{
 "metadata": {
  "name": "finding_faces"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we try the simplest possible general linear model on some example data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You are used to seeing these now:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Set defaults for the figures"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.rcParams['image.cmap'] = 'gray'\n",
      "plt.rcParams['image.interpolation'] = 'nearest'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our faithful image library"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nibabel as nib"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's get the data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "HOME = os.path.expanduser('~')\n",
      "DATA_PATH = os.path.join(HOME, 'data')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "img_fname = os.path.join(DATA_PATH, 'ds105', 'sub001', 'BOLD', 'task001_run001', 'bold.nii.gz')\n",
      "img = nib.load(img_fname)\n",
      "n_vols = img.shape[-1]\n",
      "n_vols"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "121"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's get the task.  There were blocks of different types of objects in an on-off pattern.  We'll pool the objects to get just 'on-off':"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# from sub001/model/model001/onsets/task001_run001\n",
      "block_starts_seconds = np.array([12, 48, 84, 120, 156, 192, 228, 264])\n",
      "block_length_seconds = 22\n",
      "TR = 2.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Same in scans:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "block_starts_scans = block_starts_seconds / TR\n",
      "block_length_scans = block_length_seconds / TR\n",
      "block_starts_scans"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([   4.8,   19.2,   33.6,   48. ,   62.4,   76.8,   91.2,  105.6])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make a regressor.  Let's give the HRF a delay of 2 scans or so."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delay = 2\n",
      "regressor = np.zeros((n_vols,))\n",
      "for start in block_starts_scans:\n",
      "    start_tr = round(start + delay)\n",
      "    end_tr = round(start + delay + block_length_scans)\n",
      "    regressor[start_tr:end_tr+1] = 1\n",
      "    print start_tr, end_tr\n",
      "plt.plot(regressor)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "7.0 16.0\n",
        "21.0 30.0\n",
        "36.0 44.0\n",
        "50.0 59.0\n",
        "64.0 73.0\n",
        "79.0 88.0\n",
        "93.0 102.0\n",
        "108.0 116.0\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x4022b10>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HzNokzDqZtUmY94gNWuAnQRevHczaJDq/7lEP7dACL2AOaZi1STRkzSRo86sh\nazrMHmrIKmDuAPxyvqghaybs3SdrQChRD+3QDl7AHCD5ZfFqyJqJBoTuUQ/t0JBVwNzBM2uTMJ8v\nMnvIrE3CrJNZm4R5j9igBX4SdPHawaxNovPrHvXQDi3wAuaQhlmbREPWTII2vxqypsPsoYasAuYO\nwC/nixqyZsLefbIGhBL10A7t4AXMAZJfFq+GrJloQOge9dAODVkFzB08szYJ8/kis4fM2iTMOpm1\nSZj3iA1a4CdBF68dzNokOr/uUQ/t0AIvYA5pmLVJNGTNJGjzqyFrOsweasgqYO4A/HK+qCFrJuzd\nJ2tAKFEP7dAOXsAcIP33f0dptUlsPYxGo45/hvnBR/LGG9FAB4Q2c+eUUoask41PQ9ZJiEQiqK2t\nRU1NDbq7u7Nec++996Kmpgb19fU4efJkwUUC3B38//xP6Qq8F0U0yAX+5Mkodffp1kOvCnypPCx0\ngf9/dQYfj8fR0dGBSCSCU6dOYf/+/Th9+nTaNX19fXjnnXcwMDCARx99FFu3bi2KUOZNZgyvNgnz\n4i3V/JaVcR8v+MFD9iMaVg9LXuD7+/tRXV2NefPmoaKiAq2trejt7U275uDBg7jnnnsAAKtWrcLI\nyAjOnj1bcKHMAdL4OK82CXOApAU+E794ONWQlVVbgvHxiX/LPDq49iJkhcnD73//e/PDH/4wefvJ\nJ580HR0dadesW7fOvPLKK8nbt912m3n99dfTrgGgH/qhH/qhHxYfbsibF4dCoXzfTjJRw3P/3Be/\nryiKohSfvE9GKisrEYvFkrdjsRjC4XDea86cOYPKysoCy1QURVGckrfANzQ0YGBgAENDQxgdHcWB\nAwfQ0tKSdk1LSwueeOIJAMCxY8cwc+ZMzJkzp3iKFUVRlCmR94imvLwcPT09aGpqQjweR1tbG+rq\n6rBr1y4AQHt7O9auXYu+vj5UV1djxowZ2Lt3ryfCFUVRlElwdYI/BQ4dOmQWL15sqqurzc6dO4t9\nd0Xn/fffN42NjWbJkiXmxhtvNI888ogxxpjz58+bb33rW6ampsasXr3aXLhwocRK7bl06ZJZvny5\nWbdunTEmWGO7cOGC2bBhg6mtrTV1dXXm2LFjgRpfV1eXWbJkiVm6dKnZuHGj+fzzz309vs2bN5vZ\ns2ebpUuXJr+WbzxdXV2murraLF682Dz//POlkOyIbOPbtm2bqa2tNcuWLTPf+c53zMjISPJ7TsdX\n1AJ/6dLh4w9AAAAEdElEQVQls3DhQjM4OGhGR0dNfX29OXXqVDHvsuh8+OGH5uTJk8YYYy5evGgW\nLVpkTp06ZX7+85+b7u5uY4wxO3fuNNu3by+lTFc8/PDD5q677jLr1683xphAje3uu+82u3fvNsYY\nMzY2ZkZGRgIzvsHBQTN//nzz+eefG2OM+d73vmf27dvn6/G99NJL5sSJE2kFMNd4/va3v5n6+noz\nOjpqBgcHzcKFC008Hi+J7qmSbXwvvPBCUvf27dtdja+oBf7o0aOmqakpefvBBx80Dz74YDHv0nNu\nv/1288c//tEsXrzYfPTRR8aYiQeBxYsXl1iZHbFYzNx2223myJEjyQ4+KGMbGRkx8+fPz/h6UMZ3\n/vx5s2jRIvOPf/zDjI2NmXXr1pkXXnjB9+MbHBxMK4C5xtPV1ZV2StDU1GReffVVb8Va8MXxSZ59\n9lnz/e9/3xhjN76ivqR/eHgYVVVVydvhcBjDw8PFvEtPGRoawsmTJ7Fq1SqcPXs2GS7PmTOnKG/2\n8oKf/exneOihh1Am3u0RlLENDg7i2muvxebNm/HlL38ZW7ZswT//+c/AjO/qq6/G/fffjxtuuAFz\n587FzJkzsXr16sCML0Gu8XzwwQdpr/ILQr3Zs2cP1q5dC8BufEUt8FN9Hb0f+eSTT7BhwwY88sgj\nuOKKK9K+FwqFfDn2P/zhD5g9ezZWrFiR870Lfh0bAFy6dAknTpzAj3/8Y5w4cQIzZszAzp07067x\n8/jeffdd/PrXv8bQ0BA++OADfPLJJ3jqqafSrvHz+LIx2Xj8PNYHHngA06ZNw1133ZXzmsnGV9QC\nP5XX0fuRsbExbNiwAZs2bcK3v/1tABOdxEcffQQA+PDDDzF79uxSSrTi6NGjOHjwIObPn4+NGzfi\nyJEj2LRpUyDGBkx0POFwGCtXrgQA3HnnnThx4gSuu+66QIzv9ddfx9e+9jVcc801KC8vxx133IFX\nX301MONLkGs9Buk9Ofv27UNfXx+efvrp5NdsxlfUAj+V19H7DWMM2trasGTJEtx3333Jr7e0tODx\nxx8HADz++OPJwu8nurq6EIvFMDg4iGeeeQa33nornnzyyUCMDQCuu+46VFVV4e9//zsA4PDhw7jx\nxhuxfv36QIyvtrYWx44dw2effQZjDA4fPowlS5YEZnwJcq3HlpYWPPPMMxgdHcXg4CAGBgbwla98\npZRSrYhEInjooYfQ29uL6dOnJ79uNb4C5QQ56evrM4sWLTILFy40XV1dxb67ovOXv/zFhEIhU19f\nb5YvX26WL19uDh06ZM6fP29uu+02X74ULRvRaDT5Kpogje2NN94wDQ0NaS9BC9L4uru7ky+TvPvu\nu83o6Kivx9fa2mquv/56U1FRYcLhsNmzZ0/e8TzwwANm4cKFZvHixSYSiZRQ+dT44vh2795tqqur\nzQ033JCsL1u3bk1e73R8IWP0D8UoiqIEEd/8j06KoiiKM7TAK4qiBBQt8IqiKAFFC7yiKEpA0QKv\nKIoSULTAK4qiBJT/BaN6516uf1VnAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3ba8910>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make the design:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = np.column_stack((regressor, np.ones((n_vols,))))\n",
      "data = img.get_data()\n",
      "slice_size = np.prod(data.shape[:-1])\n",
      "print(slice_size)\n",
      "Y = np.reshape(data, (slice_size, n_vols)).T\n",
      "Y.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "163840\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(121, 163840)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([[ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.],\n",
        "       [ 0.,  1.]])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fit the model!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = np.linalg.pinv(X).dot(Y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "(2, 163840)"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Make B into an image again:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = np.reshape(B, (2,) + img.shape[:-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "(2, 40, 64, 64)"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's have a look at the image:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(B[0, :, :, 40])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.image.AxesImage at 0x4534c10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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VmkUWsJRvdk8rUoKlprOxs+ustGe2v1nkiNUnBps7VjrhyJEjjo3tbcC/fAHrJxsPwMfO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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3f42450>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B_selected = B[:, 19, 12, 40]\n",
      "B_selected"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([  14.78175313,  540.37209302])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Yselected = data[19, 12, 40]\n",
      "Yselected.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "(121,)"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bselected = np.linalg.pinv(X).dot(Yselected)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bselected"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([  14.78175313,  540.37209302])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(Yselected - np.mean(Yselected))\n",
      "plt.plot(regressor * 40, 'r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[<matplotlib.lines.Line2D at 0x40408d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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R3pErF/3hw/3jnaws6uT1y/UNtE3EO/HxZBaFMextc+GL5nRPn0EgurqArVsDzJ4qh0Xf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\nq1IcApVtdsU5kdJ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HP9KfFkuXousMPBOuhc3pL1gA6U+v42eOLXD8j4E3eeAB3Yfl5lwv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\niSH+P4vs7q5h5Q2CAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x451d550>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What is the 'fitted' time course?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Yhat = X.dot(Bselected)\n",
