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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Statistical Inference : multiple comparison issues\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Thresholding with random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can read this notebook without knowing any Python programming, by skipping over the code, but reading the code will often help understand the ideas.\n",
      "\n",
      "I based the notebook on my understanding of the 1992 paper by Keith Worsley (see refs below). For me, this paper is the most comprehensible paper on random fields in neuroimaging. Please refer to this paper and the Worsley 1996 paper for more detail.\n",
      "\n",
      "An earlier version of this notebook became the [Random fields introduction](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch14.pdf) chapter in the book [Human Brain Function second edition](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Most statistics packages for functional imaging data create statistical parametric maps. These maps have a value for a certain statistic at each voxel in the brain, which is the result of the statistical test done on the scan data for that voxel, across scans.  $t$ values and $F$ values are the most common.\n",
      "\n",
      "For the sake of simplicity, I'll assume that we have $Z$ values instead of $t$ or $F$ values.  $Z$ values are values from the standard normal distribution.  The same sort of arguments apply to $t$ and $F$ values, just with slightly different formulae.\n",
      "\n",
      "The null hypothesis for a particular statistical comparison probably will be that there is no change anywhere in the brain. For example, in a comparison of activation against rest, the null hypothesis would be that there are no differences between the scans in the activation condition, and the scans in the rest condition. This null hypothesis implies that the whole brain volume full of statistic values for the comparison will be similar to a equivalent set of values from a random distribution."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The multiple comparison problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given we have a brain full of $Z$ values, how do we decide whether some of the $Z$ values are larger (more positive) than we would expect in a similar volume of random numbers?  So, in a typical brain volume, we have, say, 200000 voxels and therefore 200000 $Z$ scores. Because we have so many $Z$ scores, even if the null hypothesis is true, we can be confident that some of these $Z$ scores will appear to be significant at standard statistical thresholds for the the individual $Z$ scores. For example, $p$ value thresholds such as $p<0.05 $ or $p<0.01 $ correspond to $Z = 1.64 $ and $Z = 2.33 $ respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as sst\n",
      "normal_distribution = sst.norm(loc=0,scale=1.) #loc is the mean, scale is the variance.\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The inverse normal CDF\n",
      "inv_n_cdf = normal_distribution.ppf\n",
      "inv_n_cdf([0.95, 0.99])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "array([ 1.64485363,  2.32634787])"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, if we threshold our brain $Z$ scores at $2.33 $ or above, we would expect a number of false positives, even if the null hypothesis is true. So, how high should we set our $Z$ threshold, so that we can be confident that the remaining peak $Z$ scores are indeed too high to be expected by chance? This is the multiple comparison problem.\n",
      "\n",
      "We could call all the $Z$ scores in the brain a \"family\" of tests.  We want to find a threshold so that we can correct for a whole \"family\" of tests.  For this reason, these multiple comparison correction methods are often known as *family-wise* correction methods."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another way of seeing the problem : let's assume 1000 normal variables. For each variable, a z test would be significant at the  5% significance level if z > 1.64. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = normal_distribution.rvs(size=(1000,))\n",
      "print (a > 1.64).sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "43\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not surprisingly : about 5% of 1000 - so about 50 tests that would be declared significant if there was no correction."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Why not a Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem of false positives with multiple statistical tests is an old one. One standard method for dealing with this problem is to use the Bonferroni correction. For the Bonferroni correction, you set your p value threshold for accepting a test as being significant as $alpha$ / (number of tests), where $alpha$ is the false positive rate you are prepared to accept. $alpha$ is often 0.05, or one false positive in 20 repeats of your experiment. Thus, for a statistical map with 200000 voxels, the Bonferroni corrected p value would be 0.05 / 200000 = [equivalent Z] 5.03. We could then threshold our Z map to show us only Z scores higher than 5.03, and be confident that all the remaining Z scores are unlikely to have occurred by chance. For some functional imaging data this is a perfectly reasonable approach, but in most cases the Bonferroni threshold will be considerably too conservative. This is because, for most stastistic maps, the Z scores at each voxel are highly correlated with their neighbours."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's recall the general problem in mathematical terms:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the general case:\n",
      "\n",
      "$$\n",
      "\\alpha_{F} = P(\\textrm{ one or more } t_i > t_\\alpha) = 1 - P(t_1  < t_\\alpha,\\; t_2  < t_\\alpha ,\\;  ...,\\;  t_n  < t_\\alpha) = 1 - \\textrm{CDF}(t_\\alpha, t_\\alpha, ..., t_\\alpha)\n",
      "$$ \n",
      "\n",
      "In case of independence:\n",
      "\n",
      "$$\n",
      "\\alpha_{F} = P(\\textrm{ one or more } t_i > t_\\alpha) = 1 - \\prod_{i} P(t_i < t_\\alpha) = 1 - (1 - \\alpha)^n \n",
      "$$ \n",
      "\n",
      "$$\n",
      "\\alpha = 1 -(1 - \\alpha_{F})^{\\frac{1}{n}} = 1 - \\exp\\left(\\frac{1}{n} \\log(1 - \\alpha_{F})\\right)\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Functional imaging data usually have some spatial correlation. By this, we mean that data in one voxel are correlated with the data from the neighbouring voxels. This correlation is caused by several factors: \n",
      "\n",
      "* With low resolution imaging such as PET, data from an individual voxel will contain some signal from the tissue around that voxel;\n",
      "* Unmodeled brain activation signal, which is very common, will tend to cover several voxels and induce correlations between them;\n",
      "* Resampling of the images during preprocessing causes some smoothing across voxels;\n",
      "* Most neuromaging statistical analyses work on smoothed images, and this creates strong spatial correlation. Smoothing is often used to improve signal to noise according to the matched filter theorem (the signal we are looking for is almost invariably spread across several voxels).\n",
      "\n",
      "The reason this spatial correlation is a problem for the Bonferroni correction is that the Bonferroni correction assumes that you have performed some number of *independent* tests. If the voxels are spatially correlated, then the $Z$ scores at each voxel are not independent. This will make the correction too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An example can show why the Bonferroni correction is too conservative with non-independent tests. Let us first make an example image out of random numbers. We generate 16384 random numbers, and then put them into a 128 by 128 array. This results in a 2D image of spatially independent random numbers. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import numpy as np"
     ],
     "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": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Constants for image simulations etc\n",
      "shape = [128, 128] # No of pixels in X, Y\n",
      "n_voxels = np.prod(shape) # Total pixels\n",
      "s_fwhm = 8 # Smoothing in number of pixels in x, y\n",
      "seed = 1939 # Seed for random no generator\n",
      "alpha = 0.05 # Default alpha level\n",
      "\n",
      "# Image of independent random nos\n",
      "np.random.seed(seed) # Seed the generator to get same numbers each time\n",
      "test_img = np.random.standard_normal(shape)\n",
      "plt.figure()\n",
      "plt.imshow(test_img)\n",
      "plt.set_cmap('bone')\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - array of independent random numbers')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x386ed90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Bv/3H//gfCYKARqPB1VdfzYtf/OKHPHPzzTdz7733PurE/fCHP8ypU6dYWFjgR3/0R/mV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5iqEPGl/NmKtEi6Sl1LZJ4/GLBdbqhLeZjatiXeCfVVVVUM10DVFbLkiDzOWVwuOH16yvRsyna+\n7cGVmqEznh1Jhqeh4+kedVWxX4pR3w0HrK9XbG436I5QdF2kTU/jhKZqAAUl1DAtC9cL8UIJQk6i\nmNXtCssSason77+iSAtOzx9TZBlpFMswXFfRWg2llhnm/QF3L/OQdKu6Q/pI1mwc78mzlKapRILR\nuQ8EW15TdVKgsih7UbGiKmi62iOM6m6U0bYSaiPjEb2n0aRRhKKqjMYTDvsN+/WW9unDjuLR0nYo\nqKapKeqK9WIuGRhPIRgMcT1ZnhVZgdNlRTi+HMLpIYVaYTg+YnQ0YXwyxhuKsb7MxbNsWtIOZ0nG\nYXOgLus+KrFt2r7al7vxs3N95g62PM4wRoHMuqqao7MTTh6e4o9CdMOgrZuOKyYUU0UR+F+0OxBt\ndzIvU6S9sBybcCzZCLqhE+9jDrs9pmmhaLDfrVB1lWD0kPn1Dd//9jdx7SGuM8Ad+KJoD9o+uCTu\nAIrjkzGqroqdZrMnOcR4A5/Hn3uDYBSSJinXL19SVy2WY5MkMYfdljQ9YDk2pmHhTVycwOWw2TO/\nvObBW48JhiHL66VsgS2D5d0N86srPHfEaDrl6NEx45Mxru9KrN8nN2RpTNPU+IMQ3TRZL3Zsbte8\nfP8llm1hOqLtuj/Y7tsyGZq3+N0mtswryixht9pjWlLViTDV4M0vvUW0jrh7cdeb1MOphINYri0B\nNcs9/khkLfcBKnUlKn8hl6gomsL1q+dkecLJyWOmpyc8/fyz7sVUScWTlz1Cu8wKVrdznn//I2bn\n51i2jYKCG3jMHp2Q5zm/9/Vv8uidp4yPp9y9uCVPCryBVN5u6Pb3URbLHFJRFEzHxAkcNiuDuirZ\nr3fQKoxPJgyOBgxnI64+vGJ5uaTqDoLpxZE4MJqaLM7J04LZwxkXzy5YXC7IIqno3cChacaoqsZu\nsWF+c4PjuxxdHOOHA4ajGXUh2//PfeUd6qZhcb2SbaZn8d1v/B7L6znTsym26zF/eYdm6EyPh6iq\nbK6bzpFiBzZDZYLlOJw/u+D44rjH3q9v5qRx2i8pBkdDmm5hoN87Ijo6jW4JUeSzdH3mDjbLtVBV\nhTwtqMqSokwxLA3Hd4Wu6+k0TUuZV/2NlsQR8f7QReGpXditJF5puobtiaRhu9yyuVuheBJFZ5gm\nTuBydHHEdqWymt/ihj6j8RhVE6lE21E/7u0wavfn31cnRZaxuL5BMy4YTkdEuwN5nklIcKNgmRb7\nXUORZx0fzeL4fIY/EhnI5UevWN6kfWV1P3epygrP8zh7dIaKLVF5sTDH0kNKnuTYroVmACoEQwln\nua/gmkrEyKoqcXiKKiSQ+wrjfpNp+7YM+buKtKlF7FtXtcwom5YyE8/qfaTgdr7FG/polkq8i7qq\nTesDitu27aQ5cvvphi6zsKFPo8/IswRN0WnrRhA+uoauG0S7T4W2LQ13l9fEuwO2IxtbPwy5eOMx\niqpg+y5tlPSp7PftrKJAmRfkiYaqSy5A0zS0LR1+XO3w6TV+6NNenFCX3cyrs6zRyn04OBp0FBAD\nt0OvN3XdLWNkgXVP49AMHd93aJFlwXa+JdpFqKqGqmgyY/NcHr79mKqo2C93OLakULmhh6KK+DYc\nDqkLuY+rbrnhhpJ3m6c5RZpLJkKaE+33qJrGYDqSl7yqyAa6AwikB8mPNSyDcBLSVDXRLpZKzhZh\nrt79/yZx+mN97v+o12fuYBsej0Rdv43YLjbc3j6nbkveevenePTOG1y89YA0FsCe5VrUTc1mIQr+\n6ckJbuj1uJm2FW2YG7py0xoah9VBNqgojMbHTC+mPPrcYya7KZbl9SEnm8W2a/W6Rcbtpme+6Ya0\nwG7oopoKUbQh2vlsFw6LmxsMS+dzX/0ium6wXezYrpfQ5QRcvPGIi2fn+CMfVZMbcHW1RlFkETK9\nmHYY6w1P332TJ+885OPvveD1x9dcfXQlWKVOGhEeDWR+1CnJHd/BCRyCccjkbNqr2hVVkYe/aaiq\nCiVXSCM5HB3fEf9tZx43O+pt3TSYukaZldx8ciPD8WnIfrVjebnk2VeeoWomrz54iWEaPHj7kWRm\ndlo0VVOxfamoLdcSyoam8uz8Gaqq8OI7L0mjjO1804lJDQ6rA3mac/zwmDQ58PF3PyAcjXjyztsM\nj0Z4A5/TN0QusZ1v8Xyf8fGEukt0MiyTpml7y5Oiqj1UdHQy6scKZSbm9cF0xMmTc9Y3675tu094\n8ke++IVjafnbtu3sVhaqJpGQ81fz3n86mIrvt2kFo56lt6RRwmgyRdN11jcbzp6d8fCdh/zg937A\nzcfX3L28I5wOuHj7giIW879le8wuXNJdRpGVPadteDxkO9+SRSnxLmG33rC8u2V0NGZ8MqVIC9Y3\nG4azoVTo0P3MKrZrEY6DDjtVsttvGUwCHr/zENe1UVt4/fLmx/XI/7Guz9zBlnUC06ZtyLMUxw5Q\ndZWmVkgPggy6evGc7//+t3njnXcZHx0zOTnulO6ezKaalt1mTRrHtG1NVQ77pKg3vvQGbdN0sWTi\ngbz55KaLrvOpypp9p82Kdgeig7Qpji8CU81QuX7+ijyXXIK2bXn7y1/A9QMs20XRQDPUTm6iYNqS\nKWr7DnVRs7y5w/GsXtFe5qVou6KUm4+vJYehG9yjqsyvVyiayvRsymA64LA+sLxckkXyNp6eTfqW\nqyprFq8XAtkceOi6TlWV3L26RtU0Hjx7hGnLIVMV8nDLzEjrKSeWawlnrqoYTAdURcVhc+i3e7pp\nYNgmm7kEENuuQ54nfPDt9xgfHXF0etKhyx3R33UATbUTntZ5TaupWK7dB7YMp0MG00GfqjQ9nZAm\nDrcvb/AHQyHUdsJdGe53wTKd1SmNUvlvHWbd7OZXiqb2qVr7zZamafDDAF0XG9J2tebu+hql0XA9\nr19ENXWDaUm7ur5dk+xiwmnYz3Pv53ZZLPkJxv0Ms5HWWyjHR4IWdx2qvGS/lvnW5m7N7dVrVus7\nHrzxBuEkJI/FZjWcjXqXjKbrqHpFso1IY18Iwcstm/m6Z8u1HT4p2kT9y1YyLVKSKKalxTBNltdL\n0iQlj3PivQRmm55OXnThPknG6mb943vo/xjXZ+5gy+Mc13dRNWioGU2OsV23vxkP6wM3r17x0R98\nG98f4PsjpqczkUtkZZeRWLJdr9iv11iWIxqxtGB0MuLsjTPKQobrlx9cEm8jiqzAH/qEk6A77DLq\nsmG3WXP54jnDyYgnb78tITNVxfXzS9bzBSgKD5895u0vf4GmljnRYDrodHUtVVMIPufkmNHxhI+/\n8wHz1zfomoGmG6T7hLAjclz/4Ir55kA4DpleHHF2MSXeJ7z6wRXBKGA4G2J7di9OTqKEfCkWIcux\nKPKSZBOxvllj+7b8fteiyDKi/Q7DNjl6OMXxPbI4Y3O7ZrcUhb2iCT/NDV0G04F8BmlOMJaDPhj5\n7NcH0jhlcDTADV3uXtxRlzWnb5yyvEv58He/y8WjJ9iWx/h00vH02l4ndv/v8T5G1T5d/Oimzmg2\nZPbguJ8vDqYhTu4wns6EseZaojuMUiqzo6YkmTgcVIWkw8WLzMcSXVjHhBseD9FNjcuPX5IlGeFo\ngOGKJvHm9StuX18yO7nAcVwUTe1gjEj+gyLm9cNq31XYqrgsOh1lkcsLwPYES1TmZZfKBUcXx70F\nMN7FVJUAQa8/ueb28hVJvGd8/hVGkzHLyyX+0Gc8G7Ob74i3MYOjAaqmkCYx8SEiizJ2yx3bxYaj\ni1mv0yuzUvJMO0mSCKgT8izrYvoUltdLrj+5QmnFH1oUMdEhZL+LBOiw2rO+/cnB9v/pquuar371\nq1xcXPCv/tW/Yr1e81f+yl/h5cuXPH78mH/5L/8lw+Hwv/i6yfmE5JDgDQLe+MJb6IaIbRVk6Kub\nOucPn9D+DwqBPyY9pH2OQdNhfBzfYXp8wmg84d2f/jyqpvH8/Vcoc1nBV0XVSwFsz+bJF5+I2XsT\nsV9t2a22mKZNU7Z4TojjBKia3ER5VuB6IfZjr38jr64lb9O0RXx7T11QlM4qVHW2LMfD0C3qskHT\nYTgb4gSuoIi65KyqEOpGXTVYtkATk33CbrHrnQL+0KeqS3arDbqpddKDhcgeCkEcaarKyw8+ZnU7\np60VdMXi5XdfUZUFu82WtlKwPYu6Ej6YE7jsV3uuP7rEsE00Q+f25RWqpoi41bNJukOpzMROZI5M\nZo+OMV2dzd0G2/G6NKUUaDms9wC4oUOe5v3nbdqmtKxdRVUUFbev59R1japrXH18DYA/9EjjhA9/\n7w+YPTglHMmhG22kor5Hubdtg+VKapPpWCS7mGgXs98KuaSlJY8K2ga28y22KwZ02/IYj2eSXRu6\nJLuYqiixfYfV1apzl1SYtsnmbkueSpqT0S1X6MAKpnOfPhWjd/NXVRPa8+3LW7IoRVU0sjQljg4Y\nqstkEkIttq37ijM5xGzuVux3G+JEAqlt28V2xM9quzb+IBSfclmhaaagzA8RlmNghl5voN+vdsSH\nPdtXcx6+9ZQnF0+4e35H2zQ8+twXMB2L+Yu5zFSr6k/zaPgTuX5sB9s/+Sf/hHfffZfDQXBDX/va\n1/iFX/gFfvmXf5m///f/Pl/72tf42te+9l98ne1arK6XwsUaB/18qCpKGfw2LYPRFONNh6obhN+r\n6u83XrZrM5iM0VSV4/NjqqpCNzSyOGV5taSpRHTZ1DWW4zOcDoh2EYftnmgnlYll25K0roiHtMyl\nGqyKCst2sF27t8QcNofeSlXm0uKpWhemca/obkE3LdoWosMeT/EZHA3wQk8iAC1Jga9raZPvle9N\nF5kWbaR1NW2TcBpSljlZEvdBNbvllt1qh+060qrlJaubBbcvbzg+vUDTTNY3G/IsIY4OBMMhnu/0\nbZWqqeRJJnOfyQAncFjdLNEtnenZDMMwgZY8FnnAYByIzcxzSCNHiMNlRbQ9sL5dYbmWhNZ0yxDN\n0LBdG63zpYo3Ve0w1jmbu023oKnYrw8i9bEtgXOu9wRDgSBEu4h4L3Id1dDQG9ErarrWzxjbpiWN\npE1Mo1RySzVNZnC1DPsVRZH2UzNwPA+1+xwlcR32K5nT3eeZJodEEFFK24t2VV3tRweKItSNSlVl\nII+4KNY3K8qiYnQkPtQiK3Bs8bFqqt57PUEkS0VeiP+4qDAtCy8MsB0JWnECF0VROyCmguO6AmTo\ngqi90O0J1K5rc9gabNYVg3FAOB6wm0uFfvHmQ9Io5fqTj9ANo3PV/Dci0H3x4gWPHz/+kXzTy8tL\nfvM3f5Nf+ZVf4R/9o38EwG/8xm/w9a9/HYC//tf/Oj/7sz/7Qw+2wyZi30EWBUooc5PkkHbMeAH1\noUp1Z5gGm7sNRSqpQKZtYromdmbTVDWr5QbdMjh9esr8cs7rD1+iqTq6Icww0zGZXy5Y3ix4+cEn\naJpJMBgwe3yK7dlEm4hoG7G8WuJ01UbTMfOLtMANHU6fnHRi2BTd0LAcU1hdpejIRicjwnHA6w9e\nsbyds9stGc+mTE6neKHL8GjA8mrBbrWDbsuWp0JmXd2sem2bZIY26IbG+GRCOJG39+pmxWG7oyiy\nPrh4fb2mKRUcN0A3BCAgUEKfc++Cqqi7OVEuYtqmlTCSwO1wR6JN0w2p0OpStGb3BNhHX3iDwSTk\n8vUtt89v2K03feWcxhGWY2FakpSuqirT8ynWmxbbxa7LbK1RNLU7DMUTm+ylupo9PMF0ZNbnhUJC\n3syXXL+4wjY9FDRQwPUdhrMR8TaizCvifYLWATLd2O1tcPdC6XvLWF01HXw0AES7J7KIKXmSc/Px\nDShiPM+SrA98TqOIm5cvoVXQDbPfbt/fD1q3VEj2CUGXKaAbJrbrcvTgiDwRokge5x2cwe42ti2W\nYxJOB+L2sEzCcSBas7rtycx+hzG3PZt0n3SibsHnT86mBOOAw2qP4bs8+NIJlmXQNBXPP7zk1fdf\nyYY1cNmt991ztu+jKO9noJ+V6w892H7+53+ev/E3/gZ/5+/8HXT9T7aw+9t/+x2L9ZsAACAASURB\nVG/zD/7BP2C/3/e/dnd3x2w2A2A2m3F3d/dDv/b/+N/+V8pUVuxPnr3Ds8//lJT5u1gMzx0qx3JE\nCW5YRj+Ib9u2K+tzRuMBtmsTRyltnPX+Qcu2ZPhqCDQwOaSUZcV2sSU5xByfDxjPJhR5SlGktJWC\npqqY9qd2mmQvVhUQCsN+u6WtgVbFNA10X0fR1G49X0gLMQ5wAhcv9NAdBdf3+vg0N5CZkFRtIsvY\n3K5JDqmAG00DwxZKieM7HSFDqrtknxDvoi7gRkO3BEedHpIuIT5gMBlimGaH3zEwLRtVFfSSqmqU\nZc7d5VWfuC6SB2mz6i7J3XTMfrhepgVlWbJZbNncbsjiHNsVuYGADxuqskZRZAtXFhVVWaObzX9G\nopBovv1yT7SRQJambkFtSQ4xeZZT5XWXg2rjDwM0XaUpFVRFwxu42J4QNYJxCLRUeUm0PmC6FnVd\n9zF7piNVYdMdaHmaEe0OmJbcC2rnElA1rWOeqbLZ1dWeztt0L9SmbjE6IW+axZSLjKposD2H0fFE\n7ofVTqppQ+AC9ySUppbZq2GZqCosrmWp4wY27sDvkr1aEWJ3jDdN18iSlPnrG4LxAC/0yeO8By6Y\njkU4GaBpan/QtU1L1lFYyjwn2sZ9Wpdu6iyvV0IqiZd8/Pxb/VLks3T9oSfWt771LX71V3+Vn/7p\nn+af/tN/yl/4C3/hT+Qb/ut//a85Pj7my1/+Mv/+3//7H/p77luRH3aZqs+DJ0+wbAfTMPsMzmgb\nSdtU1QymA5zAlYeobnrVdJVXHLZ7kkPEk//lf+Thmw/43d96j+3uwLAdYXsOF289lBlPVXP54aUc\nAN1bVFN1pmcTJudTvvuNb7FbbJlMTwjHQ44vjhkcy/e9rxB1U2dxfcPH3/uAo5NTTi4u0Lzu0A1c\n0ihlv973NqbR8ah7SD3Sfcr81Zy5saAsK4qs7CuzMi+5fX6L3iUu6YbMbYKRtH/D2agLSJFwmWSf\nMjwS7V2ZlSRZTBplHD86YnoxZXA0pMorbp7fdNihqv+Z/JHPej7no299F8tyefjkmbS3dcN2ucWw\ndGaPZgyPhp3iXbaBlx9csr3b0Cqitj9+cNpVaZJGH+8TNncbom2EP/RFOtO2ZF2b7g9liXH9g6vu\nEFRwfMEOLS7nXQ6sjRt6oMDFs0c4ns3r919T5hWj2ahv048eHOGGDrfPb9ncbdBNvU/ICsYBbuhy\n9dEVm7sNZV6QJjFJspegFT/g/M0HhNMBZVGCojA+HctioKzFplXVrK5WtI3C8dmpBF3bBh9+57ss\nrm6wTJfTxw85fnBCXddsl2vyPMFyLd74wju4nifZHPMN++WO0WwMKrz/e+/hBh5/5r//c4QTCbPW\nDZ08yfoUsnAasv/Blo++/QEP3npMU7fsFjuiTURyiBmfTrAci3gnh5ft2RQULK6XbJcrVnd3+IMh\n4XiMP/QBuHtxhzf0+PP/88/2/tG6rPmtf/e//4mcAX8a1x96sIVhyD/+x/+Yb37zm/z8z/885+fn\nPU9LURTee++9P9Y3/O3f/m1+4zd+g9/8zd8kyzL2+z1/7a/9NWazGbe3t5ycnHBzc8Px8fEP/Xo/\nHJIkOwxbx/EH/fq9LGTDeI8Oauqa6+evyeIUVTGEqaaI11Q3NJKs4OrylqtXr4miRKqJDnVjWF0A\nSDeXsVwL3ZSqrC4bNrcb1NbAcXxQ5I19/z5TVQV/4JFoKtEmIt4mNBUEo4DZk1nH5KrY3G3YLtds\nlxv2uxXXL21Mw8UPQ7yBD60iM7UuPq8qq74tqauKPMtoWmk7Vc+WUOfVmsN2R7SLep7+6m7Obrlh\nUExom5rNei44pUZn2owBhfX1GsPQefj0nCRKWS3utWNaR9FNmM5OhVRx9Zqj0xO8QUieJ+RFSxoL\n3kdoInXvXMi6tCyJSgwxLNl0Do6HHbPNkmzR7vdohsZmsSbeR9S1BLF4Aw9/4BGMAkEFrfcMpsPO\npqTgD2VJ4wYupmXihR6r2wXPP3gfTTWxLV+2plnOZr6hykuGszFWR7zVOpHu/cC/Liss28awdEBB\nNwwUVarM5JBw2G7ZbVZYlocXhELzUBS2ix1tZ43Lk4I0yqiLFsfxmZzMCEfi9zUtk9mDEw7bHYqm\nYloGrSIbc3/oM5iI6DfLMkaTYxRVYXm1RDcMTp6cSrxiUbK6ncvyiRYahenpMX7oo+s6ClBXJVmW\nkCW2bPG7cGmxlwl6y6tC8rygyDM2yznHDycEo6EQajYrfv93fpvThw85Oj1j8Wrxx3ref1zX/2OP\n+W//7b/ll37pl/ibf/Nv8ou/+It/aBX1R7l+7dd+jV/7tV8D4Otf/zr/8B/+Q/75P//n/PIv/zK/\n/uu/zt/9u3+XX//1X+cv/aW/9EO/fnw04+b1Swaa5BLopi54Ghp0U8CTRnd43Dy/YrNYc3x2huv7\nKKpkQ5r2gP0hYbFYcX15