01_Unisensory_Campos_Butler_Bulthoff.ipynb

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    "colab": {
      "name": "01_Unisensory_Campos_Butler_Bulthoff.ipynb",
      "provenance": [],
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    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/john-s-butler-dit/CaseStudy_PredatorPrey/blob/master/01_Unisensory_Campos_Butler_Bulthoff.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dAqy2cYmWkbL"
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      "source": [
        "## Contributions of visual and proprioceptive information to travelled distance estimation during changing sensory congruencies\n",
        "Jennifer L Campos, John S Butler, Heinrich H. Bülthoff\n",
        "Experimental Brain Research"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u4Hdj_2SWkbQ"
      },
      "source": [
        "__Abstract__ Recent research has provided evidence that visual and body-based cues (vestibular, proprioceptive\n",
        "and efference copy) are integrated using a weighted linear sum during walking and passive transport. However, little\n",
        "is known about the specific weighting of visual information when combined with proprioceptive inputs alone, in\n",
        "the absence of vestibular information about forward selfmotion. \n",
        "\n",
        "Therefore, in this study, participants walked in place on a stationary treadmill while dynamic visual information was updated in real time via a head-mounted display. The task required participants to travel a predefined distance and subsequently match this distance by adjusting an egocentric, in-depth target using a game controller. Travelled distance information was provided either through\n",
        "visual cues alone, proprioceptive cues alone or both cues combined. In the combined cue condition, the relationship\n",
        "between the two cues was manipulated by either changing the visual gain across trials (0.7×, 1.0×, 1.4×; Exp. 1) or\n",
        "the proprioceptive gain across trials (0.7×, 1.0×, 1.4×; Exp. 2). \n",
        "\n",
        "Results demonstrated an overall higher weighting of proprioception over vision. These weights were scaled, however, as a function of which sensory input provided more stable information across trials. Specifically, when visual gain was constantly manipulated, proprioceptive weights were higher than when proprioceptive gain was constantly manipulated. These results therefore reveal interesting characteristics of cue-weighting within the context of unfolding spatio-temporal cue dynamics.\n",
        "# Introduction\n",
        "In this notebook we will simulate the results of the Leaky Integrator for one condition from the paper by Campos et al. 2014 [1]."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mc2B5yMfWkbR"
      },
      "source": [
        "## Library\n",
        "import numpy as np # vector operations\n",
        "import matplotlib.pyplot as plt # plotting data"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TSfF4uCPWkbR"
      },
      "source": [
        "## Leaky Integrator\n",
        "The presented distance travelled for the visual, proprioceptive and congruent combined conditions was each fitted by a leaky spatial integrator model.\n",
        "The model describes the change of presented distance travelled ($p$) with respect to the change of the adjusted target distance estimate ($x$)\n",
        "\\begin{equation}\n",
        "\\frac{d p}{dx}=-\\alpha p+k,\n",
        "\\end{equation}\n",
        "for $0\\leq x \\leq 10m$, where $k$ and $\\alpha$ are the sensory gain and the leak rate, respectively.\n",
        "This model has the exact solution\n",
        "\\begin{equation}\n",
        "p(x)=\\big( \\frac{k}{\\alpha}\\big)(1-exp(-\\alpha x))\n",
        "\\end{equation}\n",
        "In this simulation we set the leak rate as $\\alpha=0.05$ and sensory gain as $k=0.9$.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wvjkyC6jWkbR"
      },
      "source": [
        "alpha=0.05\n",
        "k=0.9"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n4Ry3-EEWkbS"
      },
      "source": [
        "## Discerete Domain\n",