      "plt.plot(Yhat, 'r')\n",
      "plt.plot(Yselected)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "[<matplotlib.lines.Line2D at 0x486a310>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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JNZNUUlKCEslEVFuCnIFOM8bJGlyyJT09HatWrUJVVRXsdjtuvPFGAMCiRYsQ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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x451db90>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For convenience, let's package the model fit up into a function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fit_model(data, X):\n",
      "    # Shape of design\n",
      "    n_vols, n_params = X.shape\n",
      "    assert n_vols == data.shape[-1]\n",
      "    # Reshape data to be time by voxels\n",
      "    Y = np.reshape(data, (-1, n_vols)).T\n",
      "    B = np.linalg.pinv(X).dot(Y)\n",
      "    # Reshape betas to image\n",
      "    B = np.reshape(B, (n_params,) + data.shape[:-1])\n",
      "    return B"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How would we we remove these drifts?  We need to add something to $X$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "time = np.arange(n_vols)\n",
      "time = time - mean(time)\n",
      "time2 = time ** 2\n",
      "time3 = time ** 3\n",
      "X_better = np.column_stack((X, time, time2, time3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B_better = fit_model(data, X_better)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B_better_selected = B_better[:, 19, 12, 40]\n",
      "Yhat_better = X_better.dot(B_better_selected)\n",
      "plt.plot(Yhat_better, 'r')\n",
      "plt.plot(Yselected)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "[<matplotlib.lines.Line2D at 0x50e7c50>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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VsY+IoMNKV8s2NQH5C/ToGYpW6qRgwzPP0Pqw2Fj6nol9IGEwWJpeeQreLoFg\ni8Ad1WMPDpJQsKX4zsY4WjJ7Z0svtTj7jg4SrpgYz+T20sVcDGfyesCy+tsdZ68VaYxTU0NJgJbM\n3lGMk5oaYM5+yZIlCA0NxcaNG7FhwwbU1tbi/fffx+bNmxEZGYlHHnkECxYsQFNTE4oks37p6elo\nbLQtWdyyZYv5/yMjxejoKFZ87M5OqpD56KPRG5YsQX2aAVO/vh+YepMzz1Mzubl01s7NJQfT1ARM\nnRsPPQw4dy5WtbVATQ1w9dWj35w9i8IFMfj88xD09Nhv1eprmpvpTabVPWmBt0sg2LqQzk7a+lIJ\nufsLxBhH6cTN+sew3N5dBgboMaWP5awIs8+UvdJLUVR+n7vq7JnY19ZSbx25l3U2xsnIsP+3r6io\nQIUHnaKq2O/fvx+pqalob29HSUkJ8vLyMDQ0hK6uLlRWVuLgwYNYvXo1TtppmCEovNJSsf/f/3Xs\n7BcsoOZLAP3hTrfpkXF8N5Dq2UocRm4uCfaVV1JZlU4HxGTEIx4N6GrRYcIEx++QpibJh/yKKxDR\n24vCrLfx3/cnYfnVfp0PN9PY6PkLI+7siZYW6hzpKLeXC5pa6SVbSBUWpk3sXSm9lE7Q6vXKC6dY\njOOp8suBARJQbzj70FAqeRwast30BHDN2cfG0viGhkjsi4poQZYUezGO0haJ7e205aE9k1RcXIxi\nSSOqrW52oFNVn9TRLVuSkpKwcuVKVFVVIT09Hddddx0AYOHChQgJCcGZM2eQlpaG+npLmWRDQwPS\nVFSFZfZKdHXRLDmbCOnspDf7hKxE50/LGpk+3bIrvTnXDgnBxLA+dJ9U75lgJaSnTgG3347ijtdQ\nccvzwEsvqS9/9AFWJyQPwZ090dJC71lHYu+ss2dzSIKgPbP3xgQti3FiYz2zipaJvdQkOHOiAizO\nXql00tHr6oqzDwmhE3l3NxnCggL3Y5zzzguQzL6/vx+9o6fwvr4+lJeXY86cObj22mvx7uhqoZqa\nGphMJkyaNAkrVqzAzp07YTKZUFdXh9raWqsKHiXUMvuEBOrMePLkaNnlVBeepROwGAewFsX4yH50\n1TkutmexT2oqSNTb24GbbkLxixtRMfFaKr6fNYu6iWksZ/BGuwVviD139haHnJPjWbFnEQ7g+Tp7\nFndIJ2jtnbhZjBMb67nMPiHBWjCdmW8A7Dt7wPNizx6nowP48kuKcc6ds/6MOhvjOHL2nsZhjNPa\n2oqVo1umW9BrAAAgAElEQVSwDw0NYd26dVi6dCkGBwexfv16zJkzB+Hh4Xj++ecBAPn5+Vi9ejXy\n8/MRFhaGHTt2KMY4UiZNsq1tZzCxnzbN0lbVF2LPNs9qbJSIfbQJXfWOZ2jNsU8MgKZWGrxOh8JF\nQE3rRLR98CEmf/YeUFoK/OIXVJ/5/e/bDfMNBnKJ+/Z59nl7I8bhzp4+vElJ9J52NEErd39sonZo\nSHmTcFaJA3gns2cTtKN1Fg6rcTIyPDdBOzBAH5GvvrLc5oqzj45Wjmocib0rMQ5AYv/ZZ3TCS0gg\nt28yWSqTnK3G8aWzdyj2WVlZOHLkiM3tOp0Of/vb3xR/Z/Pmzdi8ebPmAdi7xDEa6c0fFUX7on71\nFf1BlUo0PUlmJl2KG43W5YkTY4fR3ez4U2ZVziixzxERtO3tK68K2LTpclrFcfgw8MgjdCb77neB\n22+32QC2tZWSoHvusd4D1h579gBLlyoLhnyc55+vfjxn4M6e/l4pKep9z5XcHyu/ZFVcUlglDuDd\nCdrMTLpNS4zjSbGXT9A66+xtXP3ICNDXh0idHgNfNtMDTJ9uNVPrtLP/9FNgaAjx4TNQ9dYwcjOj\ngIERREeHo69PQEQEPaxU+BlKGjc4SPH0lCm+W1Tlgd0/3MNeywS284wgkB7W1NCb0NvOPiyMzrYn\nT5IozphBt8fHA10t6mJvjkdkWcnatWToN20avaGggGaeGxqAP/3JsuP3pk3AsmVASIi5UdmBA+Tu\nL7vM/mOPjACrV9MCLjUh90aMwzJl6RqFYKOlBUhOJgFztPGaktAw0bUn9szZa83stQqmvQlaX8Q4\n9iZo9XpQNnLuHF0utbfT15kzNIjOTvrq6kJeRx9+F3E+kPcKLRjo7TUfJHLgYxi/8yOg6wNa/HLh\nhQAoYR0aUm9pbKari5abz5mDhC8fxIGP4zEdJ4G4WxEzUIu+nKuQkNiPgbgURIa8DeE764HJk+kr\nORmJ+vPQ2X4ZcKabXkBBwJkz9F9fXhH7XeztOXvpNmPZ2cCbb9JZvKDA+2NiUU5jIy3cBYCJiWHo\n7hhy+HvS2EeuqCUl1Av+669lK1fT0y2xzosvAvffTxuhb9iA9vSNOO+8eKxfT/u/fvKJfdfe2Egf\nmlOn1MXeGzEOYFlYFSglpr6mpUWbs1eaxHMUOchjHF/0xlG6SmPVOJ4U+7iWzzFomo7hH9yO0NYm\nGI5egKi2PCD6e3Sn5GTKl5KS6MEnTaJ/MzKA+HhExsdjTVwcELeO3nixsfREQkIQuRAw/vk/QOn1\nVmdfZxduoamJROiTTxC/CfjX88Cyn18E/PQ7iJ4xgnNPvwtM7oDh1FlEXh9CGyC1t9OJ6osvEN/Y\nhq6uyzCSOwMhAwYgPR3tCcVIGnwA+md3w9C3Eb7oXON3sVdz9oAls09I8L6zByyTtNJYJj453Dxx\naw+bGEeiqOHhwKpVwM6dgKS7hIWoKOCWW4D166l496mn0P6r+5GUuBqrInrxp4nL8dRTIfjf/1V+\n7BMn6F+17RPZJLKnnT1gcYTBKvbuxDiOyi+djXFc7XqptoJWGuMolRI6i9EIxL/yd0SF/Rz9OXMR\nW3I5+j8sQFRrIvCXNsuAXMTc5jg1lRaXjOJ0Xs8WpsByJZKbSz+KjglBX2QiMD0RxhggMgYUy0rQ\nAYiOA3pOdiA+vA84fRrtZb1I+iugL3sRhrM3A/BOdaEUv4t9bCy92QYGrLMu6Z6QmZnkiM+e9Y3Y\nT59OkbrVBO0UPbrOOm6GJo190NQELFpk9fM1a2hOVlHsGYJAv7doEdqmGpH03xoIv70fW078FXd/\nvh3/W9hGy4pltuTECXL9amJ/9izVICvFBe4S7C0TWlqoEkeLs7cX4yghr8bxZ+ll4sRhxAx0o7d2\nEHhmD1BXR18tLXRlymZ5NTDQN4SIwT5EJUag/7sbEZsMGOoAPQC4p/NWz00u9k7n9TKxB0gjAHrN\nWAyldMXGYBU58dnRwMyZaDsCTD4f0EfNh3GnB1c3OsDvq3zsNUOTOnu9nq4A2tq840jl5OZSt8q2\nNnJqADAxPQbd/Y7DaKsYx+ob4tJL6SqmulrbONp7IzF58Vxg/37M2vMwvjo7iYL5mTOppabkQCdO\nAJdcoi72CsPyGMHeDI05e3nfcznOir00xlHL7FnfHWfF3qrrZYgRhp4BYPdu2qHjtttgWHoNho0m\nRE+ORmzpz9D7yRc0kRQWRlUBLS3mzrRaGejuR0RcBKKiBLNJcHZRlZbn5razb2kxiz0zoKyWQir2\nSldsDHlFTns7nRcj0yfBYNLeUdcd/O7sAYvYS0VIKvYARTkhIeqVJp4gN5fKQePjLR+y+Kw4dBkd\nv0PsVeMwQkKAb3+bDNCvfqU+jvZ2y05SkxZlY1gHdB38EvE1B6g8Z+lSWuXx6qv4/PMZuPJK4B//\ncHxMb0U4AHf20glaZ1bQAo6bocljHEeZ/eCgxs9Jfz/w1VeI+Pg0BrqK0Xf2HKI33Qs0vQt9mx6G\nkQrgL3+hS5Xp09FZuBIJhwUI9d2I3ReJc48CeE5SMbB7t5WgamGgZwARcXpER1kLpqeuOj3q7Ec/\nNPHxNM3GTkgxMdbO3t5x5YaWiX14chKGRkIwPExX3N4kIMReKbeXi312NjQ1IvMEGRnkkKSiODE9\nFt0jExzaAkfVOIzvfpdaMdx3n3ok2dZGE/qApSrpq5MCFrDKnUcfpQNWVODEiRl4/HHbbdKUxuiN\nyVmAO3s2QTthAgmAvcokb8Y4im/P994DPv6YJqLYV0cHkJWFyMy5MA4uRl9YDKLvvBW4aCv0ERkw\nzA2lWt5ROo4CickAInXKE7QyQdWC8ewAIhOjECXAytknJzt1GLuYO1/m2Iq905n9BRcAICP4P/9j\n+VF0tGU1sZYYh9HeDsybBwhTUqEPNcFgiHR3ikIVv8c4gP0YR7oEeto079fYM0JCyNBItTo+QUCX\nkKi8AzqonItdxmNggMrAFPLLefOowmfbNvVxsLM/IzvbsrjMPNDsbHTWdcNopD1vh4dtt0qT4s0Y\nJ9idPfv7S5fVK+FOjKNF7K1ikJERUie2uGLzZqrPPXcOqK5GxOs7MYBI9CEaMVdcCmRmQh8TanPS\nZpU4gJ1qHBfEfqB3EBEJMTZRiCuLnZRwFOO4mtnPng089ZTlR/LMXmuMwxbgISUFehh9YpIC1tl3\ndtI8JGPtWsvOLr4gN9daaOPjgS4xDmg9ZVl9IqG9XRL7fN1i+dQr8NvfkuivX08nMXvIxX7aNOvV\nhgCAlBR8/lYf8vLI/WdlOS6/bGqiE5k3COaFVQbDaCmhpFdLV5fyfKWzpZfSGEcts7cRy44OUuc/\n/EHx/iwWGh62Lb2UdoxklTiAnRW0qam2O/+oMNA3hIikCYjqgncz+6QkMl+jl0juTNDK0ZrZ24tx\nkJoKPfphNE50YkCuEdDOXh7jeHLPVDXmzLEWYr0eGEYojPXKZxxHNfZy0tKAu+4CfvITx2OQxjiA\ngrMHgJQUnPhaj7w8+jYz0/EkrWKNfVOTR5bxBXPLhNZWih+YODrK7W1EQRShDx2A8UQdzcWUlgK3\n3kqXgFlZMH16QnOdvY3YNzdbqgwUEASqghMEy9VDWBjlx9KTCltQBXjQ2RuGETE5DlFR3nH25tLL\nkBBS1tGrcndKL+VodfZKMc7kyQCSkxE53AdDn/cz6oBx9pJmmQBsxd7X/PKX1tWNggDER/Sju64L\nSh8dqyxcQ1Zy113UE+2tt2jBlZy+PnJW0j3Vp02jxplWpKTgRLMBM1fTt2pir3gemj2b3qkzZ9JK\nwYIC+po92ymbFczOnuX1DBux7+2l+uFTp2CsmorI0K+Ayr9R2eLJk4g0PAZjcgOw6FM6qy9cSLW6\nf/kLBk81IjycZurVYhybGntJJYk9IiJsl/iz+Rd2uzzGsel66UpmbxARmRyH6E4vO3s2vpYWICPD\nOWfPJl/sLB6JibGsOXCU2duNccLDKbNv6QbyNOx67gYBIfaJiYC8BY88s/c1StUME6NM6K7vtSv2\nWp09QG+2e+4B/v53ZbFnl3nSE449Z/95jwEbRqt2nBb7c+foXdrRQX+Ejz+m/gx/+QuV0mVk0GVO\nfj6dDPLyqMhYYTYpaJ29yYSWo91I1oUCO98C6uuR8FUxOn/xX+D+50nkjUb642Rmwti+GZEzo4Bv\nr6Hcbdo0RG6JhzFHAO6QHbuiAqbqs9CNipPTMY78LKRAZKRtJQj7W04cTRc6OixbHbITgNXamNRU\np1daDQwAEakJiPraIvZeyewBeg1GT0ZOPYbKTj/SCVpHMc7MmWQgh4dpGkW6laI+fBiGhk4AQSD2\nWqpxAoH42GF0NSpbV2diHEZODvDyy8o/k0c4AC0oa262rs5ASgpOGIC8GSIAAZmZwPvvKx9zZETB\n6LE3s15PvUNG+4cAIEdTWwscO0Y1/WVlNLP85ZfkdHJzSawyM4GsLOjbitEfHg30R3vOngUyGzZQ\nyWFXF1qj70JK+IXAa68BGRlISNahc/rlwA8upf4YkyaZBcPwHUC/DMANlkPZLb1MTYXp/V6Ej0aK\nLsU4bjh7RkeHZMEgLFGO+fcmTaIb5KsjHTAwGIKIKROtohBPO/uzZ0e/kVx5OOXsVV4/rTHOBRfQ\n5/lf/6I4mnXMBAB9pAhDs/peGe4SEGIvz+xF0bKTfSARHy+iu1V5F2OrBbNNTTCH6A5IT7ffMEs+\nOQuQq0tLI6PIlmsbhCg0IRXZk3oATHTo7NvbSaOtPouOTkw6HTn6/Hzr20dG6Oz25ZeWFZTvvIOo\nShGGnl7gj/fSg0yZQk3eLr/c8QvhaUSRzoj9/fTV10f269w5EqSeHstXVxfd/vOfq4qiDXv3UtOm\nefPQ8utQJA8B+NU1AICELUAnACyw/TWnqnGmTMFgd6PrpZej0YUjIiOt40LAVuylMQ5gmaQ1b2we\nEkKTFi0tsuZPdhgexsBQKCKmJFpVcTnb4tgRNjGOK85eJQbTuoIWAH70I2D7dopjpZ/tyEgBxpYe\njQNynYARe6mzNxjIBHnqj+4pJiaGoqteuRmaTYyjoZg9LY3EXmmfTCWxByx9gpjY19YC08IbEHZm\nGJjkWOwVh6XB+dkQEkICkpFh6RQHIOphuiLB724nEd28mSIhd8T+yivpyiIkhLIG6QvFromHhkgB\nBwctvTd0OrKI7Cs2lr5iYuiMN2ECZRTx8STaVVXANddoH9fICE34zZoFhIaipYWmOBgJCXQuVMKe\n2Cs2F0tNhamrVnNvHJvSy+ZmQGUDIXtiL51/kVbjACqTtFrEvqMDxpAoRMaGIzra8vl3tsWxI8x1\n9mxso1mx087eQQym1dkDwPXXA3ffDbz9tvVVuz4mBIY2D3SWUyEgxF6+NWEgRjgAED9Zh65PlbeO\nciXGiY0lTerutn2+SjEOYOntzzhxAsib0AS0iEBeHuLjSYe6uy15q+IYGa6IvR3MblAQSBny8hQm\nGZzk/fdpHiEy0npLR1Ek8Wdf4eH0YrJMwk7ZqyInTzo9uYjOTjpxjF4mtbYCS5ZYfqxWjaNUeqlY\nWpyaClOPQXO7BFcy+4gIdWcvrcYBPDBJ29yMASEDERHwnbN/800ATi6qUvl8xMRYZ/by11GKTkcN\nbUtLrf2PPiYUhnYP7POoQkCIfVyc9YpDf0/O2mNiih7dZ5VFxNlqHAaLcuRir+bsGSdOADOTOoDR\nXvuCYJmkldfaK56DPNg/wWZRVWoqsH+/6wdk1lFDJOYWLlSSyEWAtUpgOBJ7p2KclBQMnhtAuI7m\nZDxdeske29kYx+3yy5YWDCDHLPbS0ktPOXtz6aVsbAaD9XNxSHMz8I1v2P2x3NmbYy07bNgAPPig\n9WdbHxcOQ6f3y9gCos4+JMS6eVTAOvuUCHQNT6DG8hLYgtlJk0CneZPJ1lbbwV5ub0/s5c7+44+B\nWVN7SW1GsRflNDR4KMaxg027hJQUq3E5jQfH5hBXxF6W5ZpXT4/iqBmaktjbbXEcHg5TRCx0g/3s\nW6+UXjoSezaHpjnG0UJzMwbEcPNj+6T0UjJB6yln70yMA9BJZv166+69+okRMHZ6v4wtIMQesJ6k\nDcTJWYBaJnRfspxy5NtuM280ysxTSAgsTZM07oxgT+ztxThSZ19XB1RWAlcXtWsS+y++sLRmNWPe\nId19FJ29syIqRYMr9QiuOvvRsYmisrO3tw+t071xYhIQbqSyEqcmaPv76c4qGwxERtpW0krFvreX\nHlc6sW93Fa3G11FsboFpRIfwcMv7ZmjIyR2kVLApvWxrA0ZGnGuX4ITYaz3u9u1Udm0eZ7wehh6V\nvtUeIGDEPjsbOH6c/h+ozn7iRKArMZeyE1Gk4tm//AVN9cN2Ny1Rw1lnz1omiCLwxz+SS4g5L1GT\n2J84YemiaUbS0c9dbJw9+/CLyvMcqgSys5eMjWW2UsF0FON0ddnqr6Oul4PRExFupGoNpzJ7lter\nGA8lZy9dMyGPcAD3nf1AQzvCQ4cQEmIRTBbhaN5BSgUrsQ8Pp0n5M2f8UnopRV5noE+MhuGsyvZj\nHiBgxP6KKyxN9gI1s4+PH3VrCQnAjh1UxbFzJxrW3YcpYW10JyczcGfFfuJE+nCePAk8+yxN+Mjj\nEiWxHx6myh1prTQAjwqqjbNn6mczk0fU16t06QxksZdMfCqtu2HvFXmnVpOJKk/kT8thi2N9HML7\nSeydyuw1XhmpZfZsv1QpdidoNS6sGmg6g4hwMgHsfePJBVWAwtXS6CpazY9jMtltaMhgYi+KLnTT\nHEU/MQKG4XDrzXi9QMCI/ZVX0mT5yEhgO3urTobnnw+89x6OL7oF+cdfoifx3nseEXt7MQ5A7v6X\nvwQWLx7N/jSI/alTdDyrD3V//+jecJ55sW3aJQiCQyF94w0qb7e73aOvxD45mc6u0mofNSRjUxpm\nWBi91nL329hI95Wv0La3FzMAmPQToOujTMip0ksNeT2gXnr5xReWzToYis5+yhTtzr65y0rs+/o8\nm9cDstJLwPxe1OzsWU8DB5VdYWF0tWU0utBNcxR9lABDdKJ781saCBixz8qiN/wnnwRwZh+vkMMK\nAg4ZZmL+kxuBZcuAV19V7IppDyWxV+qLIyU7mzYp+dGPRm+QiT2LeqTaZTfCcbAU3FkU2yWwniQK\nVFbSyeqJJ+wc0FdiHx5OuYrSZsj2UHD2cpSinNOnlbfWTE622z0bpohYhJ/rNA9Vc4yj0dnPn2+9\nRgCwdvbHj1PHDCmKYj95Mp2xhpTXokgZaOlCRCS979gErded/WjLBM2Po/H9x9y90900pePUx/tf\n7DMzMzF37lwUFBSgULY449FHH0VISAg6Je/o0tJS5ObmIi8vD+Xl5U4NZvly4N//DlxnHx+v3KP8\n8GFgfqGONphtaIDdXcEVUBJ7pb44UqZNoz5Z5s4GSUlWH7KJE8lkSbc/dCj2HkKxEZqkJ4mcykpK\nw/7+dzu93zU6U4/gbJSj4uwB18ReaYOewfAYhPeS7Xc6s9fw+m3aRDGqFKnYHztmK/aKE7RhYeTY\n2tpUH9PY3ovIKJIfbzl7q9JLwHlnr/FkKRV7l2IcPWCImOheMYMGVMVeEARUVFTg8OHDqKqqMt9e\nX1+Pt956C+dJVstVV1dj165dqK6uxt69e7Fp0yaMOLG91JVXWsQ+EDP7CRPoDS59Si0t9KEwf4D1\neuXtiewQF0cO3NzDA44jHIC63/7f/0lOBmFh9IJJVuUUFZGYMj7/XKFc3cN7FNp19gpv4o4Oevhl\ny2hvjWeeUTigr5w94LzYS4TUniY4I/YsSlGq4DHpoqHrIbFXy+ytSi/dqGZSE3tFZw9oex3PncPA\ncBgi9CQ/PnP2o2MLNGev1wMG3QT/O3sAEBWqKe666y787ne/s7qtrKwMa9asgU6nQ2ZmJnJycqxO\nEGpccgktMf/888B09qGh5Jqll9uHD9NlsKtJiCCQu29stNxmb3KWMW0aMHeu7EZZlCMXe785ezsx\nTlUVXZ2EhlIc9fjjClf/gSr2spJGZ529vVY19qIcU5ge4d3klp2Kcdy4MmJif/YspVvyTXYUJ2gB\nba9jSwsGJqUhIoI+NGyC1huZvdvOXsPrx1bRupzZ6wFDWKzXxV51Ba0gCFiyZAlCQ0OxceNGbNiw\nAWVlZUhPT8dcmeI0NTWhSLLDSHp6OhqlKjbKli1bzP8vLi5GcXExADLES5YAr7wSmGIP0GK6t9+m\nrV8B4NAh6x21XIFFOUyM1cReEQWx/+Mf6f+i6DuxNxhkvX5SUujsLaOy0rIZTWEhVauWlVH/EAA0\nsybtA+ttnFwQJC1pdFbsr75a+bDsTyjvOzcYOir2oojwcMHjmb0S7Crt+HEaj3yOUu7sP/6YtkAI\n1fI6NjdjID7FXLfPNkvp7vaNs9cctzQ329/yTYInnL0xJNrmdauoqEBFRYXzB7SDqtjv378fqamp\naG9vR0lJCfLy8lBaWmqVxys5f4agYHmlYi/nyisDW+zZvAIT+8OHgVWr3DumPLdXi3EUkYn9nDnU\nHbO7m96EISEKS7k1dufUinSHI6s+5wof/spKWpfGuO024OmnJWLPVik50+PGHVJTgZoabfeV9Zux\nZ6CVxL6+XjnGARw4++FQ6MIFoKsLOl2CT529UoQDWIv98DCZtLIy4DKNYm+MT0WkpId+VBRdQXjS\n2bPIa2Rk9G0kiXE0O3v5ZIYC7mb2kZGAAXobZy81wgCwdetW5w8uQVXsU0ffLElJSVi5ciX27duH\nuro6zJs3DwDQ0NCACy64AAcOHEBaWhrqJVtONTQ0IM2JBUYAvbY6XeCK/RVX0Oq3oSESt0OHVGrF\nNSAXe5ecvSwuCQujHtoHD9LrOXOmQtTkhZiEOUKz2Cu0TBgZoWaYzz9vue2aa2ii0PzcfRnhAPRY\n+/Zpu69sbI6cvfTvKop0ArYn9va6S5hMQHhiLNDcjPCpCap19lFRIAU2733nPCySsyf20gnaI0eo\nHL2yclTs2epIe7S0YCBuMiIkz4OJvSedPdty0WQaFffUVKCxEUbBAP0jjwC6c5bOqVLDyjqsHjoE\n3H+/6uNIF4W5HOOIEf6doO3v70fv6F+0r68P5eXlKCwsRGtrK+rq6lBXV4f09HQcOnQIycnJWLFi\nBXbu3AmTyYS6ujrU1tbaVPCokZJCC4Y07n/gc6ZMocrKDz+kybQzZ9zfwNsjYq+gFCy3V4xwAI+u\nnmXYa5lw9qzl8/TFFySE0vYC0dGWqzrz2Dws9kNDdiYVJePUhMTZs7RJqbFWXp51RVRPDwmQve4F\nKSnKzn5wEAhPmkBirzWzP3OGHJMTxQJSmLNXKrsErJ19RQW9fJWV0PY6NjdjYEKS1WectTn29J43\nVlFOTAzw0EMwDIYhMnbUUSYn0wdw6lT6ysig55CYSJNJo6bWER6ZoB0O929m39raipUrVwIAhoaG\nsG7dOixdutTqPtKYJj8/H6tXr0Z+fj7CwsKwY8cOxRhHjfR0p3/FpyxfTqt9h4fpveBu0pCeTjvY\nMFyOcT76yOqmoiKq2snOtpPWeLAvDsOmZcKkSRjuOovZs0WsXy9gyxbrvF7K2rXAb387WrnqBbH/\n5z9pfcJrryn80NnMfnRsjtKmggIyh2wOg1Xi2PtIJCfTiVCOyQToJlFpHiu9VNoDAZCIfZN7fYXY\n37Gmxr7YswnaigraU/nRRwHxnlQISqtoRZHcUUMD8OmnGMgoUXT2TgYBqsjLL8Uf34WBnwARD/zU\nY6uMYmJoItvVvj56PWAYDCOXx7oVeqpnhASHYp+VlYUj8s1hZZyU9SvfvHkzNm/e7P7IApjly6lV\naVKS+5OzgK2zb2nxjLNftIjKNE0mKm+0wmgkO6K516s2bJx9aCjej7sa0RFDeP55HTIz7Yv90qXA\nTTeNiqJM7AcHqTxz40bXx1Zfb+20rWAxmD0VldLSYl7k4OiclJpKaUBjI/2N7ZVdMhzGOJMnAk1N\n5oRhaEjZtJtLL91co6DX0xV2aKj1FRiDufL+fuCDD8hUPPoocFrMwHknTwK//jVlVqdPW77Cwsyb\n3hiz8hApMQXM2bt7lSxHPklrNDq/3YEa0dFUShwZ6ZpG0xgF4LrrgAUL6EWdOZNWus2ZQ6V3GiaK\n1QiYFbRjiYUL6bP0z396Xuz37aM3vU1ppRoKSjFlCrmODz5QiHE0NslyFhtnD+Afwjqsv6IFe/YA\nP/0p8PrrymIfHk4TtDt3wkasqqtpElfD4ky7tLWRgCkeIyqKBqC4ukuGpMrFUcGLIND749Ah+t5R\n2SVgf4J2cBAIT0kwX3nYq7UXRYmzd7NjqF5Pr5eSq2fExtJ7Ky2Nxl5UBFR+nQp861skWAsWUBTy\nyis0np4eyoXefBMDCVOsYhxvTNACymLvStTiCKnYu4L5M7NrF73vT50Cfv97KlP78kvggQecWpVv\nj4DYvGSsERpKTvnvf6ctVt0lMZE+G729tAj3kUdcmKiyYwuLimhPbBtH6YUIB7B19gMDwGtnF+PI\n+QeQkZeBV14h927PqKxdS6/BvenWlvnYMYrNmptVt1S1S2srieTXX9v2egFgiXLUqgM0rJ5lMLFf\nscI9Z69LSQCqLGJvMtkK4+AgOdawMLjt7Nmx5W0UpMTEUPzICkaKioDKg6H4loYPhXxf8qgoirA8\nvRWpXOw9vXALsFyVuHpcG4OUkABcfDF9MUZGSHjcgDt7F1m+nN6sihOfTiII5I62bKFFWzfc4MJB\n4uLoEyRb1VRURJ0ubd4nXqp2kb9x//MfYFZCCzKG6gDQwrnaWvvZ5qWX0gen+mSklTM9doz+PX3a\n9bG1tZEY2m28pjW319AXh8Fye8Bx2SVA8zRnztj2YzOZgPApSeax2WuZ4Kkae8ByHDVn/8YbMrGv\ntH9/KXKx98kELbzn7M+ccf24ERF0onbYh88DuRMXexdZvhx4+GGXix1sSE+nVaTbt7uYrAgCZT+X\nXN9aX94AABnGSURBVEJnjYMHgZERXHcdcN99Cvf3QiUOYOvsX3wRWDv/cyvL6uj5hYSQC97bMNvG\n2cfGui/255/vptgPD9Mne3QGXauzB9SdvU5H52x598vBQSA8LckqxrEn9lFRoDynocHtzB5QF/uv\nvwYuu4y+X7AAOHpU1mnSDkrO3huuW9750tVaeEfExLgX4wiC481rPAUXexeJjQVuv91zx5s2jSZT\nNVR62Wf/fsr6zp0Dvvc9IDkZ5/1sLdYMPEu2UoqXYhxpy4Rz56hqaVXxGadqiC9cNIID5/KtZgaP\nHQNKStwT+9ZWujK2u3ZKi9i3t1uVNKqlJZmZNA/e1qYu9oBylGMyAbq0ydaZvWl0e6wPPqCZ682b\nYVh/G/RdjfTm3L/fdimuE+j19DVrlv37xMbSQ7DKseho2glNpaYDgK3DZh1eve3sXa2Fd4S7zh7g\nYh9UbN9uaW/gMjodXVM/8ggV13/yCfDNb5Lizp8P5OYC3/8+TTZUV3sts2cxTlkZXWhMynGuo19R\nbgcqhQvNgtrdTVV73/iG62IviiS4LEZSRIPYn61txUCyRbHVnD2bpD14kO6rVlqoNElrMgHhCaMb\nwVx/PcKbT8E05wIK1O+9l/ZQiIyE4ZtXQp+WQOU/ra2ObbkKYWE0TyjfrlBKbKwlwmFojXKUnD3g\nedctL730hrNnE7TuHFepsMHT8AnaACE21gsHnTqVakQ3bKAJnmPHgPffJxX++GMSCg/DnP3ICPDY\nY6MP4aCnvRI5kQ04J2SZm3IeP04O87zzqC+RK5w7R/MWqjGObDN5OT/5TTyyjLeBFRdrmfqYP59a\nbCQlqddhKzn7wcHR33v6aUAUoTuSDNPz7wEXW6/O6v8Y0O8EEOcZNVNb61FcbHslumgRzdPceafj\n37Un9mPV2Q8MuHdcX4g9d/bBQkgIfTJvvx14+WXKdC+6yOMPw5z9s8+SMV+1Ck63DxZamlEUX4MD\nB+h7tmR/6lTbNEorra0kXllZ9NQVV6FqGOfJ02H4V8+lACwdCZTq0KUUFND5VS3CAew7e50OVNL4\n7W8jPE4PU6TtMlxvZN6OuP12utqS4qqzZzGOt6txvOXs2WO5Chd7zphDrye9vP9+mnAWBFjsqtaN\nx5ubUZTRYBYNqdg7inFEka4o2JcUtipZp6PSTdlaQEKD2J9ui8TBM1k4c8YmvrfL/Pk0RaKlZFTu\n7EXRdgGVvTp7X4u9EtOm0QlZ7U8tz+zHsrNnUZc7r70vMnse43A8SlQU8NRTwLp1VJ0BgN7JUVHa\nd6VpaUHRDAG/loj9qlW0HsFopPUISrHXddfRQjdBIEFsaLB0+mxttTjw6dMpyrFpIcE2zD59mpS8\nvZ3OEm1tQGsrRppbUd/5FBbPaMDevedh1ixt1Y25ueT+tDj7lBSqaGEMDpLQSyuYHFXj+Fvsw8PJ\nsff1Oc77/ensvRHjsMdyFZ7Zc8Ycej194G06gaalAStX0r8JCbSgIC6OvmJi6Csqig5w7BgKCxLx\nyb9I7FgzLkGwRDnyQpOmJurRwtoFLFpEVTdM7KX9hnJz7eT2cXF0Rrj4YgrYJ02iX0pOBiZPRvvU\nhYh9Q8Cq21KwZw89DS1z3GyuwJUYxxzhSHBUZ+9pZ+wKEyfSpLozYu9LZx+sMQ4Xe45HufxyKvax\nmdzbvZuWSHZ2UulCTw+pWm0tzZ6eO2fpE2s0Iu6OO3DeecDevSQKrFcQi3LkYv/SS9QmmX2Qp02j\nqIZNS7S1WZx9bq6dLryCQMvT7XD6IDA1G7hyJfDTB2iCUmtB089+Rovb1JDHOCaT7aRuIMc4gEXs\nHTU09KWzl9fZe9rZe6KSiIs9Z8wxc6adVcXTptnubadCURFFQtIl+/Zy+3/8g3pvMbKzga++snzf\n2krxDUBi//rrTg0FgGUFbFoa/fv669r7Uy1fru1+cmdvrsSREMgxDmARe0f4KrOPiLDePtEbE7Sh\nofRc3K2z5xO0nKClqIhKFqXl4koVOV9+SSeAyy+33MacPUPq7Flm7yzSRmbLl1OJoaeXKiQl0dQG\nc+5KMY49sbfabNyPaBF7pRgnNNRzK9IZvpigBSiycjfG4YuqOEFLURFV1cjFXu7sX3yR+gmFSa5T\n5c5emtlPnUrf22yOroJ0BeyVV1LFiafFPjSU5gLa2+l7pRhHU28cP+KK2EdH09g93cbdF6WXAI0/