KTeVH6CgdRWD0v0jIlLbc9B1vwvUPbBbLDENB3MoIbSKoqJ1lqT7t3hd\n18xfiA7Oth3CyYDJ2Rha2K8FRriZr1kvFmRpTN1WPH72Fq7n93MfVVU7TVnV55GqqiotYFOjFIJX\nYihBG5vFmizKWF9vCEYh3tBju1qxXa2gVijKnNvb52iage+PqBsBWy6vloTDgLe/+Ab7XcRud8By\nZSi+W2xJDimzswvWiznPP/iAwWTA2JnSKpKVmcWpEGoV2dr20XNNg9qqffDLvcRidDxEM3U0Qxew\nZ9N0n7NNkWcsr+fUZcvoeMzoeMjpoxOOL454v/qAJEoIJqEE4qQiwxkeDTrVf4PpWJRVzifffx/X\nCTk9f4rSVY379U7axK7yKbvtcpELQskbCGzUVpwOqSQCWEVRJNU+yVjPl7z65COOZudYptsnm6la\n15LWLUkUkUYJSqszmh5z/vQRlm2RHVIM22D26ATLkbR3UKi6xdPgaMD0bNrFGhZMT87I04zl1QI3\n9Dh/81w8oFHCZrHqgZC263Ly6BynQyZpuoaqK6DWlEVOtIvQdB2tq1RVXcMf+WKVAm5fv2a/W6Ma\nCoOpoNCXyyve+w/fwHZtnnzuLW5+8N+IQPev/tW/yuvXr/kX/+Jf8MUvfvFH9gPcH5Z/7+/9Pf7y\nX/7L/LN/9s96uccPu0zDZnp8hmV55IkMWQ3LZDyb4IUe49m4Y0pF+MEAVdG7oJOSxfUdw+kYb3DK\nbrkj2h7wvRHaQEM3zD6P9O76is1yTlkVDMZjnr7zDsF4RDgJuPzwijSSODZFUajKmsnxkLe/9CbL\n+YbNai+bvqYhnA4wHIM0HrC+XfG7/+4/8O5XPs94MiB+cCRJ8bZJnkpSuesFpFHKJ9/+mCKTDZjW\neU7lsEgpswJFUwhHA9IkYbfd4AyEXaZrBv7QZHp6JIexqXN8doofDvCCAFVTOHnjRPR8WUMwkK2r\n964wzy5f3LBfH4g2EY7n4Awl9KNtW9Z3S9oWnr7zDiePLpicTHiLdymLoqtGCja3siCo65osStAN\nncnFtBusp72huszEr6nrGpZrkXUbyqqoMC2b6emM44cn+EMfw9RJ04zbV3fs14eenuuPfI4eHNPW\nMhc7rCXNPk9yaHROTh+jG0IJiQ8xqqZw/uYFwUiQ6Jv5mpsX15imhRv4zB7NJGGqM8bfzwxVVZUD\nsKhEnV9M2K+2XbUOm5s1RZFze/kSBY2xdkxy2BMddkxPTxjPJtiOTZlXHDYRpm1geXZv8N99sJYZ\npWFLNda9IFRV4bCVGfT4ZEqRFHzvt77HYbejLApmj05p65bN3Zo0SglGQ5K9EGmqomIwGfL0zzxl\nt9py+dELjs5OGE7HHW1Z8k6Xdze8+PBDTh9e8PjdL5HuC1587yWqpjKaHPPn/uLPcfH0kdBHZv+l\n9Oq/5usPPdh+7ud+jr/1t/7Wj/Sb/8zP/Aw/8zM/A8B4PObf/Jt/8//6Na7v43pez1qjbSV5ahDg\nj3wc36apReYRdIHCuqWzW2Uctju8QOQT8T5iv9oRTkTYes//13QNRYOyyqmbkroRCKNmaASTEM2Q\nBCfbdLq1fdENkSHa7bl9dSXkD9vC9T0cxRWu/N2c7TLhyVtP8YNAqghDw7JtTFOIr6qikhyEQKtp\n0gaj3NubMhF42rJEsF2bui7JM0DprDGeh25o+EO/F2hW5QjDtEFt8QKXycmTLrF8LxBHVWF4PKQq\na+Yv79it991cTrBP3sCjLCr26y225zB7cIo/CMXedTaTkJH/k7s3+5UtTe8ynzWPsWKO2POZcqiJ\n8lQYUbYMjURL7b6huWhLgBAl0Rd9AUgttcUlF41kXyHEHwASQkIIbgCpJdwtutUusI0Ll2vIPJl5\n8kx7jjlixZqnvnjXjsLC7nSXcJWTJZVUVcqTZ+99Tnzr+77393seGqJNxPpOytqaLlBMzRTUU9PU\nLG7uKdIKpVEwTB0UBa8rZqfCEFR6lVZYlo3S1eSI1tSkccZuvSVPE9JQ7riEhqIQDCQwvZlt2Cw3\nrWTGaO/fnBYCarHfbanKkie9p3SHXbbLHdFOLvFd30c3TKqyRDOF3CE7Y+lV6oZMm4ssp1ZKVF2j\nNxrjdzs4viOC7DCkritsz8LrejRKQaVk6LaKooNu6aRxwnI2w3YdOqUcN1EVsjRDQcHQLHarLWmc\n0B31sByZiJqWSTDosl+H3L28pahyTNfg9J0LFGB1tziIXARCmqFpKrbX4/TZeUtk+QDHc9o7TgsF\nlSLLydOMqs7xuh2Gkym3L2+JdxFu18MLPB6/8768GDbRIX3weXn+wIXtj3pR+2GfwfEAtY1taK1q\nLI0y6WWqasvKl51Bb9pDMzRWNysRY7QxDt3UKMuMvEzwese4HZ80krG9qqlMT04ZjMc4gRBM96uE\n3XJHf9onCkOicEcw6uL4kka/v77n6tPXLOYzNusVqqoS9PpcvPOMumhYz1a4gcf4dEqSFLz++C1v\nnr8S9V5R0ukGeEGHcBPSNDX9yYBg1KXT77C4XnD/5l6kyKpCZ9hpS+kVnZ5o9/xeRyamyB1KGmdo\nho7dcdBCjTzLWNzdMDoe8v5PvoNmmOz3MZv7NeEqxOvJYu92PZJ9ym6x4+71LYubORdfeMToZEi0\niTBMHduz2klrJKBKR6QrdVMRxSHdQQ+/16EocjkyFxXb9YKPfvfb9IcTpqcXAkFUhGChatJoqEr5\nZy3PJstyLj9+IxksRWezuWeznfHs/S8zmp6w30gUoTvuEq73rGdr5re3ROGe/nBMVZXMb68ZTMeM\nTycs7kqiaMtusabKKhbXS6JdjOcHTB9NCYYBt2+uKfOC/njU5v72mI516IfudztmH13Kse/0Qrqp\ngcfiak5DQ3/apzfpMzqbUBYF+82O7/7mbzO/u+Jn/szPU5FxefmcwB+iNI+lr9sfMj4dCUMvLthf\nXXJ/94aizOgPx/THgwP2m42E2h3PxQ088kQEMpOzYwzTbKekughzMrliCNd7qkJynZuFUJz/1J/7\nOoPxiKuXN5y6j3n8paeUWc3iak603bdSafmzUBSF5c2SJEroT/4r2bH9cX3KQhDXdd1QtF28qsXn\noEC42rGZb9guNlieiaO6ZEkGjUJvOMAwTaJthKKquL6L8cCjitIWu2yTphFZljB9dERTwvxyyWa2\nwut6Ag702rs1VcHv+iziiOs3tzRU2I57MGfPb27RdQvN0PG6PsGgR54VJPuYupZApe3ZuJ6HZVso\nqvzltVy7JZDU6LqO4znUVQmKcgh8NnVGkVdURdmGTMHvS2BZDPEN4SrEsAz60z55EeN3O7i+SxJn\nrO+l2K1qKvv2jWxYIvQwHZNsk5LtYtazFaZjSbRAU0mj7IASF6P5D+IK4n4I6A67FHnWhqKhyAqi\nMMLviIMg2sbtlFdaIG7XA34gvqFpJFrRCnyLrCQNM/I2HNvp+1iuLTTaNKcBbNdBNzWZ8BY5cbSl\nKgvmdzdkaQaNyup+TRIKhFPsTx6G2XLHoowkStB1ESC7gexmae/nJApko2vSRdUNIQo/7M4HR0M6\n/daUVlSoik5/PMRtXZ80CoZu4fgyCMnzhHKT0huJ8rAqU9yOx8mzM/JIiDTj87G4DNqppGmbmLaN\nrhstSDT/T1iAGfE+oshyLMuhyHOuP31LuA7JMml0uIF4SDfztXwmFAUVE4UCRa3w+x0sxybPZKLv\ndJwftGIC98f1kf+hns/dwra6W2IYOtE2ZrcMRfLR9gUBVrdrFjf3rBdLiUD0ukSbCF3TGT46pcgK\n5pcLTMPGm/gHZMx2viEYdelNely9+ZTZ7TXjswmuE5BEIXmS0NQKpm0wOpkeCur98x5JvG/L2UcM\nJq0Ad7Pm1cfP6fb7PPvSV+j0OhimIRm3WhylwbDD6Gx0sGH1Jv1DtSja7AmXO0zbYnIxYXmtkqdF\nmxXT0c2KcLNldb/Csm26ox6DkwHBIKAqK+7f3HP38o4nX33CybMTBtMBtmOimyazjy753f/rd3j6\n1XcYn01Y36/RNI3xxRjbt1ubU020i7j8+K2EcSdDqgbW92sURcgQ4XKHYRki+VU1JqfH9CayYxPy\nqnD/NU3HcXw01RAHxEKqXbphMDjqc/zsBKC1aAnocXJ+BE1DHCagNCiNTpWJeObpV59KjWm2ll2M\n79AdBliuiRv45EmGZdlcv3nD829/m24wxvN60pP1YgbT8UFu/PDzVlUDTS1Z3CyYnE948icuDke7\npm5wOg7dUY9wFbK+29AZBPQmvYPlS7qvNavrJZv5hv024ulXvkh33GW3CFExOT56xvTxESdPT/jO\nb/wH5jf3PHr2LqbpEm0jpk+OOXn3p/nd/+dbzK/uaRCC7ep2RVPXraVKFQBEiyjarTcUhWQ00yQE\nteHi2Ts0WcObjz8hCkOKPOcnfv5rPPrCMz799gt2i09xO6LZy9Oc4cmQwfEAy7Eoi5LV7Qov8Bif\nSag3SzJ6/zXu2L75zW/y+vVryrYzpigKf/Wv/tU/0i/sD3r60wG275DGOQ3C9cqzjJcfPMfxXfrD\nMX4sl/APijevJzutZJ8IqqeVCNdVg6ZLwPX03VOKLGf29o4n777De19+F1OzydOC4yenVHkNdcv1\n0jV64x6mbYqcNk4PDHzHb0kaZUF/MMEPOoewaZHmZIngZh76n47vUhXl4ZJatHwGCrLzisI96X0i\n2hZTZ7vcYliys3Q6Hr26bocL6cH8lOyTVo2Xc/PymvVsQZ4W9MZyXJIMl1B88zQT6rCps1vs2gVH\n59E7Z6jAB7/zAeF233LH9IMiz3JMFtcLsiQniVIcz2ZwNMBoBS0PasI4lLiL3+kzPJ4wvZiynq3J\nohTLtbEcm2gbSegVpFala8TbGE2XO74kitFXBsGgIxABhPj6kNMrMyHIRruY3UJwRIZpcnRxQjDq\nUCYNSZixur/BrT0efeExpm2TJ/khpjI+G5OlCa8+eMF2uWZ5vTj4OtW2s3p0cURv1JOdmyE/r3C1\nk0Cxax1w9cEwQDcNNrMNq9slWZTL96jIC/n29S0qBkF3QJU3NHpNZ9CBBja3G1zXZ3quYZrSjPD7\n/kETKQCGqjWl5SI7buoWBjmkaSqyVDqsluUIpSVNuL+Ufm0w6jA8GUEjE/6HwU20iaRX3cZ13I6L\n2boOVE1lfbf+sXzef9jnMxe2v/JX/govX77kJ3/yJ1uvpDw/roWtO+5hWiaGFbeVKpMsT7h89ZLB\ndMT5u0+oypokzFBUjaapCQay0N2/nUG7AJVlhaKUh8v26eMpN59e8/b5G37+F7/O4y884ru/+SHh\nLuLk8TlpnLKdbWRCVpSHsvPick66Tw9ECsPU24K6w3B8LEdHU3j6eVHJESIvaBqjpfnSQis1iqwk\nT8T/+GDjWtzNmF3dMj0/xfE9NvcrWdhcG7fjYtkWy9u55JailLqs2S13xLsYgNmbO7I0BRSOnqRM\nLqYoqkpv1Gc9W7KZr3j/Z76IbuoSqG11gyePj+j1O9y8vWIfRtR1jdZOMYcnQ7yeR1kIMLEuBXzY\nGXTE1RClNFUDtTQ96hKC7oDh0ZjJxQSlHYh0Bh25C1qFLcvMOBzDl9dLdFMnGApTTjd0/H6HzlBQ\n2P/p4l2X9aHFUeRikB+djJicHtMZvs/NixuuXrwhTreoToXdsXBc7+CqUBQYHg/I8pTXH31CuN5x\n9+r+MLHXDHFx9sc96laRGG1jtvNNa7PKhfyhisLQdCxM1+LF73zM/GrWEmQkDhJtQuJdiBf4dII+\nRVqgtL8ujVJuP70V1ttkdGg6BEOBjjq+w2a+IYtTOn3/0CPVTXHm2q5NWRZ89B+/L2q+iTR5ojBk\ndnVHGsf86f/uz3D06IxwJeDVVSsuEl2lvPQfuHw0HHBHDyrHz8vzmQvbt771LT744IP/Ihm2/xLP\ny+9/xPT0VFRnjoUbuAy9AafvHYsrshBSqt/32S6XhNuGR+8/QTd18ixlH24pipSTRxcMJ1OZTLpW\nS1zQ0TSD+e0KNI0a+ZBH2wgAr+cd5BqzN/dSWF/vURSN02cX9Ef9Vmgctzs56YaqqoraVo+UljU2\nuRijmwY3H98cjhV5JndI0pioRNVWge34OL4r4phGuGqC95F/r+05B5JF3d5LBcOA8dmILM2Iw0jM\nUUnJ4mpBd9Dhqz/3FV5/+Jr7qxnzqyWmFbZm8IYsyZjfryiqit50RK3qVHl1CCxHu4h4F2N7Nqfv\nnsrPNslZ3a7Yb+We59F7Fziezf31nFhVDv/u9d2K9f2apm6YPJrIcKa1IoXFHtu1AOUw5bt+cY2m\nq0wvjkn3KXcv75g+nlLXFcu7exRFw+8EB5v95n5DVUq/tK4b8lSuDDq9Ll/4iZ8GpeHm0xv8ICAY\ndOmOJc6yXe5I9jFBb0iVV9A04m84G7Ff7ymLiutPb4j3Cavb1WGC7gYeWqoTbUMUVRbBIhOism4Y\nTC+OsV3x0IarHaOzMUdPp9SF5BOz9rgb72KinWjvvJ6HbhqoqnRvk30iNGFNJVrv2S4FT1RXNWmU\n0R126Y71NupR4fmBGLyKGk016Q+mPP7SBUePpkTrhA9vPhA72zokjcWO5fXEI6KqymH49uFvfiim\ntI7k+j5Pz2cubF/5yle4vb3l5OTkR/H1fOaznq3oBAMUJOxpeTb9SZ/etEcWZ9y9ugMk6R9HO/Is\nk50RDaZtoCUKeVHi9Tz6R/1WI9dQt3o91/fYrfdUtTg2DdsgWkc/uExtJ0a7ZUgay/GvO+5y9Ojo\nYD4v8pKmrrHaClRdVYB2ACeqmopuyI4t2kUHIKHs4BryXCa0Ci2e3JVLbsMy8Psd8kSOv1krf3E8\nD6vFd5eUrXBZcNW2a2MYJvt1TJEVrO5WeL5D/3GP1awrUuI4o8xK3MA5MNBmdzNW6wW6atLpBzLy\ndyTEup1vicNY6lijLrZns7hesP5k3eKCJIfl+A5+1wOUw84q2kZkUSpHHFU9uDlVVW2ZesUPsnBx\nwnq+YHA0ZHJ2RLjatTawWsQrUYJhWgcKrm5oZG2t68FZur6XI5TtOoxOx6RRwtuPXlNkJV7gHyi+\n92/uZVHxOwIaKCuCUcDweEhZVMI6W27ZzDfML+8Ihj36kwGdYYCdFdy/vSXdi0ZvtxaSStBvJ+dq\njdYorWvBo9OX+62qFa48LOK0xfgHrLx0VvdsF2scT76v3WrLbrmlqsr2ReOiGRoKHO59hQxikMYp\nqqZjuz7j42OOL0744Lees2jBCXJN47bNGl3iLe3Rc7fcsbxZtYCDbqvz+/w8n7mwzedzvvSlL/Gz\nP/uzWJbcFSmKwr/8l//yj/yL+/0e3+sdqk9FltNvKQt5LLSLzWyD1/XoT/t0hj55mrGd7ajKmuOn\nZ4yLCWWec/rOOY7niUm9taMblnHgve1WOzrDDoZmsJvvQOFwifygrsuSlDzLMKzBITG+vF6gqCqW\nZzG5mFJX1eEOSaosNlVZ8eaDN3iBx/TJVPqbu5jV3YrNYsV2u6A36vPki++jt/mhupKEvO1KWd/2\nbWaXt8yubzh5coEXuKRRdsAoJXvxQ+rt0fihFbFfhdxfzqjqmnAbYdgmXqtai7cinTl+esS3/92/\n5/XHn/L42Rfojybopo7f8+lP+yT75EDNLfMSPMjTjM1cPoBu4PH6+Rvc6zln75+jGjo3L24OAWjL\nbflkm0gMWkXJ4HhA/7jP3cs7Fldz8jQjCnfsdiss36DIhvh9ibo0dUNV1Lh+cKj57ddh2ye16QwD\nRqcj5pdzXn33FbZr4bT497LMqeqCPBHAgNiqYL/ZkacFju9gt/CEsqi4fXXL7cs78lRApIpWsdnO\nsHwD3ZgwPBkCEIcxqqridBxmt1fcXb9G1R5TlgV312/xuz7PvvhFdsstVy/ecPH+Y4JBj/1Gjvnj\nizG2Z4s7tOejGRrLlyvuL69YLm7xvID+4IgkisglvIg/GPDky09FzJzk7R1yKS8032a32BHtBAo6\nu55Ti92a4fHwUBU0bYP9ek+4lmGVqqrt76+3VwUlm9maYNT9sXzef9jnMxe2v/N3/s6P4Mv4wz+T\n8yO8rtcSO3LiMEGbbbE9SwzW+4S6qmiohZfWKIcUf1mJKb03HGLZEoCMQiFHWI5Jp9/h9J0T7t/M\n2G8k0/OgJvtBxakiz3KyNG0jDk6bzF8KulpR5ALeFDWgAgf+2QMEsirKAxZ7mA1IorjteO5I4hhq\nBdtzGR4PqIqSZVEcQsDrxVy6jbqN6ViMzyfC2Woa9rstdVnjdqTYHQwDsiQnT0XEYZiyi0NRhOgQ\nS+1JIiRCmlB1rQUKKJiGJXdm+1S8BC100LQF7xNuduRpSl2PD+asB9lJkZfkhURUQKpWdS13itJ3\nFWM8yIvyIVKhm/rhP5Zt4dYedVWxXUpNTNNUgQykObZji7dAUQ73Qw9MPtOW1sEBOV6UctGf5zi+\nh+NKxQs47JIMU3aORVGQxJFkBxVV7gBbZ0Sv7jM+nRIMupi2ceDqWbYQYgNWHQAAIABJREFUQ6QN\nY9IfD+iN+ximyXJmoipSISuygu1sy511w2axYj1f4QU+j0fPhCCiqnJEVQQXpRsGQb+H6/ry52Mo\n2KUlyPTxAL/fId2nLTVZVINCIml/DpaJ6ZgUecHidim7OwXC7RaUjpBgVFEcVmVNrdQH2XXTNC2X\nsDmkDj4vz2cubH/2z/7ZH8GX8Yd/zt8/Q2n9jVki0o7dYtem58uWwb/l+tWl/IXw5ZI4iSKuXt4x\nPj3i4r2ncvzKC6JdKLuPtOS9n36PR1+8gHaaultuBTPdSm3zNCfcbkn2EZpm4PoevUmPPM14/psf\nMDweEYwCltdL4p1YgPy+z/BsxPp+TbSNhNfWVnXSKGV5s2R1v2BxOyfPM3RdZziZcnxxxvB0yOJm\nwX6zY/poguHovPmdT0jDjOHwhPMvXPDFP/VlwmXI8nbOejEni3I6QUZ/+i7v/My7XH98dQj32p7N\n0ZNjAFGvZSVFJhDDzqBDMOpy+/KWj/7Dx3SGA77ytRNh7O+FeBvvIjZzAQ/2j/s8/+3vk+xjqqpG\nU3UG05GISvYpnWFAZ9iRSW0oOwm1kg/bg/ykruvDEbLM5Q7qgQSLokh5vpRQ9Oz6Vui/rku03aPp\nGt1h9/ABfoAhbOdb6lq+n7qqxXxVyXBhdb9E01QGkyGO7x3aGdDQ6QVyx6kobOcr7q9u6A4G+EEg\nFbCe3xbuA7wgoKkEEPpA0VU1OUVs7td0Oj2OLs7oT/utIatpIz0FNCqW7XHz8opwv2Yfbjh+fM7J\nk3OqUl6au+VO/KWOxcmTc9yOg2GZ6LpBEiVUZSmdZ8eEBuHV3S5J45iGqsWqyz/b6XcYX4xZ30kY\n2/Ys8jxjfn1LbzxA03TS1m3hdJy2Jlgerjse6Dj7TfTj+sj/UM8fuLD93M/9HN/85jfxff8/Gxwo\nivJ7WGo/yuf25Q2GLRiWqqgYHA2kbxilFHnRei27KFoX25Fp1H67p8orbMfHDwL8rkcayaV6MOhh\nuy6aKiXp7/2778nOL0zaqgqH0KrjSQjU9YX15Qc+wSgQ6mnHPfC8jp8coSiwWawl4GqZWK5Np99p\nIZEiFnkgptYVGIZwszr9DsOjMWWV8c3//f8gXouZu8xKCQR3+nhuw2A0wPYcqqISRM0uoT8ew6hB\nU02i7Z5PvvWRHE9bG5duaITrEN2QqEmWJEICsQwMy8Tvd+iPe7z7U++IPi4v8HvNwYTUNDWzNzOO\nnx7TG3XpDfuoaDRVQxxFbBYrdF1kLlUlE+C6Ux+OsXEYE4cxui4L+4MtHiSYXDfye5mutBnUjtwR\nxvuIcLOlSEui7f5wJ1e1OzRN11rblnpg0V1/ekVTNai6humYmHXLXKtqylziPqqukkbJoT+pGzre\n0CPLksPiePz4lH27YytyiX9UWXkQ2zyEhNM4RddFdRfvIxbX9+i6UHmLtGwjRiJyMS0Tt+nIfzdt\ner0RlisKRd3Q2a9DmrLm6bvnmI5FGMWt/s9sd4X1IR+oKNLCCQYBuiW7sfNnpyiKyqvozQFymez3\n7NYrVG2A6VhMzo8xTEMaHKMuk/MxpmmQhAlvP74k2orrww08vK73x2Z4+Id9/sCF7Zvf/CYA+/3+\nR/bF/GGeq0+ucDyvdYQqDE+GdIYdXn/3NVVZiUW84+IFEjJNooT1TBaPbn9Apy+X3Zv5lmgb0xsJ\npyxPMrbLDZefXGIYBrohvUHLMTEsEzdwJafkWRRpgd/z2rsMWVy8ns/tp7fs1yFPv/IETVe5fPGW\n3TJE03XO3zunP+kS75LW5iQWISE0aDiex/hkzOh0SP9owKcffMBv/Z//N4PBKRePvkCeljQ19Ppj\nLMekO+qiGTrhMmRzvyHeJUwuJliOZOvWsxVvn7+mO+rT6Qe4XZemqtnNt9jtPVRZFsT7PfpCMNud\nYYfeKGB08i5XL66ZXc4wHWkk+L0Om9mG+dWC0ckI13foj4cojdoCOSPWsyW90UDs9llBpqYt/dWi\nN+nKZHAZogcCpJSpoPQwG0DVtPbeRyZwlmvRn/TJkw5e1+f6xSVRuMHr+KjtDq1pZBJZlhW6rjA4\nGZLFKS+/9ymmZTI4GglaSFWlJB9J2b4q6xbpnbCZyZTW7wkt1s99XM+lN+kzeTTGbl+cSRgf+GS2\n7+B05F4zT3LSfUowFNHO24/2zK7uMSwL13NJdjGKph5oHCJktqEZkqU5/Ukf2xX6cqff4dV3U4oo\n5fRsKrGRF29o2sly09SSdyyrH+DubRO/72FY4p09e3JKVZZcfnxFWZSCQI9jkjgiqLq4vktnMCWN\nMlZ3KyaPppy+e4ql6axuV7z64LXs1spK/q4Ng4Nq8vPyfO6aB27Ho2mQaVrdEO1ki5wlGZquEQwD\naBqRdayEelsXcrzxAo94F/Pp7748/EE17S4hzwrGpxPe++n3uHx+xfp+gxe4eD3/cGfxMMV6EM2m\ncUYaC5yxyOQvd5mXPP/tDzFtWQy6Q4mAJPuIT779EUG/h6bp7aRWPswP9zThKjz8RZ2cHPPf/o//\nA/EmJ92VVGV5cIA+uA+2ywWb+Zoqb6jrhvn1rMXyWAdi8IPYucxlx+d25XsKhgGT7AjbdaBR2O9C\nvvPNbxH0uoymE65fXzG7viHPU4bHI376F/4UZe6jtnywIssJW8+C0Gcbgp5cB6zuF7i+vAhMy8Tv\neYxPhpgtxTdPRWZz9ORIrgnCmLpuqAphhqmKAnVDuk9Z5HOKvCSNU6JwTxztiJMdQa/L0fl5S/RV\nD7umB7H06GQsu9/joZCG05yz986oyordYneANpZFTpal9McD3MBluxBQwtf/+5/n7vKW//Br/w61\nMVBQQVFa14LJdrEl3aesZ2v26z15kh8s64Op1Ks2sx3zq7nsRouC+8tbvEBcFg85yHgbobfeh2gb\nHajJ+1XIv/+3v0VVlyyXCxyvQ284YjVbkKcZqn4maHNdZbde8fF3PuTk8QXdUZfXH72VPu1a7GPJ\nPiHo96RXHHSwPYEr1JUg33eLLW+fX5KFCdFWWjST8wmdYXAgnCjF50vo8rlb2EzbOmzrBXGdQEML\n0msoi5w8lRxRHMaUeYFh2hK7aCrySDqHD7YqryPdziwROXB/OmB9vzmgibQ2eEkDVS0X1EVRsLi7\nkzdmLUDCB2GIgsL6boVu6UwvjmUcr2tsFyuWd0t03cTt+O1RqpI4Si27h7IoD4l6v+dz+vgZi+sF\n83SOqoiXUqawGq5ns1usWd+vsGwH3TDIkhwaC9uRDuODaKQqSoo8x7BNepM+hmW02a4A23HYLXes\nZgvmt3ds7jeEyz3hbku8j9ht1qJ52ydomkp31KWqKrbLHaZpoHjSHNB0nWDYI0sS8iw/LKiHE0wb\n/HXbnbSqqW32TBDjWZxTlRWOY2G71sHrultuoYEGGQA0TYNCg6orh5gCTYOmq2it4k5VVRxPWGl5\nnhDv9xRZhdfz8AIX0zCIo4j1Yk6aJgfZie3ZUDd0+gHn75xy8/qKqxdXBEFPnLAPoFJTFqRoIxPH\nqqrao7dM5sdnI8bnE8LVR8RhjKLIUbvICxQVDFejo/gHPwYgk/F9zH61F5erqXP56oY0jijrnMFE\nxQ96ZHEqkNGqatV9e2mnJDGqKr3W5c2KcL07oMvzFhPlBu4BL//QJ9Z09aBbTPaJfD91jd3y6R4o\n1Ptt+OP5wP+Qz+duYaNp5FhFQ5HlZHGKqsqbNNxuub18S1ODphlMz4/we+3UaBtyfzmnO+wxOZ+i\n6VKCP3t6IrRcUyNchXzv17+L7TuMLyaEyx3RRtj0ti87Pr/n0ygl3/6t36ZpKn76T/8ZxqfHrZ4t\nPiCeH6IQ2/m2xd5UeH6Hqqgpshzbt4l2exY3c0zLwvE8nI6D4zsUqaC/N4tNK1mRIHKRp9x87zWq\nNubRs5+GqmF+taQsCuq6YjAd0BkIgTfa7ttCtjQRoigkGAacPD0h2sbcvbrj4ksX9CbSf1TR6A8n\npHHE3eUVk/Njji5OuHt9S5EVfPRbHzN9csy7f/I90n1KkeYMJoLfvvzkmjzLW/fCUIr1q31LGknZ\nLUOW10sUTY5TmqEdjpvhZs/1p1cYpknQ7zI5HtEddsizku1yw2a+wnYdvK6PZTt0eyrDk6GYsnyp\nyhVZzuB4KLDJuiaP81ac/ZrF/BrHCnDsDuv7NccXR3zhJ9/h4+9/wG/9X/+Wo5NHjKdnsvAaOk/e\nv0DRFIlHFAr9wZjepN8intqFuvnB0GB4PKCh4eqTS9IkZbfcySLSlcCr49tsV2towO34rJcLXr/8\nkKPjRwzHR1iehe3aFJ64bMNVyNGTI46fHvP6eyrJ3sXtuRw/Pubk2Skvv2NJFjEQSfLVi0s0Q+XL\nX/spTNNqHbgeXtelbhryJCMJ5R7zgV4DshFQFBXbdw71vunjKXma8+p7r9i/uWe32HH89Jj+UY+3\nH21/XJ/4H+r53C1spmNhOXLngaJguhZ250G1J0dFp+O1VRyLum5IkoSqKltwodFq6jws1zwEQVez\nOUkoOGerJZHK7ilB1+VOSB9qGL6DaoLXkYmfXOKqaJomR682Z7Vb7YjDSLqppdRwDMtC04VF9kBm\nNSxDyB/94GBdfxjP53GObhrohiFKOFUV+9SgS94OSoYnI6pSRLydXnBAozueQ92vCdd7yqKgO+yK\nb7SUN/3D0Vq+xz1ZkqIbJqZpSfhT1aFWofVF1HVNmZVk0Q+qS/FedsuarmIqJoZpSJxAVVqDkkQI\nws2O27fXBIOudFXzkrxByCxl1RbSG9IoYXW/kmDubCm28gZoHRh1XVFVRavIqylSidW4gUeR5yRR\nDDUUWXmYQqa7HP9IXJpZlEpMqCjleLvPaGqlnTjKn3GjQBKlzK8XFHmF7bptzKXA7Qci+YGDf9Zu\nseyD6YCmAbfjiqR5Jxf+nUGA5Rk0jYKum6hmjWaJ3IWmkZ7mbkeShRiahW3JUEHXdSGPuLS4+A5u\n4NEd9cQgVoiU+SHwTaVQ5hVNoxxIukUuf15ZklGUGXEUMjwaY7uODC4cE729l9MN7SB6Nm1TwJir\nULJ7iiK4+s/R85kL27/4F/+Cv/23/zb39/cHU82PcyrqdQUyqbaRj+64S3fUbSMJKpblMj075vy9\nCxY3S+aXM9aLBZ1Bh3e++r6wxl7dc/ruKVXtcXc1Y359zyff/YDecMDFO88kE7bZk0YpeZpRGw/N\nBRMncHG7Lu9/+WfYb/ZUWcPqds1uGTI4HtDpy5s03kfMr+UY5QeBTPnaI49maK0kV2V8MqU77uH3\nvLZqVBMMgh9gedq7myLLcQOXL/3Jn0DTNS5f3aIocPLsuI0sQJbkclROi0N5Os8KNF3l9L0zdENj\ndbdGVVVO3j2hzEvu39yzmi2k+OyJ/q03EdH0/Zs7Nuslju8wvhijoPDid15IK0JVmL+dyW7WtQ7Y\nqGgXUaSFTA19R7BFeU4S7+kMO1i2yX4V/h5hzPTiiM1sw3a25fvr59R1RZzs0XUdP+i2mcOGNI3Y\nblZUlYhqgkGP8dmYwfGAF9/+hLtXt5imhWGbcqHe6aGdmpw8O6Ez6HD76S1pknF7NSONK0bjcyzL\nkyyfb6MaKrdXsxZeuabMK3RdYzNfEoeGNBV6NpYjjtemaYi3kh07eXYqg49WnLJbbGnqht64z+Do\nKXVds13smD6ZYtqCPkr3KYurJXdXV3z68e/y6Nl7fPmnflaOm61R6pALzAqSMMF2LTp9n9XtGkVV\nOH/vgtX9iqvnl3THPbqjnvRSa4F/7td74m3MLlxSkwu1+PT4cE2BCrZjoSgKbz+8JNpGBCNZwBdX\ni8PJ4/TZ2Y/l8/7DPp+5sP3yL/8y//pf/2u++MUv/ii+ns986qoW/ppp0Ol32K/2lHmJF3ioF1Px\nLw676JYhgdSOi9M5pTMM6I56VEWN4+8kr5MVstOrQVMtVEU0Y/1JH13TSMKYeB8T7XcotzVVVXLy\nzqlQMkZ9LMtG1eVeJ1yHcizWVeJdRJpk+F1BFdmu0+7SaiGB1KJoa5qGJEykluQ7aIsdcRwzu5wL\nsbffYZ2v2K1CgmEXVdOYvbmX0Gst9z22rpG1bK5oKzscy7XYbVas5vcYuke3P5DdpGOSRhmmYxIM\nA25e3JDsYnrjAc1QpCBxvGf19o7+SArrbs+WF4mq0dQS8m1oUBXZlemG8P7ruqHOhFqiuSpJGEuS\nXVOl9fFYSvx13eD1fHRdk10ODft1yNHFlPOnJ7z4/gvmtyscz8XvdggGvdbRmmHZLkEgFGXblZ1p\nuN4Rbnak+xSv47UVIxnOBMOAYBjQ6ftUVckn3/2AZJ/gDzyKtML3u22/uCIJY/Iko6pq+do3IU1d\noygK47PJoZmS7hPJg7W6xqqsqEqRWKMoEjxe70XqrOsy6Ckr8ZDqGoZhYBgm89mMcBWimRrHj87x\n+hbD6RH9aZ+yJWyIXDsliSM0U0gnEmsSorPeav6Gx0Ms22o7pNJjtWxLdmOWgWaojE8mmK6BYVps\nlmt2643QefsD7uM9eZbgeoE0Kdp70fH5mKqsuH15x+B48OP94P//fD5zYTs6Ovpjs6gBAr7Ly4M7\ndDPfoCwUHn/lMV5PQpcCYpTQptf16Y66UvJt82i2b9E0NVkiQVFVUfE7XXRDbEb9UZfesMv95Yzl\n3YIk2YshfRuJ3m7ca2tBCqqmCU1jG7Pcx6RJCk2N5dmMTlr3gKG16fia+HpOkRXYbk8AjNuIspDv\nR1EVsjhjtwzpDDocPTlis1gT7SL60wGKqnD96RUKCoMjoT+oqkIcJsQ7yYipmopfe8xvbnn58XNO\nz57R7Q9aE5TEAhzfoTvucffqjqqsGZ+N0S2d/XrPZjPn6vVLBtMBR0+OydMhRVpQtHJn3dIOF95O\nR8gleVoc5M9uR/qmq7sV29lWjsjDgOPHZ4canN/18Ho+naHcf1ZFzehiyOmTY+6ur7i7zvF7U7rD\nPo5vHwK+ruPjOh0sz2odqjaruyX3b+/oT4b0xn1RyDUN4XpPd9zl8VceoSgqm/mSJN2yXq7ZLqbo\nmkWn20UzZLiy3xTthXxNnmYkcXIYFkzOp/RGfcLNnnAlBngvlXzXQ+OhLIrDHVa43hNtoxZEKQFY\nVVVbVJYk+9d3K7bLLZPzKcePzngneP/Q3AjXIdVWMnPRbk+WiTZvfDomiVKyJGubGtL37I56nDw7\n5Xvf/A7LmzmOLzRpQR1J/nJwMiAYBuw3Ecu7GW8//RTX81Ge6Ny+fct2s+Jrf+7rjM/Goig0NHrT\nHrM3M+ZXcwlNf46ez1zYvva1r/FLv/RL/IW/8BcwTbnwVRSFv/gX/+If+Rf3+z2arhFtI+GDmfrh\nmHb98RV+v4MbSFE9CbcHbd3ydsluucNyLe4ur7j89CXj6Ql+0CONZTEYnY5Iopib11ccPTnCHwox\nYrAeiAPStumPR6iqxupuxfXLt9DAxXtPxG6+j9EMjZ7Xw3RM6rpicXsvb8VeD9t3sDybp1992rof\nNy2B1hHSwmp3+Hofoih+38fxHFRFY323wvYdBtMBuinHiDzJSHYxSZTQNA2jU4Fc7tchg/GUwdGI\nKoMsTnnxH18QjAIGxwMaIFyH9Kd9LNeSeMF6L8BFDLrBmLpUiXcJwaBDbhSsX1yzWiwIw6VUl1SV\nbn+I4/pomkEwkLe9pssOzXJtDCcmjRKyJD14FKJdRN4SdV8/fyEECqR8naU5imoyOT0hGHSJ45AX\nz7+DhoVry5WDGwht1/ZsgmHQxiTE/Sq4eO2Qcbx5ecnli08ZTCc4nsvpo2f0ehFV0dDpOVx88YLd\ncst2vmW7WlPmBbbrYbnSF+0f9ekMOkSbiGh7c+ggTy4mLG+WzN7ct9GJhv0mpK4bTNOkrpoWRGBi\nexK6LTJBAwGousZgOsTv+8xv7tguV/RHIxzfxbB0FjczNosNdf7g2BW72uhkRBpl7NIdmq6yzwpW\nt2t6kx6TRxO8bucgednOt5RFid/3efITT1nfr7h8LtBQVdGYHJ/SH/c5fedcalq3Hk2lkITJofPa\nP+q3FnkhAX+ens9c2LbbLY7j8G/+zb/5Pf//j2thowEJsonLU1WVw8Xzw1tMsDEpRSEYn4f+XRqn\npHGCojZUdSVF612E5VgMj8ekccJuvWW73NKbDDBdi964LxSJVqpRlTWb2Ybl7RJVVRgdT6lLqbGo\nmopmaJK8LwuaRiZ2aZzhd316gwB/0KEsKuJdhKppaKYQLXbLnVjn8xK1NaY3TYNuyCCgaWqqosSw\nTAzzAeYotSQFBUVTUHUo84I4jHADl/54SLiKiMOEcL2XD9TxUBayTYjjC9lhv94f0veqqtMfTtBV\n45A3k2AolHne1nZkl7tdbkh3OaZlS9/UNg7InqoUzJHty1E2i9OWetK03tGKzXJBU4PjSLI9TTLy\nVExVqqYJwSOJMXUFxVEYTvoMj4aEYYRqaHiBy34j0EdF4WA5l0gIbBcb7i6vePR+zdHFKb7fQ8Ni\nc79B0zWGp0OqFlJQ1zV1U7d+UQtNk6Of23EJV/tDjMTyJAC+vl+LJ9SW+MQDWSNT8kMdqmnViXkq\nEaM8LYijiKLIOXvnnG6ny+zqhmgXURfg+nKq2G/3FFmGaToYlovdkd9TVdWW/CF3qnUpL8E4lJiI\naZn0pwO2czHN54mQZwbHA1a3SzazTRsqdxkdTVvasU9/NKQuoMwq9ps9ZttZVRAiiePZVO0u/fPy\nfObC9o/+0T/6EXwZf/gnT3Nsz27vDoRA4HV9OgOfpm7Y3G9QdVWclftEiuaP2gjCes/5s8e8/zNf\nJN3nxFtBxjS13HWVWYVpOGzutxjGDbqp0+l3sJzH5FlBmZXEu5gsTtEUk6asuflE3uTHT49Z3ixY\nz5ZoSw03cDl79zF12bBf7RkfDXn87gXXl/es5psW760TbSMiBJi4W22o65rh8QjTMZm/nVOVFePz\nCYYlUYbNbCPuS9+h0/Pxj2UaF+/3vH3xkv06hFpju14