{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cahn-Hilliard with Primtive and Legendre Bases\n", "\n", "This example uses a Cahn-Hilliard model to compare two different bases representations to discretize the microstructure. One basis representaion uses the primitive (or hat) basis and the other uses Legendre polynomials. The example includes the background theory about using Legendre polynomials as a basis in MKS. The MKS with two different bases are compared with the standard spectral solution for the Cahn-Hilliard solution at both the calibration domain size and a scaled domain size. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cahn-Hilliard Equation\n", "\n", "The Cahn-Hilliard equation is used to simulate microstructure evolution during spinodial decomposition and has the following form,\n", "\n", "$$ \\dot{\\phi} = \\nabla^2 \\left( \\phi^3 - \\phi \\right) - \\gamma \\nabla^4 \\phi $$\n", "\n", "where $\\phi$ is a conserved ordered parameter and $\\sqrt{\\gamma}$ represents the width of the interface. In this example, the Cahn-Hilliard equation is solved using a semi-implicit spectral scheme with periodic boundary conditions, see [Chang and Rutenberg](http://dx.doi.org/10.1103/PhysRevE.72.055701) for more details." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basis Functions for the Microstructure Function and Influence Function\n", "\n", "In this example, we will explore the differences when using the\n", "Legendre polynomials as the basis function compared to the primitive\n", "(or hat) basis for the microstructure function and the influence coefficients.\n", "\n", "For more information about both of these basis please see the [theory section](THEORY.html)." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "import pymks\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modeling with MKS\n", "\n", "### Generating Calibration Datasets\n", "\n", "Because the microstructure is a continuous field that can have a range of values and changes over time, the first order influence coefficients cannot be calibrated with delta microstructures. Instead, a large number of simulations with random initial conditions will be used to calibrate the first order influence coefficients using linear regression. Let's show how this is done.\n", "\n", "The function `make_cahnHilliard` from `pymks.datasets` provides a nice interface to generate calibration datasets for the influence coefficients. The function `make_cahnHilliard` requires the number of calibration samples, given by `n_samples`, and the size and shape of the domain, given by `size`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "import pymks\n", "from pymks.datasets import make_cahn_hilliard\n", "\n", "\n", "length = 41\n", "n_samples = 400\n", "dt = 1e-2\n", "np.random.seed(101)\n", "size=(length, length)\n", "X, y = make_cahn_hilliard(n_samples=n_samples, size=size, dt=dt)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `make_cahnHilliard` has generated `n_samples` number of random microstructures, `X`, and returned the same microstructures after they have evolved for one time step, given by `y`. Let's take a look at one of them." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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3RZcGciubm235yhVF23MZHVh48s+OkzVX3B4d4nv0EZFHNvMC1tmCD96WNbNf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\nddl3sUq/4OozPFS5q8nQRzHGDSGE5dZ1Bq75nxclfgvlMvv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations\n", "\n", "\n", "draw_concentrations((X[0], y[0]),('Calibration Input', 'Calibration Output'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calibrate Influence Coefficients\n", " \n", "In this example, we compare the difference between using the primitive (or hat) basis and the Legendre polynomial basis to represent the microstructure function. As mentioned above, the microstructures (concentration fields) are not discrete phases. This leaves the number of local states in local state space `n_states` as a free hyperparameter. In the next section, we look to see what a practical number of local states for bases would be. \n", " \n", "### Optimizing the Number of Local States\n", " \n", "Below, we compare the difference in performance, as we vary the local state, when we choose the primitive basis and the Legendre polynomial basis.\n", "\n", "The `(X, y)` sample data is split into training and test data. The code then optimizes `n_states` between `2` and `11` and the two `basis` with the `parameters_to_tune` variable. The `GridSearchCV` takes an `MKSLocalizationModel` instance, a `scoring` function (figure of merit) and the `parameters_to_tune` and then finds the optimal parameters with a grid search." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from pymks.bases import PrimitiveBasis\n", "from sklearn.grid_search import GridSearchCV\n", "from sklearn import metrics\n", "mse = metrics.mean_squared_error\n", "from pymks.bases import LegendreBasis\n", "from pymks import MKSLocalizationModel\n", "from sklearn.cross_validation import train_test_split\n", "\n", "\n", "train_split_shape = (X.shape[0],) + (np.prod(X.shape[1:]),)\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(X.reshape(train_split_shape),\n", " y.reshape(train_split_shape),\n", " test_size=0.5, random_state=3)\n", "\n", "prim_basis = PrimitiveBasis(2, [-1, 1])\n", "leg_basis = LegendreBasis(2, [-1, 1])\n", "\n", "params_to_tune = {'n_states': np.arange(2, 11),\n", " 'basis': [prim_basis, leg_basis]}\n", "Model = MKSLocalizationModel(prim_basis)\n", "scoring = metrics.make_scorer(lambda a, b: -mse(a, b))\n", "fit_params = {'size': size}\n", "gs = GridSearchCV(Model, params_to_tune, cv=5,\n", " fit_params=fit_params, n_jobs=3).fit(X_train, y_train)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimal parameters are the `LegendreBasis` with only 4 local states. More terms don't improve the R-squared value." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MKSLocalizationModel(basis=,\n", " lstsq_rcond=2.2204460492503131e-12, n_jobs=None, n_states=4)\n", "1.0\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "print(gs.best_estimator_)\n", "print(gs.score(X_test, y_test))\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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8TekX8Xn011xEpLus+/0GfLeOjFnmm1jI6n9/ia1TK1P6zPff/B8K754c95lv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\nmfOKaXuVCO4bKdPqdHd/WdLLqn833YYUCkWl+aOKexzwh3/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_gridscores\n", "\n", "\n", "lgs = [x for x in gs.grid_scores_ \\\n", " if type(x.parameters['basis']) is type(leg_basis)]\n", "pgs = [x for x in gs.grid_scores_ \\\n", " if type(x.parameters['basis']) is type(prim_basis)]\n", "\n", "draw_gridscores([lgs, pgs], 'n_states', data_labels=['Legendre', 'Primitve'],\n", " colors=['#f46d43', '#1a9641'], score_label='R-Squared', \n", " param_label = 'L - Total Number of Local States')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see the `LegendreBasis` converges faster than the `PrimitiveBasis`. In order to further compare performance between the two models, lets select 4 local states for both bases." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparing the Bases for `n_states=4`" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "prim_basis = PrimitiveBasis(n_states=4, domain=[-1, 1])\n", "prim_model = MKSLocalizationModel(basis=prim_basis)\n", "prim_model.fit(X, y)\n", "\n", "leg_basis = LegendreBasis(4, [-1, 1])\n", "leg_model = MKSLocalizationModel(basis=leg_basis)\n", "leg_model.fit(X, y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's look at the influence coefficients for both bases.\n", "\n", "First, the `PrimitiveBasis` influence coefficients:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_coeff\n", "\n", "draw_coeff(prim_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the `LegendreBasis` influence coefficients:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(leg_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's do some simulations with both sets of coefficients and compare the results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Microstructure Evolution\n", "\n", "In order to compare the difference between the two bases, we need to have the Cahn-Hilliard simulation and the two MKS models start with the same initial concentration `phi0` and evolve in time. In order to do the Cahn-Hilliard simulation, we need an instance of the class `CahnHilliardSimulation`." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "from pymks.datasets.cahn_hilliard_simulation import CahnHilliardSimulation\n", "\n", "\n", "np.random.seed(66)\n", "phi0 = np.random.normal(0, 1e-9, ((1,) + size))\n", "ch_sim = CahnHilliardSimulation(dt=dt)\n", "phi_sim = phi0.copy()\n", "phi_prim = phi0.copy()\n", "phi_legendre = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the inital concentration field." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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t37bdNNO6+zjNfOO//RXNPPunF5zlWUMKaB1Zedk0s/CXL9EMe18BQN60gbya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\nbDTcHqV1lBQU00zjic7zec+2e5l7Yj0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations([phi0[0]], ['Initial Concentration'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to move forward in time, we need to feed the concentration back into the Cahn-Hilliard simulation and the MKS models." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "time_steps = 50\n", "\n", "for steps in range(time_steps):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_prim = prim_model.predict(phi_prim)\n", " phi_legendre = leg_model.predict(phi_legendre)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the concentration fields." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_concentrations\n", "\n", "\n", "draw_concentrations((phi_sim[0], phi_prim[0], phi_legendre[0]),\n", " ('Simulation', 'Primative', 'Legendre'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By just looking at the three microstructures is it difficult to see any differences. Below, we plot the difference between the two MKS models and the simulation." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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k9uJ949vxcdjdjo/DVlCASdLGTlw83QmKxpvb8XZubseP+3aiv7cThWdpGlMdNyWp+/d/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\nOQo5AAAAAJUUI3LNq5qa16P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Primative mse = 5.27939945401e-23\n", "Legendre mse = 7.65184826764e-28\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "from sklearn import metrics\n", "from pymks.tools import draw_differences\n", "\n", "\n", "mse = metrics.mean_squared_error\n", "draw_differences([(phi_sim[0] - phi_prim[0]), (phi_sim[0] - phi_legendre[0])],\n", " ['Simulaiton - Prmitive', 'Simulation - Legendre'])\n", "\n", "print('Primative mse =', mse(phi_sim[0], phi_prim[0]))\n", "print('Legendre mse =', mse(phi_sim[0], phi_legendre[0]))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `LegendreBasis` basis clearly outperforms the `PrimitiveBasis` for the same value of `n_states`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Resizing the Coefficients to use on Larger Systems \n", "\n", "Below we compare the bases after the coefficients are resized." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "big_length = 3 * length\n", "big_size = (big_length, big_length)\n", "prim_model.resize_coeff(big_size)\n", "leg_model.resize_coeff(big_size)\n", "\n", "phi0 = np.random.normal(0, 1e-9, (1,) + big_size)\n", "phi_sim = phi0.copy()\n", "phi_prim = phi0.copy()\n", "phi_legendre = phi0.copy()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at the initial large concentration field." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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LlVlWB1prshUqzBaqhmH3IzsnouWGO0F1BsWAZosOR7umybouNBhJ7yuzoZzd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OdGAw+aa5vcsSLFDQUgN3XpnrnE2ruj2bM0km5uZpvx8Q5SXy7O6zNnz7BtwfJ6rPqoYVqOb3pW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\nj8ezzxiz3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PbQiQ/dcdk5ukU88Mged3xJul1os2JPgHNTPi6oZVbQaEUTn6lIrKYUbBZS\nCHr1l2bGW1Zu4Dika8LEbVDO9SrMH5MNYJ0miata+XkxEknHETUnafcBHzY6/uEx2S/OzVTzsDs2\nSzlPFccxtoQKNl+3DPR8dYT3dNeA31KWgzJDEvksxa1dUu8VV0AsW6Gcj9997IvuWOvxvve9vze/\nqKZJ0L3WKY73guVClhN3prVqH56kE0NiKtj4Vjc4+eJh0OuuJ/a54/MXMT4lpPOzXVVcK1HhRCue\nP0hU2ZzULGbvwMhzrdiZ1/gUHi+EiVknZl2uO+7t5ljzCrhu1aASKZ/fcJFzsO0xuoxcr2AN+wvS\njxEjT1cv5zgoh9dj5Xukb47z1DtEnWJUkjP3/dUg9Gp/vpee3f+UO+Yb4s6G2WoGLL8GZg9dxtz4\nS3cXxesRMgctFQ0Lvic7g3mtPsu1qPhUTU5m/mcbzvBoZtMTPGIprcSA5Ks1Dp1mbq0+veydopWV\nlZXVx+seustbDNlfilZWVlZWH6P7j5/e1S/F4GUxJiQi8Y66tBXLC92xIo3bH1NTEy24s+wMqDFj\nLY626manJqq3kXrIgAQwRkgw6HCJdJrQSKYdq3Egnh4CT81KhNoHFwRtZYFSbjWCDjXSbraf8cY9\nRIwp+pydwCF24yLHl1no4JP+YdCl7q9G2mm3kaLHOQ7FyX7SbUM7j0z2gUzVJah4etWTss0WcM+H\n0lx5eSGocVzQkjrg2i86tVeB4iL0+OPdWv8wc1QuDt3AdI5vSuLqbnhAQmGRNMHdtweE/e7Bdxf8\nLO0mUCTdM/TcHL/KOtBa2/Kr4LIl2Q7OVefw8iycjH3DuF8nhmSNyzWvLsy52zicv7DvGXf8vXde\n5D0RzKnG6M1KnW5PK/u7dC0os7oaTKiu12CJORwYwQnqq6/TGsTIcH5OXz/SDhavb5Savn7WQ2kZ\nKHC6DZx8o5ZzaeQ8aTPfEnnPsjUg3ooPcc7eSmA9r9iIy7qqEhfp5LwTOygHp6pGS7726mvuWDta\nBAnKVQxck8ja27xivTt+6+dvuuMAcYir1NGqaizlPP3eHxMv+ZM3f+aOk9L5DkrPdB6htBvWQ2M7\n68oXsWiMMSbF+Q7UetRF0/33O9G6T62srKysrHyy+NTKysrKamHdh3eKd/VL0S80wPiHB5rJWgp8\ny/pAhHNj0vFAi2ETwGta6PrgYzjttHvFtA/RBbKNiUrQ7Jzgt8A0DiEoAqzqc7Aac2eHgV1PEvWl\n7r64TFxuU2mgM0VhydLYtFKwXHoihbSbC8EtWujedNV5f/5WENBoF/M4O8Rn9gsaGclgrI1mV6yh\nsfBbL//cHWetpzuCFmWvzANPadRWXAzuz/zVOOQuSRCDulW14DpqjePsfHLnAfe11w+BmG42grgK\nJPavpoXYttgkPn9YOkpMjIHozpXRQUGLmZeEgbkqy5jrhk7OmaL2Z3bRwPflw8xZZBrO0en5Li5a\ntF1+hU4pOauY3/Bo1uFIN3NUM8La0KLtv3np79xxRCyob8fDdOmIWgLKbClnnlYUcb4V9QUHgY3L\nDtMFJGsfEYKNdVxb2fNIPTyUuVOn+NGLOFh3bN3ujrUJd1wuTthsCTZojG9yx8nxBAxUVzEfF08Q\nCBCazhzU1xMjF7eRbQ53gKvVIar40Od4TpJHICkSEDGUigu6qR4nsTpF1c2dnsr1/P4p3NzR2XSp\nyE3PdsfqGn3ykSfc8RGJGxyq4PHFj378I3ccmsb51scU7jqQRywjA2BwddfHJTrfddGxoO/FkvM7\ncRESbT77rvzGZPGplZWVlZXVvCw+tbKysrJaWBaf/nIlxSaaIe+YCcsCIbVLkffkNAhwclg6YwRy\nq68IULP+EqPBnTerHBSWlU/OZHs0hbnBUryvjXoD00BCr78BHovPA6s0d4ExwuJAF+3dbH+oHVQ7\nHAnSM9K8dvY2Tq/qFtBZexbbiY8Cy8UXOm6y6AiQUUQy2CpSHKearl96A2ekN4TTpTmoilLULdvf\nB3pau4w818omnHDjg6CfrnKwozoZH/4CSEidx75i5iOXwESzg3z+6i0gPD3X6uZsaAdnqdsyOom5\n677e5I6D85gz7aKia0ybsWrYQJA0Lp6TLM/+Gzj8nv76C8YYYz48h/Ny5SbcrJote4cEc+l57ToM\nQl6yg1AGzcjUZrSaX/r1r3/DHf/sCOv5AWmufKWMxxcbnqAZdINgf3Xm1l92rq1maeQbFsfa80qu\n8AVpyvzINh51HD7D3ETmC0IWXB83wyMLPa8rN+M+VYz+zd/5A3f88tE33LGf5Jkqplyxh7VVc905\npmHJjQ0Y5FqJi2QtxaWwNnRN9jVxXlunyVOeHWLfR6XDTdk4bmp11zfUgIEDosQlvw0kOycu0Ygw\nmT/d//lM4MQMvru6G+nK8vgzdLFpmHelK1ZfNNlfilZWVlZWVj7df78V7TNFKysrKyured3VneLM\nzLSZmpkyzTeb3NfSskBCyxPBYpevgF7SUsifbJAC9FYpVJ7sByelZjvb9PPwO3uJuOVGhgQzJC3c\nZDUsDSfWQBc4NEAat66XQuJTh2gv5aetmyQr1W+J5DZmgmEGO9n+pLgmp8LBJL5WOsW9OBl9BbrG\nGJOXjvPz9A1csWEJYMw5aSWk8xEQDaYJFbflqgKCFT58/5A7Xrae1+trwT1J4q5VzF0nzuDH91JI\nf3DemeeR9lMvfP4Fd/zmEQrttU+Yv2DgGZnfF5581h2/8RE/G1YATtbmvH0GPKytytRtqa2mTl08\nw/4IPl21nzZgPmw13cV6rBwDlS0rpHC+tpbGsZGpILrBBjJDlzzAOdZCfsXMSXmgtWBBvLWt4EU9\n39rcWF3ZObtoSaSYXnF5T5SzPnPzKWLX9mENk03u+Lk9ILrX3gLf+sn50zxQ3cemNsG3kkWruFBb\nNP3Vf/4LdxycD35W967ib21/tn6Hkx+qbm/dL5+j2BhjelsIQUjKYd71c7S91UQ18xu/nxZpYYK5\ne+p5hKQ3RBn5bP+O9lwhnPveLtZKcCTfZQ03nXO2aTvO5NlZrv+L5bjD+2qdRzYB6dPGPGYWV/ff\njaLFp1ZWVlZWv0T30C+0xZDFp1ZWVlZWVvO6qzvFWy1dpr295Y5i/PZWEKhiGEWNmjPpFQfn5BiF\n/JoZGBriYARfSxRjjJmeBT15xQX2yJ797vjwUVo7ecVZpl3D+/rBIed6etzxY8+CinoHeU+ChACk\nJYCBr1WBQVNXgzje+O8/ccdmC/PhQ5navTs5DpR77C3wpmY4BggGemIXbESRmAYldPQw1+1tYLbs\nItBPvTjkwmLBWepeS46jtdDFaxTPt9Q1ueOoZAcZDjYzj6+9Qs6kKjBJ3I7SqmjwFljpjRPvuWO/\nAI57vJE5y9yGm1SdmtOSydopc6BO4sgUEGd0pBSOC9JPmHdB6/rdsJHWXCqvzPvILfZRc2kfWE8B\nfLSg32NXcPEOjlKUra3QLly66I5nh0FufV5xYq/gmDTLV+emv4752Pigs1aHRilo11zTP/o8jtfv\n/uh77tgTwLHqtXX8Ix47JOZwfYzMsn392cwkkOLVMtqDJW7IXnDf25pwi0ekk3PsnwuWLr7mbCcx\nE6emolbNG05byiOC1gqcz5t3cQ0XV5HJGifIdHIK1D8+BF5/6MDD7riiEaybJq2pyhtoq6VhHxXd\n8h03xRretWe3McaYMXEp36rmuzYwGVSdWODMRWw81+zi6f7jpxafWllZWVktrPvvd6L9pWhlZWVl\ntbC8Xue/xdjOvaK7yz5dEmT8o4LN//l7/9p97d997zvuuPE6SC9+OShl8BYOwIAInJ3ZmaCMiqMU\nIUeudDBezaVy97WUomx3/NxuUOfJa2QpzkhbqKFqPjNsIzmIRflkSJZWsf0zJaAqRXFPSa7n8G2Q\n0IAgmeJLOMGWbOW4p9pxyd6cc/CJOts6boHBvv5Hv++Oz8q+qHtSC/NL63BEPvEg+3jwNAh5RQF5\npyXHQKCpG3EedleDp1Ikr/L8aeY1QpyV/cUgnIF5x2egFILv3kx38ABxsF6ppPv6umW4ftviQLx1\nzWA8Laze9sgud1zdjONTsyBT00BSmSkg1oaeGnk/52+ohVZduatxTV+86ZzL6FQcr2d/zJzG7cIl\nPHaR82cghCY4G0x6/G1B+oLxY4vY39xUEF3ZDVoxPfgg3etPHiUgIaWA66ZHWo75y+OL/AzOcYMg\neJ+7tq6EUAH/KK5JRdh5K5gXzaXVNWlCwMwecRjrsWrO65sfSuuvoIX39+Ipwgzy1tDCrK6Cc5ks\nzlFfbrB2sX/3EMeh2ryFtmmK2YsrCMnISsfFGycBHNerec+eHZybo++RjxqTxzWkLbs0i1Xbc6lz\n/OHNe93xOz953RhjTO52nOIB8Tx2yM0g2MR33tVxbPXpZY02VlZWVlZW87L41MrKyspqYd2H/PSu\nfilGR0WZuOk483/94/8jr4EC+iQncGgAvKgoZXvRZnd85iKITotn23scLPXH/+Jb7mv/46/+xh3/\nrBdk9Mw+cjlDQiRrUAqJq5rBLl39FMuGLgH75aaATCrqQUtvnTrojp96gMJ1RUUbt3FMfUO4yWbi\ncMz6OtZnJIJXpyUf8sXv/8AdB8RyHJlLs92xOgZDgnjP+ydwrq6Ugv3uAVyh/gmgl16ZPz9BZ40t\n4sbbQb6m5tsOC8IJiHP2ISgEp5+itauHwGBBmThbPQXi2pQ8y7FSzk3YGpx0+vmKTJNTcfd1Sibp\nY9twJMdKWySfS9EYY1KWgyB1rfgQfGA26/rhP3zGHZ+7fsEdaxutoGxCFryTuKP9IpkbXTOaRXv2\nKmENuQWg1EgpdPeP43zf6gT7xSbgjh4SvH/5FNv0F0R3oczJ9YwtlMcbgpL7gjl/ms+qjxTUkd12\nBSdzby5ffCFRzOnoMOd4bpI1P9fPNntS2YetD+7g9QHBwxKqEejPV9cXvvpFY8ydBe1Fa0D06vzU\nUJFZySCdbmLuOoIlJOASjykKtnHOdG5CM8GWA7Wcm03SRu7YR+TF+suaCAtlDR06BWoPnHfaNhXz\nuEBb1+mafXjLHmOMMQmBi9866n6UvVO0srKyslpY96H71D5TtLKysrKymtdd3SmGBoeaJaHhpvcW\nWK63A7S1/wlckJrfGZ9ATqgWnaemiwNvS7Y79rV3OnsDx6Qih+gYMEFlE3ih6izusLT1uNmKluI4\n7egRx6CoZ4gib+00PdNGcfn5MtBLdwOuyfoJkJC26XnuCbBbd78zZz53ozHGzE6Ab7I34PS7E5OC\njE5eJbtzshGMuGLXWnd84wzbv4PjC7qbk9xNLQL+8uNfYDs1FDC3XGeOw5ZKl/oxB5dPTYLNy6px\n9Cry0/09OnrEHav77oEvPuKOtQN9o7RB0tZGnU2cg9g01phmg+rP+jJ1jTGmsxvM1SFZvgEpznz0\nCWLujcGJunwpbsjSThzTcYIxxyZxQWv4wu3brKVzpaxtTwB/m/bKOqxuAU2qa3l2gPO35wDtot49\nA0ZXXD43ITh3vhWThjOMDuMsDZHs3J2rcWpqK6oUCZ1QaShDcxvtl57dj1v8zZPv8wPSbqupuckd\nNzaA8TWjdts2kP6FKzi02xqczwqQRwENx1m/oYLi166j5VSttK4akXOwLBOEXT5JnmqDhBw0+rOP\nX3rs8+74pfdfdcfHLxLQsHW7tPsq5RrNSeWxTWkngSD+kc6xhORwfXaW8Jm9gpuvn3fa5xWlFZgv\n/ymPDhZHi/RM8Td0q+jxeP61MSbOGJNrjGnwer1/frfbsPjUysrKyuqel8fj+Y7+EvR4PK95PJ7X\nvF7v53/Zz/2iLD61srKyslpY3kX879coj8cTZYx5yOPxRMrL/8kY87zH48m+m23d1Z3iyPioGRwd\nMktzQZPZO3BEnb2BM2/kPEXes+vBhCuX4Y7UnMC2enCLD/GkJuMuzC7gM4ODpJN4O0ijYAeOs7LX\ncD6u/BOQl6LRxGiQlxa+zs2BbHpudy34unbbzloNbmmpYn9e/h45qI/8joOQJprBiKt3kqmZFAv+\nO3YQF9o6aW/V2MkcJaymQF0Vkcsx5aVT4FtyAdQXvYxCYl/OrDHG/PC732f7RZxXxXu5adnuuLnL\nOce71oKGyurATZ1zzF3WcoreNZcyO4XPOVcKEhtrZ54SpbXSnKBqzRjt7wQnaThA6U2K4bV9jxEc\nufsAXeV9yHJLIefm4FnOh2aybn+YUIHL10DrRpaJJ0gyfSNwGqoLuaoCt/NAG3M26Icbd9eBPe74\n3CUeTag7ek5cr3NjXHN+ERTYT3c7c1BdiiPTL4x5nJgkj/jYhZPu2PsxCK29hPWuKHz2Np//1gmQ\n6eM7yAnVRwldN0CDmRt5lNBex5qvbeGzpttwtD76paeNMXfmEcftBnmrU1NzmNfkr3LHnmVczz2D\nrKXta0HIur9fevh5d/zTD193x/m5fBcUZtNmrLqFRxCKs8tKWJ+PPMLjg6b5a73iDMeUuSGf4+ji\nMdBMj+OEnQ3j3C2m7iGPTI5xsKlv0nwLJtcY0/SrbsTiUysrKyure1per3fo/2vvvKPjOs8z/17M\nDHrvvXeAqOydICmqWd1yLDtxt9M2m5yzu8mes9mTc3KycTbZOE6ixLZsOY6sYvVKihQJdgIsIHov\nHACD3nsdzP5xZ+7zQAJEQYKc0PweHx9/Bu/cueW7M3N/93mfV/RniawU0b/TOz76ivWlvhSVlJSU\nlNaWQzapeP+zr+JT6Hsi8oHD4bBu5EUb+lIsKdonmfNZq1rdXKsHlkuKgZOqPgUOypVpoBR2FWqE\nIHl8eNdBERE5XYqCV3MAORl7yS0Xi/UtLsEFGX0MuZ9nL5/D38nx2lEHpGEmp6R9DBjCTLmejFtO\n1gPrcPssSxhQjUZ47/xNJ84lxx1ng7LLlHEsu0DNVLAcS22s6urh+AwMpw7wdJ7EBASalQSs09AB\ndJe6C/sXS3jv2jywY80H141xSIGOcDnXlBVLeaSdjWtjttZKYDxTALCqTyyK7qMpN9KL3JEWM7Cg\njRynHxwH7mTMnZ2O/Z6exT6FUzG6KzjivctwyEZQS55BKibn1keaB86lRh8A3j6YDwMn8bhAQMpk\nyxYUhc8vwVnaRi2+KlsxD/i9GGumJAFRd/Uj03a6Dhg2MF8/JymEwZdXgPO4tRO31Gqpblxz7B5D\nrcf8cS2yE7W7Fuf+tX993hh7bcEjA8cSmLOtCe/LGrwFp7slDm2kTp/TB1W3uwAAIABJREFU21eF\nxcAVy0j/tTPIW12ZBX63XcX1v/0BZPZ20rErIBR/gK5RRql8DlpbsM52K92gUPssxtWp8ThnJ08S\npne2LsvZD7csZ6n6B+BYTznRryXyc8g+vUPrFDVNKxKREhEput2yH5a6U1RSUlJS+rWopKTkB2fP\nnp340J9fdDgcL/IfNE37jogclfW/TjXnv/3pOneCfy0iRQ6HY2qNf/tYqS9FJSUlJaVfi0pLS/9E\nRG7ebjmHw/GMiDxzu+XWkqZpPxKR732aL0SRDX4p3miqkpZRq3h6UPsncg9GhwFzhQbgmSe7TNkB\neGQb2q9cIOeqy0XmEQx0uTCKrMGHH3vEGL97BgXLXYPAFWl5wKdj3QgbYATBeavc+seNske5HVUp\nYVgueuesS855jYiBe9aFStML0Yn9zHEgulp6z6P74IY88Tqcez7JQKPLK8BAGnWA587tfG66u4CE\nrjdgTjrmsJ5Iah01RwXo8z1A4bsfggvy+lXdcekVBpSlaTimowMoRI/LSDTG7EA8UQZEzvmlEUFA\na+HkzK0jd2si4frpWiDC5P0Ia+hqwJxgV+oLr75kjBnDdtr0IvWIcByLQDqmA0N4n8Q4vD+j8Jk5\nzFVuiRRA871rAMi9ewDod2fOVmPc0Q1H5pMlDxvjZ3/xc2Ocu42CG47DlWqJBdbc/QhaEt1s1K+t\nIGpf1ETtuDS6EAZGsK+x6dhXWwsK+eOj4YLuG4Gz05tczTsPI2DgRgNQOz+mcE8A+ttZjCzhq7XA\nlPfuRmH68VPHjbFfmL4v7DItqwXmDw0GHk/KxX5cr6HwBWoRxZ9d79P8dKO53XcBx8wzHajfjcI7\nuDB/dBKZyBMT+AxiRzlj1QcP6jnLnF9cexrHwi8bSF/sK6v/dzN1hwWCO+8wv++6e9Q0rVBEHA6H\no+pjX0hSd4pKSkpKSuvrDqnJ0DTtCREJFJEUTdNSRCRIRI6IyP/YyHrUl6KSkpKS0h0tZ/H+y/LR\nr3CHw+H43Q2ta72i3A+pSEQq7v3Zt6VuoEUWrLj990ha2/EUGQb8xOgg2B+oITMBRbrsVnMt7+8L\nBMRIg3NVxwmHZiZifdwuZsUOvBkdBqTJ+27tshpjP3J27cwFzqprxzp7+6h4theFxBZqkeSYAZp0\ndQf/nW9+3fgbY8EfPv8vxlizAMUtT8NR6yDn3PIgMLRnFo5NcCAw0MgQnJLuPkDeY+eBv3y2AXkX\n5QLFTVCn9bYOuCBXqD2Yq3USu0NthGnZ8SqEmP0jMAfiI5BHWn0JeIiL3rl4f2wKLckWu7GN2bvy\naBnMiQJyDJ+9iVZlbpQFuzAOVFxcpJvV2mxAl+N9wMBp2XCw8n6fP3sO+5SB0AQHuY1tVqAyzuDk\nOezmhmPGiJUR7/wsttdOObarXKk0V7btQwG6Kyt42oYWUV996qvGmLNPS29cMMbNp4Dc3XyBCD1S\ngGF527dlYf8unjhrjA89CATKWcJbafmrVxHi4BGERyh+1EpruBdo181L3+/FXlwT9z+GlnJv/wh5\npEWPIXDhVh+ug7kRzCWeV1uObTPGLW1ApqHhuHZj6DOFP3c425gDHdx9cS0uTOJccq5vZJI+5wc6\n4bjNzMUjoWbaFpfdOTcyXU5++1kRkWL5BM/tbqMiEak4/BdPSk1n420Xvp3yErLkzF+8vFnb9rlK\n3SkqKSkpKa2tO7Qk47NIfSkqKSkpKa0ph/M/m7GeO0Ub+lI0u5vF4mGR7MPAMXU1KCpOyUQ2H3dU\n9yI02tcDHMBFvZnbUcDcP6y7EBkvNncC4dkGsA4f6lzdQcXGabEoir15HpimfQhoxIU0RUQi8xKN\ncc9FuGXLCLFO2IDRVjnnCCGx+3SuEcuH7de358VTrxl/y08H2ttFGYtlNdheN08qCic8tu8QMNDI\nJFBYUhQcb3PJ2MbKFmQsehfAufa/votn0H/17N9he0OosJrQJ8uVYWqzAplm5SDbtonahHFxNndu\nry5jkgKkmb8DNbd1Teh+zseAEVlFI8xlwwNw7NkCgZYZ0e/aAix2srwU66nQHYnsTC45CPcmB0GE\n0rr37kfx9yJ1qZ+ew3Xw6ANwTXObJ84s5XCHLdmYH9WV2L/AKLxv8XYgb86OXXDAAVt/CwENEUH6\nuZ+fB7Y7X4mcYFuLFdtCmbdZ9+IxQnMZrvnFTjiTzeE4vpdOA71aIuAKZaetfRLX3yw5dhk5zw/i\n+MXmAqMvhOK1Y436owxzNFzQpRVos2YOAhLuo+zTuVGsOyIeYRWB2Xh8kh6HII3oUGBSjfD72avY\n1xXKfPWPxGOCsVvAvXM1GBd+EddxXTnOcV+zjtrztgMrV55GuzF+bLW7YKeIiCT54/gofXqpO0Ul\nJSUlpbWl8KmSkpKSkpJT6kvx45WbnCU+of6ruoZzph8X5vdWAY1aCGtwB/iCPUAyjHiWbDrinInE\n+rhlECOK7EPAbOWX4UodnYDjNT4PBdS78oDN3rvygTFmN1vwdiDIRw48YIyfe+MFY7z/EMIrL1Er\nHy7A9SZn5+yMjod25GOfuXCXO7R7egFD+XgCD/dRe52GACDeoSYgqfF84KzBYexTdDjQz6QnlvnL\np79vjDkEYLAXmImdczsP7DHGN5urRUQkKAKO14VFYK0V6hDvTbmMXCitMR6mnNK6ZhTpe/gCf0UG\nw9Xc2o05xsjy0J6Dxvj9n79hjOMOwr134uT7eF/a7/A4/TgNDeLYLdsx94SWPf8CEOi2R1GYb+WC\nbHJksts5MhgIm9sAMX5foBxUE3WVH+8Flr+yhGvR1wvX2YIARyZEosC+i/Cl8Tpv4E1TCObeQiuu\nIauPFesrwmOS/iEELsRFwUnsk4l1chDErRZ0u7eTs5qv/8hEYMDDxcCLfFzbGoDmzdH6e7nRueG2\nTV2ecPHGR2Ib0+LxucCF9ufIpfzOKbTm4sctvklA2KlJWE9uMubYmx+8Y4zD0oBnRyw4ZpPTuBZX\n5SI7nd3s3OfPlpBgvP+VSn0OTEamiyAnQelTSt0pKikpKSmto7vvVlF9KSopKSkpra277ztxY1+K\nIxOjMjA2uMpJ6OEP3MKFphZqKeNGhdiMF2oa4WLz9cfyMbt1HGF2w+ZxYffjX37SGDPqyClAAXdc\nBHDF8beBQHo64ZTkwueAVOAsuwP79+pZtJ3JzkKmZks3MFBuNv7OOa9Fmdieiio98zHQFxhxawac\ng++8i/fhPIWFMGyjmdBWCBXpj0ehoH1wANhvsR/uOs84IMgDxWAs56/Cpcdo0EG4msVtdexzOrIc\nIdS4Eo+Nf/gLyOucJYQ2ScEAZsqKPLQDCPLMJRR8TzXCTZp8GIXx49PY7/R4uARHJuDGDd+F5YP8\ncOxnIoAXudC8vUdH1MmJcC+fe/8Mtpcyb83hGA9PAGlyBifjxclJoDK+hhyUWenmiTnPrm1exj5F\ngQ6hON4hAXA7+nkDpdZfhqvR4myFtkSZvq0OzOWAAByjmKNAkLUVWEdYBtzDESG4blq6sB5/Hyq0\nH8exuecwivf5PN24huu7fwy484VuFN4LZUHs3Ys57AprGBpHWEUytcZibF3TiDZrnBXaStfzcCtw\ndkgqHoEIyL0MlONRhs8ePOLgFnBefpgHE+OYq4xB2aXvTnm1LrTMObOORbiUp2Ywl+bbdMS6uEQo\nVulTS90pKikpKSmtrzvoLm8zpL4UlZSUlJTW0d3HTzf0pTg6OSYDo0MSHQknI2clphQmGmNu3TLR\nBawxH4uCcs635NxSV0dzsyfyHk1hQEmvv/G6Mc7fBvTFhcENDSj4DksFSuWcQkY/g6NAdJVXgHJM\nPtiGpkU43gJ8UeBb30ROST8cj4VFYK7kFB3HtdrgmJxfwLEITcR2zcwD7S3MYhluY7UKQXpgG5PJ\nRbcUDwTK2DMqBByIcx79s/H3WXLFZeejiJyPk9lbR59bsvDvNTUICXj7JNpeLbTDRRexG249Tx+g\nJ3YgFuYBLdd441x29AJbLS7Bcfrk4UeN8d8//Q9Yz85iY1zbgvX4+QFVnXkfLmSTt34ss7YAiTOu\njM5JNMYeETjuiXTc3/+nV4yx7264HfcWoxv8hXLC1nb6wCBEaO2F29I+jHkQSKifsXSbFQgwNBTh\nC9xybGlZnxPxsTgHvVbgyvElIM3fffQbxpgLx2+ex9gchvO31A+3eFU7kLpHPJBseR2uLc5B3rYD\n7aKul2H9W7Yg1GPJjvPNTtTeXv2xTW4mztlrL75sjIVczRxEkbYL89bVMkxEJC4HyL2zHI9DHv6d\nLxrj93rwmRZIWP5Xp+F25lxftxCcWMbGnGmblQRc7QqaOP3OSbxPBlCuiVqVufJnLZGY05ulO6xz\n1KbI7faLKCkpKSkp3R3a0J1iWFCYxMictNrwizSDYpBOl5/DwtS0NzoDzW69qe6O63I8LDBcpDhN\nDlnUReONl141xgX7UWs4SE04x4fwC6xkH5rhnnoNRpuRABgfTP54KJ6ejP34o9//L8b46V/+2Bgv\n2fBQ3J6Gh+jLw5R0T3Vm5gQc3lutVhER8acOHPOL+PUfFgjzAsfbrazgl+18DEw3HTdxV5VSDPPS\n9Cx+rS8s4Q5nkeKyVrLI2EEP/TPIrBJZiLuR9z/Ar9Vt2/GL/kaV/qufaYG443fWfDXOTdIx/OIf\nGMQ52LoFd3JsyCgpRmwad5G41Yy5t0SdQpo6cRfPdYe11JQ4PxPbUHEJUXoBCTj2s7P6XXpHD+5I\nPVIR4zfOXTpmcXwtNH999lDcFt2llNWBnvgF4e7CRDWqUdSou7ER3QkCEzEncpIzjfEVqs3NK8w3\nxpUUbZi3D7WxLd16XGLfAOpQNTpnFuqm8ue/hwjAe76HO3E+prwtbXTM2HS3NAzyYUnA/J8gs8gg\nmWT4GvKmGEeODcxIQK1kT49OiKrLERkYnA7yMmbFXWtQCmgI05PlEVyLfUvYdr8cLH+lFnewbl64\nbsIo7q+9HfPT3YK7wH5q2Dw9g2txfxHqfi9So/VZZ9NsSxQMUzPTmO+BQZiTxm3Y53E7dvfRU3Wn\nqKSkpKSk5JL6UlRSUlJSUnJqQ/i09WaD1HY3yZb9QF71LUApj9+DurRf/fIlYzxsBh6KDSe0RPFh\nbEAZ6NHRDhtRLHF4iMy1gMVZMGQwguwfBa549Ct4QP7Gi8CwSVnAhdzE+LnjqI2aOoMH+l55QFjc\nFLXMDizGNWo1LaiJyk3Xu0fwQ3bGOtNUk9ZLSf5cL7ireKcx7jDhGLRXAqUypkgpAtoKzANirWhG\nzVlIGmGmSaDBinPouOCXjP1up+a7y87YqwvPIzIt+Qh1OyEj1Sjt91wdUNnVSSCjnELUdf79c08b\n44gIIKyCYhx3Pk6MeP/sj4D9nnnrF8Y4wAformAX5jDHqQ2O6ds2QUaj5DgYL7qp8S9rZQWTOTwU\n6NliwiXWWYNOL/ZIYLGVGWBYfgSQkQnjBdcscieUukggVsbYETl4ZNFQD4ORy7jC6JANL2waGaA4\nviYrmtryvO2netmhIeDy4Ghci0G0fu4scuUUuksUHQCWX6H96x1CzSC/7/VxnJ/9O/SaxcvVwJtB\nfsCLkcU4H8vUcNydkHd2Pq6tSxVA0hFBmPttl3E9lzx+rzEeoUhJnwCc175hPCaYocca8VGI3Tt7\nDvW4W6jOutX5mck1lis0ZoNOYLB+fP38Mb83TQ7ZJKfNZ1/Fr0uqJENJSUlJaW2pZ4pKSkpKSkp3\nrzZ0p2jyNovJ17IqyiiNXJsvv0SRTNQ9gzVAWJO7MffWW43xY08+ISIib76Fmh+fKCCYmT7gCsZ5\ngzWoNcorAY7x8gR6MgUDMVnb8Vru8DHRBxdk0EPYv0BCMi3U9HimB9hxIQTINzUeUWGutPvuOmBi\njvpi7DpmA4Zy8wfiKasEHrrvIXTv4G4RTSfhwGOn7zLVeLEOFiEuq6IJWJUb37JLNptqqQZuWvVt\npKi27hpsC3fAKN6LGr1JquljtyzXIGakwF3Y1AA83NtMnUVCcV6548L/+du/Nsb+icB4tiG4Cjna\n7cwNYDxXDCGjOEaNXHvWVoXtahvAYwRukltcAiznswN4rJsaZbtRV5SZGRyPljYgS67Be+cScPX0\nJJyME9Nw6Q53A92tUDzYjTf0fQ3YRvtxHdtuobrDsChg6/EZrNvVwUFEZIzcuFwDyDXAA1TbynMp\nJg9YuraempWn4pqz2YCreU56eWPOlb59SkREUrejwTUjcb7OQ6OxXflpqFPkuseEWKr1pe4rIXk4\nZpduAPsnxAFV7yvAPG8nNy5j29YKHO+UQjziqG8E5nZ1E/Lyx+fCPNWkDvbi/IrTrTslQNlKn14K\nnyopKSkpraNNqt6/g/ip+lJUUlJSUlpbd+EzxQ19KTqWV8SxtCJDY3APmsldF5gUvtbL5LeOPmaM\n//lvf2iMs0vQIDggG+7St0/rxfZu1Fh1ZhD4JqeIipTfuWyMM+/B+m71AqV29gF/mbjoNgzb298O\nTGMKxPsWpAN53WyqNsbfffRrxrgtCZiEuzsM0nHSnDhk+0HgFU93oFwuRh7OAL595+xxYxxOLszj\nr6GB6YH7Dxtj/8fQaYKLrO2TwEmHD2F52yAwXlspItoe/jY6kZwqxz5x09OY7Trm4obEu7dh/ziK\nqroVzr0latobSHF5i/NAoIyzDh8oMcYXquAM5Eay15vRLSU4Hw5ndmTyttvJLTrYBYfj3LyOqEKD\n4JIctGH/+i3A/35xwFXB1KHi1jVgVcZ4zYSBg6PhaowJhQM4nRrfvn4KnVNWxSnGAjveOAOM12YC\nuk7JwnzqsOLvJh99O9kV6x6Nay+VuoM03sA500ywH5iCcX1wRwkzXTfsyDy6HUEar5560xgnJ2A/\nBuhTs7UezmpurhycjmCD4QrMD1d3CX4E4k7uTO4wwg7rk68ihtCdQgXYHdpjQ3Skhx8wN3fYWKSQ\njPcvnjbGYeE4x9wdaCQVDuP2auwrPw5wzC073wbXyo5chDCUVyKcIcsZs5gUBIyr9Oml7hSVlJSU\nlNbUXXijqL4UlZSUlJTW0V2YCL6hL8Xc4gLxTg2VHkJunT3AlCnJQD/plIn60zf+3RiHFgBNzM4h\nE7G9HW5O18+KmEhgMEYjHu5wnuXchxzU5uvAPdnk9Gul5qfzrcA6XY3AlJ6ZwGVhIcAeBymbkJHM\nCycRAsD5jHsIH16pAeJYmdVdbJWTwMDc5HhmG45FdT0wZl4OiuEbrEAtlii40q42VMhaWpkDeolO\ngnPuvX9BB4GCL8J9GrET6Izxs2MJzrm+EbjeokN1nGWOxXm6fBEYk7Nl7VSgXlgMzF3TjHMWE4lu\nJlnUNaWDtiUyGMibnY9b78d5au6CazPan7JEr8Lh+MowOq1sycdcqXM2oY2h7My+KaC6uCxso7sZ\n85BDGdhVXXsW50YjQ/bwApBsXgqcpdcbK7Eeco1eu4IwhYhkHG9LLIrFF23oeOKTijnpmME8cGV2\nclH4XD3coU1j1MUGmyt52xCSwfP96g3McY0eTfiQ89lG3Ws4+9c2iL9HxeC49vUAyS4P4bqYjQTC\nDS0GKpxyNm8e7idnOzlVU3OA2dsakJ8aXwzEHEChBew4FQ+85+Icrlcx4+8dZzCv7vsmHhWdv4lH\nO7yvE8OYt+4U4sAI3jXP+RFE2VXMAZ4b4UG6wzqY3PGbprvwVlHVKSopKSkpKTmlvhSVlJSUlJSc\n2hA+zUxIlYD5ILlWjsJm/0jc8nf0WI0x5/7Zx4Fk5tzxloxwDu0+aIxbunSU2t0GbGYOgvuuuhm4\nYnkU6zZTYT67CxOigFqGCOtwHuEctTn63j8hO/P5k2gY68IUIqtxLreCcSNGxqEBEdH6NjBGWfEC\nAqm8DsyWmgvcU10Dxyu31MkvBM6qbapbc5mvPvJlY9zSDYTs8TCwZlQI8GJLO7Dj5CSyJfdQc9yz\nryNjNGq/7obltj9u1JQ5JARI2iMSqJFbQaUnAbNzkfeJt9Duyz0G7kjGp4uEuYao7ZSHBftnNmF7\nNAt+A/r4A1vV3ERoQWSyjpnbKBQiMAk4fZwyUftv4Vxyw+ydx9D2amoWc6PdZjXGjIfZoWqjov6F\nWzhOlmhsbwEVnb99BoEZcSUoXl9cBq4u2gHXYsUVPadXC8I8jd6LbVkmZzAX2jd0wDnr7oFzyUh4\nsRPHJnYLcCgfA3Zhct5xPzmYwyk0oKcX89YnEdfuaMtHW1/98e//V+Nv//hzZOd2cDunYAq0oLZs\n3NB5qgUY1o0ctXZqL8XttpIO43ycOUkNq6kxet1J5COnHMQjkWhqes5BJK7Pl44GXJP5WxE4wU5q\n12OVldC1Azo+k+7CZ4rqTlFJSUlJSckp5T5VUlJSUlpfd85N3qZIc3yy29oiEak49uNvSF1/iyx2\nw+XGOYhcaBsVAgTSRy1+PKgImd1SA2NAZ4t9Om7ZUwIMdfHdUmPsmQJkuzgCd9rKBDCUZzKW4TYr\n85NYPoZck93NQBeRqXDIelGBPbvSegfJIdcHlMoFuCFUvOvvoyPAtDg4PE9dwj65U5bj0jIQFmdt\nssNx6CLQE7e04tzNlSkgtPhsvG93i9UYc24p59U6prCvmblAXuy4bHfi8lBqMXSrDriHjwV3GD/9\n5gls4wzeh9HrgQePGOMrN+G68/YDRkwiLL5MRc6c5/p+2RlsG6EoUwDOq6utl4hI1VU9O3bPQazj\nWgPyZBnfcvswfnQwThmkjEmbKS+Xl5ki/B4XgTnZ2Y51xiZhTnJbtCPbENZw8jzQXXgUsHjPTeBD\n1zXKARWM3B84gJZIbz6PRwe+GdjvhVlgxIJsOHfZscxObVs5zQnKVn3yCbR0e+Wt14xxUjpc7Dzn\np0aBZxnHRcXpqLafXKuhkdhe3pbeASyz1IPjXnAALvbqcpzvuGwEDHCrKd6ukZsIBwnflmiM/bwx\nV7voXDrmgW3tdI3uuh/ncnJG39cZcuj39gCtc66wa325kely8nvPiogUiwh24tOpSEQqDv63R6Sm\no+G2C99OecnZcu7v3tysbftcpe4UlZSUlJTW1F34SFF9KSopKSkp3fnSNC1ARFz5lCkiEigif+pw\nOCbWf9VHtaEvxW0FWyV8KkZOvg5nILc2WpkECrCNUvE3FZo6AoFqbIPAIYxzDhzVsxLPl54z/lZw\nCK2gqi7eMMa+yXA4LgQCn05eBNLw3QEnnH8winRb34bjM+hAojE+XLzfGH9wHduwsIj1swPvO7+P\nHNSbzSi8r+tAV/T+Ov14MK729AVeDA+Es7WjCkX67b1w/bED1yMF6HlrPrrIc/sgdnOyUzMwFu8V\n6Ivj0UVd5TUP4JkWCj8IC+LX6oXYC+R0TCsAau3oBJK+WI2MTvcEvGcatddqrAGmuVyOjNPkNOA0\nV2CAiMi595AzuTyEtjqMn9sr6fiF4HgHBQGvV13BfHK1FuN2XPyew+PAZm+dQDZpQSFQ6iA9CvCh\nQnc3N/jaNLJtam4Yj1JmKFfP8yOAFQpTmCA3bHoaUC27ivtacS0UbNODE9jxWn8Nc5adxCZCnYuL\nOMdiJ0RPLu95uj5GmoEpV+ZxPrio/kYDtSojjD4xg31KJERuMwMfTs7gEc7AoI6TD+9DRu6Zi3g0\nEREDh2dSXKIxngkDmmT8/t1vf9cYv3UB2cOdZZhLT3zrKWP8Zg/yXOeovRPnGXc24BriUI2wPGDx\nqlZy1Tsd+57BCOngz9GQcFyHI/Ou+fY53I7dWbeKfyMiP3I4HFUiIpqm/UhEXhGRezayEuU+VVJS\nUlL6TVCSiByh/98uIofXWXZdKXyqpKSkpHTHy+FwHPvQn1JE5IO1lv04behLsXeoT26NdoqJkOmX\njz5ujF98F261koNAGbXtwGLcZoXRi8udKSJysVzPz0zLQ1fqugZ0pQ7LgkNvtAtOvGhyjfZmAeUc\n3A4Xa3k9UFnKg0BePbeAmF4uJRzSClzmyi8VESl8EG7Kn73zS2Ps6wncMdWAAAP3OB01BvsDe7bX\nIYdxjpxq7AhdojxLE7k5uRC9lQrzxwexvcWFyBitvwX0k5+G4mFu0bQWGhVZ7aK7fgVZl4Fx+vJT\n48Bdy+tkZ2qE4rJTcF6ry2BEM5H7tKAA4QSrnMyUvWqOxLE2+eKYMaIu2gfszgEGQ21AcXsPw/U3\nM68jtUjqHN9NBfUh5LS92YOC7KoqoMDEFDgW+bXTA8i81Cg784++/vvG+NXSt4yxlxfOdycVlzN+\n45ABzhutaML2+EVjm13YdE/eTuNvo9ROqeyDC8b44P340c3Hjq/bmxcxH3wS8D58Dry2wB1tHwZe\ntHZg23ccwvV0sxGBFcNNCEh46mu/bYzfOIfWaQ5nPmnvEFzuK4Qa+zrwWMA+ivd3o2zeQV+8trkN\n16VjGfsRsRXnlT+v2LUdSI76q5RVGpEKF7mnO963sxGY/mtf+R1j/N6VUyIi8sBukL/jV/D5Pk2B\nCMaFxhfcZukOzT7VNC1Z9LvEI7db9sNSd4pKSkpKSmvLIZv0TPGzr+KTStO074jId0Xkew6Ho/N2\ny39Y6pmikpKSktKvRSUlJT/QNO3tD/33y7d/5SeXw+F4xuFwbBORP9M07b9v9PUbulMM8Q+WSJmT\n3nCghlfOAvdwd/fTlAHIjrOCfchh5FZInLm45CyGd6Tg58ViFxDdXACwUkA03KfehI+4uJULq+dn\n4Tiz3gRWid2DvNGhEbgHHUtARR7JcE229wB7MFbVvMEw2O3o5a+jvmsXytf89wHK0XTlb4qI9C0C\n62r0a8s3DJhmchqI1U74srIFbjYuGGana3kZXKEpmXDLsZqsKDrnczk5omM3P3L0Tk4Dj1vCgDeX\n6e+chWkKAPaMS4DT0EROzXdfg8szJANOQgdhRM6LtduxjdxGanEJ58lC6PXKVRwDi7Oof0cOHL3v\n/AKF5XsfA43xiYWDdcYG1+jkLM4HY0Q3aq107/6jxvgf/uWHxphNgEJlAAAgAElEQVSL2/nXNWf8\nfv2rcDu/fRFBCF29mCvchmtuAa9tqtMd0eFBQJocELEjG/v9yj89Z4wLH0OYAReuR2UnGOMIWucY\nYWY7ZYxO+uDc37Pj0Jr7wVnJTzz1pTWXWZrGZ01Bno7aG+nzhOcy5xQPrOA6cwsCxlxsA0L2zcJ+\n7M1H7m/PEFD4uZtokRYWB6fv0DB9dlCQxvAAHvPYJzEPp8kl/5zXC8ZYM+mfI4ythzvxubvvABzy\nl6udWdRmfOb9Z1VpaemfyCco3nfe7R2V9e8xNee//anD4bCus8zfiMgHmqa98jHLfEQKnyopKSkp\nra//gMJ7h8PxjIg880mXd9YoPiMi33Y4HK47KNedyxER+eknXZf6UlRSUlJSWlt3Tp2iy1gTLCKu\nL0UXTutY8xXraENfijW11VLb2yKxycBc3AbIzsXlPkCDO3OATM+eP2uMueM5FzZXO/NJ22qAQ9xj\n4faKCCJnYD8QqJ8PXJKJSXCKdXaTw5LySPsjgGA441TIceaRCBfmzuIdxrimDY7alEwUoC/bgUY4\nt9Dl5pzxAQbWyLXGXeq5vQ4HCTz3b7/AawOxXXvysV2XNbT14iLrlBQUwNfStjPiaa1E2MDXv/Z1\nY/y89WW8rxcQzcqsji9nPIGnGJnaF4A37TPAp61n4S586JvIvzz+HgqlrYvAnpYYnNe4cDiPo6io\nvrkdcyUqAoh1bhi4zk4IsvgIsFhNG5zNy04s9+N/xw/Lkifvw/tTNikXll+pwXHnfE3OFbVTNu/x\nE9jXvO1wQddTi6YVQuEWwqqcMToxQsX+JlxDtm4KYiCncnCMPv85x5dDG/jvD3z3CWPMxfBPPQSk\nyc5yzi9mJMvbO1JuNcbWeFyXdsLrfMz6yW0824/PmohknIeKS7oD1s0X7uWEXDjRS89h2xlDu9Py\nYQU4lxPjeJ+zV+HGjYvGPllr8UhBaHsL98PtnJGAtmjHryBoonAb3N83YuASnqP9i0rTt6fswmXj\nb+xY7qU86egw/ToIC8KjpLtNDoejUtO0n3wIk35JRCocDkfpOi9bU+pOUUlJSUlpXd1BsaXf1zTt\n+6JvsiYiAaKK95WUlJSUNk13UJ2iM+P0zz7rejb0peiwO8RhX5ElcopOD+OW/8uPAqs0dQJ/lZ4G\nOtA88Zb1bcB1keEo0P6KE8/84ifPGn8zEeoYmkCXdX8/YMTePspbJByzdSfawrAjMzYdzrlhctTF\nxxEepizR8ioUaz9+9CFj/NopuCNjY4B1vKhN1r27dNfiGfN542+dnVZjvDwMrHOtHpmsdgfQDDsT\nuXiYC9q5AH+wD3/39gDOrq6nTvNJ2N7xKTjwnv3nnxhjbukUnApk6XKRsouQnbBXypBfagnC++/a\nj0LtsxUXjbErDEBkdWd1B2Vn8vlgZ2deJpBUTUudMU7OAMLi11ZS3qk5BOfJ4eyovkxthRj/9Qxh\njnFG53074Uo9eRW0ZoqcqEvuQM9RoZjvVRcwryzhwM/eUXAYf/PBrxjjf3z6n4wxo9HULXDgMgo3\nR2DejHTrLsi0PQj/4HCGSsrurbyM7WI0+9zPgfGXBvGI4J5vPmyMTz//rjEO2YrribvXcz5rFe0H\nt6ObngWav/detLU6dQEtwQp26Y7ZmlpsO7f78gmDOzqC5gO7aEc74Q5NyUWGLAdsdJvgXPWOxTrz\nUnON8Y1avK/FjM+6qS58ZjW4A/U/euABY9xoxXu5HNTziUDuY4NYR8s1IH+LM9Qj2I65s2m6c54p\nbppUnaKSkpKSkpJT6ktRSUlJSUnJKc3xyW5ri0Sk4uHn/0DqB9tk7BpcY7EHkGM5MoK2M/fvA545\nUQ58yg48zZ2+k6mVjre/jnOmB4Hz3Ag9PXYvME01OQc5k7G1Aq44bs2TWghnp5XyJIuzkLXZcAt4\nI5McZNGhcDWeugZE5u8DhDvYBbwWFP3RFk1cYM2BBKsyQ8llVvLU/cZ4iNr6cFuo8W6M4zLguuV2\nURyOwCjVZqVwABOOk51a+ZgILy73A5c98MiDIiJy6iocxX5eQHHDtXA1WqIp29UbWInb4fj4YZmx\nBhzH2K04BxysEBYCJ/HgIPDXsb14ts4toNixx/mTM1TcvbSo77d9DPPUHIz95/fckpJtjLmFU207\n5qS7GeEEnBHrIGdwUjLOWUcTXI379iGz9+IlYGafcKA7dirfqCXsTm3csguBll3u0vYOFIVz9/eA\nWDgYJ3qA61a1uiLUGRINJzhj2JgwXCtlVchHjY+BK7T9BhDv1hK4gasJf3t64thzC6/2Wzivru3J\nScZnUW09HpOERQFVcygEu8NdmbciInPVmGOJh3COIymDd4mCIOpbsB+LnUD0ftk4NrHha7uWmwiZ\n8vwUpyucnbgcnBEeh+MbGqCfs9SgePnRsT8X2Zzu9kUiUnHgD78g1TSfP63yU3Lk/D+/s1nb9rlK\n3SkqKSkpKSk5pdynSkpKSkrr687xyGyKNpZ9GhAkkfZwKfptFN2X1cGhFhYKtNTZDyzHBeLbtqO4\nldGtyQQ86nL7LQYRwqLO4yfK4TxLiU40xjWVKAo/cAytqzj7kB1n3BW97ARcoWFbgHhulGP/eD8Y\nZbgl4oabC8Tz9ucY4wtXdPzFWC4kB0hlog+oyiMELrKqVqAkvq0fuoy2O0e+AScsO1G5E3o0Of0a\nyPXLBc+7cuHSvfA+kGiwPzI+R2i/T17UsTjnw44NAT25kdOYEeEsdSdnh+zWLBSxn+nAeo7twLl8\n7s0XjfH4JArXl3rg8uRcyvlRnHve18l6oCpGux7OXN2M7Th3NTVwNaZsSTTGtkHKqw0GWpu1AaHN\nEpL2jcZxZIzHLZQWu4FYGZdzYAZfN2VngFVzd+H4RQYD3Z0rw9x2zWEPfyD0mV44bcdacT4SCoCt\nbS1WrIPQr7cn1sNu3KYTQLkxB+CKvdUMbBuUjjl5oxT