NBSeV1923HHHRM1l04I6AyuPltXywu3KLhFJw30mq766KrrI488Yk/a6TtAS7BuuukmexJCS9j0j/qfzv7qdd16oM/Q/6pcqo/qGp0gW2KJJdqsYNGKgubmZvPBBx/UVLdEAP/3pnLHmY4vXdVQW2q1jdpE3x0aZHVipHfv3k4F9HLmSQK6vgs1DpRaYaPP0BUAtd8tt9xi25qtcoFy7ZQ0oB966KGt3/Mqgb4/dLUm+m5xMaDntd76PtSkXN9rnTt3tuOc5lgaC5LMrzRe66KIbj2KtiiotTeO6oSOK6sb81z34m8GjSWakxWftNb3qMZFjf8KbuXa1MeAnrd6Ryfxo1v5on6g2/Y0d9WFCbVzuflj4Zww+nvN/3RrGkvcKx9zvfiLJA+7UuOrE0X3hWoSrftItZSueFOAdHWJeGFZNZHWFUtd9ddVZE2ytdT/jjvusMs0XdyqCegKvgq3OhmhTfcP6wqprohp6arOtDf6XtGof5UK6Priau/kQ2HdiusZTVA1KckyoBf+PGHxcdPeAz00idY/CsWFm+4vVVspmEf3oeu+b11Z0YCsE0y6Gq9lYrqSooletOmqWXRvokKTlpzrBE7cptUj6hPlAnrhz6zJVYOGBgj1TS3N0z8KBVq6r8FIZdOJhOhnuLSUS1fDJ0+ebI81PftA9dJJPS3J1KRTJwkKN51wik4YVFu3uLoXvl7uOFOdFXR0ckErFhRetSJFJxwiG5euoKtepcz1HV78E2nFV9D13aFVAeUCupZi6nOiZxT8z//8TyXcvPf/BEq1k1as6HjS90S0aWWK+l7hPejtBfTC7xYXA3q5/hlyvbUaUc/3UPvpKqlWFGkSrxVGSeZXCujFc5VyAb3wJH2jD7g8173YvtTFCc1BdZJd43+pgB61qY8BPW/11hxHV7vVVt/73vfadAOdoNN8rvjnrYvnjwT0Rn9zNWD/mmhqiazCgLb2DvbijrL55pvbJa3R8qwGFLumXWrpt5ab6B4Q3cuhTcuG9f9dD+g6w1a4zFa3Gegqerkl7lo6Hj0YTgFSJyR0xk5n3xSKtZS8kZuWputKrMJZtAxP5VS5dA9yuSXuUd20nFMrIHS1Odo0uOnf6xHQqzlu2gvo5Za4a8KmB8Zo08RNk3QtV1UYV50UaNWuWhKnqxLtbbq6qSvp6vMyLrfp6rDeo6v6pZa4lwvou+yyi71NJPpe0EkvXdXXP+39Traunmliqofa6R+1t+6nj04mxfXJSuoW91mFr0dL3Ns7znTfl9pEoTy6JUH9Vn3N1YBeWLdCcz1bQPcAFx4zxQFdIV7hPG6Ju5boyk1jifqiL79OUEm/yPK9he2kyZ3Ce3SM6zWdCNeErjCg66RztJxdZdVKKZ3cc3mJe7Fpnuqt1Se6LUYnJLUqTsejtiTzq3IBXSuYisdRPWfClSXuqmOe617Y5zVn0Zir9ilc4q6TnTq5rbFGx3m5NvUxoOet3tHtg3rOjuYKxVuS3KUl7roQ9bvf/a71z/WAXp3w4gp6lqNzhvvSMis1rgZ/XSnR0hMtoS13JVATYy2d1ZVX3dusK+b6O12B0z2jrm8KDgoSuhqpK6yabGvJtwKR6wFdD4lTaFWQ0XJm/f/x48fbf9dZ1+ghcXrImOqkq1vRQ+KidtGyOF1R1dLxwnsWG9lueqiUJpKaqOjKgvqW7teJHhIXV7foIXF6SqaCov5Wn6EJn/py2ls1x017AV0Tb4VvHXuFD4mL7mWOyq370HU1TGfNdVVcm1a16JhToI6edK4lklryri9yHZe6oq3bNrTkPMnKFgWyaGmsJopauqyl2/pOKH66d/EVdJ3w0cMXdb+czvbq4W76XtEEQwFdQUNPqtfJDR1/+nc9J0Cv6VjU/e26h14PPtK/a3m8HoSo9lOAr7VuSftA9JC49o4zrRrSiQStXNAVdD2ASU/g1TMCXAzo5cxVXt0zrtUMulqjWwnUTwrbWSd2FLq1BFcnA/Ue3Rake+6LHxKn1RBqaz0/QX0gye+oJ22T0N9Xrp00Pqn/61jSk/N1HMhX3wWFAV3Hib7z9F2pE3/qozr2tbpDm4tX0PNab7WH2khjldpF34OnnHKKback86tyAV3Hn77Do3FU8zvNC1xa2ZLnuhd/lymIa0zXie3oIap6rpCuqkYPhS3Xpj4GdBnkrd46vvUEd83X9QBerQbUakLN9XShIu4Kuk7S6GG5Cuj6e90uqbGAh8QFPDvQxFKNri8CnYmJfmatXECPBhE9+V2TPF0t0RV1XXXTpNaHTQ9jUBjQcl5NNBVyNDF3PaDri1onGK6//np7r7mCuZY6F/7Mmr7cdW+L7gvWygg9MbJwU3hV4NKETydYXNh0Fb3wZ9YUSDW5LP6ZtXJ109lJBUzdF6xJqc4+azm/rhKmvVVz3JT6zUpNwEv9zFpUbj3sTpM51UcrCqIBThMxhUT1C20y0Be4JmTqH1o+qZMWCvNJNvUtBWR9jh74qLCvIKqrcXEBXe5aZqsQriXrOomhuukqnkK4HianEK8TSxqcNCip3vpptmhTv1Z5dVJJS+S1akADucJIrXVLUn+9R98D5Y4zPaleD09Tv9J9owqu+uUAFwN6OXOdfNHJun/84x/2AYulfmZNJ191EkKrjNSnop9Z08Sg+D52mUS3TUXfUUnd8/y+cu2kFTIK25qgRc+d0EmS4p9Z07Gnk2n6rtAJWvVL/V20uRjQ81pvtYlOHmsVjo4ZhTEdT9GmkF5uflUuoGtFjE7OawzQ/c363tT/urTlue7F7aCVa7rVUuOKrrS29zNr5drU14Cet3rrYozm45qfKXfo+1vzB80lNO+KC+jqN5rrK5TLTref6SScviu4gu7StxtlQaAGAZ1508RNAcyls+o1VKndP9XJIi0b1E95sSGAAAJ5FtDJNv3yQ/HtK6Gb5LXeobcr9fuvgAKaVpwptIU8nytu77zWO+R+3/SfsxgLQ64gdUOglICeNK0H/enBcPqpk7PPPjsoLP2Ul55griuvWrqvq/A6W5m3CWlQjUplEECgJgF97+sWIK0q0v/qvsU8bHmtdx7aljr+V0DPo9GqQa1a03NC8rLltd6hty8BPfQWpn4lBbTEWqFcS9/1UDnd+xLSpofgaLmXlolpuaCWT2t5NhsCCCCQVwE920JXznUrm54LkZctr/XOS/tSz/8+PFbzHV2I0K+15GXLa71Db18CeugtTP0QQAABBBBAAAEEEEAAAQS8ECCge9FMFBIBBBBAAAEEEEAAAQQQQCB0AQJ66C1M/RBAAAEEEEAAAccFpk+fvsivYzhe5JqL5+tTx2uuOB+AAAJlBQjodBAEEEAAAQQQCE5Av4uunyWcM2dOcHULsUJ5COjRzy7qmQDaCOjp9GSO9XQc+RR3BAjo7rQFJUEAAQQQQACBFAT0e+n6CU0CegqYGX0EAX2pRNLq2506dUr03jy8iWM9D62cvzoS0PPX5tQYAQQQQAABrwTuvfdec9ZZZ5mpU6eajh072p9Hu/DCC81qq61momB300032Sc4P/744+bSSy81hx56aJs6jhw50ujXO9gaK/Dtt9+asWPHmiuuuMLMnDnTLLfccuaoo44y+++/v13iftttt5mLL77YPPHEE2aNNdYwl112WevP4X3yySdmyJAh5tFHHzWzZ8+27X/SSSeZfffdt7VSt956q/25rTfffNN06dLF9OvXz/5Si35yVNvEiRPNeeedZ39mtVevXubYY481gwcPrjvKIYccYq655po2+1FZBg0aZB544AFz4oknmldeecX07dvXlnHNNde071WfvfPOO205dQyovy9YsMDa6ddZ9LNiHTp0MDvttJN1k+fcuXPN0ksvbZ588kn7dHP9ovIyyyxjvZ566in7uTfccIMZNmyYmTVrVt3rXskOONYr0eK9oQoQ0ENtWeqFAAIIIIBAIAIKbU1NTWbdddc1n3/+uTnttNNsUHn++efNjBkzbLBT2Bo/frwNZArxd9xxh31f9JvI+inN0H5O08fmVRBVOD///PPNFltsYQPiq6++an8aS+241lprmXHjxtlwfvLJJ9tAqbC92GKLmXfffdcGS723W7duZtKkSebXv/61/U37jTfe2H7WyiuvbAP4HnvsYX92S2H+oIMOsm2v/epEzSWXXGL7yXPPPWeOOOII+5N7+um9em4KzQMGDDB9+vQxZ5xxht3Vyy+/bOuisp977rmmR48e9udQFcBVpyigy0NWo0ePtn1bx4GCt046aLn8N998Y08ydO3a1S6b16bX99tvP3PccceZF154wWyzzTb22Pnoo4+snU6KqEw33nhjPatd8WdzrFdMxh8EKEBAD7BRqRICCCCAAAIhCyhkfPe73zUvvfSSDV4KdgoqQ4cOba0296W61wMUmBVCFZAPP/zwNgWMVkJceeWV5rDDDrOv6YryOuusY6ZNm2aDe3vbwIEDzdprr21D/bPPPmuDqT5rlVVWWeTtCu8KwoVX3HVV+u677zaPPfZY3cFK3YOuK+jbbbed3b/Kojp9+eWXZvHFF7dX0M855xx7ckJ22u6//34b9rUKoGfPnm2sdNV8o402ssH89ddfN3fddZddbTJlyhTz9ttvmzPPPNPsvPPO9gq9Tm7ohIDLG8e6y61D2eolQECvlyyfiwACCCCAAAKpCLz11lvm1FNPtcvXP/74Y6Nl0roaqCuovXv3tgFdAWTzzTcnoKciXp8PUXjU1WIFRbVZ4RYF9Chg6rVPP/3ULtV+5JFHzFZbbWWvLI8ZM8bodgYF1vnz59t/dLX85ptvtq/379/fLu3W/+64445mr732Mt27d7dXjnVSZ4kllrBLwqNNV5+bm5vNBx98UJ9KF3xqqYD+4YcftoZvXdXfYIMNzDvvvGNXAyig63kKb7zxRusnXXTRRXYFggJ64aZ6KoxrxYCC+YEHHmhvBZCBTgDIXSsRFMxXWGEFewJEJzdc2jjWXWoNytIoAQJ6o+TZLwIIIIAAAggkElAI15XCE044way44oo2oGupsJax655dhT0FG/3/aOMKeiLaTN+kFQ/rrbde2YBe2I56Ar9C50MPPWQUbrV0Xf9otYSWeWuJtx4EqNCp+7S16X5rXQ2fPHmy7R/vv/++vZ9d96Mvv/zy5tprr7UnCQo3LRsvPmFQD5gkT3HXbRtafh/dIx/dg67/Hm0K4fpHgbtwW2qppex96Arm0X3oqruutmvpu8KvrsZrpYncsjgpUakjx3qlYrw/RAECeoitSp0QQAABBBAIREAPBlt22WXN3/72N7PlllvaWulquf5/uYB+/fXX2/tstayazQ2Br776yl4R1xXgUkvcywX0XXbZxV4Fv+qqq2yFdKJGV4D1TxTQC2uqK+pa6q6HoemflVZayfYJrcZoxKYr+lparhCtrb2fWUsS0Mstcdc9+xtuuKH9fC3314kMLZtXGNcJD52k0BV1Pf1cqw5c2jjWXWoNytJIAQJ6I/XZNwIIIIAAAgiUFVAIUyjTVUA94EsPhRs+fLh9eFi5gK6rqFryrvt7119/fXsFVf+wNVZAT1jX1V9dBVf7aOm5HpamJdjFKyGKr6BrabYeIqYHm+nKuh7uppCpB6ApoOtqsZ5qriCsPqN/P+CAA+xr6j+6v11PQ9fD1vTvWh7/9NNP26X0CvD13o488kj7YEOVWc9OePHFF229tX9d/daWJKBrlYDCtz6j8CFx+vfoIXH6LN2HLmvdAnDLLbfYz9fVea1k0EmSLJ5eX4kpx3olWrw3ZAECesitS90QQAABBBAIQEAhW8FKS3p1BVLhQsuFywV0Vfvoo4+2wURX5viZNTc6gkKYArKeqP7ee+/Ze6H1oDI9uC0uoOt+av18nkK4TrYo8OqEjZZzK4TrYXIK8XpYXEtLi716rp8i00+zRZtWVuhn3nT/tZbI6wqzlnsrxNZ700Pb9LR4PVVdD4GLfmat0oCucqrepX5mLarHX/7yF6NVB3oo3zHHHGP/s+qq0K6fLNQD+FzbONZdaxHK0wgBAnoj1NknAggggAACCCCAAAIIIIAAAkUCBHS6BAIIIIAAAggggAACCCCAAAIOCBDQHWgEioAAAggggAACCCCAAAIIIIAAAZ0+gAACCCCAAAIIIIAAAggggIADAgR0BxqBIiCAAAIIIIAAAggggAACCCBAQKcPIIAAAggggAACCCCAAAIIIOCAAAHdgUagCAgggAACCCCAAAIIIIAAAggQ0OkDCCCAAAIIIIAAAggggAACCDggQEB3oBEoAgIIIIAAAggggAACCCCAAAIEdPoAAggggAACCCCAAAIIIIAAAg4IENAdaASKgAACCCCAAAIIIIAAAggggAABnT6AAAIIIIAAAggggAACCCCAgAMCBHQHGoEiIIAAAggggAACCCCAAAIIIEBApw8ggAACCCCAAAIIIIAAAggg4IAAAd2BRqAICCCAAAIIIIAAAggggAACCBDQ6QMIIIAAAggggAACCCCAAAIIOCBAQHegESgCAggggAACCCCAAAIIIIAAAgR0+gACCCCAAAIIIIAAAggggAACDgj8P0oTjl1/CQHNAAAAAElFTkSuQmCC\" width=\"1000\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "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": 2,
   "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": 3,
   "id": "09dee3cb-9c39-4832-81be-963306efdce2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_162680/3049401489.py:76: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_xticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n",
      "/tmp/ipykernel_162680/3049401489.py:78: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  axes[0].set_yticklabels([0, 'A', 'B', 'C', 'D', 'E'])\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f95ccefc5df047c4a8277b32bed099b9",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "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": 26,
   "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": 26,
     "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": 27,
   "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": 28,
   "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",
       "_image_mode": "diff",
       "_model_module_version": "^0.11",
       "_size": [
        1000,
        400
       ],
       "_view_module_version": "^0.11",
       "layout": "IPY_MODEL_936d6e3be67e45ce8ed9ddfb4ee54806",
       "toolbar": "IPY_MODEL_a71471f899ec49ccbb15fc62719ef2c6",
       "toolbar_position": "left"
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}