xu76h0+sR9Pt0x13cwKUsSu7f3vL2o1f4\nnS6O94OsUp7mGIZJd9DFaOMY0S4+LAKdoU+eXRwW3c3dljiUO8M8yYk2Edv5lvX9iiyV4vzFFx9R\nFRWLywVez28x50uSfc7o6KjdyeyIdnvqpmGzWFDkOWVe0BkE/Ox/8wtkUUEeFbz7hcccn0349OUV\n+0RaDfJy2ovlqpQ7Ma39+jRVxzSl+ub4Drcvb9ktd1Qt8DPayM7fcmyCQY+mbugMAkGGxxnXL65o\nqGURGp3Q1DVZlLG+XVPmpVjWXcEmme0LYjffymTbNQnXe7bzrbgVbOnYzu9vuH37BtPWmZyecPzo\nnN1yy/xmLhP0uqE76DM8HlOX4kkNRh1UVePy4ytRGp6OiDYRtmczfSyY+t1yh9Ny0x4WwdIXYEG6\nFxqIaQvrTtc1+pMehi2U36qshAizS0j3Kd1Jl3KxZXEtQ7cHqOXn6fnMhe3y8pK/+Tf/Jr/+678O\nwC/8wi/w9//+3+fs7MczJXF8CdvGYUS42EEjdIfdeo2m6xiOJUTVFpYHEo58QOYEwx7DkyGztzPS\nfYbX9Q/3JEWRU5Y5ZSFp+jiUVoNMphQ0XaeuMkEzOw5aO+VUVPVAQrUcG0UVg7iKBorc9VVlxX63\n5/rlGxb3SzrdHnXVoOoqWZIS7/fQcKjWmK2p3LQNGMhtbpZkJGHCfheyms0oyxxFVeXu0LaklVE1\nUIu13vRMKNWW0FAThxFxuGd1vyKLcjQSaOTXNzRSGh/5nL93RtRqALeLrYijPZtg2MV2p2yXG3aL\nrfy8TYk9FHnRuj0zmoZ2MlcT76SSp2oqfs9jcDIkDRPKvEBTNTBN3MDDdiXDp1kjqrJEVQxsx2Ew\nmUiKvtxSVpXYtZYbqqZhOO5jWyZ1JTGFwpDv07RNvJ4vP3tTBh/RNkI3pJmiaSqGZbC6XQES3TAt\nq5XnaIBC4zRUdUldVxiWidl2e7M4I237rQ9uWcPU5X7XNqkLGRSUWSE7b9MAmpYA7GPf2zSVuBvy\nJKfT76CgsFuHBL2A8elE0geKIh3XdsKbhDH79Z5GqVsHhIrtSa0rS9as7pZMLHGjqqqKqims79ds\nlxvyLKMsCvy+30Z9JFKk6RpZmUuu0JGGwsP0tcxLOV5XlXDukv/KKlXf+MY3+Mt/+S8fBMb/5J/8\nE77xjW/wa7/2a3/kX9zv9/SnA1Hqzea8ef4pnW4PVdVYLm4Zn0746te/xna2Y3V3S11WqLrGbrHD\nDVwcz279iBJclDCj7PTCdUieZ+yjDZp5geWavH1+y34TYdlSUO8f9dFj8Y/aviOwymmfzWzD5Ydv\n8fsdphdHqJpGVVRs5ttDRWq53LDebPj+7/wuu9WGi8fv4QUBtmOxjvaE2y3Ts2OCgRAhdFNnfDaS\nqWIlk7aqrBidjSkvM16/eM56viRc7BmdjuhN+jz90nuUeclusaV/PGD6+IiPfvM5ty9uhRyRpyzu\nbjFMm+5gKPklSz/s2BRFoT/p8v5PvcPr5295u4lY3i1p2l2kG7gMjgbcvL7k9fNP8YMehimEibKV\ntNiezeBY4iL7bciL73yE2/E4Oj9t3/4duuMueZYTroQXNz6d4gYObsclGEme7+71vaB0WrBnWVW8\nvbzj8uqeNx++YjQd8BM/80W2vQBVFQvUA37I7bhyFJ/2GCcTbl/ecffqjvP3z+hNemiGzvp+zd3L\nO4JhILBJFMpSjo4PVvjepNd2ehuiXSwgzocq1kMhvqrQTVkwHc+mqRvW92vCzZ7x6UgwVVWN49t0\nJz12qwmbuxClkaP+g8GsPx5y9s4p7/yJp7x+/obtcsfgSHrMm9laTFVVxc3rS6Iw5OzpIyzXPsjB\nF7cz+kfSOXUDl6ou2X6wbiuHDdOLY3qTAdF6j6opgCJRnZZKgiLy7geoQpbInajjOTi+e0BMfV6e\nPxRo8hvf+Mbhf/+1v/bX+Ht/7+/9kX5R/1/PbrVjMO1LgTsKaRruROcoAAAgAElEQVRwPJfhdEx/\nPBI6hGPSm/RY3s7YrbdkWULDkGDYaS+XG6Fz9KQ/2TRCr+h0A7J4eAjSjk7HOL5LGqY4vs1g2kdV\nlJbRJgIMq81wHb9zIguFqR8qXoqqUBVVS/EoxMR+fs7xo3OmJycierFM7i49FrcLjp+c0B2JDags\nSuaXc6E+OCbL2wX7zV4umHWL6ekZSiM7j+HRgMG0z2q2oShKglGPKq94+8Fb5jf3hOEG1VAEBWS5\nKIoqF+WeLfgb22xDmB5VVfG93/gem2XYGsY7h9zgbiGxinib4rgeftfD70oouMyFvCFhT4kZeIGH\n7Rsy7NA0kn3KZrahLCpMx6IzAJCq2Hq2YnF7x7nyGMMyePPJRzSNwqN33yHchKzuFuy3OzRNo0Gh\nquHqzR277b6FJsr3ounawTxVlQKxDNdbdqsN+YchwX2XwXhKkYp0GUUiRHEk94xVWeL3OliuRbyN\nSCKpL9muzfh8TNPIAjCeDvB8l/n9knAX8fbD122wVq5ITMtkdDykN+6yvF+TJTnzyznxJhY/hi6T\n8ixOqesGw5KFbnY1Z3W3FpNXVuB0XCzHPHRJdU2n0+3i+I6IpxEAalMjoekWMb5b7lA1nbou2W6W\nmK5gj+T00XD3+oYHBHsUiaLP97ptJEhUlEKzkeuSh13q5+X5zIVtOBzyj//xP+Yv/aW/RNM0/NN/\n+k8ZjUY/iq/t9302sw3dUQA0oNSUVYqiORw/Oj94O3VTp3/UZzm7JwoFD+50JI1dN8IDe3grPwAf\nHd+hLLqUWY2hy73J5HxKOki4f30vXsauQ55JkjvaxZR5SbyNCUZCbM2zvEUpVwfXaRanxDsxIZmq\nyaP33iEYBrgdB8e1cWzpHuqWxehsTKfvAw3zywU3L24JRgHdSZfV3ZLtfEtv3MfxXM6ePJEjZlEy\nPh3RHQRcfnRFUZb0Jz1ml3Nef/8V+3BDVRV4VQfbcel0e+SphH6Vlnn2wPYyTIPZ2zu++++/h6rq\nMkl87xTbs1sjU0i8i1EUhU63hxf49KY9jh5P2W/2XH6UAQ1VJXwyv+sLnbeuScP0cNSRibZx0L1l\nUcrqbsF6scD2XCzX5NVHH6FpOv3hmHAVsrpfCP3DNumNB5RVzcuP3ghppeuLgtGTSEK8i0VGnZfi\njthHpGnE3YevMB2Hx88KXF/gBgpK29FNiHYRVSHO0M7AZ7vcShVMVWS3OQwOndLp6ZjJdECW5Szu\nlty9ucF2bU6enrVXERrdYUB/0me7Ctkud8SbmCiM24VfjoLJXhYMTVMJN3uibcz6fsV+s2d9v6Y3\n6fPoSxc0SI3LctwDAaWhpsjzg9mszCt26x2zNzPSfYphSrOgqBKi7Q5Ld+kf9Wmahtn1jCIr0FSd\n9XpGmu1598tfpjtwSaIE0xGySpZkbSSn+nF95H+oR2ke6gR/wPP69Wv+xt/4G/zGb/wGAF//+tf5\nB//gH3BxcfFD/6abzYa//tf/Ot///vdRFIV/+A//Ie+++y6/9Eu/xJs3b3j8+DH/7J/9M3q93+sy\nVBSF//l/+VVOnp2QxBFRGOIFHqZtUxcNZS6gvgd5yuzyXkS9D6Z0RSY9qKC21qAHPn532GW72DJ7\nOztkftQWNZPuU6L9ln24wQ96dLp9gkEgTgTLkIJzIgVnRZFGRBqlLK4X5O2d0wNOaXg6RNM1Zm9m\nlJmo7pS2v5fGSYuX2VFmFU2pMz6bMDodsZmv5bicyE5rcDQQv2fdHO6N7t/cU5aCULp59ZaXH3yM\n53UI+n0mF0cHWXS6FwaZYRnY7Tjf9mzqsqbhYaIoWrmz98/QDZ2bT28wTIP+tMfdq3sW1wvsVjV3\n9OSIxd09z7/1PaqqRDcMjs7PCPoDSbe3/Uq/LwvQ4mpBtI0OhA1N11jPlqzvV/RGfVRd5f76miLP\nsWxHKkRZxfBkhO1ZLO9m5KnY7ofTMZPTY2xfSMZ3r2/Jk0zCwK29yglsVB3uXt9Q5CX94eiA/67a\nipmiyAsvXO3bCXhHjGRlhdf16I66jM7GWK4lQ4swJd0lxElKtI8JVzshqCgK2/WKOAr5wk99meGR\neFsbkL5vVgi/z3dQVbWdgBYo0E5O8/bnInd9tic/46qS+714G7Pf7dhs5Y7Vtl08v4vX6ba52h8Q\ni+Mwxhs4jM77bO9CwmV8yLa5gdtKuRvmNzO2izXdYR9NN9ittmLlOhriePLSa6qa/+1//Z/4jOXi\nj83zmTu2x48f86/+1b/6L/qb/q2/9bf4xV/8Rf75P//nlGVJFEX83b/7d/nzf/7P88u//Mv86q/+\nKr/yK7/Cr/zKr/xnvzZLkkNEY3LaYTDtoxka86sFWbwjjx8urxVs18V2XSmW/7/cvUmMbdl1nvmd\nvr99xI329dkxk0yRFMsulGhSg4LLhTIgG7YAQbABEwUJMGDDI6tmhuEB4YkhW4ZnlMEBB4In5Yk1\nISDKYEmWUyJFUlS2L/M10d/+nr6vwTpx0yqSRSFtkiD38L18GTci7t1n77X+9X1FyXa+kYyRqnQO\nAlXmGzWZb5TIhEqe5gJk7ECBXt8jSbYsbxbomkV/OJaT1KTf2edDNrMNVlfovXVqlllBkUtwU6/0\nXYK+qmrmF3OSTULbtvRGAd7AF3Hzcs31xTm6bjDZP9x1K03bwuu1lNlaIiRpvANe3lqFblvyRVZ0\nRW8NN/Dwez1BBnVuSk3TsFybcLVlu9zQn/RoLCke9yd99u/uo5tXrGfr7tqdEm8jeiNBSXv9kGhj\no3YY9O1iy2a+JtxsaZpaiuhNs0PeaIbUJQ3L2AVUi6zoNr2WupET9HC/k0dnBb3+hDxLicMttAqW\nYzPcH+H4Njfnl2RJgtf3BWkeuB26vMayDFTY1U7tXATQigLhItoBJQFhmjUCrTRsAxQViCgLiQsZ\nloEb2J2pyd2hsltaZpcLlhcLhocjesMATdXYLrdsZhvC1YYwWnL57JIya6TGFohj4BaxrhtilVK2\nilw+VGUXD7kdzWrblqqqWd7MMS0Ly3FQdTGYRZstcRSiqxYHJxrj6XQ3e2t7ojAsi5LR/oQXPvES\nj5vHhMtnYop3TUYH4931F8CybMG5p/luZK6pajRDww2c3djeT8v6gSe2f/kv/yW/8Ru/wT/6R//o\ne/+RovBv/s2/+UhfcLPZ8MlPfpL333//L/z5yy+/zO///u8znU65urri85//PG+99db3fN3/45d+\nnenR8W74/ODBIV7PZT3bkGxj6VrFGUVeMj4c4fgO0Vr0aZouVAnTkRZ427T09/voht4JdwVFE22E\njd+fDBkdjNk73qOqBCNeF40Y4R0BUdquLWjmizluT4bg19drikzeQHmSy3hN52ds2qbrpBlyBYoy\nFEU6c/deu4duabz5R39OXTaMD/cksd5K9/Q2hhBuVizmVxycnnDnhYfUZU2e5mwXW3RDruF1XZEl\nCXlckicFZS5p9WDUJxgEeH2Pt7/55ywuZ7zw+st4vYCwm3e988opN89umJ8vRGyz2rC4vsILAjmJ\njQOcwKXKS+GkbSR4m4SRSJUdC8t16Q377N3Zk0xX23D5WIr4bSPfjxu4xNGWq7Pn7B8dcXjnlPVs\nLdddVUEzZFOsioq6qDh+4QTLtXn8p++gmRoPP/mIpmqJ1wmWbeJ4Nv1hAChsNxGKpmLaJldPrrh+\nesnV8+coqsLJ/fu0jUKyjZneO6A3Drh4fNFhxRssx8LreTIepuvolv4hMjsTosytj+Dln3+J3qTH\n9dNr5hcLVtcrFrMrNqsFo8mU4WSP/qSPaZmSk+twUpqh7VSHt42bphY7Vhp1IuiyJk0ituECP+gz\nnkzRDB1VU2ioSKOEzc0GXTdwfZ/hwRCv75PFqUixTYlDDfeHfPCd97l4LNfl/l6f6b0DCYYvwk4/\nqXL95JosyemNAwzL3EEaTMfE67n8X//nr/z0n9g+9rGPAfDpT3/6L2CBb6mdH3V98MEH7O3t8Q/+\nwT/gW9/6Fp/+9Kf5zd/8Ta6vr5lORfA6nU65vr7+vv/+nTf/mPfe/iaapnN0+hBFE1a7qmpUZUW8\nlSvOoC85nZa2U4uJPT1PUzYL4aI5noc/9NE0bScqiaMtbduIlNkwdgLiW4lLMOiJoONyQbyJGR2O\n5INX1riOTTDwWTybkWxj0f11YEK147pVmdATJscTqqJkebnssEYl29Ua27MIBj003WC4LzXDPM2x\nukFlWigKW+ztui41vaoW0GKcYdoGbd3gBT798YCzd5+SxCG2I/Yov++hm3rnD7Dpj/u7NzHIaW+7\n2O5Omm3T0tZNh1gPeZK8y/7plPHBBAWVumy6mIqD47md3Fgj3soImh9KxECYcDKcX7dS1N+u1iLT\nibqQ6TbEsHQG+/1O0iJZbKAbpq8o8wi/30M1VJIwpkgrknVK25Fbiqzs+GHxbkRJDE6Cjm9p2KyW\nBP2+TGooDev5kixOJT9XlRiWnC6LvCBLM6zK3kV2qqLsRuAMub63IoXeLNfUTcX4aIyiC3bcdlza\ntiGNEqqyRDcMdF0HBcqs2F2DBV9udQSThrYVq1jbFOiG3kWLxFeq6hqmbeP1R9TjGsfxqcsaRVV3\nGO+6qqAbO0y2MZvFiuX1grIQLpuma+SJuGy3yy1e5WE6BmmSdHCCMaZt8uSdt3jy+C3atv3ZmTz4\nm3/zbwLgui6//Mu//Bf+7jb68VFWVVV84xvf4N/+23/LZz7zGf7JP/kn33PlVDpMzfdbn/orv8jF\nk6f0BiMGowlXTy7QDJXjR3cEgDhfcfryHR69/oirJ1dE66hr6UtN5f0/u+KtP/kOd198gWDYx7KF\ntiHmqYTLp885vn+XvaMDjG7O7+LxBUkUUeQJn/lf/wrHD464eO+cOEwY7PV3Jvfp4ZiD430u3rtg\nNV939RIZONd0DU1TpQbW87jzyqkU08sKbZOQhjHvfPNNFA3uvviI8eEEv+9T5MWuJiNikAbDmnDy\nwilVIYBG4fhX5GlG08jpze17uD2HKNywWc44+aufYv/kAFVT2dxsuH5yjRv4jKZ7OK7d/X91siTj\n4vHl7skcjAKxPWk6NxdnPH/yDsv5Nb3ekN5wTG84EPt5t3nf+geW1yvWN2vKQugiVV4RjAOOXzgW\ngc3VnOX8hqZq8bwh6Tbn2Vsf8PATLzC9cwBAGqasZxvcvkswCnj63SdsF1uOHh6TpTHf+L3/iqFb\n9AcTLMcizwpunstDpcwrnMAhGAWCYtd1bNsliUMunz6j96mP8dovvMa3vv4NHn/rHYL+EM1Q2Ww2\n6LZMW2xX4vAcTsf43SlX1QKJlWgiTI42EdfPQp6+/QGDvQH3/6cHUkv0BSZa5CXLa6lHTu8cCSrI\n1IkSkd7UVY3j2/gDmb6o64Zg1MP2HCGYtD1M+85uc9Y0rQNpSt7RH3gdeBUsT97LVmbTklEVJYvr\nOVfPzlFawWaZttQ10zAh2Uo27tYFu14u5XdVSu33+N5DAn+PNEw5fuGYr/3u//2RP/c/7vVDa2xf\n/OIXv2dj+35/9pddJycnnJyc8JnPfAaAv/N3/g5f/OIXOTg44OrqioODAy4vL9nf3/++/952XPxg\ngOv7OIErA+20xJuEZBuRJjHr+ZqrJ9dSm3IsoZ4aOlVeoWkmvf6IKpcUvyjPFNazDeEyou02DyEr\niL1nendKtHFZXS9Io5z5xYKyO6UtL5fCPwscNpuIqm6wew79vR6b5RrTthjujaUmst2iKBpZ0pOZ\n1kJ49CKMcRgwEhijYVBmJWETsl2u2a42BP0eji/wwjzLmJ3diFy4rHECD9uxOH3pVNR2Zc3Nsysu\nn1SsZyupOdJpALugZTAKdqLdaB2RxinRKpTXsTcgT0vRCBoSX3E80RY2TYXr+/j9Hr3hcEcINmyJ\ndyyu5szPb9guhG7h9V10U6gYiqoKRVZR8Ac+/f0AFJW2lthDkeU7+c52saauG2zbIVzJaNR2HqK0\ncj11DZ/hZEJbS/g32SbQtvQm4ndYXa3EeRGmGLZBb9InSSKqquosU5o0RAyT6d0jNvMVZVEymIyY\nHO4z2B9geTb9SZ9wFbJdrAnGfXRd/1DMoir4I+GkTY72u+urzFn2xj0un50RrrbYtttJqwUhfluH\nbbvTXpkVEhGqxWdwew2uq7oziZXCvdO0XcOrLGSkLg2THbJ8/v41eZ4yOTjA8WyBXgYe916+z+zi\nhiSMUQ052VmOCIYUVTKMLS3eyO0ewBqGaTAajXZ4pSRMPtLn/Se1fuDG9ru/+7v8p//0nzg/P+cf\n/+N/vHuCh2GI0cH2Pso6ODjg9PSUd955hxdffJGvfvWrvPrqq7z66qt8+ctf5jd+4zf48pe/zC/9\n0i99/xdsmAxG0tWyXQvTM6mritnTOZvlhjyX6ECdN4yPJ4ymw92sWxql6JrJeHpIlZdEqxDD1Knr\nmvmFgA0t05LrXne184c+hw8PiTc9lFYhi3Kunl53HbOKWTd2MjoYMb9ZcXO5wB94+COP8w+eYhUi\nPQnXG66en2MaNnmaY7s2Cip53JEaXFv0Z6oCrUISJrRNw+z8itnlDf3BkPHhPscvHFPkmXT/shxF\n1ZjqGoNJn/27QkA9f/ec2fkNi+sbmqbG6WxWWZSSJVIU7+/3RUISC+E2XIVE2203ZD8RTHScU5uS\nx1N1RXSGnghP3J6L3/dRVEWE0JqK23c5e5xw+eQCRYHB/oj+Xh/Tsthq2k7rpukqg70hB/cPUFSV\n7VJIxSId1giXW56+/QGGZXL/lYdsL9c8efsxluXSH41oW3GhHpye7HDWaSQb28nLp53LoCLdppRF\nSb8vJvPVbE5TNfTHQ5pS4cmfPWFyPOHowSmLm2uyLOXo3h32jg8Ixj0G0yFFWvDnf/QdNst1F9GQ\nemyVlygKBOOAYNRHVbWuKaFgWoKdj7YrVosFD1/5GKbuEC63u432FkgpFOimo4oU5EnO/t19/IEv\n4pjuVGe5Fk7g7ALLtwrD7XwrgXHP5uKD52xWS/qjIa7nyYjYsMfkaEJZFMShGMqcnkO/u8XQiu+D\ntmUwHaKqKvPzOZquMTwYSo11viVP8o/8mf9JrB+4sR0dHfHpT3+a//gf/yOf/vSndxtbr9f77w7o\n/tZv/Ra/+qu/SlEUPHz4kH//7/89dV3zy7/8y3zpS1/axT2+30rjiP7egDwtuDm75vL6Pao64/6D\njzPYG1LXIrvN84SHr93hwYt3yOuK+eWSxcVCuk6OxfTeFL/DzqxuluRpjOVI7cvvB1iO6NUURWF1\ntUJRxIB0S6mINluSSE4AcbQl3oRyMtR1ZheXFHmO3+thudKR9ft9Tg0hqfaGPU4enYiPU9dkDrWs\nCFeiPFNUVeQzfQ838Bk3EkLWDEEktW3D8cMTrs8uuLm4Yl/ZR1FV5mezXSZvcrSP7TkdlVclT0rm\n6YKmqoXQm5cyhK8J3sbtubg9p6ONdJ1CSwxVSRxy8fQprh9wdOcuqqrQdqiepm4Jl+EuFuH3fE5f\nuIumqTiBK8HcuGOYeTb+0MfriVZPURWyREbUboXE/sAnS1XKKiPPUjazDY7r8+jjr6AgAMWLD54L\nj28w2M2p2r6NHTi7cGl/3MPxHMq83EU0vCCgyoXfr6oahmawvFrKg8XwcSa9HSk27GCYcqJqMA05\n9Rd5znq+IIlCWrXh+JUjNF1jfbPGCQTIuUkyolXE3vSI8f4Bk8MpmirdxbKsduFtzdA4enjUNQwk\nCFyoyq4Uc/t7MSyj8772xEgWJrvOpe3bO/LyyaN7TItDiqRikc7F3Vo3RJuI/niE5dh4/YAqr9gu\nQpIuyHu7zt8939X9pLMuJ9PJyeRnZ2N7/fXXef311/nVX/3V/64T2g/6f7/xxhvf8+df/epXf+i/\nbZqaYOijGxl5nhJHW5J4w/FJim2Ka9FyLAxXpT8O6A0Dbm6WgqA2dFRFQe1mBnvjHvEmQpkr1HWF\nYwkRw3RMiYB0hvEiK3A8G38YUKT5zmEqUhKo66obXVForXY3xjI5mNICm+US07QI+gMUVSUY+tie\nI5k7XaOOM9IoIVqHFHmJ7QjnrK5kJtW0bMoiJ4kiou0ax/cYTydE2y3KFRKZqEQmAtKxlXqXimlL\naHWzWFHmFYZhSkzCNHaGrrZtMbpiuKqr4i/oXKiGZVA3OXEYoWm65Ks6lE7bCh032oQ0TU0v7FGW\nBYre4g98LEfqREUqMYSqkg/1baB2s9iQxRl5nFFXnSW+aWjqupv/lJ/rYG/EcDomT3KiTUh0FaKo\nKoYpfogiK9AtjboqyVNxYBiWsatJ3n6fbiAPsngboqCgmV3HtarpDYbYvo3jiWwmWkXUtVwFFbrZ\nX1XbFfhljrQiCUMsy6bIcpljNoTWEq0ieuMRXjcAX5WVDJKrSKebFl3XCUa9bkKi3s0d30IeVFVB\nVTX8Ttbs+A553Ml/dMk+yhhURZ7m9IYDTMtkebWkSHL53ZW1TMjYNn4vEGdrC+FiS7JN5GrsCDA0\njUKJ4egayTYhSzKhewTi0/1pWj9wY/u7f/fv8h/+w3/gU5/61Pf8naIofPvb3/6RvrAftPxeH9O1\nGR1NuPfxe+zdGXH59Izl9Zy6WGDqHg8+8ZAXPvkCXuBzfb3k/PEFmqry8b/6MdaLDZfPb0jDVGYR\n6xpaBcOw0TXZwOuiplZqAVqaMrxs2mZHvZVxKcd16Y8H9Ca9jl0vdRIUhZOHdzAdC9MyuXz2nA/e\neYt+b8xoMpX5P13CtPE2YXW1Io5CsjihbVos12HvZA/N0AXX3RNszPtvvsPV8+cURcre4SH9UR+/\n1+fw+A40MuTtBsLn38w3zK4uuLk8p9cbYRgWy8UVtArDwRSv5+IPfQEirmPRuXWD0VUmNZ2D+wdM\njidyrQpsbp7NaOqW7SL80PZkmxRZRrRdU9UFg+2AJ++8y9mT93nl9U8yGO4xv7gRQe/JAdvFltXV\nEse3aRVYzzZsZxvxEOSywWwXW6qyREVAAHXZ7DRx4XJLuApxPB9ahe1sQ1VKp3J+uSHcmvgjoeum\nYUK0jonWMuZldNdDN3ApsiEg6sOq0xSKI0NwUEkoUp7B/kDS90kuNSYFHN8TaGaxT1kUXH5wxfx8\nzvT0mMG+6AeTbUy4ChkdjfEGHkmYsJltmJ/PRJbsuxi20Q2X59RlBS1d08AmGAUALC7mVFVNgMyq\nhqto5x6t61o6p7oQiBcXc44eHeMcOTKLmxYUSS7TMHklkY1Abh1N3XD95IoiK7E8Szh3fY/+Xl/w\nVUlGvBEU0na52RF4f5rWD9zY/vW//tcA/8PDuf+9yx8Iblu4VAam4WCZPo6bUaolKjqmaWPaNs/f\nfyIFfM0lCAKyRNyjg72BAAbna7y+mO5Ny8IJPIKR0BbquiYuI8q8kJGobjhaUZRuBEnGWgzL6EaT\nHDbzFfEmQVECGWcxxPFpmjaWI12sNElI4pAsTVFVHctx8TUfyzV3RirbdyhzMcZbjljRdV1H102K\nvACkC2uYFrbjoWnya1R1lTzLWFxfU2Q5waCH63nouklQ91A1neF4iG4aAj1U5CpTFiVtI6WGJI6Y\nX14zOR1iOQazy2vmV3Ns1yVPctbzJaitSER0Dc3Q6U8GGIZgjmzHoT8cYtpCYXEDFxQBGG6XMrO5\nvJ4IKaVqcH0H33dZ3qyYXy5Jooi6rrBsB8OQsSulUxVW3TXONm0RsJj6bi5Ua0A3NfI4JyTcBU17\n457EaYoSyzG7+I2MctVljdZNPojUJ5OTVSFUGMd36E/6LC4W0t3tOqGaptEb9dENjYsnZ1RVidX9\nP2+e3RCtpeZouxaOZ8s1Tqw0ZElKWeQMp2McUyIUdSWBbqECOyxurgg3W/KsxnZcdEtC5HVdd6Hd\navc6NF3DCVz8UYDlWN28qkaja1Sa2p2qpR7c1A3DfCSh61g2PUVVaDratNHpAG+78E7gEK62pGFM\nHv+MzIoeHR0BsLe3h23baJrG22+/zdtvv83f+Bt/48f2Av+/Kxj6aLpKvIlZXMx5/u5T4k3Ewd1T\n2hqWl7K5PH/7OX/y9d9ns17y1/73/w00lTf/5G0mJ3scvXDE9fNLrp5ccvrCHVRNcm69UcD+6R4g\nYpQszghvVizOl/IkHQcoqsJwOtphoRcXCwzbYLA34ObskpvzCzZzh8FkxMmLp3hBnzsPXugELRZP\n33rMzfkFaRZxdO8Or718TzYFhV0INF5/CH7UTR3dMugNRuiaTbgKCYYSoMyTQgaou7lLBYUkjri5\nPGPv6IAHH/uEWLFayJIjdFOnP+qzvFzy7K3n3Hv1HuNTQX/naS7Muu2aJ++9yd1X75AlU775n/+I\n+cWM07svoGgtq9m8u05ptEg9794rD4X9WTXce+lF7r74wg5ptHeyz/JqyZM/e0K4XlOUKcurBYZp\nEgx8xqf7TA8nvPPtx6znGzbrLWVZsH90iN/rddw9oaVIgd6gaVqcwOHkxRPCVcjNsxscT4CW6TYj\nXiVops7keMLhg0Mu379kebkkS3PUXE7WaZwRr2OGB+JZnT2f7T7QhmXsKBneQK5ieZKjGTKCVOYF\n46Mx4+MxZjcsr2k66+sNi4sFKOD1fWzfwezmOp3AZbBXM7u4ZH4+xx/6GNZIivedsMd2bYEQvPHH\nnD15wquv/xUmB2Kid3wX0zG5eXrDdrEVPL0nv3Pbt5mcTmRMsJHOqjhMOycuLck2JdmmBKNAiL4d\nmqvMSqzuIV11V9o8LRhMB9x99S6Xjy85f+eMJEx/Yp/5j7J+aNzjs5/9LF//+tdZrVb89b/+1/nM\nZz7D7/zO7/CVr3zlx/H6vmctbuZMTw+73FZBfzTEcT2qQuxMu81hE1NkFWVWsZ2HNLlOEgpfTLd0\n0jClzCtuzq47vV3TgXlb8rQg2SQd0UDBG3goQLJJpPbhqiiagmmY9Ca93aiNYZgEgz624+L1/V0o\n1+iYY8HIJ9rskSQRi8cXxNFmJ34WX4AriJxNIqFc1yIONyVJS4YAACAASURBVKxXN0xPjpkc7QEy\nDpZsYqq8xDD13RvSsA1c32N6fExvNMQwzS68qbB3vC/F+ihDNw2m96aoukoaJViuRd3UrG4W0Cjc\nefiIKm24+uCaoDfEMFypT9U1bdPsun5t05JsE/kaisQuslRiG5Zt4/gujKSm1Bv1GOz30EyVMqu5\neXbN/PyK1bhPvI5IooTepI8VmKgaDPfGVEXN4nKB4zn4owB/5KMaKuvZks1ihXvlUpcVmqYyu7qg\nbgqO791DU6XOFK2jLqsVEm0iesOALM+5PjvDMG0GQ3mICdVDrrtNXZNGJUVe0NKwnW1F82doO6Xe\nrXA6XITEq5h4IzGhW4zR7fhRGgnIdH2zZruQK7dl2xzdP0XTJUsmusYPcUl7R2MevPIyrhfgBwFV\nWRGtBaduWia2L6TiW/uUN/B2VA/D0Glp2cxXNLV0RG1PmmDr2Zq8cy/4fY+Xfu4Fom3MZrHFG4jo\nx/bsLtSbEC5Dnr35jHgluKK905+Rq+jtatsW13X50pe+xD/8h/+Qf/pP/ymvv/76j+O1fd81v7hh\ncrgn84ZpwXB/TNu0nL97ThIJ7bXpBoZNw8K2XMJFRJ0Kvnm73MqsZZTT1i3L6wW6oeP5/V0XKQ1T\nqfukJbouUossztnMRE5i1FKU1WwVr+/K6S4SL2d/NJS6mO90YzLNX/CH7p0ckMQRT97/c7IsIU8z\naBQpHndyjiRMKIuSYBiwOZsxuzpjeueA3l6PaBNRpDnxJt6x3opu9hLEd3p0557gmSqxYmm6hj+U\nbt/qcoluGRwfHbOdb4lWkXC9ioLLJ0tc3+PhK6+SRinXT2aM9g92lJK0Q6S7gYs/8EgjIZfEmxhV\nVbE9i/VsSbjeEAyH9MeDjnShMzocMZyKbOXtN97m7N2nROEG23NYXm8Ihj16kx6mLWFbJ3CYn88I\nF2IUG05H6D0dlJbZRU4axyiKiuMKWmc5uybLQl74uVdw7IDrZ9dEq5DNbC3Y9W2MP/ApipzLs6eM\n9qecPniwk25ruoaqqyiqShYlrG5kssTrrRns9YXE0UUrTMckiRLSKGV1vSTeSONI0N3qDoUltOWc\n+cVcGkNpxuR4j/3TKdtlSLSO8IdBl4trsByT4f6Qlz7xCfb2j9nMNhRpQVVUaIaOYRscv3CM4zuC\nQAqTzoqWMH8+Fwy7rrC4mqPpH4Iovb5HVVa77J3Xc9k7GBNtIs7ev0TvNIi3mHOA7XzL8mIpykjH\nYq+7yfy0rL+UMPkP//AP+cpXvsKXvvQlQNjyP6mlorO52bCaL1jPFxw2p/i93m7I2LCNLuxYc++l\nl2jamiaXcRxFVaQu0T3ZdFNn784epmVSpFU3pGzjVfL9iTW77UQh1g7tAy2LyznhakOSbAmGA6bH\nki/bLFa7E1xVVPKzatmJPJq6YTAe8/Jrn6Qqap6/8xS/3yPo98SNqij0Rr0uyAqjvT38foCmmqyv\nV2wXK1RN7aYZdHl9gSOMry6/VVUVeZbLByvNUQBN/dBpqmqSn7v1JgjdQsELAmGbORYARVoQrqSD\nqJsawbDXwSJl0iBPBdMugd6caBXi+B6W5+AGnhTJLaNrvBgMJ316fZ/xwVBOip5NVZRsFoLTtj2b\ncBESKiFezyVcbimKnDwV0fHtDKXr+ZRGQbheY3sme6eH7J3+NRS1xXIC6rLh6OGxREHystuMPaqi\nwvV8fv7zn4VGYAcy86lz8uhY5nwXG+qmghsY7PfZP5l2voxcJlHSlIv319iui2lazK+vaNuGo7un\nNA2sb1ZYrt05D1ryNGNxc4VhGtz/xEPaWkCUMr/cGddMg2AktcD3v/OBPKhS6X7WtUySDKcj0SEG\nEqIdToe7mu8tnVfVZQxtuC+qPJlMyXaU46qo2C6FYRitYlRNOuhZkhOtInRDI41S1rMlhmWKe7fr\n5m7nPxmP8EddP3Rj+83f/E2++MUv8rf+1t/i1Vdf5fHjx/ziL/7ij+O1fd9lO3JCSqNEOFtximUL\n9UA3xfhdlRVKodAbjzAsg83NuiOQNrI5WQamZYiceNhHNwy21bY70W2oi7oTqUh4N89kczAsA8sx\nBfO9irh+dk0cr1FQObp7iqYLJeT2xBhvYjRNw/EdsiijaWQG1bId7r34Euv5iuvnl+iage24qIlc\nJ28L3uFii2lYWLYDtUKapuRZjmmZuyuRqqs7xn+WJJSZdPlu5TVVXgEtXLKbJSzzUk6F3eRCWcjc\nomXb2I5EPm4JEcvLpXhbB0KUHU1HVGXZiZi1D8kYKtRVhdXYMrSvSoQmjROZrHBt8Rus5APi9X28\nvk8aJWyX690pJ0+z3Qc7iWIBBHSI9M1calH7J3vUVcXV8wvquqKqCg5OD3B9j6unMsjtD335GcRZ\np0qUDJxp2ezf2Sdchly+f0HTtJLCdwQrlSYZru/S3xsQDGWjT8IE3dCkrtpUbNcrVEVDRevYc+I8\nqLKKIpOr/m1UqCwK6rrENiz8vk+eFBJ8ruU0necZtmsTDHtCFV6FRGFIlqSorUZdSjFf01X6YwE2\nNHUjOPemARQqQ+TTCoCi4Pjy35RFSdWVIjRNEPp5t2GG61AaN10QOA1TcTqkWRdjUlC0Bk1RaVsh\nl/w0rR+6sX3uc5/jc5/7HGEYEkURDx8+/Mhkj/8Ra3w0pqlr+tUIXTcxTYsyK3Zdm6qsdm/Suq5R\nK5X9e1Pqsma7EE6/BFQH3Qkgp6lSMTdtQs7fe4rj+1hd/qssCpIw7sggwkETommNYZgMhnt4fn93\nXfL6PmVWksX5juhhOiYtbUefTXB7LkePjnD7XhdnaIi38X8zjtMnXIbMns/IkoS6rhkfTiRbZruo\nnX9U7zBEtC1JFPP8vQ8AhYPTE+pSoy5qUKTQ3zQtVSE0jjRM5WehaQIwTOVr9waDHdbcDVxs32Yz\n3+y6Z47vMDkZc/XBFdv5Bre74jx/+ynBKODOy/fYLrYsr5asZyuSMKZpa3rjAQd3jnj61orNbIlh\nOvTGA+6+Iky/xdW8Q/eIhKdNi50+zg0CDu8dcf+1+xI2XYa8/IlHoIBhm8wur/nTr/8x9156xHAy\nZn42p2lbaQp0JI3bB1TZeQjCZcj6ZsVmvhL/rKHzuJWN/7bwv3e6R7SOmZ8vsFxLmgGejT8SQKXl\nysnW8iXsXCQyyF+Wgoxq27YLtbZMj05ompbzdy8YToccPTpGf6ZzfVZwc3km2czFgPuvPmJ675Sn\nv/c2T99+zP7eHVynJ2I22CG1sjgjTzLaFlxfHuRlV29VVYWyO53d4pF2neFuiL5tGpI46zKA5Y56\nI+UNlYM7h2w3a/7sjW/S6w0J+sOfnYDu7frOd77D3//7f5/FYgFIl/TLX/4yr7322o/8xX2/5Q/E\nmGN7DuPDMe3t+FOSo2mqyDHUjnGlKFRlyeLmWt7A3MZEdLyOclGXdTevKZtFEkWoihAVDNugriui\njajq+uNhZz7XxGakKFR5hapocpQ3Jd6hqgIJrMuatpVWvmZouxOOorAzfRudI1TVVaLtlrxIduYj\nJ3DQTI2mqXbtesd3uivyLXdNYhplUWA5DgoKTdWgGRr+yKfpRDVN0xKHMVEYUhcSCJW6kNKZnaQz\nfAsfVHU5Efp9TxLwgUvbNKyuV9ycXzM7u2avPZDYRtPS1NIEqbvMWVXUXZxCpalq4o4Om8Q5dqPt\nmGyKokjjpmmBeheYbaHzDgzxRwF5Kqo7t+dR1XUXUdABlSqvSaMU04jJ4kw26yilcZoPZy67eEdd\n1TJXqsDhgyO54oYpm45oMjwYgQJJmJB141q3P++yEOCAP+hRFjnxdivdU082eNu1GR1OCIZ9esP+\njhZsew7b5ZqLp09pKEWkbBkEw4C8GMiNQO0CsIpo+PojmcOVGqJBkeU8ffP97ncsqYBbU3xVCq25\nKiuabnLFsIxdLCpchZ3XQKGuKhRV1ILhZs3Zn7/Lwckpk+kBmq51yP2INE6o84btakMai2/2p2n9\n0I3t137t1/hX/+pf7a6fX/va1/i1X/s1/uAP/uBH/uK+37JcC1uVVrwTOMQbUb7lcYbl2hy/cCyn\nhssl/sAnzxK+81/eABQefezj6IYk7h3fxvEkw5WYorYry4Iyt3D7grz2Bz6bxZqb5xd4fZfTl08F\nb1TXTO8dEAwDFucL8qxgcbHA9mzsLv8jLs6WdCsUhWAUyHiMaVBXFRfvXQg5VZFTqDf0+PYf/jHh\naiPzsOMRk5PJDor47K2nROs1+yf7WI48pbM4I71eo3ezgndffEBd1czPFti+nC6zOBWv6DIkXG/Y\nbpZ4fsBoMkVR6DZQtzuFSA3uFqyidY2TuvvgxJuY8/cuuD57zna9pGlahpMJwz2h+V4+vpTgaN2g\n67oMyk96gHQIbcfB63XXsSTn+dtnu43GtCWyknbSEtuTK+P9j99jebXi8Xc+EAGxb/P08bnMVaYF\npmGzf3CM60kX2riNLXTQxVsNY57kOwx4nubceeUOr/4vr/LszWecvXPGdrGhqqodEvz9b7+L3+/h\n97uywGrLer7E63kc3DtmfnXF/OKa+688YjTdE3quKvEUr5sSiFZhV4Jomd9ccnn+mLLMUFqpiY2m\nY/rjvnThwxRVNQgXISf3HnJ4co8iLbumjM3V0zPe+pNvce9jLzCe7rNdhESrkDzL6U/67J3uMz+b\nE60i+pO+lA4mfeJtwtmbz2k7ivHtkP3hg0O237nmG3/0+3xS+Sz7R0ciz05izt7/AFXRmEyPmF2d\nc33xnOHo4Cfyef+o64dubEmS/IWa2uc//3niOP6Rvqj/vyVzdemOvrFdbEk2cTdILjOB4XrDxZNn\n9EcjNF3F9QZyLTFlTCjo6gq3WZ/boKPX83A80eplsYyT6LqOphmkYcbl44tO0iwdQNMxOXhwSBql\nxOuIPBPbt2ZouL7DsBPSFmlBnslrFWWfzcHdKWVRsplvSENBdQe9gcyX2tZOaSeiDqnNuYHLa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1EUujQlUVDu4fsF1uuDm7kjEuVaUsC4E0mjI7aRg6P//pV2nrhvefXbCYr1jPt1iOw/HwHn5f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+E2Lq0uhbm1W28pi5JOv7s/WT34QUVAK1ytZBcTbiToRVEU8va0UpVVG6YiWKG6FV42VU20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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3754210>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this picture, whiter pixels are more positive, darker pixels more negative. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Bonferroni correction is the right one for this image, because the image is made up of 128*128 = 16384 random numbers from a normal distribution. Therefore, from the Bonferroni correction ($\\alpha / N = 0.05 / 16384$ = [Z equivalent] 4.52), we would expect only 5 out of 100 such images to have one or more random numbers in the whole image larger than 4.52."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Bonferroni threshold for this image using an approximate formula\n",