5s/H0vtzSbYKyjcX00T5JcRQYUNuI62aI\n5hhnALMr/eppFMnHHwSS7mmC87jPF9mnETHAlyGhQM4Lfrh2o8OxzMQM5icHHhSl47PU1oHHOREJ\nenYtPy7w8sW6h/oHPjI2ReIRyebpDqrJ2CQpfKqkpKSkpOSUwqdKSkpKSmvqLixT3NiX4uDYsPQM\n9Ur/KJx+K1RYPe0OB5ePF8bcUqqXip97yPloH8cyxYf0ruDcioYzIcOC4eqsqUAhOju1uKP8xBSw\nzkgNOSKpSLiwBPmh9a3AG5n5cJ+1tCOQIDCYkKIVKCO6AJiQW/akpuutbDhjtfpapTFO2YKCYe76\nfpUK+bdlFxnj2WgED7Az0eQHt6M34WF21EZTW6Eeysjk7MrcPUBx8ZT3mX4P0Naz7z6v/y0euapm\nE6ZUH7np+kYwzkmCSzAsAOiJ358duJcpVzQqGkiq1wacZaLc3YUpcvKS03VlemnN5R+9D27mNz/Q\nO7pXXkZxfwgFFpx9Ce2LOI+0heYSF8u78mFFRP7giW8Z45dPv4ntXcLcd6RhXjU34pwx09mzfbcx\nZiwXTF3fz98EDlwhZOhqX7W0hO3KOwiM6G4BYubQAs0X84rbk3U1wQX66COPGePXGoGWC9Lhfi1b\nxGu5LdPbLa8b484bcGQeeRS5sx/8CoEAX//D7xjj5996SURETlw8ZfwtkuZJdiLw7SC5tituwgQZ\nnYfr1qRRkEAY8LCZivEHB3DNb8lE8T6HO/QOYc5PUcjJF7+A4/TqSbTe40dLWYn658Eb57DPx3bi\nMQK7qm+e168Puyfm0abp7qOn6k5RSUlJSWk93X3fiuqZopKSkpKSklMbulNcXlyWpfklSU4Bahjy\ngENuVYEvjZdsQDwp+/FaDyqgHhmHK9TlrmNkOt+A9/G7J9EYH/kSMiGff/tXxrinF/jG1x85oYzl\nUnOAVdgtm56Mrt1uGlyx7t7Y3olJINkVKnTPJjTYOwyU4iqWdtiBePOpZdAcYaWyMjjxhEx2zZQn\ny93rNcql9PQC7kmJxbGubUUBLheac+F2uxVIhkMW5nLgFj1fCSw33aY7ZjvdgdZG+3Ce2H2amYJj\nfbMa2JgLqycom9TNH+vkHM/kPGDmzEysc4xamHH389AQoHZLOLaHXZNciL2tQG9zxq5Oxm987NwI\ns3HbsiDCmO3U/uynb6OTva8XnIRLs9Q2iVGnB+ZeQCg5V8mpPdWD6+byCLJmhZzSIXHA8fnOnE5+\nvDBLheutNszZhR5qc0bOXc6iDU0Dxn/1l7j+HnwSSPrE+0DOhw4BAa44sK+cd+pmWruDvCUG1zE7\nOI1Wbybs8+AwHvFwWMXiEo71li3AusOUp8yPhzRyCc/x8aDPEc445fVPjWJOmqk13CvvAhVrFuwr\n5xm/fVE/ZskxiXjd668aYw7ACEzVryG/sGDZdN19N4oKnyopKSkpraO78EtR4VMlJSUlJSWnNnSn\naJ9akOXx+VUYb5lax+wrOWCM2bnmkYnb+os3gHjYxeYTCzxkoC3y8WYegfOSM04vVGF9jBEP7z5o\njM9cOWeM/TLgaGVxbuLVahTsJ8QmrLW4hBGWm/QgDEzhAE1VQDzp+XpBcFsrsi3r24EFWUnpcHO6\nMb6hoveIYOwHH+upDuDLXip2ToxZez8YxfFxnaGsWestqzG2j2Abth7W3YNVVXAAM7aLCAe2YzGa\nNccQIvRFpmdIDNBvYxOO060WFH9zHq7mhanMSHjIDpS6NIBC/owdcAy+c4LaHDlRo5s3cGFoIByy\nXoTi5qawvjEqtD/2OLJXb7UBSTOmZMS6MkdF15Qryn9PiESgxNn3PjDGplBsD6N5zpQd7oAL8vyY\nHngQHIx96q/D/LFEAQPn7EAecFMHOWHJuRvgi9zfnlHMDQ5QCIzBtRJHTuYayi1ebEPOcewe4OqL\n1XiU4BuC96ptQHG+5qefq8UWhDmYI4CnO+ZxDvJyqcVYFcI+2EUvlJVsIozP7aLmhyjwgND944e+\nYIzZIVpWi88Usx8+L2brMT/NezGfR1p1jD3cBIe1mY57Sgpc4AMjwL2fj+6g27xNkMKnSkpKSkrr\n6+76TlT4VElJSUlJyaUN3Slm5GaJOdZXYsJQ/N1wCw5RbsXUa0VRuBsVlGcmwz3IOLCTXutqi+RY\nxk+UniFghKPb0On9vVI42xg3Mb6JikTx9SAViLe3AGXaAuFW5bZJje8Ae8QdQSG/hwX7lEouz1VI\nlMIE2hr1gmRzIBAII7HhcbjfuNv3PfeiBVcjFeCzu9eHnIzj7Va8fQbOU1stvZaccwttQE7u8cBT\ncVnYJyFTW0gu/k+jVV+nfxhQ4GgLFex34Zz1LuD8ulEhuBe5QLsGMGeC/bHOIHLVmdyAmH77vi8Z\n43957afG2CMceGq6A8c1exdyJjkXNiMX6LzNquPZ/CKgw8ZOnA/OLPUPAk7bvR+F17YBzCVXlqrI\navTK5zuI8OL4IPD7Fx5Epu17V1CYfuA+4NnSF4/jvXKARJfHgJDz9xYb45rrOupeDsC1YonE/Dm4\nHe2qTh/He5qpfZhmxty7RS2cCh5GqEB9OdBkWD7c3D/7wY+MsSc9VgkuwrXAmqf5WXg/Hs9cL0Og\ng5vzWrTQ/GXHe3ghHh1we6a4FPzdQtnKXf2YhxykwVnJboT966/TvhJqb6S2UPwoqCgj3xj3hWB7\nTryDcxnsDIzgZevps7a9DZ9dR/fr8yHBF4EFSp9eCp8qKSkpKa0pFfN2G/UN9Yt1qEsqSsuNv/3W\n154yxi/+7JfG+NgXHzTGXH/WbrMa4/Eh/Cr2DkKNzq0O/ddncgoMJ7e68Tq+OywuwK9grhHiOiZb\nC4wE5hD8WudItK2ZqBlcooa81zT8IuUmqi3leNBfXLLTGMs6DY3bqvVfeSEB+HXccWvtusDUfNy5\nVFOXDDbx8HrG+qnDRjIMS1xHZwrE3RM3CmZDghst02vD3Q53BOBtcDXknevDr3KvBNzhhQfhDqir\nCr9sTR6Ydh4WvGcMNXGuu4RaRo8E3JFxhwiOwFqchmlraQgEgg0n9eexzrySrcY4yBfb3Dyp3+nX\ntcAEwnWr+Wkw6Jw/hU4iNz3QSWOWmtdmJoKM1NRjGTtFzu0/hDugS0OoA23pxjFbWcCcLH0Z8z9x\nP+gF19ppUTivHJ/nE6Pvq92O4+JNzZ2TKD5w/9GDxpjreLkhL1/D07MwHnEXmY4ruBY9M3EnlZGE\n49ozCKowN4/zxzF51y7jcycmHV1D+vv0u62sTFxv9TM41geL9hrjK7VoeNwzgPdcHsH84Wi3Rw/g\nc+z//dX/Ncbu8fi8Kt4DSnCtGrGMAUQSuJMMfzZx8+/gZNTsTk7oNZHhZKjj4z5owx3mBxf0rkG5\nUeki239PNlV34beieqaopKSkpKTklPpSVFJSUlJScmpD+HRheVHml+ZX1YS99ByavvplUmPTG4jJ\n+sJ+JN1XVAFhcQeD2TEguGVnLZx3NjAGm2jCYoAZbtxEN4MMiv3SqBGqTzTw2EwP6qEC4uihOJkp\n4qlZqasGSkSkvR7LWKgTQiF1AaiqwP4NewFn7TywR0REys8DjyXkAA/PhwOfrsIkViAeRjA1k3i4\nz/V3j30N5pP3LpzEawlDRVOj3If34dz89PVfGGN3H6pFo/gpiwnHw9V8uH4FOCghCoYJrp+yzwIX\nci0cIz8LddiIzAXGG7ahI0FYHExTLaWoj3RPhMnCzQfbaAoHRoyJhvGoOANGmpZu1D5aQvXzmpsM\nFMeGsEnqSpG1DSi1rRuNgrmLSxdhx3mqo/POx7Vy9nWcJwvh7H6KKnPM4Py5x+J8+PtifKBojzF+\n6wIQ6xChtvuP3i8iIu+dfM/4W2JasjF+6TQiyHyozpXHrqg4EZHS9tPGOD0etXOj1ACaUb+tH1i+\nobLWGHPXElboVmDS5NhEY8yRaIXpuhnl/XJsS0gCjm9dB8xv/AhkfAqfBQuTFDFIn2/VbXh8wVh1\nsRORb5WCa94+iUc4E1TLcHDnfmPMHUzcKSJxfAjHzOScw1wTzgg7kaI2Ozut8rnpLky0UUYbJSUl\nJaW1pZ4pKikpKSkp3b3a0J3iVHW/jHd0i2cusKNQ1BY788ovIX7teBliqZKScdvPzqryK4hzKtiv\nNz3lCLKvPPpbxvj5N1/COmKA07h+sqkK7kF3f6C1EKq/iwwBhr12Ae/PEVyMfjxCgTrY0Xe9ERgv\nPi3RGHc2wl0qTheiRsfLRg1+2SXpoKi0YOpwwLWRseGIy+IGwnysvX2AvJY9gd+4iepPXnpW1tLc\nBPDQTABwbu8guii46rZmq3EshgPguButpybA5PT1D8D5GKaOFvlZqCPkzhUhAXDU1l8AqoreCfdi\nyTbgqVdOUBcCD+xrd6vVGP9qHO9bkAb8vexsUHzjA8xfSwyQG3dE4S4g33jid4zxT/4VtXip2+AO\njX0YNYBDhI0Lv4q62zd/ik4T+fuwTyupQOfnT5bi7xTN9+4lYNjZUWBejyDMg3ff1JvaxuUAmVqo\nsXBsGBzALU14XNBPjcLZgZyQi0cAlS1wfHLt7BBF4P3WsceN8ZUaOEF7qQk1nw+uXa0sw6MSPvbF\nW3UHOtcmziXRYw9C2/fuOmKMW6qBVZN2wPHd3U6xd1S/aKJOF+yujY7FtdjbSTWOVB/dYMU1ur8Q\n9Zxnz+Jcbt+JRudbs3Q3/I9f/7nxt0M0x9lp76r1TQoCalb69FL4VElJSUlpfd055HNTpPCpkpKS\nkpKSU5rjkz0ALRKRim8f/9/SMtopLRVAk4V7thljLk4OjwI6GBqCiy6A8Nr4CNxWGhV0u5L3R7vx\nOq8IuM0ma+FGfOwbcFsevwJ0uNRDTXgplspMXQXcvYBD2I14+QrcYbl5QDltNup40A+86BEBvOZG\n8WvLy0AsAX76Pvl7Yz+4sfBgH/YpLRUuPi5ub++1GuP5GTgij+4GfuPGzNxo2dsPOMtMLs+MBCDI\ndhswE7sHNeyGREcCr7mw2GwXXHyueCqR1U2ke67CRcfnIH/b2t1Pqi4gXi86D8i7rxUOPI66C4yD\n45ML5hcozo2X57g/LtB+64IetcXuRsZ5z78GtzUjNHaNxhHa9qQOKk11a3dF0agzhoPCH4TcxoER\nwPi8HxPkmszPIBd0EwUFjOEYBMTqjz5W6LrnjivscFymrhfJWZgn1m7gxaT4RGPMSI8/V6bn4I7m\n5thCDnEOr8jMB3JuKIPLevc9FPNWgyL5tCQd4XJ4QFc9rtXoLDiZ2T1cQI97Ovuw37ZmCvugubpI\neJa7Z5gotpC7xFg8gV4nynEtbv8Srld2xiZGAX82leqPCTyz8KiKG1MXZ+Lz6uQvdSSel5AlpX/5\nqohIsYjclM+mIhGp2Pute6W6pe62C99O+em5culn72/Wtn2uUneKSkpKSkpKTqkvRSUlJSWlteXY\nxP/+mqVp2qnbL/VRbcho09nYIS09zasKbftHgTiXqOGwrQe5jXseBC6oIKcmd8HYVojs0atOJyrn\nHs