        "To numerically approximate the solution we discretise the continuous domain using a step size, $h=1$, \n",
        "which gives\n",
        "\\begin{equation}\n",
        "x_i=0+i h,\n",
        "\\end{equation}\n",
        "for $i=0,...10$.\n",
        "\n",
        "The Figure below illustrate the discrete domain."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q5jWBAwBWkbS",
        "outputId": "d49dc496-94a2-42d5-a52e-9a505a00c513",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        }
      },
      "source": [
        "h=1\n",
        "x_end=10\n",
        "# CREATES A LIST OF NUMBER BETWEEN 0 AND 10 (x_end)\n",
        "x=np.arange(0,x_end+h/2,h) \n",
        "\n",
        "## THIS MAKES PLOT\n",
        "fig = plt.figure(1,figsize=(5,4))\n",
        "ax = fig.add_subplot(1,1,1)\n",
        "ax.plot(x,0*x,'o:',color='k')\n",
        "ax.set_xlabel('Distance Presented (m)')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 360x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V3knBSivWkbT"
      },
      "source": [
        "N=int(x_end/h) # Number of Steps\n",
        "\n",
        "P=np.zeros(N+1) # Numerical Solution of the differential equation\n",
        "\n",
        "p=k/alpha*(1-np.exp(-alpha*x))\n",
        "# Initial Conditions\n",
        "P[0]=0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZXOQaROAWkbT"
      },
      "source": [
        "We numerically approximate the differential equation using Eulers method to give the difference equation\n",
        "\\begin{equation}\n",
        "P_{i+1}=P_{i}+h \\big(-\\alpha P_{i}+k \\big),\n",
        "\\end{equation}\n",
        "where $h$ is the stepsize and where $P_i$ is the numerical approximation of $p(x)$ at distance $x_i$, for $i=0,...,10$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K8XY-V1kWkbT"
      },
      "source": [
        "for i in range (0,N):\n",
        "    ## THIS IS THE DIFFERENCE EQUATION\n",
        "    P[i+1]=P[i]+h*(-alpha*P[i]+k)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q8BC6TlUWkbU"
      },
      "source": [
        "## Results\n",
        "The plot below shows the Numerical solution $P_i$ (left plot in red), the analytic solution $p(x)$ (middle plot in green) and the error $p(x_i)-P_i$ (right in red) as a function of presented distance $x$. The dashed black line in the left and middle plot represents perfect recall of the distance."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0pJxXyWAWkbU",
        "outputId": "c70bb9a9-cc55-4cfd-caf4-eb58b38ef414",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        }
      },
      "source": [
        "## Plotting Figure\n",
        "fig = plt.figure(1,figsize=(12,4))\n",
        "\n",
        "# --- left hand plot\n",
        "ax = fig.add_subplot(1,3,1)\n",
        "ax.plot(x,P,'o:',color='blue')\n",
        "ax.plot(x,x,'--k')\n",
        "\n",
        "ax.set_xlabel('Distance Presented (m)')\n",
        "ax.set_ylabel('Response Distance (m)')\n",
        "#ax.legend(loc='best')\n",
        "ax.set_title('Numerical Solution')\n",
        "\n",
        "# --- middle plot\n",
        "ax = fig.add_subplot(1,3,2)\n",
        "ax.plot(x,p,'-',color='green')\n",
        "ax.plot(x,x,'--k')\n",
        "\n",
        "ax.set_xlabel('Distance Presented (m)')\n",
        "ax.set_ylabel('Response Distance (m)')\n",
        "ax.set_title('Analytic (exact) Solution')\n",
        "\n",
        "# --- right hand plot\n",
        "ax = fig.add_subplot(1,3,3)\n",
        "ax.plot(x,p-P,'o:',color='red')\n",
        "ax.set_title('Error')\n",
        "ax.set_ylabel('Error(m)')\n",
        "ax.set_xlabel('Distance Presented (m)')\n",
        "\n",
        "# --- title, explanatory text and save\n",
        "fig.suptitle('Leaky Solution', fontsize=20)\n",
        "plt.tight_layout()\n",
        "plt.subplots_adjust(top=0.85)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XMFz9PLZWkbU"
      },
      "source": [
        "# References\n",
        "\n",
        "[1] Campos, J. L., Butler, J. S., & Bülthoff, H. H. (2014). Contributions of visual and proprioceptive information to travelled distance estimation during changing sensory congruencies. Experimental brain research, 232(10), 3277-3289."
      ]
    }
  ]
}