\n0DN7LvacgCU/nxyTVOwzMqzFXhQpwlm71vp35c6e1dkDJKhZWdYnAy1IxX7RIqoO8sbOidIdq+zF\nOGMhs3eEkth7Y3LZV86enaxchYs9J6gJDQXeeYf20mXInf2nn9KHWd4fPy2N5oKZe5fGOIBrUY5U\n7ENDafJ40SLnjqEF6SStMzGOS9tZegGtmb1U7DMyqIOmp+HO3gIXe05AU1ho3d2VbfTCFk099xy5\nevnlf0gINSGrqyMXfPasdYn/3LnAu+86NxZ5I7MFCzyfMQPWk7T2qnGUxL6hITC29NTq7KXiKAi0\nKZCn8aWz5xO0HI4H0etJTFpbScCff97+VoUst29vp5J56UnjjjtoY6ATJ7Q9rtFIE6dutIjXjNTZ\nK8U49jL7sSb2UmfvLXzR4higuNHdGIdP0HI4MliU8+yzwJIl9hcrsdxeaQP3pCTg5z+nXfO0dHFg\n+0B7cu9Se6SnWyqO7MU4Spk9F3tb5F0vveXsb7uNOqq6Co9xOBwFpk6l9ruPP05ibQ/m7KWTs1I2\nbSKB3L1b/THVdpnyJNLJZa0xzrlzJKBqOyr6gkASe1+0SwBom1J3TrRc7DkcBaZOBXbsoGoYpY3L\nGVJnr9SZUqejNsx33aV+Ca22WbgnkZaNal1U1dhIYuPp0kVXUBN7UbSdoPUWvpqgdRee2XM4Ckyd\nSm35f/Qjx+LGRFMpxmGUlNAk8Pe/7zjO0bLLlKfIzKTHGx7W3hsnUCIcQF3sh4YkG6N7GV9N0LpL\nQGT2mZmZmDt3LgoKClBYWAgAuOeeezBz5kzMmzcP1113HXp6esz3Ly0tRW5uLvLy8lBeXu69kXOC\nlqlTaVOTVasc3y8ri+Ke5mbHPeeffpra9jzwgP37+FLs9XqaUGZ997XU2Y8lsfdVhAOMHWcfEDGO\nIAioqKjA4cOHUVVVBQBYunQpPvvsM3z66aeYPn06SktLAQDV1dXYtWsXqqursXfvXmzatAkj8sbi\nHI6bXHEF8NZb6mWPUVFUbnn4sONdl6KigH/9C3jhBRJ+JXwp9oAlgtIa4wSS2MfFkdjbu1Lyp9gH\nsrP3u9gDgCj7q5WUlCBktCxh0aJFaGhoAACUlZVhzZo10Ol0yMzMRE5OjvkEweF4iqgo7XtpT5sG\nVFWp7yY1eTLw5pvAL34B/OAHlnYFDH+I/Vdfjc0YR9rTXglvTZIq4avSS3cJiK6XgiBgyZIlCA0N\nxcaNG7Fhwwarnz/zzDNYs2YNAKCpqQlFkhmz9PR0NDY22hxzy5Yt5v8XFxejWL5rMYfjIbKzgf37\n1fdTBWhV7WefAQ8+SCeTrVupYkcUfTtBC9C4T56kfXe1OvsrrvDd+NRw1NOeO3tblCZoKyoqUFFR\n4bHHUBX7/fv3IzU1Fe3t7SgpKUFeXh4uvZT24PzNb36D8PBwrJU3JpEgKMygScWew/EmrKuyFrEH\nqHTxD38gd3/11TSReMMNJLATJnhvnHKmTaNoacqUsZfZA4572vtS7OV19oHs7OUTtHIjvHXrVrce\nQzXGSR3t9JSUlISVK1eaY5lnn30We/bswQsvvGC+b1paGuol/WcbGhqQlpbm1gA5HHfIzqZ/tYo9\nY8YMinW2bgX+/GffunrAUkmktTdOoIq9Er4Ue1bxMzRE21kODgams5fGONXVwPe+5/nHcCj2/f39\n6O3tBQD09fWhvLwcc+bMwd69e/Hwww+jrKwMkZJXbsWKFdi5cydMJhPq6upQW1trruDhcPzBtGnk\nyF35gGdn0562Dz3k27wesEzQamlxzPblZVswBgKOxN5XNfYMFuU89xztZhYa6rvH1goTe1GkVh4v\nvOD5DN9hjNPa2oqVK1cCAIaGhrBu3TosXboUubm5MJlMKCkpAQBceOGF2LFjB/Lz87F69Wrk5+cj\nLCwMO3bsUIxxOBxfMWcOcPvtrv/+okXAq6+qrwj1NElJJOjt7batf+XOvrGR4h5ftHLQipqz96W7\njoyk7qfbt1OLjUCEZfavv059kWbMoL5N8+d77jEcin1WVhaOHDlic3utg96wmzdvxubNm90fGYfj\nAWJjrbcrdAV/THwKArn7zz+3baMsz+wDLcIBAifGAUhIX32VxsT2JA40WNXQT35C5b//93/AsWOe\nFfsA8gIcDkdKdjaJvVo1Dhd7x0RGAo88or7i2p+EhNBrMn8+ba85Zw5w/LiHH8Ozh+NwOJ5i2jTq\nx6+W2XOxdwyLSG64wXeP6Qrf+AadlABg9mxy9p7EB90pOByOK2Rn04SdWjVOQwOQm+vbsakxcSK1\noFDCl4uqADqx3Hab7Ukz0JB2l5kzx/Niz509hxOgsDUCanX23Nk7ZutW4Ic/9N3jeYLzzqMKq85O\nzx2Tiz2HE6CwNQI8s3ePq66ifj1jCUHwfJTDxZ7DCVCmTqWJO6XeONJ+L1zsxyeenqTlYs/hBCjh\n4ST4cmefnEy97l9+mRx+R4d6ozdfo7aoKhBXsQYannb2fIKWwwlgcnJshTE6mvrmLF1KYp+SEnir\nQrmzd585c4CdO+n/CsudnIaLPYcTwDzzjHJfn/PPB/72N+Daa+n/gYa0p728tn1ggBa7cRzDYhxR\npNW/7sLFnsMJYBw1YFu2DPh//8+yOXkgIe1pL29zPDAQWH18ApXERLqKO3iQejS5Cxd7DmcM443u\niJ7CXk97XzdCG8uw3k7f+had2N2BT9ByOByvYC+393UjtLHM7Nm009odd7h/LO7sORyOV3Ak9tzZ\na+Pii2lfA63bcDqCiz2Hw/EKXOzd57rraBLeE/AYh8PheAV7Yt/bq7w3LUcZT+1TwMWew+F4BXti\n39YWeIvAggEu9hwOxyvYE/vWVuf3BOa4Dxd7DofjFZTEXhRpq8WkJP+MKZjhYs/hcLyCkth3d9Oe\nurz00vdwsedwOF5BSex5hOM/uNhzOByvEB9vu/kGn5z1H1zsORyOV5gyBWhqsr6NO3v/wcWew+F4\nhfR02lhFFC23tbVxsfcXqmKfmZmJuXPnoqCgAIWFhQCAzs5OlJSUYPr06Vi6dCm6JcFcaWkpcnNz\nkZeXh3LpDrocDieomDCBFgT19Fhu4zGO/1AVe0EQUFFRgcOHD6OqqgoAsG3bNpSUlKCmpgaLFy/G\ntm3bAADV1dXYtWsXqqursXfvXmzatAkjIyPefQYcDidgYe6ewWMc/6EpxhGl12EAdu/ejRtvvBEA\ncOONN+Kfo82Wy8rKsGbNGuh0OmRmZiInJ8d8guBwOMGHXOx5jOM/VBuhCYKAJUuWIDQ0FBs3bsSG\nDRvQ2tqK5NFrseTkZLS2tgIAmpqaUFRUZP7d9PR0NDY22hxzy5Yt5v8XFxejuLjYzafB4XACESWx\n5zGONioqKlBRUeGx46mK/f79+5Gamor29naUlJQgLy/P6ueCIECQ7zsm+7kcqdhzOJzxC49xXEdu\nhLdu3erW8VRjnNTUVABAUlISVq5ciaqqKiQnJ6OlpQUA0NzcjMmjf720tDTU19ebf7ehoQFpaWlu\nDZDD4YxduLMPHByKfX9/P3p7ewEAfX19KC8vx5w5c7BixQo899xzAIDnnnsO1442XF6xYgV27twJ\nk8mEuro61NbWmit4OBxO8CEVe6MRMBhoM3KO73EY47S2tmLlypUAgKGhIaxbtw5Lly7FggULsHr1\najz99NPIzMzESy+9BADIz8/H6tWrkZ+fj7CwMOzYscNhxMPhcMY3UrFnk7NcEvyDIMpLbbz9gIJg\nU93D4XDGJ52dwLRp1CPn44+BjRuBTz7x96jGJu5qJ19By+FwvEZ8PGAy0e5UfHLWv3Cx53A4XkMQ\nKMppbOSTs/6Giz2Hw/EqLLfnzt6/cLHncDheJSODxJ6vnvUvXOw5HI5XYc6exzj+hYs9h8PxKjzG\nCQy42HM4HK8idfZc7P0HF3sOh+NVeIwTGKg2QuNwOBx3SE8HTp+mWvukJH+PJnjhK2g5HI5XEUUg\nMhKIiQE6Ovw9mrGLu9rJnT2Hw/EqbGFVeLi/RxLccLHncDheJz3d3yPgcLHncDheJz0dGBz09yiC\nGy72HA7H66SnA319/h5FcMPFnsPheJ1164CBAX+PIrjh1TgcDoczBuD97DkcDoejChd7DofDCQK4\n2HM4HE4QwMWew+FwggAu9hwOhxMEcLHncDicIICLvYepqKjw9xC8Cn9+Y5fx/NyA8f/83EWT2A8P\nD6OgoABXX301AKCqqgqFhYUoKCjAwoULcfDgQfN9S0tLkZubi7y8PJSXl3tn1AHMeH/D8ec3dhnP\nzw0Y/8/PXTSJ/fbt25Gfnw9BEAAA9957L371q1/h8OHDePDBB3HvvfcCAKqrq7Fr1y5UV1dj7969\n2LRpE0ZGRrw3eg6Hw+FoQlXsGxoasGfPHtx6663m1Vupqano6ekBAHR3dyMtLQ0AUFZWhjVr1kCn\n0yEzMxM5OTmoqqry4vA5HA6HowlRhVWrVomHDh0SKyoqxKuuukoURVE8deqUmJ6eLmZkZIhpaWni\n6dOnRVEUxR/+8Ifi3//+d/Pv3nLLLeIrr7xidTwA/It/8S/+xb9c+HIHh43Q3njjDUyePBkFBQVW\nedgtt9yCxx9/HCtXrsTLL7+M9evX46233lI8Bot+GLwvDofD4fgeh2L/4YcfYvfu3dizZw+MRiPO\nnj2L7373u6iqqsLbb78NAFi1ahVuvfVWAEBaWhrq6+vNv9/Q0GCOeDgcDofjPxxm9g899BDq6+tR\nV1eHnTt34vLLL8ff/vY35OTkYN++fQCAd999F9OnTwcArFixAjt37oTJZEJdXR1qa2tRWFjo/WfB\n4XA4HIc41c+eRTJPPvkkbrvtNgwMDECv1+PJJ58EAOTn52P16tXIz89HWFgYduzYYRPjcDgcDscP\nuJX4O8mbb74pzpgxQ8zJyRG3bdvmy4f2CqdPnxaLi4vF/Px8cdasWeL27dtFURTFjo4OccmSJWJu\nbq5YUlIidnV1+XmkrjM0NCSef/755sn58fTcurq6xOuvv17My8sTZ86cKVZWVo6r5/fQQw+J+fn5\n4uzZs8U1a9aIRqNxTD+/m2++WZw8ebI4e/Zs822Ons9DDz0k5uTkiDNmzBD/85//+GPITqH0/O6+\n+24xLy9PnDt3rrhy5Uqxu7vb/DNnn5/PxH5oaEjMzs4W6+rqRJPJJM6bN0+srq721cN7hebmZvHw\n4cOiKIpib2+vOH36dLG6ulq85557xN/+9reiKIritm3bxPvuu8+fw3SLRx99VFy7dq149dVXi6Io\njqvn9r3vfU98+umnRVEUxcHBQbG7u3vcPL+6ujoxKytLNBqNoiiK4urVq8Vnn312TD+/999/Xzx0\n6JCVGNp7Pp999pk4b9480WQyiXV1dWJ2drY4PDzsl3FrRen5lZeXm8d93333ufX8fCb2H374obhs\n2TLz96WlpWJpaamvHt4nXHPNNeJbb70lzpgxQ2xpaRFFkU4IM2bM8PPIXKO+vl5cvHix+O6775qd\n/Xh5bt3d3WJWVpbN7ePl+XV0dIjTp08XOzs7xcHBQfGqq64Sy8vLx/zzq6ursxJDe8/noYceskoP\nli1bJn700Ue+HawLyJ+flNdee01ct26dKIquPT+f9cZpbGxERkaG+fv09HQ0Njb66uG9zqn/394d\nvLIfx3Ecf05ISYnY6GulCc3B0qRc5aIs2QU1JTlwIn/DRLvwB1hWHBxdZocl5cBBX84kKzV2cJvU\nqM/voH1/v8l+/NbP9P3s/Th+9qnv51Wf3t9vfT/vfVMpLi4uGBoaIpPJ4HQ6AXA6nWQymR9eXWlW\nVlaIRCJUVf3eJrpku729paWlhbm5OQYGBlhYWODp6UmbfE1NTayuruJ2u2lvb6exsZHR0VFt8uUV\ny5NOpzEMw5qnQ72JRqOMjY0BpeUrW7HX+UVtNpslGAyytbVFQ0NDwW8Oh8OW2f/ssVBFeiPsmg3g\n9fUV0zRZWlrCNE3q6+tZX18vmGPnfDc3N2xubpJKpUin02SzWXZ3dwvm2DnfRz7LY+es4XCY2tpa\nZmZmis75LF/Ziv37M/h3d3cFdya7enl5IRgMEgqFmJiYAN6eMB4eHgC4v7+ntbX1J5dYknyPRWdn\nJ9PT0xwdHREKhbTIBm9PQoZhMDg4CLz1i5imicvl0iLf+fk5w8PDNDc3U11dzeTkJKenp9rkyyu2\nH3Xq+dnZ2SEej7O3t2eNlZKvbMXe7/dzfX1NKpUil8uxv79PIBAo1+W/hVKK+fl5vF4vy8vL1ngg\nECAWiwEQi8Wsm4CdFOux0CEbgMvloqOjg6urKwCSySR9fX2Mj49rka+3t5ezszOen59RSpFMJvF6\nvdrkyyu2H3Xp+UkkEkQiEQ4ODqirq7PGS8r3n94rfEk8Hlfd3d3K4/GotbW1cl76W5ycnCiHw6H6\n+/uVz+dTPp9PHR4eqsfHRzUyMmLL420fOT4+tk7j6JTt8vJS+f3+gmNtOuXb2Niwjl7Ozs6qXC5n\n63xTU1Oqra1N1dTUKMMwVDQa/WuecDisPB6P6unpUYlE4gdX/jXv821vb6uuri7ldrut+rK4uGjN\n/9d8DqXkz2qEEEJ38qUqIYSoAFLshRCiAkixF0KICiDFXgghKoAUeyGEqABS7IUQogL8Aqe9Md95\nDYkSAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3229310>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B_better.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "(5, 40, 64, 64)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(B_better[0, :, :, 40])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.image.AxesImage at 0x530e990>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mJTvklI3RsjMbEza6n17RHSZwrlq1yrGNGzfOsVkCDDsUmYlHTLS0Dl9m42Rl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\n/8nyx0u3HXtsAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fe594159150>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Can we do better than this?  Time for some hemodynamic modeling!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import nipy.modalities.fmri.hrf as hrfs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tab completion right?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What does an HRF look like?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(0, 30, 100)\n",
      "plt.plot(t, hrfs.glovert(t))\n",
      "plt.xlabel('time (seconds)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.text.Text at 0x6dc7510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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66r7kG0wmWWdz9Cib8fqj+nrg4EFZFHvkiFyqquRIwMePy5u0TgeEhsolJET+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\nH4/nnnsO//rXv+ydhN577z3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       "text": [
        "<matplotlib.figure.Figure at 0x6c24b50>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How do we apply that to our data?  Convolution!"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}