Skip to content

Instantly share code, notes, and snippets.

@peci1
Last active November 15, 2024 18:13
Show Gist options
  • Select an option

  • Save peci1/720e7df143dd20cd25296127c89868cf to your computer and use it in GitHub Desktop.

Select an option

Save peci1/720e7df143dd20cd25296127c89868cf to your computer and use it in GitHub Desktop.
PINN example: Ballistic curve
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": [
"# PINN simple example with ballistic curve\n",
"\n",
"Inspired by the article at https://towardsdatascience.com/physics-informed-neural-networks-pinns-an-intuitive-guide-fff138069563 ."
],
"id": "e604377df7b898dc"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-14T16:34:22.618238Z",
"start_time": "2024-11-14T16:34:22.608681Z"
}
},
"cell_type": "code",
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def f(mu, pos, vel, duration, step):\n",
" ps = [pos]\n",
" last_pos = np.array(pos)\n",
" last_vel = np.array(vel)\n",
" g = np.array([0, 9.81])\n",
" ts = np.arange(start=0, stop=duration, step=step)\n",
" for t in ts:\n",
" accel = -mu * np.linalg.norm(last_vel) * last_vel - g\n",
" vel = last_vel + accel * step\n",
" pos = last_pos + vel * step\n",
" ps.append(pos)\n",
" if pos[1] < 0:\n",
" break\n",
" last_vel = vel\n",
" last_pos = pos\n",
" \n",
" return np.array(ps), ts"
],
"id": "5031825e938433f9",
"outputs": [],
"execution_count": 179
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-14T16:34:40.311449Z",
"start_time": "2024-11-14T16:34:40.301941Z"
}
},
"cell_type": "code",
"source": [
"mu_gt = 0.03\n",
"init_pos = [0, 0]\n",
"init_vel = [200, 200]\n",
"duration = 5\n",
"step = 0.1\n",
"\n",
"s_gt, t_phys = f(mu_gt, init_pos, init_vel, duration, step)\n",
"\n",
"idx_train = range(0, s_gt.shape[0] * 3 // 5, 3)\n",
"t_train = t_phys[idx_train]\n",
"s_train = s_gt[idx_train] + np.random.normal(np.zeros_like(s_gt[idx_train]), 0.7)"
],
"id": "d25e1de4615cd069",
"outputs": [],
"execution_count": 180
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-15T06:28:54.746504Z",
"start_time": "2024-11-15T06:28:54.573181Z"
}
},
"cell_type": "code",
"source": [
"from PIL import Image\n",
"import io\n",
"\n",
"fig = plt.figure(figsize=(15, 5))\n",
"plt.plot(s_gt[:, 0], s_gt[:, 1])\n",
"plt.plot(s_train[:, 0], s_train[:, 1], 'o')\n",
"plt.savefig('/tmp/gt.png')"
],
"id": "c30bb1fd4d6315a7",
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 1080x360 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"execution_count": 219
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-14T16:55:44.785534Z",
"start_time": "2024-11-14T16:55:44.774684Z"
}
},
"cell_type": "code",
"source": [
"import torch\n",
"import torch.nn as nn\n",
"import torch.nn.functional as F\n",
"\n",
"class Net(nn.Module):\n",
" def __init__(self, N_INPUT, N_OUTPUT, N_HIDDEN, N_LAYERS):\n",
" super().__init__()\n",
" activation = nn.GELU\n",
" self.fcs = nn.Sequential(*[nn.Linear(N_INPUT, N_HIDDEN), activation()])\n",
" self.fch = nn.Sequential(*[nn.Sequential(*[nn.Linear(N_HIDDEN, N_HIDDEN), activation()]) for _ in range(N_LAYERS-1)])\n",
" self.fce = nn.Linear(N_HIDDEN, N_OUTPUT)\n",
"\n",
" def forward(self, x):\n",
" x = self.fcs(x)\n",
" x = self.fch(x)\n",
" x = self.fce(x)\n",
" return x\n",
" \n",
" def reset(self):\n",
" for layer in self.children():\n",
" if hasattr(layer, 'reset_parameters'):\n",