      "alpha_corrected = (alpha / n_voxels)\n",
      "bonf_thresh = inv_n_cdf(1 - alpha_corrected)\n",
      "\n",
      "# a more precise formula optained from the finds:\n",
      "alpha_corrected = 1. - exp(log(1 - alpha)/n_voxels)\n",
      "bonf_thresh2 = inv_n_cdf(1 - alpha_corrected)\n",
      "\n",
      "print bonf_thresh, bonf_thresh2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "4.52277137559 4.51736545771\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The situation changes if we add some spatial correlation to this image. We can take our image above, and perform the following procedure:\n",
      "\n",
      "* Break up the image into 8 by 8 squares;\n",
      "* For each square, calculate the mean of all 64 random numbers in the square;\n",
      "* Replace the 64 random numbers in the square by the mean value.\n",
      "\n",
      "(In fact, we have one more thing to do to our new image values. When we take the mean of 64 random numbers, this mean will tend to zero. We have therefore to multiply our mean numbers by 8 to restore a variance of 1. This will make the numbers correspond to the normal distribution again).\n",
      "\n",
      "The following is the image that results from the procedure above applied to our first set of random numbers:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Divide into FWHM chunks and fill square from mean value\n",
      "sqmean_img = test_img.copy()\n",
      "tarr = np.ones((s_fwhm, s_fwhm)) * s_fwhm # mutliply up to unit variance\n",
      "for i in range(0, shape[0], s_fwhm):\n",
      "    i_slice = slice(i, i+s_fwhm)\n",
      "    for j in range(0, shape[1], s_fwhm):\n",
      "        j_slice = slice(j, j+s_fwhm)\n",
      "        vals = sqmean_img[i_slice, j_slice]\n",
      "        sqmean_img[i_slice, j_slice] = tarr * vals.mean()\n",
      "plt.figure()\n",
      "plt.imshow(sqmean_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Taking means over %s by %s elements from image 1' % (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x3bc8f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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irqYRhs520TilSM7rQ5gxkstITUZKcgJyczM61G8swZ/JtUH8V9uKpTWMgQKP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\nxkWOMSZrXOQYY7LGRY4xJmvfALaRAHXu3VqBAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3885250>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We still have 16384 numbers in our image. However, it is clear that we now have only (128 / 8) * (128 / 8) = 256 independent numbers. The appropriate Bonferroni correction would then be ($\\alpha / N$ = 0.05 / 256 = [$Z$ equivalent] 3.55). We would expect that if we took 100 such mean-by-square-processed random number images, then only 5 of the 100 would have a square of values greater than 3.55 by chance. However, if we took the original Bonferroni correction for the number of pixels rather than the number of independent pixels, then our $Z$ threshold would be far too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Smoothed images and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The mean-by-square process we have used above is a form of smoothing. In the mean-by-square case, the averaging takes place only within the squares, but in the case of smoothing with a smoothing kernel, the averaging takes place in a continuous way across the image. We can smooth our first random number image with a Gaussian kernel of FWHM 8 by 8 pixels.  (As for the mean-by-square example, the smoothing reduces the variance of the numbers in the image, because an average of random numbers tends to zero. In order to return the variance of the numbers in the image to one, to match the normal distribution, the image must be multiplied by a scale factor. The derivation of this scaling factor is rather technical, and not relevant to the discussion here)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# smooth random number image\n",
      "import scipy.ndimage as spn\n",
      "sd = s_fwhm / np.sqrt(8.*np.log(2)) # sigma for this FWHM\n",
      "stest_img = spn.filters.gaussian_filter(test_img, sd, mode='wrap')\n",
      "\n",
      "def gauss_2d_varscale(sigma):\n",
      "    \"\"\" Return variance scaling for smoothing with 2D Gaussian of sigma `sigma`\n",
      "\n",
      "    The code in this function isn't important for understanding the rest of the tutorial\n",
      "    \"\"\"\n",
      "    # Make a single 2D Gaussian using given sigma\n",
      "    limit = sigma * 5 # go to limits where Gaussian will be at or near 0\n",
      "    x_inds = np.arange(-limit, limit+1)\n",
      "    y_inds = x_inds # Symmetrical Gaussian (sd same in X and Y)\n",
      "    [x,y] = np.meshgrid(y_inds, x_inds)\n",
      "    # http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function\n",
      "    gf    = np.exp(-(x*x + y*y) / (2 * sigma ** 2))\n",
      "    gf    = gf/np.sum(gf)\n",
      "    # Expectation of variance for this kernel\n",
      "    AG    = np.fft.fft2(gf)\n",
      "    Pag   = AG * np.conj(AG) # Power of the noise\n",
      "    COV   = np.real(np.fft.ifft2(Pag))\n",
      "    return COV[0, 0]\n",
      "\n",
      "# Restore smoothed image to unit variance\n",
      "svar = gauss_2d_varscale(sd)\n",
      "scf = np.sqrt(1 / svar)\n",
      "stest_img = stest_img * scf\n",
      "\n",
      "# display smoothed image\n",
      "plt.figure()\n",
      "plt.imshow(stest_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - smoothed with Gaussian kernel of FWHM %s by %s pixels' %\n",
      "          (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.text.Text at 0x3c31410>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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92ggkFO8BHypUPqBu1RlM2JOpK4RWnBcYwKR5YKVuFGgEHxSGq7lrgnjZdZNA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\n9GR93NnnAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x389e990>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In our smoothed image, as for the mean-by-square image, we no longer have 16384 independent observations, but some smaller number, because of the averaging across pixels. If we knew how many independent observations there were, we could use a Bonferroni correction as we did for the mean-by-square example. Unfortunately it is not easy to work out how many independent observations there are in a smoothed image. So, we must take a different approach to determine our $Z$ score threshold. One approach used by ``SPM`` and other packages is to use Random Field Theory (RFT)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Another view at the problem using a covariance structure"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What if we had a few variables with some correlation ? to give idea of the problem when in this case, take 3 random variables and correlate them.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mvnormcdf import *\n",
      "import numpy as np\n",
      "import scipy.stats as sst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# checking the mvstdnormcdf function\n",
      "# non independent:\n",
      "corr = [[1.0, 0, 0.5],[0, 1, 0],[0.5, 0, 1]]\n",
      "# integrate from -inf to zero in all directions : H0 : all 3 values are negative\n",
      "p = mvstdnormcdf([-np.inf,-np.inf,-np.inf], [0.0,0.0,0.0], corr, abseps=1e-6)\n",
      "\n",
      "# independent:\n",
      "p0 = mvstdnormcdf([-np.inf,-np.inf,-np.inf], [0.0,0.0,0.0], np.eye(3), abseps=1e-6)\n",
      "print \"p in case of corr, p in case of independence:\", p, p0, \n",
      "print \" independence should also be: 1/8 = \", 1./8\n",
      "\n",
      "z_nocorr = sst.norm.isf(.05)\n",
      "pz_nocorr = mvstdnormcdf([-np.inf, -np.inf, -np.inf], [z_nocorr]*3, np.eye(3), abseps=1e-6)\n",
      "print \"p not corrected : should give same results: \", pz_nocorr, .95**3\n",
      "\n",
      "# create a corrected threshold for 3 independent tests\n",
      "p_5pc_corr = 1 - (1-.05)**(1./3)\n",
      "z5corr = sst.norm.isf(p_5pc_corr)\n",
      "pz5corr = mvstdnormcdf([-np.inf]*3, [z5corr]*3, np.eye(3), maxpts=100000, abseps=1e-6)\n",
      "\n",
      "print \"z corr = \", z5corr, \"p FWE: \", 1-pz5corr, \"expected: \", 0.05, \"p_corrected (bonf)\", p_5pc_corr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p in case of corr, p in case of independence: 0.166666133554 0.125  independence should also be: 1/8 =  0.125\n",
        "p not corrected : should give same results:  0.857375 0.857375\n",
        "z corr =  2.12120142968 p FWE:  0.05 expected:  0.05 p_corrected (bonf) 0.0169524275084\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can think of the application of RFT as proceeding in three steps. First, you determine how many resels there are in your image. Then you use the resel count and some sophisticated maths to work out the expected *Euler characteristic* (EC) of your image, when it is thresholded at various levels. These expected ECs can be used to give the correct threshold for the required control of false positives ($\\alpha$)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is a resel?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is a \"resolution element\". The number of resels in an image is similar to the number of independent observations in the image. However, they are not the same, as we will see below. A resel is defined as a block of pixels of the same size as the FWHM of the smoothness of the image. In our smoothed image above, the smoothness of the image is 8 pixels by 8 pixels (the smoothing that we applied). A resel is therefore a 8 by 8 pixel block, and the number of resels in our image is (128 / 8) * (128 / 8) = 256. Note that the number of resels depends only on the number of pixels, and the FWHM."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# No of resels\n",
      "resels = np.prod(np.divide(shape, s_fwhm))\n",
      "resels"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "256"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is the Euler characteristic?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Euler characteristic of an image is a topological property of the image after it has been thresholded. For our purposes, the EC can be thought of as the number of blobs in an image after it has been thresholded. This is best explained by example. Let us take our smoothed image, and threshold it at $Z > 2.75$. This means we set to zero all the pixels with $Z$ scores less than or equal to 2.75, and set to one all the pixels with $Z$ scores greater than 2.75. Note that when the threshold is low, there is some chance to obtain \"holes\" which will be counted negatively in the EC."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We make a function to show the thresholded image:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def show_threshed(img, th):\n",
      "    thimg = (img > th)\n",
      "    plt.figure()\n",
      "    plt.imshow(thimg)\n",
      "    plt.set_cmap('bone')\n",
      "    # axis xy\n",
      "    plt.xlabel('Pixel position in X')\n",
      "    plt.ylabel('Pixel position in Y')\n",
      "    plt.title('Smoothed image thresholded at Z > %s' % th)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 2.75 and display\n",
      "show_threshed(stest_img, 2.75)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BioqKxC6tS1J6zMff37/DYy2HDx9WeVHt4dsrGBOXkrh4JqK8Lvl5cfgwJi5V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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3bc2890>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Zero in the image displays as black and one as white.  In this picture, there are some blobs, corresponding to areas with $Z$ scores higher than 2.75. The EC of this image is just the number of blobs. If we increase the threshold to $3.25$, we find that some of the blobs disappear (the highest $Z$ values at the blob peaks were less than 3.25)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 3.25 and display\n",
      "show_threshed(stest_img, 3.25)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LFi2ihoYG4XVRURFNmDBBq5tfmkIP2Ozkxu1ZbtrE13YxxjSmzbjo9FD7okWL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\nUEqk0uZcAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3c49090>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One blob remains; the EC of the image above is therefore 1. It turns out that if we know the number of resels in our image, it is possible to estimate the most likely value of the EC at any given threshold. The formula for this estimate, for two dimensions, is on page 906 of Worsley 1992, implemented below. The graph shows the expected EC of our smoothed image, of 256 resels, when thresholded at different $Z$ values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# expected EC at various Z thresholds, for two dimensions\n",
      "plt.figure()\n",
      "Z = np.linspace(0, 5, 1000)\n",
      "\n",
      "def expected_ec_2d(z, resel_count):\n",
      "    # From Worsley 1992\n",
      "    z = np.asarray(z)\n",
      "    return (resel_count * (4 * np.log(2)) * ((2*np.pi)**(-3./2)) * z) * np.exp((z ** 2)*(-0.5))\n",
      "\n",
      "expEC = expected_ec_2d(Z, resels)\n",
      "plt.plot(Z, expEC)\n",
      "plt.xlabel('Z score threshold')\n",
      "plt.ylabel('Expected EC for thresholded image')\n",
      "plt.title('Expected EC for smoothed image with %s resels' % resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x40182d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IYNCgQZZLWURs3w7e3vZX8AGaNNHa9yMi4Lnn9E4jhCgIs236Z86coUqVKqbl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\n0M5TRUZCSIh06xSFy+aLvjTtiOLIy0t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       "text": [
        "<matplotlib.figure.Figure at 0x411d1d0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the graph does a reasonable job of predicting the EC in our image; at $Z = 2.75$ threshold it predicted an EC of 2.8, and at a $Z = 3.25 $ it predicted an EC of 0.74"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expected_ec_2d([2.75, 3.25], resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "array([ 2.82495998,  0.74493991])"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the Euler characteristic give a Z threshold?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The useful feature of the expected EC is this: when the $Z$ thresholds become high and the predicted EC drops towards zero, the expected EC is a good approximation of the probability of observing one or more blobs at that threshold. So, in the graph above, when the $Z$ threshold is set to 4, the expected EC is 0.06. This can be rephrased thus: the probability of getting one or more regions where $Z$ is greater than 4, in a 2D image with 256 resels, is 0.06. So, we can use this for thresholding. If $x$ is the $Z$ score threshold that gives an expected EC of 0.05, then, if we threshold our image at $x$, we can expect that any blobs that remain have a probability of less than or equal to 0.05 that they have occurred by chance.  The threshold $x$ depends only on the number of resels in our image."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Is the threshold accurate?  Show me!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can test the treshold with a simulation:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simulation to test the RFT threshold.\n",
      "# find approx threshold from the vector above. We're trying to find the Z value for which the expected EC is 0.05\n",
      "tmp = (Z > 3) & (expEC<=alpha)\n",
      "alphaTH = Z[tmp][0]\n",
      "print('Using Z threshold of %f' % alphaTH)\n",
      "\n",
      "# Make lots of smoothed images and find how many have one or more blobs above threshold\n",
      "repeats = 1000\n",
      "falsepos = np.zeros((repeats,))\n",
      "maxes = np.zeros((repeats,))\n",
      "edgepix = s_fwhm  # to add edges to image - see below\n",
      "big_size = [s + edgepix * 2 for s in shape]\n",
      "i_slice = slice(edgepix + 1, shape[0] + edgepix + 1)\n",
      "j_slice = slice(edgepix + 1, shape[1] + edgepix + 1)\n",
      "for i in range(repeats):\n",
      "    timg = np.random.standard_normal(size=big_size) # gives extra edges to throw away\n",
      "    stimg = spn.filters.gaussian_filter(timg, sd, mode='wrap')\n",
      "    # throw away edges to avoid artefactually high values\n",
      "    # at image edges generated by the smoothing\n",
      "    stimg = stimg[i_slice, j_slice]\n",
      "    # Reset variance using scale factor from calculation above\n",
      "    stimg *= scf\n",
      "    falsepos[i] = np.any(stimg >= alphaTH)\n",
      "    maxes[i] = stimg.max()\n",
      "print('False positive rate in simulation was %s (%s expected)' %\n",
      "      (sum(falsepos) / float(repeats), alpha))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using Z threshold of 4.054054\n",
        "False positive rate in simulation was 0.049 (0.05 expected)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the random field correction compare to the Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I stated above that the resel count in an image is not exactly the same as the number of independent observations. If it was the same, then instead of using RFT for the expected EC, we could use a Bonferroni correction for the number of resels. However, these two corrections give different answers. Thus, for an alpha of 0.05, the $Z$ threshold according to RFT, for our 256 resel image, is $Z=4.05$. However, the Bonferroni threshold, for 256 independent tests, is 0.05/256 = [$Z$ equivalent] 3.55. So, although the RFT maths gives us a Bonferroni-like correction, it is not the same as a Bonferroni correction. As you can see from the simulation above, the random field correction gives a threshold very close the the observed value for a sequence of smoothed images. A Bonferroni correction with the resel count gives a much lower threshold and would therefore be way off the correct threshold for 0.05 false positive rate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "To three dimensions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Exactly the same principles apply to a smoothed random number image in three dimensions. In this case, the EC is the number of 3D blobs - perhaps \"globules\" - of $Z$ scores above a certain threshold. Pixels might better be described as voxels (pixels with volume). The resels are now in 3D, and one resel is a cube of voxels that is of size (FWHM in x) by (FWHM in y) by (FWHM in z). The formula for the expected EC is different in the 3D case, but still depends only on the resels in the image. If we find the threshold giving an expected EC of 0.05, in 3D, we have a threshold above which we can expect that any remaining $Z$ scores are unlikely to have occurred by chance, with a $p<0.05$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More sophisticated random fielding"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Random fields and search volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I oversimplified when I said above that the expected EC depends only on the number of resels in the image. In fact, this is an approximation, which works well when the volume that we are looking at has a reasonable number of resels. This is true for our two dimensional example, where the FWHM was 8 and our image was 128 by 128. However, the precise EC depends not only on the number of resels, but the shape of the volume in which the resels are contained. It is possible to derive a formula for the expected EC, based on the number of resels in the area we are thresholding, and the shape of the area (see Worsley 1996). This formula is more precise than the formula taking account of the number of resels alone. When the area to be thresholded is large, compared to the FWHM, as is the case when we are thresholding the whole brain, the two formulae give very similar results. However, when the volume for thresholding is small, the formulae give different results, and the shape of the area must be taken into account. This is the case when you require a threshold for a small volume, such as a region of interest."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "t and F statistic volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Keith Worsley's 1996 paper gives the random field formulae for $t$ and $F$ statistics.   ``SPM`` and other imaging packages generate $t$ and $F$ statistics maps. They use the random fields formulae for $t$, $F$ to work out the corrected (family-wise) error rate at each $t$, $F$ value."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Estimated instead of assumed smoothness"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`SPM` and other packages also *estimate* how smooth the images are, rather than assuming the smoothness as we have done here. `SPM` in particular looks at the the residuals from the statistical analysis to calculate the smoothness of the image, in terms of FWHM. From these calculations it derives estimates for the FWHM in x, y and z. Other than this, the corrected statistics are calculated just as described above."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A brain activation example in SPM"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is an `SPM8` results printout for a first level FMRI analysis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Display some saved SPM results output\n",
      "from IPython.core.display import SVG\n",
      "SVG(filename='./images/spm_t_results.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "prompt_number": 19,
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z7KOxcfCNrd0eTis605mo9MYan4TFI5f6OqX2O9MH3p0iWdvnHjhk6jyRPTZaZ3EXM7xDxHB/t456Kwine1JYCS2m2vZG36rmbH6r6/v99KORSxf1dtYWL6fzX7K97V3xXvxfYcDocyHA71xETd0e+GKOFiWqmeOqqcamFmsX1cn9PBwcHUveq5tD2ubPt1sV4m1OLAYj9S7ylTf6zq97Haa25WolMD+R5qIN/Tlgby5MmTViJYfKEGMg01kO9RfbmTUVi4kZ7aV8eWLkVh4cAfDAba+YYDFiNpmtoCwYc69a86kfHZs2dTLyVsH7QrY/tg/1Evz/39/SlHOra5SeCItBPB4sv6+vrUhpIu4bplz9AUTm3qgyHGU1OTmhcvXug01gtfrtjXTk5OdL/C9sTJDX6/GO2m6oHfRw0Y+12T7TmXUVhVpBb1lGIUUkxSa0cRkXv37nnnwSisPPMIQd1JbZFU2mLuorBsSC3qKcUopJik1o4iP/iVXFCz0tx8ID6kEkGVShQWmtVdSKUtOuUD+cMf/qDTqDpi9EsqdtQ2QBspqrhNnbfchg+kLrjY0LQ9BNqi6/Yf9Edh28a0H/syHo+nzCMpmjljUtavv/nmG502+cbQDIU7F2C/wDNAEBvfbZd9IFE0kFCkNuMNlQ/6hXIitXYMlRc1kDzzCEHddURFUmmLWH04KwGSms09VD5l6xByILV2DJUXfSB55hEC350MUmiLXq8XrQ83FoWFquPCwoJWp3wcxrlHYZlIbS8sDHE0hTIuLCzI9va2PHjwwFstL2tH19Bm22eCdSmSUxSWqZymkPHiQVOpRFA1ZVbFvonRU+/fv9dpNFXt7u6WlgPNpbPO/CirR93xgXm47gkWqw835gNBAYIx9yhAUowlnwfqxMvPEiCKHJ/dLLv0eDzOxgdiKqetAOkSZf0aN9O0ESCmUGjsL9ieTbehqwCJ1YejmLB8j7RVpGZzTy2f2ITy3dAH4gZ9IOHxLUcqbZG9D+Tu3bv6evr0qXz22WcyHo9lbW1NhsOhrK2tyfb2tty6dct6ib+i6S0Pcs3H5/e2trb0fW9vT1/Hx8eyv78vx8fHsru7K3fu3JHd3V09a79161ZS9X/27NnM/1f1PDk5ke3tbTk5Ofnoe7n5QMrqqZ7TnTt3ZH9/X+7evSv7+/tTn9u0l81d0eRzcy3H48eP5eTkRB4/fiwXFxdy+/Ztubi4kLt378qVK1fk7t27MhqNZHFxUUajkbEc6j1169Yt2d3dldPTU9nd3Z0aN03U4/T0VA4ODuT09FS2trb0tbe3J4PBQN+L+cTqw42ZsDDsbWtra+rcAlfUA/Klq/n4/B4+LzR/fPLJJzr91VdfVeYTqjxN5IV1nHXgUr/fz8IHEqKcIdo+lzxMoeFoGjo4OKgsB54rgibBhw8fBq+H2udMZNqSgyHbZeHbsfpwFAGCqztzsC13nVACJDdsBUgXfCDzSAgBYrOWZpYACY2rAMneB/Lw4UN9KXucb4WKKl7X89nZ2dHX69ev9YWfh+Lk5ERfp6en+nr//r2+bMtdl1D5VOV1cXGhr8lkoq8i9IGkm4fPOECzOr6fVldX9WVTjsuXL+sL+9Tm5qYMBgPjyYe2mMqA41LtPG06vyR7HwjCvbDi5BObFOvPdSD1SGHdQqg8QuBbDt+9tEKUQYR7YZWS2ow3tXxik2L9Q+RFDSTPPELgWw7fvbRClEGkY3th5bS/UBVoR206ph5/CzEtssNYdaS4zqHMVoy2VtxfCdfq4FkJTey7hL4XtFHjXkWmPYxCrkXJxbdQPA8ECXU2CIKmIptt3uti039njb/YwSgu1F3XgfXFjUJxYeMXX3zx0d9l7wNB1tfXg1QmtRmv7745ilRmX3VJ7XmEyosaSJ55hMC3HKm0BX0gJaRmc/fdN0eR+qzJRGrPI1Re9IHkmUcIfMuRSltkvxcWEmpflpjrDjCSQp2RLDK9BQJu0YLUNWeZylN3PyhU9U3mABOoEqP56N27dzqN5pKLiws5Pj6WlZUV7/BFVX/T9tloV0a1f1ZePuS0F5apPTD8GtsPtysXqRf6ajqJr4k1HKb+2/Txz751qfp7HFumPbUwD9OebVW7e3TyRMIUVrzWyUcNPPWgZ22iJvKDSautehXvphX+pt87ODgQkR/8DOhvmEVTz0MdtKV8Muqunosqr7qrgedbnq5oIKq/qgmQumN9bdpL2d6Lz6F4EJpPu5eVw3aHipDjyLf/2Py96r8qBFfdTfWoMpWX/U72K9GRUKsiU9ZA0JwVSgPxYdZmgWW/h849fDH84x//0OlLly7p9MrKSnANBEENxLToq+zM+BBtmdNKdBsNBLVLHw0ExwG2/fHxcaMaiG0QQBOaUOi/x/cKPjs82x7zwMASFCQfPnzQ6Z/97Gcf/U72K9ERjAjABsSOndrOoC9evNBp006cGKGEkSjYGVKkSoCoGb2Iue4Y737z5k2dNmktOFjKokZmgcKk7qphF3KKwnr+/Ln+N7Y9mj6wLqaZKY5LfGlhPiiUEPwOjunY46CJiVhocJzZ9F/cTRjHAT7r3/72tx/9XeeisEJQVPHazicUqZUnNiHrHyIvRmHVwxRKHLscIfAtR4h65NSHGYWVAKmVJzaMwnIjlSgs1MTbLEcIGIVVj+hRWKjuohpmY/P0UVGLJhqlauPiOIzwMC1Sw89PTk703/uo66mp3viM0GSEn+MePLjwEM1ctovZqupfx8cSoi1zisIymUFMfiNka2tL+7HQ11F0jiuw7yM4hjBdh5BjAE1wMf2ROzs7MhwO5fbt28aFljZmKyyD6TnOOlFTpKNRWL6E6mBop/XBdbAUSUl4tAE1EDdClNPniOmQpDIGfMtx+/bt1ssgwr2wSgllJ8UZsw8YleJDKvbftqAPxI0Q5TRpG7FJZQz4lsO0O27MMohkuhcWmqHQsWba1wjTJlWt7sIhVF+xDCg0UokaaYsqNR2jPbDd3r59q9NofkQbOIY243PE75jOnU6FnKKwfMr58uVLnTZF2yEm8ySO0WKYcExUv8Z3AE7yTFGTPuBv4YJN/C2f9wpGYeE7Et9hX3755Ud/F6sPRxEgm5ubcv369VA/Q1oC18CYBMiVK1eilqkJ3r17l4UPpN/vBxtX+GzrChBTeC9pj1h9OIoTHaU9NZD2cdVAyg6VKmJywOemgeTA06dPg2kgNs/WBPoCqYF8/FttaSAxCCpAMNIGFzi9ffu2NNQPF6DhywZnOqjVbG9vVzqYTPsmoaA4Pj4O4gC3idjADoZgdEhqUVgY9YTRa7gvlinKxGWwhKz/vEVh+Zbz7OxMlpaWpp4najWmCC4coycnJ97OY5fnhmNL+XJevnw51U9t/hbrbvOOQXAc+2wpX3zPqfeVaeeFqj3hOhWFFSJOXCRcpEZq0VMpCY82YBSWGyHKGWJsphJ5FIIU1oGEiBLtVBRWiJWqIuEiNVKLnkolAqUtGIXlRohyhhibqUQehSCFleghokSzjMJCsAJoj0M7Hs5+UG02zWhMi/vQzILCAVVT0wJGxHTins/CJJNPJsaeTiZSM5mlRE6nZzYVaVN3v6aYmLb5N0UImvbbw/HX1ljEEx5NQsN0GieaENuMwoqigYRCbe/sS2oaUSqzr7qkWH9qIPVIZe+mVMZAChpIiPdTp/bCCsWDBw+C5JOaTyZXbSDF+tMHUo9U9m5KZQyk4AMJ8X7Kfi8s0745qKqZ0ngGBZqqDg4OdL5oqsI0RmCY9o65dOmS/jeqgqgi4izA5HS3MQWh2oxbZqMpbzAYyL1790Sk+RPXQhLzfJaYec1TFFZZe2Hfx2MNcNsT7KdNnMOBpl91oJXItKnKtFgZxz2OXXwH2JwGaLM/H37n5ORERqORLC8vG5co1H1X4d8iVYfbdSoKKxQmoVSXqo3IbAn10lPCIzeogbQLNZDw+JYDz8lpk05FYfmipLaSxupe98hZhen7xaNc1e+qk8Bcj6wtHmVZvKsZlrr7HKlpc1c0/Ttt3NXlk09uPpDQ7Vg8AleNt9j9VI23uuPbhGn8lR2NLPKDz7XqaF31/6Z8i5/XrUex/sW/LytX9lFYGGGAqynxWEZc/YrHpWLkBKqp+LkpigLthyZbIj4AjFRAFd0ULeZjYsLoFjTZmbaUbwpGYZWD0YLzHIWF/Nd//ZdOm1ZX+6y0xjGB7wzc5BHHCr4PZh23rMBFsfj+QGsGfge3tccoLzRv4/sGTWoY5IPlRAuDaQsgLJvpt0wLr8t2dmAUVgaEihxBG29OMAqrXboUhYXHKLdJrmOxCKOwMoA+kO74QFD7oA8kfh6ffvqpdx4hyHUsFsk+CstmEZ9p8QwuFjLtZ4UmJjRJoQnos88+K/3bq1ev6nxN+8vUPTnMBlOeuZqUGIXVLuvr694bKla1F26O+OrVK51G09NwOCx98WLEkelIB8wHzdsYoYTj2xSVZHo3fPjwofT7ONbRxI5RVSZtBMuDZi7TomHME83VaHrChdTn5+e6fE+ePCktQxWMwmqQqo3IbElxBh6TFOvvkldx51JqIPXoyqw9FUK8nxiF1SCmrUzqkqIPICYp1p8+kHqEaK+u+A1SIcT7KfsoLARNUr/85S912rSwBz83mbkwSgO///nnn+s0qn/4UExqZN19rnIlV5NZE5jOTcglCksRo7x/+MMfdBrHJa59MK2xwvGHZUXzDpqw8HOT2QrHMeaJM/j79+/rNI5vjIDCdwmekYILf9HsZqojClLTe+snP/mJTvf7/dKyhaBTUVgoQLpEijPwmKRY/3nVQFwPEMq173WZnPpwFAGCcdZdIkUfQExSrH+dvEwv3Vx9IC5CJNe+12Vy2k0hypG2W1tbukJ/+ctf9Oc//elPdRpNWKj+ofBBlRLVV1SPcVETqqn4nStXrsizZ88+GnDFf1epgClGIcUkxfrb5jXrZZtbFJYPddr+17/+tU5/8803Oo3ngeA4Nm09hBFHOI4xlBfHKy7WwzzxLHYc6yZzk+nzf/7zn6XfMS08NB0ti3VHsx6W3wbf8TAej6P14SgCJLUZnXo4swTEeDye+ZLp9XpJzsBjkmL9fYWHSHr91URZOev6RVR7xbKZk2py0kCimLCUPa54bwubvXh6vZ5sbGyU3tfX12U8Hku/3y+9p7An1Kx7nXbI7V61F5aanYmY+2Xb/dOWqvLb9EfVb03/P+ueG8pZru6xVr/HHgfr6+vdisIyzfhwsc1vfvMbnb569apOoyqIKi5GLeBip7apmt2mMMvL1WTmSx0fQQrPqQpXx7mJlOqMEUoYnWU6bRBNYWjOwjphVCbueYWLj9FMjgsnMRAITVX4rvr222+N9bHFVxOMHZkXVQNJhSajh3q9nvES+cE0hg861xldLlFYVebIIqn1VxMhypnKWpJUxgCuLHchRD1QeNpS7OPUQP5FbhqILXUd9iFpWgNJyZ7uOktPpfyzCKmBpFbfedZAFFXPJAVrRxQB0u/3nZw6xQZILeonVD7YPjEeetP1Vx3bti5NRGH5vFxzicJyHVdIjP205imPEGUoPlfTs0khkrBVDWQWqc2IYhDLfhlDA0FiPcsuz8jLCFXfHOpqQ1d8ezk916x8IKnZ3EPnU+YrSRnb+pf5fVzysck7Fb9ADFKpa5d8IL7lSGUV+Vz4QEx0ZUbkQ5Oz+NgaSBW+tt4myKEP5jRTjUFXNBCRMM+WGkiBVDWHJvIpPvwUtRFT/et2XLVewXTVIafZmy8hyrmxseGdBzWQcH8fKg9qIKS03UK0TYyZWooCrw459MFcZqmxoAYyTec0ENt7Ciua276bVkyHWOmuiLEiNvYdV+H63lMnVD1T6O8h7oq2y5HC+KEGMsfYtFfbYZdVUANpnlxmqbGgBjJN5zQQX3LwXfjmY9txUnhBh6p/yNkSfSD1SMVmTx9I2DzmWgMR6dbMyJZY7dT0TC0F4eZLDv0vl1lqLLqkgYj4P19qIAVS1hx883HtLG2+rMvq71IeaiBuUAMJDzWQelADaZk2Vk83NVPrguayYfTFAAAZEklEQVShyKH/UQOZhhrINHOtgZQ1Xoqagw8hV09jfrFQ9fddNU8NxI0Q5XTZ+bVIKrPuEFADqUeyGohIt2ZHRZp+2c9qu5AztS5pHUgOfY8r0afpkgaSi3aZrAYi8nEjpqI5+OZTrFcTs4Wm99LCk+x8oQbiRip1TWXWHQJqIPVIWgMR6c7sSNHWjB3b0Wem1lWNo0gO/Y4ayDTUQKbpnAbics/hjHHbu5qxt7FCG89sf/fu3cwz3Wfd2yp/G/fUCVVP1zPRU7sr2i4HV6ITQgghFUTRQAghhHQPChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnKAAIYQQ4gQFCCGEECcoQAghhDhBAUIIIcQJChBCCCFOUIAQQghxggKEEEKIExQghBBCnPi3r7/++uumf6Tf78vy8rL88Y9/zPZ+eHgor1+/lp2dHfn73/+u7+rzxcVFGQwG+m7KZ2lpSf7v//5PRET+/Oc/f3SfTCby/Plzfb98+bL86U9/ar3+83Z/+PBh08OCkOz50Xffffdd0z/S7/fl6dOn3vmsr6+3ks+rV690+vz8XKcnk4ksLS2JiMja2pr+XH3W6/Wm8jk8PNTps7MznT4+PpaVlRWdp2JxcVGnV1dXrcuLjMdjp7+zoa3n0XRe6+vr8qtf/SpIeQjpMlEESJMvsRiYBAi+4FGA3L17tzQfkwBBQguQIuPxOOgLu6sUhT8h5GMWYvxIajNVm3xGo5FOX1xclKYvX75c+jliEhrXrl3T6e3tbXn27JlFyf3p9Xpy/fr1j16QLkI+tecaKi9qIITYQQ3EAAqQvb09nUYNRJmqRKY1BNRGbATIrVu3ApTYnsFgYC2wcnx2IaAGQkg1UaKw1tfXO5lPKAaDQdtFMNLr9fTVFCGfR4i8UusfhKQKNRADu7u7On10dKTT6Je4efOmTi8vL+v0nTt3dBo1kNPTU51+9OhRuMLWpI4GgmBdFhYW5MWLF/LVV19NmfK6AjUQQqqhBlKC7csDBYIPKWsgs7h+/XqQfKiBEJIn1EAKKOHx4sUL/Rk1kO8paiAK9OHk9KxnQQ2EkGoYhfUvii8MNMvg/924cUOnR6NR5YsYhQmmEdcXelO8efOm9PNieHJZuVVb1REkjMIiJE+ogUj5bBPXfmD0FAqQNrUIH6oElq0AqUPqfaAINRBCqplbH0iI6KJQvotcfSB1yj2rvekDISRP5k4DiTGz3Nra0mn0mfjM4ENSpYGgr8NkdgtFSn0DoQZCSDVzoYEUZ7+paQ7zoIGY6PV6srGxEeyFTQ2EkHh0VgNpcwZJDcSftjUTaiCEVNM5DcTGr9G05nDt2jV9+eTTFnfu3NHXmzdv9PXy5Ut9bW5uymAwkM3NTe/fK6u/q4+KGggh8eiUBpLKrBHXjeAmi7loIAhGZOH+YKhZxYpGi6mVpNKXCEmZqBpIU3dlQ1cz2bbv29vbU/f9/f0kylWc6dt+X5VfhTOruxIoscqtnvPGxoaIlPcHdZn+v86dEDKb7DUQzhTLmeXHqKOB7Ozs6DT6dhA8vQ93Io5BU32L/YqQarL1gfis4Ugteio1H0hsfOpf9JXQB0JIPLLUQDg7rGZeNJAyQvQ39jFCqkleAxkOh/paX1+X09PTqQOeXEhNcwiVz97enr5OT0/1hZ/X5eLiQl+TyURfo9FIX+fn5/pyoaz+Ozs7+qqbl+8OA9RACLEjigAJtVFeqO3DQ21cmFo+uRKy/piXqxDhefGE2JG8BtIEqWkO9IGEq38xLxchklp/JSRVkvSB4LkZL1++1GlcR7GyslL6+TyDfo+TkxOdLp7dXscHggsF0ZyE+d++fVunHz9+rNN1z3rH8qM5DM8ewXSd5163D9IHQkg1WWkgrjb2IqlpDtRAmtNAFHUEAjUQQuzIygeCq599SM13QR9IMz6QIrZChD4QQuxI5kRC3CYDzSaTyUSncVsN1EbqmrBCnQCYWj42px/WBU9mRAGOaTQ54kFcagW7iMinn36q07u7uzp9+/ZtGQ6HU2YwkennbjrQq4yqtuz1epXmLJ5ISIgdWWkgoUhNc5h3DaQoPHywacsqTSS1/kpIqmTlAwlFar6LefeBDIfDYHnZtuUsIZJafyUkVVqNwkLTh9r6vNfrTUX74MsFF8LhrPXnP/95sLLOA6678aJJ6v379zqN5kQ0PaH5C01q+DnuVoyRdaaACVz1HgJT32QUFiHVJKWBxBq0qWkO866BhIquE6nflk2f0U5Il0nGBxJzxpea72LefSChoutEwrQlfSCE2BE9Cuv4+Fh/rkwWReGBG/LhwjE0YaH5qy6pRU+FyqcJMMIN23xpaUnOzs5kaWlpymyFpi38HNNffPHF1G+ErL9LXsXILEZhEWJHVA1EmQaUj2N9fd3qIKiDg4OZ+Td9oFIu+TT9e2r1Oa5CF/nBBFVlilL+jibr/+zZM+e/V/2TGgghdkRxovf7faMGUmW6Qq0DXzi4Pcd//Md/1CpPappDbA3E9fdev36t0xcXF7U0kE8++USnnzx5EqQ8ZbjmRQ2EkPq0GoVV1+/xP//zPzqN0Vn4Qop1PndOoBCuuxdWqN9FYZLCmSFlYD9lFBYh1SQVhRWL1KKnco3CSrH+IfJKrb8SkiqtRWG1OcNLLXoqVQd6FSnWn1FYhMQjGQ3kzZs3+jJx9epVWV1dldXVVVlcXNTX1tZW6WUitZlz0xrIwsKCvr799lv58OGDfPvtt975VpVbPavV1VVZW1vTV918bDg6OpKjoyNqIIREpBUfSJn2gYLDtDkiCgU8JwTXEaAPJPSq5VzBtsVV/j/72c/aKE4jHB0d6XTdc0gQ1VfpAyGkmmQ0EBswgsuH1DQH+kDC1X97e9s7D2oghNgRXQPBmR3OGjGqCve5Ms0mUQNBzQTDe9FcMs/RWRgNNRqN5Pz8XBYXF+Xdu3f6c+4n9j3UQAixJysNJLUZb2r5xCbF+vvm1ev1qIEQYklUDaQ4q6MGEgdqIPUYj8fUQAixoFUNZHt7W1/n5+f6Oj091ReCs8sbN27oC6N9bt68qS+M1DLl40Nq+Zi4uLjQ19u3b+X9+/fy9u3bqeiswWCgr52dHX3FKHdKGogIfSCE2NKqBoKDHTdNXF5e1mlTJBXOqk3OdTxfYnV11bq8XQM1NBQKKFgvXbqk06gBprpqvEmogRBiRzQNJMSATG3Gm1o+sUmx/tRACIlHNA1ECRBck4AzYzRX3bhxQ6dRc8CT7M7OznTadArePM6eyzg8PNTp3/3udzr9k5/8RKfR14SayTy2ITUQQuzIKgprd3c3SD6pzZypgVADISRHou6FpQY3nq1tQ/E8ECVIlO9jNBpN3VVEVy7neITKx3RX7VUlgNU5H6r9cmtH3/NA1J17YRFiR7TzQL788ksRmRYGeL4EHlKETvSiCUWF6aKpCtPXrl3TaVMIcGrneDSxvbppa49f/OIXOo0vSnScm7aSKZJi/UPk1e/3eR4IIRZE0UCU8PAF13j4kNoustyNl7vxEpIjUQQILvrzAR3nPqRmu6cPhD4QQnKkMRMWmlAwwmpzc1OnUbCgcLhz545O37t3T6fRFIORWpj22Yk1d7DNEWyTb775Rqcxws0UbWWzS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        "<text id=\"text3078\" transform=\"matrix(1,0,0,-1,306.4168,570.25)\"><tspan id=\"tspan3080\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0\" y=\"0\">}</tspan><tspan id=\"tspan3082\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"-40.8336 -31.9376 -26.6096 -22.1616 -7.9376 0.9584 10.7344 16.9584\" y=\"-179.084\">stim_hrf</tspan></text>\n",
        "</g><g id=\"g3084\" transform=\"scale(10,10)\"><text id=\"text3086\" transform=\"matrix(1,0,0,-1,68.4168,479.75)\"><tspan id=\"tspan3088\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 10.672 21.344 34.672 40.896 49.792 58.688 68.464 72.912 78.24 87.136\" y=\"0\">SPMresults:</tspan></text>\n",
        "<text id=\"text3090\" transform=\"matrix(1,0,0,-1,155.5,479.75)\"><tspan id=\"tspan3092\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 2.78 5.56 10.56 16.12 21.12 26.12 31.68 34.46 41.13 47.8 56.13 61.69 67.25 72.81 78.37\" y=\"0\">./sess1/SPM8_ana</tspan><tspan id=\"tspan3094\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -79.8632 -74.3032 -72.0832 -66.5232 -60.9632 -58.1832 -55.4032 -52.6232 -47.0632 -43.7332 -38.1732 -33.1732 -27.6132 -22.0532 -19.8332 -14.2732 -11.4932 -5.3832 -2.6032 3.2368 6.0168 11.5768 14.3568 19.9168 25.4768 31.0368 36.5968 42.1568 47.7168 53.2768 56.6168 62.1768 68.0168 73.5768 76.3568 81.9168 87.4768 93.0368 95.8168 99.1468 104.7068 110.2668 115.2668 118.0468 121.3768\" y=\"11.6664\">Height threshold T = 3.162616 {p&lt;0.001 (unc.)}</tspan><tspan id=\"tspan3096\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -80.4132 -75.4132 -72.6332 -67.0732 -61.5132 -58.7332 -55.9532 -53.1732 -47.6132 -44.2832 -38.7232 -33.7232 -28.1632 -22.6032 -20.3832 -14.8232 -12.0432 -7.0432 -4.2632 1.5768 4.3568 9.9168 12.6968 17.6968 23.2568 28.2568 33.8168 36.0368\" y=\"23.4164\">Extent threshold k = 0 voxels</tspan></text>\n",
