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@patricksnape
Last active August 29, 2015 14:04
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Cosine on Tumour Data
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"worksheets": [
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Experiments regarding the distributions on Tumour data from the BraTS MICCAI challenge database\n",
"We start by loading in the 10 brains the Stefan gave me. The atlases represent the healthy brains, the masks give the tumour area and the images list are the images with tumours. All images have been prealigned to a corresponding frame of reference."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import irtk\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Two different sets of ids, HG and LG\n",
"tumour_ids = ['HG{:02d}'.format(i) for i in range(1, 6)] + ['LG{:02d}'.format(i) for i in range(1, 6)]\n",
"\n",
"# Healthy brains\n",
"atlases = []\n",
"for i in tumour_ids:\n",
" atlases.append(np.asarray(irtk.imread('/home/pts08/TIP_images/atlases/atlas_in_space_of_{}.nii.gz'.format(i)), dtype=np.float))\n",
"\n",
"# Masks : true where the tumour is\n",
"masks = []\n",
"for i in tumour_ids:\n",
" masks.append(np.asarray(irtk.imread('/home/pts08/TIP_images/masks/{}.nii.gz'.format(i)), dtype=np.bool))\n",
"\n",
"# Images with tumours\n",
"images = []\n",
"for i in tumour_ids:\n",
" images.append(np.asarray(irtk.imread('/home/pts08/TIP_images/images/{}.nii.gz'.format(i)), dtype=np.float))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Save down for Matlab experiments\n",
"from scipy.io import savemat\n",
"\n",
"for i, t_id in enumerate(tumour_ids): \n",
" xs, ys, zs = np.nonzero(masks[i])\n",
" min_bounds = np.min(xs), np.min(ys), np.min(zs)\n",
" max_bounds = np.max(xs), np.max(ys), np.max(zs)\n",
" tumour_bounds = min_bounds + max_bounds\n",
"\n",
" print(tumour_bounds)\n",
" savemat('/vol/hmi/projects/patrick/tip2014/lk_3d/data/{}.mat'.format(t_id), {'atlas': atlases[i],\n",
" 'tumour': images[i],\n",
" 'tmplt': tumour_bounds})"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define a normalisation method\n",
"We define a simple method that normalises the image. We set all useless data (denoted as ``-1`` in the original data) to ``nan`` because the Numpy gradient method ignores ``nan`` values. We then set to the ``nan`` values back to ``-1``.\n",
"\n",
"We also calculate and return the $\\varrho$ value as denoted in Stefan's paper."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def normalise_image(img, mask, eta=0.01):\n",
" a = img.copy()\n",
" \n",
" a[a == -1] = np.nan\n",
" agx, agy, agz = np.gradient(a)\n",
" agx[np.isnan(agx)] = -1\n",
" agy[np.isnan(agy)] = -1\n",
" agz[np.isnan(agz)] = -1\n",
" a[np.isnan(a)] = -1\n",
" \n",
" agx = agx[mask]\n",
" agy = agy[mask]\n",
" agz = agz[mask]\n",
"\n",
" mag = np.sqrt(agx ** 2 + agy ** 2 + agz ** 2)\n",
" \n",
" rho = eta * np.mean(mag)\n",
"\n",
" return (agx / mag), (agy / mag), (agz / mag), np.ones_like(agz) * rho"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculate angles/similarities between every image\n",
"We calculate the various similarities we are considering for each image pair (normalised gradients). This yields 10 seperate results.\n",
"\n",
"The four similarities being considered are:\n",
"\n",
" - **Inner product** \n",
" $x^T x = \\cos{\\sigma}$\n",
" - **Inner product squared** (from Haber's paper) \n",
" $(x^T x)^2 = \\cos^2{\\sigma}$\n",
" - **Azimuth differences** (same as IGO) \n",
" $\\phi = \\arctan{\\frac{y}{x}}, \\Delta \\phi = \\phi_1 - \\phi_2$\n",
" - **Elevation differences** \n",
" $\\theta = \\arccos{z}, \\Delta \\theta = \\theta_1 - \\theta_2$\n",
" \n",
"In the graphs below I show each distribution calculated on the 10 image pairs, and the single distribution when considering all of the pixels as if they were drawn from a single distribution."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"inner_products = []\n",
"azimuths_atlases = []\n",
"azimuths_images = []\n",
"elevation_atlases = []\n",
"elevation_images = []\n",
"delta_phis = []\n",
"delta_thetas = []\n",
"inner_product_squareds = []\n",
"\n",
"for atlas, image, mask in zip(atlases, images, masks):\n",
" # Calculate the gradients and normalise each image\n",
" norm_agx, norm_agy, norm_agz, rho = normalise_image(atlas, mask)\n",
" norm_igx, norm_igy, norm_igz, tao = normalise_image(image, mask)\n",
" \n",
" # Calculate the inner products\n",
" inner_products.append((norm_agx * norm_igx) + (norm_agy * norm_igy) + (norm_agz * norm_igz))\n",
" # Calculate the inner product squared\n",
" inner_product_squareds.append(inner_products[-1] ** 2)\n",
" \n",
" # Azimuth differences\n",
" azimutha = np.arctan2(norm_agy, norm_agx)\n",
" azimuths_atlases.append(azimutha)\n",
" azimuthi = np.arctan2(norm_igy, norm_igx)\n",
" azimuths_images.append(azimuthi)\n",
" delta_phis.append(azimutha - azimuthi)\n",
" \n",
" # Elevation differences\n",
" elevationa = np.arccos(norm_agz)\n",
" elevation_atlases.append(elevationa)\n",
" elevationi = np.arccos(norm_igz)\n",
" elevation_images.append(elevationi)\n",
" delta_thetas.append(elevationa - elevationi)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Azimuth Differences"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's interesting to note here that the actual distribution ranges between $[-2\\pi, 2\\pi]$. This makes sense because the range of $\\phi$ itself is $[0, 2\\pi]$ and so we can obviously calculate $0 - 2\\pi = -2\\pi$. We can shift the values back in to $[0, 2\\pi]$ because the cosine is symmetric in that range.\n",
"\n",
"The rightmost histogram verifies Georgios findings on this dataset."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"\n",
"# Calculate the distribution over ALL images by creating a single vector\n",
"total_phis = np.array([])\n",
"for p in delta_phis:\n",
" total_phis = np.concatenate([total_phis, p])\n",
" \n",
"total_phis_shifted = np.array([])\n",
"for p in delta_phis:\n",
" p2 = p.copy()\n",
" p2[p2 < 0] += (2.0 * np.pi)\n",
" total_phis_shifted = np.concatenate([total_phis_shifted, p2])\n",
"\n",
"\n",
"\n",
" \n",
"plt.subplot(131)\n",
"h = plt.hist(total_phis, bins=100)\n",
"plt.title('$\\Delta \\phi$ WITHOUT shifting the values')\n",
"\n",
"plt.subplot(132)\n",
"h = plt.hist(total_phis_shifted, bins=100)\n",
"plt.title('$\\Delta \\phi$ WITH shifting the values')\n",
"\n",
"plt.subplot(133)\n",
"h = plt.hist(np.cos(total_phis), bins=100)\n",
"plt.title('$\\cos[\\Delta \\phi]$')\n",
"\n",
"plt.gcf().set_size_inches(15, 5)\n",