" layer.reset_parameters()\n",
" \n",
"\n",
"fc_net = Net(1, 2, 32, 3)\n",
"print(fc_net)\n",
"t_phys_torch = torch.tensor(t_phys, dtype=torch.float32, requires_grad=True).view(-1, 1)\n",
"t_train_torch = torch.tensor(t_train, dtype=torch.float32, requires_grad=True).view(-1, 1)"
],
"id": "fbaeffb501f1a040",
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Net(\n",
" (fcs): Sequential(\n",
" (0): Linear(in_features=1, out_features=32, bias=True)\n",
" (1): GELU(approximate='none')\n",
" )\n",
" (fch): Sequential(\n",
" (0): Sequential(\n",
" (0): Linear(in_features=32, out_features=32, bias=True)\n",
" (1): GELU(approximate='none')\n",
" )\n",
" (1): Sequential(\n",
" (0): Linear(in_features=32, out_features=32, bias=True)\n",
" (1): GELU(approximate='none')\n",
" )\n",
" )\n",
" (fce): Linear(in_features=32, out_features=2, bias=True)\n",
")\n"
]
}
],
"execution_count": 216
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-15T06:35:57.593385Z",
"start_time": "2024-11-15T06:35:57.583784Z"
}
},
"cell_type": "code",
"source": [
"def train(net, loss_fn, opt, iters, n_plots=4):\n",
" net.reset()\n",
" optimiser = torch.optim.Adam(opt, lr=1e-3)\n",
" t = torch.tensor(t_phys, dtype=torch.float32).view(-1, 1)\n",
" s_train_t = torch.tensor(s_train, dtype=torch.float32)\n",
" frames = []\n",
" for i in range(iters + 1):\n",
" optimiser.zero_grad()\n",
"\n",
" s_hat = net(t_train_torch)\n",
"\n",
" loss = loss_fn(s_hat, s_train_t)\n",
" loss.backward()\n",
" optimiser.step()\n",
" \n",
" # plot the result as training progresses\n",
" if i % (iters // n_plots) == 0: \n",
" u = net(t).detach().numpy()\n",
" plt.figure(figsize=(6,2.5))\n",
" plt.plot(s_gt[:, 0], s_gt[:, 1], label=\"Exact solution\", color=\"tab:grey\", alpha=0.6)\n",
" plt.plot(u[:, 0], u[:, 1], label=\"PINN solution\", color=\"tab:green\")\n",
" plt.plot(s_train[:, 0], s_train[:, 1], 'o')\n",
" plt.title(f\"Training step {i}\")\n",
" plt.xlim((np.min(s_gt[:, 0]), np.max(s_gt[:, 0])))\n",
" plt.ylim((np.min(s_gt[:, 1]), max(np.max(s_gt[:, 1]), np.max(u[:, 1]))))\n",
" plt.legend()\n",
" buf = io.BytesIO()\n",
" plt.savefig(buf, format='png')\n",
" buf.seek(0)\n",
" frames.append(Image.open(buf))\n",
" plt.show()\n",
" frames[0].save('/tmp/train.gif', save_all=True, append_images=frames[1:], duration=1000, loop=0)\n",
" "
],
"id": "d9939dc6c20a888d",
"outputs": [],
"execution_count": 228
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-15T06:36:02.043811Z",
"start_time": "2024-11-15T06:35:58.849931Z"
}
},
"cell_type": "code",
"source": [
"loss_fn = nn.MSELoss()\n",
"train(fc_net, loss_fn, fc_net.parameters(), iters=2000)"
],
"id": "4863d6d7db630b79",
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAC3CAYAAAALgwWHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAgAElEQVR4nO3deVRc153g8e+lAIHYJBYJKCgECIQESIAACSRZdhZvcRxb48RZPLHGid3pyeKc6XbHS8bpuOOxuu22naU7GduTpZOOW44dO2kvSbfdsbUiCQkQmySMkMQOQuxQQFXd+YOCIAkQS1GvCn6fczhUvXrvvh9Pql/duu8uSmuNEEII7+NjdABCCCHmRhK4EEJ4KUngQgjhpSSBCyGEl5IELoQQXkoSuBBCeClJ4MLjKaVMSqk+pZTFlfsK4e0kgQuXcybQsR+HUmpwwvMvzLY8rbVdax2stb7gyn1dRSm1Vim1oAMqlFIPKaValFLdSqmXlFL+C3k+4R0kgQuXcybQYK11MHAB+OSEbf965f5KKV/3R+k9lFKfAP4KuAFIBNYBjxsalPAIksCF2ymlvqeU2quUelkp1Qvco5QqUEoVKaW6lFLNSqkfKKX8nPv7KqW0UmqN8/mvnK+/o5TqVUodVkolznZf5+u3KKXOOGu2P1RKHVRK7Z4i7q1KqRNKqR6lVKtS6mnnS/ucr499y8hzPv+yUuqUUqrTef74K2L8ulKqTil1USm1Ryk11fvxXuAFrXW11voS8D1g0hjF0iIJXBjlTuDXQBiwF7ABDwKRwDbgZuAvpjn+88D/BsIZreX/3Wz3VUqtAl4BHnKetw7In6acHwJPa61DgbXAq87t18Fl3zyOKaXucpb7KSAKOOL8eyf6FJAD5AJ3AV+c4rzpQNmE52WAWSkVNk2sYgmQBC6MckBr/e9aa4fWelBrfUxrfURrbdNanwVeAHZOc/yrWutirfUI8K9A1hz2vQ0o1Vr/zvnac8DFacoZAVKUUhFa616t9ZFp9v0L4P9orU9rrW2M1przlVLmCfvs0Vp3aq3PAT8APjdFWcFA94TnY49Dpjm/WAIkgQuj1E98opRKU0q95bxR1wM8wWiteCotEx4PMJrkZrtv7MQ49OjMbg3TlPM/gA3AaaXUUaXUrdPsmwD8k7NJqIvRDwYHEDdhn4nX4Lwznsn0AaETnodO2C6WMEngwihX9tr4v0AFsNbZRPE4oBY4hmYmJFSllALMU+3srE1/FlgF/CPwmlIqgKv/FhhNzl/SWq+Y8BN4Ra09fsJjC9A0xakrgU0Tnm8CGrXWXdP8bWIJkAQuPEUIo00D/Uqp9Uzf/u0qbwI5SqlPOnvCPMhoe/WklFL/XSkVqbV2OGPVjNaq2wCtlEqasPtPgMecfwtKqRXOdvGJ/sa53QJ8g9F7AZP5F+B+57eUcODbwM9n+8eKxUcSuPAUf8Vob4teRmvjUyUzl9FatwJ3A88CHUAyUAIMTXHIrUC1s+fMM8DdWuthrXUv8BRwxNlkkqu1/o2z3N84m4ROAjddUd6/A6XOc77OFElZa/0mo+3z+4BzQA2jTUxiiVOyoIMQo5RSJkabMe7SWu9fwPP4MnpDNNF5A1OIOZEauFjSlFI3K6XClFLLGO1qaAOOGhyWEDMiCVwsdduBs4z2ErkZuENrPVUTihAeRZpQhBDCS0kNXAghvJQkcCGE8FJunQUuMjJSr1mzxp2nFMLttNY4HA7sdjt2u3388VTNlUoplFL4+PhwoceGzXH1Pr4+kBDmN17+2DmmK9NkMl324+Mj9TVvdfz48Yta66vGKLg1ga9Zs4bi4mJ3nlKIBWWz2ejs7KSjo4Oenh56e3sZGBgYf93Hx4fg4GBCQ0MJDg4mMDCQZcuWsWzZMvz9/fH3978ssSY+/NakwzoVULXnE1dt11ozMjLC8PAwQ0NDDA0NMTAwQE9PDz09PfT19aG15lgbvHnBh0tDELXcxFevi+ee7evw9ZWZfL2BUur8ZNvlX0+IWbDb7Vy6dImOjg4uXrxIV1cXWmuUUgQFBREWFkZcXByhoaGEhISwfPnyWdV8Y1cE0tg1OOn2ySilxj8IgoOvng7Gbrezt6iWvUc+ZMg2+tHQPmDnyf+oo67uHDenhRMVFUVUVBShoaGMziYgvIUkcCGmYbfbx2vYYwnb4XCglCIsLIykpCQiIyMJDw93SW32oZvW8chvyxkcsY9vC/Qz8dBN6+ZUnslk4p/2N4wn7zEjDsU7DSZuSByiurqa6upqAgICiIqKIiYmhqioKGly8QKSwIW4gt1up729naamJlpbW7HZbACEhYWRmJhIREQE4eHh+Pn5ufzcd2SPzqX19B9P09Q1SOyKQB66ad349rlomqRGD9Deb+f6669ncHCQ9vZ22tvbaWlpob6+nmXLlhEXF0d8fDwhITJrraeSBC4Eo0m7ra1tPGnb7Xb8/PyIiYkhOjqa8PBw/P3dswzlHdnmeSXsK12rWSYwMBCLxYLFYhm/DvX19Zw9e5ba2lpWrlxJfHw8sbGxC/KhJeZOErhYsmw2G21tbTQ3N1+WtM1mMzExMURGRi6KZoTZNMuYTCZiYmKIiYnBarXS2NhIfX09J0+epKKigtjYWJKTkwkNDb3qWOF+ksDFkqK1prOzk/Pnz9Pc3Izdbsff3x+z2UxsbCwRERH8vqyZ//nTCpc1YRhtrs0yAQEBJCcnk5SURHd3N/X19dTX19PQ0EB0dDQpKSmsWLHCHX+CmIJbh9Ln5uZq6UYojDAyMkJDQwPnz5+nt7cXk8l0WdIeq2m/UdI4aW31qV2ZXp3EXWV4eJi6ujrq6uo41DjC2w2+dAw6FsUHnSdTSh3XWudeuV1q4GJR6+rq4vz58zQ2NmK32wkNDWXjxo1Ttuc+/cfTlyVvgMERO0//8bQkJ8Df359169ZR0RvA3v2VDNlHRx01dg3y8Gsn0VpzZ07cNUoRriIJXCw6NpuNpqYmzp8/T1dXFz4+PpjNZhISElixYsW0fZ2n6rEx1fal6tl3axmyX/7t3Wpz8OS/l/OxlDDpueImksCF13mjpHHS9tyBgQHOnj1LfX09NpuN4OBgMjIyMJvNM+5BMtuBNEvVVB9oFwcdfPDBByQlJZGSkiK9VhaYJHDhVa5so27sGuTh357k/PlzJPt2AhAbG0tCQgLh4eGzHlno6oE0i9WUH3RhAcTFRVBbW0tDQwPr168nLi5ORnguEO/vIyWWlMnaqK0jDn5e0kVCQgIf+chHyMnJISIiYk5J445sM0/tysS8IhAFmFcEyg3MSTx00zoC/UyXbQv0M/E3N6eRlZXF9u3bCQwMpLS0lIMHD9LV1WVQpIub9EIRXmW6yZ7qJpnsSSycqZqyxmitaWhooLq6mqGhIZKTk1m3bh0mk2maUsVk5twLRSn1U+A2oE1rneHc9rfA/UC7c7dHtdZvuy5cIS6ntaa9vZ2IQMXFwatTuLRRu9+1RowqpYiPjyc6Opqqqipqa2tpb28nOztbBgK5yEyaUH7O6FqBV3pOa53l/JHkLRaE1pqWlhb279/PkSNH+FSiD8t8L28akTZqz+bn58emTZvIy8vDarWyf/9+amtrp5zLXMzcNWvgWut9Sqk1Cx+KEJe7dOkSVVVVdHZ2EhQUxKZNm7jVbCbzZItLJ3sS7hEdHc3KlSspKyujqqqK1tZWsrKyWL58udGhea0ZtYE7E/ibVzSh7AZ6gGLgr7TWnVMc+wDwAIDFYtl8/vyk85ILMa6vr4/q6mpaWlpYtmwZ69atIz4+flHMSyJGv1XV19dTUVGBUoqNGzdiNssH8HSmagOfawJfDVwENPB3QIzW+r5rlSM3McV0rFYrZ86c4cKFC/j4+LB27VqSkpJk1ZhFqr+/n5KSEjo7O0lMTGTDhg3yIT0Flw6l11q3Tij4ReDNecQmljibzUZtbS21tbU4HA4SEhJITU1l2bJlRocmFlBQUBCFhYVUVVVRV1dHb28vmzdvdtu0vYvBnBK4UipGa93sfHonUOG6kMRS4XA4uHDhAmfOnGFoaIiYmBjS0tImXRpMLE4+Pj5kZGQQGhpKeXk5+/fvJy8vT3qpzNBMuhG+DFwPRCqlGoDvANcrpbIYbUI5B/zFAsYoFpmxniXV1dX09/cTHh5Obm4u4eHhRocmDGKxWAgJCeHYsWMcOHCArKwsYmNjjQ7L48lAHuFWfX19lJeXc/HiRYKDg1m/fj2rV6+WodYCGL0PUlxcTGdnJykpKaxbt07+byDTyQqD2e12ampqqK2tHf/anJCQIDetxGUCAgIoKCigvLycmpoa+vv7ycrKktGbU5AELhZca2srFRUVDAwMYDab2bBhAwEBAUaHJTyUyWRi06ZNBAcHU11dzcjICLm5udIbaRJyRcSCGRgYoLKykpaWFoKDgykoKCAyMtLosIQXUEqxdu1a/P39KSsro6ioiPz8fOmhcgVJ4MLlHA4HZ8+e5cyZM2itSUtLIykpSb4Gi1mzWCz4+flx4sQJDh06xNatW+Xb2wTSAClcqqOjgw8++IDq6moiIyO54YYbSElJkeQt5iwmJob8/HwGBgY4ePAg/f39RofkMSSBC5ewWq2UlJRw6NAh7HY7eXl55OfnyzwXwiWioqIoKChgZGSEgwcP0tPTY3RIHkGaUARw7bmdpzI2r0VVVRU2m42UlBTWrl0rN5yEy61cuZJt27ZRVFTEoUOHKCwsXPIDfqQGLsaXKWvsGkQzukzZI78t542SxmmPGxwc5OjRo5SVlRESEsLOnTtJS0uT5C0WTEhICIWFhfj4+FBUVERfX5/RIRlKEriYdJmywRE7T//x9KT7j9W6P/jgAy5evEh6ejqFhYWyErlwi6CgIAoKCtBaU1RUxMDAgNEhGUYSuJhyhfHJtlutVo4dO0ZpaSnBwcHs3LmTpKQkGS0n3CokJIStW7dis9koKirCarUaHZIhJIGLKZcjm7h9bH3D999/n/b2djZs2EBhYaFMPCUMExYWRn5+PlarlcOHDzM0NGR0SG4nCVxMucL42DJlY/NTlJSUjNe6k5OTZRi8MFx4ePh4F8OioiKGh4eNDsmt5B0ouCPbzFO7MjGvCEQB5hWBPLUrk09lxdLY2Mj7779PW1sb69evl1q38DiRkZHk5ubS29vL0aNHsdvt1z5okZDZCMWkhoaGKC8vp7m5mRUrVpCVlSU3KYVHa2pq4vjx48TGxpKTk7Oo7svIbIRixpqamigvL8dms7F+/XqSkpKkuUR4vNjYWAYGBqiuriYoKIi0tDSjQ1pwksDFOJvNRnl5OQ0NDYSFhZGVlbXkB0oI75KcnExfXx81NTUEBQURHx9vdEgLShK4AKCrq4sTJ07Q399PSkoKqampUusWXkcpRWZmJgMDA5SVlbF8+XIiIiKMDmvByDt0idNaU1tby4EDB7Db7RQUFJCWlibJW3gtk8lEbm4uy5cv59ixY4t6tKa8S5ewoaEhjh49SlVVFatWrWLnzp0yX7dYFPz9/dmyZQsAR48eXbTdCyWBL1Ht7e3jQ+EzMjLIy8uTyfLFohIUFEReXh6Dg4MUFxfjcDiMDsnlJIEvMQ6Hg+rqaoqKivDz82P79u0kJiYuqi5XQoyJiIggMzOTjo4OTp+efG4fbyY3MZeQ/v5+Tpw4QVdXFxaLhfT0dJk5UCx6FouFzs5OPvzwQ1auXEl0dLTRIbmM1MCXiMbGRvbt20dfXx+bN29m06ZNkrzFkpGRkUFoaCilpaWLakUfSeCLnM1mo7S0lBMnTozP2R0bG2t0WEK41VjPFK01x48fXzTD7SWBL2Ld3d3s27eP+vp6UlJSKCwslCXOxJIVFBREdnY23d3dVFZWGh2OS8h36EXq/PnzVFRU4O/vT0FBgXQPFAKIjo4mOTmZ2tpaVq5c6fUjNSWBLzJ2u53y8nLq6+uJjIwkJyeHZcuWGR2WEB4jLS2Nrq4uTp48SVhYmFdPFyFNKIvIwMAABw8eHG8y2bJliyRvIa7g4+NDTk4Ofn5+lJSUeHV7+DUTuFLqp0qpNqVUxYRt4Uqp/1RK1Th/r1zYMMW1tLW1sW/fPvr7+8nLy5Ph8EJMIyAggE2bNtHT0+PV/cNn8g7/OXDzFdseBt7TWqcA7zmfCwNorTlz5gxHjhwhICCAHTt2LKp+rkIslNWrV5OQkEBtbS0dHR1GhzMn10zgWut9wKUrNn8K+IXz8S+AO1wcl5iB4eFhjh07xunTpzGbzWzfvl1WyxFiFjZs2EBQUBAlJSWMjIwYHc6szfU79mqtdTOA8/cq14UkZqK7u5v9+/fT1tZGRkYG2dnZMjBHiFny9fUlKyuLwcFBr+xauOCNpEqpB5RSxUqp4vb29oU+3ZLQ0NDAgQMHcDgcFBYWylwmQsxDeHg4KSkp1NfX09zcbHQ4szLXBN6qlIoBcP5um2pHrfULWutcrXVuVFTUHE8n4M9dBEtKSlixYgU7duwgPDzc6LCE8HqpqamEhYVRVlaG1Wo1OpwZm2sC/z1wr/PxvcDvXBOOmMrg4CCHDx/m3LlzJCUlUVBQQEBAgNFhCbEo+Pj4kJ2djd1up6ysDHcu9j4fM+lG+DJwGFinlGpQSn0J2AN8XClVA3zc+VwskIsXL7Jv3z56enrYvHkz6enp0kVQCBcLCQlh/fr1tLW10djYaHQ4M3LNu15a689N8dJHXRyLuILWmrNnz1JdXc3y5cspLCwkJCTE6LCEWLTWrFlDY2MjlZWVrFq1yuMXOZFqnIey2+2UlpZSVVVFdHQ0O3bskOQtxALz8fFh48aNjIyMUFVVZXQ41yQJ3ANZrVYOHz5MQ0MD69atY/Pmzfj5+RkdlhBLQlhYGMnJydTX1+PpPeckgXuYsf7d3d3dbN68mdTUVOkiKISbpaamEhQURHl5uUfPlSIJ3IM0Nzdz8OBBALZt2yYLLwhhEJPJRGZmJv39/Zw5c8bocKYkCdwDaK2pqamhuLiYkJAQduzYwYoVK4wOS4glLSoqivj4eGpra+nu7jY6nElJAjeY3W6npKSEU6dOYTabKSwslP7dQniIDRs24Ofnx8mTJ3E4HEaHcxVJ4AayWq0cOnSIxsZG0tLSyM7OxmQyGR2WEMLJ39+f9PR0urq6qK+vNzqcq0gCN0hXVxf79++nt7eX3NxcUlJS5GalEB7IbDYTHh7OqVOnGB4eNjqcy0gCN0BTU9NlNytjYmIMjkgIMRWlFBkZGQwPD1NTU2N0OJeRBO5GWmtOnz7N8ePHCQsLY8eOHYSFhRkdlhDiGsLCwrBYLNTV1dHb22t0OOMkgbuJzWbjxIkTnDlzhri4OJmMSggvk5aWhslkorKy0mMmu5IVABbYGyWN/MMfqmnqHmLlMs1XCmK5LStL2ruF8DLLli0jNTWVqqoqWltbPWLpQqmBL6A3Shp5+LWTNHUPAdA5pHj+YDu/K20yODIhxFysWbOGoKAgqqqqPGKEpiTwBfTU25VYbZf3HR0