{
"cells": [
{
"cell_type": "markdown",
"id": "d1719058-4f0f-4d23-82a6-e79ba6653be1",
"metadata": {},
"source": [
"# Distribution of maximum for 1-D prior example (RBF covariance)"
]
},
{
"cell_type": "markdown",
"id": "ea0336ee-2b35-4978-85d4-585bbe872030",
"metadata": {},
"source": [
"> Investigation into the distribution of the maximum for a 1-D toy example."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "90c1b7f9-ee23-4bb1-bf64-03271905688e",
"metadata": {
"nbsphinx": "hidden",
"tags": []
},
"outputs": [],
"source": [
"import warnings\n",
"warnings.simplefilter(action='ignore', category=FutureWarning)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "cdd0bb80-2bc6-4a5d-a8cd-b5e164404121",
"metadata": {},
"outputs": [],
"source": [
"from dolfin import *\n",
"import numpy as np\n",
"import numba\n",
"import ot\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import pandas as pd\n",
"# import required functions from oneDim\n",
"from statFEM_analysis.oneDim import mean_assembler, kernMat, cov_assembler, sample_gp\n",
"from scipy.stats import linregress\n",
"from scipy import integrate\n",
"from scipy.linalg import sqrtm\n",
"from tqdm import tqdm\n",
"import sympy; sympy.init_printing()\n",
"# code for displaying matrices nicely\n",
"def display_matrix(m):\n",
" display(sympy.Matrix(m))"
]
},
{
"cell_type": "markdown",
"id": "98375cee-63c6-45b6-a2cf-f40176df08d8",
"metadata": {},
"source": [
"Let's first import the `wass` function created in the sub-module `maxDist`."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a71254c3-f452-42ab-99ea-05d1d042ea3c",
"metadata": {},
"outputs": [],
"source": [
"from statFEM_analysis.maxDist import wass"
]
},
{
"cell_type": "markdown",
"id": "52e34362-0a2e-4bca-8eb4-33c81c50119d",
"metadata": {},
"source": [
"## Sampling from true maxiumum distribution in 1D"
]
},
{
"cell_type": "markdown",
"id": "29e3b2ec-0bc9-46d2-9275-bc080999b7ba",
"metadata": {},
"source": [
"We will be interested in the toy example introduced in oneDim, however we will use different values for the parameters in the distribution of $f$. To obtain a sample for the maximum from the true prior we must first sample trajectories from the true prior."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "34bbf8ef-8305-4d7c-8a69-439dd6ad9ed9",
"metadata": {},
"outputs": [],
"source": [
"# set up true mean\n",
"@numba.jit\n",
"def m_u(x):\n",
" return 0.5*x*(1-x)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "a2947c89-3411-4c1a-9964-2a27a2669da8",
"metadata": {},
"outputs": [],
"source": [
"# set up kernel functions for forcing f\n",
"l_f = 0.01\n",
"σ_f = 0.1\n",
"\n",
"@numba.jit\n",
"def c_f(x,y):\n",
" return (σ_f**2)*np.exp(-(x-y)**2/(2*(l_f**2)))\n",
"\n",
"# translation invariant form of c_f\n",
"@numba.jit\n",
"def k_f(x):\n",
" return (σ_f**2)*np.exp(-(x**2)/(2*(l_f**2)))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "7a66c962-f5fb-4169-aad7-91838e8c0155",
"metadata": {},
"outputs": [],
"source": [
"# set up true cov function for solution\n",
"# compute inner integral over t\n",
"def η(w,y):\n",
" I_1 = integrate.quad(lambda t: t*c_f(w,t),0.0,y)[0]\n",
" I_2 = integrate.quad(lambda t: (1-t)*c_f(w,t),y,1.0)[0]\n",
" return (1-y)*I_1 + y*I_2\n",
"\n",
"# use this function eta and compute the outer integral over w\n",
"def c_u(x,y):\n",
" I_1 = integrate.quad(lambda w: (1-w)*η(w,y),x,1.0)[0]\n",
" I_2 = integrate.quad(lambda w: w*η(w,y),0.0,x)[0]\n",
" return x*I_1 + (1-x)*I_2"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a5eb5c68-8c33-4478-a6e0-bd70f5d0f090",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1.24 s, sys: 102 ms, total: 1.34 s\n",
"Wall time: 21.8 s\n"
]
}
],
"source": [
"%%time\n",
"n_sim = 1000\n",
"grid = np.linspace(0,1,100)\n",
"np.random.seed(235)\n",
"u_sim = sample_gp(n_sim, m_u, c_u, grid, par = True, trans = False, tol = 1e-8)"
]
},
{
"cell_type": "markdown",
"id": "372e2b7b-30d2-48aa-ab02-d6ff44315bbe",
"metadata": {},
"source": [
"We now plot the sampled trajectories from the true prior."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c9c84977-6233-4e9b-8744-0c93c20e4511",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.rcParams['figure.figsize'] = (10,6)\n",
"plt.plot(grid,u_sim)\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$u$')\n",
"plt.title('Trajectories from the true prior')\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ad6f5eb1-4908-4e27-bf29-4ad0a3b67d7a",
"metadata": {},
"source": [
"
\n",
"\n",
"Note:\n",
"\n",
"The maximum is __not__ always located at $x=0.5$. We will demonstrate this by plotting the $\\operatorname{argmax}$ for each simulated curve below.\n",
" \n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "c361eede-6e7d-418b-9c2e-9fbb28635dfb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.arange(1,n_sim + 1),grid[u_sim.argmax(axis=0)])\n",
"plt.hlines(0.5,1,n_sim,colors='red',linestyles='dashed')\n",
"plt.grid()\n",
"plt.xlabel('Sample number')\n",
"plt.ylabel('$\\operatorname{argmax}$')\n",
"plt.title('Location of $\\operatorname{argmax}$ for each simulated curve')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4cda9d4f-99a2-4d60-b9ee-90141c3d887e",
"metadata": {},
"source": [
"Let's now get the maximum value for each simulated curve and store this in a variable `max_true` for future use. We plot the histogram for these maximum values."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "56a070ce-c93f-444a-b8c4-fcd502c5247f",
"metadata": {},
"outputs": [],
"source": [
"max_true = u_sim.max(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "e39ed763-d791-464c-8674-48b600e0ce08",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.displot(max_true,kde=True,stat=\"density\")\n",
"plt.xlabel('$\\max$')\n",
"plt.title('Histogram of maximum for true prior')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e3a911a2-283e-4deb-b500-53710bd4ffc4",
"metadata": {},
"source": [
"## Sampling from statFEM prior maxiumum distribution in 1D"
]
},
{
"cell_type": "markdown",
"id": "df8d3ec8-61f0-46d2-ac77-51dcb3e4806f",
"metadata": {},
"source": [
"We now create a function to utilise FEniCS to draw trajectories from the statFEM prior."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d97ba9c0-7a41-496f-81e2-cf6654c8f36f",
"metadata": {},
"outputs": [],
"source": [
"# create statFEM sampler function\n",
"def statFEM_sampler(n_sim, grid, h, f_bar, k_f, par = False, trans = True, tol=1e-9):\n",
" # get length of grid\n",
" d = len(grid)\n",
" \n",
" # get size of FE mesh\n",
" J = int(np.round(1/h))\n",
"\n",
" # get statFEM mean function\n",
" μ_func = mean_assembler(h, f_bar)\n",
" \n",
" # evaluate this on the grid\n",
" μ = np.array([μ_func(x) for x in grid]).reshape(d,1)\n",
" \n",
" # get statFEM cov mat on grid\n",
" Σ = cov_assembler(J, k_f, grid, parallel=par, translation_inv=trans)\n",
" \n",
" # construct the cholesky decomposition Σ = GG^T\n",
" # we add a small diagonal perturbation to Σ to ensure it\n",
" # strictly positive definite\n",
" G = np.linalg.cholesky(Σ + tol * np.eye(d))\n",
"\n",
" # draw iid standard normal random vectors\n",
" Z = np.random.normal(size=(d,n_sim))\n",
"\n",
" # construct samples from GP(m,k)\n",
" Y = G@Z + np.tile(μ,n_sim)\n",
"\n",
" # return the sampled trajectories\n",
" return Y"
]
},
{
"cell_type": "markdown",
"id": "368bfe29-b4d1-489c-9f8b-2f91942ed2d2",
"metadata": {},
"source": [
"Let's test this function out by using it to obtain samples from the statFEM prior for a particular value of $h$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "aa92e51f-3a08-4191-aa6e-60d7ab18aaf3",
"metadata": {},
"outputs": [],
"source": [
"h = 0.1\n",
"f_bar = Constant(1.0)\n",
"np.random.seed(2123)\n",
"u_sim_statFEM = statFEM_sampler(n_sim, grid, h, f_bar, k_f)"
]
},
{
"cell_type": "markdown",
"id": "cad9d667-e298-4b14-a768-ee2ccea2339c",
"metadata": {},
"source": [
"Let's plot the above trajectories."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "8305bc05-4196-4de7-8957-9b2f28215f88",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.rcParams['figure.figsize'] = (10,6)\n",
"plt.plot(grid,u_sim_statFEM)\n",
"plt.grid()\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$u$')\n",
"plt.title('Trajectories from statFEM prior with $h = $ %0.1f' % h)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "3390d045-7447-404e-addb-4e901edb5f26",
"metadata": {},
"source": [
"Let's now get the maximum value for each simulated curve and store this in a variable `max_statFEM` for future use. We then plot the histograms for these maximum values together with those from the true prior."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "bf664dbf-c53c-466e-84fc-1422077745da",
"metadata": {},
"outputs": [],
"source": [
"max_statFEM = u_sim_statFEM.max(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "4336370a-6a6d-42fe-a7d6-83e4b4263cc8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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TgAIrgMuBScC9QBWwBLhEVa1tyOxmu7eaiaUFnH7lN3Z7fumVZ+32eP60clbVtrKypjWV4RljMkjSmhZFZArwBWChqh4AeIELgRuAn6nqXKAJuCJZMZjs1NodpLugiul9eioOprokn6kVAd7c0owiKYjOGJNpkn2PzAcERMQHFAK1wInAg+7224FzkhyDyTKvrW8E8TCtMhDX/vOnldPeE6KteHqSIzPGZKKkJTJV3Qb8BNiMk8BacJoSm1U15O62FZgS63gRuVJE3hCRN+rr65MVpslAL61rQCIhJpYWxLX/rHFFlAX8NFbsm+TIjDGZKJlNixXA2cAsYDJQBJwa7/GqeouqLlTVhdXV1UmK0mSil9btJNBVj88b38fTI8LBU8voKhzP8q3Wg9GYsSaZTYsnAxtUtV5Vg8BfgKOAcrepEWAqsC2JMZgs09jRyzvb2yjq3D6i4/abXIon3MufXtyYnMCMMRkrmYlsM3C4iBSKiAAnAauAp4GPuPt8AvhbEmMwWeatLU6NKtC1Y0TH5fu8lLWs5Z/La6hr7U5GaMaYDJXMe2Sv4nTqWIrT9d4D3AJ8HfiyiKzF6YL/h2TFYLLPm1ua8QgEuhtGfGxl8zuEIsrdr2xKQmTGmEyV1F6LqvptVd1HVQ9Q1UtUtUdV16vqIlWdq6rnq6rN+mp2eXNLM3tNKMGzqz9Q/PKC7Zyw93jueX0LwXAkCdEZYzKRzexhMoaq8tbWZk7ZbyLLR3mOSw6fweW3vc5jK+s4/SBneqtLP3kl9U0tA/atrijjjj/esgcRG2MygSUykzE2NXTS3Blk/vTyUSeyY/eqZmpFgLte2bQrkdU3tbD4qusH7PvYzdfuQbTGmExhkwabjPGW23X+4Knloz6H1yNcsHAaL69voKa5K1GhGWMymNXITFr1bfarq16IlO/Flz9/JSv7TA48UmfNn8xPH3+Pf7xVw2eOm5O4YI0xGclqZCatos1+i6+6nsI5h1JdVsQpV32X3uDIO3tEzagqYv60cv7+Vk0CIzXGZCpLZCYjqCo723uoLslPyPnOOngyK2taWbujPSHnM8ZkLktkJiN09ITpDkYYV5yYRHbKARMBeObdkQ2sNsZkH0tkJiPUtzvDCasTlMimlAeYXV3E82t2JuR8xpjMZYnMZISdbiIbV5yXsHMeO6+aVzc0EBH7mBuTy+wv3GSEnW09lBb4yPd7E3bOY+aNozsYoSswPmHnNMZkHktkJiPsbO9N2P2xqMNnV+H3Ch2FkxN6XmNMZrFEZtIuHFGau3qpSmCzIkBRvo/9J5fRFRiX0PMaYzKLJTKTds2dvUQUKosSm8gA5k8rp6ugiohqws9tjMkMlshM2jV29ALJSWQHTS1DPf5dZRhjco8lMpN20SRTUZj4RHbwNGfeRlts05jcZYnMpF1jRy+lBT783sR/HGdVFeEJ91LXasveGZOrLJGZtGvo7E1KsyKAxyMUdDdYjcyYHGaJzKSVIjR3BKkqSmzX+74C3Q3sbO8hHLEOH8bkIktkJq2C/mLCqkmrkQHk9zYRUad3pDEm91giM2nVk1cKQEWRP2ll5PU4651Zz0VjcpMlMpNWvW4iKw8ks0ZmicyYXGaJzKRV0F9Cvs9DgT95H0WPhikL2FgyY3KVJTKTVr15pZQF/IhIUsupLMqjwRKZMTnJEplJq15/CeWFybs/FlVZlEdTZy8R67loTM6xRGbSpjcUIegvSur9sajKojwiCi1dwaSXZYxJLUtkJm22NHWCeFJSI6tyu/db86IxuccSmUmbTQ0dAClJZNEymrsskRmTayyRmbTZsLMTgLJA8hNZvs9LwO+lpdOaFo3JNZbITNpsaujAE+4l4PempLyygJ9mu0dmTM7xpTsAM3Zt2NlBXrA1YV3vVyxfzmnnXjDg+bdXrmQxUFbop6a5KyFlGWMyhyUykzabGjrJ621L2PmCEWXxVdcPeH7plWcBTo3sve1thCIRfB5rjDAmV9hfs0mL3lCErU2d+BOYyIZTHvCjQFtXKGVlGmOSzxKZSYutTZ1EFPKCrSkrM9qpxO6TGZNbLJGZtNjU4PRYTGTT4nCiicwGRRuTWyyRmbTYsNMZQ5YXTF0iK8zz4veKdcE3JsdYIjNpsamhg5J8H95wd8rKFBG3C74NijYml1giM2mxoaGTGeMKSe6c9wOVFvhp67bOHsbkEut+b1Li0k9eSX1Ty67Ha2edQ6C7gSZ3jFeqlBb42dLUiarNgm9MrrBEZlKivqll1xivSER555m17L3XDJ77d2prRyUBH8Gw0hOKpLRcY0zyWNOiSbn2nhCqTu0o1UoKnGs3a140JndYIjMpF00i0aSSSiVu8mzttp6LxuQKS2Qm5aJJpDQFs973V2o1MmNyjiUyk3LRRFaSn/oaWcDvxecRq5EZk0MskZmUa+0KUZjnxedN/cdPRCgp8Nl8i8bkEEtkJuXauoNp6egRVVLgp63HamTG5ApLZCblWrtDu+5VpUNpgY9Wq5EZkzMskZmUUlXau0OUpKGjR1RJgZ+uYJiIpGZlamNMclkiMynV0RsmrJrWGlm023/QV5S2GIwxiWOJzKRUq7uESkka75FF788F/ZbIjMkFlshMSkXHb2VEjcxfnLYYjDGJY4nMpFQ6B0NHFef7ELEamTG5whKZSanW7iABvxd/GsaQRXk8QnG+j5DdIzMmJ1giMynV1h1KyxyL/ZUU+KxGZkyOsERmUqq1K72DoaNKC/x2j8yYHGGJzKSMqjo1skCG1Mh8hYTCti6ZMdnOEplJma5gmFBEM6JGVlLgB/FQ19aT7lCMMXvIEplJmdYM6HofFY1hW1NXmiMxxuwpS2QmZdoyYDB0VDSGmmZLZMZkO0tkJmV21cgy5B4ZwDZLZMZkPUtkJmVau4Pk+zzk+9I/Wa/f68Eb6mKrNS0ak/UskZmUyZQxZFH+UIc1LRqTA5KayESkXEQeFJF3RGS1iBwhIpUi8riIrHH/r0hmDCZztHUHM+L+WJQ/2GFNi8bkgGTXyH4BPKqq+wAHA6uBa4AnVXUe8KT72IwB7T0hivMzqEYWdGpkqpruUIwxeyBpiUxEyoBjgT8AqGqvqjYDZwO3u7vdDpyTrBhM5oiIl+5ghOIMa1rs7A3T3BlMdyjGmD2QzBrZLKAe+JOILBOR34tIETBBVWvdfbYDE2IdLCJXisgbIvJGfX19EsM0qRDyFQJQkkE1Ml+wA7Cei8Zku2QmMh9wCPAbVV0AdNCvGVGdNp2Y7TqqeouqLlTVhdXV1UkM06RC0E1kmdW02A5YIjMm2yUzkW0Ftqrqq+7jB3ESW52ITAJw/9+RxBhMhojONJ9pTYtgs3sYk+2SlshUdTuwRUT2dp86CVgF/B34hPvcJ4C/JSsGkzkysWnRG+6hwO+xLvjGZLlkf6tcDdwtInnAeuBynOR5v4hcAWwCPprkGEwGCPqLKPB78KVxQc3+BJhcHrCmRWOyXFITmaq+CSyMsemkZJZrMk/IV0hJfuaMIYuaYonMmKyXOZfHJqcFfUUZdX8sampFwJoWjclylshMSoR8hRnVYzFqclmAne29dAfD6Q7FGDNKlshM0nUHw4R9BRlZI5tSEQBsORdjspklMpN0tS3dQGb1WIyaXO4kMrtPZkz2skRmkq62xUkSmdi0OCWayGwsmTFZyxKZSbraZqdGlolNixPLCvCINS0ak80skZmk296auU2Lfq+HCaUFbLVEZkzWskRmkq6muQtvqDujBkP3NbncuuAbk80y85vF5JTtLd34Qp3pDmNQNijamOxmicwkXW1L964JejPR5PIA21u6CUdsgU1jspElMpN0tS1d+IIZXCOrCBAMK/VtPekOxRgzCpbITFJ1B8M0dQYzukY2dddYssxNtsaYwVkiM0kVHQydyffIprqze2xptPtkxmSjzOsPbXJKdDC0P5h5NbIVy5dz2rkXEBEv7HUR3/v1n/hdwwqqK8q444+3pDs8Y0ycLJGZpIoOhvZnYI0sGFEWX3U9AFueX8/4A4/jg/t9lMduvjbNkRljRsKaFk1SRQdDZ3LTIkBZwE9rVzDdYRhjRsESmUmq2pYuKgr9eDSzl0kpDfhp6bZEZkw2skRmkqq2uZtJZYF0hzGssgI/7d0hG0tmTBayRGaSqralm0llBekOY1ilAR8KtFmtzJisY4nMJFVtSxcTsyCRlQX8ALR2h9IciTFmpCyRmaSJDoaOLl6ZyUoL3ERmHT6MyTqWyEzSRAdDTyzN/BpZcYEPj0CLJTJjso4lMpM00cHQk8ozP5F5RCgpsC74xmQjS2QmaaKDobOh1yI4HT6sC74x2ccSmUma6GDobOi1CE4X/NYu6+xhTLaxRGaSJjoYusDvTXcocSkN+OkKhomIzdxmTDaJK5GJyF9E5HQRscRn4pYtg6Gjol3we/3FaY7EGDMS8Samm4GPA2tE5IcisncSYzI5oralOyvGkEVFu+AHLZEZk1XiSmSq+oSqXgQcAmwEnhCRl0TkchHxJzNAk71qWrqYnAU9FqNKA06ToiUyY7JL3E2FIlIFXAZ8ClgG/AInsT2elMhMVuvsDdGcJYOhowJ+L36v0JtXku5QjDEjENddbRF5GNgbuBM4U1Vr3U33icgbyQrOZK8at+v9lCxKZCJCacBPj9XIjMkq8XbPulVVH+n7hIjkq2qPqi5MQlwmy9U0O4Ohs6lGBk4X/G2WyIzJKvE2LX4vxnMvJzIQk1uiiSxbxpBFlQb89PqLUbXlXIzJFkPWyERkIjAFCIjIAkDcTaVAYZJjM1msprkLj8CELJhnsa+ygB/1+NnZ3kt1SX66wzHGxGG4psVTcDp4TAVu7PN8G/DNJMVkckBNSzcTSgvwe7Nr6GF0LNnmxk5LZMZkiSETmareDtwuIh9W1YdSFJPJATXNXVl3fwz6JrIODp1RkeZojDHxGK5p8WJVvQuYKSJf7r9dVW+McZgx1DR3ceDU8nSHMWKlBc6fxOaGrjRHYoyJ13DtPkXu/8VASYx/xgwQiSg1Ld1MzrKOHgA+rwdfsIPNjZ3pDsUYE6fhmhZ/5/7/ndSEY3JBQ0cvvaFIVjYtAuQF29jc2JHuMMwYJl7fViLhKQk7oce7TcOhqYOW50x48aT7cCIQBurdx4tUtTdhsSRBvAOif4TTBb8LeBQ4CPiS2+xozG6iC2pmayLzB9utRmbSKxKeMuPr/0xYBWLTDWd8e6jtqtoAzAcQkeuAdlX9Sd99REQAUdVIouJKlHi7lC1W1VbgDJy5FucC/y9ZQZns9v5g6OxrWgTwB9uoa+2hOxhOdyjGpJWIzBWRVSJyN7ASmCYizX22Xygiv3d/nuCulPKGiLwmIoenKs54E1m05nY68ICqtiQpHpMDtrnTU03OoiVc+srrbQdgi9XKjAHYB/iZqu4HbBtiv18CP3Jne/oo8PtUBAfxT1H1TxF5B6dp8XMiUg10Jy8sk60u/eSVvO2bh5TP42MXX7JrBP3bK1eyOE0xdbS38/D9A1vBO9rbY+6fF2wDnLFk8yZYnyYz5q1T1Xjm1D0Z2NtpgQSgQkQCqpr0LsBxJTJVvca9T9aiqmER6QDOTm5oJhvVN7VQefQitKOHU666ftfzS688K20xqSrnLpo54PklD8eehsrvJrJNDVYjMwbo2/MpwvszPAH0vX8gpKljyEimXdgHuEBELgU+Amm7wDYZrq0nSElB9i5T5w33UJTntQ4fxvTjdvRoEpF5IuIBzu2z+Qng89EHIjI/VXHF22vxTmAO8CZOt0wABe5IUlwmi7V1hxg3LnundxJgWmWh3SMz6ePxbhuup+FIz5ewc8HXgf8AO4AlQPSP/fPAb0Tkcpzc8jR9ElsyxXuPbCGwn9qU4GYYEfHQ2RumJD/ej1ZmmlFVyLp6G0tm0mOoMV9JL1v1uj4/r8Xtlt/nufuA+2IcV4/TWpdy8X7bvI0zSK52uB3N2BbyOYsiJKtpcbCOG9FtiTK9spBn3q0nElE8Hhn+AGNM2sSbyMYBq0TkNaAn+qSqpu8OvslIQZ8zq1lJQXJqZIN13IDBO2+MxvSqInpCEXa09TAxC6faMmYsiffb5rpkBmFyR9DvJLLiJCWyVJle6dQsNzd2WiIzJq7QNSwAACAASURBVMPF2/3+WRGZAcxT1SdEpBDwJjc0k41C0RpZGu6RhcKhmM2OoXBoxOfqm8gWzarc49iMMckTb6/FTwNXApU4vRenAL8FTkpeaCYbBf3FBPxefGlZUDN2s+OrD468yXFKeQCPwOYG6/BhTKaL97L588Ai4FUAVV0jIuOTFpXJWr3+4l2LU8ZjpLNupEqez8OksoCNJTMmC8SbyHpUtTc69YiI+HDGkRmzm6C/mLLC+BPZSGfdSKXplYVsskRm0sDvla2hCAlbxsXnYVswrCPq0i8iXwRuUdUh/wj67yciG4E23h9zfBVQA6wG3u1z6I2qeoe7/xZVPabPOd8EfKp6QDyxxpvInhWRbwIBEfmgG9g/4jzWjBG9oQhBfxFlWTyrR18zqgp5YnVdusMwY1AowhT9dmnClnGR77SOZnD1F4G7gOGu5mLtd4Kq7txVvshMnDkbB5vto0REpqnqFhHZd6SBxnsj4xqcRdZWAJ8BHgH+Z6SFmdxW09wF4hlR0+KeEo2QH+nEF0n89G7TKgvZ2d5LR8/IO4sYk01EpEhE/iUib4nI2yLybWAy8LSIPO3u8xt3iZaVIvId97kv9N9vlO4HLnB//hhwz0gOjrfXYkRE/gr81R29bcwA0ftJyU5k43u3sHfXMqb1vMe4YC1enHX+PnwFNDbdy1tFR7Ejb9oelzOj6v2ei/tOKt3j8xmTwU4FalT1dAARKQMuZ/ea1bdUtVFEvMCTInKQqv5SRL7cbz9wElsY57bUB9zn5rhNhlFXq+rz7s8PAX8CfgKcCVwEXBJv8EMmMndF0G8D/4Vbe3ODu0lVvxtvIWZsSGYiEw0zu/F5/nNuJ0fX30gYD9vy57C0+Hg6vCX4NETNu//m7JI3OaDzVVYHDuWp8o/Q6xn9GLC+XfAtkZkctwL4qYjcAPxTVZ/vsxxL1EdF5EqcvDEJ2A9YPsj5+ic2GLppsQFnMuILce6ljejm9HA1si8BRwGHqeoGABGZjTMx5JdU9WcjKczkts2NnUgkTFF+AocYqjKr6QWO3vQrxnWuZ1OJ8EzZ2awqXESPp3C3Xa959AluPP7bLGx7isPan2Ji7yYeHnfliItcsXw5p517AWFPHsy7kGt/+jt+3rSK6ooy7vjjLYl6ZcZkDFV9T0QOAT4EfE9Enuy7XURmAV/FyQVNInIbuy/hkgj3Ab8GLhvpgcPdI7sE+Fg0iQGo6nrgYuDSkRZmctvmhk78wTZiXMmNysS2FZz/9mc4Z/WX8UZC/Guv73PgnYUsKz5+QBKL6vUEeKnsdB4cdxUF2sX59b9mTtnIekAGI8riq67ntM9eS77Pw8QFJ7H4quupb7KF0U1uEpHJQKeq3gX8GDgEp+dhdGXZUpx1yVpEZAJwWp/D++63Jx4GfoQzs/6IDFcj88eoHqKq9SISV/uR2576BrBNVc9wM/u9QBXOEgCXpGMhNjN6V11xCe1NA2+VLpl+Ib3NAz4uI1YRrOPu07o4Z/kn6fBX8uTsr/P2hHOIeHyE9f/iOse2/Dk8OO4qPrLzZv52dpDHI52DJr+hlAX8tHQHR3ycMXvC52HbKHsaDnq+YXY5EPixiESAIPA54AjgURGpUdUTRGQZ8A6wBXixz7G39N1viDL63yP7o6r+MvpAVduAG4ARXwwPl8iGSjDxJp//xmnzjN5kuAH4mareKyK/Ba4AfhPnuUwGaG+q546rj9vtOVU46KlKIptXjfq8xaEmjmj7D/t1vkb7NOWlaVeydMpFBL0jT0AAO/2T+XvlJzk3eBOnNd7JX6s+DTKyGUfKAn7q23qG39GYBBrpmK89par/YWBN6A3gpj77XDbIsTf1229mjH02AoFBjh9s/7jGkMHwTYsHi0hrjH9tOBl8SCIyFTgd+L37WIATgQfdXW4Hzok3WJO5moNe2kJe6GgY8bEloSaOa36Yy+t+wD6db7Cs6FgOvKOIV6d/etRJLKomfzZfedbHrJ53WNDx/PAH9FMa8NPaHSRiS/EZk7GGrJGp6p7etf858DXebz+tAppVNTowZyskbvS6SazBmhBXr1wB7F4j29SZB4C2x5nINMKktre59eRuLqj7HgKsKlzIKyWn0uarYGf3kj2M/n23rPDwpQ/tx9Et/2Jj/j40+SfEfWxZwE9Eob3bxpIZk6mSNkW5iJwB7FDVJSJy/CiOvxJnomKmT5+e4OhMPGI1IQIsuGJgktnc5SSyIWtkGmFy23Lm7XySeQ1PUdK7g/bZ8FbRsSwtPo42X7JmmRceL7+AT9T9kBNbHuKhqs9BnG3w0aEELV12n8yYTJXMKcqPAs5y59G6F6dJ8RdAuTtXI8BUiH0TUlVvUdWFqrqwuro6iWGaRNgSTWTtu3f2EA0zpWUJP/hAC59+/XQuWPFpDtr+F3YU78Oj877DvNuKeLb83CQmMUent5QXSz/E9J417NX15vAHuHYlMuvwYUzGSlqNTFW/AXwDwK2RfVVVLxKRB4CP4CS3TwB/S1YMJnU2d+ZTnRdkezgIGmFqy1L2aniCuQ1PUxRspGsubC39AGuqTmJDxVH0+ooBaO39ccpiXFF0JAd0vsLRrf9gbWDYW7yAs66aR6Cl0xKZMZkqHcv4fh24V0S+BywD/pCGGEyCberMY3qgm7P26+TypR+mvHsrQU8BGyqOZs24E/mv//0FX7j5R2mNUcXDi6VncF7D7zig45W4jvF4hJICP61dQVtJ1pgMlZJEpqrPAM+4P6/HWdvM5IpImC1tyiJdwbWHdbAtbx4vTf8M6yqPJ+R1Bv93hm4a5iSpsSl/b7bmzeYDbY8T8MXXEzE6lszWiTYmM6VjGV+TSzob6V16NzWhIqYV9vLBv1dw/4G38m71qbuSWEYR4aXSD1EcaeXKA+NrLiwL+K1p0ZgMZonMjF7zFlh2O9u6/CgeZsyYzTtN6WitHplt+XPYmL8PXz6kl7zQ8CtRlwX8dIcihD25sc6aMbkm8791TGZq2gQr7oeCMjZN/TisgGmFvbS1t/Pw/XcN2L2jffiEkUovlZ7Gx3ve4eDaB3h92uVD7lsacP5Mev2JmE7OGJNolsjMiO1TGYGVD0GgAuZ/nA01zt2jWYW9oBHOXTRzwDFLHs6smTHq8qbz2CYvR/nvZemUjxP25A+6b3nAGVoQ9BenKjxjzAhYIjMj09vJjSeEwFcKB10A/kLWd+RT4gszLm/w2S9C4VDMmloonL4ZM36+1M/iGY3su+MR3p547qD7RWtkwTyrkRmTiSyRmfipwjt/p7IA2P88yHe+2Nd35DO7qGeYyTI0Zk3t1QfTV1N7dpuXuqJ9OLTmbt6ecPagEwrn+7wE/F5rWjQmQ1lnDxO/mqXQtJGfvO6Fkom7nl7Xkc+cou40BjZawhtTLqGyaxOzG4eeULg04LOmRWMylCUyE5+uZlj/NFTO5sH33v/YtIc8bO/JY05Rdi51smbcibTkT2bhtjuH3K8s4LcamTEZyhKZGZ4qrH3caXrb6zTg/TbEDR1OJ4lsTWQqPpZO/hhT2t5iYtuKQfcrC/gJ+osIhiMpjM4YEw+7R2aG17AGGtfBnBN33ReLWu8mstkJTmSp7ByycsJZHLH5dxxScw+P7B17DsaygB/EQ21zN9Or9myNNGNMYlkiM0OLhJ0mxcJxMGXhgM3rOvPxoMwojHfB8HilrnNI0FvI2xPO4ZCaeyieuT3mPtFZ8Dc1dlgiMybDWNOiGVrdCuhqglnHxezVt64jn2mBXvI9mTVObKTenPRRQJlf+0DM7dFEtrmxM4VRGWPiYTUyMyi/hGHjC1A6Barmxtwn2vU+G/VvvpxdMYfDttyHdg+