"# plt.savefig('phi_hg01.eps', format='eps', dpi=1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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LLyMpKQmVlZXSD/qtra04duwY1q9fjzNnzuDtt98G0H5I+I9//GMEBARYXL6t3xUA7P6+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\njPjvJLM4pPiln4NAYV9AZmRkBKWlpVi8eDGsViseeOABNDQ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abuvTefjhh2EymXDrrbdi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\ndfJFtaRmEYcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7f023312bd90>"
]
}
],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = plt.hist(total_phis_shifted, bins=100)\n",
"plt.xlim(0, 2*np.pi)\n",
"plt.yticks([])\n",
"\n",
"plt.gcf().set_size_inches(11, 7)\n",
"plt.savefig('delta_phi_all.eps', format='eps', dpi=1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f02a73aeb10>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure()\n",
"plt.suptitle('Uniform distribution of all $\\Delta \\phi$ images')\n",
"\n",
"for i, p in enumerate(delta_phis):\n",
" p2 = p.copy()\n",
" p2[p2 < 0] += (2.0 * np.pi)\n",
" \n",
" plt.subplot(4, 3, i + 1)\n",
" h = plt.hist(p2, bins=100)\n",
"\n",
"plt.gcf().set_size_inches(15, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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h5WovH0aV1RWTofd0z2NOfIbj1L0+YVSc5m4fw3Wbtp2MYfx2Qb8y2uvD1DrN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\nJ+wAAAAqJ+wAAAAq9wAAeDWaqBUYzAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0233ed1910>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Elevation Differences\n",
"It's interesting to note here that the actual distribution ranges between $[-\\pi, \\pi]$. This makes sense because the range of $\\theta$ itself is $[0, \\pi]$ and so we can obviously calculate $0 - \\pi = -\\pi$. We can shift the values back in to $[0, 2\\pi]$ because the cosine is symmetric in that range."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"\n",
"total_thetas = np.array([])\n",
"for t in delta_thetas:\n",
" total_thetas = np.concatenate([total_thetas, t])\n",
"\n",
"total_thetas_shifted = np.array([])\n",
"for t in delta_thetas:\n",
" t2 = t.copy()\n",
" t2[t2 < 0] += np.pi\n",
" total_thetas_shifted = np.concatenate([total_thetas_shifted, t2])\n",
" \n",
"\n",
"total_thetas_sin = np.array([])\n",
"for t in delta_thetas:\n",
" total_thetas_sin = np.concatenate([total_thetas_sin, np.sin(t)])\n",
"\n",
"plt.subplot(131)\n",
"h = plt.hist(total_thetas, bins=100)\n",
"plt.title(r'$\\Delta \\theta$ WITHOUT shifting the values')\n",
"\n",
"plt.subplot(132)\n",
"h = plt.hist(total_thetas_shifted, bins=100)\n",
"plt.title(r'$\\Delta \\theta$ WITH shifting the values between 0 and pi')\n",
"\n",
"plt.subplot(133)\n",
"# a = np.zeros_like(total_thetas_sin)\n",
"# a[total_thetas_sin<0] = total_thetas_sin[total_thetas_sin<0] + 1\n",
"# a[total_thetas_sin>0] = total_thetas_sin[total_thetas_sin>0] - 1\n",
"h = plt.hist(total_thetas_sin, bins=100)\n",
"plt.title(r'$\\sin[\\Delta \\theta]$')\n",
"\n",
"plt.gcf().set_size_inches(15, 5)\n",
"# plt.savefig('theta_hg01.eps', format='eps', dpi=1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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JjY2Fh4cHPDw8sGHDBlmspKQEYWFhUCqVGDNmDHJycmTx9PR0eHt7Q6VSITw8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\nASEAAAAAZKn/B/eNgthkQu8CAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f02326190d0>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure()\n",
"plt.suptitle(r'Uniform distribution of all $\\Delta \\theta$ images')\n",
"\n",
"for i, t in enumerate(delta_thetas):\n",
" plt.subplot(4, 3, i + 1)\n",
" h = plt.hist(t, bins=100, normed=True)\n",
" plt.xlim(-np.pi, np.pi)\n",
"\n",
"plt.gcf().set_size_inches(15, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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kpqbCYrHYg8fChQuRlZWFDRs2qGb8xBNP4MCBA3jttdcAALfffjsqKiqwZMkS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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f02d0faf410>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, here things are much more interesting. The rightmost histogram is not really a sensible uniform distribution, even when shifted back in to range.\n",
"The leftmost histogram actually looks very much like a normal distribution, which we test below:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"from scipy.stats import norm, laplace, vonmises\n",
"\n",
"size = len(total_thetas)\n",
"x = np.linspace(-3.2, 3.2, 100)\n",
"\n",
"# Try fitting a normal distribution to the data\n",
"normal_params = norm.fit(total_thetas)\n",
"normal_pdf_fitted = norm.pdf(x, *normal_params)\n",
"\n",
"# Try fitting a von mises distribution to the data\n",
"kappa = vonmises.fit(total_thetas)[0]\n",
"vonmises_pdf_fitted = vonmises.pdf(x, kappa)\n",
"\n",
"# Try fitting a laplacian distribution to the data\n",
"laplace_params = laplace.fit(total_thetas)\n",
"laplace_pdf_fitted = laplace.pdf(x, *laplace_params)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.subplot(131)\n",
"plt.title(r'Fitting Normal Distribution'.format(*normal_params))\n",
"plt.hist(total_thetas, normed=True, bins=100, alpha=0.3)\n",
"plt.plot(x, normal_pdf_fitted, 'r', lw=2)\n",
"plt.legend(['N({:.03f}, {:.03f})'.format(*normal_params), r'$\\Delta \\theta$'])\n",
"\n",
"plt.subplot(132)\n",
"plt.title(r'Fitting Laplace Distribution')\n",
"plt.hist(total_thetas, normed=True, bins=100, alpha=0.3)\n",
"plt.plot(x, laplace_pdf_fitted, 'r', lw=2)\n",
"plt.legend(['L({:.03f}, {:.03f})'.format(*laplace_params), r'$\\Delta \\theta$'])\n",
"\n",
"plt.subplot(133)\n",
"plt.title(r'Fitting VonMises Distribution')\n",
"plt.hist(total_thetas, normed=True, bins=100, alpha=0.3)\n",
"plt.plot(x, vonmises_pdf_fitted, 'r', lw=2)\n",
"plt.legend(['VM({:.03f})'.format(kappa), r'$\\Delta \\theta$'])\n",
"\n",
"plt.gcf().set_size_inches(15, 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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D3759cfPmzXJfd+bMGfj6+sLKygqurq6YPXs2ioqKVOrExcWhV69esLa2hpOT\nEyZPnoycnBxx+tOnTzFmzBi0adMG5ubmaNSoUbnLLU1+fj6mT58OV1dXSKVSdOrUCRcuXCj3devX\nr0fLli1hbW0Nd3d3hISEqPWC9eeff8LPzw+2trZwcHBAz549cf78eZU6586dQ8+ePeHg4ABbW1v4\n+/vjr7/+Eqfb2Njggw8+wMyZMyu9jowZqqCgIPTo0aPMOsHBwRgyZAjq1q0rlukyP82bNw8SiUTj\no+T3vzyVzU87duxA69atIZPJULt2bQwaNAg3btxQqZOcnIy33noLtra2sLW1xbBhw/DgwQON8ysq\nKsLrr78OiUSCsLAwsZzzE2O6FxgYiA4dOmiclpeXB3t7e8yZMwcBAQGQSCT45JNP1Op99913kEgk\navtTx48fx/Hjx/H++++LZbt370afPn3g4uKilhNK8++//2LkyJHw9PSElZUVvLy8MHXqVKSnp6vU\nKy/n3bp1q9T8+t5774n1goODERISopKbXxrSM3oYkl4w5O0SFBREVlZWZGlpSYmJiWL57du3SRAE\nOnr0qFj2+++/k4ODA+Xn55c738DAQGrQoAGFh4dTVFQU9e7dm7y8vCg3N7fU1yQlJZFcLqexY8dS\nbGws7dmzh+zt7WnmzJlinczMTHJzc6P/+7//o+joaDpy5Ah5eHjQ0KFDxTrZ2dk0adIkCg0NpVGj\nRlGjRo0qullEH374ITk4OND+/fvp8uXLNGrUKLKzs6OUlJRSX7N27VqysrKizZs3U0JCAu3bt4/q\n1KlDn332mVjn5s2bZGFhQR988AFdv36dLl++TIMHDyYHBwfKzs4mIqKsrCyyt7enIUOGUGxsLMXF\nxdGUKVPI0tKSbt26pbLdTE1N6caNG6XGVNZn1JA/v8UZy3pUN0PebkFBQdSjR49Spz969IgsLS3p\nwoULKuW6zE9ZWVl0//598ZGSkkJvvvkmNW7cuMLrX5n8dPz4cZJIJLRw4UJKSEigc+fOUZcuXahJ\nkyZincLCQmrTpg21b9+eIiMj6fTp09SmTRvy9fXVOM/g4GD6z3/+Q4IgUFhYmNp2q+n5yRjWgRnu\n+/jHH3+QIAgUHR2tNm3r1q1kampKiYmJFBAQQO7u7uTk5ETPnj1TqdesWTPy8PBQ258aPHgwffDB\nByplW7ZsoXnz5tGePXs05gRNfvrpJ3r33Xfp77//poSEBDp8+DA1atSI+vTpo1KvvJxXWFiokl/v\n379Pv/7R63ndAAAgAElEQVT6KwmCQMePH1eZV6NGjWjDhg1lxlUVuUnvPjWG+kF+2Qx5uwQFBdHr\nr79OHTp0oOHDh4vlmhpzQ4cOpdGjR5c7z2vXrpEgCPTnn3+KZY8fPyYLCwvatGlTqa+bNWsW1atX\nT6Vs5cqVZG1tTTk5OUREtGbNGrKysqKMjAyxjjJRJSQkqM0zODiYGjZsWG7MmqSnp5OlpSWtW7dO\nLCssLKQ6derQvHnzSn2dn58fTZ48WaVs2bJlKuuxe/duEgSBsrKyxDqXLl0iQRDo0qVLREQUFRVF\ngiDQ5cuXxToZGRkkCALt27dPZf7t27enL774otSYjH1nich41qO6GfJ2Gz16NHXv3r3U6aGhoeTu\n7q5Spk/5iYjoyZMnJJVKaenSpaUuW5PK5qdly5aRg4ODStm+fftIEAQx7kOHDpEgCBQXFyfWiYmJ\nIUEQKDw8XOW1f//9N7m7u9OjR49K3XGr6fnJGNaBGe77WFRURO7u7vTee++pTevSpQv17duXiIgC\nAgJo7Nix5OnpST///LNYJyIigmxsbGjatGkq+1OZmZlkbm5O//zzT6nL1rYxp8muXbtIIpFQZmYm\nEVU+57399tvUokULtfLp06dTt27dyoyhKnITX2bJXjoigiAIWLp0KbZv317mZT7Hjh0r9VR9cSdO\nnICZmRlef/11saxWrVpo3749jh8/XubrevbsqVLWq1cv5OTkICoqSqzj6+sLuVwu1unRowckEglO\nnjxZbmwVcf78eTx9+hS9e/cWyyQSCXr06FHmejx9+hQWFhYqZZaWlsjJycHZs2cBAL6+vqhVqxbW\nrFmD/Px85ObmYv369WjYsCGaNm0KAPD29oanpyc2bNiAvLw85OfnIzQ0FA4ODujYsaPK/F977TUc\nOXKkqladMaNw9OhRtZylb/lp8+bNKCwsRFBQUIXWrbL5qXv37sjOzsbOnTtRVFSEJ0+eYMuWLfD3\n9xfjPnHiBLy8vFQuqWrWrBnc3NxU5n3//n2MHj0amzdvhr29fanL5PzEmO4IgoBx48YhLCwMeXl5\nYvn169dx7NgxTJw4USyTSCQYN24c1q1bJ5atXbsWw4cPh7W1tcp8T548iYKCArRr1+6lxP348WNY\nWFjA1NQUQOVy3sOHD7Fr1y5MmjRJbVqHDh1w8uRJ5Ofnv5T4xRhf6txZ9RKEl/d44dAE+Pv7IzAw\nEJ9++qnGOllZWUhOTkb9+vXLnV9ycjIcHR0hlIitdu3aSE5OLvV1KSkpqFOnjkqZ8rnydcnJyWp1\nzMzMYG9vX+a8K0M5v5LLK289+vTpg82bN+PkyZMgIly5cgXLli1TmaezszMOHTqEpUuXQiqVQiaT\n4fDhwzh06BDMzMwAABYWFjh8+DB+//13WFtbQyqVYvny5Th06BAcHR1Vlunu7o64uLgqW3fGVOhp\n7ipPXFycWs7St/y0Zs0aDBo0CA4ODtqtVLH1KB6DtuvRokUL/Prrr5gwYQIsLS1hb2+P27dvY8+e\nPSrzLjlf5bJSUlIAKO6TGz58OMaNG4fOnTuXGSvnJ1Zj6GmuHDduHDIzM7Fz506xbP369XB1dUX/\n/v2LhS9g7NixOHbsGG7duoXHjx/jt99+w8SJE9Xu+4+Li4OdnZ1aI68qpKSkIDg4GO+99x4sLS0B\nVC7nbdq0CSYmJhg1apTaNA8PDzx9+hSJiYlVHL0qbsyxaqH8gi5atAgnTpzA/v371eoob0ItfsQZ\nAGQyGeRyOeRyOfr161fuskruQFXUi76+Onz++ed466230LVrV5ibm6NLly4YOXIkAMVRJABISEhA\n//79MXjwYERGRuLEiRPw9vZG3759kZWVBUCxzfv06YPWrVvj1KlTOHPmDPr374//+7//w+3bt1WW\naWNjgydPnlTvijKm5zIyMtRyVlmqOz+dOHECsbGxGo8avyyRkZEYNmwYpk2bhnPnzuHIkSMwNzfH\ngAEDVDpzKbnjVrLsq6++wrNnzzB37lyVaZpex/mJMd1ydXVFv379xDNu+fn52LRpE8aOHSvulyi5\nuLigb9++WLduHbZs2YJmzZqhVatWavNMT0+vUH7VVmpqKnr27IlWrVph4cKFlZ4PEWHt2rV46623\nYGNjozZdWfaycxM35owJ0ct7VJFGjRph0qRJmDFjBgoLC1Wm1apVC4CiF7jiLl26hOjoaERHR2P9\n+vUAFIng4cOHaj/q9+/fh4uLS6nLd3FxUTu6cv/+fXFaaXXy8/ORlpZW5rwrQzk/5ZHo4jG5urqW\n+jpzc3OsXr0aubm5SExMRHJyMtq0aQMAaNCgAQDF0Xh7e3t8//33aN26NV577TXs2LEDSUlJ+OWX\nXwAA27dvR0pKCsLCwtC+fXu0adMGoaGhsLa2xtq1a1WWmZ6eLr5HjFU5Pc9dpalVq5ZaztKn/BQa\nGgpvb+9yz2yVFg9Q8fz07bffwt/fH5999hleeeUVBAQEICwsDBEREQgPDxfnXXK+ynkrl/v333/j\n5MmTsLCwgJmZGczNzQEAo0ePRrNmzVRex/mJ1Rh6nCsnTpyI48eP4+rVq9i3bx8ePXqE8ePHl1p3\nw4YNWLt2rcplmMVpyq8v6s6dO+jSpQs8PT2xa9cumJiYiNMqmvOOHDmC+Ph4vPPOOxqXpTxJ8bJz\nEzfmWLUofjQ5ODgY9+7dw5o1a1TqWFtbw8XFRe10tJeXl/hQftH8/PyQn5+Pv//+W6z35MkTREZG\nwt/fv9Q4/Pz88Oeff6rsZB08eBBSqRStW7cW65w6dUolgfz5558oKiqCn59fJda+dG3btoWFhQUO\nHjwolhUVFeGvv/4qcz2UJBIJXF1dYWJigm3btsHLy0ts1BGRSpICFO+DRCIR17+oqAgSiUTtaH/J\no2gAkJiYiCZNmlR4HRkzdGWdDWvUqBFu3bqlUqYv+SktLU28fKkyKpufNOUeZU5Rrpufnx8SEhIQ\nHx8v1omNjcWdO3fEeW/cuFHlYN7FixcBKM7Ylby6g/MTY7rXp08f1K9fH+vWrcP69evRq1evUm+d\n6d27NywsLJCUlIS3335bY51GjRrh8ePH4tVEL+rGjRvo1KkTWrRogV27dom3nChVNOetWbMGPj4+\naN++vcblJSYmwsLCQqvbh16IVt2kVCM9DEkvGPJ20dQb3MKFC8nKykqtN8thw4bRqFGjtJrvG2+8\nQQ0bNqSjR49SVFQU9enThxo0aEB5eXlinW7dutGsWbPE57dv3yYbGxsaN24cXb58mfbu3UsODg4q\ndbKysqhevXpqXX8PGzZMZfkxMTEUFRVFkyZNovr169PFixcpKipKrbvd8nz00Ufk5OREv//+O12+\nfJlGjx5N9vb2Kl1/jxw5UmW7xMfH06ZNm+jatWt07tw5mjx5MpmZmdGhQ4fEOidOnCATExOaOXMm\nXb16lS5dukRvv/022djYiENE3Lhxg6ytrSkoKIhiYmLo6tWrNHXqVDIzM6PIyEiVONu1a0chISGl\nrkdZn1FD/vwWZyzrUd0MebuNHj2aXnvtNfH7rXxcuXKFiBS9S9avX1/tdbrOT0RE3377LVlZWdHj\nx48rvf6VyU87duwgExMTWrZsGcXHx9PZs2epR48e5ObmJvYaV1RURG3btqUOHTqIQxO0bdu21KEJ\nlErrua6m5ydjWAdmHO/jF198Qba2tmRiYkJ79uxRmdalSxcaP368+DwzM1OlZ96SvYNnZGSQubk5\nHTlyRGU+aWlpYi4WBIG++uorioqKoqSkJLHOihUrqGnTpuLzmJgYcnFxod69e9Pdu3cpOTlZfBQW\nFor1tMl5REQpKSlkZmZGq1evLnVbTJs2jbp27Vrm9qqK3KR3nxpj+CC/DIa8XTSN05SXl0f169cn\niUSi0pj7448/tB5nLjMzkyZMmED29vYklUqpT58+auMMeXh40JgxY1TKTp8+Tb6+vmRpaUl16tSh\n2bNnU1FRkUqda9euUc+ePUkqlZKDgwO98847YtfgxectCAIJgkASiUT8W3wsPXd3dwoKCipzPfLz\n82n69OlUp04dsrS0JH9/fzp//rxKnYCAAJWEEBcXR6+++ipZW1uTTCajbt26UUREhNq89+zZQx06\ndCBbW1uyt7en119/nU6cOKFSJyIigrp27Ur29vZka2tLHTt2pN9//12lTlJSEpmYmFB8fHyp62Hs\nO0tExrMe1c2Qt1tQUJD4PS/+8Pb2JiKihw8fkqWlpdp3Vtf5iYjI29u7zINjLys/ERGtX7+efHx8\nSCaTkbOzMwUGBlJMTIxKneTkZHrzzTdJLpeTjY0NDR06lB48eFBmPKWNM1fT85MxrAMzjvfx7t27\nZGpqSnXr1lVpJBEpcsWECRNKfe28efPUxpl788036f3331cp27hxo9r+lyAIKvl03rx5JJFIVJ6X\nrK9pv02bnEekOCkhl8vFA1SaNGzYkH788cdSpxNVTW4SnlfWG4IgaLy5uaarKduFiNCsWTPMmzcP\nQ4YM0XU4LyQnJweOjo7YuHGjwa/L/PnzcebMGfz++++l1inrM2osn19jWY/qZuzbbeLEiTAxMcHq\n1at1HYrWOD9pN81QGMM6MH4fNTlx4gTeeOMNJCYmQiqV6jocrUVERGDw4MG4desWrKysSq1XFbmJ\nG3MGoiZtl3379uHzzz/HpUuXdB3KC9m3bx+WL19u8GMfZWRkoGHDhvjnn3/QvHnzUusZ+84SYDzr\nUd2MfbslJyejRYsWuHTpEurWravrcLTC+Um7aYbCGNahxouNhdC8Ob+PGgwcOBAdO3bEtGnTdB2K\n1nr06IFBgwaV2jmKEjfmahDeLkzfGfvOEmA861HdeLsxXTP2/GQM61DjTZsGYelSfh9rmKrITeX2\nZpmWloYBAwZAJpPBw8MD27dvL3emr7/+OiQSicp4MpWZD2OMMcYYY0atqAg5P27UdRTMQJmWV2HK\nlCmwtLREamoqoqKi0K9fP/j4+KiN8aIUFhaGgoICta6cKzofxhhjjDHGjN7585A+fqTrKJiBKvMy\ny+zsbNjb2yMmJgYNGzYEoBis09XVVeOI6enp6Wjfvj02b96Mjh07oqCgABKJpELz4UsFNOPtwvSd\nsV/GBBjPelQ33m5M14w9PxnDOtRon30GfPUVBIDfxxrmpV9mGRcXB1NTU7EBBgA+Pj6IiYnRWH/2\n7Nl49913Ubt27ReaD2OMMcYYYzXCnj26joAZsDIbc1lZWbCxsVEpk8vlyMzMVKt77tw5nDp1Cu+/\n//4LzYcxxhhjzJBp20/Ajh070LRpU9ja2sLR0REDBw7EvXv3xOkBAQGwsrKCXC6HXC6Ht7d3da0C\nqyb7vlkDxMYix9xS16EwA1XmPXMymQwZGRkqZenp6ZDL5SplRUVFePfdd7F8+XJIJP9rHypPDWo7\nH6V58+aJ/wcEBCAgIKDcFWGM6Y/w8HCEh4frOgzGGNMJbfsJ8PPzw7Fjx+Ds7Izs7GxMmjQJH3/8\nMXbs2AFAcZnVypUrMXbsWF2sBqsGTifPAAAuuDQGEg17SCamG2U25ho3boyCggLEx8eLl0hGR0ej\nRYsWKvUyMjJw/vx5ceDRwsJCAICbmxt+/fVXtGrVSqv5KBVvzDHGDE/JgzAhISG6C4YxxqpRdnY2\ndu3ahZiYGEilUvj5+SEwMBBbtmxR6yegXr164v9EBBMTEzg5OanU4XuojJtHtKIxd87NmxtzrFLK\nvMzS2toaAwcOxNy5c5GTk4Pjx49j//79GDlypEq9WrVqITk5GdHR0YiOjsaBAwcAABcuXED79u21\nng9jjDHGmCGraD8Bx48fR61atWBjY4OkpCQsWrRIZfqsWbPg5OQEf39/HD169KXGzqpZejpqJ1xF\nkcQE/7o0LL8+YxqUO87cqlWrkJubC2dnZ4wYMQKhoaHw9vZGUlIS5HI57ty5AwBwdnYWH46OjhAE\nAbVr14aZmVmZ82E109SpU7FixQpdh8EYYxXG+YuVpaL9BPj7++PJkye4c+cOzMzMMG3aNHHaokWL\nkJCQgHv37mHixIno378/bt68+VLjZ9UoPBySoiI8afIacs2M7545zpXVo8yhCXSBu9fVrLTtEha2\nH9Xdj4xcDgwf3r/Sr3/48CHatGkDALh58yZMTcsd7pAZAH3r+jstLQ3jxo3Dn3/+CUdHRyxcuBDD\nhg3TWPfmzZv44IMPcOzYMVhYWGDs2LFqR8cBzk+VpS/560VzF8D5y1BVZ36KioqCv78/srOzxbKl\nS5fi2LFj2LdvX5mvPXPmDHr37o3Hjx9rnN6nTx/069cP7733nkq5IAgIDg4Wn3N/AwbivfeAlStx\nbdg8hMAE27fP0YtcCfC+XnUpnn9K9jcQEhKiVW7iLWvgMjOBunVfbOekou7e3f9Cr//xxx+xc+dO\n+Pv7IywsDKNHj1arQ0RYvXo1zMzMcOHCBXz11Vews7N7oeWymkXbDgiePXuGHj164P3338fOnTth\nYmKCa9eu6SjqmqW689eL5i6A8xcrn7b9DWiSn58PqVRaqeVyfwOGJSxsP/rt3INaAB606gFcPFJq\nXd7Xqxkq299AuZdZMlaVsrOzkZ2djQ4dOuCtt97CkiVLNNb77LPPYG1tjQkTJqBVq1b48ccfqzlS\nZsiUHRDMnz9frQOCkjZt2gQ3Nzd89NFHsLKygrm5OVq2bKmDqJm+4/zFtFGRfgK2bduG27dvAwAS\nExPx2WefYdCgQQAUvX4fOnQIeXl5KCgoQFhYGCIiItC7d+9qXR/2clDiA9RKvYscMws8adxe1+FU\nKc6V1Ysbc6xabdq0Sexiefr06YiNjcX+/apHf06ePIlffvkFo0aNAgDk5OTg+vXr1R4rM1wV6YDg\n9OnTcHd3R9++feHk5ISuXbvi8uXL1RkuMxCcv5i2tO1vIDY2Fr6+vpDJZAgICEDHjh2xePFiAIqz\ndHPmzIGzszOcnJywcuVK7N27VyWvMcPldiUKABDr7AkyMa4L5ThXVi/j+vQwvVZQUICkpCR4eHgA\nUOxc9+rVC4sWLUL//v+7fOCLL77A2LFjIQgCAOD8+fMq3TczVp6KdEBw584dhIeHY//+/Xj99dex\nfPlyBAYG4urVq2IHToxx/mIVYWdnh927d6uV169fXyUPLViwAAsWLNA4D0dHR0RGRr60GJluuV2J\nBgD8W6chHHUcS1XiXFn9uDHHqs327dvVOqCYOXMmunbtihMnTsDPzw9paWn4+++/0aJFCyxatAhE\nhP3792Pr1q06ipoZIplMhoyMDJWy9PR0yOVytbpSqRSdOnVCr169AACffvopFixYgKtXr2q83LL4\nfSncyUDNwfnLeJTsZICxakcE1zjFmHKX63ghQLfRVCnOldWPG3OsWhARLl68qHbPQJcuXdChQwcs\nWrQI+/btw7lz5+Ds7IylS5cCUFwCt3LlSvTr108XYTMDVZEOCF555RWcOHFCfF5ez1HcyUDNw/nL\nuFS2kwHGqsz165BmpiOvVm0ky43nvBznSt3ge+ZYtThw4ECpX9IZM2bgjz/+QGxsLB4/foy2bduK\n00JDQ/Hxxx9DIuGPKtNeRTogGDFiBE6fPo2///4bhYWFWL58OZycnHgcTCbi/MUYq1LHjgEA0pp1\nAp5fZmgMOFfqBp+ZY9Vi69ateOeddzRe2mJjYwN7e3ssXrwY77//PmQyGQDF9dMpKSnYsGFDNUfL\njMGqVaswduxYODs7w9HRUaUDgubNm+PKlStwc3ND48aNxc9namoq2rZti3379vGYOEzE+YsxVlXC\nwvbj1fXb0ARAWvNOQFZGua8xFJwrdYP3VthLd/bsWfz888/4+eefy6y3Y8cOLFy4EC4uLtiwYQNu\n3bqFX3/9lY/UsErRtgMCABgwYAAGDBhQXaExA8L5izFWlTIzgXoJCQCAR807A2d+13FEVYNzpe5w\nY87AyeVVMxBuRZdZEe3atUNRUZHW9b/55psKRsQYM0TVnb8qmrsAzl+MsaplnfYA0tRbyDGzQIZ7\nS60ac7yvx8rCjTkDN3x4//IrMcaYHuL8xRiraVziYwEA15zcARMTrV7DuZKVhc9pMsYYY4wxVg1c\n4mMAAFed3HUcCTMW3JhjjDHGGGOsGqicmWOsCvBllowxxhhjjL1EYWH78TQ1G0HJt1FkaoYEe1e0\nLf9ljJWLz8wxxhhjjDH2EmVmAt5ZjpCAkO7VBvkmZroOiRkJbswxxhhjjDH2ktldPQUAeNzkNR1H\nwowJN+YYY4wxxhh7yeziTgMAHjftqONImDHhxhxjjDHGGGMvExHsrj1vzPGZOVaFuAMUAyIIgq5D\nYIyxSuH8xRiricLC9iMzE0j86wjMM9Pw2EqOXKf6pdbnXMkqis/MGQgi0r/Ho0cgiQRkZgbKyBDL\nt27dh9Wr92HMmPkYNmw+9u2jCv0tbdrq1ftA8+eDANDEibpff36oPRjTRNefS60e48crcsuqVf8r\nmzJFUbZsme7j48cLPxjThcxMoG7d/qh/9zYA4LpDPaCUBltV7jNp+ntp4vcgAOGerbFvH2HMmGCs\nXr0PW7fu0/n3syY/XhQ35ljlHT4MFBUB/v6AXC4WKxNXXt5LWGafPoq///0vwD/OjLGqcveu4m/d\nuv8rU/5/7171x8MYMyqNHikac/GO9XQWg/LyzkYPFbHk5Zmibt3+yMzUWUisCnBjjlXewYOKv8oG\n1ksWGXkeoWfuINfGFrh9G4iNrZblMsZqgLIac8ppjDFWSQ0fKs/MuekshgwPHzwzMYVr5kOYZT3W\nWRysapXbmEtLS8OAAQMgk8ng4eGB7du3a6y3Y8cONG3aFLa2tnB0dMTAgQNxr9jRzICAAFhZWUEu\nl0Mul8Pb27vq1oJVPyLgyBHF/z17AlBcFx4auh+RkdEvZZF5eaaoWy8Qt5u2UhQol88YYy+qrMbc\nnTvVHw9jzGhInuaiXnoqSCLBLXtXncVBZuZIrOUCALC9fk5ncbCqVW5jbsqUKbC0tERqairCwsIw\nefJkxGo4I+Ln54djx44hPT0diYmJkEql+Pjjj8XpgiBg5cqVyMzMRGZmJq5cuVK1a8Kq140birNj\nDg5Ay5YAXvLllcXcbfKK4h9uzDHGqkJeHvDoEWBqCjg7/6+83vPLoW7f1k1cjDGjYJtwESZUhMx6\nzfHU1FynsdxwUBykqnX9rE7jYFWnzMZcdnY2du3ahfnz50MqlcLPzw+BgYHYsmWLWt169erB+fmP\nIBHBxMQELi4uKnX4BmQjomxIde0KSKr3at17ysZceDhQWFity2aMGSHlVSQuLqr5zO355VB37yru\nD2aMsUpQNpyeNGqn40iAm/bPG3Px3JgzFmXuhcfFxcHU1BQNGzYUy3x8fBATE6Ox/vHjx1GrVi3Y\n2NggKSkJixYtUpk+a9YsODk5wd/fH0ePHq2C8JnOKBtz3bpV+6IzHWoDnp7AkyfAxYvVvnzGmJHR\ndIklAEilgL098OwZ8OBB9cfFGDMKetWY4zNzRqfMxlxWVhZsbGxUyuRyOTJL6fbG398fT548wZ07\nd2BmZoZp06aJ0xYtWoSEhATcu3cPEydORP/+/XHz5s0qWAVW7YrfL6eDxpzKcvlSS8bYi1JeRllP\nQy9zfKklY6wSivcjIDbmGr6q46iAZLkDcswsYPXoLmrlKvbnIyPPIzR0P8LC9us4OlYZZTbmZDIZ\nMjIyVMrS09MhL9YNvSaurq6YP38+Nm/eLJa1b98e1tbWMDMzw6hRo+Dn54cDBw5ofP28efPER3h4\nuJarwqpNTIziKLWrK9C4sW5i4MacXgsPD1f5HjOm17gxxxirYsp+BISMPMjuXkO+xAQZHq/oOiyQ\nIEGCnaITFq9His6deIgCw2Za1sTGjRujoKAA8fHx4qWW0dHRaNGiRbkzzs/Ph1QqrVRQvPOn54qf\nlRMEhIXtR2YmEBkZjQED+r/0xUdGnoe0iSdGAUBEhOISKHPd3lDMVAUEBCAgIEB8HhISortgGCsP\nN+YYYy+JZ5rintykWnVAZvqxr3LDoS6apyagQRoPu2IMyjwzZ21tjYEDB2Lu3LnIycnB8ePHsX//\nfowcOVKt7rZt23D7+Y9dYmIiPvvsMwwaNAiA4mzeoUOHkJeXh4KCAoSFhSEiIgK9e/d+CavEXjrl\n2dKuXQFUXy+WSnl5prBrNhppdeoB2dnAOe5elzH2ApKSFH/r11efpuwEhRtzjLFKaJCmOPul7EVS\nHyg7QfF6xI05Y1BuN4SrVq1Cbm4unJ2dMWLECISGhsLb2xtJSUmQy+W483z8ndjYWPj6+kImkyEg\nIAAdO3bE4sWLASjO0s2ZMwfOzs5wcnLCypUrsXfvXpWOVZiBIAKOH1f837mzTkNJbtRc8U9EhE7j\nYIwZOG3OzPFYc6wCqmqMXm3nw/SX1/Mzc8oGlD64+Xzgcq+0u4r9OmbQyrzMEgDs7Oywe/dutfL6\n9eurdISyYMECLFiwQOM8HB0dERkZ+QJhMr1x7Zrifrk6dYAGDXQaSkrDZmgecVDRmJsxQ6exMMYM\nGF9myapY8TF6o6Ki0K9fP/j4+KBZs2Yq9ZRj9Do7OyM7OxuTJk3Cxx9/jB07dlRoPkx/eT6/lPGm\nfV3oS3PuodQWT20cIc94CKvURF2Hw15Q9Q4Qxgyf8ixYp06AIOg0lOSGz8/MnTjBY0AxxionJ0cx\nYLi5ueqA4UrcmGMVVFVj9FZkPkw/mWWmwTn7CQrNrXDPxlHX4fyPICC9QVsAgO2NCzoOhr0obsyx\niinemNOxLHsnxY7WkyfA5cu6DocxZoiUjTQ3N9UBw5WUY8/dvQsUFlZfXMxgVdUYvRWdD9M/yoZS\nuqcPiiQmOo5GVXqDNgCAWjfOi2U8RIFh4sYcq5hijbniY6jojLJRqbyPjzHGKqKsSywBwNIScHJS\nNORSUqovLmawqmqM3orOh+kfsTH3/CyYPklvqH5mjocoMEzl3jPHmOj2beDWLcDGBmjZEpmnbz/v\nxd5bgOQAACAASURBVFI3jbnIyPNoRrboDCgame++q5M4GGMGTNmY09STpVK9eop7he/c+d+ZOsZK\n8aJj9Pbu3RvfffddhedTfFinksPDMN2wfX7WK71BG+DhvXJqV68nXoozc7Y3zgONfXUcDQMUY/RW\nZnxtbswx7SnPyvn5ASa6v1wgL88UhX5TgO2rFbER6fw+PsaYgVEOS1DamTnltAsXFA2/Dh2qJy5m\nsKpqjN6KzofH6NU/4pm5hm31rjGXW9sDWeZWkKU/gH1uRvkvYC9dZcfo5cssmfaUlzLqwf1ySllu\n3siysFLcz3Lrlq7DYYwZmvIusyw+jTtBYVqoqjF6KzIfpn/Mc7MhS47HM4kpMuvpYe+jgoBbdorO\ndjzS9KuhySqGG3NMe6dOKf76+ek2juIkEsQ5PL886uRJ3cbCGDM82lxmyQOHswqqijF6y5oP03+O\nt28CAG7Xqg0yNdNxNJrdtHcFAHg+5sacIePLLJl2MjOBS5cAU1PsiE/Fk1hFxycDBvTXdWS47lgP\nbe5dUzQ2hw/XdTiMMUOi7WWWADfmmNaqYozesubD9FtY2H6YHlfcmpLwvMGkj27ZPW/MpSXjro5j\nYZXHZ+aYds6eVYzl5uODJ88snnd8ouugFK47Pt/RUp45ZAxAWloaBgwYAJlMBg8PD2zfvl1jvU2b\nNsHExARyuVx8HDt2rJqjZTpBpN1llu7uir+JPLguY6x8mZmAW6ribFeCnf425hL4zJxR4DNzTDvK\nhlLHjrqNQ4Mb9nVRJEggiY4GsrMBa2tdh8T0wJQpU2BpaYnU1FRERUWhX79+8PHxQbNm6vcu+Pn5\ncQOuJnryRJEz5HLA1rb0etyYY4xVkMfzBtItexfU0XEspUmV2SFfagO7nAxYPOahVwwVn5lj2tHj\nxtxTMwuk1XVXjAN17pyuw2F6IDs7G7t27cL8+fMhlUrh5+eHwMBAbNmyRWN9IqrmCJleKH6JZVk9\n4bq4AKamQGoqkJtbPbExxgyW6dM8uGQ8QpGJKW7b1tZ1OKUiQYIMz1YAAJubF3UcDassbsyx8hEB\np08r/tfDxhwA3PdqqviHL7VkAOLi4mBqaip25w0APj4+iImJUasrCAKioqLg5OSEJk2aYMGCBSgs\nLKzOcJmuaHO/HKAYikVZR/kaxhgrhcPdW5CAkFmvGQpM9PsiuHSv1gAA25tRYllk5HmEhu5HWNh+\nXYXFKoAbc6x8168Djx4h17YWQg/+i8hI3QwSXpYUbsyxYrKysmBjY6NSJpfLVToeUOrcuTNiYmLw\n4MED/Pbbb9i+fTuWLFlSXaEyXVJeNunhUX5dZR0eAoUxVg5lT5YZzxtK+kxTYy4vzxR16/aHhp9M\npof0+3AB0w/PG0gpHk1R1+0/yIu4pOOA1P2ZWYDXAeSFH4UlDx5e48lkMmRkqA6Cmp6eDrlcrlbX\n09NT/L9FixaYO3culixZgpkzZ2qcd/GBeUsO8MkMjLJhpk1jju+bMxrh4eEIDw/XdRjMCIWF7Udm\nJuB94SyA5w2lbP1uESkbczY3o4D6r+g4GlYZ3Jhj5XvemLvv1UTHgZQuycwJT20cYZnxELh5E2jQ\nQNchMR1q3LgxCgoKEB8fL15qGR0djRYtWmj1+rLuoSvemGMGjhtzNVLJgzAhISG6C4YZlcxMoG7d\n/qj38B0AzxtK/+p351pZ9bzxTGIKWXI8rPL1pJtyViF8mSUrX2QkAOC+p/425iAIeNz0+f18z+Nl\nNZe1tTUGDhyIuXPnIicnB8ePH8f+/fsxcuRItbr//e9/cf/+fQDA1atXsWDBArzxxhvVHTLTBW7M\nMcaqmFCQj3pPFL8pGZ4+Oo6mfGRqhju1nAEA9blHS4PEjTlWttxcxWDhEgke1NPvs11PGrVX/MON\nOQZg1apVyM3NhbOzM0aMGIHQ0FB4e3sjKSkJcrkcd+7cAQAcOXIEPj4+kMlk6NevHwYNGoTZs2fr\nOHpWLZQNM2VDrSzKBh835hhjZZDdvgKzokLcl9mhwLqMIU/0SGItFwCAx+NkHUfCKoMvs2Rli4pS\ndPnfsiUKLK10HU2ZnjR+3pg7c0a3gTC9YGdnh927d6uV169fX6UjlCVLlnCHJzVRVhbw8CFgYQHU\n1qLrcGWDjztAYYyVQdmRyC07Fx1Hoj1lrB6Pk5FRTl2mf/jMHCubsmHUvr1u49DCk0btFP9cuADk\n5+s2GMaYfit+Vk6ixU+hm5uiY6V79zi/MMZKZZugGK/NEBtz7nxmziBxY46V7fkli6dhqZdDEhSX\nL7NDio0D8PQpDixaqetwGGP6THmGTZtLLAHA3BxwdQWKioDnl+gyxlhJNs/PzCXaueo4Eu0l2dUB\nCQLc0lMhyX8qlvN4c4aBG3OsbM8bc7frNEaeAXRydN3eDQAgi43TcSSMMb1WkTHmlPi+OcZYWYgM\n8szcU1NzZLs2hikVQZYUK5bzeHOGgRtzrHQPn3fzL5UizaW+rqPRyg0HRWPO+RY35hhjZahIT5ZK\nfN8cY6wM8rRUmGWnI93CGk8sZboOp0LSvVoB+N9losxwlNuYS0tLw4ABAyCTyeDh4YHt27drrLdj\nxw40bdoUtra2cHR0xMCBA3Hv3r0Kz4fpkbOKQS/Rti3IxES3sWjphn1dANyYY4yV40Uac3xmjjFW\nTFjYfoSG7kfakSMAgEQ7F8U9tgYkw1PRmLPhxpzBKbcxN2XKFFhaWiI1NRVhYWGYPHkyYmNj1er5\n+fnh2LFjSE9PR2JiIqRSKT7++OMKz4fpEQPq/EQp0c4FRaZmsEu5A2Rwn0yMsVJU9J654nW5MccY\nK0Y5WLhrqmKcNkO6xFIp/XljzvYmN+YMTZmNuezsbOzatQvz58+HVCqFn58fAgMDsWXLFrW69erV\ng7OzYtBBIoKJiQlcXFwqPB+mR86dU/xt1063cVRAgYkpMjx8IBAB58/rOhzGmL6qzD1znp6Kv3yZ\nJWNMA2VvkIl2dXQcScVleP0/e3ceHfV95vn+XaWS0FKlvQRISCqEEAjJyMYEL6I7SmcxbpqmId0T\nzwV8x5m5bju4z9zuScbHzpgLgZ4e57gn7ekxozMnYcZNV8i93QE7ShM7CVjYEBvZCGQjCYR2CSQk\ntJRKu0qq+0fVr7SiDam+tTyvc3zAxU8/fbBNuZ7f9/t9ngkrc06n4jRiIWYt5qqqqjAYDGRmZnpe\ny8vLo7y8fMbrL168SGxsLNHR0TQ2NvL6668v6j7CBzid49ss/aiYg/ERBR///T9IByYhxHT9/dDW\nBqGhsHoBT9AzMlw/1tYuTy4hhF8bL+b8b2VuKG4V3eFGQvt7MPd1q44jFmDWYq63t5fo6OhJr5lM\npkkDdyfavn073d3dNDc3Exoayve+971F3Uf4gOZm14ed+Pjxp9F+ojtzKwBp7f3SgUkIMZ22KpeW\nNr8Zc5q0NNc5mKYmGB5enmxCCL8Uau/E3G9jNCyCFmOC6jiL0hDrWlGUeXP+xTDbLxqNRnqmnDuy\n2WyYTKZZb5qcnMzRo0fZsWMHb7755oLvc/jwYc/PCwoKKCgomPX7iWWgbbHcutXvDvFqK3Ox1Z8B\n+9WGCVLFxcUUFxerjiHEzOrqXD8uZIsluGbNpaZCY6Prrwm7TYQQwS26zjWLt8eyGedCHhL5kIa4\n1eS1VpPeLcWcP5m1mMvKysLhcFBdXe3ZIllWVkZubu6cNx4ZGSEyMnJR95lYzAlFtC2WW7eqzbEI\nvanZDIWEEtVay4peaYKiwtSHMEeOHFEXRoiptG2S69Yt/GszMlyFXG2tFHNCCA+tpb/W4t8faY1b\n0rtakXLOf8z66CAqKoq9e/dy6NAh+vv7uXjxIkVFRRw4cGDatT/96U9pamoCoKGhge9///t885vf\nXPB9hI+YuDLnZ5whBs8bkrmxRnEaIYTPqXG/L2hn4BZC+xptdU8IEbS0kQQlJWVEu7tAai3+/ZHW\nuEW2WfqXOdeBjx8/zsDAAElJSezfv5/CwkKys7NpbGzEZDLR3NwMQEVFBU8++SRGo5GCggKeeOIJ\nfvjDH855H+GDnE6/LuYA6uKTATA33FKcRAjhcx50ZW7iPYQQQUsbSTA4OD6fzebHxVyrMQHHikjM\n/TZC7Z2q44h5mnWbJUBcXBxnzpyZ9npaWtqkBibHjh3j2LFjC76P8EG1tdDVBStXYr1wFXvvNUpK\nylSnWhBteLi5sVpxEiGEz9EKscWszGkNoaSYE0K4GUYdmJoqGEOH3fIQXP2t6kiL4tTrsac/RFzV\nZc8ZQOH7/POEplheE1bl7L06z1Mnf1KX4CrmkhqkmBNCTOB0ysqcEGJJpdja0I86aDUlMBoepTrO\nA9HO/GlnAIXvk2JOTOfnWywBWkwJOCKMGLvuQWur6jhCCF9x965rzlx8PMTELPzr5cycEGIKS7fr\nc4Y/DgufSjvzp50BFL5Pijkx3ZUrrh8ffVRtjgfg1OnpXufOX1qqNowQwnc8SPMTALMZoqJcW9G7\nupYulwgonZ2d7NmzB6PRiMVi4dSpUzNe9/bbb7N161ZiYmJITU3l5ZdfZnR01PPrBQUFREREYDKZ\nMJlM0mvAR2kNQ+r9cFj4VNqZv+gJK3MlJVewWotURRJzkGJOTOZ0jhc/flzMAdjWbQGgpNAqb0JC\nCJcH2WIJrrmbsjon5nDw4EHCw8Npa2vDarXy4osvUlFRMe26gYEB3nzzTTo6Orh8+TLnzp3jjTfe\n8Py6Tqfjrbfewm63Y7fbqays9OZvQ8xTmrYyF+v/xZzd8hBj6DA1VxIy6gBgcNDAhDYZwsdIMScm\nq6kBm42BmDgKf3HF7xqfTGRzr8yltfXJm5AQwuVBmp9opAmKmEVfXx+nT5/m6NGjREZGkp+fz+7d\nuzl58uS0a1944QXy8/MxGAwkJyezb98+Ll26NOkap9PprehiMZxO0rtcxVxjAGyzHA2PotUUj94x\nwpqedtVxxDxIMScmc2+xbEtd55eNTyayZbqKuZiaK4qTCCF8hrbNcrErcyBNUMSsqqqqMBgMZE4Y\nKp+Xl0d5efmcX3vhwgVyc3MnvfbKK69gNpvZvn07Fy5cWPK84sFEtDUQNTLIUEwS3eFG1XGWRINn\neLjMm/MHc44mEEHGXcy1p2XOcaHv603OYsAQRsS9ZsJ7ulXHEUL4gqVYmZNiTsyit7eX6OjoSa+Z\nTKZJ45xmcuLECUpLSzlx4oTntddff52cnBzCwsI4deoUu3bt4tq1a2Q8yH+/YklpXR9tGQ+7tmEH\ngIbYVTzReJ30rlYc7tdKSlyfD00m2Ldvl7pwYhop5sRknmLuAZ5a+wq9nvq41WS3N2BuqlGdRgjh\nC5ZiZU772hp5XxHTGY1Genp6Jr1ms9kwmUz3/Zp33nmHV199lXPnzhEfH+95fdu2bZ6fP/vss5w6\ndYqzZ8/y0ksvTbvH4cOHPT8vKCigoKBg8b8JMW9a18cePx4WPpVnZa67Be1dbnDQQErKLm7flh4E\ny6W4uJji4uIFf50Uc2LchOYn99IziVUcZynUxSe7irlG+dAlRNDr73eNKgkNhZSUxd9H2z5369bS\n5BIBJSsrC4fDQXV1tWerZVlZ2bTtk5r33nuP559/nrNnz5KTk7Po7zuxmBPeE13v6i1gW/sw3AmM\nzxrj2yxbqZEzm14z9SHMkSNH5vV1cmZOjKurg+5uWLmSvpj4ua/3A/VxyQCEXPuMwsIi6WopRDDT\ntkWuXQshIYu/j8Xi+vrGRhgaWpJoInBERUWxd+9eDh06RH9/PxcvXqSoqIgDBw5Mu/b8+fPs27eP\n06dPs3XKbFebzcb777/P4OAgDocDq9XKRx99xI4dO7z1WxH3YbUWUVhYRElJGTGelbk8xamWTne4\nkaGYJKJGBolob1QdR8xBijkxbuJ8uQDZ910X7yrm0u61kJKyS7paChHMqqtdPz7oeaOwMEhPd+1m\nkHNzYgbHjx9nYGCApKQk9u/fT2FhIdnZ2TQ2NmIymWhubgbg2LFj2O12nn76ac8suZ07dwIwPDzM\na6+9RlJSEmazmbfeeot33313UmMVoYbdDikpu9D3DBDZVs9QSCi9KRtUx1o6Op3rDCAyPNwfyDZL\nMc5dzF1xGikpKWPPHv8/4HrHlIgjPApzv42wnnuq4wghVNK2RWZlPfi91q93FXK3boEMchZTxMXF\ncebMmWmvp6WlTWqEcv78+fvew2w2U1JSsiz5xNLQ5ss1xa58sNV+H9Sz9mGSrv7a3eAlsH5vgUZW\n5sQ493m5sUf+tV+PJJjIqdd7DiXH1JQqTiOEUEor5tavf/B7affQVvuEEEHH0ulq3d8Q6//z5aay\naZ+daq8qTiLmIsWccJnQ/MS2boviMEur2/37kWJOiCBXVeX6calW5kCaoAgRxNLdK3Naw5BA0qNt\ns6yTbZa+TrZZCpemJujoYCDKxEBiquo0S8o2sZh7YvGdwoQQfm4pV+ako6UQQcdqLcJux3MURRuq\n3RC3CrPibEutNzmLoZBQItsaiBoeoC8sApB5c75IVuaEizaSIG1dwDQ/0dgyZGVOiKDX2wt37ria\nl6SlPfj9ZJulEEFHa3wyOAi6kWHW9LTj1OlojFmpOtrSCwlxnQUE0rpaPS9r8+akoZzvkGJOuGjF\nXGoADAufojc1m2G9gajWGsL6e1XHEUKooBVd69YtTaOCieMJAuWQsRBi3kxNFRjGRulLXs9Q6ArV\ncZaFdhZQW4EUvkmKOeEycWUuwDgNoZ6nS4nNdYrTCG/p7Oxkz549GI1GLBYLp06dmvNrvvrVr6LX\n6xkbG/NCQuFVS7nFElyDxy0WGU8gRJDSzpJpjUICkWd4eHfrHFcKlaSYEwAMXPwdAL/tGlGcZHlo\n8+YSG2sUJxHecvDgQcLDw2lra8NqtfLiiy9SUVFx3+utVisOhwNdgG0zFm5LXcxNvJecmxMi6IwP\nCw/kYk5W5vyBFHMCWlqIsHUxEhVDU2ic6jTLot79dCmxSYq5YNDX18fp06c5evQokZGR5Ofns3v3\nbk6ePDnj9TabjR/84Af88Ic/xOl0ejmt8IqlnDGnkXNzQgQtrWV/z9o8xUmWT2PMSpw6HWtsbRhG\nHarjiPuQYk6MjyTIeCTgmp9o6uK0lTnZDhUMqqqqMBgMZGodB4G8vDzKy8tnvP7VV1/lO9/5DitX\nBuAhduGijSVYypU56WgpRHByOse3WWY8ojjM8hkKXUFf8noMzjHW2NpUxxH3IcWcmFDMBdZ8uYma\nY5MYCzEQd7fZ1dVOBLTe3l6io6MnvWYymbDP0H7rs88+4+OPP+Yv/uIvvBVPqLAc2yw3bHD9qBWK\nQoigkNTXRWh/D93hRobiA2/G3ERasWqRrZY+a85ibr5NBN5++222bt1KTEwMqampvPzyy4yOjnp+\nvaCggIiICEwmEyaTiezs7KX7XYgHM3FlLkCNhIRiT8tB53TC55+rjiOWmdFopKenZ9JrNpsNk8k0\n6bWxsTG+853v8Hd/93fo9eNvh7NttTx8+LDnr+Li4iXNLZZJdze0t0NkJCQnL919tWLuxo2lu6dY\ndsXFxZP+HAuxUNoZsvoAHBY+lfbZUM7N+a45h4ZPbCJw9epVdu7cSV5eHps2bZp03cDAAG+++SaP\nPfYYbW1t/PEf/zFvvPEGL7/8MgA6nY633nqLb3/728vzOxGLpxVz67ZAa73aLMvIlrGFmLoyPvpv\n/0BjXYcMuwxgWVlZOBwOqqurPVsty8rKyM3NnXRdT08PV65c4Vvf+haA5wHUmjVr+Od//mfy8/On\n3Vs+/PkhbVUuMxP0S7ghJS0NwsOhpQVsNoiJWbp7i2VTUFBAQUGB5++PHDmiLozwSxbPsPDVAb/F\nrWfCypzsQfBNsxZzWhOB8vLyaU0E/uZv/mbStS+88ILn58nJyezbt48PPvhg0jXSWMAHdXRAYyMj\noWH0pmxQnWZZ2dZtgXP/i/SOEcpl2GVAi4qKYu/evRw6dIgf//jHlJaWUlRUxMcffzzputjYWFpa\nxp82NjY2sm3bNkpLS0lMTPR2bLFctJWzDUv8HqfXu+5ZVgY3b8K2bUt7fyGET7JMWJnLUJxluWkr\nc2ndrVRNGNtTUnIFAJMJeTiu2KwPFBbaRGCiCxcuTHsK/sorr2A2m9m+fTsXLlxYZGSxpK66ujF1\npGYszSBdH6a9IcXUlCpOIrzh+PHjDAwMkJSUxP79+yksLCQ7O5vGxkZMJhPNzc0AJCUlef5KTExE\np9OxcuVKQkNDFf8OxJLRirnl2N6/cePk7yGECDhWaxGFhUWUlJQBwbXNcjjGTEdENBGOYaJaxjv3\nDg4aSEnZxQxH0YWXzboyt5AmAhOdOHGC0tJSTpw44Xnt9ddfJycnh7CwME6dOsWuXbu4du0aGRmB\n/kzDx2nDwtcE/r+HnrV5jKHD1Hid0o8vY5WnSQEtLi6OM2fOTHs9LS3tvu9hFotl0llfESAqK10/\naoXXUtJW+27eXPp7CyF8gt0OKSm7GBwsI6y7jfgBOyMRJtqMgTnOaaqGuNUkDPR4xjEI3zJrMTff\nJgITvfPOO7z66qucO3eO+Ph4z+vbJmw/efbZZzl16hRnz57lpZdemnaPiWdSpu5tF0vMvTJ3Ly3w\ni7nRCCMt0Qmk9NzDfLdDniYto+LiYmkOInyHtmq2gGLOai3Cbp/HFiJZmRMiqIzPl3sYpy7QT8y5\n1MetZsudm0TXXoUwo+o4YopZi7n5NhHQvPfeezz//POcPXuWnJycRYeSBgNe5F6Za09bR7jiKN5Q\nH7ealJ57pHe1MDb35WKRpMGA8BkjI+NDvRdwZk57En/7dtHsF0oxJ0RQ0Yo5W8bDipN4T0PcKsD9\ne9/4e4rTiKlmfaQwsYlAf38/Fy9epKioiAMHDky79vz58+zbt4/Tp0+zdevWSb9ms9l4//33GRwc\nxOFwYLVa+eijj9ixY8fS/m7EwtjtUFXFaIiBXzd3q07jFfXu4eFrO6XFrhBBobbWVdClp7tGE8zC\nai3Cap2jeJsqK8v1461b4HAsMqQQwl9EaytzATzOaSrts1NM7VWQZoY+Z8714fk2ETh27Bh2u52n\nn37aM0tu586dAAwPD/Paa6+RlJSE2Wzmrbfe4t13353UWEUoUOY6yNub/hB9I3NOqQgIde43JEvX\nHcVJhBBesYAtlnY7991+rTVAmFbsRUVBaqqrYKyvf7CsQgifN74yFzzFXHtULH2h4aywtRM3IGdU\nfM2cn+Dn20Tg/Pnz972H2WympKRkkRHFsnFvsexet0VxEO/Rtgqkd7eik0YXQgQ+rfnJPDtZau22\nS0rK2LNn15S//0+cOXN4+lm6jRuhqclVOMpDSiECVsTIIMY7txjRh2BPy4HLv1QdyTt0Ourik8m9\nW8taeRjuc4Lj5KaYmbuYC6atAn0rIulPshA26iC2tVl1HCHEcpvHytzEtuNau+3BQdev3e/vJ63g\nybk5IQKW1TpxJEErAI2xq3Aagmt8jTaGwdIpxZyvCY69dWIaq7WIp357gUTcw7SvnlMdyWts67YQ\n2VZPz4VzFBamy8BLIQLZDGMJtE6Vn39+hc2bH/Wsug0Oli3ue2j31r6XECJg2O14HuZohUwwzJeb\navyYSgvSdcC3yMpckOrvHCa+pYkxnY4ey2bVcbzK5t5WmtJ2VwZeChHInM4ZB4ZrnSq7uyevui2a\ndu+Kige8kRDCl2lbDOvikxUn8b76eFcBO3WbZUnJlZnPEwuvkZW5IBV/uwH92CjN0WZGw6NUx/Eq\n7dDy2s4WqhVnEUIso5YW6OmBuDgwm5f01tpZOpMJ9n39MdeLFRWuAlKnW9LvJYTwDZYu15pUfdxq\nVirO4m2tpgQcEUYS+nsI627zvK5tPZ9zjItYNrIyF6QSm2qA4Hy6pK3MpXe1wJhMmxMiYE3cYrnE\nBdaks3NJSZCY6Cocm+UsrhCBKGSon5Sedsb0ITTFBlspB06dHtta12w9raOn8A1SzAWpxKZaYHx2\nSDAZiltFV4SJSMcQka21quMIIZbL9euuH3Nzl+1blJRccW0vyslxvVBevmzfSwihjqnuc/ROJ/a0\nHEZCgqv5iUZ7GB5TU6o4iZhIirkgZW7UVuaC7xAvQJ378HJMrbwhCRGwtMLKXcxN7Fq5VAYHDa7V\nOSnmxASdnZ3s2bMHo9GIxWLh1KlTM1739ttvs3XrVmJiYkhNTeXll19mdMLYnPneRyw/7fOCLYjG\nOU1ly5BizhdJMReMRkaIv10PQENscBZz2oqkvCEJEcCmrMxpjU8euOHJFCUlV/io071lW4o5ARw8\neJDw8HDa2tqwWq28+OKLVMzQIGdgYIA333yTjo4OLl++zLlz53jjjTcWfB+x/GKrXedkg7qY86zM\nXVGcREwkxVwwqqzE4Bihb9U6BsLCVadRQmsrHCvFnBCByen0FHP/fOP2kq/ITTQ4aCBk8zOuv5Fi\nLuj19fVx+vRpjh49SmRkJPn5+ezevZuTJ09Ou/aFF14gPz8fg8FAcnIy+/bt49KlSwu+j1h+WgGj\nrU4Fo97UbIZDDETdrSNqqF91HOEmxVwwKpWtAvXuxi/RtVddH/qEEIGlqcm1FGc2c08fuywrchPZ\n09zbLLWOliJoVVVVYTAYyMzM9LyWl5dH+TwK/QsXLpDrXkl+kPuIBzdxW3aoYwRTY7lrnFPGw6qj\nKeMMMXh2dK3tkmlzvkKKuWCkFXPuFv3B6F5kDPawCFb03KP6gw9kRooQgUb7wKudZVtmw9GJ9EfH\nQm8vNDZ65XsK39Tb20t0dPSk10wmE/Y5hpqeOHGC0tJSvvvd7z7QfcTSmLgtO627Ff2oIyjHOU1V\n634YvrbztuIkQiNz5oJQ2/u/JQmwZT4KN0pUx1FDp6M+LpmH7taQ3HpXZqQIEWjcWyy/IIqSkjL2\n7Nm17N+yc3UakT3dru+dnr7s30/4JqPRSE9Pz6TXbDYbJpPpvl/zzjvv8Oqrr3Lu3Dni4+MXx11R\nfgAAIABJREFUdZ/Dhw97fl5QUEBBQcHifgNimoxObVh4iuIk6mkjrTI6b9M2x7ViYYqLiykuLl7w\n10kxF2xGR4lrqAPc2yyDtZjD1cnzobs1WDplq4AQAcddzDk37WKwq90r3/KGPpw1wNV//Cce2bnT\nK99T+J6srCwcDgfV1dWeLZJlZWWe7ZNTvffeezz//POcPXuWnAkryQu9z8RiTiytDPcqVF18MgmK\ns6hW6y5o13bemVTMlZS4zhSaTLBv3/I/PAtEUx/CHDlyZF5fJ9ssg82tW4QODdIeGcNwdKLqNEpp\nT5csXXcUJxFCLDl3MdeTtnwz5qaqN64CILJOtlkGs6ioKPbu3cuhQ4fo7+/n4sWLFBUVceDAgWnX\nnj9/nn379nH69Gm2bt266PuI5bXWvTJXKytz3IlOxLEikqS+bkJ7OjyvDw4aSEnZhewC9j4p5oLN\nFdeTE60BSDDTxhPIIV4hAszoKFRWAhMak3hBU+xKABLco19E8Dp+/DgDAwMkJSWxf/9+CgsLyc7O\nprGxEZPJRHNzMwDHjh3Dbrfz9NNPYzKZMJlM7Jywqnu/+wjvCXMMs6anjTF9CA2xq1THUW5MH0KP\nu+dCrIwo8AmyzTLYuJuf1MetJjiHEoxrM8YxEhlNXH8PK2SrpRCBo64OBgbojIzGYYz12rdtinEV\nc3GtTTAyAqGhXvvewrfExcVx5syZaa+npaVNamBy/vz5Rd1HeE96Vyt6pxNbeg4jBvkzDdCd+Sjx\nlZeIufWZ6igCWZkLPu5iri5OVuacOv2EAZgyb06IgFHmmifX6C6uvGUwdAV9q9YR4nDw//2gUDrk\nChEA1rqPYtgyt85xZfDQ/lnIypxvkGIuiFhPvsvQJ66GJ3WyzRIYH/4pxZwQAcRdzKnYEtVj2QxA\nZn+8nB0RIgBkdLian3RLMeeh/bOIvfWp4iQCpJgLKrq6VlYM9tMVYcIWcf8WycHElvkoIE+XhAgo\n164B0BinoJhbmwdAdF0ZJSVXZIalEH5O62TZvV6KOU1vchb9hhVE3GsieqBXdZygJ8VcEDE31QJQ\nF7dacRLfMXGbpXzwEsL/Wa1F2C99AkCDgvc6TzFXXybd3YTwc4Y+G8k99xjRh2B3r7oLICTEs8Nr\nnQwPV06KuSCS2FgNjHdxFNC7ej2DhjAi7jUR2j0kH7yE8HPDrXZMne0MhYTSYvT+RChtm2V0/ede\n/95CiKUVU30FPU4a4lYzFrpCdRyfUpPgGtOwrqNZcRIhxVwQMTfUAHJebpKQEOrdT++1OTJCCP+l\njQVoil2JU+/9/8X1J1noN6wgvKuV6EHZfiSEP4u75eozUCPz5aapSVgDSDHnC+b8P11nZyd79uzB\naDRisVg4derUjNe9/fbbbN26lZiYGFJTU3n55ZcZHR1d8H3EMnE6SWySYm4mdZ55c7JVQAh/ZbUW\nUVhYRN+liwA0qpoHpdd75s2ldd8FkC3cQvgR7b2kpKSM2CpXMVebIMXcVDXx7mKu8zY4nZ7X5f3O\n++Ys5g4ePEh4eDhtbW1YrVZefPFFKioqpl03MDDAm2++SUdHB5cvX+bcuXO88cYbC76PWCZ1dYT3\n9zIYu5LOiGjVaXyKVtzKypwQ/stuh5SUXSS3twJQr6D5iUYrJNO6XFnk7JwQ/kN7LxkchFhtZc69\nCiXGdUZGMxi3CuPwAJEtNZ7X5f3O+2Yt5vr6+jh9+jRHjx4lMjKS/Px8du/ezcmTJ6dd+8ILL5Cf\nn4/BYCA5OZl9+/Zx6dKlBd9HLJMrrm6NtsxHQadTHMa3SDEnROBI72oBFK7MAQ3uQjK9u0VZBiHE\ng4nt7yGi4zb9oStoMXn//K3P0+noXr8NkBEFqs1azFVVVWEwGMjMzPS8lpeXR3l5+Zw3vnDhArm5\nuQ98H/HgrNYirv74ZwDY1j2qOI3vuWNKxBEehbnfRpitXXUcIcQi6UaGSelx/RlWW8zJOVwh/J3W\npbE2PgWnTlpMzKR7/ZeA8bOFQo1Z/+vs7e0lOnryljyTyYR9jrXTEydOUFpayne/+90Huo9YGnY7\nrLlrA6BbirlpnHo9toxHAFfnKhEY5ntO92c/+xkbN24kJiaGxMRE9u7dy5078iHcX0w832JsvkHo\n2Ch9q9YxqLDzXGPsSsZCDCTb7xEy2Od5Xc6SCOE/tMYe0vzk/rqz3CtzVVLMqWSY7ReNRiM9PT2T\nXrPZbJhM9x84/c477/Dqq69y7tw54uPjF3Wfw4cPe35eUFBAQUHBbDHFXJxOYmpKAbCt3wp1XygO\n5Hts6x4loeKia3j4Kpkl86CKi4spLi5WmmHiOd2rV6+yc+dO8vLy2LRp06Tr8vPz+fDDD0lKSqKv\nr48///M/56/+6q/42c9+pii5WIjx8y1lrj+/jM+PVGUkJBR7Wg4xdWVE15V5XtfOkty+LcWcEL4u\nUyvm5LzcfWkrczG1pYRs/rriNMFr1mIuKysLh8NBdXW1Z4tkWVmZZ/vkVO+99x7PP/88Z8+eJScn\nZ9H3mVjMiQdnuneXsN4uusONDEonyxnZMl0rljHVVygJHQHAZIJ9+3apjOW3pj6EOXLkiFe/v3ZO\nt7y8fNo53b/5m7+ZdG1qaqrn506nk5CQEMxms1fziqURU/0ZAN2ZW2F4WGkWW8YWYurKiKmR1X4h\n/M7oKBkdrm2W1Ympc1wcvEaMcdwxJZJsv+fp3iu8b9ZtllFRUezdu5dDhw7R39/PxYsXKSoq4sCB\nA9OuPX/+PPv27eP06dNs3bp10fcRS8/sHhZeF58szU/uQ9t+GlNzRToxBYCFntO9ePEisbGxREdH\n09jYyOuvv+6tqGIJxVZPaPSkmJYhVrZuC+F3TE0VRDqG6E9Kpzvi/rvRBNxyF7vrO5oUJwlec57o\nPH78OAMDAyQlJbF//34KCwvJzs6msbERk8lEc7NrGfrYsWPY7XaefvppTCYTJpOJnTt3znkfsfzM\nje75cnGyKnc/vSkbGDSEEdneiGnCGRfhnxZ6Tnf79u10d3fT3NxMaGgo3/ve97wRUyyhkLFRouuu\nAeq3WU7MoG1xn6ik5IqcmxPCx0w8fxt38xMAujY8rjiV7/MUc/ekmFNl1m2WAHFxcZw5c2ba62lp\naZM+GJ0/f35R9xHLz9xwC3ANvdygOIvPCgmhPm41G9sbyOiU4eH+bjHnfQGSk5M5evQoO3bs4M03\n35zxGjnT65tSbG2EjAzRaoxnxBinOg49a/MY0+kwNlUQ6hiZ9GuDgwZZ+VfIF870Ct8z8fxtXOPH\nAHRlPQ79vYqT+bZq95nC9feauKw4S7Cas5gTfm5szLMyVxsvxdxsauNTpJgLEAs9pzvRyMgIkZGR\n9/11OdPrm7QxAHU+ci54dEUkzdFm0mxtpHW3qo4jJlB9plf4vrgq98rcxieg9DeK0/i2ppiVOMKj\nSOrrIqxr/NxcSckV6T3gJTI4I9BVV7NioI+BhBTZ9z0Hrf2wFHP+byHndH/605/S1OTaHtLQ0MD3\nv/99vvnNb3o7snhAGZ5iznfaiNe7t7av7ZJRF0L4i6jhAUxNlYzoQ+jJeFh1HJ/n1Os9w8O17akg\nOxC8SYq5QPeZq7ubLXPrHBeKugStmJMPXoFgvud9KyoqePLJJzEajRQUFPDEE0/wwx/+UHF6MZeJ\n51tgvGCq9aGzwdoqYUaHvKcI4S+0+XJ18cmMKZxX6U+6Nj4BTC7mhPfINstA9+mngLtV95jiLD6u\n1RjPSFQMcX02wjtkdc7fzfe877Fjxzh27Jg3o4klMPF8i84xQlqXaytjffxq8hRn09S6HxCt62zm\nmuIsQoj5yXQ38qhOkJEE86U1iomr+gRyv6o4TfCRlblA516Z0wY7ilnodK6iF4i59ZniMEKI+TI1\nXCdszEHv6kz6wyJUx/Goj1vNmCGUFFs7hv7JDXlKSq5QWFgkXS2FUGzqKn+Wu5i7lSjDwudLK+Zi\nq0oIGRtVnCb4SDEXwH76D+8wUuJamfOFuUv+oDvTVfTGVn8qH7aE8EFTP3gBxFW5eqh1Zz2mKtaM\nRkJC6bHkocc57QGRzLMUwjeMr/IDo6OelbmqxHS1wfzIcIyZO6YEDEP9nl0SwnukmAtgIbeaCR0e\noi0qjuHoRNVx/IJtvWtlLvbWZ/JhSwgfNOmDl5svz4TqcheYcbdKFCcRQswluuEL97BwC12R0XN/\ngfDQit8N7Q2KkwQfKeYCWJI2X85HWnX7A207amz1p+B0Kk4jhJiP8WLOt1bmALrdmWKrZAKTEL4u\nvvISAJ2btitO4n9umtMA2HCvUXGS4CPFXAAbL+Z8p1W3rxtITMW2IooweydJfV2q4wgh5hA1PIDx\n9k2G9QZ6LL7S+mScZ2Wu6rI8IBLCx8VXXASgMztfcRL/U+Uu5rLaGzzvdXJcxTukmAtg5npXMVct\nh3jnT6ejJsH1z0trTyyE8F0T24g7Q8MUp5muL3k9vWERhHe2ED+lCQrIhx0hfImszC1eiymRoehE\n4gZ7ibxbB8jZYG+RYi5QDQ6S0FyHU6+nzofmLvmDGq2duIwnEMJnzNT4BCa2EffRh1Y6HTXu3RGZ\nHU3Tflk+7ASmzs5O9uzZg9FoxGKxcOrUqRmvu379Ok899RRmsxm9fvpHsoKCAiIiIjCZTJhMJrKz\ns5c7etBK6Osm4l4TfaHh2FM3qY7jf3Q6utwrmtoKp/AOKeYC1dWrhIyNYk/NYUiGXi6IrMwJ4Xtm\nanwCkOn+c+rLOxC0bJnynhI0Dh48SHh4OG1tbVitVl588UUqKiqmXRcWFsYzzzzDT37ykxnvo9Pp\neOutt7Db7djtdiorK5c7etDKaned9aoyp8EMhbWYW4d7RVNb4RTeIf+1BiCrtYhLPzoBQFfWNsVp\n/I/2FH1t1x10jhHFaYQQ9zU2Nl7M+fCAXy3b+nvTV+ZE4Onr6+P06dMcPXqUyMhI8vPz2b17NydP\nnpx2bVZWFs899xybNt1/JcgpZy29QmvcUZWYpjiJ/5KVOTWkmAtAdjukt/UD0L1eirmF6lsRSe/q\nTMJGHZgarquOI4S4j6g7tzAODzAYt4qOyBjVce7rVmIqTp2OjM7b6IcH5/4C4deqqqowGAxkZmZ6\nXsvLy6O8vHxR93vllVcwm81s376dCxcuLFXMoDd16/bGNtc5r5tmmS+3WN3rHmUoJBRTUwWmoT7V\ncYKGFHMBKrbKNdOoW1bmFkX75xZ3q0QaFAihmNU6/awcTOk8p9N5O9a89YdFYE/LJXRslNjqz+b+\nAuHXent7iY6ePKPMZDJhX8TByNdff526ujru3LnD888/z65du6itrV2qqEFt4tbtsJ57pNnaGA0L\n993zt37AGRrGrUTXToSNbfVqwwQRg+oAYumt6O3B2FLNUEgo9vRcuPxL1ZH8TnfWY6y58FNiq0oY\nNK8lJWUXt29LMSeECnY7087KASRUfARA56bfgz7f7iDSuWk70Q1fyPajIGA0Gunpmdy51GazYTKZ\nFnyvbdvGH8g+++yznDp1irNnz/LSSy9Nu/bw4cOenxcUFFBQULDg7xes4std7yVdGx7HESIfjR9E\nZZKF3Lu1ZLfV82lqjuo4fqW4uJji4uIFf538FxuAtPlydfHJOOVNaVG63NtTY6sug3mt4jRCiJl4\nVuY2bYdPf6U4zew6s/Ox/Op/EFd5CTJ9b7i5WDpZWVk4HA6qq6s9Wy3LysrIzc1d1u87sZgTC5Nw\nvRiAjpwvqw0SACqTLABku7etivmb+hDmyJEj8/o62WYZQLT938OXXE+YZFj44vVkPIxDp8fUVEHE\niJxxEcLXxA7YiWqtYcAQRs9a3xsWPpU2hDi+8hI659i0X5ft3IEjKiqKvXv3cujQIfr7+7l48SJF\nRUUcOHBgxusHBwcZHh4GYGhoiKGhIcC1mvf+++8zODiIw+HAarXy0UcfsWPHDq/9XoJFwnXXWcSO\nXCnmHlRNwhpGQ1eQ2t1G1FC/6jhBQYq5AKLt/17b6uqYpu1bFgs3FhZOQ9xqdE4nazvuqI4jhJhi\nQ3sD4G4u4gc7EAaS0umIiCast4vknnvTfl3mzQWW48ePMzAwQFJSEvv376ewsJDs7GwaGxsxmUw0\nN7u6sNbX1xMZGUlubi46nY6IiAjPLLnh4WFee+01kpKSMJvNvPXWW7z77ruTGquIBxc1PEB0/eeM\n6EPo2vC46jh+byQklO6sx9DjZKP7fVoeVi0v3/8/oFiYCa26byWkkqE4jj+rTljDus7brO9oVB1F\nCDGFVszdNKcTrjjLvOh0VJnTeKLxOhvaG7gdk6Q6kVhGcXFxnDlzZtrraWlpkxqhWCwWxsamr9QC\nmM1mSkpKli2jcNnQVo/O6aQmcQ1jKyJUxwkIHblfJqH8Q7Lb6hll/GGV9B5YHrIyF2C0Vt0D8cl0\nRkbP/QXivrSVzfX3XMVxSckVeaokhI+YWMz5Cy2rln0m8gRbCO/a5O66qJ31Eg9O264q5+a8Q1bm\nAkzczY8B6Nr4hE+36vYH1e5iLrOjidtOJ4ODBtkCJYQXWa1F2O1MG0tg6O8hvbuVsRAD1Qlr8P0T\ncy6VZgsAm9rq4D6DoOUJthDetemua9RDZdJaHlKcJVB0bXyCEX0I6V2t3LR3qo4T8OZcmevs7GTP\nnj0YjUYsFgunTp2a8brr16/z1FNPYTab0eun37agoICIiAhMJhMmk8mzJ1wsrbibnwDIvu8l0BYV\nx1BMEtFD/US21KiOI0TQmTgHaqL4ykvonU66M7cybAhTE24RmmOTGDYlkNDfQ1Jvl+o4QgSlicPC\nw2ztWLpbGQ1dwc3ENNXRAsboikiqEtPQ4yTxiw9Uxwl4cxZzBw8eJDw8nLa2NqxWKy+++CIVFRXT\nrgsLC+OZZ57hJz/5yYz30el0vPXWW9jtdux2O5WVlQ+eXkyjFXPdUsw9OJ3OUxRr/1yFEOolfH4e\ngI6HvqI4ycI4dXrP9qNNbTL4WQgVJj4kSnS/l3Ru2s6IIVRxssBSvtLVtSHx2m8VJwl8sxZzfX19\nnD59mqNHjxIZGUl+fj67d+/m5MmT067NysriueeeY9OmTfe9n/M+20rE0ggd7Ce64QscOj3d6x5V\nHScgjBdzHytOIkTwmPjkfCbak957flbMAdx7qACATXdnP0siZ+eEWH6JZecAuLf5q4qTBJ7rq9YB\nkPj5OcVJAt+sxVxVVRUGg2FSG9y8vDzKy8sX9c1eeeUVzGYz27dv58KFC4u6h5hO++DT8f776MbG\naIhbLR2ZlkjXxicAWZkTwpvut70SXG3EY2pKcehD6NqU7/1wD6gjtwCA7Lb6+56bAxlVIIQ3aIVG\n+8NfU5wk8NTGJ9MfugLjnVsk9HWrjhPQZi3ment7iY6e3BHRZDJNaqs7X6+//jp1dXXcuXOH559/\nnl27dlFbK9tMloL2wSf9jmu+XHXCGsWJAkd35lbGdDqi68pY4RhWHUeIoLfR3Ub8VsIaRldEqo6z\nYPa0HHpWRJIw0ENUS7XqOEIELXNvF1GttfSFhmPL2KI6TsAZ04d4OoTm3pXP+8tp1m6WRqORnp6e\nSa/ZbDZMJtOCv9G2bds8P3/22Wc5deoUZ8+e5aWXXpp27eHDhz0/LygooKCgYMHfLxhl3XPNQ6tK\nTMOiNkrAGI0w0hC7irVdLazraAa+pDqSXyguLqa4uFh1DBGActwfCipWZuA/rU8m0OupTLLwWFMF\nCV8Uq04jRNDKuetqbFa+ci2EhChOE5iur1zHo7dvktNaQxeu7eMAJhPs27dLbbgAMmsxl5WVhcPh\noLq62rPVsqysjNzc3GUNNbGYE/M0NkZWu7uYM0sxt5SqEtNY29VCVnsj0mB3fqY+hDly5Ii6MCKg\naGfNyleu5RHFWRarIimDx5oqXFu81izv/0+FEDN7qFUr5taRqDhLoLq+ytUEJfduLR+NjcnolWUy\n6zbLqKgo9u7dy6FDh+jv7+fixYsUFRVx4MCBGa8fHBxkeNi1FW1oaIihoSHAtZr3/vvvMzg4iMPh\nwGq18tFHH7Fjx44l/u0EL2NzJVEjgwwkrqEjKlZ1nIBSZXa1K9ZWPoUQaoTZ2kmz3WU0LJzqhFTV\ncRbtC3djAPO136JzjilOI0QQGh31FHOfr86c42KxWLejkxhISCF2sJfo+s9VxwlYcw4NP378ON/+\n9rdJSkoiMTGRwsJCsrOzaWxsJCcnh8rKStasWUN9fT0ZGa4KXKfTERERgcVioba2luHhYV577TVu\n3LhBSEgI2dnZvPvuu5Maq4gHE19xCYDObP9rCODrbiamA7D+XhN/f/kzQLYICLEcJg4J37Nn+p8v\n87XfANCZvR1HyJz/+/JZraYE2qNiMds7sHS1zHqtbEsSYulYra4uud/OTsQ4PEDfqnXcNSWojhW4\ndDratuwg/Tc/IenKr1SnCVhz/t8wLi6OM2fOTHs9LS1tUiMUi8XC2NjMTxjNZjMlJSUPEFPMJb5y\nQjFntylOE1g6o2IYSEwl6l4TCXc7ZYuAEMtkvIvlzCMJzKXvA9C25SlmbHXpL3Q6vli1jj+oucJD\nczRBkW1JQiwdu9311mEufQ+Ati2yQ2y5tT/6tKuYK30PNn9ddZyANOfQcOEftGKua+OTipMEJm3F\nU7ZaCqGI04n52q8BaA+AD2BfrHLtTNG2egkhvCdJK+Ye9f/3El/XvvmrjOr0xN34HRHDfvwQzodJ\nMefnrNYibly4RFRrDYOGMHrW5qmOFJC0Ym5De4PiJEIEp7TuVsK7WumIiMaelqM6zgO7vjIDp07H\nhnuNhAz0qo4jRNAwDfURe+tTRvQhdDz0FdVxAp7DGMutxFT0ow5PN2KxtKSY83N2O6Q3uwqM6oQ1\nOP34HIkvk5U5IZaP1VpEYaHrLMv9bHZvR/xiVSbodN6Ktmz6VkTSvf5LGMZGSSj/UHUcIYLGQy3V\n6JxObpgtjIZHqY4TFMrcTWYebrmlOElgkmIuAGxoH58vJ5aH3fIQA4YwVvZ2saLjjuo4Yp46OzvZ\ns2cPRqMRi8XCqVOnZrzu7bffZuvWrcTExJCamsrLL7/M6Oiol9MGr/Gzcve/ZnOrq5gLpM5z7Q9/\nAxg/vzObkpIrWK1ybk6IB5XnLigC6b3E15WtzgIgr6UKnE7FaQKPFHMBYGN7PQA3kixKcwQyZ4jB\nUywnVHykOI2Yr4MHDxIeHk5bWxtWq5UXX3yRioqKadcNDAzw5ptv0tHRweXLlzl37hxvvPGGgsRi\nJiscw2xob8Cp03Hd3dY/ELQ9+jQAKz/7lzk/4AwOGpjQc0wIsQi60VEevlMFQGnKBsVpgkdD3CoG\n41eT0N9DdO011XECjhRzfi50oB9LVwtjIQZuJfrv3CV/oBXL8bIlyi/09fVx+vRpjh49SmRkJPn5\n+ezevZuTJ09Ou/aFF14gPz8fg8FAcnIy+/bt49KlSwpSi5nkttYQOjZK9/ov0bsiUnWcJdOV9Rj2\nsEiiWmtJtt9THUeIgLeqthLT8AC9yetpiTarjhM0nDo9d7/kGq2y8tMiSkquUFhYJLsNlogUc35u\nVW0leqeT7sytDBnCVMcJaFoxl1D+obwR+YGqqioMBsOkeZZ5eXmUl5fP+bUXLlwgNzd3OeOJBdhy\n+yaA58NAwAgJ4VryegAecf8ehRBLTzuXu+L9fwHg7rY/Vpwo+LS6/5mvKvmFZ+SK7DZYGlLM+bnV\nt1wfTDtzfl9xksBXE5/CcIiB6IbrhNqG5I3Ix/X29hIdHT3pNZPJNGk+5kxOnDhBaWkp3/3ud5cz\nnmB+jU8YG+PhO+5ibluAFXPA1WTXVi9t65cQYulp53LzGm8A44WF8J57m/+AwZBQYquvEN8v85CX\nkhRzfm51tauY65Bibtk5QgzcSnBtZZURBb7PaDTS09Mz6TWbzYbJZLrv17zzzju8+uqr/OpXvyI+\nPn65Iwa9+TQ+iam5QtxgL/ciY+ixbPZeOC/5fHUmY/oQNrY3YOjtVh1HiIAV1XyT1fYO7GERdGXL\nTF5vG1sR4TnzLDsRlpb0sfdTVmsR/R1DPFdXxRg6V+v86quqYwW8G0np5LTVsbGtAel16NuysrJw\nOBxUV1d7tlqWlZXdd/vke++9x/PPP8/Zs2fJybn/HLPDhw97fl5QUEBBQcFSxhZTrCpxbWUuTdkQ\nECMJpuoPi6Bz03YSr1/wDEW/n5KSKwCYTLBvX+CtUnpLcXExxcXFqmMIL1tV8gsAriVnyRgnRa6k\nbGTr7Rs8evsGTarDBBD5r9lP2e2wuTcRw9go9bGrcBhjVUcKCjfMFsDVQXTuk1dCpaioKPbu3cuh\nQ4f48Y9/TGlpKUVFRXz88cfTrj1//jz79u3j3XffZevWrbPed2IxJ5bfSq2YS96I/48Kn9ndL/0R\nidcvsOryu5Ccfd/rtHMmt2/LWd0HMfUhzJEjR9SFEV6z6uPTgKugCJyeuP7lasoGnDoduXdraemT\nrZZLRbZZ+rGE6xcAGUngTdWJqYyFGLB0tWCQNyKfd/z4cQYGBkhKSmL//v0UFhaSnZ1NY2MjJpOJ\n5uZmAI4dO4bdbufpp5/GZDJhMpnYuXOn4vQivs9GTN01Bg1hVK60qI6zbFof+xMAVn76S0JGHYrT\nCBF4ojrbib/5CUMhoZQlZ6mOE7R6wo105Pw+hrFRVpZIV8ulIitzfizx8/MAVKxcy3rFWYLFkCGM\n7qzHiK+8REL5hzSkqE4kZhMXF8eZM2emvZ6WljapEcr58+e9GUvM07Zm10zAstXrGQkJVZxm+fQn\nZ9IQu5L07rvk3K1THUeIgJNx9XcAXEteL52/FWvJ/zMSr18g+Xf/zGDGVtltsARkZc5PGYaHiLv5\nMWPoqExaqzpOULn30FcASPjiA8VJhAhs25pcm5lLUjcpTrL8Pl3j+j1qBawQYuloxdzlVBk5o1rL\n43sYQ4e59D3CR4ZUxwkIUsz5qVU1FegdI9THr6YvLEJ1nKByb/MfAOMro0KIpbeis4Wt72g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3UinyLFnA9aU3wSgJYn/5RRfYjiNGIxPk3dxJghlJy2WiK7ZY+3Kp2dnezZswej0YjFYuHUqVMz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\nXcZ4KIsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7f023201f190>"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Inner product"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assuming my hypothesis above is correct about the cosine being a uniform distribution, the inner product then represents a robust measure.\n",
"\n",
"Logically, I think this makes sense. Just as Georgios hypothesized that the normalised gradients can reasonably take any value between $[0, 2\\pi)$ with equal probability, this will hold for the inner product.\n",
"\n",
"The relationship between two unrelated vectors could feasibly be in any direction with equal probability. Therefore, the distribution of inner products between two unrelated vectors can take the values $[-1, 1]$ with equal probability. \n",
"\n",
"Thus\n",
"\n",
"$\\cos{\\theta} \\sim U(-1, 1)$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Calculate the \n",
"total_inner_product = np.array([])\n",
"for c in inner_products:\n",
" total_inner_product = np.concatenate([total_inner_product, c])\n",
"\n",
"plt.subplot(121) \n",
"h = plt.hist(total_inner_product, bins=100)\n",
"plt.title(r'The inner product $\\cos{\\sigma}$')\n",
"#plt.savefig('cosine_inner_product_hg01.eps', format='eps', dpi=1000)\n",
"\n",
"plt.subplot(122) \n",
"h = plt.hist(np.arccos(total_inner_product), bins=100)\n",
"plt.title(r'$\\sigma$')\n",
"\n",
"plt.gcf().set_size_inches(12, 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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qo+wHdiACgAeAGWdPCtBMsjyVOvFQVks71FBWSzvUVlZLO9RWDr2OynezYafR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\nrkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0233ee0810>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure()\n",
"plt.suptitle(r'Uniform distribution of all $\\cos \\sigma$ images')\n",
"\n",
"for i, c in enumerate(inner_products):\n",
" plt.subplot(4, 3, i + 1)\n",
" h = plt.hist(c, bins=100, normed=True)\n",
" plt.xlim(-1, 1)\n",
"\n",
"plt.gcf().set_size_inches(15, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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jDnPNNdekrLN69Wpz++23x/7ftm2bmTdvntNNy7mhoSFTXFxsdu/e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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0233ee0190>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can actually help verify this by taking a look at the distribution of the angle itself. Here we see that the angle itself almost perfectly represents a $\\sin$ function between $0$ and $\\pi$. This makes simple sense. In order to get a uniform distribution over the cosine, you would need a sine over the angular domain in order to have the frequencies 'cancel out' to form the flat line of the uniform distribution."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = plt.hist(np.arccos(total_inner_product), bins=100)\n",
"x = np.arange(0, np.pi, 0.1)\n",
"# It is very close to a sine wave!\n",
"plt.plot(x, np.sin(x) * max(h[0]), 'y', lw=2)\n",
"plt.title(r'$\\sigma$')\n",
"plt.legend(['Sine wave', '$\\sigma$'])\n",
"\n",
"plt.gcf().set_size_inches(7, 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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VNeU1ihZQWvot+fnvotN5kJgIJpOf1pGEEyssDGH+/NcB2LfvMerqjmucSLiK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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0232af5110>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Inner product Sqaured (Haber)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For completeness, and as a sanity check, we show the distribution of Haber et. al., the cosine squared. Here we clearly see its heavy bias."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"total_inner_product_squareds = np.array([])\n",
"for ips in inner_product_squareds:\n",
" total_inner_product_squareds = np.concatenate([total_inner_product_squareds, ips])\n",
" \n",
"h = plt.hist(total_inner_product_squareds, bins=100)\n",
"plt.title(r'The inner product squared $\\cos^2{\\sigma}$')\n",
"# plt.savefig('inner_product_squared_hg01.eps', format='eps', dpi=1000)\n",
"\n",
"plt.gcf().set_size_inches(7, 5)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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aIxHRRU6n0+F8442PhCMiIlJhMBIREakwGImIiFQYjERERCoMRiIiIhUGIxER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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0230450c10>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure()\n",
"plt.suptitle(r'Distribution of all $\\cos^2{\\sigma}$ images')\n",
"\n",
"for i, t in enumerate(inner_product_squareds):\n",
" plt.subplot(4, 3, i + 1)\n",
" h = plt.hist(t, bins=100)\n",
"\n",
"plt.gcf().set_size_inches(15, 10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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TEwICAlBaWgoAOHfunE55SEiIWFZaWgp/f384OzuL5aGhoWI5ERER0VDCZJCI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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f0232e2c190>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Save all Figures for Paper"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Delta Phi\n",
"plt.figure()\n",
"h = plt.hist(total_phis_shifted, bins=100)\n",
"plt.yticks([])\n",
"plt.tick_params(axis='x', labelsize=16)\n",
"plt.xlim(0.0, 2.0*np.pi)\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.savefig('delta_phi_all.eps', format='eps', dpi=1000)\n",
"\n",
"# Delta Theta\n",
"plt.figure()\n",
"h = plt.hist(total_thetas, bins=100)\n",
"plt.yticks([])\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.xlim(-np.pi, np.pi)\n",
"plt.tick_params(axis='x', labelsize=16)\n",
"plt.savefig('delta_theta_all.eps', format='eps', dpi=1000)\n",
"\n",
"# Sin Delta Theta\n",
"plt.figure()\n",
"h = plt.hist(total_thetas_sin, bins=100)\n",
"plt.yticks([])\n",
"plt.xlim(-1.0, 1.0)\n",
"plt.tick_params(axis='x', labelsize=16)\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.savefig('sin_delta_theta_all.eps', format='eps', dpi=1000)\n",
"\n",
"# Inner Product\n",
"plt.figure()\n",
"h = plt.hist(total_inner_product, bins=100)\n",
"plt.yticks([])\n",
"plt.tick_params(axis='x', labelsize=16)\n",
"plt.xlim(-1.0, 1.0)\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.savefig('inner_product_all.eps', format='eps', dpi=1000)\n",
"\n",
"# Inner Product Squared\n",
"plt.figure()\n",
"h = plt.hist(total_inner_product_squareds, bins=100)\n",
"plt.yticks([])\n",
"plt.tick_params(axis='x', labelsize=16)\n",
"plt.xlim(0, 1)\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.savefig('inner_product_squared_all.eps', format='eps', dpi=1000)"
],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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