        "</g><path d=\"m 3734.17,4563.33 1270.83,0 0,1831.67 -1270.83,0 0,-1831.67 z\" id=\"path3098\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6395 0,-1831.67 1270.83,0 0,1831.67 -1270.83,0\" id=\"path3100\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3102\"><g clip-path=\"url(#clipPath3106)\" id=\"g3104\"><g id=\"g3110\" transform=\"matrix(1270.83,0,0,1831.67,3734.17,4563.33)\"><image height=\"1\" id=\"image3112\" transform=\"matrix(1,0,0,-1,0,1)\" width=\"1\" xlink:href=\"data:image/png;base64,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\"/></g></g></g><g id=\"g3114\"><g clip-path=\"url(#clipPath3118)\" id=\"g3116\"><g id=\"g3122\" transform=\"scale(10,10)\"><text id=\"text3124\" transform=\"matrix(1,0,0,-1,406.167,432.334)\"><tspan id=\"tspan3126\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 7.22 12.78 17.78 20 25.56 31.12 33.9 42.23 47.79 50.57 53.9 56.12\" y=\"0\">Design matrix</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3128\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3130\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3132\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3134\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3136\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3138\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,4563.34 0,18.33\" id=\"path3140\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6395 0,-17.5\" id=\"path3142\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3144\" transform=\"scale(10,10)\"><text id=\"text3146\" transform=\"matrix(1,0,0,-1,391.833,444.25)\"><tspan id=\"tspan3148\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 4369.17,4563.34 0,18.33\" id=\"path3150\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6395 0,-17.5\" id=\"path3152\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3154\" transform=\"scale(10,10)\"><text id=\"text3156\" transform=\"matrix(1,0,0,-1,434.167,444.25)\"><tspan id=\"tspan3158\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">2</tspan></text>\n",
        "</g><path d=\"m 4792.5,4563.34 0,18.33\" id=\"path3160\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6395 0,-17.5\" id=\"path3162\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3164\" transform=\"scale(10,10)\"><text id=\"text3166\" transform=\"matrix(1,0,0,-1,476.5,444.25)\"><tspan id=\"tspan3168\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">3</tspan></text>\n",
        "</g><path d=\"m 3734.17,6111.67 17.5,0\" id=\"path3170\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6111.67 -18.33,0\" id=\"path3172\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3174\" transform=\"scale(10,10)\"><text id=\"text3176\" transform=\"matrix(1,0,0,-1,359.417,607.5)\"><tspan id=\"tspan3178\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">20</tspan></text>\n",
        "</g><path d=\"m 3734.17,5820.84 17.5,0\" id=\"path3180\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5820.84 -18.33,0\" id=\"path3182\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3184\" transform=\"scale(10,10)\"><text id=\"text3186\" transform=\"matrix(1,0,0,-1,359.417,578.417)\"><tspan id=\"tspan3188\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">40</tspan></text>\n",
        "</g><path d=\"m 3734.17,5530.84 17.5,0\" id=\"path3190\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5530.84 -18.33,0\" id=\"path3192\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3194\" transform=\"scale(10,10)\"><text id=\"text3196\" transform=\"matrix(1,0,0,-1,359.417,549.417)\"><tspan id=\"tspan3198\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">60</tspan></text>\n",
        "</g><path d=\"m 3734.17,5240 17.5,0\" id=\"path3200\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5240 -18.33,0\" id=\"path3202\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3204\" transform=\"scale(10,10)\"><text id=\"text3206\" transform=\"matrix(1,0,0,-1,359.417,520.334)\"><tspan id=\"tspan3208\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">80</tspan></text>\n",
        "</g><path d=\"m 3734.17,4949.17 17.5,0\" id=\"path3210\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4949.17 -18.33,0\" id=\"path3212\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3214\" transform=\"scale(10,10)\"><text id=\"text3216\" transform=\"matrix(1,0,0,-1,353.833,491.25)\"><tspan id=\"tspan3218\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 3734.17,4658.34 17.5,0\" id=\"path3220\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4658.34 -18.33,0\" id=\"path3222\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3224\" transform=\"scale(10,10)\"><text id=\"text3226\" transform=\"matrix(1,0,0,-1,353.833,462.167)\"><tspan id=\"tspan3228\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">120</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3230\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3232\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3234\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3236\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3238\" transform=\"scale(10,10)\"><text id=\"text3240\" transform=\"matrix(1,0,0,-1,413.333,702.334)\"><tspan id=\"tspan3242\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 16.12 18.9 22.23 27.79 32.79 35.57 38.9 43.9\" y=\"0\">contrast(s)</tspan></text>\n",
        "</g><path d=\"m 3734.17,6450 1270.83,0 0,494.168 -1270.83,0 0,-494.168 z\" id=\"path3244\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6450 0,494.17 1270.83,0 0,-494.17 -1270.83,0\" id=\"path3246\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"M 3734.17,6450 5005,6450\" id=\"path3248\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6450 0,494.17\" id=\"path3250\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6450 0,-12.5\" id=\"path3252\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6450 0,-12.5\" id=\"path3254\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6450 0,-12.5\" id=\"path3256\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6491.67 -13.34,0\" id=\"path3258\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6903.34 -13.34,0\" id=\"path3260\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3262\"><g clip-path=\"url(#clipPath3266)\" id=\"g3264\"><path d=\"m 3734.17,6491.67 423.332,0 0,411.664 -423.332,0 0,-411.664 z\" id=\"path3270\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6491.67 0,411.66 423.33,0 0,-411.66 -423.33,0\" id=\"path3272\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4157.5,6491.67 423.332,0 0,0 -423.332,0 z\" id=\"path3274\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4157.5,6491.67 423.33,0 -423.33,0\" id=\"path3276\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4580.83,6491.67 424.168,0 0,0 -424.168,0 z\" id=\"path3278\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4580.83,6491.67 424.17,0 -424.17,0\" id=\"path3280\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3282\"><g clip-path=\"url(#clipPath3286)\" id=\"g3284\"><g id=\"g3290\" transform=\"scale(10,10)\"><text id=\"text3292\" transform=\"matrix(0,1,1,0,362.417,666.917)\"><tspan id=\"tspan3294\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 4574.17,0 0,2930 -4574.17,0 0,-2930 z\" id=\"path3296\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 557.5,1267.5 0,2930 4574.17,0 0,-2930 -4574.17,0\" id=\"path3298\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3300\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,2930\" id=\"path3302\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,45.83\" id=\"path3304\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3306\" transform=\"scale(10,10)\"><text id=\"text3308\" transform=\"matrix(1,0,0,-1,53,114.667)\"><tspan id=\"tspan3310\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 1014.17,1267.5 0,45.83\" id=\"path3312\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3314\" transform=\"scale(10,10)\"><text id=\"text3316\" transform=\"matrix(1,0,0,-1,94.5,114.667)\"><tspan id=\"tspan3318\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.1</tspan></text>\n",
        "</g><path d=\"m 1471.67,1267.5 0,45.83\" id=\"path3320\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3322\" transform=\"scale(10,10)\"><text id=\"text3324\" transform=\"matrix(1,0,0,-1,140.25,114.667)\"><tspan id=\"tspan3326\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.2</tspan></text>\n",
        "</g><path d=\"m 1929.17,1267.5 0,45.83\" id=\"path3328\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3330\" transform=\"scale(10,10)\"><text id=\"text3332\" transform=\"matrix(1,0,0,-1,186,114.667)\"><tspan id=\"tspan3334\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.3</tspan></text>\n",
        "</g><path d=\"m 2386.67,1267.5 0,45.83\" id=\"path3336\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3338\" transform=\"scale(10,10)\"><text id=\"text3340\" transform=\"matrix(1,0,0,-1,231.75,114.667)\"><tspan id=\"tspan3342\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.4</tspan></text>\n",
        "</g><path d=\"m 2844.17,1267.5 0,45.83\" id=\"path3344\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3346\" transform=\"scale(10,10)\"><text id=\"text3348\" transform=\"matrix(1,0,0,-1,277.5,114.667)\"><tspan id=\"tspan3350\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.5</tspan></text>\n",
        "</g><path d=\"m 3301.67,1267.5 0,45.83\" id=\"path3352\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3354\" transform=\"scale(10,10)\"><text id=\"text3356\" transform=\"matrix(1,0,0,-1,323.25,114.667)\"><tspan id=\"tspan3358\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.6</tspan></text>\n",
        "</g><path d=\"m 3759.17,1267.5 0,45.83\" id=\"path3360\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3362\" transform=\"scale(10,10)\"><text id=\"text3364\" transform=\"matrix(1,0,0,-1,369,114.667)\"><tspan id=\"tspan3366\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.7</tspan></text>\n",
        "</g><path d=\"m 4216.67,1267.5 0,45.83\" id=\"path3368\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3370\" transform=\"scale(10,10)\"><text id=\"text3372\" transform=\"matrix(1,0,0,-1,414.75,114.667)\"><tspan id=\"tspan3374\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.8</tspan></text>\n",
        "</g><path d=\"m 4674.17,1267.5 0,45.83\" id=\"path3376\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3378\" transform=\"scale(10,10)\"><text id=\"text3380\" transform=\"matrix(1,0,0,-1,460.5,114.667)\"><tspan id=\"tspan3382\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.9</tspan></text>\n",
        "</g><path d=\"m 5131.67,1267.5 0,45.83\" id=\"path3384\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3386\" transform=\"scale(10,10)\"><text id=\"text3388\" transform=\"matrix(1,0,0,-1,510.417,114.667)\"><tspan id=\"tspan3390\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 45,0\" id=\"path3392\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3394\" transform=\"scale(10,10)\"><text id=\"text3396\" transform=\"matrix(1,0,0,-1,47.3332,123.083)\"><tspan id=\"tspan3398\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 557.5,1754.17 45,0\" id=\"path3400\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3402\" transform=\"scale(10,10)\"><text id=\"text3404\" transform=\"matrix(1,0,0,-1,41.75,171.75)\"><tspan id=\"tspan3406\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">50</tspan></text>\n",
        "</g><path d=\"m 557.5,2240.83 45,0\" id=\"path3408\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3410\" transform=\"scale(10,10)\"><text id=\"text3412\" transform=\"matrix(1,0,0,-1,36.1668,220.417)\"><tspan id=\"tspan3414\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 557.5,2727.5 45,0\" id=\"path3416\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3418\" transform=\"scale(10,10)\"><text id=\"text3420\" transform=\"matrix(1,0,0,-1,36.1668,269.083)\"><tspan id=\"tspan3422\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">150</tspan></text>\n",
        "</g><path d=\"m 557.5,3214.17 45,0\" id=\"path3424\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3426\" transform=\"scale(10,10)\"><text id=\"text3428\" transform=\"matrix(1,0,0,-1,36.1668,317.75)\"><tspan id=\"tspan3430\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">200</tspan></text>\n",
        "</g><path d=\"m 557.5,3700.83 45,0\" id=\"path3432\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3434\" transform=\"scale(10,10)\"><text id=\"text3436\" transform=\"matrix(1,0,0,-1,36.1668,366.417)\"><tspan id=\"tspan3438\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">250</tspan></text>\n",
        "</g><path d=\"m 557.5,4186.67 45,0\" id=\"path3440\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3442\" transform=\"scale(10,10)\"><text id=\"text3444\" transform=\"matrix(1,0,0,-1,36.1668,415)\"><tspan id=\"tspan3446\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">300</tspan></text>\n",
        "</g><g id=\"g3448\" transform=\"scale(10,10)\"><text id=\"text3450\" transform=\"matrix(1,0,0,-1,55.75,409.917)\"><tspan id=\"tspan3452\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:12;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 8.004 12 18.672 22.668 26.004 32.676 36.672 40.008 46.68 53.352 57.348\" y=\"0\">Statistics: </tspan></text>\n",
        "<text id=\"text3454\" transform=\"matrix(1,0,0,-1,119.25,409.917)\"><tspan id=\"tspan3456\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-weight:bold;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica-BoldOblique\" x=\"0 6.11 11.95 17.51 23.07 25.85 31.96 37.52 43.08 45.86 51.42 57.53 60.31 66.42 71.98 75.31 80.87 86.98 89.76 93.09 99.2 103.09 105.87 111.43 116.99 122.55 126.44 132 138.11 140.89 146.45 152.56 155.34 161.45 170.34\" y=\"0\">p\u2212values adjusted for search volume</tspan></text>\n",
        "</g></g></g><g id=\"g3458\"><g clip-path=\"url(#clipPath3462)\" id=\"g3460\"><path d=\"m 557.5,4050.83 4574.17,0\" id=\"path3466\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:30;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3468\"><g clip-path=\"url(#clipPath3472)\" id=\"g3470\"><g id=\"g3476\" transform=\"scale(10,10)\"><text id=\"text3478\" transform=\"matrix(1,0,0,-1,60.25,394.167)\"><tspan id=\"tspan3480\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 13.34 19.18 21.4 26.96 31.96 37.52\" y=\"0\">set\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3482\"><g clip-path=\"url(#clipPath3486)\" id=\"g3484\"><path d=\"m 557.5,3916.67 502.5,0\" id=\"path3490\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3492\"><g clip-path=\"url(#clipPath3496)\" id=\"g3494\"><g id=\"g3500\" transform=\"scale(10,10)\"><text id=\"text3502\" transform=\"matrix(1,0,0,-1,92.3332,383.167)\"><tspan id=\"tspan3504\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 4.5 -27.5 -22.496\" y=\"0\">c p </tspan></text>\n",
        "<text id=\"text3506\" transform=\"matrix(1,0,0,-1,156.3332,394.167)\"><tspan id=\"tspan3508\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 7.22 12.78 17.78 20.56 26.12 29.45 35.29 37.51 43.07 48.07 53.63\" y=\"0\">cluster\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3510\"><g clip-path=\"url(#clipPath3514)\" id=\"g3512\"><path d=\"m 1197.5,3916.67 1372.5,0\" id=\"path3518\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3520\"><g clip-path=\"url(#clipPath3524)\" id=\"g3522\"><g id=\"g3528\" transform=\"scale(10,10)\"><text id=\"text3530\" transform=\"matrix(1,0,0,-1,124.333,383.167)\"><tspan id=\"tspan3532\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3534\" transform=\"matrix(1,0,0,-1,129.333,378.667)\"><tspan id=\"tspan3536\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3538\" transform=\"matrix(1,0,0,-1,165.4998,383.167)\"><tspan id=\"tspan3540\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3542\" transform=\"matrix(1,0,0,-1,170.4998,378.667)\"><tspan id=\"tspan3544\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3546\" transform=\"matrix(1,0,0,-1,234.083,383.167)\"><tspan id=\"tspan3548\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3550\" transform=\"matrix(1,0,0,-1,239.083,378.667)\"><tspan id=\"tspan3552\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3554\" transform=\"matrix(1,0,0,-1,211.2498,383.167)\"><tspan id=\"tspan3556\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">k</tspan></text>\n",
        "<text id=\"text3558\" transform=\"matrix(1,0,0,-1,215.7498,378.667)\"><tspan id=\"tspan3560\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">E</tspan></text>\n",
        "<text id=\"text3562\" transform=\"matrix(1,0,0,-1,348.4168,394.167)\"><tspan id=\"tspan3564\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12 16.68 21.68 27.52 29.74 35.3 40.3 45.86\" y=\"0\">peak\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3566\"><g clip-path=\"url(#clipPath3570)\" id=\"g3568\"><path d=\"m 2752.5,3916.67 1830,0\" id=\"path3574\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3576\"><g clip-path=\"url(#clipPath3580)\" id=\"g3578\"><g id=\"g3584\" transform=\"scale(10,10)\"><text id=\"text3586\" transform=\"matrix(1,0,0,-1,279.833,383.167)\"><tspan id=\"tspan3588\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3590\" transform=\"matrix(1,0,0,-1,284.833,378.667)\"><tspan id=\"tspan3592\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3594\" transform=\"matrix(1,0,0,-1,320.9998,383.167)\"><tspan id=\"tspan3596\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3598\" transform=\"matrix(1,0,0,-1,325.9998,378.667)\"><tspan id=\"tspan3600\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3602\" transform=\"matrix(1,0,0,-1,430.7498,383.167)\"><tspan id=\"tspan3604\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3606\" transform=\"matrix(1,0,0,-1,435.7498,378.667)\"><tspan id=\"tspan3608\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3610\" transform=\"matrix(1,0,0,-1,362.1666,383.167)\"><tspan id=\"tspan3612\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">T</tspan></text>\n",
        "<text id=\"text3614\" transform=\"matrix(1,0,0,-1,398.7498,383.167)\"><tspan id=\"tspan3616\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">(</tspan></text>\n",
        "<text id=\"text3618\" transform=\"matrix(1,0,0,-1,401.6666,383.167)\"><tspan id=\"tspan3620\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">Z</tspan></text>\n",
        "<text id=\"text3622\" transform=\"matrix(1,0,0,-1,407.08301,378.667)\"><tspan id=\"tspan3624\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Symbol;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Symbol\" x=\"0\" y=\"0\">\u2261</tspan></text>\n",