5RU89dDwGjtPcC+XEhsz0VjjtNgJuiwuA4bb2FbWSXm2cIcGjlSbhS9z4K55otADjE1xtYo6UN\nmDAjDRjP2qd3ichJgsutiQpzo6KBJblpKTv9uKC86hoIRDflRnKz5EBq2ltXDwRyeH+JMeYmzXvz\nkOHq2l4REWsPcFJXHQrdo5xYanoGKHJyDNvu5Y/j4pEGB2lhJlymlQ3AfBkpOF5cKD3YBcdr8S7g\n+kZy9I21Az/3EvpklzB3MHA3A3k9/csfG+PsrBwRWd1UN4UaHvuHYz+CyRXb3Yf5kxyTaIw599cj\nGHNyshL7FLcP58yXG0NTDmlZHXAyZ9pGhQFXV9Hji4dK7jfGb5582xhPjerYXyNMu0QdSSKD4Xbu\nmQRS7LRhPmzdAuTNzuf0eDhRRyeA34cq8VqPJLzX1x/5ijH+t3eeN8bcnNccjuPRO4Rj5qAONC5H\n9PA1zNOc+5FHyljyUjXyU8uuYswF+7lb0ZmirgL4VqiJc0YOzlkrdazg7QqlRw2LRdR5h4JC+POg\nlq5RS7T+GfTUPU8Yfyuvh/v23DWEoxx5Ssf/if5w39/t0jTtCRE5fNsF15BynyopKSkpra07sHhf\n07QAEUm67YLrSOFTJSUlJaXfJH1RRH7yaV+8oTtF9zAf8XT4ycQVKlB9Co634ifhiOJMy2vXUaTL\nRdw8vn6T8JCP/vf77kUu5/unUZjcQxilvwdjbp5rJufX4hhcdF5elKdK7sHRSTgo2UWXtAdOuMFR\noLgVBzBJaxdwT1gE8NMIISRfLx2HXLwM7BEcDdefOxUJu9y3Iqvb6FSex3E0U2ug6tP4++weOOrY\nreZG7t7LNcBGjG/OfIDsyOQcuA3ZJRicAlzncoJyO66kRPxAa28EHl6h7NOCh4BP3ahp8NVzcP0W\n7QX+qmkGVhogXM+uV80T6+msxPsWHsB6OFPWYsbxYJTY5MSBnLX73kXMveR4ypwkx+LyENZ9tR7O\nSC8PPGrYno02Z5cXcA4YWfJ2nbt2wRgf2wN0f6EKSD+aiu37hoGQGbvv3AYsXnZWb769QmERNjdc\nz2ZPXJN8DFa14KJmtzMDwMM3B7DfnD/L4QdmL/y9qhXZpytTmB9eYeTQnoDj053CK+yzuEZHu3ud\n74l/Z/frmSto8ZWUgPNnXQLWXa+ZcE4x5irj9+YuaoXmjX1aIsfuqqbEZsxP+zKOa20tjoGZwgGW\np/X9Y2TKj0PcvbCvl2v09nYTEWkiyAW4K6VpWqGI3Ljtgh8jdaeopKSkpLS27jyjTbHD4ai6/WLr\nSz1TVFJSUlJaW3dQlwxN0x53OBw//azr2dCXYlpskrj5WeQS4VN2bS4soQC3sQbthLiglREIF6DH\nxqPl0KwTGR5/B+1tMotyjHFLAxxvSelwvHlQG5bOfmxXXCZaQd2ywq3qGQi8OD0AFMfYqHsCjras\nLUCpVqvVGIdFAr0Ek5Ov/hqFGaTpBd2aLxX0TiMAIDASaKStFWjm/pJ7jXG1L1AL58b2hwOb3WrE\na71pnTFRcKZ1d2CfqmexTi6AZ9QohBcnhoGEzU4XsichaWsvkFRAJNyZQf4YP/NvmLcr08BgjNlq\n2hAQERSI13KYQWoR3LhddL79qSs6Y0R2CXcNwD28e+suY3yx9Ly+b1S0nZuK815TTW5EutDdqIB7\n2Q4UmBgFR+3lKiBTbgPWO4zcz9FRbC8fdy56H6vBto/QPIiPxDzn4ITzb57BKp1F59EZuN48adkH\n9xwzxk//7F+NsVcEkD4jUy5iL9kOV/jJN3DtpmzFeeqogfNyJgrF9oywFxbwObLUh2VaZvGZsvMQ\n2mTVOTvZc2Zxyw3MH49YbHt7A95/6w44mfupzRm7XHu6caxHKWc5IRLHz0SPAMKSgFjNlN0cEYTz\nxGEGCxba1zmMHfP6Z1AH5bY+dACO4mvn4Rr3jdffkx3Vm6vN+0YrKSn5wdmzZyc+9OcXHQ7Hi/wH\nTdO+IyJHP+bNNee//anD4bBqmpYkIuMf+vdPJXWnqKSkpKT0a1FpaemfyCdItHE4HM+IyDMbWPUR\nEUnWNM318D1IRETTtL8WkesOh+P1dV/5IakvRSUlJSWlNeWQTarI+Oyr+Pj161+ihpyGm+84HI7/\nudF1behLMdA/SMLc5sUjATjiW1/4qjH+u2d+aIzvOwbsd6ESbrmZwbXRSxIVKp+/oCMsoUzIxmvA\nfEX74CisbQYmCQgELtyVCzTSSp3V2Vq0OIfs0Zhk4BBbOxCgfRxIo6kRrju+OR8agit1Xz6cfvVX\ngU/d3PQ3ZuxibYVr1erAe2ZmZhjjNhu2vaMUx2BuL9yhY4Nw+pqC4XacG4Zzr5cctewMzEuHW9Xb\nA8jw8mU4QeNScW78qDB+eFx/34EWci9S0b0b4aNbDcC67FbNLEahdM0FmMby9m81xtZ+HJvdW3Du\nuaB9oRPzyp4J11/fAFCYfRpYk9v0rGrrc/igiIhcPA/nZ5gNdlAAAAV3SURBVG0j3K+JqWi5xMEA\n85PAzQcKgfY4Y5RbgrHGqAN8ZATCJRIjqej88iVjHFaIv7NT2taB48SPNSwxOGcxE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations([phi0[0]], ['Initial Concentration'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the resized coefficients.\n", "\n", "First, the influence coefficients from the `PrimitiveBasis`." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(prim_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the influence coefficients from the `LegendreBases`." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(leg_model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, we are going to march forward in time by feeding the concentration fields back into the Cahn-Hilliard simulation and the MKS models. " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "for steps in range(time_steps):\n", " ch_sim.run(phi_sim)\n", " phi_sim = ch_sim.response\n", " phi_prim = prim_model.predict(phi_prim)\n", " phi_legendre = leg_model.predict(phi_legendre)\n", " " ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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N12AN+0Bd/AXcPJseOFXX3jW034xtJ+X57u3VbGz748XReXkB5aP5vP//uG1ej7fEbDaW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\nPre5HY+DCyEv16OEAM0yVk6+hvJNkAMRCQ5duBj6dwMLF6PcDfdh9/5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fGEeNrCaxxPtPJt/KDY833hrWLl2RhjjDHGGGOMMcYY042VZ2OMMcYYY4wxxhhzMdrh/94773kf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\noHNNryjenEgr9o8mmPnZiB5D5o0kDi7x2IQwThB9bXU1xoYXV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_concentrations((phi_sim[0], phi_prim[0], phi_legendre[0]), ('Simulation', 'Primiative', 'Legendre'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both MKS models seem to predict the concentration faily well. However, the Legendre polynomial basis looks to be better. Again, let's look at the difference between the simulation and the MKS models." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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yfYZ1RXvN/h417T7uDsq0fez37nh02k57e/X2zm5pj3dKexj0meuPsu15Pi/t6bS0Z2ij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\namVfGPvOkAol1cqivI32i0LZ3Llz2k7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igmVy2lbpv0RFc1QpiBwlVXJ5TKoMiiFHKZRO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Primative mse = 4.41565263124e-23\n", "Legendre mse = 7.97143930325e-28\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "draw_differences([(phi_sim[0] - phi_prim[0]), (phi_sim[0] - phi_legendre[0])], \n", " ['Simulaiton - Primiative','Simulation - Legendre'])\n", "\n", "print('Primative mse =', mse(phi_sim[0], phi_prim[0]))\n", "print('Legendre mse =', mse(phi_sim[0], phi_legendre[0]))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the resized influence coefficients, the `LegendreBasis` outperforms the `PrimitiveBasis` for the same value of `n_states`. The value of `n_states` does not necessarily guarantee a fair comparison between the two basis in terms of floating point calculations and memory used." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }