diff --git a/README.md b/README.md index 6594e65..a26aa26 100644 --- a/README.md +++ b/README.md @@ -186,6 +186,72 @@ metric.fit(Xi, Xj) dist = metric.score(Xi, Xj) ``` +## Dynamic stochastic shape metrics + +In addition to above, we provide methods to compare between stochastic and dynamic neural responses (e.g. biological neural network responses to stimulus repetitions as a function of time, or latent dynamic activations in diffusion models). The API is similar to `LinearMetric()`, but requires differently-formatted inputs. + + +**1) Dynamic stochastic shape metrics using** `GPStochasticMetric()` + +The first method models network response distributions as Gaussian Process, and computes distances based on the analytic solution to the bi-causal optimal transport distance between two stochastic processes. This involves computing class-conditional means and covariances for each network, then computing the metric as follows. + +```python +# Given +# ----- +# Xi : Tuple[ndarray, ndarray] +# The first array is (num_neurons*num_times x 1) array of means and the second array is (num_neurons*num_times x num_neurons*num_times) covariance matrices of first network. +# +# Xj : Tuple[ndarray, ndarray] +# Same as Xi, but for the second network's responses. +# +# alpha: float between [0, 2]. +# When alpha=2, this reduces to the deterministic shape metric. When alpha=1, this is the 2-Wasserstein between two Gaussians. When alpha=0, this is the Bures metric between the two sets of covariance matrices. + +# Fit alignment + +metric = GPStochasticMetric( + n_dims=num_neurons, # number of neurons + group="orth", # nuisance transformation + type='adapted', # adapted or non-adapted optimal transport distance + alpha=alpha # alpha described above +) + +metric.fit(Xi, Xj) + +# Evaluate the distance between the two networks +dist = metric.score(Xi, Xj) +``` + +**2) Dynamic stochastic shape metrics using** `GPStochasticDiff()` + +We also provide dynamic stochastic shape metrics based on the differentiable optimization. The metric computes the same metric as in the previous section, but instead of alternating minimization it uses a differentiable optimization strategy. + +```python +# Given +# ----- +# Xi : ndarray, (num_neurons*num_times x 1) +# First network's responses. +# +# Xj : ndarray, (num_neurons*num_times x num_neurons*num_times) +# Same as Xi, but for the second network's responses. +# + +# Fit alignment +GPStochasticDiff( + n_dims=num_neurons, # number of neurons + n_times=num_times, # number of time points + type="Bures" # distance type, options are Bures, Adapted_Bures, Knothe_Rosenblatt, Marginal_Bures +) + +# Evaluate the distance between the two networks +dist = metric.fit_score( + Xi, Xj, + lr=1e-3, # learning rate + tol=1e-5, # tolerance of optimization + epsilon=1e-6 # used for well-conditioning covariances +) +``` + ### Computing distances between many networks Things start to get really interesting when we start to consider larger cohorts containing more than just two networks. The `netrep.multiset` file contains some useful methods. Let `Xs = [X1, X2, X3, ..., Xk]` be a list of `num_samples x num_neurons` matrices similar to those described above. We can do the following: diff --git a/examples/multiset_demo.ipynb b/examples/multiset_demo.ipynb new file mode 100644 index 0000000..8c213cf --- /dev/null +++ b/examples/multiset_demo.ipynb @@ -0,0 +1,278 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/mnt/home/anejatbakhsh/anaconda3/envs/netrep/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy as sp\n", + "\n", + "from netrep.multiset import pairwise_distances, frechet_mean\n", + "from netrep.metrics import LinearMetric\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Helper functions for generating a mean pringle shape and some noisy, rotated, and scaled shapes from it \n", + "\n", + "* First, a (mean) pringle shape in 3 dimensions is generated.\n", + "* Then noisy pringles are sampled which are rotated and scaled using random rotations and scales (either in 3 dimensions or higher dimensions).\n", + "* Then the frechet_mean function is run on the unaligned shapes using alpha = 0 or 1 (refer to the documentaion of alpha in LinearMetric class).\n", + "* Finally the inferred mean is aligned with the true mean using the same alpha to visualze the inferred mean." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Generate a pringle shape in 3 dimensions\n", + "def generate_atlas(\n", + " params={'a':1,'b':1,'radius':1},\n", + " num_points=100\n", + " ):\n", + " # Generate points on a circle in the x-y plane\n", + " theta = np.linspace(0, 2 * np.pi, num_points)\n", + " x = params['radius'] * np.cos(theta)\n", + " y = params['radius'] * np.sin(theta)\n", + "\n", + " # Calculate the corresponding z values\n", + " z = (x**2 / params['a']**2) - (y**2 / params['b']**2)\n", + "\n", + " return np.stack((x,y,z)).T\n", + "\n", + "\n", + "# Generate noisy samples from the pringle and rotate/scale them\n", + "def generate_point_clouds(\n", + " mean,\n", + " n_samples=10,\n", + " d=3,\n", + " noise_std=1e-3,\n", + " scale_rng=[1,1]\n", + " ):\n", + " \n", + " Xs = np.zeros((n_samples,len(mean),d))\n", + " latent = np.zeros((n_samples,len(mean),mean.shape[1]))\n", + "\n", + " # Sample around each point in the mean\n", + " for k in range(len(mean)):\n", + " sample = sp.stats.multivariate_normal.rvs(\n", + " mean=mean[k],\n", + " cov=noise_std*np.eye(mean.shape[1]),\n", + " size=n_samples\n", + " )\n", + " latent[:,k] = sample\n", + "\n", + " # Roatate sampled shapes\n", + " for i in range(n_samples):\n", + " R = sp.stats.ortho_group.rvs(d)[:,:mean.shape[1]].T\n", + " scale = np.random.uniform(scale_rng[0],scale_rng[1])\n", + " Xs[i] = scale*latent[i]@R\n", + " \n", + " return Xs\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "alpha = 0\n", + "mean = generate_atlas()\n", + "Xs = generate_point_clouds(\n", + " mean,\n", + " d=3,\n", + " n_samples=5,\n", + " scale_rng=[.9,1.1]\n", + ")\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "ax.plot(\n", + " mean[:,0], mean[:,1], mean[:,2], \n", + " color='k',label='Mean',lw=3\n", + ")\n", + "\n", + "for i in range(len(Xs)):\n", + " ax.plot(\n", + " Xs[i][:,0], Xs[i][:,1], Xs[i][:,2], \n", + " color='b',lw=1,label='Sample' if i == 0 else None\n", + " )\n", + "\n", + "plt.legend()\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Xbar, aligned_Xs = frechet_mean(\n", + " Xs, group='orth', \n", + " return_aligned_Xs=True,\n", + " method='full_batch',\n", + " alpha=alpha\n", + ")\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "\n", + "ax.plot(\n", + " mean[:,0], mean[:,1], mean[:,2], \n", + " color='k',label='Mean',lw=3\n", + ")\n", + "\n", + "for i in range(len(Xs)):\n", + " ax.plot(\n", + " aligned_Xs[i][:,0], aligned_Xs[i][:,1], aligned_Xs[i][:,2], \n", + " color='b',lw=1,label='Aligned' if i == 0 else None\n", + " )\n", + "\n", + "plt.legend()\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "metric = LinearMetric(\n", + " alpha=alpha,\n", + " center_columns=True,\n", + " score_method='euclidean',\n", + ")\n", + "metric.fit(mean,Xbar)\n", + "mean,Xbar=metric.transform(mean,Xbar)\n", + "\n", + " \n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "ax.plot(\n", + " mean[:,0], mean[:,1], mean[:,2], \n", + " color='k',label='Mean',lw=3\n", + ")\n", + "\n", + "ax.plot(\n", + " Xbar[:,0], Xbar[:,1], Xbar[:,2], \n", + " color='b',label='Inferred',lw=3\n", + ")\n", + "plt.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "netrep", + "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": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/stochastic_process_metrics.ipynb b/examples/stochastic_process_metrics.ipynb new file mode 100644 index 0000000..f6c7567 --- /dev/null +++ b/examples/stochastic_process_metrics.ipynb @@ -0,0 +1,211 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/mnt/home/anejatbakhsh/anaconda3/envs/netrep/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], + "source": [ + "# %%\n", + "\"\"\"\n", + "Tests metrics betwen stochastic process neural representations.\n", + "\"\"\"\n", + "import numpy as np\n", + "from netrep.metrics import GPStochasticMetric,GaussianStochasticMetric,GPStochasticDiff\n", + "from netrep.utils import rand_orth\n", + "from sklearn.utils.validation import check_random_state\n", + "from sklearn.covariance import EmpiricalCovariance\n", + "\n", + "from numpy import random as rand\n", + "from netrep.utils import rand_orth\n", + "\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# %% Class for sampling from a gaussian process given a kernel\n", + "class GaussianProcess:\n", + " def __init__(self,kernel,D):\n", + " self.kernel = kernel\n", + " self.D = D\n", + "\n", + " def evaluate_kernel(self, xs, ys):\n", + " fun = np.vectorize(self.kernel)\n", + " return fun(xs[:, None], ys)\n", + "\n", + " def sample(self,ts,seed=0):\n", + " np.random.seed(seed)\n", + "\n", + " T = ts.shape[0]\n", + " c_g = self.evaluate_kernel(ts,ts)\n", + " fs = rand.multivariate_normal(\n", + " mean=np.zeros(T),\n", + " cov=c_g,\n", + " size=self.D\n", + " )\n", + " return fs" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "seed = 0\n", + "t = 5\n", + "n = 2\n", + "k = 100\n", + "\n", + "# Set random seed, draw random rotation\n", + "rs = check_random_state(seed)\n", + "if n > 1:\n", + " Q = rand_orth(n, n, random_state=rs)\n", + "else:\n", + " Q = 1\n", + " \n", + "# Generate data from a gaussian process with RBF kernel\n", + "ts = np.linspace(0,1,t)\n", + "gpA = GaussianProcess(\n", + " kernel = lambda x, y: 1e-2*(1e-6*(x==y)+np.exp(-np.linalg.norm(x-y)**2/(2*1.**2))),\n", + " D=n\n", + ")\n", + "sA = np.array([gpA.sample(ts,seed=i) for i in range(k)]).reshape(k,n*t)\n", + "\n", + "# Transform GP according to a rotation applied to individiual \n", + "# blocks of the full covariance matrix\n", + "A = [sA.mean(0),EmpiricalCovariance().fit(sA).covariance_]\n", + "B = [\n", + " np.kron(np.eye(t),Q)@A[0],\n", + " np.kron(np.eye(t),Q)@A[1]@(np.kron(np.eye(t),Q)).T\n", + "]" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DSSD: -7.450580596923828e-09 , Marginal SSD: 0.0 , Adapted SSD: 9.125060374972147e-09\n" + ] + } + ], + "source": [ + "# Using alternating optimization and Orthogonal Procrustes\n", + "# Compute dSSD\n", + "metric = GPStochasticMetric(n_dims=n,group=\"orth\")\n", + "dssd = metric.fit_score(A,B)\n", + "\n", + "# Compute aSSD\n", + "metric = GPStochasticMetric(\n", + " n_dims=n,\n", + " group=\"orth\",\n", + " type='adapted',\n", + ")\n", + "assd = metric.fit_score(A,B)\n", + "\n", + "# Compute mSSD\n", + "metric = GaussianStochasticMetric(group=\"orth\")\n", + "A_marginal = [\n", + " A[0].reshape(t,n),\n", + " np.array([A[1][i*n:(i+1)*n,i*n:(i+1)*n] for i in range(t)])\n", + "]\n", + "B_marginal = [\n", + " B[0].reshape(t,n),\n", + " np.array([B[1][i*n:(i+1)*n,i*n:(i+1)*n] for i in range(t)])\n", + "]\n", + "mssd = metric.fit_score(A_marginal,B_marginal)\n", + "\n", + "print('DSSD: ', dssd, ', Marginal SSD: ', mssd, ', Adapted SSD: ', assd)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Iteration 700, loss 0.04: : 0it [00:01, ?it/s]\n", + "Iteration 200, loss 0.00: : 0it [00:00, ?it/s]\n", + "Iteration 200, loss 0.00: : 0it [00:00, ?it/s]\n", + "Iteration 700, loss 0.01: : 0it [00:02, ?it/s]" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DSSD: 0.03943214 , Adapted DSSD: 0.0023483392 , Marginal SSD: 0.005165683 , Knothe Rosenblatt SSD: 0.0023267935\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "# Using differentiable optimization and Cayley orthogonal parameterization\n", + "\n", + "metric = GPStochasticDiff(n_dims=n,n_times=t,type=\"Bures\")\n", + "dssd = metric.fit_score(A,B,lr=1e-3,tol=1e-5,epsilon=1e-6)\n", + "\n", + "metric = GPStochasticDiff(n_dims=n,n_times=t,type=\"Adapted_Bures\")\n", + "assd = metric.fit_score(A,B,lr=1e-3,tol=1e-5,epsilon=1e-6)\n", + "\n", + "metric = GPStochasticDiff(n_dims=n,n_times=t,type=\"Knothe_Rosenblatt\")\n", + "kssd = metric.fit_score(A,B,lr=1e-3,tol=1e-5,epsilon=1e-6)\n", + "\n", + "metric = GPStochasticDiff(n_dims=n,n_times=t,type=\"Marginal_Bures\")\n", + "mssd = metric.fit_score(A,B,lr=1e-3,tol=1e-5,epsilon=1e-6)\n", + "\n", + "print('DSSD: ', dssd, ', Adapted DSSD: ', assd, ', Marginal SSD: ', mssd, ', Knothe Rosenblatt SSD: ', kssd)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "netrep", + "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": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/examples/stochastic_process_twostep.ipynb b/examples/stochastic_process_twostep.ipynb new file mode 100644 index 0000000..06b2ee5 --- /dev/null +++ b/examples/stochastic_process_twostep.ipynb @@ -0,0 +1,351 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 137, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import scipy as sp\n", + "from tqdm import tqdm\n", + "from scipy.stats import ortho_group\n", + "\n", + "from netrep.metrics import GPStochasticMetric, GaussianStochasticMetric\n", + "\n", + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": {}, + "outputs": [], + "source": [ + "def plot_line(estimated,true,variable,constant):\n", + " plt.figure()\n", + " \n", + " plt.plot(variable[list(variable.keys())[0]], [e['dssd'] for e in estimated], 'o', label=\"dSSD\")\n", + " plt.plot(variable[list(variable.keys())[0]], [e['assd'] for e in estimated], 'o', label=\"aSSD\")\n", + " \n", + " plt.plot(variable[list(variable.keys())[0]], [t['dssd'] for t in true], '--', c='tab:blue')\n", + " plt.plot(variable[list(variable.keys())[0]], [t['assd'] for t in true], '--', c='tab:orange')\n", + " \n", + " plt.xlabel(list(variable.keys())[0])\n", + " plt.ylabel(\"Distance\")\n", + " plt.title(\n", + " \"Varying \"+ list(variable.keys())[0]+\" - \"+\\\n", + " \"Constant \"+ list(constant.keys())[0]+\\\n", + " \" = \"+ str(constant[list(constant.keys())[0]])\n", + " )\n", + " plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define metrics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example two step process with analytical distances\n", + "\n", + "### Define processes" + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [], + "source": [ + "# Constants\n", + "n_dims = 1\n", + "T = 2\n", + "\n", + "# Define the two processes in terms of mean and cov\n", + "process_1 = lambda gamma, epsilon: (np.zeros(T), epsilon**2 * np.array([[1, gamma], [gamma, gamma**2]]))\n", + "process_2 = lambda gamma, epsilon: (np.zeros(T), epsilon**2 * np.array([[0, 0], [0, gamma**2]]))\n", + "\n", + "# Analytical distances\n", + "true_dist = lambda gamma, epsilon: {'dssd': epsilon, 'assd': np.multiply(epsilon, np.sqrt(2 * np.square(gamma) + 1))}\n", + "\n", + "# Metrics\n", + "metrics = {\n", + " 'dssd': GPStochasticMetric(n_dims=1, group=\"orth\", type=\"non-adapted\"),\n", + " 'assd': GPStochasticMetric(n_dims=1, group=\"orth\", type=\"adapted\") \n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test shape metric implementations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Stochastic metrics" + ] + }, + { + "cell_type": "code", + "execution_count": 142, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Estimated: {'dssd': 0.3, 'assd': 0.3117691451831648}\n", + "True: {'dssd': 0.3, 'assd': 0.3117691453623979}\n" + ] + } + ], + "source": [ + "# Example test, comparing analytical against estimated\n", + "gamma = 0.2\n", + "epsilon = 0.3\n", + "\n", + "A,B = process_1(gamma, epsilon), process_2(gamma, epsilon)\n", + "\n", + "estimated = {k:metrics[k].fit_score(A,B) for k in metrics.keys()}\n", + "true = true_dist(gamma,epsilon)\n", + "\n", + "print('Estimated: ', estimated)\n", + "print('True: ', true)" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 12/12 [00:00<00:00, 498.34it/s]" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Compute over gamma given epsilon\n", + "epsilon = 0.3\n", + "gammas = np.linspace(0.0,2.0,12)\n", + "\n", + "estimated, true = [], []\n", + "for gamma in tqdm(gammas):\n", + " A, B = process_1(gamma, epsilon), process_2(gamma, epsilon)\n", + " estimated.append(\n", + " {k:metrics[k].fit_score(A,B) for k in metrics.keys()}\n", + " )\n", + " true.append(\n", + " true_dist(gamma,epsilon)\n", + " )\n", + "\n", + "plot_line(estimated,true,{'$\\gamma$': gammas}, {'$\\epsilon$': epsilon})\n" + ] + }, + { + "cell_type": "code", + "execution_count": 133, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 12/12 [00:00<00:00, 521.49it/s]\n" + ] + }, + { + "data": { + "image/png": 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qyvj444+Nf//734aXl9clvw7z5s0zOnXqZPj4+Bienp5GVFSUcfvtt+db5+XatWuXce+99xr169c3PDw8DD8/P6NLly7G+++/b2RkZORqu2nTJqN///6Gr6+v4ePjY/Ts2TPPkOeifp0yMzONxx9/3GjdurXh5+dnVKtWzWjdurXx3//+N9fjXnjhBSMsLMxwcXHJ9fjL/V4o6H0r6PUK8sorrxiA8corrxTarqydPXvWeOyxx4zg4GDD09PTuPLKK40FCxbkanNuCPqFUx4YhmGsX7/eGDBggBEcHGy4u7sbjRs3Nl566SUjOzu7HI9AnInFMEqxF6KIFFlOTg6hoaEMHDgw11+3ZWnIkCFs376d3bt3l8vrSdl7++23GTt2LCdPntQyBSL/0GgpEQf54YcfOHbsWL5rWpWGi+cW2b17Nz/99BM9evQok9cTx9i2bRt169ZVsBG5gM7ciJSz9evX8+eff/LCCy9Qu3btfCd8Kw0hISGMGDGCBg0acODAASZPnkxmZiabN2+mUaNGZfKaUv46dOhA7dq1+emnnxxdikiFoQ7FIuVs8uTJfPnll7Rp04bp06eX2evExsby9ddfk5CQgKenJzExMbz88ssKNk7EMAx27NjB/fff7+hSRCoUnbkRERERp6I+NyIiIuJUFG5ERETEqVS5Pjc2m42jR4/i5+dX7KnORURExDEMwyA1NZXQ0FBcXAo/N1Plws3Ro0dLvAaNiIiIONahQ4cuucxIlQs3fn5+gPnFKe5aNCIiIuIYKSkphIeH2z/HC1Plws25S1H+/v4KNyIiIpVMUbqUqEOxiIiIOBWFGxEREXEqCjciIiLiVKpcn5uislqtZGdnO7oMp+Hh4XHJoXsiIiKlQeHmIoZhkJCQwOnTpx1dilNxcXEhMjISDw8PR5ciIiJOTuHmIueCTWBgID4+PprorxScmzgxPj6eevXq6WsqIiJlSuHmAlar1R5satWq5ehynEqdOnU4evQoOTk5uLu7O7ocERFxYuoEcYFzfWx8fHwcXInzOXc5ymq1OrgSERFxdgo3+dBlk9Knr6mIiJQXXZYSERGR0mGzwoE1kJYIvkEQ0RlcXMu9DIUbJ9ajRw/atGnDO++84+hSRETE2e2YBwuehJSj5/f5h0LsqxA9qFxL0WWpMmK1Gazde4K5W46wdu8JrDbDofXExcVx2223ERoaipeXF3Xr1mXw4MH8/fff9jYrVqygV69e1KxZEx8fHxo1asTw4cPJysoCYPny5VgsFiwWCy4uLgQEBNC2bVueeOIJ4uPjHXVoIiLiaDvmwaxhuYMNQEq8uX/HvHItx6HhZvLkybRq1cq+iGVMTAw///xzoY/59ttvadq0KV5eXrRs2ZKffvqpnKotugXb4un66lJu/WgdD8/cwq0fraPrq0tZsM0xASA7O5u+ffuSnJzM7Nmz2blzJ9988w0tW7a0z+ezY8cOYmNjueKKK1i5ciVbt27l/fffx8PDI08n4J07d3L06FF+++03nnzySRYvXkyLFi3YunWrA45OREQcymY1z9iQ3x/x/+xb8JTZrpw49LJU3bp1eeWVV2jUqBGGYfDZZ58xePBgNm/eTPPmzfO0X7NmDbfeeisTJ07k2muvZcaMGQwZMoRNmzbRokULBxxBXgu2xTP6y0153uKE5AxGf7mJyXe0I7ZFSKm/bnp6OqNHj2b27Nn4+fnx2GOP2e/bvn07e/fuZcmSJURERAAQERFBly5d7G0WLlxIcHAwr732mn1fVFQUsbGxeV4rMDCQ6tWrExwcTOPGjRk8eDBt27Zl9OjRrF69utSPTUREKrADa/KescnFgJQjZrvIbuVSkkPP3AwcOJCrr76aRo0a0bhxY1566SV8fX1Zt25dvu3fffddYmNjefzxx2nWrBkvvPAC7dq144MPPijnyvNntRlM+HFHYdmVCT/uKJNLVI8//jgrVqxg7ty5LFy4kOXLl7Np0ybAnGPGxcWF7777rsCh2MHBwcTHx7Ny5cpiv7a3tzejRo3i119/JSkp6bKOQ0REKpm0xNJtVwoqTJ8bq9XKzJkzSU9PJyYmJt82a9eupU+fPrn29e/fn7Vr1xb4vJmZmaSkpOS6lZUNcSeJT84o8H4DiE/OYEPcyVJ93bS0ND755BPeeOMNevfuTcuWLfnss8/IyckBICwsjPfee4/nnnuOGjVq0KtXL1544QX27dtnf46hQ4dy66230r17d0JCQrjuuuv44IMPivz1atq0KQD79+8v1WMTEZEKLu1Y0dr5BpVtHRdweLjZunUrvr6+eHp6MmrUKObMmUN0dHS+bRMSEggKyv3FCQoKIiEhocDnnzhxIgEBAfZbeHh4qdZ/oaTUgoNNSdoV1d69e8nKyqJjx472fTVr1qRJkyb27TFjxpCQkMBXX31FTEwM3377Lc2bN2fRokUAuLq6Mm3aNA4fPsxrr71GWFgYL7/8Ms2bNy9SZ2HDMM9GaT4bEZEqwmaDla/Dwqcv0dAC/mHmsPBy4vBw06RJE7Zs2cL69esZPXo0w4cPZ8eOHaX2/OPGjSM5Odl+O3ToUKk998UC/bxKtV1p8/PzY+DAgbz00kv88ccfdOvWjRdffDFXm7CwMO68804++OADtm/fTkZGBlOmTLnkc//1118A1K9fvyxKFxGRiiQtCb68Hpa+CIYNIrr+c8fFf+D+sx37SrnOd+PwcOPh4UHDhg1p3749EydOpHXr1rz77rv5tg0ODiYxMfc1u8TERIKDgwt8fk9PT/torHO3stIhsiYhAV553tpzLEBIgBcdImuW6utGRUXh7u7O+vXr7ftOnTrFrl27CnyMxWKhadOmpKenF9imRo0ahISEFNoG4OzZs0ydOpWrrrqKOnXqFP8ARESk8ti3AqZ0hX3LwN0HhkyGu/4HN30B/hcNmPEPhZs+L/d5bircJH42m43MzMx874uJiWHJkiU88sgj9n2LFi0qsI9OeXN1sTB+YDSjv9yEhdyD4s4FnvEDo3F1Kd1LN76+vowcOZLHH3+cWrVqERgYyP/93//h4mJm1y1btjB+/HjuvPNOoqOj8fDwYMWKFXz66ac8+eSTAHz44Yds2bKF6667jqioKDIyMvj888/Zvn0777//fq7XS0pKIiMjg9TUVDZu3Mhrr73G8ePHmT17dqkel4iIVDDWHPjpcbNzcJ1mMHQ6BJp9LokeBE2v0QzF48aNY8CAAdSrV4/U1FRmzJjB8uXL+eWXXwAYNmwYYWFhTJw4EYCHH36Y7t278+abb3LNNdcwc+ZMfv/9d6ZOnerIw8gltkUIk+9ox4Qfd+TqXBwc4MX4gdFlMgwc4PXXXyctLY2BAwfi5+fHv//9b5KTkwFzyH39+vWZMGEC+/fvx2Kx2LcfffRRADp06MDq1asZNWoUR48exdfXl+bNm/PDDz/QvXv3XK/VpEkTLBYLvr6+NGjQgH79+jF27NhCz6CJiIgTcHWDGz+B3z+Ffi+Bx0ULTbu4lttw78JYjHM9QR1g5MiRLFmyhPj4eAICAmjVqhVPPvkkffv2BczlA+rXr8/06dPtj/n222955pln2L9/P40aNeK1117j6quvLvJrpqSkEBAQQHJycp5LVBkZGcTFxREZGYmX1+X1i7HaDDbEnSQpNYNAP/NSVGmfsalMSvNrKyIi5WjPEkg+BO1HOLSMwj6/L+bQcOMI5RVuJDd9bUVEKhlrDix/GVa9BS5ucM9iCG3jsHKKE24qXJ8bERERcbDkI/D9SDj4zzxy7e6EOk0dW1MxKNyIiIjIebsWwpx/wdmT4OEHg96DFtc7uqpiUbgRERER05L/wKo3zf+HtDZHQ9Vs4NCSSkLhRkREREzeNcx/O/wL+r0Abp6OraeEFG5ERESqsqx08Khm/j/mAQi7AiIqxvxxJeXwGYpFRETEAXKy4OenYGoPyEwz91kslT7YgM7ciIiIVD0n4+C7u+DoZnN71wJoeaNjaypFCjciIiJVyY65MPcByEwBr+pw3RRoMsDRVZUqhRsREZGqIDsDFj4Dv31kbod3hBs+gerhjq2rDKjPTVmxWSFuFWz9zvzXZnV0RaxYsYJevXpRs2ZNfHx8aNSoEcOHDycrK8ve5qOPPqJ169b4+vpSvXp12rZta1/bC+D555/HYrFgsVhwc3Ojdu3aXHXVVbzzzjsFLngqIiIVwKJnzwebLo/AiP85ZbABnbkpGzvmwYInIeXo+X3+oRD7arkv+24vaccOYmNjefDBB3nvvffw9vZm9+7dfP/991itZvD69NNPeeSRR3jvvffo3r07mZmZ/Pnnn2zbti3XczVv3pzFixdjs9k4ceIEy5cv58UXX+SLL75g+fLl+Pn5OeIQRUSkMN0eg/2roe8L0KiPo6spUwo3pW3HPJg1DLhoya6UeHP/TZ+XWcBZsGABL774Itu2bcPV1ZWYmBjeffddoqKiWLhwIcHBwbz22mv29lFRUcTGxtq3582bx0033cTIkSPt+5o3b57nddzc3OwrgIeGhtKyZUv69u1L69atefXVV3nxxRfL5PhERKQYss/CX/Oh1VBz2y8IRv0KLs5/0cb5j7A82azmGZuLgw2c37fgqTK7RJWens7YsWP5/fffWbJkCS4uLlx33XXYbDaCg4OJj49n5cqVBT4+ODiYdevWceDAgWK/dtOmTRkwYACzZ8++nEMQEZHScGwXfNQbZt8D2y74vVwFgg3ozE3pOrAm96WoPAxIOWK2i+xW6i9/ww035Nr+9NNPqVOnDjt27GDo0KH88ssvdO/eneDgYDp16kTv3r0ZNmyYfXXV8ePHc/3111O/fn0aN25MTEwMV199NTfeeCMuRfiBaNq0KQsXLiz14xIRkWLY8jX8byxkn4Fqdc7POlyFVI0IV17SEku3XTHt3r2bW2+9lQYNGuDv70/9+vUBOHjwIK6urkybNo3Dhw/z2muvERYWxssvv0zz5s2Jj48HICQkhLVr17J161YefvhhcnJyGD58OLGxsdhstku+vmEYWCyWMjk2ERG5hKx0+GEM/DDKDDaRV8Go1RDV09GVlTuFm9LkG1S67Ypp4MCBnDx5ko8++oj169ezfv16gFyjocLCwrjzzjv54IMP2L59OxkZGUyZMiXX87Ro0YL777+fL7/8kkWLFrFo0SJWrFhxydf/66+/iIyMLN2DEhGRS0v6Cz7qBVu+BIsL9Hga7vwB/IIdXZlD6LJUaYrobI6KSokn/343FvP+iM6l/tInTpxg586dfPTRR3TrZl7yWr16daGPqVGjBiEhIaSnpxfYJjo6GqDQNgB///03CxYsYNy4ccWsXEREisRmNbs1pCWafyRHdAYXV/O+k3Fw7G/wDYYbPi6Trg+VicJNaXJxNYd7zxoGWMgdcP65XBP7yvlvxlJUo0YNatWqxdSpUwkJCeHgwYM89dRT9vs//PBDtmzZwnXXXUdUVBQZGRl8/vnnbN++nffffx+A0aNHExoaSq9evahbty7x8fG8+OKL1KlTh5iY82uN5OTkkJCQkGcoeJs2bXj88cdL/dhERKq8/KYY8QuBAa+ZI3CbXg2D3ofGA8C3juPqrCB0Waq0RQ8yh3v7h+Te7x9apsPAXVxcmDlzJhs3bqRFixY8+uijvP766/b7O3ToQFpaGqNGjaJ58+Z0796ddevW8cMPP9C9e3cA+vTpw7p16xg6dCiNGzfmhhtuwMvLiyVLllCrVi37c23fvp2QkBDq1atHjx49mDVrFuPGjWPVqlX4+vqWyfGJiFRZ56YYuXjASmo8zLrTvB+g3TAFm39YDMPI7/qJ00pJSSEgIIDk5GT7KKFzMjIyiIuLIzIyEi8vr8t7ocJOH1ZBpfq1FRGpKmxWeKdF4SNx/cPgka1O/xlT2Of3xXRZqqy4uFb5a54iInKZLjnFCGU6xUhlpctSIiIiFZWDpxiprBRuREREKioHTzFSWSnciIiIVFQRnc1RUQWymH1uymCKkcpM4SYfVayPdbnQ11REpBiS/jI7E7u4msO981W2U4xUZgo3F3B3dwfgzJkzDq7E+ZybJdnVVT+AIiIFMgxYOwmmdINVb5n7ogfBTV+YU4pcqIynGKnMNFrqAq6urlSvXp2kpCQAfHx8tFZSKbDZbBw7dgwfHx/c3PQtJyKSrzMn4Yf7YdfP5nbSDjPsWCz/TNR3jaYYKSJ90lwkONhch+NcwJHS4eLiQr169RQWRUTyc3A9fHc3pBwGVw/o/zJceY8ZbM7RFCNFpnBzEYvFQkhICIGBgWRnZzu6HKfh4eGBi4uugoqI5GKzwZr3YMl/wLBCzQYwdDqEtHZ0ZZWawk0BXF1d1T9ERETK1qk4WPayGWxa3AgD3wFPP0dXVekp3IiIiDhKrSi4+nXAgHbDc1+GkhJTuBERESkvNhusfgsa9IS67c197Yc7tiYnpE4QIiIi5SEtCb68Hpa+AN+NgKx0R1fktHTmRkREpKztWwGz7zWHcbt5Q/enwKOao6tyWgo3IiIiZcVmhRWvwYpXAQPqNDNHQwU2dXRlTk3hRkREpCxkpMDM22D/KnO77R0w4HXw8HFsXVWAwo2IiEhZ8PAFdx9wrwbXvg2tb3Z0RVWGwo2IiEhpseaALRvcvcHFBa6bAmdOQO1Gjq6sStFoKRERkdKQfAQ+GwjzHz2/z6emgo0DKNyIiIhcrl0LYUpXOLgG/poPpw44uqIqTZelRERESsqaba4LteY9czukNdw4DWpEOLauKk7hRkREpCROHzJX8j68wdzu8C/o9wK4eTq2LlG4ERERKTabDb68AY7vBM8AGPwBRA9ydFXyD/W5ERERKS4XFxjwCtS9EkatVLCpYBwabiZOnMiVV16Jn58fgYGBDBkyhJ07dxb6mOnTp2OxWHLdvLy8yqliERGpsk7Gwd6l57ejesHdC6FGfYeVJPlzaLhZsWIFY8aMYd26dSxatIjs7Gz69etHenrhi4n5+/sTHx9vvx04oF7pIiJShnbMhQ+vglnD4eS+8/tddAGkInJon5sFCxbk2p4+fTqBgYFs3LiRq666qsDHWSwWgoODy7o8ERGp6rIzYOEz8NtH5nbdDuDi7tia5JIqVORMTk4GoGbNmoW2S0tLIyIigvDwcAYPHsz27dvLozwREXFWNivErYKt35n/2qxwYi980vd8sOnyMNz1E1QPd2ytckkVZrSUzWbjkUceoUuXLrRo0aLAdk2aNOHTTz+lVatWJCcn88Ybb9C5c2e2b99O3bp187TPzMwkMzPTvp2SklIm9YuISCW1Yx4seBJSjp7f510Dss9CTgZ414TrPoTG/RxXoxSLxTAMw9FFAIwePZqff/6Z1atX5xtSCpKdnU2zZs249dZbeeGFF/Lc//zzzzNhwoQ8+5OTk/H397+smkVEpJLbMQ9mDQMK+Cis3QTunAMBYeValuSVkpJCQEBAkT6/K8RlqQceeID58+ezbNmyYgUbAHd3d9q2bcuePXvyvX/cuHEkJyfbb4cOHSqNkkVEpLKzWc0zNgUFG4DMVPBTH8/KxqHhxjAMHnjgAebMmcPSpUuJjIws9nNYrVa2bt1KSEhIvvd7enri7++f6yYiIsKBNbkvReUn9ajZTioVh/a5GTNmDDNmzGDu3Ln4+fmRkJAAQEBAAN7e3gAMGzaMsLAwJk6cCMB//vMfOnXqRMOGDTl9+jSvv/46Bw4c4J577nHYcYiISCWUlli67aTCcGi4mTx5MgA9evTItX/atGmMGDECgIMHD+JywTwCp06d4t577yUhIYEaNWrQvn171qxZQ3R0dHmVLSIiziA7o2jtfIPKtg4pdRWmQ3F5KU6HJBERcUKGAVu+gv89BjlnC2loAf9QeGQruLiWW3mSv0rXoVhERKTcLH8F5o4xg03QualHLBc1+mc79hUFm0pI4UZERKqWFteDpz/0ehb+tQpu+gL8LxqU4h8KN32uBTErKV2WEhER52YYkLAVQlqd33fmJPhcMBu+zWqOikpLNPvYRHTWGZsKpjif3xVmhmIREZFSl5EC8x+B7XNgxP/M0AK5gw2YQSayW7mXJ2VDl6VERMQ5xf8BU7vDtu8BCxzb6eiKpJzozI2IiDgXw4DfPoZfngZrFgSEw42fQngHR1cm5UThRkREnMfZ0zDvQfhrnrnd5GoYPCnvZShxago3IiLiPP7+nxlsXNyh73+g02iwXDzMW5ydwo2IiDiPNrdB4nZoeQOEtXd0NeIg6lAsIiKV15mTMH8sZCSb2xYLxL6sYFPF6cyNiIhUToc2wHd3Q/IhyEyBGz52dEVSQSjciIhI5WKzwdr3Ycl/wJYDNSIh5gFHVyUViMKNiIhUHukn4IdRsHuhud38ehj4Lnhpxnk5T+FGREQqh/g/YcbNkHoUXD1hwKvQfoRGQ0keCjciIlI5+IeZ/9ZqBEOnQ3CLQptL1aVwIyIiFVdGyvlLTtVqwZ2zzRmHPX0dW5dUaBoKLiIiFVPcSvjgCtgy4/y+wGYKNnJJCjciIlKx2Kyw/BX4fDCkJcKGj8wRUiJFpMtSIiJScaQmwOx7zbM2AG3ugKtfAxf9LS5Fp3AjIiIVw96lMPs+SD8G7tXg2reg9S2OrkoqIYUbERFxvJNx8OWNYFghsLk5GqpOY0dXJZWUwo2IiDhezUjo+oi5VlTsRHD3dnRFUokp3IiIiGPsXgS1GprBBqDXs5qQT0qFwo2IiJQtmxUOrDFHPvkGQd0rYfnL8Ou7ENoO7v4F3DwUbKTUKNyIiEjZ2TEPFjwJKUfP73N1B2u2+f+w9oDhkNLEeSnciIhI2dgxD2YNI094ORdsOj8E/V4o97LE+WniABERKX02q3nGprCzMtu+N9uJlDKFGxERKX0H1uS+FJWflCNmO5FSpnAjIiKlLy2xdNuJFIPCjYiIlK6cTNg+p2htfYPKthapktShWERESs+JvfDdXRD/xyUaWsA/FCI6l0tZUrXozI2IiJSObbPhw+5msPGuCV3/DVj+uV3on+3YV8DFtZyLlKpAZ25EROTyZJ+FBeNg4zRzu14M3PAJBIRBaJu889z4h5rBJnqQQ8oV56dwIyIiJWcY8PlgOLQesEC3sdDjaXD95+MlehA0vSb3DMURnXXGRsqUwo2IiJScxQLthpt9ba6fCg17523j4gqR3cq/NqmyFG5ERKR4ss5A8iGo08Tcbns7NL0avGs4ti6Rf6hDsYiIFF3S3/BRL/jiOjhz8vx+BRupQBRuRESkaDZ/BVN7wLG/wJYDpw84uiKRfOmylIiIFC4zDX56DP742txu0AOu/wh8Ax1alkhBFG5ERKRgidvh2xFwfBdYXKDn0+b8NS468S8Vl8KNiIgUbPU7ZrDxCzHnrqnfxdEViVySwo2IiBTsmjfA3Qt6j4dqtR1djUiR6LyiiIicF/8HLHzGnJwPwCsABr2vYCOVis7ciIiIGWZ++xh+eRqsWVCnKbS9w9FViZSIwo2ISFWXkQzzHoQdc83txgOgydWOrUkqJavNYEPcSZJSMwj086JDZE1cXS5eOLXsOfSy1MSJE7nyyivx8/MjMDCQIUOGsHPnzks+7ttvv6Vp06Z4eXnRsmVLfvrpp3KoVkTECR3ZCFO6mcHGxR36vwy3fg0+NR1dmVQyC7bF0/XVpdz60ToenrmFWz9aR9dXl7JgW3y51+LQcLNixQrGjBnDunXrWLRoEdnZ2fTr14/09PQCH7NmzRpuvfVWRo4cyebNmxkyZAhDhgxh27Zt5Vi5iIgT2PQFfNLfnIyvej24+xeIGWOuFyVSDAu2xTP6y03EJ2fk2p+QnMHoLzeVe8CxGMa5XmOOd+zYMQIDA1mxYgVXXXVVvm1uvvlm0tPTmT9/vn1fp06daNOmDVOmTLnka6SkpBAQEEBycjL+/v6lVruISKWz/1f47Fpz1e5BH4B3dUdXJJWQ1WbQ9dWleYLNORYgOMCL1U/2uqxLVMX5/K5Qo6WSk5MBqFmz4NOha9eupU+fPrn29e/fn7Vr1+bbPjMzk5SUlFw3EZEq6+zp8/+v3wXuWQI3faFgIyW2Ie5kgcEGwADikzPYEHeywDalrcKEG5vNxiOPPEKXLl1o0aJFge0SEhIICgrKtS8oKIiEhIR820+cOJGAgAD7LTw8vFTrFhGpFGw2+PU9eLcVHNt1fn9YO12GksuSlFpwsClJu9JQYcLNmDFj2LZtGzNnzizV5x03bhzJycn226FDh0r1+UVEKrz0E/D1LbDoWXNk1J+l+3tWqq7tR5P5at3BIrUN9PMq42rOqxBDwR944AHmz5/PypUrqVu3bqFtg4ODSUxMzLUvMTGR4ODgfNt7enri6elZarWKiFQqB9bC9yMh5Qi4esKAV6D9XY6uSpyAzWYw5qtN7D9xptB25/rcdIgsvxF4Dj1zYxgGDzzwAHPmzGHp0qVERkZe8jExMTEsWbIk175FixYRExNTVmWKiFQ+NhusehOmX2MGm1oN4d4lcMXdugwlJfbHodNk5lgBcHGx8ECvRgxqHcpz1zbDghlkLnRue/zA6HKd78ahZ27GjBnDjBkzmDt3Ln5+fvZ+MwEBAXh7ewMwbNgwwsLCmDhxIgAPP/ww3bt358033+Saa65h5syZ/P7770ydOtVhxyEi4jA2KxxYA2mJ4BsEEZ3BxRW2fAVL/mO2aXUzXPMWePo6tlaptDYeOMV7S3azYtcxXr6uJbd1rAfAje3rcmN784pLaHVvJvy4I1fn4uAAL8YPjCa2RUi51uvQcDN58mQAevTokWv/tGnTGDFiBAAHDx7ExeX8CabOnTszY8YMnnnmGZ5++mkaNWrEDz/8UGgnZBERp7RjHix4ElKOnt/nHwqxr0LrW2Hb99DiBnMZBZ2tkRL4bf9J3l28m9V7jgPg6mLh8Kn8L0PFtgihb3RwhZihuELNc1MeNM+NiDiFHfNg1jDMgbYXs8BNn0OzgQo1UiLr9p3g3cW7WbvvBABuLhZuaFeX+3tGEVGrmkNqKs7nd4XoUCwiIsVgs5pnbPINNv9Y8JQ5OZ/FtdzKEufx3+V7WbvvBO6uFm5sH879PaIIr+nj6LKKTOFGRKSyObAm96WoPAyzE/GBNRDZrdzKksrJMAxW7T5O0xA/+3Dth3s3ol5Nb0b3aEhYdW8HV1h8CjciIpVNWuKl2xSnnVRJhmGwfNcx3l28my2HTjOyayTPXhsNQPuIGrSPqOHgCktO4UZEpLIp6qUm36BLt5EqxzAMlv6dxHtLdvPHYXPZI083FzzdKsy8vpdN4UZEpLIJboE5g0hBfW4s5qipiM7lWJRUBkv/TuStRbvYdsRcZ9Hb3ZU7OtXj3qsalOsMwmVN4UZEpDIwjPMjn2o3gm6PwarXyRty/mkT+4o5343IBVbtPs62Iyn4eLhyZ0wE93ZrQG1f55vFX+FGRKSiSz4M398L3Z+AqJ7mvt7PQEirAua5eQWiBzmmVqkwrDaDn7bGE1m7Gi3CAgAY1T0KHw9XRnZtQM1qHg6usOxonhsRkYps58/ww2g4e8pcQmHMhtxnZAqaoViqLKvNYP6fR3l/6R72JKXRs0kdpt3VwdFlXTbNcyMiUtnlZMGSCbD2A3M7tC3cOC1vcHFx1XBvASDHamPulqNMWraHfcfTAfD3cqNtvRrYbAYuDpgp2FEUbkREKppTB+C7u+DIRnO742joOwHcnK9vhBSd1WYUuLTBgm3xTPz5bw78s0J3dR937ukayfDO9fHzcndk2Q6hcCMiUpEkH4YPu0FGMngFwOD/QrNrHV2VONiCbfF5FqUMuWBRyuNpWRw4cYaa1Ty4t1sD7oyJwNez6n7EV90jFxGpiPzDoPEAOLkXbvwUqtdzdEXiYAu2xTP6y015Bv7HJ2cw+stNTL6jHUOvqEu21cZNV4RTrQqHmnPUoVhExNFO7gOv6uBT09zOOgOu7uZNqjSrzaDrq0tznbG5WEiAF6uf7OWQ1bfLU3E+v51nOkIRkcpo22yYchX8cL85lw2Ah4+CjQCwIe5kocEGzDM4G+JOllNFlYPOXYmIOEJ2BvwyDn7/1Nw+ewoyU8x+NiL/WLQjoUjtklILD0BVjcKNiEh5O74Hvh0BiVvN7a5joef/gat+JUtuoUVckduZlk4oDbosJSJSnv6cBR9eZQYbn9pwx/fQZ7yCjZCWmcN/l+9h8vK99n0jOtenhk/BlygtmH1uOkTWLIcKKw/9NImIlJesM7D0BchOh/rd4PqPwD/E0VWJg6VkZPP5mv18vDqO02eyqebhyi1XhlOjmgduri5MvL4lo7/cBOS7ihjjB0Y7fWfi4lK4EREpLx4+cON02L3QXCdKyyRUaclns5n2axyfro4jJSMHgAa1q/FAr4b4eZ3/eI5tEcLkO9rlmecm+IJ5biQ3DQUXESlLW2aY6z+1u9PRlUgFsnhHIo9+s4XUTDPURNWpxkO9G3Ftq9ACz8IUNkNxVaC1pUREHC0zDX56DP74Glw9oV4M1G7o6Kqkgmga4sfZbCuNg3x5qHcjBrQIuWRQcXWxEBNVq5wqrNwuO9xkZGTg5aVe2iIidonbzdFQx3eBxQWuehxqRjq6KnGQE2mZfLQqjqSUDN66uQ0AdWv4MOf+LjQP9a9SC1qWlxKNlrLZbLzwwguEhYXh6+vLvn37AHj22Wf55JNPSrVAEZFKwzBg42fwUS8z2PiFwPAfofvj6l9TBSWlZvDS/3bQ9dVlTFmxl9mbj7AnKdV+f8u6AQo2ZaRE4ebFF19k+vTpvPbaa3h4eNj3t2jRgo8//rjUihMRqTQMA+aMgh8fgpwMaNgHRq2G+l0dXZmUs8SUDCb8uJ1ury7jo1VxnM220qpuAJ8Mv4KoOr6OLq9KKNFlqc8//5ypU6fSu3dvRo0aZd/funVr/v7771IrTkSk0rBYoFYUWFyh97PQ+WFw0VRiVc2avccZMe03snJsALQJr87DfRrRo3EdLBadpSkvJQo3R44coWHDvB3jbDYb2dnZl12UiEilYBiQcRq8a5jb3f4NTQZAcEuHliXlK8dqw83VDLJtw2vg7+VGRK1qPNy7Ed0a1VaocYAShZvo6GhWrVpFRERErv3fffcdbdu2LZXCREQqtIxkmPcQnNgD9ywGd2+zX42CTZVx6OQZ/rt8L38ePs2PD3TFxcWCt4cr8x/sRpC/p0KNA5Uo3Dz33HMMHz6cI0eOYLPZmD17Njt37uTzzz9n/vz5pV2jiEjFcmQTfHcXnNoPLm5wcB1E9XR0VVJODpxIZ9KyPczedIQcmzlV3Lp9J+jcsDZgTq4njlXiSfxWrVrFf/7zH/744w/S0tJo164dzz33HP369SvtGkuVJvETkSKzWeHAGkhLBN8gc66a3z6Ghc+ALRsC6sHQaVD3CkdXKuUg7ng6Hyzdww9bjmD9J9R0a1Sbh3o34sr6WtuprBXn81szFIuI5GfHPFjwJKQcPb/PzcscCQXQ9FoY/MH5/jZSqV1q9t8dR1O49v1V/JNp6NGkDg/2akT7CL3/5aXMZyj+7bffsNlsdOzYMdf+9evX4+rqyhVX6K8YEanEdsyDWcPIvUwh54NN2zth0PvmCCmp9BZsi8+zblNIgBeP92/M9e3CAWgW4kfLsABq+3ryUO9GtA6v7qBqpShKNE5xzJgxHDp0KM/+I0eOMGbMmMsuSkTEYWxW84zNxcHmQnuXgmErt5Kk7CzYFs/oLzflCjYA8ckZjJ31J3M2HQbAYrEw874YPhlxpYJNJVCicLNjxw7atWuXZ3/btm3ZsWPHZRclIuIwB9bkvhSVn5QjZjup1Kw2gwk/7igsxjJh/g57/xpvD80yXVmUKNx4enqSmJiYZ398fDxublqLU0QqsbS8v9suq51UWBviTuY5Y3Ox02ey2RB3spwqktJSonDTr18/xo0bR3Jysn3f6dOnefrpp+nbt2+pFSciUq5sNohbWbS2vkFlW4uUuaTUwoNNcdtJxVGi0yxvvPEGV111FREREfZJ+7Zs2UJQUBBffPFFqRYoIlIu0o7BnH/B3iWXaGgB/1CI6FwuZUnp2388nfq1qxHoV7T5aIraTiqOEoWbsLAw/vzzT7766iv++OMPvL29ueuuu7j11ltxd3cv7RpFRMrW/tXw3UhISzCHe7e5HX7/BLCQu2PxP6OjYl/RKt+V0G/7T/Lu4t2s2XucRWO70yGyJiEBXgVemrJgTsjXIVJz2FQ2Je4gU61aNe67777SrEVExDFSE8xgU7sJDJ0OQdHQoEfeeW78Q81gEz3IUZVKCazbd4J3F+9m7b4TALi5WNi4/xRRdXwZPzCa0V9uAvKNsYwfGJ1rvhupHEo8id/u3btZtmwZSUlJ2Gy5h0Q+99xzpVJcWdAkfiICmIteXjhPzZavzdDiUe38votnKI7orDM2lYRhGKzZe4J3l+y2dwh2d7Uw9IpwRnePIrymj71tQfPcjB8YTWyLkHKvXfJX5jMUf/TRR4wePZratWsTHByca3Ewi8XCpk2bil91OVG4ERH2LTeXULj9e/BTx2BndCYrh86vLOX0mWw8XF24+cpwRvWIIqy6d77tLzVDsThemYebiIgI7r//fp588skSF+koCjciVZjNCstfgZWvAwZccTdc+7ajq5JSYBgG6/adpFODmvY/uD9auY8jp88yqnuUFrN0AmW+/MKpU6cYOnRoiYoTEXGIlHj4/h44sNrcbjcM+r3k2JrkshmGwZK/knhv6W7+PJzMJ8OvoHcz82zcvVc1cHB14iglCjdDhw5l4cKFjBo1qrTrEREpfXsWw+z74MwJ8PCFa9+BVvoDrTKz2QwW/ZXIe0t2s/1oCgDe7q4cPX3WwZVJRVCicNOwYUOeffZZ1q1bR8uWLfMM/37ooYdKpTgRkcu2fQ58O8L8f1BLczRU7YaOrEgug81m8Mv2BN5dspu/E1IB8PFwZVhMfe7pFkltX08HVygVQYn63ERGRhb8hBYL+/btu6yiypL63IhUMZmpMLWHObS730vgrr4XlZnNZnD1e6v4OyEVX083RnSuz91dI6lZzcPRpUkZK/MOxaVl5cqVvP7662zcuJH4+HjmzJnDkCFDCmy/fPlyevbsmWd/fHw8wcHBRXpNhRuRKuDQb1D3ivNDvTNSwEs/75WR1Wbwv63x9GkWiI+HebFh8Y5E/jySzN1d6lPdR6GmqijO53eJ1pYqLenp6bRu3ZpJkyYV63E7d+4kPj7efgsMDCyjCkWkUsnJgl/+Dz7pA+v+e36/gk2lk2O1MXvTYfq+tYKHvt7MV+sO2u/rEx3E2L6NFWykQCWeofjw4cPMmzePgwcPkpWVleu+t956q0jPMWDAAAYMGFDs1w4MDKR69erFfpyIOLFTB+C7u+HI7+b2hTMLS6WRbbUxZ/MRJi3bw4ETZwCo7uOOp7tD/xaXSqZE4WbJkiUMGjSIBg0a8Pfff9OiRQv279+PYRi0a9eutGvMo02bNmRmZtKiRQuef/55unTpUmDbzMxMMjMz7dspKSllXp+IlLO/5sPc+yEjGbwCYPB/odm1jq5KimnWb4d4f9luDp00RzzVrObBvd0acGdMBL6eJf5bXKqgEkXhcePG8dhjj7F161a8vLz4/vvvOXToEN27dy/T+W9CQkKYMmUK33//Pd9//z3h4eH06NGj0BmRJ06cSEBAgP0WHh5eZvWJSDnLyYSfn4RvbjeDTdgV8K9VCjYVjNVmsHbvCeZuOcLavSew2vLv6rl8VxKHTp6ltq8HT1/dlFVP9GR0jygFGym2EnUo9vPzY8uWLURFRVGjRg1Wr15N8+bN+eOPPxg8eDD79+8vfiEWyyU7FOene/fu1KtXjy+++CLf+/M7cxMeHq4OxSLOIP4P+KgX2HIg5gHoPR7c1A+jIilo3aanr27KqTPZ9GgcSL1a5jpPOxNSWbX7GLd3jMDbQ2t4SW5lPkNxtWrV7P1sQkJC2Lt3L82bNwfg+PHjJXnKEuvQoQOrV68u8H5PT088PTXvgYhTCmkNA14D/zBoEuvoauQiC7bFM/rLTVz8F3R8cgYPfr0FgFuuTOGVG1oB0CTYjybBfuVbpDilEoWbTp06sXr1apo1a8bVV1/Nv//9b7Zu3crs2bPp1KlTaddYqC1bthASolVbRaqE7AxYPB7a3gnBLcx9V450bE2SL6vNYMKPO/IEmwu5WKBFWEC51SRVR4nCzVtvvUVaWhoAEyZMIC0tjW+++YZGjRoVeaQUQFpaGnv27LFvx8XFsWXLFmrWrEm9evUYN24cR44c4fPPPwfgnXfeITIykubNm5ORkcHHH3/M0qVLWbhwYUkOQ0Qqk+N7zJmGE7fC3qUwei24qi9GRbUh7mSuS1H5sRkQVce3nCqSqqREvxkaNDi/GFm1atWYMmVKiV78999/zzUp39ixYwEYPnw406dPJz4+noMHz89tkJWVxb///W+OHDmCj48PrVq1YvHixflO7CciTuTPb2H+I5CVBj61IXaigk0Fl5hStDWeklILD0AiJVGiDsUNGjTgt99+o1atWrn2nz59mnbt2mn5BREpHVlnYMGTsMk8e0tEV7jhY/DXpeiKKiUjm89+3Y+Physv/O+vS7b/+t5OxETVumQ7kTLvULx//36sVmue/ZmZmRw5cqQkTykikltqInwxBJJ2ABbo/gRc9YTO2FRQyWezmfZrHJ+ujiMlI4crImoQ7O9JYkpmvv1uLEBwgBcdImuWd6lSBRTrt8S8efPs///ll18ICDjfEcxqtbJkyRLq169fasWJSBVWrfY/t0C44SNz4UupcE6fyeLT1XFM+3U/qZk5ADQM9OXOmAg8XC3c/9VmLJAr4Pyz4hfjB0bj6mK5+ClFLluxLku5uJhz/lksFi5+mLu7O/Xr1+fNN9/k2msr7gRauiwlUkHYrHBgDaQlgm8QRHSGnAywuJ5fuTs10fzXL8hxdUqBvli7n1cX7CTtn1DTOMiXh3o3YkCLEHtoKWiem/EDo4ltocuLUnRldlnKZrMBEBkZyW+//Ubt2rVLXqWIVF075pl9aS5c/6laHXB1h8axcO3b5j6FmgrNz8udtMwcmgb78XDvRvRvHozLRWdiYluE0Dc6mA1xJ0lKzSDQz7wUpTM2UpZK1KE4P6dPn64Ui1nqzI2Ig+2YB7OGQUEzoHjXgAc3gY/6YlQkSakZfLRyH1F1fLmlQz3AXLl71e7jdG9cJ0+oESltxfn8LtHaUq+++irffPONfXvo0KHUrFmTsLAw/vjjj5I8pYhUBTarecamsKndXD3NxS+lQkhMyWDCj9vp9uoyPloVx7tLdpOZYw4ocXN1oWfTQAUbqXBKFG6mTJliX4By0aJFLF68mAULFjBgwAAef/zxUi1QRJzIgTW5L0XlJy3BbCcOFZ98lvFzt9HttWVM+3U/mTk22oRX5+XrW+LhWqKPDpFyU6IxlQkJCfZwM3/+fG666Sb69etH/fr16dixY6kWKCJOJC2xdNtJmZix/iDPz9tOltXsZ9k+ogYP925Et0a1sVh0lkYqvhKFmxo1anDo0CHCw8NZsGABL774IgCGYeQ7/42ICGCOiirNdlJqDMOwB5cWYf5kWW10iKzJI70bERNVS6FGKpUShZvrr7+e2267jUaNGnHixAkGDBgAwObNm2nYsGGpFigiTuLoZrBmgX8opMSTf78bi3l/ROfyrq7KOnAinUnL9uDr6c5zA6MBaFW3Oj891I3oUA26kMqpROHm7bffpn79+hw6dIjXXnsNX19z4bP4+Hjuv//+Ui1QRCo5w4ANU2HhM+BRDXqPh/mPQkFTu8W+Ai6uDii0atl3LI1Jy/byw5YjWG0GHm4uPNCrITWreQAo2EilVmpDwSsLDQUXKUdnT8HcB+Dv+eZ202th8AcQtyrvPDf+YWawiR7kmFqriD1JqXywdA/z/jiK7Z/f/j2a1OHBXo1oH1HDscWJFKJMJvGbN28eAwYMwN3dPdcyDPkZNEi/nESqvMO/w3d3wemD4OoB/V6EDveBxWIGmKbX5J2hWGdsytQPm4/w6KwtnPuTtnfTQB7s3Yg24dUdWpdIaSvymRsXFxcSEhIIDAy0L8OQ7xNaLBW6U7HO3IiUMcOAtZNg8Xiw5UCN+jB0OoS2dXRlTslqMwqd/Tcrx4aHm/k7+1hqJle9toyujWrzUK9GtKyr+YSk8iiTMzfnll64+P8iIrlYLHB8lxlsoofAoPc0KV8ZKWzdpvCaPry/ZA/pWTl8MdKcoqOOnycrn+hJHT9PR5UsUi6K3aHYZrMxffp0Zs+ezf79+7FYLDRo0IAbbriBO++8U8MFRaoqmw3OndUd8CrU7woth5phR0rdgm3xjP5yU54xZ/HJGYz6cpN922IxOw83qGMO/FCwkaqgWNNMGobBoEGDuOeeezhy5AgtW7akefPm7N+/nxEjRnDdddeVVZ0iUlHZbLD6bZhxk/l/AHdvaHWTgk0ZsdoMJvy4o7BFLAAY1DqUhY9cZQ82IlVFsc7cTJ8+nZUrV7JkyRJ69uyZ676lS5cyZMgQPv/8c4YNG1aqRYpIBZV+HOb8C/YsNrd3/g+aDXRsTVXAhriTuS5FFeTWDvVoFORXDhWJVCzFOnPz9ddf8/TTT+cJNgC9evXiqaee4quvviq14kSkAtv/K0zpagYbNy8Y9L451FvKXFLqpYNNcdqJOJtihZs///yT2NjYAu8fMGCAVgUXcXY2K6x4HT67FlLjoXYTuHcZtBumy1DlYO3eE3y4Yl+R2gb6eZVxNSIVU7EuS508eZKgoILXfAkKCuLUqVOXXZSIVGD/Gwsbp5v/b3M7XP26OfOwlBnDMFiz9wTvLtnNhriTl2xvAYIDzGHhIlVRscKN1WrFza3gh7i6upKTk3PZRYlIBXbFSNgxF/pPhDa3Oroap2YYBit3H+e9JbvZeMD8w9HD1YWbrwynWYgf/zdnm9nugsecO3c2fmB0rvluRKqSYoUbwzAYMWIEnp75DyXMzMwslaJEpAKxWeHIRgjvYG6HtIJHtoGnRuCUtW1HUhj+6QYAPNxcuK1DPUZ1jyI4wLzcVLOaR555boL/mecmtkWIQ2oWqQiKFW6GDx9+yTYaKSXiRFLi4ft74NB6GPkLhLU39yvYlAnDMNh7LI2GgeYIp5Z1A+jVNJD6taoxqnsDAv1z96GJbRFC3+jgQmcoFqmKtHCmiORvz2KY/S84cxw8fOH6qeZ6UFLqbDaDhTsSeX/pbvYdS2fVkz2p7WueITcMQ5OjilBGyy+ISBVhzYFlL5oT8wEEtTTXhqrd0KFlOSObzWDB9gTeW7KbvxNSAajm4crWI8n0bBIIoGAjUgIKNyJyXvJh+G4kHFpnbl95D/R7Cdw1pLg0WW0GP22N5/2lu9mVmAaAr6cbIzrXZ2TXSGpU83BwhSKVm8KNiJz3149msPH0Nxe8bK4lVcrC8bRM/j3rD7KsNvy83LirSyQju0QS4OPu6NJEnILCjYic1+Ff5sR87UdAzQaOrsZp5FhtrNt3kq6NagMQ5O/FvVdF4uHqyogu9QnwVqgRKU3qUCxSlZ0+CEtfgmve1AioMpBttTFn8xEmLdvDgRNnmP9gV1qEBTi6LJFKSR2KReTS/v4f/DAaMpLNGYavfcvRFTmNrBwbszcdZtLyPRw6eRYw56Q5fOqswo1IOVC4EalqcrJg0XOwfrK5HdYeujzs2JqcRFaOjVm/H2Ly8r0cOW2Gmtq+Hvzrqihu71QPHw/9yhUpD/pJE6lKTsbBd3fB0c3mdswD0Hs8uGl0TmmwGQbvL91NYkomdfw8GdU9its61MPbw9XRpYlUKQo3Is7IZoUDayAtEXyDIKKzuT3zNshMAe8aMGQKNIl1dKWVWka2lblbjnBj+3BcXSx4ubvyRP+mpGZkc0uHeni5K9SIOILCjYiz2TEPFjwJKUfP7/MPhe7jwM0TAjvBjZ9AQF3H1VhJWG1GvksbnM2y8tX6A0xZsY/jaZl4ubsyuE0YADe019dVxNEUbkScyY55MGsYudeJxlwj6seHIPYVuHIkuGro8aUs2BafZ1HKIH9PukTVZuXuYxxPywIgrLo3Hq4ujipTRPKhcCPiLGxW84zNxcEG/tlngTXvQYd7y7mwymfBtnhGf7kpz1cyMSWT2ZuPABBe05sHejbkurZ18XBTuBGpSBRuRJzFgTW5L0XlYUDKEbNdZLdyK6uysdoMJvy4I9+IeE6AtzuLHu2uPjUiFZT+3BBxFmmJpduuitoQdzLXpaj8JJ/NZvPB0+VTkIgUm8KNiLNI3Fa0dr5BZVtHJXb6TBbT18QVqW1SauEBSEQcR5elRJzB0S2w+u1LNLKYo6YiOpdHRZXKyfQsPlm9j8/WHCAtM6dIjwn000rpIhWVwo2IMwhtY07IlxIP278HLOTuWGwx/4l9BVzUT+RCb/yyk09/jeNMlhWApsF+JKRkcPpMdr7tLUBwgDksXEQqJl2WEqmMDAO2zIDkI+f39X8Jhn4KN30B/iG52/uHwk2fQ/Sg8q2zEkhKzeBMlpUWYf5MvbM9Pz3UjVeub4kFeyS0O7c9fmA0ri4X3ysiFYVWBRepbDJTYf5Y2DoL6sXA8PngetFJ2PxmKNYZGxJTMvhwxT5uvjKcJsF+ABw6eYZdian0ahqIxXI+sOQ3z01IgBfjB0YT2yIkz3OLSNmqNKuCr1y5ktdff52NGzcSHx/PnDlzGDJkSKGPWb58OWPHjmX79u2Eh4fzzDPPMGLEiHKpV8ThErbCtyPgxB6wuEKjfmDJ5wSsi6uGe18gPvksU5bv5evfDpGVYyMpNYMPbmsHQHhNH8Jr+uR5TGyLEPpGB+c7Q7GIVGwODTfp6em0bt2au+++m+uvv/6S7ePi4rjmmmsYNWoUX331FUuWLOGee+4hJCSE/v37l0PFIg5iGLBxGvz8FFgzwT8MbvwU6nVydGUV2pHTZ5m8fA+zfjtMltUGwBURNbj5yvAiPd7VxUJMVK2yLFFEyoBDw82AAQMYMGBAkdtPmTKFyMhI3nzzTQCaNWvG6tWrefvttxVuxHllpsK8B2H7HHO7cSwMmQw+6tBamNcW/M1Hq/aRbTWvvHeMrMnDvRsRE1Ur1+UnEXE+lWq01Nq1a+nTp0+uff379+eRRx5xTEEi5cHiCsd2gosb9HneHBWlD+dL8vd2J9tq0DmqFg/1bkSnBjoDI1JVVKpwk5CQQFBQ7gnIgoKCSElJ4ezZs3h7e+d5TGZmJpmZmfbtlJSUMq9T5LIZhnlzcQEPHxg6HTJSIPxKR1dWIcUdT+eDpXvo3zyIfs2DAbizUwTtI2pwZX2d4RKpaipVuCmJiRMnMmHCBEeXIVJ0Z0/DvAcgtC10+7e5r04Th5ZUUe1JSmPSsj3M3XIEmwF/xafQNzoIi8VCNU83BRuRKqpShZvg4GASE3Ovi5OYmIi/v3++Z20Axo0bx9ixY+3bKSkphIcXrTOhSLk7vBG+GwGnD8LuxdD2TvANdHRVFc7uxFTeX7qHH/88yrnJLHo3DeSh3o3Un0ZEKle4iYmJ4aeffsq1b9GiRcTExBT4GE9PTzw9Pcu6NJHLYxiw7r+waDzYsqFGfbhxmoJNPt5auJP3l+2xh5q+0UE83LsRLcICHFuYiFQYDg03aWlp7Nmzx74dFxfHli1bqFmzJvXq1WPcuHEcOXKEzz//HIBRo0bxwQcf8MQTT3D33XezdOlSZs2axf/+9z9HHYLI5TtzEn64H3b9bG5HD4ZB74OXPqzPMQzDfkamZd3qGAYMaBHMA70a0jxUXycRyc2hMxQvX76cnj175tk/fPhwpk+fzogRI9i/fz/Lly/P9ZhHH32UHTt2ULduXZ599tliTeKnGYqlQsnJgv92gpN7wdUTYl+GK0ZqNNQ//jx8mveW7KZdRA3u79EQMIPO3mPpNAz0dXB1IlKeivP5reUXRBxtw0ewbrI5IiqklaOrKTdWm1Hg7L9bDp3m3cW7WLbzGAC1fT1Y81RvPNy0HJ5IVVVpll8QqZLST0D6MQhsam5feQ+0ud0c8l1FFLRu052d6rEu7hQrd5mhxsUCQ9qEMaZXQwUbESkyhRuR8nRgDXx3N7h5wr9Wmv1qLJYqF2xGf7mJi08Zxydn8NovuwBz2YPr2oYxpmdDImtXK/8iRaRSU7gRKQ82G6x+E5a9DIYNajeG9ONVrtOw1WYw4ccdeYLNhbzdXfnp4W4KNSJSYgo3ImUtLQlm3wf7lpnbrW+Da94Aj6r34b0h7mSuS1H5OZttJSE5Q+FGREpM4UakLO1bAbPvhbREcPeBa96ENrc5uiqHMAyDFbuSitQ2KbXwACQiUhiFG5GytO6/ZrCp08wcDXWuE3EVYhgGy3ce490lu9ly6HSRHhPo51W2RYmIU1O4ESlLg/8Lv74NPZ6uUp2GL/TV+oM888M2ALzcXXC1WEjPsubb1gIEB5jDwkVESkpjK0VK054l8Mv/nd+uVgv6vVilgo3NZnA8LdO+PbB1KEH+ntx3VQNWPdGLN29qjQUzyFzo3Pb4gdH2+W5EREpCk/iJFJfNag7pTksE3yCI6GyuDbX8ZVj1FmDATV9A9CBHV1qubDaDBdsTeG/JbrzcXZlzf2f7kglZObZc89QUNM/N+IHRxLYIKffaRaTi0yR+ImVlxzxY8CSkHD2/zzcIvKrD8Z3m9hV3Q6O+DinPEaw2g5+2xvP+0t3sSkwDwNfTjYMnzxBRyxzxdPEEfLEtQugbHVzgDMUiIpdD4UakqHbMg1nD4OJZWtISzZubFwyZDC2ud0h55c1qM5j/51HeX7qHPUlmqPHzcuOuLpHc3aU+1X08Cn28q4uFmKha5VGqiFQxCjciRWGzmmdsCpt+zivAXNG7iljyVyIPz9wCgL+XGyO7NmBEl/oEeLs7tjARqfIUbkSK4sCa3Jei8pOWaLaL7FY+NZWzbKuN/cfTaRTkB0DvZkF0qF+T7k3qMCwmAj8vhRoRqRgUbkSKIi2xdNtVIlk5Nr7fdJhJy/aQmWNj1RM98XJ3xdXFwjf/6mTvNCwiUlEo3IgUhXcR513xDSrbOspRZo6Vb38/zOTlezly+iwAtX092JOURoswc00sBRsRqYgUbkQu5dR+WPrCJRpZwD/UHBZeyWVkW/nmt0NMXr6XhBRzqHYdP09GdY/itg718PZwdXCFIiKFU7gRKcyOuTD3QchMBg9fyErDnG7uwo7F/5y9iH0FXCr/B/++Y+mMn7cdgCB/T0Z3j+KWDvXwcq/8xyYiVYPCjUh+sjNg4TPw20fmdnhHuOETOLo57zw3/qFmsKmkk/adycph44FTdGtUB4DoUH/u6FSPJkF+DL0iXKFGRCodhRuR/Kyfcj7YdHkEej0Dru5QPRyaXpN3huJKeMYmPTOHL9Yd4KOV+0jJyGb54z0Jq+4NwItDWjq4OhGRklO4EclPp9GwfxV0HJV3tmEX1wo/3NtqMwqc/Tc1I5vP1x7g41X7OHUmG4Dwmt7Enz5rDzciIpWZwo0IQPZZ2PARdLofXN3AzRPu+N7RVZVIQes2PRnbhEMnz/Lx6jiSz5qhpn4tH8b0bMiQtmG4u2odXRFxDgo3Isd2wbcjIGk7ZCRD72cdXVGJLdgWz+gvN+WZRzkhOYNHvvkDTzcXMnNsNKhTjQd7NWRgq1DcFGpExMko3EjV9sdMmD8WstOhWiDU7+roikrMajOY8OOOfBeIMDDHdHm6ufDKDa0Y1DpUi1SKiNNSuJGqKSsdfnoCtnxpbkdeBdd/DH6VdxK+DXEnc12KupgBpGTkEOzvpWAjIk5N4UaqnmM7zdW9j/0NFhfo/hRc9VilHPF0ob3HUovULim14AAkIuIMFG6k6jFscOoA+AbDDR9X+JFPl5KemcPbi3bx+doDRWof6OdVxhWJiDiWwo1UDTbr+TMzgc3gli8huDX41nFsXaXA082FRX8lkmW14e5qIduaX68bs89NcIA5LFxExJlpmIQ4v4StMLkzHFh7fl/DPpU22MQnn+W1BX+TlWMDwM3VhecHNmfaXVfy3i1tsGBfEMLu3Pb4gdHqbyMiTk9nbsR5GQZsnAY/PwXWTFj0LIxcBJV0Jesjp8/y32V7+Pb3w2RZbdSt4cNtHesB0LNpoL3d5Dsseea5CQ7wYvzAaGJbhJR73SIi5U3hRpxTRgr8+DBsn21uN+oHQ6ZUymBz6OQZ/rt8D99tPGy/5NQxsiaNg3zzbR/bIoS+0cEFzlAsIuLsFG7E+RzdAt/dBSf3gYsb9B4PMQ+AS+W6CptttfF/c7Yye9MRcmxmqOnSsBYP9mpEpwa1Cn2sq4uFmKjC24iIOCuFG3EuiTvgk75gzYKAcLjxUwjv4OiqSsTd1YXElExybAbdGtXm4d6NuKK+OgOLiFyKwo04l8Bm0Li/OTpq8CTwqTxhYE9SGpOX7+XJ2CYE+pvDtcdd3ZSH+zSiXb0aDq5ORKTyULiRyu/IJqgVBV4BZp+a6z8CN69K079mV2Iq7y/dw/w/j2IYUN3HnWevjQagabC/g6sTEal8FG6k8jIMWPdfWDQeml0LN04zA427t6MrK5K/4lP4YOkeftoWj/HP1DT9ooO4rm2YYwsTEankFG6kcjpzEuaOgZ0/mduGzexn4+bp2LqKwDAMHv1mCz9sOWrfN6BFMA/0akjz0AAHViYi4hwUbqTyObQBvr0LUg6Dqwf0fxmuvKfSXIayWCzUqOaBxQLXtAzhwV6NaBLs5+iyRESchsKNVB42G6x5D5b8Bwwr1GwAQ6dDSGtHV1aoLYdO896S3TzQq6G9Y/D9PRpyW4d6NApSqBERKW0KN1J5ZJyG9VPMYNPiRhj4DnhW3HCw8cAp3l2ym5W7jtn3fTriSgDq+HlSx6/iX0ITEamMFG6kYrFZ4cAaSEsE3yCI6Hx+wUufmnDDJ3BiN7Qb7rDLUFabUejsvxviTvLekt2s3nMcMCfUu75tGGN6NnRIvSIiVY3CjVQcO+bBgich5XxHWzz9oM3tMOBVc7t+F/PmIAu2xedZtynkgnWbxn6zhdmbjwDg5mLhxvZ1ub9HQ+rV8nFUySIiVY7CjVQMO+bBrGGAkXt/Zqp5KapOM7hihCMqs1uwLZ7RX266uELikzMY/eUmJt/RjrYRNfjxz6MMvSKc+3tEUbeGQo2ISHmzGIZx8e9qp5aSkkJAQADJycn4+2uCtArBZoV3WuQ+Y3Mxv1B4dNv5S1TlzGoz6Prq0lxnbC5kwVx5e8m/u3P6TDah1SvHXDsiIpVFcT6/K9dKguKcDqwpPNgApB412znIhriTBQYbMM83xSdn8MehZAUbEREHU7gRx0tLLN12ZSAx5WyR2iWlFhyARESkfFSIcDNp0iTq16+Pl5cXHTt2ZMOGDQW2nT59OhaLJdfNy8urHKuVUucbVLrtysCPf8QXqV2gn74XRUQczeHh5ptvvmHs2LGMHz+eTZs20bp1a/r3709SUlKBj/H39yc+Pt5+O3DgQDlWLKXGmgPpx83h3v6hhTS0gH+Y2a6c2GwGGdlW+/aILvUpbOC5BXPUVIfIyrMKuYiIs3J4uHnrrbe49957ueuuu4iOjmbKlCn4+Pjw6aefFvgYi8VCcHCw/RYU5Li/6KWEko/AZ9fCV0PNDsWxr2JGhIsjxD/bsa+US2diq83gxz+OEvvuSt5bstu+v2vD2rx5U6vCKmT8wOhc892IiIhjODTcZGVlsXHjRvr06WPf5+LiQp8+fVi7dm2Bj0tLSyMiIoLw8HAGDx7M9u3bC2ybmZlJSkpKrps42K6FMKUrHFwLx3dD0g6IHgQ3fQ7+Ibnb+oea+6MHlWlJVpvB3C1H6P/OSh78ejO7EtOYs/kI2VYbYAbq69uFM/mOdgQH5L70FBzgxeQ72hHbIiS/pxYRkXLm0Hlujh8/jtVqzXPmJSgoiL///jvfxzRp0oRPP/2UVq1akZyczBtvvEHnzp3Zvn07devWzdN+4sSJTJgwoUzql2KyZpvrQq15z9wOaQ03ToNaUeZ29CBoek3BMxSXgRyrjblbjjJp2R72HU8HIMDbnZFdIxneuT7urrnzf2yLEPpGBxc6Q7GIiDhWpZvELyYmhpiYGPt2586dadasGR9++CEvvPBCnvbjxo1j7Nix9u2UlBTCw8PLpVa5wOmD8N3dcPg3c7vDv6DfC+B20fpKLq4Q2a3cynp78S4mLdsLQHUfd+7t1oBhMRH4ebkX+BhXFwsxUbXKq0QRESkmh4ab2rVr4+rqSmJi7iG+iYmJBAcHF+k53N3dadu2LXv27Mn3fk9PTzw9tUChw8170Aw2ngEw+IMyv8xUkKwcGykZ2dT2Nb8nbu1Qj+82HmZE50jujInA17PS5X0REbmIQ/vceHh40L59e5YsWWLfZ7PZWLJkSa6zM4WxWq1s3bqVkBD1d6jQrnkLGvSAUSsdEmwyc6x8ue4APd9YzjNzttn3163hw69P9mJ0jygFGxERJ+Hw3+Zjx45l+PDhXHHFFXTo0IF33nmH9PR07rrrLgCGDRtGWFgYEydOBOA///kPnTp1omHDhpw+fZrXX3+dAwcOcM899zjyMORip/bDvhXQfri5XSsKhs0t9zIysq3M+v0Qk5fvtc8wnGMzz974/3Ppyc3V4YMGRUSkFDk83Nx8880cO3aM5557joSEBNq0acOCBQvsnYwPHjyIi8v5D59Tp05x7733kpCQQI0aNWjfvj1r1qwhOjraUYcgF9sxF+Y+CJkpUL0eRPUs9xIysq3MWH+QKSv2kpSaCUCQvyeju0dxS4d6eLk7Zo0qEREpe1o4U0pPdgYsfAZ++8jcrtsBbvzEDDjl7PO1+3lurjlFQGiAF6N7NmRo+7oKNSIilVRxPr8dfuZGnMSJvfDtCEj409zu8jD0ehZcCx51VJrSM3OITz5Lw0A/AIa2D2f2piPcdEU4N7QPw9NNoUZEpKpQuJHLt32OeRkqKxW8a8J1H0LjfuXy0qkZ2Xy+9gAfr9pHHT9PFjx8FS4uFrw9XPlhTJdyqUFERCoWhRu5fFnpZrCp1xlu+BgCwsr8JVMysvns1/18vDqO5LPZgDn5XnxKBmHVvcv89UVEpOJSuJGSseaA6z/fPm1uB49q0HTg+X0lfVqbUejsv8lns5n2axyfro4jJSMHgAZ1qvFgr4YMbBWqkU8iIqJwIyXwx0xY9RbcvQB8aoLFAs2vu+ynXbAtngk/7rAP2QZzpe3xA6Pt6zZtOniKdxabC1o2DPTlwV4NubZVqJY/EBERO4UbKbqsdPjpCdjypbm9fgr0fLpUnnrBtnhGf7mJi4fuxSdnMOrLTUz5Z2HKHo3rcH3bMHo1C+TqFiG4KNSIiMhFFG6kaJL+MkdDHfsbsECPp+Cqx0vlqa02gwk/7sgTbC40ft52+kYH4+pi4a2b25TK64qIiHNSBwUpnGHA5i9hak8z2PgGwfB5ZrgppdW6N8SdzHUpKj+JKZlsiDtZKq8nIiLOTWdupHC/fQw/PWb+v0FPuH4q+AaW6kskpRYebIrbTkREqjaduZHCtRwKNRuYE/LdMbvUgw1AoJ9XqbYTEZGqTeFGcjMM2LvU/BfAuzqMXgtXPQYupfftcvjUGWb9dgiADpE1CQkoOLhYMEdNdYisWWqvLyIizkvhRs7LSIHvR8IX18HG6ef3u5feGZNDJ88wbvaf9HxjOU/O/pM9SWm4ulgYPzAaC2aQudC57fEDozXcW0REikR9bsQU/4c5GurkPnBxg5zS7d9y4EQ6k5btYfamI+TYzLNCnaNqYf3n/7EtQph8R7s889wEXzTPjYiIyKUo3FQlNiscWANpieaop4jOYHExOw3/8jRYsyAgHG78FMI7lMpLHkvN5JWf/+aHLUfsQaZbo9o81LsRV9bPfZkptkUIfaODC52hWERE5FIUbqqKHfNgwZOQcvT8Pr9gM8wc/s3cbnI1DJ5kzjpcSrw9XFnydyJWm0GPJnV4qHcj2tWrUWB7VxcLMVG1Su31RUSk6lG4qQp2zINZw+DiafJSE8ybiyv0fRE6jTaXUrgMuxJTmbP5CE/0b4LFYsHX042XhrSkbg1vWodXv6znFhERKQqFG2dns5pnbAqb/9e7JnT812UFm7/iU3h/6W5+2poAwBURNejdLAiAa1qpv4yIiJQfhRtnd2BN7ktR+Uk/ZraL7Fbsp992JJn3l+7ml+2J9n1XtwymXk2fYj+XiIhIaVC4cXZpiZduU5x2/0g+m82/Z21h8V9JgHnS55qWITzYqxFNgv2KW6WIiEipUbhxdtXqFK2db1CxntbP043Dp87iYoGBrUN5oGdDGgUp1IiIiOMp3Diz9BOw5v1LNLKAf6g5LLwQGw+c5NNf9/P6ja3w8XDDxcXCxOtb4u/tTlQd39KrWURE5DIp3DirE3th+rWQehRc3cGanU+jfzoQx75S4ArfG+JO8u6SXfy65wQAbepW596rGgDQtpAh3SIiIo6icOOsqteD6uHgUQ2GTjdnHr54nhv/UDPYRA/K9VDDMFi77wTvLdnNun0nAXBzsXBj+7r0bx5cjgchIiJSfAo3ziT9OHj6g5uHebbmps/Bwxc8fSG4BTS9Ju8MxRedscnKsXHnJ+tZH2eGGndXCzddEc7oHlHUraERUCIiUvEp3DiLuJXw/T3Qcij0f8nc55f7LIsVFzbYokmyNiDQ5kUHXLj4YpSHmwu1fT3xcHXh5ivNUBNa3bt8jkFERKQUWAzDKGR2N+eTkpJCQEAAycnJ+Pv7O7qcy2ezwsrXYcWrYNigTjO4dyl45D7LsmBbfN5FKf09uaF9XdbvO8lbN7WhXi3zMYdOnsHd1YXggNJbDVxERORyFOfzW2duKrPUBJh9r3nWBqDtHTDg9XyDzegvN+WZozghJZNJy/YCMHnFXiZe3xKAcE3AJyIilZjCTWW1dynMvs+cXdi9Glz7FrS+JU8zq81gwo87Clt8gWoerjzSu1HZ1SoiIlKOFG4qo7OnYdYIyEyGwObmaKg6jfNtuiHuZK5LUflJz7Ky73g6QboMJSIiTkDhpjLyrm6eqdm/yhzK7Z5/h1+rzSAx5WyRnjIptfAAJCIiUlm4OLoAKaLdi873rQFoeSMMfDffYJNjtfHD5iP0e3sFSalZRXr6QD+dtREREeegMzcVnTUblr4Av74L1QJh9K/gG5hv0xyrjblbjvLBsj3EHU8HYO3e44QEeJGQnJFvvxsLEBzgRYfImmV3DCIiIuVI4aYiO30IvrsbDm8wt6MHm5P0XSTbamPOpiN8sGwPB0+eAaCGjzv3dGvAsJgIft1znNFfbsICuQLOP4svMH5gNK4uloufVkREpFJSuKmo/v4JfhgNGafBMwAGv2+Gm3zc89nvrNh1DIBa1Ty496oG3NEpAl9P8+2NbRHC5Dva5Z3nJsCL8QOjiW0RUuaHIyIiUl4UbioamxUWPgvrJpnboe3gxk+hZqS9SWaOFQsWPNzMLlND2oay/WgK/7qqAbd3qoePR963NbZFCH2jg9kQd5Kk1AwC/cxLUTpjIyIizkbhpqKxuJhz1wB0uh/6TDDXigIysq1889shJi/fy+geUQzvXB+Aga1CiW0egrdH/it7n+PqYiEmqlZZVi8iIuJwCjcVhTUHXN3AYjGHebe6CRr1BcxQM2P9Qaas2EtSaiYAczYfsYcbN1cX3ArPNSIiIlWGwo2j5WTCwmcg+TDcMsMMN55+0KgvZ7Jy+GrdQT5cuY/jaWaoCQ3wYnTPhtx0RV0HFy4iIlIxKdw40om98N1dEP+HuX1wLUR0tt/99Oyt/LDlKAB1a3gzpmdDbmhX197XRkRERPJSuHGUbd/DvIchKxW8a8J1U0gL7kDOmSyq+5h9bO7qEsnmQ6cZ06Mh17ULw91VoUZERORSLIZhFLamotMpzpLpZSL7LCwYBxunmdv1Yki99kOmb83i49VxDGkTyoTBLezNrTZDI5pERKTKK87nt87clLfv7oadPwEWMjo9woeuN/HJf/8mJSMHgA37T5FjteH2z1kaBRsREZHiUbgpb93+je3IZmbXG8eEtcGkZsYB0CjQlwd7N+KaliEKNCIiIpdB4aasZZ2Bo5ugfldzu+4VvBU9iw9WHgJyaBLkx0O9GzGgRTAuCjUiIiKXTeGmlFhzcvh7/S+cPXUE7xphNO3YH9eTe+DbERin4jhy43zqNr0SgOHdmrBmfyr3XdWAftEKNSIiIqWpQgy/mTRpEvXr18fLy4uOHTuyYcOGQtt/++23NG3aFC8vL1q2bMlPP/1UTpXmb/Mvn3H8xcY0X3QbV/z+OM0X3Ubai/WwTu4Kx/7iWLYX05b+aW9fx8+T2fd3IbZFiIKNiIhIKXN4uPnmm28YO3Ys48ePZ9OmTbRu3Zr+/fuTlJSUb/s1a9Zw6623MnLkSDZv3syQIUMYMmQI27ZtK+fKTZt/+YzWax6ijnHCvu+s4U4A6bga2ay0tuTqzIn8bjQlLTPHITWKiIhUJQ4fCt6xY0euvPJKPvjgAwBsNhvh4eE8+OCDPPXUU3na33zzzaSnpzN//nz7vk6dOtGmTRumTJlyydcrzaHg1pwcjr/YmDrGCVwscMzwByzUsSRjNSy8lTOUlbaWPHrnUHo2C8Zi0VkaERGRkijO57dDz9xkZWWxceNG+vTpY9/n4uJCnz59WLt2bb6PWbt2ba72AP379y+wfWZmJikpKblupeXv9b8QhBlsABJsNaljSSbBqMGE7GHEuOxgnsezBJ3apGAjIiJSThwabo4fP47VaiUoKCjX/qCgIBISEvJ9TEJCQrHaT5w4kYCAAPstPDy8dIoHzp46kmu7ictBFliv4KCtDhPcP6Or6zYslrztREREpOw4vM9NWRs3bhzJycn226FDh0rtub1rhOXa9rDYiHX9nQ6uu7jwRM3F7URERKTsOHQoeO3atXF1dSUxMTHX/sTERIKDg/N9THBwcLHae3p64unpWToFX6Rpx/4kLqpl73NzMZsBSZZaNO3Yv0xeX0RERPJy6JkbDw8P2rdvz5IlS+z7bDYbS5YsISYmJt/HxMTE5GoPsGjRogLblyVXNzeOxowHzCBzoXPb8THjcXXTdEIiIiLlxeGfumPHjmX48OFcccUVdOjQgXfeeYf09HTuuusuAIYNG0ZYWBgTJ04E4OGHH6Z79+68+eabXHPNNcycOZPff/+dqVOnOqT+tv2HsxkIXTuBIM4PB0+y1CI+Zjxt+w93SF0iIiJVlcPDzc0338yxY8d47rnnSEhIoE2bNixYsMDeafjgwYO4uJw/wdS5c2dmzJjBM888w9NPP02jRo344YcfaNGiRUEvUeba9h+OtfftbL9ohuJgnbEREREpdw6f56a8leY8NyIiIlI+Ks08NyIiIiKlTeFGREREnIrCjYiIiDgVhRsRERFxKgo3IiIi4lQUbkRERMSpKNyIiIiIU1G4EREREaeicCMiIiJOpcqtD3BuQuaUlBQHVyIiIiJFde5zuygLK1S5cJOamgpAeHi4gysRERGR4kpNTSUgIKDQNlVubSmbzcbRo0fx8/PDYrGU6nOnpKQQHh7OoUOHnHLdKmc/PnD+Y9TxVX7Ofow6vsqvrI7RMAxSU1MJDQ3NtaB2fqrcmRsXFxfq1q1bpq/h7+/vtN+04PzHB85/jDq+ys/Zj1HHV/mVxTFe6ozNOepQLCIiIk5F4UZEREScisJNKfL09GT8+PF4eno6upQy4ezHB85/jDq+ys/Zj1HHV/lVhGOsch2KRURExLnpzI2IiIg4FYUbERERcSoKNyIiIuJUFG5ERETEqSjcFGLSpEnUr18fLy8vOnbsyIYNGwpt/+2339K0aVO8vLxo2bIlP/30U677DcPgueeeIyQkBG9vb/r06cPu3bvL8hAuqTjH+NFHH9GtWzdq1KhBjRo16NOnT572I0aMwGKx5LrFxsaW9WEUqDjHN3369Dy1e3l55WpT0d7D4hxfjx498hyfxWLhmmuusbepSO/fypUrGThwIKGhoVgsFn744YdLPmb58uW0a9cOT09PGjZsyPTp0/O0Ke7PdVkq7jHOnj2bvn37UqdOHfz9/YmJieGXX37J1eb555/P8x42bdq0DI+iYMU9vuXLl+f7PZqQkJCrXWV+D/P7GbNYLDRv3tzepqK8hxMnTuTKK6/Ez8+PwMBAhgwZws6dOy/5uIrwWahwU4BvvvmGsWPHMn78eDZt2kTr1q3p378/SUlJ+bZfs2YNt956KyNHjmTz5s0MGTKEIUOGsG3bNnub1157jffee48pU6awfv16qlWrRv/+/cnIyCivw8qluMe4fPlybr31VpYtW8batWsJDw+nX79+HDlyJFe72NhY4uPj7bevv/66PA4nj+IeH5gzal5Y+4EDB3LdX5Hew+Ie3+zZs3Md27Zt23B1dWXo0KG52lWU9y89PZ3WrVszadKkIrWPi4vjmmuuoWfPnmzZsoVHHnmEe+65J9eHf0m+J8pScY9x5cqV9O3bl59++omNGzfSs2dPBg4cyObNm3O1a968ea73cPXq1WVR/iUV9/jO2blzZ676AwMD7fdV9vfw3XffzXVshw4dombNmnl+DivCe7hixQrGjBnDunXrWLRoEdnZ2fTr14/09PQCH1NhPgsNyVeHDh2MMWPG2LetVqsRGhpqTJw4Md/2N910k3HNNdfk2texY0fjX//6l2EYhmGz2Yzg4GDj9ddft99/+vRpw9PT0/j666/L4AgurbjHeLGcnBzDz8/P+Oyzz+z7hg8fbgwePLi0Sy2R4h7ftGnTjICAgAKfr6K9h5f7/r399tuGn5+fkZaWZt9Xkd6/CwHGnDlzCm3zxBNPGM2bN8+17+abbzb69+9v377cr1lZKsox5ic6OtqYMGGCfXv8+PFG69atS6+wUlKU41u2bJkBGKdOnSqwjbO9h3PmzDEsFouxf/9++76K+h4mJSUZgLFixYoC21SUz0KduclHVlYWGzdupE+fPvZ9Li4u9OnTh7Vr1+b7mLVr1+ZqD9C/f397+7i4OBISEnK1CQgIoGPHjgU+Z1kqyTFe7MyZM2RnZ1OzZs1c+5cvX05gYCBNmjRh9OjRnDhxolRrL4qSHl9aWhoRERGEh4czePBgtm/fbr+vIr2HpfH+ffLJJ9xyyy1Uq1Yt1/6K8P6VxKV+Bkvja1bR2Gw2UlNT8/wM7t69m9DQUBo0aMDtt9/OwYMHHVRhybRp04aQkBD69u3Lr7/+at/vjO/hJ598Qp8+fYiIiMi1vyK+h8nJyQB5vt8uVFE+CxVu8nH8+HGsVitBQUG59gcFBeW59ntOQkJCoe3P/Vuc5yxLJTnGiz355JOEhobm+iaNjY3l888/Z8mSJbz66qusWLGCAQMGYLVaS7X+SynJ8TVp0oRPP/2UuXPn8uWXX2Kz2ejcuTOHDx8GKtZ7eLnv34YNG9i2bRv33HNPrv0V5f0riYJ+BlNSUjh79mypfM9XNG+88QZpaWncdNNN9n0dO3Zk+vTpLFiwgMmTJxMXF0e3bt1ITU11YKVFExISwpQpU/j+++/5/vvvCQ8Pp0ePHmzatAkond9bFcnRo0f5+eef8/wcVsT30Gaz8cgjj9ClSxdatGhRYLuK8llY5VYFl9LxyiuvMHPmTJYvX56r0+0tt9xi/3/Lli1p1aoVUVFRLF++nN69ezui1CKLiYkhJibGvt25c2eaNWvGhx9+yAsvvODAykrfJ598QsuWLenQoUOu/ZX5/atqZsyYwYQJE5g7d26uPikDBgyw/79Vq1Z07NiRiIgIZs2axciRIx1RapE1adKEJk2a2Lc7d+7M3r17efvtt/niiy8cWFnZ+Oyzz6hevTpDhgzJtb8ivodjxoxh27ZtDuu/VVw6c5OP2rVr4+rqSmJiYq79iYmJBAcH5/uY4ODgQtuf+7c4z1mWSnKM57zxxhu88sorLFy4kFatWhXatkGDBtSuXZs9e/Zcds3FcTnHd467uztt27a1116R3sPLOb709HRmzpxZpF+Sjnr/SqKgn0F/f3+8vb1L5Xuiopg5cyb33HMPs2bNynMJ4GLVq1encePGleI9zE+HDh3stTvTe2gYBp9++il33nknHh4ehbZ19Hv4wAMPMH/+fJYtW0bdunULbVtRPgsVbvLh4eFB+/btWbJkiX2fzWZjyZIluf6yv1BMTEyu9gCLFi2yt4+MjCQ4ODhXm5SUFNavX1/gc5alkhwjmL3cX3jhBRYsWMAVV1xxydc5fPgwJ06cICQkpFTqLqqSHt+FrFYrW7dutddekd7Dyzm+b7/9lszMTO64445Lvo6j3r+SuNTPYGl8T1QEX3/9NXfddRdff/11rmH8BUlLS2Pv3r2V4j3Mz5YtW+y1O8t7COZIpD179hTpjwxHvYeGYfDAAw8wZ84cli5dSmRk5CUfU2E+C0uta7KTmTlzpuHp6WlMnz7d2LFjh3HfffcZ1atXNxISEgzDMIw777zTeOqpp+ztf/31V8PNzc144403jL/++ssYP3684e7ubmzdutXe5pVXXjGqV69uzJ071/jzzz+NwYMHG5GRkcbZs2fL/fgMo/jH+MorrxgeHh7Gd999Z8THx9tvqamphmEYRmpqqvHYY48Za9euNeLi4ozFixcb7dq1Mxo1amRkZGRU+OObMGGC8csvvxh79+41Nm7caNxyyy2Gl5eXsX37dnubivQeFvf4zunatatx880359lf0d6/1NRUY/PmzcbmzZsNwHjrrbeMzZs3GwcOHDAMwzCeeuop484777S337dvn+Hj42M8/vjjxl9//WVMmjTJcHV1NRYsWGBvc6mvWXkr7jF+9dVXhpubmzFp0qRcP4OnT5+2t/n3v/9tLF++3IiLizN+/fVXo0+fPkbt2rWNpKSkCn98b7/9tvHDDz8Yu3fvNrZu3Wo8/PDDhouLi7F48WJ7m8r+Hp5zxx13GB07dsz3OSvKezh69GgjICDAWL58ea7vtzNnztjbVNTPQoWbQrz//vtGvXr1DA8PD6NDhw7GunXr7Pd1797dGD58eK72s2bNMho3bmx4eHgYzZs3N/73v//lut9msxnPPvusERQUZHh6ehq9e/c2du7cWR6HUqDiHGNERIQB5LmNHz/eMAzDOHPmjNGvXz+jTp06hru7uxEREWHce++9DvulYxjFO75HHnnE3jYoKMi4+uqrjU2bNuV6vor2Hhb3e/Tvv/82AGPhwoV5nquivX/nhgVffDt3TMOHDze6d++e5zFt2rQxPDw8jAYNGhjTpk3L87yFfc3KW3GPsXv37oW2Nwxz+HtISIjh4eFhhIWFGTfffLOxZ8+e8j2wfxT3+F599VUjKirK8PLyMmrWrGn06NHDWLp0aZ7nrczvoWGYQ5+9vb2NqVOn5vucFeU9zO+4gFw/VxX1s9DyzwGIiIiIOAX1uRERERGnonAjIiIiTkXhRkRERJyKwo2IiIg4FYUbERERcSoKNyIiIuJUFG5ERETEqSjciIiIiFNRuBERERGnonAjIiIiTkXhRkScxscff0yrVq3w9vYmICCAXr16ObokEXEAN0cXICJSGmbPns0TTzzBhx9+SMeOHUlNTWX//v2OLktEHEDhRkScws6dO4mIiKBv375Ur14dgObNmzu2KBFxCF2WEhGncO+992IYBjVr1sTX15e4uDhHlyQiDmIxDMNwdBEiIpcjOzubAQMG0LhxY0aOHElAQABRUVFYLBZHlyYiDqDLUiJS6c2ZM4c9e/awePFiR5ciIhWALkuJSKWXlZVFfHw8X3zxBfv372fbtm18+OGH5OTkOLo0EXEAXZYSkUovJyeHJ598klmzZpGYmEjNmjXp3bs3X331laNLExEHULgRERERp6LLUiIiIuJUFG5ERETEqSjciIiIiFNRuBERERGnonAjIiIiTkXhRkRERJyKwo2IiIg4FYUbERERcSoKNyIiIuJUFG5ERETEqSjciIiIiFNRuBERERGn8v9/dNxRr5vtwwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Compute over epsilons given gamma\n", + "gamma = 0.8\n", + "epsilons = np.linspace(0.0,2.0,12)\n", + "\n", + "estimated, true = [], []\n", + "for epsilon in tqdm(epsilons):\n", + " A, B = process_1(gamma, epsilon), process_2(gamma, epsilon)\n", + " estimated.append(\n", + " {k:metrics[k].fit_score(A,B) for k in metrics.keys()}\n", + " )\n", + " true.append(\n", + " true_dist(gamma,epsilon)\n", + " )\n", + " \n", + "\n", + "plot_line(estimated,true,{'$\\epsilon$': epsilons},{'$\\gamma$': gamma})\n" + ] + }, + { + "cell_type": "code", + "execution_count": 134, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 12/12 [00:00<00:00, 518.90it/s]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Vary gamma and set epsilon such that AW is constant\n", + "\n", + "desired_AW = 0.5\n", + "\n", + "estimated, true = [], []\n", + "for gamma in tqdm(gammas):\n", + " epsilon = desired_AW / np.sqrt(2 * np.square(gamma) + 1)\n", + " A, B = process_1(gamma, epsilon), process_2(gamma, epsilon)\n", + " estimated.append(\n", + " {k:metrics[k].fit_score(A,B) for k in metrics.keys()}\n", + " )\n", + " true.append(\n", + " true_dist(gamma,epsilon)\n", + " )\n", + " \n", + "\n", + "plot_line(estimated,true,{'$\\gamma$': gammas},{'$\\mathcal{AW}_2$': desired_AW})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Project and evaluate distance in higher dimensions" + ] + }, + { + "cell_type": "code", + "execution_count": 135, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Create orthogonal projection matrix\n", + "\n", + "dims = [5,10,15,20,25,50]\n", + "\n", + "gamma = .8\n", + "epsilon = .3\n", + "\n", + "estimated, true = [], []\n", + "for i, obs_dims in enumerate(dims):\n", + " # Metrics\n", + " metrics = {\n", + " 'dssd': GPStochasticMetric(n_dims=obs_dims, group=\"orth\", type=\"non-adapted\"),\n", + " 'assd': GPStochasticMetric(n_dims=obs_dims, group=\"orth\", type=\"adapted\") \n", + " }\n", + "\n", + " A, B = process_1(gamma, epsilon), process_2(gamma, epsilon)\n", + " \n", + " CA = np.kron(np.eye(T),ortho_group.rvs(obs_dims)[:,:1])\n", + " CB = np.kron(np.eye(T),ortho_group.rvs(obs_dims)[:,:1])\n", + "\n", + " A_p, B_p = (CA@A[0], CA@A[1]@CA.T), (CB@B[0], CB@B[1]@CB.T)\n", + " \n", + " estimated.append(\n", + " {k:metrics[k].fit_score(\n", + " A_p, B_p\n", + " ) for k in metrics.keys()}\n", + " )\n", + " true.append(\n", + " true_dist(gamma,epsilon)\n", + " )\n", + "\n", + "plot_line(estimated,true,{'D': dims},{'$(\\gamma,\\epsilon)$': [gamma,epsilon]})" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "fi_gp", + "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": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/netrep/metrics/__init__.py b/netrep/metrics/__init__.py index f7a2e8a..c316693 100644 --- a/netrep/metrics/__init__.py +++ b/netrep/metrics/__init__.py @@ -3,4 +3,5 @@ from netrep.metrics.perm import PermutationMetric from netrep.metrics.stochastic import GaussianStochasticMetric from netrep.metrics.stochastic import EnergyStochasticMetric -from netrep.metrics.stochastic_process import GPStochasticMetric \ No newline at end of file +from netrep.metrics.stochastic_process import GPStochasticMetric +from netrep.metrics.stochastic_differentiable import GPStochasticDiff \ No newline at end of file diff --git a/netrep/metrics/stochastic_differentiable.py b/netrep/metrics/stochastic_differentiable.py new file mode 100644 index 0000000..f167e40 --- /dev/null +++ b/netrep/metrics/stochastic_differentiable.py @@ -0,0 +1,92 @@ +# %% +import torch +from torch import nn +from torch import optim + +from torch.nn.utils.parametrizations import orthogonal + +from typing import Literal, List + +from tqdm.auto import trange + +class GPStochasticDiff: + + def __init__( + self, + n_dims, + n_times, + alpha: float=1.0, + type: Literal["Bures", "Adapted_Bures", "Knothe_Rosenblatt", "Marginal_Bures"] = "Adapted_Bures", + ): + + self.n_times = n_times + self.n_dims = n_dims + + self.alpha = alpha + + marginalize = lambda cov: torch.block_diag(*[cov[i*n_dims:(i+1)*n_dims,i*n_dims:(i+1)*n_dims] for i in range(n_times)]) + + def sqrtm(cov): + v, u = torch.linalg.eigh(cov) + s = torch.einsum("jk,k,lk->jl", u, torch.sqrt(torch.maximum(v,torch.tensor(0))), u) + return s + + self.type = type + + self.cov_dist_fns = { + 'Bures': lambda A,B: torch.trace(A) + torch.trace(B) - 2*torch.trace(sqrtm(sqrtm(B)@A@sqrtm(B))), + 'Adapted_Bures': lambda A,B: torch.trace(A) + torch.trace(B) -2*torch.diag(torch.cholesky(A).T@torch.cholesky(B)).sum(), + 'Knothe_Rosenblatt': lambda A,B: ((torch.cholesky(A)-torch.cholesky(B))**2).sum() + } + self.cov_dist_fns['Marginal_Bures'] = lambda A,B: self.cov_dist_fns['Bures'](marginalize(A),marginalize(B)) + + def fit_score(self,A,B,patience=4,tol=1e-6,lr=.1,momentum=.9,epsilon=1e-6): + n,t = self.n_dims, self.n_times + cov_dist_fn = self.cov_dist_fns[self.type] + alpha = self.alpha + + Q = orthogonal(nn.Linear(n, n)) + optimizer = optim.SGD(Q.parameters(), lr=lr, momentum=momentum) + + mu_A = torch.tensor(A[0]).float() + mu_B = torch.tensor(B[0]).float() + + Sigma_A = torch.tensor(A[1]).float() + Sigma_B = torch.tensor(B[1]).float() + + counter,l = 0,0 + loss = [] + + pbar = trange(0,bar_format=None) + pbar.set_description('Optimizing ...') + + total_iter = 0 + while counter < patience: + # Update parameters + optimizer.zero_grad() + Q_ = torch.kron(torch.eye(t),Q.weight) + + mean_dist = ((mu_A - Q_@mu_B)**2).sum() + cov_dist = cov_dist_fn(Sigma_A+epsilon*torch.eye(n*t),Q_@Sigma_B@Q_.T+epsilon*torch.eye(n*t)) + # cov_dist = ((cholesky_A-torch.cholesky(Q_@Sigma_B@Q_.T+epsilon*torch.eye(n*t)))**2).sum() + + dist = alpha*mean_dist + (2-alpha)*cov_dist + + dist.backward() + optimizer.step() + + l_new = dist.detach() + loss.append(l_new) + counter = counter + 1 if torch.abs(l_new-l) < tol else 0 + l = l_new + + total_iter+=1 + + if total_iter%100==0: + pbar.set_description("Iteration {}, loss {:0.2f}".format(total_iter,l_new)) + + self.loss = torch.tensor(loss).numpy() + self.Q = Q.weight.detach().numpy().T + + return dist.detach().numpy() + diff --git a/netrep/metrics/stochastic_process.py b/netrep/metrics/stochastic_process.py index 7104ac3..b7f29a7 100644 --- a/netrep/metrics/stochastic_process.py +++ b/netrep/metrics/stochastic_process.py @@ -3,12 +3,14 @@ import multiprocessing from typing import Tuple, Optional, Union, Literal, List +import scipy as sp import numpy as np + import numpy.typing as npt from sklearn.utils.validation import check_random_state from tqdm import tqdm -from netrep.utils import align, sq_bures_metric, rand_orth +from netrep.utils import align, sq_bures_metric, rand_orth, sq_adapted_bures_metric, safe_cholesky, safe_sqrt class GPStochasticMetric: @@ -42,6 +44,7 @@ def __init__( n_dims, alpha: float=1.0, group: Literal["orth", "perm", "identity"] = "orth", + type: Literal["adapted", "non-adapted"] = "non-adapted", init: Literal["means", "rand"] = "means", niter: int = 1000, tol: float = 1e-8, @@ -52,6 +55,7 @@ def __init__( raise ValueError("alpha parameter should be between zero and two.") self.alpha = alpha self.group = group + self.type = type self.init = init self.niter = niter self.tol = tol @@ -104,10 +108,17 @@ def fit( elif self.init == "rand": init_T = rand_orth(means_X_t.shape[1], random_state=self._rs) - T, loss_hist = _fit_gp_alignment( - self.n_dims, means_X_t, means_Y_t, covs_X, covs_Y, init_T, - self.alpha, self.group, self.niter, self.tol - ) + if self.type == "adapted": + T, loss_hist = _fit_adapted_gp_alignment( + self.n_dims, means_X_t, means_Y_t, covs_X, covs_Y, init_T, + self.alpha, self.group, self.niter, self.tol + ) + elif self.type == "non-adapted": + T, loss_hist = _fit_gp_alignment( + self.n_dims, means_X_t, means_Y_t, covs_X, covs_Y, init_T, + self.alpha, self.group, self.niter, self.tol + ) + if best_loss > loss_hist[-1]: best_loss = loss_hist[-1] best_T = T @@ -182,7 +193,12 @@ def score( mY, sY = Y A = np.sum((mX - mY) ** 2) - B = sq_bures_metric(sX, sY) + + if self.type == 'adapted': + B = sq_adapted_bures_metric(sX, sY) + if self.type =='non-adapted': + B = sq_bures_metric(sX, sY) + mn = np.mean(self.alpha * A + (2 - self.alpha) * B) # mn should always be positive but sometimes numerical rounding errors # cause mn to be very slightly negative, causing sqrt(mn) to be nan. @@ -300,7 +316,6 @@ def pairwise_distances( return D_train, D_test - def _fit_gp_alignment( n_dims: int, means_X: npt.NDArray, @@ -316,17 +331,16 @@ def _fit_gp_alignment( """Helper function for fitting alignment between Gaussian-distributed responses.""" vX, uX = np.linalg.eigh(covs_X) - sX = np.einsum("jk,k,lk->jl", uX, np.sqrt(vX), uX, optimize=True) + sX = np.einsum("jk,k,lk->jl", uX, safe_sqrt(vX), uX, optimize=True) vY, uY = np.linalg.eigh(covs_Y) - sY = np.einsum("jk,k,lk->jl", uY, np.sqrt(vY), uY, optimize=True) + sY = np.einsum("jk,k,lk->jl", uY, safe_sqrt(vY), uY, optimize=True) loss_hist = [] n_times = covs_X.shape[0]//n_dims for i in range(niter): - Qs = align(np.kron(np.eye(n_times),T.T) @ sY, sX, group="orth") A = np.row_stack( [alpha * means_X] + @@ -347,14 +361,85 @@ def _fit_gp_alignment( return T, loss_hist +def _fit_adapted_gp_alignment( + n_dims: int, + means_X: npt.NDArray, + means_Y: npt.NDArray, + covs_X: npt.NDArray, + covs_Y: npt.NDArray, + T: npt.NDArray, + alpha: float, + group: Literal["orth", "perm", "identity"], + niter: int, + tol: float, + ) -> Tuple[npt.NDArray, List[float]]: + """Helper function for fitting alignment between Gaussian-distributed responses.""" -def split(array, nrows, ncols): + # Cholesky factorization of covariance matrices + # sX = np.linalg.cholesky(covs_X) + # sY = np.linalg.cholesky(covs_Y) + sX = safe_cholesky(covs_X) + sY = safe_cholesky(covs_Y) + + loss_hist = [] + + n_times = covs_X.shape[0]//n_dims + + # Evaluating the tensor M_{A,t} + # [F_0(\Sigma),F_1(\Sigma),\dots,F_T(Sigma)] for \Sigma_A + # where F_t(\Sigma) is [\Sigma_{tt},\vdots,\Sigma_{Tt}] + # Check appendix F for details + sX_splitted = split(sX, 1, n_dims, separate=True)[:,:,0] + + # Evaluating the covariance part of the tall matrix N_A + # G(\mu,\Sigma) = [\mu_1^{\top}\vdots\mu_T^{\top},\Sigma_{11},\vdots,\Sigma{TT}] + # Check appendix F for details + sX_splitted_T = split(sX.T, n_dims, n_dims) + + # Evaluating N_A + A = np.row_stack( + [alpha * means_X] + + [(2-alpha)*sX_splitted_T] + ) + + for i in range(niter): + # Evaluating M_{B,t} + sY_splitted = split(np.kron(np.eye(n_times),T.T) @ sY, 1, n_dims, separate=True)[:,:,0] + + # Solving for Qs (noise rotations) + Qs = [align(sy, sx) for sx, sy in zip(sX_splitted, sY_splitted)] + + Q_flat = sp.linalg.block_diag(*Qs) + sY_splitted_T = split((sY@Q_flat).T, n_dims, n_dims) + + # Evaluating N_B + B = np.row_stack( + [alpha * means_Y] + + [(2-alpha)*sY_splitted_T] + ) + + # Solving for the spatial rotation + T = align(B, A, group=group) + + loss_hist.append(np.linalg.norm(A - B @ T)) + + if i < 2: + pass + elif (loss_hist[-2] - loss_hist[-1]) < tol: + break + + return T, loss_hist + +def split(array, nrows, ncols, separate=False): """Split a matrix into sub-matrices.""" r, h = array.shape blocks = array.reshape( h//nrows, nrows, -1, ncols - ).swapaxes(1,2).reshape(-1, nrows, ncols) + ).swapaxes(1,2) + + if separate: return blocks.transpose(1,0,2,3) - return blocks.reshape(-1,blocks.shape[-1]) + return blocks.reshape(-1, nrows, ncols).reshape(-1,blocks.shape[-1]) + diff --git a/netrep/multiset.py b/netrep/multiset.py index c839383..008133b 100644 --- a/netrep/multiset.py +++ b/netrep/multiset.py @@ -2,7 +2,7 @@ import numpy as np from tqdm import tqdm from sklearn.utils.validation import check_array, check_random_state -from netrep.utils import align +from netrep.utils import align, whiten def euclidean_tangent_space(Xs, Xbar, group="orth"): @@ -209,7 +209,8 @@ def frechet_mean( Xs, group="orth", random_state=None, tol=1e-3, max_iter=100, warmstart=None, verbose=False, method="streaming", - return_aligned_Xs=False + return_aligned_Xs=False, + alpha=1. ): """ Estimate the average (Karcher/Frechet mean) of p networks in the @@ -259,12 +260,12 @@ def frechet_mean( if method == "streaming": Xbar = _euclidean_barycenter_streaming( Xs, group, random_state, tol, max_iter, warmstart, - verbose + verbose, alpha ) elif method == "full_batch": Xbar = _euclidean_barycenter_full_batch( Xs, group, random_state, tol, max_iter, warmstart, - verbose + verbose, alpha ) if return_aligned_Xs: @@ -276,7 +277,7 @@ def frechet_mean( def _euclidean_barycenter_full_batch( - Xs, group, random_state, tol, max_iter, warmstart, verbose + Xs, group, random_state, tol, max_iter, warmstart, verbose, alpha ): """ Parameters @@ -324,10 +325,14 @@ def _euclidean_barycenter_full_batch( # Check random state and initialize random permutation over networks. rs = check_random_state(random_state) + for i in range(len(Xs)): + Xs[i], _ = whiten(Xs[i], alpha, preserve_variance=True) + # Initialize barycenter. Xbar = Xs[np.random.randint(len(Xs))] if (warmstart is None) else warmstart X0 = np.empty_like(Xbar) + # Main loop itercount, n, chg = 0, 1, np.inf while (chg > tol) and (itercount < max_iter): @@ -343,6 +348,8 @@ def _euclidean_barycenter_full_batch( Xbar /= len(Xs) + Xbar, _ = whiten(Xbar, alpha, preserve_variance=True) + # Detect convergence. chg = np.linalg.norm(Xbar - X0) / np.sqrt(Xbar.size) @@ -357,7 +364,7 @@ def _euclidean_barycenter_full_batch( def _euclidean_barycenter_streaming( - Xs, group, random_state, tol, max_iter, warmstart, verbose + Xs, group, random_state, tol, max_iter, warmstart, verbose, alpha ): """ Parameters @@ -409,9 +416,11 @@ def _euclidean_barycenter_streaming( rs = check_random_state(random_state) indices = rs.permutation(len(Xs)) + for i in range(len(Xs)): + Xs[i], _ = whiten(Xs[i], alpha, preserve_variance=True) + # Initialize barycenter. Xbar = Xs[indices[-1]] if (warmstart is None) else warmstart - print(Xbar.shape) X0 = np.empty_like(Xbar) # Main loop @@ -430,7 +439,9 @@ def _euclidean_barycenter_streaming( # Take a small step towards aligned representation. Xbar = (n / (n + 1)) * Xbar + (1 / (n + 1)) * XQ n += 1 - + + Xbar, _ = whiten(Xbar, alpha, preserve_variance=True) + # Detect convergence. chg = np.linalg.norm(Xbar - X0) / np.sqrt(Xbar.size) diff --git a/netrep/utils.py b/netrep/utils.py index ccb6bba..4abc67b 100644 --- a/netrep/utils.py +++ b/netrep/utils.py @@ -4,6 +4,7 @@ from typing import Tuple, Literal, Union, Optional import numpy as np +import scipy as sp import numpy.typing as npt from scipy.linalg import orthogonal_procrustes from scipy.optimize import linear_sum_assignment @@ -99,6 +100,27 @@ def sq_bures_metric(A: npt.NDArray, B: npt.NDArray) -> float: ) + +def safe_sqrt(x): + return np.sqrt(np.maximum(x, 0)) + +def safe_cholesky(C): + try: L_C = sp.linalg.cholesky(C) + except sp.linalg.LinAlgError: + L, D, _ = sp.linalg.ldl(C) + L_C = L @ safe_sqrt(D) + return L_C + +def sq_adapted_bures_metric(cov_A, cov_B): + '''Compute the square of the Adapted Bures metric between two + positive-definite matrices''' + L_A = safe_cholesky(cov_A) + L_B = safe_cholesky(cov_B) + # assert (np.diag(L_A @ L_B.T) >= -1e-6).all() + # return np.trace(cov_A) + np.trace(cov_B) - 2 * np.trace(L_A.T @ L_B) + return np.trace(cov_A) + np.trace(cov_B) - 2 * np.linalg.norm(np.diag(L_A.T @ L_B), ord=1) + + def centered_kernel(*args, **kwargs): """ Lightly wraps `sklearn.metrics.pairwise.pairwise_kernels` diff --git a/netrep/validation.py b/netrep/validation.py index 6135eb4..803870a 100644 --- a/netrep/validation.py +++ b/netrep/validation.py @@ -5,14 +5,14 @@ import numpy as np import numpy.typing as npt from sklearn.utils.validation import check_array - +from typing import Tuple def check_equal_shapes( X: npt.NDArray, Y: npt.NDArray, nd: int = 2, zero_pad: bool = False - ) -> tuple[npt.NDArray, npt.NDArray]: + ) -> Tuple[npt.NDArray, npt.NDArray]: """Checks that X and Y have equal shapes.""" X = check_array(X, allow_nd=True) diff --git a/tests/test_stochastic_process.py b/tests/test_stochastic_process.py index a980147..2456dce 100644 --- a/tests/test_stochastic_process.py +++ b/tests/test_stochastic_process.py @@ -13,7 +13,8 @@ from numpy import random as rand from netrep.utils import rand_orth -TOL = 1e-6 +TOL = 1e-5 + # %% Class for sampling from a gaussian process given a kernel class GaussianProcess: @@ -61,7 +62,6 @@ def test_gaussian_process(seed, t, n, k): np.kron(np.eye(t),Q)@A[0], np.kron(np.eye(t),Q)@A[1]@(np.kron(np.eye(t),Q)).T ] - # Compute DSSD metric = GPStochasticMetric(n_dims=n,group="orth") @@ -86,11 +86,13 @@ def test_gaussian_process(seed, t, n, k): assert abs(marginal_ssd) < TOL # Compute full SSD - metric = GaussianStochasticMetric(group="orth") + metric = GaussianStochasticMetric(group="orth",init="rand",n_restarts=100) + A_full = [A[0][None],A[1][None]] B_full = [B[0][None],B[1][None]] full_ssd = metric.fit_score(A_full,B_full) - assert abs(full_ssd) > TOL + assert abs(full_ssd) < TOL +