ciqoo34dEwmxusERmTKaxRGYG9cFx26G3HfY9K+aKyhF1OnscWZlZ00/Fb/fmyx09p1Gy85d8bO+Be3pE8AfbrUZmTAaypkUTW1czZ1Rvg8rZUD495i413X66I56s7bHYX23eTLb7p3PVwc5UW/35g22WyIzJQJbITGyv/o5iXxhmHjvoLsnqsZg2IiwtPpa9K5SZzS8P2JwXbGdzQyeq2X0/0JhcY4nMDNTTDq/+hqWtFbvN4NHfuiwfQxbLmsDB1LQLC2ruHbDNH2yjrSdEs61NZkxGsXtkZqAlf4KuJv6x4wAOibF5c3OI0657mO2zPoRnXBWX/N8Du4ZId4eyu7YSER+/W+HnO8WvUNW5jobCObu25QWde4GbGjupKMpLV4jGmH6sRmZ2F+yGl34Fs45lXWfsKZnCHj+LL/4sxbMOorrIyykXf5bF7j8deubgrPCnlX5CnvwBtTJ/bxtgXfCNyTSWyMzu3rwb2rfDMV8ZdtemXh+V/vQtw5IsDd3CquoPsW/9vykINu96Ploj22KJzJiMYonMvC8cghd/AVMOdQZAD6E3IrSHvZQPsQZZNls2+UJ8kR4O3P7wruc8GmJccT6bGjrSGJkxpj9LZOZ9Kx+G5k1ObWyYJsLmoBeACn84FZGlXGPhbDaWH8787Q/gibzfuWNGVaE1LRqTYSyRGYcqvPAzqN7HneF+aI29Tj+hyhytkYFTKyvurWdew5O7npteWWizexiTYSyRGceax2HHSjjqv8Ez/MeiKehFUMpytEYGsLH8CBoDMzik5s9OosdJZLWt3fSEcvd1G5NtLJEZxws/g9KpcMBH4tq9qddHqS+ML/s7KQ5OPCybdCET21czuW054CQyVdja1JXm4IwxUTaOzMDmV2HzS3DqD8EX3/iopqCXirzcr5WsGn86R23+DQtq7uEry1fzy5/eANNP5bIvXktxZ82u/aoryrjjj7ekMVJjxi5LZAZe/DkEKuCQS+M8QGgO+pgWyP17RSFvgBUTzuHQbXcxIVDFyR//HH94YQNzTv4YB08t37XfYzdfm8YojRnbLJGNdTtWw7uP8JftU/nrhR/ebdPqlSuAgd3wpbiSkErO1sj6L+/yotfHvROUS+Y0E8nz4vUIrV02TZUxmcIS2Vj34i/oiXg477wPc54/sNumBVcsiXmIt8yZf7EiBwdDOwauTr2ucT6X7beMuyJdlBX4abFEZkzGsM4eY1nzFljxAE83TIB+SWwonl2JLDdrZLEsLT6W8nzYb8c/KQ34LJEZk0EskY1lL/8agEd3ThrRYd7ySeR5IhR6B67Zlau2583kte0eDqn5M+UBH61dIVvOxZgMYYlsrOpogKW3w0EX0BjMH9GhnrKJVPjDw03+kXN+uiSP8u5tzA2vozccoTs4dhK5MZnMEtlY9epvIdjpDIAeIW/ZpJycLHg4/9rgpb5wLke1/hvAmheNyRDW2SMHXXXFJbQ31Q94vriimpv/cCd0NTmJbN8zoXrvEZ27I+TBU1xJeV5bosLNGorw2rRPst/qmwFo7Q4ysawgzVEZYyyR5aD2pnruuHpgt/lLb3rW+eGV30BPKxx3zYjPvaHTaYYcSx09+lpTdSIHFd4OvdDS2ZvucIwxWNPi2NPV5CSyfc+CiQeM+PB17U4iy+XJgoei4uXtaRcxjha0eXO6wzHGYIls7NlVG/v6qA5f15mPRiI5PVnwcN6t/iCTvM0EW3fsmkzYGJM+lsjGkEJvaI9qYwDrO/KJtO/M7cmCh6HiI1BczvZwMbOaXkh3OMaMeXaPbAw5vXob9LSNujYGsK4jn0jzJmBi4gLLQlI+g5qWRg7dfAMbKo5m9coVXHreqQP229XBxhiTNJbIxoqeNhaP2w4Hnj/q2lhEYUNHPuGW7Yz1RFZSmEcED5G2OmY3Pkc42Dt0BxtjTNJY0+JYsekFvCic+K1Rn6K22093xEOkuTaBgWWnsoAfgJX+Azhq8814xO6VGZMulsjGgs4GqF3OU40ToGLmqE+zrsPpsejUyMa2aCJ7ruJcxnWu59xZPWmOyJixyxLZWLDhOfD6+Vvd1D06zXo3kUVarEZWlO/DK8Iazxzqivbhy/M7IDI2hyQYk26WyHJdaw3sfBemLqIt7N+jU63ryKfEF0a7WhMUXPbyiFAS8NHaHeKFGZ9nekkEat9Md1jGjEmWyHKZKqx/BvyFMPWwPT7d+o58ZhdZE1pUdF2yzeUf4KVaP2x6CcI224cxqWaJLJc1bYCWzTDjSPCNbIb7WNZ35jPHEtkupQF3gU0Rfri0yJmEeevr6Q7LmDHHut/nKo3A+qehoAwmLQDgreWxxzqtXrkCGNh1vK+OkIfa7jzmFDUkI9qsVBbw0xOK0B0Ms2ynH6rmwZbXYPICpxZsjEkJS2S5qm4ldNTDvmeDxwuAJxJ7rNOCK5YMe7roZMGzC61GFhXtudgaXc5l1nHwxh+cJsa5J6cxMmPGFktkOcgvYdj4HJRMgup9EnLONe5kwfOKx24iC4VDPHz/Xbse93oLofxAHn/qKdo72qFoHEw6CGqWwpRDIVCRxmiNGTsskeWgxeO2O1NR7XMmiVrGeU17AT5RZozpGply7qKZux71hIXfboS9Z0xkbcRdLXrGMVC3yhnysN/ZaYnSmLHGOnvkmo4Gzhy/DarmQvn0hJ12TUc+swp78NsnZpd8r1LgidAS8vZ5shimLYL61c7QB2NM0tnXUq55/icUeMIw6/iEnnZtewHzirsTes5cUOYP0xr07v7k1EVOZ4/1TwM2dZUxyWaJLJc0boDXbuXZxvHO/ZoE6Q4LmzrzmDuG748NpswfpqV/IvPlw8yjoWUL80ua0hOYMWOI3SPLJU9dD14/D9dN44QEnnZDZz4RhHlFViPrr9QXZm0of+C9yIkHw9Y3OLviPS477xQi7L7dlncxJnEskeWKbUvg7Yfg2K/RvOT5hJ7aeiwOrswfJoIgRZW7b/B4YfbxzOn6C7cdVg6T5++22ZZ3MSZxrGkxF6jC49+GwnFw1BcSfvq17QV4UGbZrB4DlPrCAHhLxg/cWDWPZTsENj1vU1cZk0RWI8twV11xCe1N9QOe361pasOzsPF5OO1HkF+S8BjWdOQzs7CXfI91XOiv3O/MeO8prR64UYSfv+Hl9vEdzowfM49OcXTGjA2WyDJce1P90CsPq8JT34fSKXDoZUmJYU17AXOtx2JMxb4IXhRP2YSY25fv9MC4vWHLq87UVXlFKY7QmNxnTYvZbu0TsPU1OParCZkYuL/eiLCxM9+63g/CI1DqD+MpjZ3IAGfqKg3DxhdSF5gxY4jVyLKZKjz9fWfg8/yLE376zc0hTv3xc4TmH8jD/3mRp+5eAUB3yJoY+yr3h9lZOgFojL1DYSVMmg81y2DqQiisSml8xuQ6q5Fls3cfcb4cj/s6+PISfvqwx88+p1wEwHEnHMfiiz/L4os/iyZo2qtcUe4P4SkdT2So/D7jaPD6nfXhjDEJlbREJiLTRORpEVklIitF5L/d5ytF5HERWeP+bzOrjorCszdA5Ww46MKkldLY6wOUCrdTgxmo3B9GfHnU9QyxAndeIUw7HBrWQMuW1AVnzBiQzBpZCPiKqu4HHA58XkT2A64BnlTVecCT7mMzQgcWt0DtW3D0l8GbvBbixqCPMl/Y5lgcQrnf6YK/oWOYWvHUwyCvGNbZ1FXGJFLSvp5UtVZVl7o/twGrgSnA2cDt7m63A+ckK4Zcdub4rU5PxYMuSGo5Db1eKvPCSS0j20W74G/sHKazjdcPM4+BthoOKxvkfpoxZsRScp0tIjOBBcCrwARVrXU3bQdidvcSkStF5A0ReaO+fuA4qjGtZQv7FLfBkV9Iyr2xXTxemnp9VOZZs+JQin0RNBxkU2ccv4uJB0JRNedP3AwhGyRtTCIkPZGJSDHwEPBFVW3tu01VlUHaWFT1FlVdqKoLq6tjDDYdyza/QmvIB4dcmtRiPOWTiSBU5wWTWk628whEWnfsWkV7SOKBWcczMb8bltyW9NiMGQuS2v1eRPw4SexuVf2L+3SdiExS1VoRmQTsSGYMOae9DhrXcfvbebx+4Xkxd1m9cgUwcBD1SHkrpwFQnW81suFEWnewsTPObvWVs1nZVsr+z/4QDr4ACsqSG5wxOS5piUxEBPgDsFpVb+yz6e/AJ4Afuv//LVkx5KQtr4E3j/tXK8//NnayWnDFkoQU5a2ajk90V2cGM7hwax2bOg8mok4NbUgi3Ld9Bt8tWQEv/gJO+t+UxGhMrkpm0+JRwCXAiSLypvvvQzgJ7IMisgY42X1s4tHT5qw8PPEg2oPJH8vlrZpOVV5o+C9mQ6Sljp6Ih+3dQ3TB72NjVzEceD68/Gto2Zbk6IzJbcnstfiCqoqqHqSq891/j6hqg6qepKrzVPVkVbXuW/HatsSZzWPKwqQXpeo0LVbn2/2xeERa6wDYGE+Hj6gTrwWNwDM/SFJUxowNNjooW4R7oXYZjNsLAuVJL66224+noJhx1mMxLuFW51bvsF3w+6qYAYuuhGV3Q93KJEVmTO6zRJYttq+AUA9MXZSS4la2BQDr6BEvbW8kzxMZWSIDOOYrUFDqrCdnjBkVS2TZQCOw9XUomQxlU1JS5FstATQStq73cVOmB3pH1rQIzoTCx3wV1j5u8zAaM0qWyLJBwzrobnamOEqRN1sKCTdutampRmBmYc/Ia2TgNC+WTYfH/xcikcQHZkyOs6+pbFCz1Jmjb9xeKSkuovBWSyHh+vUpKS9XzCrqZVNn3tCz4MfiL4CTrnXmznz7oaTEZkwus0SW4SbkdUHTBmc9K483JWWu78inLeQlvMMS2UjMKuyhJ+JhW5xd8HdzwEdg4kHw5HchaIuYGjMSlsgy3ElVdc60RpPmp6zMt1qcjh4hq5GNyFx3Fe217QUjP9jjgcXXQ8tmeP3WBEdmTG6zFaIzWW8Hx1TsgHF7Q35xyop9s6WQYm+Y5pba4Xc2u8wt6gFgXUc+J1S3DbnvW8tXcOl5pw54/mvzxnPAcz+G+Rc5HUGMMcOyRJbJVjxAkS8Mkw9JabGvNxUxv7yTrWprZo1EZV6YqrwQa+KokXkivdxx9cApxr55awc/CKyAF26Exd9LRpjG5BxrWsxUqvDa79ncVQhlU1NWbFOvl3faAxxR2Z6yMnPJnKJu1naMoueia2t3kVMbe/V30LQpgZEZk7sskWWqLa9C3QqeaJgIkrrJDl9tKgLg8IqOlJWZS+YW9bC2PZ89qsye8E0QLzxlNTJj4mGJLFO9divkl/FS07iUFvtKYzEBb4QDy7pSWm6umFfcTUvIR33vHrTal02BI66CFfdDzZuJC86YHGWJLBO11cGqv8H8j9OrqelyH/VKYxELyzvI89j9sdGIdvhY2z765kUAjvpvKKyCx69lz6p3xuQ+S2SZaOntEAnCYZ9KabE7e5z7Yx+wZsVRm1vsJrKOUXTB76ugDI77Omx4DtY+kYDIjMldlsgyTTgEb/wJ5pwI4+amtOhndpYCcPwwXcfN4CbmByn1hVjdtoeJDODQy6Fytjt1lS1uasxgrPt9pnn3X9BWA6f/NOVFP11fwvj8IPuX2P2x0RKBfUu6R53I+o8vO6zMx9UzVnHHF0/k0l8+m6gwjckplsgyzWu3OhPI7nVKSosNRuC5hhJOn9Ccyk6SOWnfkm7u21ZJeBS3tgaML1OFZXdyRu8q6O2EvMLEBWpMjrBElknqVsHG5+Hk76RsXsWo15uKaAt5h52Rwgxvv5IuusIeNo90SZdYRGD2CVS23c0DVy/iH/UDxxQWV1Rz8x/u3POyjMlSlsgyyeu3gq8ADrk05UX/Z0cZ+Z4IR1fZQOg9tW+JM+fiandx0j1WPo2nNwvnz6rj/PPOHVAru/Qma3I0Y5t19sgUXc3w1r3OLOgpnmNPRXhkexknVrdS5LP1sPbUvOJuvKKJ6fDh+uVSH4SDsPnFhJ3TmFxhNbJM8dY9EOyERZ9OedE1BXMp7PWz/LnHOe2vq3Y93x2y8UujUeBVZhf2JK5GBmxsFWcFhJplMGUhBCoSdm5jsp0lskwQiTidPKYugsmpW64lyjv3SPwS4exTj8XvOXbX808tvyblseSK/Uu7eLkxwSsWzDwK6t6G9c/A/ucm9tzGZDFLZJlg3VPQuM6ZYy/FusOCf9ZhzCrqwW8NzaPW3RPktOse3vW4ceIi6madRnuwNHGF5BXDtA/AphegdRuUTkncuY3JYpbIMsFrt0DReNj3rJQX/diOUjwFxexf0pTysnOJ+vwsvvizux5v7/Zx3zaQCXsltqBpi6B2Gax72pkl38ZKGGOdPdKucT2seQwWXg6+BHTXHqH7t1USadvJtEBvysvOZePyQ3hRvONnJ/bE3jyYcQy0boWGNYk9tzFZympk6fb6H8Dj5Rt/Xsa2mwauGLx65Qpg4AKMibCly8+LDcX0vPckMv+IpJQxVvnESWY91bOBBF8kTDoItr3u3CurSu00ZsZkIktk6dTdCkvvgP3OZtubNTFXDF5wxZKkFf/gNqebf+97zwOWyBJtYkGQ7eNmEYq8iy+RbR/igVnHw8qHbJkXY7CmxfRachv0tMKRV6e86LDCg9sqOLqqHe1oTHn5Y8HE/CDiz+ed9sSNJ9ulai6Uz4CNz1LiDSb+/MZkEUtk6RLqhVd+AzOPgckLUl78Sw3FbOvO46NTLIkly1T3vmPCu+GD08lj3mIIB7lw0qbEn9+YLGKJLF3efsiZ5f6o/05L8fdsraTcH+KD41vTUv5YUOyLEG6u5aWGJCQycBbenPYBjqmsh40244cZuyyRpYMqvHQTjN8P5p6csmI3N4c47bqHOfn7j/NIbQmeTa9x7vV/sRk8kihUs5rXmooIJmvmr+lHUt+bD//6ijOFlTFjkCWydFj7JOxY6dwbS+E4oLDHGetUvfgz4PFyxgf2YvHFn0VtLFLShGpW0RH28lZLkpZf8fq5c9tMqF8Nz9+YnDKMyXCWyFJNFZ69wZmV4YCPpLz4iMKK1gDTAj1U5Nmqw8kWqn0HQXkhWc2LwJttlXDg+fDcj6D2raSVY0ymskSWamufgK2vwbFfTcsA6I2d+bSHHzTjLgAAEmJJREFUvBxUaqtAp4L2dLCgvJPHdpQlt6DTfgSF4+Dhz0GoJ7llGZNhLJGlkio8/X0onw7zL05LCMtbAhR5w8wqsi+7VDltQgur2gKJWWhzMIWVcNYvnSbrZ29IXjnGZCBLZKn03qPOMhzHfi0ttTFPSTWbuvLYv7QLr90WS5lTx7cA8GhdAicQjmWvU5wLpBd+BhueS25ZxmQQS2SpEq2NVcyCgz+WlhDy9jkOAQ6wZsWUmlYYZP+SLh6pS3LzIsBpN0DVPHjwk9Bak/zyjMkAlshSZcWDsH0FHH8NeFM/M1hPRMjb61hmF/VQYqtAp9yZk5p5s6WIte35yS0ovxguuBN6O+GBy61LvhkTbK7FVOhpg8evhckL+Pwv/0lb020Ddknm5MAAj24vwxMo4cBSW64lHT4yuZGfrpnAn7dW8r/71Ca3sOq9nftlD10B//kWfOhHyS3PmDSzRJYKz/0Y2mrhgrtoe/R/Uj45sCrctrmKcEsd0xO8qoiJz7j8MIsntPLQtgq+Nm978gs88COwbSm88mson5aW+TyNSRVrWky2nWvg5ZudRRCnLkxLCG80F7KspYietx+zdRjT6KKpDbSEfDxcU5GaAhdfD/udDY/9Dyx/IDVlGpMGlsiSSRX+/XXwB+Dk69IWxu82VFPhD9H73gtpi8HAEZUdHFzayc0bqlHxJr9AjxfOvQVmHA1//RyseSL5ZRqTBpbIkunNP8O6J+GEb0Hx+LSEsLY9nyfqy7hkegOEbRXodBKBq+fUsaUrn94ZKVr/zV8AF94N4/eBez8G7/wrNeUak0J2jyxZmjfDo9c4V8OLrkxbGL/fOI58T4RPTN/Jd9MWhYk6qbqNA0o7Wb7fOZzy3VvwRHbvVbi5OTTic761fAWXnjdwdfHiimpu/sOdECiHT/wD7vow3HcJnHeLcw/NmBxhiSwZQr3OOB5VOPtX4ElPxXdHj4+/1FRw/tQmqmxexYwgAt/ep4bzW+dSesoXOLKqY7ftL3/jmhGf0xPpjdmB6NKbnn3/QaACLvkr3HMhPPQpaK+Dw69K6aTVxiSLNS0mw+PXwtbXnSRWOSttYdy6sZrQ/2/vzsOrqs8Ejn/f3Cw3JCQxRpZAMAjEABJjVRStoLggLtQFlxlGZEaLikvHdtzah7ZKW7VT7ehYtRZ3bUWtC62KgohakYoIhglLWEQIILIlhiQ35N77zh/nBK5ZhIS7836e5zy593dODm/Ow73vOb/zO+9PhasP3xqzGExbxx/SwO5V8/msJoua5ijcK2vhzYEJL0PpufD2T+FvP3JOuoxJcEl7RTblqivYtbP9L/A9XS6RsHA6/PNROPF6GHpBZP6N/bDZl8bT6w/lwsKd9M+yL6tY8TU1M/aXr7Zpr1m1g6ySE/lgW3fG9a6JyL/dUZfjshUr+fmoPoz77GlWfPAKf1hfQq0/PbKfC2MiKGkT2a6dW9vtboFWXS7hVPkqvHkLDBrjDH2OoQfX9EAV/nPAlpjGcbDTVGcOuNbm3no7J+TX84/t3Vlbn8ERESji3FGX4zFXLWLcpZNhSyWlVW/xv0cvh9Lzmfj8+rDHYEw0JG0ii7rKV517D32Hw/gnmPLDSe1eEUa6ggeAP7eIGdX5TOy3naJuVqIoXpXnNrC8zsu7W7vT27ubTE+UZ+ruORSye8Ky12DpDEampDHpojEEaXvfzK7WTDyzRHagVGHBw04poKLhMOElyMju8IowkhU8WsJpPGYCuWkBbh5oV2PxzCMwpsc3vFCdz7xtOYztWRv9ILIK4HtXwpo5XM3nXJ2zAUrPcwaHhIhYL4YxYWCDPQ5Eww54aZJz47z0XJj4unNDPYZe2nQI/h6l/GTQV+Sm2UjFeHdYhp8T8uup2uWlKtIFhTviSYOSsdzxgQfqt8GnT8Cmz5yzImMSgF2RdUWgGRY/B3Onga8WzrgTTropZsPsW2xqTGPaikL8m5bz3Mcv8nyr9T6/fTHFo+Py6llbn8F7W3OQbnkxi2PWOg93H38VrHwLVr0DW6vgyLHgjcL0M8YcAEtknbF9DVS+AouehtoNUHQinHe/c68hxlTh9sq+BBQaPnySMT/9SZtt5lZ0/hklE3kpAmf1qOWF6nyyRl9Hc9BHWqzOiTJyYNilsHkJrJnrXJ31H4lgJ0Emfh2Uiaz1sOQ0CdDNE2DTl6spG1REt5QAmR4/3TwBclN3MyDHT3nvdKh1R3X1HwXn3s+Ue59h1xttEwZEZ1BHqBkb8/lge3emDd7IjXX23FiiyU8PcPphdczSEu5csY1pgzfF7lllESg8xpkEtmoWrJ7NzwdmwaYlUFgeo6CM6djBk8iCAWcqlbrN/OKEBi46dj3s3uVMQNhSJmgIQNsb7pubvND3HBgxBY48Bw45HIBdO+/vcIh/pAd1hFpR5+WuFb05Kb+OCUXbsQk7EtOR3X28NucjnuMcenubuf6IGJ+QZOZB2WWwdTmHVrwFfzoNTrjWmRzWuhtNHEnuROb3wdaVsH2VU/vQLZp7WhEgKZDbF9K6OUuqlzsen8PdUy6C1IyQJZPbHp7PM3c/Gdu/pQM7d3v44eLD6Z4a5H/KNpBiFYcSmu+Tl7lszAj+e1VvmgIp3DxwS2yrSIlAjyHcvnIzj04aBgsegc9fgFG3wXH/AanpMQzOGEdyJrItlVzfrwrmfwIacM4eewyFQ4ohty+jr/sjix+f0ObXZq17j7sPHRD9eLvIH4QbPu/HFl8aM4avoUdG5wvOmnij3HfUBjJSlAfX9mRZnZd7hlbHOigagqlw3u+dofqzp8Ks25wKNqf8GMout4RmYio5E1nQz+DsWqc/v8dQ6N476YqjKnDnikI+2tGd3x61gWPyGmMdkgmT1BS4d2g1Jdk+flvVi1M/LMV/1EWsb0inX7cYlxsrLIeJM2HVbHjvVzDzRph3L4y4Hsr/pc3zZ8ZEQ3I+R9arjB8tOxYGngk5hcmXxBQayy7h2Q0FXFP8NZf22RnrkEyYicDVxdt486RVnFJQh2/IOEZ+WMqFCwbw+LoCvmyI4RWQCJScBZPfhwl/hbwiePsOuK8UXrkG1s6DgPUOmOhJzisyEQJJmqP9QZi6vA9NpWXkfbWQ9z9+kw9abWPPiyWPgdlNPFK+noKJv6D/989nWcEwFtcWMm1lIekNW8neWcVG7wD8QedKLlK+e86zWbC5AhY9CRUvQcULkJnvFAkYeDoUn+JUEDEmQpIzkSWpDY1p3FzRj09rsvAt/hsTLx6OnNxOQVp7Xizp+Bu/4V9HDwOgpnkb6+rT+SIzh+puJ9Gtz8l87z0/pxbUcfphdYwqqCMvzPPP7XPOs95lzj20s34Nq+fA8pmw7HVY7NZn7DHEGdLf+2hn6XkUZGSHNUZz8IpJIhORs4EHAA8wXVXviUUc+6ujs9FoPSv2dVMqT31ZwONfFpAmygPD1nPl9FeQ8cMj/m+b6Opo2pfQq+y8tADleY2U5zWyOyj85uG/kHvsSN5oLGHmV/1Ag2Tu2kjNgHEs2tmNo3MbIna11tFno3JFFcNKh1CcuYuh2bWUfLOJ4o2ryE0LqTeT3Qvyj4D8/sx8fxEbagJsb86gpjmNWn86zeoEHemCxTGb8smETdQTmYh4gD8AZwLVwEIRmamqy6Idy/7q6Gy0/KpFqLKn5sGenwoqKTQHW9plz3pNScUX+PY9OwXUk06DX6j1p7J9dypf+VJZUZdJ3ahbOOn9wfhVGNdrJ7eWfEXfTKton6w6nPalg6vs9BTFt34Jk264HNVdbGny8UVDBuu9PWnIuoCLP0kh2xNgSE4jQ7r7KMn20dyrjOV1XnJTA2R6gmR6gmSkdK07+ruminnqxlNb/XHKTY/O4cFpt8KWpbBjHexYC2vmMi53M7R+NC3VC+nZVG5ZBi9e6Yw+zswDb57zOj3LeUTGk+GMmkz1QkoaaNAZrRwMhLx2fwZ2OyXmQn6e7Klgwg+KnfUadH/P+f2p73/RpeNioisWV2TDgdWquhZARF4AfgCELZHNX72Nfwy8hsFznD+vpfZpy0e16eI/UTLbs6ehpb15/HQGvuP5VkICCF7yBP3flj0JaY9Ln6L/Ox0EcckTDJrdTvv46ZTOaaf94scY8m7b5hSvn8nFW7mszw6bINN8JxHo5fXTy+tnRH49d/1yGs/+7hYW7MhiWV0mMzbm0xhIgZE/Zuz8dnZw8XQGvZOy93+57P3RdNFjlM5O3TNuqqVkVcOFjzB0TtuBJ/UdtPuKB/Pu8wDD3MVt9zXiTUsJKVSs0ATUK8FUJWWxuOtaJ9wA0OAunZHuLlmQP5XfLG9vG+G07Nc7uV8TC6JRrnAtIuOBs1X1avf9FcAJqnpDq+0mA5Pdt0cCK6Ma6P4rALbFOogusLijK1HjhsSNPVZxb1PVtv2tJmLidrCHqj4GPBbrOPZFRD5V1eNiHUdnWdzRlahxQ+LGnqhxm86LxRj1jUBRyPu+bpsxxhjTabFIZAuBQSLSX0TSgcuBmTGIwxhjTBKIeteiqvpF5AbgbZzh90+oamW04wijuO/+7IDFHV2JGjckbuyJGrfppKgP9jDGGGPCKTnrOBljjDloWCIzxhiT0CyRhRCRs0VkpYisFpE2pRREZKSIfCYifvd5uNB1s0SkRkT+3qr9KRH5QkSWuEvY54rvatwiUi4iH4tIpYhUiMhlIev6i8g/3X3OcAfmhF2EYo/nY364277Ejf3akHXHishSd58PioR/2oYIxT3P3WfL8e4RL3GHrM8RkWoReSikLeLH20SJqtri3Cf0AGuAI3Ae+f8cGNJqm2KgDHgGGN9q3enA+cDfW7U/1XrbeIkbKAEGua8Lgc1Anvv+ReBy9/WjwHUJFHs8H/N0IMN9nQ2sAwrd958AJ+IU03gLGJsgcc8DjovH4x2y/gHgz8BDIW0RPd62RG+xK7K99pTOUtXdQEvprD1UdZ2qVgDB1r+squ8CdVGJ9Nu6HLeqVqnqKvf1JuBr4DD3zHQ08LK76dPABYkQewRibM+BxL1bVZvctxm4vSIi0hvIUdUFqqo4X8jhPuZhjztKDuizKSLHAj2Bd0LaonG8TZRYIturD7Ah5H212xYOv3a7v34vIhlh2meLsMQtIsNxznbXAIcCNaraMjtiOI9FqEjE3iJuj7mIFIlIhbuPe91E3MfdT5f2uZ8iEXeLJ91uxakR6KLrctwikgLcB/xXO/uM9PE2UWKJLPLuAEqB44F84LbYhtOWe3b6LPDvqtrmjDaedRB7XB9zVd2gqmXAQOBKEekZ65j2x3fEPUFVhwGnuMsVsYqxHVOAN1W1ep9bmoRliWyviJTOUtXN6mgCnsTpJgmnA4pbRHKAN4CfqeoCt3k7kCciLQ/MR6qMWCRij/tj3sK9ovk/nC//je5+Dmif+xCJuFHVje7POpz7UPF0vEcAN4jIOuB3wEQRuYfoHG8TJZbI9opI6Sz3igG3u+UCnC+AcOpy3O72rwLPqGrL/TDcewbvAS2jv64EIjGfRdhjd9fF8zHvKyKZ7utDgO8DK1V1M/CNiJzoxj2R8B/zsMctIqkiUuC2pwHnEUfHW1UnqGo/VS3G6V58RlVvj9LxNtES69Em8bQA5wBVOPdafua23QWMc18fj9OXXo9z1VIZ8rsfAluBRnebMW77XGApzof7OSA7XuIG/g1oBpaELOXuuiNwRnWtBl7CHbGWILHH8zE/E6jAGXlXAUwO2edxbsxrgIdwK+/Ec9xAFrDIbavEnfk9XuJutY9JfHvUYsSPty3RWaxElTHGmIRmXYvGGGMSmiUyY4wxCc0SmTHGmIRmicwYY0xCs0RmjDEmoVkiM8YYk9AskRljjElolshMUhGRYhFZIc6cZFUi8ryInCEiH4nIKrfAMCLymogscufWmuy2He8WGvaKSJa77qjY/kXGmH2xB6JNUhGRYpxqJMfgVJpYiFON4ipgHE5x4QtEJF9Vd7hllxYCo1R1u4j8CvACmUC1qt4dgz/DGNMJqfvexJiE84WqLgUQkUrgXVVVEVmKMwEjwE0icqH7uggYhFPa6C6cxOYDbopq1MaYLrFEZpJRU8jrYMj7IJAqIqcCZwAjVLVBRObhXIWBMxdbNpDmttVHI2BjTNfZPTJzMMoFdrpJrBRnuvsWfwSmAs8D98YiOGNM59gVmTkYzQKuFZHlwEpgAYCITASaVfXPIuIB5ovIaFWdG8NYjTH7YIM9jDHGJDTrWjTGGJPQLJEZY4xJaJbIjDHGJDRLZMYYYxKaJTJjjDEJzRKZMcaYhGaJzBhjTEL7fz2W9LSnkuPNAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"max_data = pd.DataFrame(data={'True': max_true, 'statFEM': max_statFEM})\n",
"sns.displot(max_data,kde=True,stat=\"density\")\n",
"plt.xlabel('$\\max$')\n",
"plt.title('Histograms of maximums for true and statFEM priors')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "a9ca76aa-bf16-497b-9851-958793fca846",
"metadata": {},
"source": [
"Our `wass` function requires the number of bins to be specified. Let's investigate how varying this parameter affects the computed distance between the true maximums and our statFEM maximums."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "982c1317-3388-456a-8727-a2c609e2f5b8",
"metadata": {},
"outputs": [],
"source": [
"n_bins = np.arange(10,200,10)\n",
"wass_bin_dat = [wass(max_true,max_statFEM,n) for n in n_bins]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "69d3b477-ac2a-448e-a3be-113e31036fcc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(n_bins,wass_bin_dat)\n",
"plt.grid()\n",
"plt.xlabel('number of bins')\n",
"plt.ylabel('2-Wasser distance')\n",
"plt.title('Plot showing how number of bins influences the computed distance')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4abba7e1-a033-4918-957b-8465e5e653b8",
"metadata": {},
"source": [
"From the plot above we see that the distance flattens after around $50$ bins. We choose to take `n_bins=100` for the rest of this example."
]
},
{
"cell_type": "markdown",
"id": "305d71d4-587b-4b36-966e-760298eb055f",
"metadata": {},
"source": [
"We now set up a range of $h$-values to use for the statFEM prior."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "1086fe26-a716-46cf-990d-5de0c1b070aa",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.25, 0.2 , 0.17, 0.14, 0.12, 0.11, 0.1 , 0.09, 0.08, 0.08, 0.07,\n",
" 0.07, 0.06, 0.06, 0.06, 0.05, 0.05, 0.05, 0.05, 0.04, 0.04, 0.04,\n",
" 0.04, 0.03, 0.03, 0.03, 0.03, 0.02, 0.02, 0.02])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# set up range of h values to use\n",
"h_range_tmp = np.linspace(0.25,0.02,100)\n",
"h_range = 1/np.unique(np.round(1/h_range_tmp))\n",
"np.round(h_range,2)"
]
},
{
"cell_type": "markdown",
"id": "22633614-b251-4115-8994-f7fbfe4b3023",
"metadata": {},
"source": [
"We now loop over these $h$-values, and for each value we simulate maximums from the statFEM prior and then compute the 2-Wasserstein distance between these maximums and those from the true prior."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b881fdc6-9ffd-4299-97d0-458fb8f01280",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 30/30 [00:00<00:00, 38.58it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 777 ms, sys: 6.76 ms, total: 784 ms\n",
"Wall time: 781 ms\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"%%time\n",
"errors = []\n",
"###################\n",
"n_bins = 100\n",
"##################\n",
"np.random.seed(3252)\n",
"for h in tqdm(h_range):\n",
" # sample trajectories from statFEM prior for current h value\n",
" sim = statFEM_sampler(n_sim,grid,h,f_bar,k_f)\n",
" # get max\n",
" max_sim = sim.max(axis=0)\n",
" # compute error\n",
" error = wass(max_true,max_sim,n_bins)\n",
" # append to errors\n",
" errors.append(error)"
]
},
{
"cell_type": "markdown",
"id": "dbe0a02f-fce2-452a-895b-89f3257989de",
"metadata": {},
"source": [
"Let's now plot these errors against $h$."
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b103592a-bf21-4960-9a50-e1cb6b6e5781",
"metadata": {},
"outputs": [],
"source": [
"errors = np.array(errors)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "15747cdc-e594-4d19-8488-6a6963d10726",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(h_range,errors)\n",
"plt.grid()\n",
"plt.xlabel('h')\n",
"plt.ylabel('error')\n",
"plt.title('Plot of errors vs h for max')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "0b77d546-0c6d-4790-adf7-d48f87876d2f",
"metadata": {},
"source": [
"We see that as $h$ decreases so too does the distance/error. Let's investigate the rate by plotting this data in log-log space and then estimating the slope of the line of best fit."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "b1b049a7-5d5c-469d-8735-ff11d7b32278",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope: 1.346020 intercept: -3.028927 r value: 0.971118 p value: 0.000000\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"log_h_range = np.log(h_range)\n",
"log_errors = np.log(errors)\n",
"\n",
"# perform linear regression to get line of best fit for the log scales:\n",
"lm = linregress(log_h_range,log_errors)\n",
"print(\"slope: %f intercept: %f r value: %f p value: %f\" % (lm.slope, lm.intercept, lm.rvalue, lm.pvalue))\n",
"\n",
"# plot line of best fit with the data:\n",
"x = np.linspace(np.min(log_h_range),np.max(log_h_range),100)\n",
"plt.scatter(log_h_range,log_errors,label='data')\n",
"plt.plot(x,lm.intercept + lm.slope * x, 'r', label='fitted line')\n",
"# plt.plot(x,2+2*x,'--',c='black',label='reference line, $p=2$')\n",
"plt.plot(x,-1+1.35*x,'--',c='black',label='reference line, $p=1.35$')\n",
"plt.grid()\n",
"plt.legend()\n",
"plt.xlabel('$\\log(h)$')\n",
"plt.ylabel('$\\log(W)$')\n",
"plt.title('Plot of $\\log(W)$ vs $\\log(h)$ for maximum')\n",
"plt.show()"
]
},
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"source": [
"We can see from the above plot that the slope is around $1.35$ - this differs from our theory showing the results for the $\\max$ are out of the remit of our theory."
]
}
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