        "<text id=\"text3626\" transform=\"matrix(1,0,0,-1,410.9166,383.167)\"><tspan id=\"tspan3628\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">)</tspan><tspan id=\"tspan3630\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"65.5832 73.0802 80.5772 83.0792 90.5762 98.0732 100.5752 108.0722\" y=\"-6.0832\">mm mm mm</tspan></text>\n",
        "</g></g></g><g id=\"g3632\"><g clip-path=\"url(#clipPath3636)\" id=\"g3634\"><path d=\"m 557.5,3770.83 4574.17,0\" id=\"path3640\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3642\"><g clip-path=\"url(#clipPath3646)\" id=\"g3644\"><g id=\"g3650\" transform=\"scale(10,10)\"><text id=\"text3652\" transform=\"matrix(1,0,0,-1,181.333,130.667)\"><tspan id=\"tspan3654\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 2.502 7.506 12.51 14.508 19.512 22.014 26.514 31.518 36.522 43.02 47.52 50.022 55.026 57.528 59.526 64.53 69.03 74.034 76.032 78.534 86.031 91.035 95.535 97.533 105.03 110.034 112.536 120.033 125.037 128.034 133.038 135.54 138.042 143.046 148.05 153.054 155.556 160.56 163.062 168.066 175.563 183.06 185.562 190.566 195.57 200.574 203.571\" y=\"0\">table shows 3 local maxima more than 8.0mm apart</tspan></text>\n",
        "</g></g></g><g id=\"g3656\"><g clip-path=\"url(#clipPath3660)\" id=\"g3658\"><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3664\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3666\"><g clip-path=\"url(#clipPath3670)\" id=\"g3668\"><g id=\"g3674\" transform=\"scale(10,10)\"><text id=\"text3676\" transform=\"matrix(1,0,0,-1,55.75,117.083)\"><tspan id=\"tspan3678\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.498 11.502 13.5 18.504 23.508 26.01 28.512 31.014 36.018 39.015 44.019 48.519 53.523 58.527 60.525 65.529 68.031 70.533 76.032 78.534 83.79 86.292 91.296 93.798 98.802 103.806 106.308 108.81 113.814 116.316 121.572 124.074 129.078 131.58 136.584 141.588 146.592 149.094 152.091 157.095 159.597 164.601 169.605 174.609\" y=\"0\">Height threshold: T = 3.16, p = 0.001 (0.999)</tspan><tspan id=\"tspan3680\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 13.005 18.009 23.013 25.515 28.017 30.519 35.523 38.52 43.524 48.024 53.028 58.032 60.03 65.034 67.536 70.038 74.538 77.04 82.296 84.798 89.802 92.304 96.804 101.808 106.308 111.312 113.31 117.81 120.312 122.814 127.818 130.32 135.576 138.078 143.082 145.584 150.588 155.592 160.596 163.098 166.095 171.099 173.601 178.605 183.609 188.613\" y=\"9.75\">Extent threshold: k = 0 voxels, p = 1.000 (0.999)</tspan><tspan id=\"tspan3682\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 44.523 49.527 54.027 59.031 61.029 65.529 68.031 73.035 78.039 81.036 83.538 88.038 90.036 95.04 99.54 102.042 107.046 110.043 112.545 115.047 120.303 124.803 130.059 132.561 137.817 140.319 145.323 147.825 152.829 157.833\" y=\"19.5\">Expected voxels per cluster, &lt;k&gt; = 7.463</tspan><tspan id=\"tspan3684\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 45.027 50.031 57.528 62.532 67.536 70.533 73.035 78.039 80.541 83.043 87.543 89.541 94.545 99.045 101.547 106.551 109.548 114.048 116.55 119.052 124.308 128.808 134.064 136.566 141.822 144.324 149.328 151.83 156.834\" y=\"29.25\">Expected number of clusters, &lt;c&gt; = 6.75</tspan><tspan id=\"tspan3686\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.499 13.995 19.998 25.002 27.504 30.006 35.01 37.512 42.516 47.52 52.524 55.026 57.528 63.027 69.525 76.023 81.027 83.529 86.031 91.035 93.537 98.541 103.545 108.549 111.051 113.553 119.052 127.548 133.551 138.051 140.553 143.055 148.059 153.063 155.565 158.067 163.566 170.064 176.562 181.062 183.564 186.066 191.07\" y=\"38.91641\">FWEp: 4.810, FDRp: 4.894, FWEc: 69, FDRc: 69</tspan><tspan id=\"tspan3688\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 235.165 240.169 245.173 248.17 253.174 258.178 262.678 265.18 270.184 272.686 275.188 277.69 280.687 285.691 290.695 295.699 300.703 308.2 310.702 315.958 318.46 320.962 325.966 328.468 333.472 335.974 338.476 343.48 348.484 353.488 355.99 360.994\" y=\"1e-05\">Degrees of freedom = [1.0, 115.0]</tspan><tspan id=\"tspan3690\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.166 242.662 249.16 256.657 259.159 264.415 266.917 271.921 276.925 279.427 284.431 286.933 291.937 296.941 299.443 304.447 306.949 311.953 316.957 319.459 324.463 326.965 334.462 341.959 344.461 351.958 359.455 361.957 369.454 376.951 379.453 381.955 386.959 389.461 394.465 396.967 401.971 404.473 409.477 411.979 416.983 419.485 424.489 426.991 429.997 434.497 439.501 444.001 449.005 451.003 455.503\" y=\"9.75001\">FWHM = 12.2 12.1 12.4 mm mm mm; 4.1 4.0 4.1 {voxels}</tspan><tspan id=\"tspan3692\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 241.672 246.676 254.173 259.177 261.679 264.181 269.185 274.189 279.193 284.197 289.201 294.205 299.209 301.711 306.967 309.469 314.473 319.477 324.481 329.485 334.489 336.991 341.491 346.495 350.995 355.999 357.997 362.497 364.999 370.255 372.757 377.761 382.765 387.769 390.271 395.275 397.777 400.774 405.778 410.278 415.282 417.28\" y=\"19.50001\">Volume: 1202364 = 44532 voxels = 592.9 resels</tspan><tspan id=\"tspan3694\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 244.174 249.178 251.176 253.678 258.178 260.176 264.676 269.68 272.182 274.684 279.688 282.19 287.194 289.696 294.7 297.202 302.206 304.708 309.712 312.214 317.218 319.72 327.217 334.714 337.216 344.713 352.21 354.712 362.209 369.706 372.208 374.71 377.707 380.704 385.708 390.208 395.212 397.21 399.712 404.968 407.47 412.474 417.478 419.98 424.984 429.988 432.49 436.99 441.994 446.494 451.498 453.496 457.996\" y=\"29.25001\">Voxel size: 3.0 3.0 3.0 mm mm mm; (resel = 67.06 voxels)</tspan></text>\n",
        "<text id=\"text3696\" transform=\"matrix(1,0,0,-1,60.25,364.91699)\"><tspan id=\"tspan3698\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 32.0832 36.8832 64.0832 68.8832 73.6832 78.4832 83.2832 105.25 110.05 114.85 119.65 124.45 146.4168 151.2168 156.0168 173.8332 178.6332 183.4332 188.2332 193.0332 219.5832 224.3832 229.1832 233.9832 238.7832 260.75 265.55 270.35 275.15 279.95 292.75 302.35 307.15 311.95 316.75 333.9168 338.7168 343.5168 348.3168 353.1168 375.0832 379.8832 384.6832 389.4832 394.2832 416.25 421.05 425.85 430.65 435.45 440.25 445.05 449.85 454.65 459.45 464.25\" y=\"0\">0.000370.0000.0009030.0000.0000.000 7.14 6.480.000 36 \u221278 \u221218</tspan></text>\n",
        "<text id=\"text3700\" transform=\"matrix(1,0,0,-1,279.833,355.25019)\"><tspan id=\"tspan3702\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"0\">0.0000.000 6.39 5.900.000 33 \u221287 \u221221</tspan><tspan id=\"tspan3704\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"9.75\">0.0000.000 6.20 5.740.000 21 \u221296 \u221218</tspan></text>\n",
        "<text id=\"text3706\" transform=\"matrix(1,0,0,-1,124.333,335.75019)\"><tspan id=\"tspan3708\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 82.3336 87.1336 109.75 114.55 119.35 124.15 128.95 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 228.6668 238.2668 243.0668 247.8668 252.6668 269.8336 274.6336 279.4336 284.2336 289.0336 311 315.8 320.6 325.4 330.2 352.1668 356.9668 361.7668 366.5668 380.9668 385.7668 395.3668 400.1668\" y=\"0\">0.1100.106460.0170.0060.010 5.40 5.090.000\u221218 0 72</tspan></text>\n",
        "<text id=\"text3710\" transform=\"matrix(1,0,0,-1,279.833,326.00019)\"><tspan id=\"tspan3712\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 225.4668 230.2668 239.8668 244.6668\" y=\"0\">0.2880.180 4.25 4.090.000\u221224 3 66</tspan><tspan id=\"tspan3714\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 220.6668 225.4668 230.2668 239.8668 244.6668\" y=\"9.75\">0.8610.509 3.66 3.550.000 \u22126 \u22126 69</tspan></text>\n",
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        "</g></g></g></g></g></svg>"
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       "text": [
        "<IPython.core.display.SVG at 0x4141910>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You will see the FWHM values at the bottom of the page - here they are 4.1 voxels in x, 4.0 voxels in y, and 4.1 voxels in z. These values are rounded; I can get the exact values from MATLAB by looking at ``xSPM.FWHM``.  These are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FWHM = [4.0528, 4.0172, 4.1192]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is therefore a block of volume approx:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resel_volume = np.prod(FWHM)\n",
      "resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "67.064316892672011"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's the value you see at the bottom the SPM printout after ``resel =``.  The resel count of 592.9 in the printout comes from a calculation based on this estimated FWHM smoothness and the shape of the brain. In other words it applies the search volume correction I mentioned above.  If it did not apply this correction then the resel count would simply be the number of voxels divided by the resel volume:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "44532 / resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The table gives statistics for each detected cluster in the analysis, ordered by significance level.  Each line in bold in the table is the peak voxel for a particular cluster.  Lines in standard type are sub-clusters within the same cluster.\n",
      "\n",
      "Look at the peak voxel for the third-most significant cluster.  This is the third bold line in the table, and the seventh line overall. On the left-hand side of the table, you see the values for the \"peak-level\" statistics.  The extreme left gives the voxel location in millimeters.  Our voxel of interest is at location x=-42, y=18, z=3.\n",
      "\n",
      "The value in the \"T\" column for this voxel is 4.89.  This is the raw $t$ statistic. The column $P_{FWE-corr}$ gives the random field corrected $p$ value. In this case the value is 0.037. 0.037 is the expected EC, in a 3D image of 592.9 resels when thresholded at $t = 4.89$. This is equivalent to saying that the probability of getting one or more blobs of $t$ value 4.89 or greater, is 0.037.\n",
      "\n",
      "There are other corrected $p$ values here, based on cluster size, and based on the false discovery rate, but I didn't cover those corrections here.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Worsley, K.J., Marrett, S., Neelin, P., and Evans, A.C. (1992). [A three-dimensional statistical analysis for CBF activation studies in human brain](http://www.math.mcgill.ca/~keith/jcbf/jcbf.abstract.html) Journal of Cerebral Blood Flow and Metabolism, 12:900-918.\n",
      "\n",
      "Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., and Evans, A.C. (1996). [A unified statistical approach for determining significant signals in images of cerebral activation](http://www.math.mcgill.ca/~keith/unified/unified.abstract.html) Human Brain Mapping, 4:58-73."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Thresholding with the False Discovery Rate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The false discovery rate is a *very* different correction than family-wise correction. Instead of controlling for the risk of error under the null hypothesis FDR will control for the number of test falsely declared significant as a percentage of the number of test declared significant."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A basic idea on how the FDR works is the following:\n",
      "\n",
      "Let's assume a significance threshold of a voxel $p(i)$. The expected number of false positive (FP) in N voxels at this significance threshold  would be \n",
      "$$\n",
      "E(FP) = N p(i)\n",
      "$$\n",
      "\n",
      "Now, we want to make this number less that $\\alpha$ percent of the number of detection. If we have ordered the voxels with increasing p-values, the $p(i)$ threshold corresponds to $i$ detections. Therefore, we want that:\n",
      "\n",
      "$$\n",
      "E(FP) = N p(i) < \\alpha \\textrm{i}\n",
      "$$\n",
      "\n",
      "therefore, if we choose the largest p(i) for which this holds we protect ourselves from too many false detection at the level $\\alpha$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are a number of interesting properties of the FDR  - and some not so interesting if you want to do brain imaging.\n",
      "\n",
      "* In the case of no signal at all, the FDR threshold will be the FWE threshold\n",
      "* Under some conditions (see Benjamini and hochberg, JRSS-B 1995), the FDR threshold can be applied to correlated data\n",
      "* FDR is an \"adaptative\" threshold\n",
      "\n",
      "Not so \"interesting\"\n",
      "\n",
      "* FDR can be very variable \n",
      "* Activation is large : control of risk of error is weak"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This figure shows the principle:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import IPython.display as d\n",
      "\n",
      "d.Image(filename=\"/home/jb/code/pna-notebooks/images/figure_FDR.png\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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HjAEAGz8/K1dXatbBKgAf/WNBPNnaMWN6Gz0kT6fMEt4uJ7VNJ1Ut03h0dZw0\nlnSyr+D32yT2NPdrlFDoMXMmyeF0nzt6z/7vf+cmTrwUFdUgFNIE8cJ//+uTnW2ediKzEY8Z822V\nS4pCAMVagAJqrgtZX1hIq1Q6leoi+BnhFWgtQXJpoulnoEQ6qnlhMJqsb6TdAzTs2xw88em/Rv7j\nH+M+//zg+PGxa9YYsj+l0Uw5fXrK6dOmbhhiVopCEF2bIfTw4IrFJGFtw3ZypcQS0lgDCtpGFu2u\ncOcDAOga2BqP+rFuTUnEslaNcKc5fBrnM/dfblOnNhQVVaWlVSYnM90WZHFIDoe0sQNrWwrYHLaz\nq7q0mDBa9NRwS+jqh5/W/bXFLq2Bc628Zu7TpdENrAY1LbLTUQBleRROKeynxn3xxcjXXju5YMGe\nkSOZbguyRASHQ3C4hMiWArVKXVWtk8tolQr49//N+6Pl3N3fNE8RY13bb+vySO1YZ609AABIb4r2\nJbDwPlz9DsnhRP/00/Uvv6R1urwDB5huDrJQtEpFq5R0XQ1F19eqy4r1fT3GiZ52tDX8vzbwTwq1\n1lxQ1LMasY+nfwp+772hK1fmHz165Y039FtSgoJ2LVlSJxKx1eqxV68+vGcPVmYhnUqlq60GNos6\nXKIDlivwAfgQxJMZ4bl5Q2tm0qL9GW2mDKkaWJUNRnhyZHkErq7z4+PPLFly9+DBisRE/cZro0dv\neO45/c8airoUFXUrIOD9Dz7gYqn6ABbEk10EP6gFqG2gjs6zb367AIA0qbsVBg1DaAMXVbLjhXEJ\nvMIG7FDu50hycEyMlZsbi88vO3u2efPuxYtb70UThJbFOjdx4vQTJ8zeRGQRpElJa1vP6yk+ezb7\nzz+N+xpETS6H9q1bPb62NM0qLs4qrQhvst4vOY0bN/fixUvPP7+Zz9eq2lxK19rYtNuZ0mjuDB2K\n0TNgSVNS9HMGXcaPtwsMNEUNl47MvyI6lGNzxFkRHNY4dXXDzFL+lTirxFvsRkyg/sNm6FCSw1FV\nVxedPdsudwCAo1Kp2W2qhB0qK83YOmTpTFDDpcy2OZZHAICslHfpoMPXnzruvUa6T6p87R/SRRMU\nLgLjvyIyu8ExMUtv3x40ffp2iaS+s5nH4+LjW1dm8eVyBY8X1MuJ8qgfMcFZD60lWt/UmFZSWVdE\n2df4wTHVcydVj5hE3j1vv+MsG2983GeNWr8+98CBvEOHkj/6qKt9FuzfnxYYKOfzuUqlXXW1nM/n\nqFQRcXHmbCeyZCaIHoKt49Gk/N50eq8zAAAgAElEQVSsQY69cvS4hoixKlv9GVY9VV6Flet9l8ec\nOWGffy5wdT05f75+i5LLJXU6trrNlwlbrX7no49iIyNvBQQAQGhCQkRcHIl3NEb3mCB6uN51M3Q2\n+7PAzks+LrIhxKfpPjnyYv7lS1aJ6Ww5vv/6JJLDmXv27LXPPju9eHHOnj0AkD5s2KZVq+pEIgAQ\nNjQs3bkzNCGheX+2Wj3x3LmJ584x1WBkyUzRzUzoPCJrHp+l8LZr+ndFutWlS1Y3C3Gcq09zDAlx\nCg8XBwUlffABANTY2n63Zk3zgl4NQuGO5csJmg5pNVcDoa6YZJVC2m6w0g4AdKysBGFsvCCvBnCJ\njL6MJ5E8kpmZ/ssv2xwdlfcGqo7OmtVuIUE1m71v4UKMHmQIk0QPoZJxbl4UxiZzK3Hqap/HsbXl\n2tmRLFZFQoKy1QB5uUTSbk8dSTYIhTKBQCAzxrR41K+ZInpo4s4h28PpuBhYPyDy9l6amVl44sTm\nVktZ6knKy2/7+7feYltTUycScTrM8UGoIxPM61HcsdvbnDskbW2rtRXiAj19kdvUqSSPJ01Kin3l\nlY6PzvnrL0rTsvoJpdEMzssLSUxsvRGhrpj4ZjikSP7Y2vK1D6vwHhR9jbWX1+wTJ8Zv3Lg/NLQu\nM7PjDqK6uqe2bOEpFK7FxUMyM92Kiqrt7B7es8f8TUV9kWluhoP6uMgffihPTLzyxhtpP/7YzW5j\nr171yc6OHzdOweMNKigYfe0anvIgA2H0oPasXFwCXnjB5vTpo9Om3Xdnu+rqmceOmaFVqJ/B6EEt\nSDZ70bVrVampu4YNq+3sIgshYzH7jY+RpSLZbLZQKPLxUdbU1GZkAI0jlMiE8KwHAQCQXO6TVVX1\neXmb+HwMHWQGJo4eXR3/1695LC2BUwstmMjbmyDJhvz8a59+irmDzMN00UPSdk5qOz4o6qjqGgLf\nz5aKxeUuychQlJXtcHNjui1oADFN9Ah965YsavRoucEFWZomuHBWeFuKGWRRfJcvp3i8m//3f+kb\nNzLdFjSwmCB6SGvF/KWNHmwAAHkDCVwdn61zDmxYEii7ddhhfzKlxvixDCQ5aetWOZ7vICaYIHrY\nTvLBbGi8ZbP9oKBMCQDAEmg8/ORhUQ0Bc6WEynH3DRau2MO0iVu38sTig5GRVTdvdr9nkZvb5pUr\ny5ycCJr2zcpavmMHrrKMes8Eg+u0mlADdeUsv+xe37JWRuVes/7zv07bLlC+s+r8rIz/oshwBAEA\n3kuWWLm7l1+5omls7Gbfaju7/7z1VqG7u5rNVnE4twIC/v3eex1r1hF6UCaIHlWJ1Y0anUP7QmcA\nHZl7zv7AXVW4nw6nEzFnSVra8qKi7Q4Oe4OC7rvzvoULNVSbU2NKozkUE2Oy1qGBwhQZoGKf+4sn\niZDbdHxyHZmdxBF6q3E6ERMoKysrd3eCoopOn9bI5YaMoxcMGtRui0wgaLdWBkI9YIq+HteGKYFQ\nY1u/ZDJ59CqntIbUtnqL6zQEJaDxrIcJj+Xns3i8zVYPcMFr1eFyzKmsTM7nd7ozQoYzQfSwRMrg\nIBUAgGP105EAOqKyhFNcxC4q5hQXU+RQFUsmaOlm5ipnTCbOHuXgnENTsh06VBIenr1zZ9nlyw/0\ni9NPnMjx9taRTd8VpE4nKS8X1dWZoI1oYDHNlU9DgdWVHNrRRePsrJaIaAc3pYObcsS9R+na+gXz\nKWkFu6ycLVWr3O04uJCYiS24epVkszfxeA/6iyNTU0MSE2+MGCFsaLCur+eoVAWDBr35ySemaCQa\nUEwQPZoKq5NHuTdKmmYPEmydvZPaxVnt7KJxcVa5OGsFNir/0a0W0cyzN34jUJMhjz/us3TpiXnz\nZEVFPXuGp7ZsSQkKSgwJUbPZPtnZz2zciEsvo94zRfRU8lJb/ZNWk5WF3MpCbvP0Ea5I4+yidnZW\nu7ioXVxVDjjD0ITCv/6axeEcnzsXenr7PYKmg5OTg5OTjdswNMAxMdSkrKPu1lF37/ABgLCSPzKH\ngTYMABM3bfKYO3fnkCFahaLHuYOQiTA9yk3LuWdjAe+/blwEwbWzE48dq6ypUdXV0Vq89SKyOExH\nD+jI0kKm29DfzL98WRwcvNXGRiOXG7I/TRAXo6MvRUUpudwhmZlz/vrLtqbG1I1EAxzj0YOMiRII\n3B56qDwxsSY93cDcAYCNzzyTHBys/7nU2flKWNhrX37pefeuyZqJEEZP/7IoJUXk67vVzk5t8NSb\nIje35tzRU7PZ/3v22Q/ffZeFV2rIZDB6+gmRn1/Iv/996cUXuQ+SOwCQNGZMuy00QdAEUejujic+\nyHQwevqJGQcO2AwdeunFF5UPuKJFp5N0OCpV8wxmhEwB3159nu+yZStKSo5Mm/abh8eD5g4AhCQm\nkm2H3r1yc2ttbJzKyozXRoTaw+jp21gczrBVq9jW1uqGhp7NV7aprZ128iRPoeAqlQKZLDAtrU4k\nmnv4ME5ZRiaFF1x9WPjXXw9/+eXffXwaCwp6cyeJ+QcOSMrLL0ZHlzo7qzic+QcOhCYkGLGdCHWE\n0dM3EYQkJETd2Fh965a8tLSXd7AhaDoyNjYyNtZYrUPovvCCq0+aumfP/Pj47J0794wapVOp7v8L\nCFkYPOvpYyg+P+Sjj25++21dTk71/VZ0R8hi4VlPHzPp119HrFunUSiurF/PdFsQ6jmMnj5D5Ou7\nNDMz4e23D0RGViQmMt0chHoFo6fPGLluncjbm2Szy+PimG4LQr2FfT19gGdMzNTduw9PmRK/fn33\nt80yUImLy7GZM6vt7FyLi+cePixsaOj9cyL0QDB6LJ21pydfIlE3NNRlZRkld66EhW156imaIAAg\nw88vNjLyhf/+N+DWrd4/M0KGwwsuizZ8zZplubnqxsZtDg7ykpLePyFNEDuWL9fnjp6azf5l9Wq8\nvw0yM4weyxX40kulsbEFJ07k7t1rrOeUisUqDqfdRuv6+uujRhnrJRAyBEaPhRq1fn3k999LQkKO\nzZxp6kmDwoaGjnmEkElh9Fgcis+PuXCh8MyZcytX3tqwwbhP7lhRwWkbZAKZrNbGxq2nt8pBqGcw\neiyO74oVzlFRDqNGZWzZYornf3jPHq5SqV8ow6mszCM/37W42DsnxxSvhfoogsUy9UvgCJcFsfby\nWpSSErd27W+DBjWa7DRkwvnzlEZzdNasGlvbCkfH4Tdvxhw6RPSuABX1eQRhM2SIY0iIJDTUOTJS\nNGTI3qCgelN+IWH0WAq2tbXI25vF4zUWFJgud/T0deoKHo+jUpF4i66BSuDiIgkNdQwJcQoPl4wb\nBwAEQZBcLkGSQNMTNm36a9Ik0706Ro9FkISEzIuPv/nddz24LXqP8RQKs70WsgQcGxvxmDGS0FDJ\nuHHOERFskYjWallcrv7yitbptCqVVqmkNZryK1eOzZ5t0sZg9DDPdfJkeVlZbUZG6pdfMt0W1K+w\nuFyHUaMcQ0MloaHO0dFWrq5atZrF5ZIUBQA0TetUKq1CQVBUVWpq6aVLFYmJ5YmJdVlZZmgbRg/D\nnKOi5pw+nbF9+y5/f6bbgvo8giRthw1zDAlxDAlxiY62HTZMp1aTbDbJZgNB6JeU0ymVoNPV5eaW\nXrxYnpBQkZhYffOmTqMxc1MxepgU9d//Zu/cef2zzxLfe4/ptqC+SjhokP68xikiQjxmDNA0QZIs\nLlefNQRJalUqGkBRUVEaG1seH1+RmChNTtYwvfY2Rg9jHENDA557jsXlnl+1ium2oL6Ea2fnGBoq\nCQmRhIc7hYezeDyCpkkejyBJ0HfZKJUahUKnUpVdvlx2+XJFYmJFQoLiwe9WYlIYPQxg8XgPX7+e\n9dtv+0JCpElJTDcHWTqKz3cICnIMCXEKC3OOiuI7Oek0GpLDadNlI5cTJClNSSmNja1ISChPTGyw\n7Ds4YvSYG0GS1p6eIm9vGsA8uVNja5sYEsLSakdfu2ZfVWWGV0S9RLBYdoGBkpAQx9BQl/HjRT4+\nWpWKxWaT+noXmgYArVIJNF1z507pxYsViYnlCQk16el037lXNUaPWfEcHB4rLCw6c2YTn2+ejr1D\nMTFHZ83Sl6rvWrJkXHz8il9/xZupWyBrLy9JaKhjaKhzZKTDqFG0VkuwWM1dNkAQOqUSAGQlJaUX\nL5YnJpYnJFReu6btszMkMHrMx9rLi2CxlNXVtzdsME/u5Hh7H2k1O4MmiJSgIJva2gX795vh1VH3\n+BKJfijKKTzcadw4gqJaZvQB0FqtVqnUKpXqxsayuLjy+Hj9aJSqtpbphhsHRo+ZWLm4PJKdXXX9\n+g5XV7O96N8PPdRui4LHOztp0ryDB3ESs/mxhUJxcLBjaKgkLMw5KoprZ0drtS1dNjqdfpYNAFRc\nvVoWG6vPGlNPbWcKRo85+D3+uKykJGfnzvjXXzfn68oEgo4bSZ2u0crKur7enC0ZmEg22374cElY\nmGNoqHNUlLWnp1atZnE4JJsNAEDTWpVKP8umKi1NP6OvIiGhJiOjl/d07BMwekyOJxZP3Lq16saN\nPWZfjiswLS0tMLD1Fo/8/ApHR1yM2VTaFmHajRhBq1Skvnu4uctGpQKAhvz80kuXyq9cqUhMrLx+\nXadWM910c8PoMa0pu3Y1Fhcfj4kpOnXK/K8effHi0Vmz5Hy+lsUCAOfSUoKmJ509i3XqRtRShBkR\nIQkLg9ZFmAA0i6VVKmmVSlVT0zyjryIpST3gzzoxekyIIxJ5LVxYfO7c5bVrmWmASvXmJ59sfOYZ\nqVhsXV9fa2MTffHi3MOHGWlMv9FUhBkWJgkL67wIU6lsLsIsu3xZ32UjLytjuuGWBaPHJEiKWpqV\npZRKt4nFqpoaBlsilkrf/OSTEhcXBY/nWFGBXTw9YMlFmH0XRo/xsYVCFo/HFgpz9+1jNnf0CJp2\nLS5muhV9yQMXYV65UpGYWJ2WZv4izL4Lo8fICBZrRXm5uq5uu1jMdFvQA2hdhOk4dmy7GX0WW4TZ\nd2H0GJPD6NFcB4eSc+du/fQT021B92FoEaZSWRYfXxYXV3H1qgUWYfZdGD3GQ5ILEhPVDQ3b7OyY\nbgrqBMXni4ODm0a+o6J4Tk503y/C7Lsweoxj+Msv2/j5nV+1qvjsWabbgprctwhT1/eLMPsujB7j\nCPviC1VNTezLLzPdkIFO5O3tGBJiaBFmQkJ5YmJlSopWqWS64QMORk9vTT940MbP74/Bg5XV1Uy3\nZSBqLsJ0joiQhIUNtCLMvgujp+cIkiS5XMm4cY2FhbLSUqabAzRBJI0ZkzRmDFepjIiL88vIYLpF\nJvEARZiJiWVxcf27CLPvwujpuaV37vBdXLYIhUw3BABAR5Kfv/56rpeX/p9XwsJG3LjxzMaNVN+f\naUKy2fYjRkhCQyVhYU6RkZ0WYWoHahFm34XR0xMckcg2IKAuK6vg+HGm29Lk7KRJzbkDADqSzBwy\n5O+HHpp28iSDreohLMIcADB6euKRnByOSPQLjwcWs+pN/Lhx7bYoudxzEyf2legRuLpK9OtmGVaE\nWZ6QIE1OxiLMvguj58E4BAUNWbHiyuuvKyorLSd3OsVVKmttbJhuRZeaizCdxo1zCg/HIsyBBqPn\nwcw+eZJjY7NZILC0ap1R168XDBqkX4NZzzcrS2HG2yjfl+FFmJXXr5fFxmIRZv+G0WOogBdfHLFm\nzYGwMK1KZWm5AwBTT526MH68gsdTcrmkTjf85s27np6Pb9/OYJOaijBDQyUhIc5RUbb+/k0z+rAI\nE2H0GIokR7zyCl8iacjPt8wPBlep/Oenn/722GO3/f3ZanWRm9uyP/4YfvOmmZtxnyJMgsAiTKSH\n0XN/D/3+u9eCBdvEYp1SaZm5o2dfVfXy99+rOBwNRQnM9WHm2ts7hoR0WYSp1WpVqjZFmImJFYmJ\nWISJMHq6Q5CkjZ8fSVHVt25pFYo+UdrDUak4KpXpnr9NEWZ0NE8i6bQIE0iyEoswUdcwerozLy5O\nEhq6TSxWWsxNOy9FRV2Mjpbz+d45OfMOHrQzffWGIUWYOn0RZnp60xp9WISJ7gejp3Nsa+vha9bc\n+vHHkvPnLSd3tj3xRFxEhP7nMienq2PHvvrNNz7Z2UZ/IZG3t2NoqGNIiHNUlMPIke2LMAH0M/qw\nCBP1GEZP5+aePy8ePXqHq2vGr78y3ZYmFY6Ozbmjp6Go/z377H/eeqv31RJYhInMDKOnPfuRIydu\n3fr3o4/yJRJLKAptdmPEiHZbaIJgq9UFgwZ55eY+6LOxhULxmDGOISGGFGGW6mfZJCTIcI1nS0Fy\n/EKtyhOqa4wxr5VlZz9WXJ+QqTZj0RtGT3sR33zjMHKksrq6Jj2d6ba0wZfLO26kNJrW0wi70boI\n0zkqSujhgUWYfZXAz/ujLeNfsbsWMLq6xhhDCpSr16/Xhxd/dX7lv/JyOnmbmQJGT4uhq1ZFfv/9\n7oAARVWVuq6O6ea0N/raNVKn05Fk85bBeXnlEolTV7UFrYswo6Lshg+n1WqSotoXYdJ0Q0GBvsum\nYxEm5f/MhAPf+HhKC95fdObzq6quUogQex0pmDoz+8rQoOvl02eUHfbgdLZb3R9/uT1a3OHWp1T4\n/5bFPcNvvznpokfY7YI+3lfd+shk9L66laACn4o+sGmIb3XxR49l5qoAAGznGOeAD3l9WmbMnSfn\nx+64ozH91w1GTxO+ROIwYoRWLldWV1tg7gAAXy6ff+DA0VmzAICl1Q4qKJCKxXP++suqsbF5n6Yi\nzNBQp4gISWgo9LIIkxB7fPu9jx8HwGPQpz94/x6Z3lUQiCf6P8SDG1tyc9WgPnbGd7RjxFT/b77w\ncQEAgMYL1179v6JradW3s2Wd3XJZE79mt+9G+6Dxw7792tcN1Oe+uPL90dIrV6uL+njuQNsj01ss\n/vQvZh951Z6VcWvepLhDxU3XWjXGOeDl+c7+f/zhvz3VPmDWsXfOKEx87DF6AADCv/xyxLp1e4OD\n4xi6TaiBpp84YVtTczE6utjVVUNRcw8fHn/7tvihh0xWhEkSVPNJFqvV+Vb73fiTnnblQtXWgw1q\nANCqC64X78zQRK/zedEFAICrlu7fXyTt+puUViqyk8q4MyLdADSxV55661ae5U7dfBDtjkyvnoo3\n5euY42tsoDJnaavcATDiAY+dRPCu/+71z9Mx3MmHXvtbYcr66AEfPQTh9/jjxRcv2gcFVd24wXRr\n7i/i2rW5NN1UhPnCC/ctwtRnTV3PBuDpiruv/uPusf/zdK0q+dcrWV2d8pCOrk9PIuH6nYN5rd6r\n8tpT13UvupAAQI1wG8LPkXY7wZp09vzsTTuA+m9fzbhf7hDWEra8XGV4OnHteKxahczsKw10fmR6\n9Ew+z0w+tMYGQL71sYt7ijt7NiMccF3hzovLZ7gcfdz21cMPpY84vjHHdIdsoEfP+I0bh61efXji\nxCOTJzPdls4xWoRJa1K/O+H2PUHQ3fQ1E5LJ/hPYcG3L3bttXlF940QNzLAHAJA4jXMhL2d38z6m\nxq4fN8cK6vZe/jyp+3aT7gujL/7udm75wWf2NBpyKiEIDNx3Mczhx6PT3i+tNmv6dHVkHhhnSMCv\n37vxARSn4t85rezijzDGAdcpTr4df2bpxMkC9x+3+/89KS3LVKuvDdzoYVtbT92z59JLL1Wmppac\nP890c9poX4Sp0xEk2a4IEwDk5eWlsbH6rDFlEWZ3uQNA8qc87cwG6eZDDW0/X7rS+NJSsHcGALCd\nOpz9TXaXMw6pwUO+WiMEkH7wZn5Fd+lADnp4/KXdfh4AT+6eRz988Nm990kfQWDg3rjI6SKAd+ac\nhL/Mmj5dHpkHfp55X4WEUwAg2/pBXtf9X8Y54NrC3A+2h01+mk9Fhn4Rk7Nor9w0B2zgRk/Ihx+6\nT50qdHNL+/57pttyrwgzNFQyblwfK8Iknd2fjiYh6c7hgvZvUXlG4XVVgDMHAMhRk0X8gxWdj9sS\nnInvh0RRUPRj3M9Z3b7POcK5z3t7NP1D+NSeGHrRoef2dZk+goDAPbGRM0RNLR27alj4/5Ud7aYL\nxKi6OTIPhDPU/4O5bACAgqyfk7pLWiMdcPXVn7OLnh7uBuz5/x7mdzgl3SQlgQMxeuyGD4+5cOHo\ntGk3f/iBqZWoWooww8Kco6IsrAiTEj57cdmGcS3zhRSHjznHFHQ2dZlwmTYsigVXN98t7PDNTtdV\nnbgD00cAALhGSSSsirudfWNzhgV8/SQPZPnrPy6r7z4WVHU/LThsezTm40gWAABYr9wbQy84+NwB\nWcfTCn5AwO64yJnN6zSW5TwRdbGHucPmBc8ftupRz8nhDn5OFAEAGnV5UWN+bu2d29U3r5ef3H03\nuardM3d3ZJr24FpFLvN/+rHBU8LtXa0AaG1Vfu2tG9K4M/n79+ZfKdCPcLNGrB7mDwAA5Udz0xXd\nNdNYB1x+K+dk5fCnHAAC/FcPT30t2RSDXQMueig+32XCBLZQqFWpzJk7JEXZBgQYXoSp7x6uuX2b\nZmAZVk3D/yI27/WVLP9p5jeTKQC4e6W+8+9PlmD6084kVGw60tjJ50sjuxwrhxF8AIBh7gHCtLsd\n04vkz/0kaATAzf9c2Vdy/1yg6yo+mXUIWqXPqv3z6AUHn2+bPnz/gD2xUbOac6c858mIs9tzevAR\nIl0mj9qwKSTGE6BKemD/7d15CjWP6+JlGxTqHDbRduxET4AGcWJBclXbJ+/+yAA5aPaYrZuDHpIA\n6BrO70zbnqGgHWyj5/tEzbGPmuP3QsQR1yVF9QDAs12ySH/PE13K8Zr7XFIb64DLao5e0z01mQQQ\nLlps+3ZypQmK8wZW9HjMnj390KGzK1aYZ0X3ToowKYrVPKOvVRFmycWLFfeKMG9MVO78BqpXAEcG\nEVth7vvA7varzjRorTSrpoKnf39oM5JlnZ50s1wHrQ4HSEg/Wtjpm1iTcbJS/Zw7GwD4Dg/5sI51\n+P4UBI/8Yh4byu+s/bHawPd3x/RZvT9GN+/Qi4ea0oc/LGB3bNQs23u/UJ7zZPjZbT3IHYId9OrU\nv79ytwVN7Menln1YUNCqiYTY+++yKRNJAG3d5Q5nF90dGZIz7s0ZZz5yFgAU7Y2dt/pWUs29fdbF\nz9+4YP+Tgrz4pqynXF1meOofq4+7/5REIx1wWp1xpREmWwPA4Jkuru9W5hp/rsMAih7nyEhVXV1D\nfn7BiRMmyp0HKsIsu3xZ32XTuggzbTp8dwyAAABQCuHUPyB1Drw9hpH04QlDm+6uU3+l8+Fuwm3m\nsHAC4n8p6Krvsz618A64DwcAEE4I5rGSG9vsSAkf/XKEF+jOvpl0vuYBmtYhfUTPHIyhYw69dFjG\nHua/Ky5qtt29XctznoroUe4A6b1qyvmv3K2BTvnX4Rn/rmhomyG8wU6++plOd8sy28/b6+bIUAFr\npp/7yJkLULrj5Ngn80pb76BuPHegWvskO+2aXH/EBX6uQ5r+Ztmtsvu/a410wLWlt2QA1gAAQ1z9\nBDdzjT/JdqBEj9/jj0/cti3+tdf+aHWzqt5rLsJ0GjfOKTKy90WYf/zYlDt6OhbI7OHSapj0gxFb\nbRjC2ibYFQAAFLUpnU4koaxmrZYAXbbpWGNXn2x1SVlsOQyXAAD4T7cT/NLYeuK0TXTwxxNIyExZ\n98cDjwF1TJ9nD8Ww195xfj9kVnPuVOQ+FXF2a3ZPuiq4w4b/+b9B1gCQnPDop+1zBwBEQx3dAQBA\nlVGe3+78oesjYzU2eP83LlwAyLo+7/m2uQMAAOrKhmqaH5+nf4B0Gm7TVO9QLzPkssdYB1xeIZcB\nCABAIAp0JE/UGf27egBED0FE/vDDjW+/Tf/llxvfftvLJzN1EWa1e/st3HpIm8FE9PA8JU0pfbci\nt7OeHsrdc3UI0LHpx7rpo5HXnryue3YqCQDCYBcvbmFq8+eHY/vs18MkoPzj1RupPSpZ7Jg+K78N\naXm4Ivep8L97ljvAEiz8ZmwICQCKretv3+nkM08NjmgaObt7ua5dF0yXR4YtembDaD8AANWutdcT\nO6txUBWVHj/ceKlU/1EnJUPvVVo1KmSG/ClGOuDaRkWjPnqAP1RCQndThHqm/0ePz9KlgS+80FhQ\ncOHpp3vy+wRh6+cnHjvW8CLM8oSEqtTUnt0Jky0HDbfNFttCoA0qTTc26yFiNwAAUGRIizvp6SEH\nzR06BuhLvxR2/OpuQatST9bCVDsAAG/XIHsitenTSDjODnl7NGjjr75zsucT9jukzz29yR0Ajq/f\n2zMoAID8jO/jOiuaJTkBYwQAAKC5ndjY9vB0eWSsQke+PgYAAArvfPG3otPAVufeWTGv5alELuym\nH+VKg2ZjG+mA62TKe+nEcbHpsoSmF/pz9LCFwoXJyZfXrTs8aVLJuXOG/2J3RZg03bM7YV5aBWde\nhUZ7cMyGJa+C59XOdxuzB2JXAn3vv5rbABo+jN1teNuNhvIMtdb/lJ9Q19lyHcKYlWLQlv5ysvsv\nY11xXFk52EkAAOymDaO2lagBAPgO677wEkHDN2vv5PRuvixdV/HdP26ujh/V6kqajv/wyu89zR0A\n0mfJ0EAAACg9ktP5eDZPFOmj/6khLrvttUuXR4YdvNLbGQAAivdlpRl0okdYie5FqlpnWDm5cQ44\nrdHe+6tYIoEpvvv6b/QQhCQ0VOTjw5dI8v/6q/t929wJMyKCbW3dSRGmQkFrteXx8WWXL5cnJj7Q\nnTB3/h/8vabp51oX+CwOlj8LEVs62XPxOrg9BbRs4CjA7i6orABoiNxk+J9tLAR7yBgrAOhqeIvt\n6fnUaNBeSD9Zep8PhPxOQapm2BQKADhjo4Wcs9UqIAY9Mm6dD9QfvPxZYm/HTgSBgXtOjmrbg0eM\n+27OxpJDT+/pUdEmSxAdox+W110/WdvpeDbLwS5IDAAADVVJJW3OIbo8MjybBdP0t2TUJByrNSx5\nSG7zyZxWa+BKFkY54LRW149RORYAABMUSURBVLwfxSUIAGNPxOyf0SMcPHjpnTvXP/98i7V1p+UF\nLC7XYfTo5hl9vS/CrPCB0+ugxg08r8LUr4Dd6o2lFMLZl9rsrGXDH99D4HGwKWn/PLx6eH84XHoa\nbk0DoCFkJ4RvBcqEN5joSsvwVkNCJyOrpOf8oaNAd+7nwvuOutB1VSczYEoAAIDvQw62H1ZXWDu/\n8x9XDkjfeeOuAYM23REE3KuTaE/4xO4YerGhdV5t8EXjffU/NV7ropKV5+3cdHhyy9qurdXlkSFt\n7cY19eQ1XDW0MJ/WNn/iScLAyx6jHHCCbFmogDbJ8hn9MHqsvbxYPJ5GJis8dao5d7oswrw3ow8I\nol0RZlLNxU8/ySgPpSEUbErgkZchuIvkSXgUNv/adJV0bR6ceB1enQyDE5sezQttuYBq5pQJaTM6\nP/HhNsLkb2FybzvEe6dleEtZm9xxeIttveApe9AU/3zagAIfdWNcnAICeABADncbKsixeTr8GWco\n2XD5fxm9Ch5BQMCeuOY6CYDynKem33T9Yfa9fh+hgXVe7RACgXfTnCBVYU2nX/ak40h7/TBa7Y3K\n8tYx0vWRYYttHJt+VOVXG3YOQesUzV87FIsyMHuMccAJinWvk4lWKnQmqD2xmOhhW2tcXTS2VjqK\nINRKslZKlZSzulwUr0t2gYGLb9zI2bVrm52d0MPDa9GiByjCTEiQpqTo00puA/8sBpWg6WlrXWDL\ndgACgve0f0UtG7ZvahMuCmv48TD8x6vp3Me6vLM/VwEsU5UEGwPPQ+Ktv8C/W95xeIvt7fVkIKjP\npJ8pN+R/SHPnZKVmtRsFAA5OUaMHB70rBnnh6x+V1vXiHc33D9gdGzWz9Xzl8LPbcrREm15n4VN7\n5tGLDnZT59URS8C9N6pEq7SdNpHlHdkUeDmX2nSEdXNkCC51bwBB18XTdkTXS9UAbAAAikUZ2uVi\nhANOUKx72aCRdpxZYAQWED0ciWxaTN1Y9w5/noKddNz2xHXqQQKI7+RUl5vLcXB4srpaxaVVtNKO\nJ+m0CLMkPna7475zIzJZteqI3TB6HxCtXuf0qy25o6fhwZ/fdRI9BUGg5rXfyG2A1DkwZjcAgEsa\ncBpBZdXyqCQLyvxgcILhf5bZWQ8RN530ZEqL2l/vkT6L/AJAd/rnom6rzFvUXi/KALcAAADbl3+M\ncrGB2+/H7y7q+Rua7x+wO67VfOWK3OZ5gx3GvIQr98bQCw89t7/TgoZO6NTNPawcVxEJ0OF6g80P\nHq4/J1Bcu9F6Nb/ujoxOob43zM12FJIgNeTY6arzlU3Rw+cKDB5o6v0BJwWce/mrzDdJsT/T0UMI\nlHOW11vfst51hlNexZIpCS0Ai62zEmmcPRVjJ1fNrHc8lE0YdsxcJ00av3Gj0MOj1ps9GiJuw20A\n4AN/rWbNi4mzpZfim4swdRR8lAJFw5t+8eYs8L0EL80G7r21RosD2z+5jgSlFTSIQShts13b2SG0\nrgDFvesAgoZVy2HTb8CRAw0w6DpUu0PUz+CUYdAfxQjKI9S66aQnoUP1Fkf08OO2oCr8+ayhg+Lq\notLLUggQAwC4jOKBNOOV76t6XBakr5OY3Sp3Vka0GUfvpM5rXwx0UWXaka5BVqIA4AGA9eQQ7odp\nHYbw+KKIwfqf6mJzWz3Y7ZFRl1blqsGXDQCiCcOoH/IM6cHTld6SAQgBAGwEIoM/rb0/4JRI0DTA\nCbJbpaaIHlMM2D8IjotcdNXht+NWt3LZ0lpSpiCUCkJWz6oo4t6Is9m+TWAzUt3petedIVgshVSq\nkjWE0WH63AEAOci/VH/27OnxV15/PWfPHn3x94n1LbkDADoWFI2Ak+tbtjh26NaxrgANt5OCBq8E\nINu+oQXVUCcBl1stW0YfgBfngs8loFSgEMLM/8CCNw39o5hAUM3DW5lJ7SatAGeIz+NDQXk2/WyF\nwd+ispoTqc076y68dfVsT2+ayh/atk5Cmrcq4u8tWe3DQZ8+b8c2b7detX/eT/MFBn14G6tPN715\niKgPgifZt7nOIQTW014aOVl/eMqkaa16bbo/MnRN+e+X9dvZMW/4DO7YFDY/8vmw92fwWa1/6XZl\n0zgqz2qwjcGD3L094KS9F7+pr6dUml5rigsupqMHALTqLsftaC2hM/CMBwCg6PTp+Nde++T9iBKi\nzdCRmg+nX4V6ScuWpMXtf1duC3FPtfxz+udtxpVILfidA//TwO0wAZXUwMxPgHdvTo8kEzySwe0m\neMW32W3Y3/DCfPjcFd4Mg/Bt8AB/FQN41l0Pb7H8lgwZAtqzPxc/wPoTtCr11L1CtezUdb/1dOks\nju3aPdFz2uTOmc0dcqfpNTukz+rfxi9yNuDTq2nc/2NJU9+QR8CptNkbPxj50ksj/vnviG1HFhY3\nLDvxnlvTKW12WV7Ld9H9joy2ce/bafn6v2Ni9N/bhz/kzWYBAIuS+Ls++sb483dXXPq3fYO0TT+Q\nPKPwetMbUThmEKvDk3ahtwecdA9u6iFQXSvMNMntcZi+4FKV8BrnVD/MF6ZksitqSIWa0NFAUjq+\ntVbirgyKkMuPix9kaLn00qVboZ1styuEMr+WHl9Wh/8JXk2bbLKqgqeXwuZfwT4fhJWgI6FwJKyd\n1vmLxrwH/Fo4/iaouSD1hsDjMP8dCw+XbhFC0Rj9RGbQ8XztfSpqcis0TefcXJtHlotAkf/z+c4n\n43ZBV3iprBJsHUC1e11qSo9XU1TVfLv4Ytil6HkOAJV5qyPObM7sbuC37ZVX7U9LL+y93ywkfWsL\ndlxYu2Thj9PYAADOrk+/53rvIdnpT08vrwo6/bkDABQl1tQ2X4sYcGTqYxNmvSQ694OHGMBrWcSZ\nZa1vJqu9sT02/NVb8W3X/aFrynclwbRwAOCFBPFYcQ2GjXT37oBT/KDgpg7Mq7srOh/l6y2mo4eW\n8Y78SU+LqXt0fIfrSRnn6in7k5nkA/7hg64D0G2KMEkNqHlt5toE7YO7Y9oMS/nGte8tHn0APvCH\ny0+A3BbcUiFofyenPM2mfgVTv4IGMQhq2l9/9T08D4lX0+Gze/PgwjcB5CdOe87MqaCBO8z3UW+Q\nH0m/8IALJMruFKZqh05IuvrWsV7d50CefntpmHbjNvcLK89v6jZ39PTpo/s9TPLDmfXH5YbOUFHW\n/jdmd/YrY996enCkL4cFOml66bFdGf/dkBVfQs09Mkn/3FmX65tPegw6MrQm7ccTQ2J9XvtnwNKp\nEl97EkBXmVn+96GsTRsyT2WpOzkyWtmJX0q14c4sgIAYR7v/Nhh4stmbA07YSeYF6F+95OcTBpWO\nPTji9COPZP/5p0me+4GwRWo3Z62NUMcmQK1g1VSwiyvIDvdh1Tg5VS9c6PjTT908k44F/8yHWteW\nLWN3QXEgvDsKyHsHUc2D929DowMorIFSQuAJyAuBlStg2Bkj/1noHspqwfsjXfck/ni9jyczz+HT\n24veGAwADZ8H73wjxeS3CiPsPXbmzlgsApDnLxh0/ICBod/zA044Lp5ZsMudC1C767j3I/n3zsMq\nnn/ebt8+yuBJ/F1xGT/eLjCQ6bOeZuo6dl4d+/773R+phbXT4auzIKgGoRQoJWSMh1emt+QOALAV\n8Hok7PoGri0AQgflQ+Dx1Zg7JqVp3P/uZaYbYQSE0CZMvzq0pja+0/VHjY2uKnzvP5WLP3UAvvur\n84WHNxl2zdXjA05ZLVrrxgUAkH78XmH7dV+NxmKix6hcb8IH/nB9HpQNAcccCN4LVh2+KmyL4Zml\noOGAltPdlRRCbXA9JT73VgjLarzPzkaiS//+/MdPLHzbnxz/r5Hhu+IudVeo3FuiyNHvRhAAkPb/\n7d1ZTBz3HQfw3/xndvZmD3YD5gg2YNzYcQsCLCeKJRNHhtix1aqt3TZtpTw0VSu1qaq+5KHqkT70\noZeqWmnSRq5cpU5dV4lbO3ai2E7j1EmxMQVTCODI5mbNsni9sMfM7EwfNixHbGDl3R0mfD9PyzLs\nDMuf78785n88986hXqzDNUcpKoo89thKtvz0ANEAEZFaR0v/rXQYIwUG5WrypkZiyZMDVTsiRXna\nbeTiL96++vudW8sefOUPnd9+aSyam5MRzlbyjec3lxBJHed++d71hxf8oylF2fxtDRY9QiDgOXZM\n8Xr1PhBYo4QNNe5UCX6sMxyOc3kbDRPva3/2B47f/rqh8uDnvtv95+fOrfBWVyYE565nPvvFElL7\nW7//bEd/ZFFHBM/Ro/de6JnbWbZeKG8s3d3LbwSQE5y14uep9SGUK8fp/LuOvO793faLl7Xjpxt3\n/eQr4wOvP33kVhbPfTi7+6k/7v3xo9bQG++3HLx6KWxf/mfuySroUghgGBbnQ5WpR4p0v7e6kOV3\nAklt6mJ7ywOv/+xfpif/dKDtULk/S/+/fFHFC+0HXvoS/9aPTm1+ovNSTrovL4LoAVgx5nbXr0s9\ntBx4cX9/8Mu/asj3hYM8OvzDR482PP1BsMbjzdLOBZ+neqz7qdpXmn86EshT54dV068HADLDOKZq\n2bkFxRhT87bWZKpfD856AAwqW7lDRPnLnTREDwDowHh3uOaIRdGWx6PeJBPs2s1W15n2jCYVA4A7\n4+1SQ3O4UXG9+A8xZ33eDBs9nEVqfjJie8N/5H+M3NGvfWtyd+i+UzcMPF4cQH+cVtYQebhaca1X\n7D053ZNhL7hsVZHPmMXL15hKpIat7w9otTsSVl3WygP45OBCXQV/O+bqCi+/6b0xavRohdWyEDGF\nUzcCNZoaZcK6hC8r408B1iyNorGsL7l1R4aNHodXI4klPnqTuMQ0I5viWPEsbgCgK4NGD0ciT6SR\nNpvPapKINBHRA2AMBo0ejaQkEUfpfuyMJyJOysf0KQBw7wwaPcRNTzIyJ8XZ6DE7VYoKORjMCwC5\nYNjoCV4zyU7Znaorc1phqaqMi5OreUFPAJhj1Oih2IeOjpjUUK0yIt4d234/67xgydH8SQCQbYbt\nUqglxDf/UrBnT+jrtYzZtckz3jPoT5gfTH1gf/ALW6nruO9ED5s/9oezx776nemRw/5zU/LOz4fr\nqmUXT0QsNCqMX3OePC+mPxuYM757//SmCtkj0sxNse8/rlNtgsHni/9E4NVN22eq/PL6QrJaI/ue\nME0O2S52CDno02zY6CEiKWB77bBt+e0gu/hkRWWS56lyQ5JfGD3OjdGy29bTQaKk6e2jvo7twWda\nZIpY/n7YNbLwWliNWM78lY9/M7htzHvoVTNOV1eLJOv9t7OXiF7L9Z6MHD2gD9l0/mVPqIIGOkwL\n8oQlNzXKoSvu0GyxPzIohkl2OaUKJ42EFr+Mpy78SIH5xBHkztpk2FoP6CgRsLS2WgKJBU/ynliD\nT7jcw6fPg5RJ83CCiJSNJeqiIS7MEW/epYyedXXncnEFWMVw1gOZKHroVkt9fINPo6Dzd887gnO9\nGTTvgzH3qKPv9rytJVPvOG2poOIaxdQ1bww0p1Y0hTeGHS9c4dEdYq3CWQ9kIvCe+9hZUSWSJ0yR\n+bEhKLW16uAl8/T8qyeNjfQLRGQtT3jmfciZimf21nKtJ+0TKCyvXYgeyIzmKlMY0dTQghtSpuLo\nVrPYep0tqtvcviFGiMiTKEvfD+CV+r0zlquud4ZxR3ItQ/RARjitsDRJxE2Mz19IWittiPP9tsHY\n4s3loGVEJiK5pvijEpBz8+2dPvH0WXMMwbOmIXogI0KyzEtE/ODUXOGYs0iNNdTTJiY+vn3C1Bsg\nIirdmDQRcdbErmYp8JarB9XltQ7RA5ngRKW0gChmCsxbbty6fqZSsl4Zu9NEbRo33M8TkWO9VMBr\nJY+Et0w7Tv6Xz/sk5LDaIHogE4Jb9hDRLXEqXenh1KptUqzTdvPOA+i48HUxSkS+eHlZdO82rvWf\nqC4DIXogMxa/7CSKjpmis+ctzJloLOXbO/m75Yk8YRlViDhp98GI86rrwihmsQVC9EBGNHe5QkRT\nQywdNK5PzRSHbF2huwaKljD1ThAR2Zj59DkxjuoyECF6IBNM8xerRGx0YvYmOq9saVACl63hJYo3\nKj90jSei628WfDCdl+MEA0D0wMoJSrmHiNTN+0IHmuNunoTCWJ3LdKmPLV02Dn0oTg0XnOpAdRnS\nsOY6AOQV1lwHAN0gegBAB4geANABogcAdIDoAQAdIHoAQAeIHgDQAaIHAHSA6AEAHSB6AEAHiB4A\n0AGiBwB0IJQ0NZkcjvTXwba2YHu7jgcEq5yvrs5XX//x59FyYGnpluOqqbGXlAh7ToSIqlLfq7NE\nv1dfjwYES/DV1/8mtK49vmCxe7QcWNZcyxlNEg0J+1yDkZCgSZIqSReoRu/DAwNoj9t2hPuYKHKi\niJYDK5dqOY5Sv9lbIDC3XzRbOTmWDN0kIrOTc/hRAIK7Mjs5IjIXmHnvfZzFqsXRcmBF0i2Hs1vI\nKgjOrU3yjUEtPKXFZYoRsxQyZ4XeBwmrF7MUEhGzeZjDy/uLkhOBlbYcDbMy60vn95+ZvUTEbG45\nabVvqP8/ntxjMujV2LEAAAAASUVORK5CYII=\n",
       "prompt_number": 88,
       "text": [
        "<IPython.core.display.Image at 0xb907790>"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's implement the FDR for some simulated data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s_fwhm = [7, 7]\n",
      "sd = s_fwhm / np.sqrt(8.*np.log(2)) # sigma for this FWHM\n",
      "stest_img = spn.filters.gaussian_filter(test_img, sd, mode='wrap')\n",
      "\n",
      "# Restore smoothed image to unit variance\n",
      "svar = gauss_2d_varscale(sd[0])\n",
      "scf = np.sqrt(1 / svar)\n",
      "stest_img = stest_img * scf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 125
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = hist(stest_img.ravel(),bins=50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0SRcuXFBpaan6+/vldDolSU6nU/39/ZKknp4ePfLII9Fz3G63wuFwzOfbt29f9GOfzyef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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xafc1f50>"
       ]
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#add signal\n",
      "\n",
      "t_values = stest_img.ravel()\n",
      "signal = 3.\n",
      "n_vox_signal = 100\n",
      "signal_pos = np.arange(n_vox_signal)\n",
      "t_values[signal_pos] += signal\n",
      "p_values = sst.norm.sf(t_values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 147
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rank_i = np.arange(1,N+1)\n",
      "np.zeros((len(rank_i))).shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 148,
       "text": [
        "(16384,)"
       ]
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alph = .05\n",
      "ind_p_sorted = argsort(p_values)\n",
      "N = len(p_values)\n",
      "rank_i = np.arange(1,N+1)\n",
      "rank_i_x_alph = rank_i*alph\n",
      "efdr = N*p_values[ind_p_sorted] - rank_i_x_alph\n",
      "first_values = slice(0,200)\n",
      "plot(rank_i[first_values], efdr[first_values], \n",
      "     rank_i[first_values], np.zeros(first_values.stop))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 149,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb57b090>,\n",
        " <matplotlib.lines.Line2D at 0xb35ce10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb59dc10>"
       ]
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = slice(0,200)\n",
      "a.stop"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 145,
       "text": [
        "200"
       ]
      }
     ],
     "prompt_number": 145
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# find the \n",
      "\n",
      "ind_efdr = np.where(efdr <= 0)[0]\n",
      "\n",
      "print ind_efdr\n",
      "\n",
      "if len(ind_efdr) == 0:\n",
      "    indmax = 0\n",
      "else:\n",
      "    indmax = np.max(ind_efdr) # why is max(i) returning the whole thing ???\n",
      "\n",
      "pmax = p_values[ind_p_sorted][indmax]\n",
      "zmax = sst.norm.isf(pmax)\n",
      "print indmax\n",
      "print pmax, zmax, (t_values > zmax).sum()\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
        " 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39]\n",
        "39\n",
        "0.000100835783806 3.71691335451 39\n"
       ]
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "What would be the effect of more / less correlation in the data? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 87
    }
   ],
   "metadata": {}
  }
 ]
}