csfP0H713FWwhljKTyURGRgb9/f3U1dUZHY4k8IWgtaa2tpbW3sm7HDV1Dbo5IiGEq6xatYpVq1ZRU1Nj+Oo9ksBdzOFwUFlZSVVVFZHLJx+UE7si0M1RCSFcKT09Hbvdbni3QkngLmSz2Th+/Dh1dXUkJSXx2G2ZBPpdnsQD/Uw8dNM6gyIUQrhCcHAwFouF8+fP09/fb1gcksBdZGhoiKKiIlpaWkhPTyc9PZ07c+J4alcm5hWBKMC8IpCndmVyR7bZ6HCFEPM0Nnr69Gnj7mlJN0IX6Ovr48iRI1itVnJzcy8bWXlHtlkSthCLUGBgIElJSXz44YckJycbMihPauDzdOnSJQ4cOIDNZqOgoECGxQuxhCQnJ+Pn58epU6cMOb8k8Hlobm7m8OHD+Pv7s23bNsLDw40OSQjhRv7+/qxdu5a2tjYuXrzo9vNLAp+js2fPUlxcTFhYGNu2bSM4ONjokIQQBkhMTCQgIIBTp065fYi9JPBZ0lpTUVFBZWUl0dHRFBQUsGzZMqPDEkIYxGQykZqaSmdnJ62trW49tyTwWbDb7ePdBBMTE9m8ebMswCCEID4+nqCgIKqrq926co8k8BkaGhri8OHDNDc3k56eTkZGBj4+cvmEEODj40NaWhp9fX00Nze777xuO5MX6+vr4+DBg3R3d7N582aSkpKMDkkI4WFiYmIIDg7mzJkzbmsLlwR+DZ2dnRw8eJDh4WEKCgqIjY01OiQhhAdSSpGamurWWrgk8Gk0Nzdz6NAhfH192b59u3QTFEJMKyYmhqCgIGpqatxSC5cEPoW6ujqKi4sJDQ1l+/bt0k1QCHFNPj4+pKam0tPTQ0tLy8Kfbz4HK6XOKaXKlVKlSqliVwVlJK01VVVVVFRUsHr1aukmKISYldjYWJYvX+6WWrgrauA3aK2ztNa5LijLUA6Hg7KyMmpra0lISCA3NxdfX5kuRggxcz4+PqSkpNDd3U1bW9vCnmtBS/cidrud4uJi6uvrSU1NJTMzU7oJCiHmJC4ujsDAwAXvkTLfDKWB/1BKHVdKPeCKgIwwMjJCUVERra2tZGRksG7dOll0WAgxZ2O18K6uLtrb2xfuPPM8fpvWOge4BfiqUuq6K3dQSj2glCpWShUv5B8yV1arlUOHDtHZ2UlOTg6JiYlGhySEWATi4uIICAhY0FV75pXAtdZNzt9twOtA/iT7vKC1ztVa50ZFRc3ndC7X39/PwYMH6e/vJz8/H7NZ5u0WQriGyWQiOTmZS5cucenSpQU5x5wTuFIqSCkVMvYYuBGocFVgC627u5uDBw8yMjLC1q1bWbVqldEhCSEWGYvFgp+fH2fPnl2Q8ufTxWI18LqzrdgX+LXW+g8uiWqBdXR0cPToUXx9fdm2bRshISFGhySEWIR8fX1JSEjgww8/pL+/n6CgINeWP9cDtdZngU0ujMUtWlpaOH78OIGBgWzdupXly5cbHZLXGRkZoaGhAavVanQoYhoBAQHExcXh5+dndChLWmJiImfPnuXs2bNkZma6tOwl1cm5vr6esrIyQkND2bJliwzQmaOGhgZCQkJYs2aN9NbxUFprOjo6aGhokBvzBgsICMBsNnPhwgVSU1NdmneWTEfn2tpaSktLiYiIkNGV82S1WomIiJDk7cGUUkRERMi3JA+RlJSEw+Hg/PnzLi130SfwsaHxVVVVxMTEkJ+fL18pXUCSt+eTfyPPERoayqpVq6irq8Nut7us3EWdwK8cGp+TkyMr6CwSJpOJrKys8Z89e/a4rOzS0lLefvttl5Q1k0nQnn/+eQYGBsaf33rrrXR1dbnk/MJzJCcnMzw8TENDg8vKXLRt4Ha7nRMnTtDS0kJKSoqMrlxkAgMDKS0tXZCyS0tLKS4u5tZbb12Q8q/0/PPPc88994zfUHfVh4fwLBEREYSFhVFbW4vFYnFJPlqUNfCRkRGOHDlCS0sL6enppKWlSfJeArq7u1m3bh2nT58G4HOf+xwvvvgiAH/5l39Jbm4u6enpfOc73xk/5tixYxQWFrJp0yby8/Pp7u7m8ccfZ+/evWRlZbF3797LzlFZWUl+fj5ZWVls3LhxfJTds88+S0ZGBhkZGTz//PNXxfb+++9z2223jT//2te+xs9//nN+8IMf0NTUxA033MANN9wAwJo1a7h48eKU5Z47d47169dz//33k56ezo033sjg4KCrLqNYIEopkpOT6e/vd9nix4uuBm61Wjly5Ai9vb1kZ2cTFxdndEiLWkVFBT09PS4tMzQ0lIyMjGn3GRwcJCsra/z5I488wt13382PfvQjdu/ezYMPPkhnZyf3338/AE8++STh4eHY7XY++tGPcvLkSdLS0rj77rvZu3cveXl59PT0sHz5cp544gmKi4v50Y9+dNV5f/KTn/Dggw/yhS98geHh4fGFrn/2s59x5MgRtNZs2bKFnTt3kp2dfc2/9Rvf+AbPPvssf/rTn4iMjLzstanKXblyJTU1Nbz88su8+OKLfOYzn+G1117jnnvumcnlFQaKiYkhICCAc+fOER0dPe/yFlUC7+/vp6ioCKvVSl5eHqtXrzY6JLFApmpC+fjHP85vfvMbvvrVr1JWVja+/ZVXXuGFF17AZrPR3NxMVVUVSiliYmLIy8sDRj84rqWgoIAnn3yShoYGdu3aRUpKCgcOHODOO+8cH6Sxa9cu9u/fP6MEPp2pyr399ttJTEwc/wDbvHkz586dm9e5hHv4+PiQkJDA6dOn6evrm/dCMYsmgXd3d3PkyBEcDgcFBQWy/JmbXKum7G4Oh4Pq6moCAwO5dOkScXFx1NXV8cwzz3Ds2DFWrlzJ7t27sVqtaK1n3bT2+c9/ni1btvDWW29x00038dJLL81oulBfX18cDsf485l075uu3IndYE0mkzSheBGLxcKZM2c4d+7cvN8/i6IN/NKlSxw6dAilFIWFhZK8l7DnnnuO9evX8/LLL3PfffcxMjJCT08PQUFBhIWF0drayjvvvANAWloaTU1NHDt2DIDe3l5sNhshISH09vZOWv7Zs2dJSkriG9/4BrfffjsnT57kuuuu44033mBgYID+/n5ef/11duzYcdlxCQkJVFVVMTQ0RHd3N++99974a1OdbyblCu8TEBBATEwM9fX12Gy2eZXl9TXw9vZ2jh49KkPjl5gr28Bvvvlm7rvvPl566SWOHj1KSEgI1113Hd/73vf47ne/S3Z2Nunp6SQlJbFt2zYA/P392bt3L1//+tcZHBwkMDCQd999lxtuuIE9e/aQlZU13rY+Zu/evfzqV7/Cz8+P6OhoHn/8ccLDw9m9ezf5+aOTcX75y1++qvkkPj6ez3zmM2zcuJGUlJTLXn/ggQe45ZZbiImJ4U9/+tP49pycnEnLleYS75eYmEhTUxMNDQ2sWbNmzuUod6ycPCY3N1cXF7tu6cyxeU2CgoLYunUrAQEBLitbTK26upr169cbHYaYAfm38kxaa/bt24fWmp07d16zKU8pdXyyZSu9tgmlsbFxfNX4wsJCSd5CCK+hlCIxMZHe3l46OjrmXI5XJvALFy5w4sQJVq5cydatW/H39zc6JCGEmBWz2Yyfn9+8msS8LoHX1dVRVlZGVFQUWx+/pOoAAAq4SURBVLZskXlNhBBeyWQyYbFYaGlpmXMvIq9K4DU1NVRUVLB69Wry8vLw9fX6e7BCiCUsISEBrfWcZyn0igSutebUqVOcOnUKs9lMbm6uTEolhPB6QUFBREVFUV9ff9k4gZny+ASutaayspKamhosFgtZWVn4+Hh82EIIMSMWiwWr1Up7e/usj/XoTOhwODh58iR1dXUkJiayceNGSd4C+PN0shkZGXz6058en451bGjyuXPnUErxwx/+cPyYsQmkAHbv3o3ZbGZoaAiAixcvzqs/7pjrr7+ea3WVfeONN6iqqhp//vjjj/Puu+/O+9zCO61evRp/f38uXLgw62M9Nhs6HA5KS0u5cOECKSkppKeny4yCYtzYXCgVFRX4+/vzk5/85Kp9Vq1axfe//32Gh4cnLcNkMvHTn/50oUO9ypUJ/IknnuBjH/uY2+MQnsFkMhEfH09ra+usV1DyyAQ+NsNbY2MjaWlpMh2smNaOHTv48MMPr9oeFRXFRz/6UX7xi19Metw3v/lNnnvuuWmHM/f39/OJT3yCTZs2kZGRMT697HvvvUd2djaZmZncd9994zX5iSZOVPTqq6+ye/duDh06xO9//3seeughsrKyqK2tZffu3bz66qvTlrtmzRq+853vkJOTQ2ZmJqdOnZr5BRIez2KxoLWe9WIPHteNw2azUVxcTHt7OxkZGbIgq4f7+6N/z6lLrk0maeFpfCv/WzPa12az8c4773DzzTdP+vrDDz/MLbfcwn333XfVaxaLhe3bt/PLX/6ST37yk5Me/4c//IHY2FjeeustYHTSNKvVyu7du3nvvfdITU3li1/8Ij/+8Y/55je/ec14CwsLuf3227ntttu46667LnvtWuVGRkZy4sQJ/vmf/5lnnnmGl1566ZrnE94hODiY8PBwLly4QHJy8owrrIbUwN8oaWTbnv8i8eG32Lbnv3ijpBH480IM7e3tbNq0SZK3mNLYXCi5ublYLBa+9KUvTbpfYmIi+fn5/PrXv5709UcffZSnn356yh4AmZmZvPvuu3zrW99i//79hIWFcfr0aRITE0lNTQXg3nvvZd++ffP+m65V7q5duwCZPnaxslgs9Pf3z2pkpttr4G+UNPLIb8sZHBld2LOxa5BHfluOzWZjtfUC3d3d5OTkYDab3R2amIOZ1pRdbTZLqj366KPcddddXHfddVe9tnbtWrKysnjllVcmPTY1NZXjx4/z9ttv88gjj3DjjTdy++23z+i8E2tR850+Fv48hazJZJr3LHbC88TExFBRUcGFCxeuWtxjKm6vgT/9x9PjyXvM4Iidp96qpKenh9zcXEnewqXS0tLYsGEDb7755qSvP/bYYzzzzDOTvtbU1MTy5cu55557+Ou//mtOnDhBWloa586dG293/+Uvf8nOnTuvOnb16tVUV1fjcDh4/fXXx7dPNX3sTMsVi5Ovry9xcXE0NzdPeeP9Sm5P4E1dkw8Z7bBq8vPzXbLMkBBXeuyxx6a8QZSenk5OTs6kr5WXl4+vgfnkk0/y7W9/m4CAAH72s5/x6U9/mszMTHx8fPjKV75y1bF79uzhtttu4yMf+QgxMTHj2z/72c/y9NNPk52dTW1t7fj2mZYrFi+LxYLD4aCxsXFG+7t9Otlld/0DjZMk8ehQf4oe/bjbYhFzJ1OUeg/5t/I+H3zwAUqpy5r8PGY62YduWkeg3+XD4AN8fXj4lg3uDkUIITxOXFwc3d3dU64KNZHbE/gd2Wb+9y3JhDuX9IsJXcae/7aRO7Kl3VsIIcbuAc6kT/i8eqEopW4Gvg+YgJe01nuudUxnZyfhPbX8/XZ/CgoK5r0qsxBCLCYBAQGsWrVqfCDjdH3C51wDV0qZgH8CbgE2AJ9TSk3bDmKz2Th8+DB+fn5s27ZNkrcXc+e9EzE38m/kveLi4hgcHLxmn/D5NKHkAx9qrc9qrYeBfwM+Nd0B/f39BAYGUlhYKIsPe7GAgAA6OjokQXgwrTUdHR2y1KCXWr16Nb6+vtdsRplPE4oZqJ/wvAHYcuVOSqkHgAdg9FOlsLBwfECC8E5xcXE0NDTMafpL4T4BAQHExcUZHYaYA19fX2JiYmhubiYjI2Pq/eZxjskaZq6qkmmtXwBeANi8ebOW5O39/Pz8ZJoDIRZYXFwc9fX1tLa2TrnPfJpQGoD4iecDmqY7QGYUFEKImYmIiCAgIGDaZpT5JPBjQIpSKlEp5Q98Fvj9PMoTQgjhpJQiLi5u2qbKOSdwrbUN+BrwR6AaeEVrXTnX8oQQQlwuLi5u2s4Cbh1Kr5TqBU677YQzFwlcNDqISXhqXOC5sUlcs+OpcYHnxmZEXAla66grN7p7OtnTk43nN5pSqljimh1PjU3imh1PjQs8NzZPissjl1QTQghxbZLAhRDCS7k7gb/g5vPNlMQ1e54am8Q1O54aF3hubB4Tl1tvYgohhHAdaUIRQggv5ZYErpS6WSl1Win1oVLqYXecc6aUUueUUuVKqVKlVLGBcfxUKdWmlKqYsC1cKfWfSqka5++VHhLX3yqlGp3XrFQpdasBccUrpf6klKpWSlUqpR50bjf0mk0TlydcswCl1FGlVJkztu86txt9zaaKy/Br5ozDpJQqUUq96Xxu+PtyPLaFbkJxTjt7Bvg4o8PvjwGf01pXLeiJZ0gpdQ7I1Vob2t9UKXUd0Af8i9Y6w7ntH4BLWus9zg++lVprty4DP0Vcfwv0aa0nXwnYPXHFADFa6xNKqRDgOHAHsBsDr9k0cX0G46+ZAoK01n1KKT/gAPAgsAtjr9lUcd2MwdfMGd//AnKBUK31bZ7wvhzjjhr4rKedXYq01vuAS1ds/hTwC+fjXzCaCNxqirgMp7Vu1lqfcD7uZXQ0sBmDr9k0cRlOj+pzPvVz/miMv2ZTxWU4pVQc8AngpQmbDX9fjnFHAp9s2lmP+A/tpIH/UEodd05960lWa62bYTQxAKsMjmeirymlTjqbWAz7CgmglFoDZANH8KBrdkVc4AHXzNkcUAq0Af+ptfaIazZFXGD8NXse+BvAMWGb4ddrjDsS+IymnTXQNq11DqMrC33V2WQgpvdjIBnIApqBfzQqEKVUMPAa8E2tdY9RcVxpkrg84pppre1a6yxGZw/NV0pNPdm0G00Rl6HXTCl1G9CmtT7uzvPOhjsS+KynnXUnrXWT83cb8DqjTT6eotXZpjrWttpmcDwAaK1bnW84B/AiBl0zZ3vpa8C/aq1/69xs+DWbLC5PuWZjtNZdwPuMtjMbfs0mi8sDrtk24HbnfbJ/Az6ilPoVHnS93JHAPXbaWaVUkPNGE0qpIOBGoGL6o9zq98C9zsf3Ar8zMJZxY/95ne7EgGvmvPH1/4BqrfWzE14y9JpNFZeHXLMopdQK5+NA4GPAKYy/ZpPGZfQ101o/orWO01qvYTRv/ZfW+h486X2ptV7wH+BWRnui1AKPueOcM4wrCShz/lQaGRvwMqNfE0cY/dbyJSACeA+ocf4O95C4fgmUAycZ/c8cY0Bc2xltijsJlDp/bjX6mk0Tlydcs41AiTOGCuBx53ajr9lUcRl+zSbEeD3wpidcr4k/MhJTCCG8lIzEFEIILyUJXAghvJQkcCGE8FKSwIUQwktJAhdCCC8lCVwIIbyUJHAhhPBSksCFEMJL/X+EgoctNeFIPgAAAABJRU5ErkJggg==\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAC3CAYAAAALgwWHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAgAElEQVR4nO3deXzU1b34/9fJZN/3PSEJSUgISwhJ2EHcoYiWKlbrrVys9nZTe1s37E97vbVyv1q1drFVa13aKmrFKi5YcEFAgQRCgOyBQBYSspB9m2TO74+ZxABJCNlmEt7Px2Memfks5/OeA/OeM+dzPuejtNYIIYSYeOysHYAQQojhkQQuhBATlCRwIYSYoCSBCyHEBCUJXAghJihJ4EIIMUFJAhfjTillUEo1K6UiR3NbIS42ksDFeVkSaM/DpJRq6/P6Oxdanta6W2vtrrU+MZrbjhalVKxSaswukFBKzVZKfayUqlVKdfWzfqdSqr1PHR85a/2VSql8pVSrUuqTvl9uSik7pdQTSqk6S/mPKaXUWL0XYV2SwMV5WRKou9baHTgBXNNn2d/P3l4pZT/+UU4oncDrwO2DbPNffeo4qWehUioIeAt4APADsoB/9NnvB8BKYAaQDKwBbhvd8IWtkAQuRkwp9Sul1Cal1GtKqSbgFqXUAqXUV0qpeqXUSaXUM0opB8v29koprZSKsrz+m2X9h0qpJqXUl0qp6Avd1rJ+hVKqQCnVoJT6nVJql1Jq3QBxz1dK7VdKNSqlqpRSj1tW7bCs72kBp1lef08plaeUOm05fsRZMf5EKXVMKVWjlNqolOr386W1ztVavwjkDKO6vwVkaa3f1lq3Ab8E0pRSsZb1twJPaK0rtNalwJNAv+9fTHySwMVo+SbmlqAXsAnoAu4C/IFFwNXA9wfZ/2bg/wN8Mbfy//dCt1VKBQJvAPdYjnsMSB+knN8Bj2utPYFYzC1bgKVwxi+PfUqp6y3lXgsEAHs4s+WLZV0KkApcD3x3kGOfz+OWL4KdSqmlfZYnAQd7XmitGzG/z6T+1lueJyEmJUngYrTs1Fq/p7U2aa3btNb7tNZ7tNZdWuujwHPAskH2f0trnaG1NgJ/x/zz/0K3XYW5dfovy7qngJpByjECcUopP611k9Z6zyDbfh/4tdY6X2vdBfwKSFdKhfXZZqPW+rTWugR4BrhpkPIG83MgGggDXgTe7/kFArgDDWdt3wB4WPq6Xc9a3wB4DDMOYeMkgYvRUtr3hVIqQSn1vlKqUinVCDyCuVU8kMo+z1sxJ6oL3Ta0bxzaPFNb2SDl/CcwHchXSu1VSq0cZNspwB8sXUL1mL8YTEB4n2361sFxSzwXTGv9lda6WWvdYelq2QOssKxuBjzP2sUTaLK839az1nsCTcOJQ9g+SeBitJw9auPPwGEg1tJF8RAw1qMhTtInoVpapGEDbWxpTX8bCAR+A/xTKeXMue8FzMn5Nq21d5+Hy1mt9og+zyOBihG8lzNC5eu6OwLM7lmhlPLA3Fo/0t96y/MzRrGIyUMSuBgrHph/vrcopRIZvP97tGwBUpRS11hGwtyFub+6X0qp/1BK+WutTZZYNeZW9SlAK6Vi+mz+J+BBy3tBKeVt6Rfv617L8kjgTsznAvo7rrJ8UThaXjsrpXqe+1qGCTorpRyUUt8FFgAfW3b/J5CslLrOUsbDQIbWusiy/hXgZ0qpUKVUOPBT4KXz1JuYoCSBi7HyM8wjIpowt8b7TWajSWtdBdyIeeRFLTAVOAB0DLDLSiDXMnLmCeBGrXWn1roJeAzYY+kySdVav2kp901Ll1A2cNVZ5b2HeVjfAWAzAyfOqUAb5hOMBsvznhEpDsCvgWrL47+Aa3sStOU9rgX+H3Aa80nTm/uU/UdgK+ZWdzbwL+AvA8QhJjglN3QQk5VSyoC5G+N6rfUXY3gce8wnRKMtJzCFGBfSAheTilLqaqWUl1LKCfNQwy5gr5XDEmJMSAIXk81i4CjmUSJXA9dprQfqQhFiQpMuFCGEmKCkBS6EEBOUJHAhhJigxnXWOH9/fx0VFTWehxRCiAkvMzOzRmt9zjUN45rAo6KiyMjIGM9DCiHEhKeUOt7fculCEUKICUoSuBBCTFCSwIUQYoKy+q2vjEYjZWVltLe3WzsUMQBnZ2fCw8NxcHCwdihCiD6snsDLysrw8PAgKioKufeq7dFaU1tbS1lZGdHR0effQQgxbqzehdLe3o6fn58kbxullMLPz09+IQlhg6yewAFJ3jZO/n2EsE02kcCtzWAwkJyc3PvYuHHjqJWdlZXFBx98MCplubsPdpcxs6effprW1tbe1ytXrqS+vn5Uji+EsC1W7wO3BS4uLmRlZY1J2VlZWWRkZLBy5WC3Wxw9Tz/9NLfccguurq4Ao/blIYSwPdICH0BDQwPTpk0jPz8fgJtuuonnn38egB/84AekpqaSlJTEww8/3LvPvn37WLhwIbNnzyY9PZ2GhgYeeughNm3aRHJyMps2nXlTmiNHjpCenk5ycjKzZs2isLAQgCeffJIZM2YwY8YMnn766XNi++yzz1i1alXv6x//+Me89NJLPPPMM1RUVLB8+XKWL18OmK9+rampGbDckpISEhMTuf3220lKSuLKK6+kra1ttKpRCDGGbKoFfvjwYRobG0e1TE9PT2bMmDHoNm1tbSQnJ/e+fuCBB7jxxhv5/e9/z7p167jrrrs4ffo0t99+OwCPPvoovr6+dHd3c9lll5GdnU1CQgI33ngjmzZtIi0tjcbGRlxdXXnkkUfIyMjg97///TnH/dOf/sRdd93Fd77zHTo7O+nu7iYzM5O//vWv7NmzB6018+bNY9myZcyZM+e87/XOO+/kySef5NNPP8Xf/8wbwA9Uro+PD4WFhbz22ms8//zzrF27ln/+85/ccsstQ6leIYQV2VQCt5aBulCuuOIK3nzzTX70ox9x8ODB3uVvvPEGzz33HF1dXZw8eZKcnByUUoSEhJCWlgaYvzjOZ8GCBTz66KOUlZWxZs0a4uLi2LlzJ9/85jdxc3MDYM2aNXzxxRdDSuCDGajc1atXEx0d3fsFNnfuXEpKSkZ0LCHE+LCpBH6+lvJ4M5lM5Obm4uLiQl1dHeHh4Rw7downnniCffv24ePjw7p162hvb0drfcGjNW6++WbmzZvH+++/z1VXXcULL7zAUG6wYW9vj8lk6n09lCF+g5Xr5OTU+9xgMEgXihAThPSBD+Kpp54iMTGR1157jfXr12M0GmlsbMTNzQ0vLy+qqqr48MMPAUhISKCiooJ9+/YB0NTURFdXFx4eHjQ1NfVb/tGjR4mJieHOO+9k9erVZGdns3TpUt555x1aW1tpaWlh8+bNLFmy5Iz9pkyZQk5ODh0dHTQ0NLB9+/bedQMdbyjlCiEmFptqgVvL2X3gV199NevXr+eFF15g7969eHh4sHTpUn71q1/xP//zP8yZM4ekpCRiYmJYtGgRAI6OjmzatImf/OQntLW14eLiwrZt21i+fDkbN24kOTm5t2+9x6ZNm/jb3/6Gg4MDwcHBPPTQQ/j6+rJu3TrS09MB+N73vndO90lERARr165l1qxZxMXFnbH+jjvuYMWKFYSEhPDpp5/2Lk9JSem3XOkuEWLiGtd7Yqampuqz5wPPzc0lMTFx3GIQwyP/TkJYj1IqU2udevZy6UIRQogJShK4EEJMUOdN4EqpCKXUp0qpXKXUEaXUXZblvkqpfyulCi1/fcY+XCGEED2G0gLvAn6mtU4E5gM/UkpNB+4Htmut44DtltdCCCHGyXkTuNb6pNZ6v+V5E5ALhAHXAi9bNnsZuG6sghRCCHGuCxpGqJSKAuYAe4AgrfVJMCd5pVTgqEcnhBAXsVZjKzvKdwy4fsgnMZVS7sA/gbu11kOesEQpdYdSKkMplVFdXT3U3cZVz3SyM2bM4IYbbuidjrVn+taSkhKUUvzud7/r3adnAimAdevWERYWRkdHBwA1NTVERUWNOK5LLrmEs4ddnu2dd94hJyen9/VDDz3Etm3bRnxsIYR1tBhbeP/o+9z96d0s3bSUez6/Z8Bth5TAlVIOmJP337XWb1sWVymlQizrQ4BT/e2rtX5Oa52qtU4NCAi4oDcyXnrmQjl8+DCOjo786U9/OmebwMBAfvvb39LZ2dlvGQaDgRdffHGsQz3H2Qn8kUce4fLLLx/3OIQQw9fc2cx7xe9x5yd3svT1pdz/xf1kV2ezJm4NL141cF4ZyigUBfwFyNVaP9ln1bvArZbntwL/GkH8NmPJkiUUFRWdszwgIIDLLruMl19+uZ+94O677+app56iq6trwLJbWlr4xje+wezZs5kxY0bv9LLbt29nzpw5zJw5k/Xr1/e25PvqezOHt956i3Xr1rF7927effdd7rnnHpKTkykuLmbdunW89dZbg5YbFRXFww8/TEpKCjNnziQvL2/oFSSEGBWtxlY+PPYhd31yF8s2LWPDzg0cqT3C2mlreWXFK2y7YRsb5m0gLThtwDKG0ge+CPgP4JBSqmfKvg3ARuANpdRtwAnghhG+H/5v7/+RVze6ySTBN4H70u8b0rZdXV18+OGHXH311f2uv//++1mxYgXr168/Z11kZCSLFy/m1Vdf5Zprrul3/48++ojQ0FDef/99wDzneHt7O+vWrWP79u3Ex8fz3e9+l2effZa77777vPEuXLiQ1atXs2rVKq6//voz1p2vXH9/f/bv388f//hHnnjiCV544YXzHk8IMTLtXe3sKNvBRyUf8UXZF7R3txPoEsjaaWu5KuoqZgXMwk4N/fKc8yZwrfVOYKBp9i4b8pFsWN+5UJYsWcJtt93W73bR0dGkp6fzj3/8o9/1GzZsYPXq1XzjG9/od/3MmTP5+c9/zn333ceqVatYsmQJBw8eJDo6mvj4eABuvfVW/vCHPwwpgQ8mPz9/0HLXrFkDmKePffvttwcsRwgxMkaTkT0n9/DB0Q/4pPQTWowt+Dr7cl3sdVwVdRUpQSkXlLT7sqnJrIbaUh5tF3JLtQ0bNnD99dezdOnSc9bFxsaSnJzMG2+80e++8fHxZGZm8sEHH/DAAw9w5ZVXsnr16iEdt+9UtSOdPha+nkLWYDAM2u0jhLhwWmuyqrN4/+j7fFzyMac7TuPh4MGVU65kRfQK0oPTMdgZRnwcm0rgE0FCQgLTp09ny5YtvTP79fXggw8O2AKvqKjA19eXW265BXd3d1566SXuvfdeSkpKKCoqIjY2lldffZVly5ads29QUBC5ublMmzaNzZs34+HhAQw8fWxCQsKQyhVCjJ6jDUfZUryFD459QHlzOc4GZy6JuIQV0StYHLYYR4PjqB5PEvgwPPjggwPeIScpKYmUlBT2799/zrpDhw5xzz33YGdnh4ODA88++yzOzs789a9/5YYbbqCrq4u0tDT+67/+65x9N27cyKpVq4iIiGDGjBk0NzcD8O1vf5vbb7+dZ555pvfkJTDkcoUQI1PTVsOHxz5ky9Et5NTmYKfsmB8ynx8l/4hLIy/FzcFtzI4t08mKIZF/JyG+1t7Vzmeln/Fu8bvsrthNt+4m0TeRVTGrWBG9ggDX0R0yPdB0stICF0KIIdBas//Uft4rfo+tJVtpNjYT5BrEuqR1XDP1GqZ6Tx33mCSBCyHEIEqbSnmv+D3eLX6X8uZyXOxduGLKFVwz9RrSgtJG5WTkcEkCF0KIszR1NvFxyce8W/wu+0/tR6FID0nnh8k/5PLIy3F1cLV2iICNJPDh3NFdjJ/xPE8i4J0D5Ty+NZ+K+jZCvV2456ppXDcnzNphTXrGbiM7y3ey5egWPiv9jE5TJ1GeUdyVchffiP4GIe4h1g7xHFZP4M7OztTW1uLn5ydJ3AZpramtrcXZ2dnaoUxIWms6OjpobW2lra0No9HY76Orqwuj0ciusg5ezTPRaTLvX17fxr1vZpGdfZB5weaf6gaDAQcHBxwcHLC3t8fR0RF7e/veZU5OTri6uuLq6oqjo6N8rgZh0iayq7PZcnQLW0u2Ut9Rj4+TD9+K/xarYlYx03+mTdef1RN4eHg4ZWVl2OpMhcL8JRseHm7tMGyW0WikqampN0mf/ddkMp2zT89Q0p4k3KJaqDJUsemoJ52mM8cKd5rg1eJG9rn8nU7didFkxNXOFW+DN9523ngpLzzwwBNPvOy8cFfuvVf22dvb4+rqSmaN4rWcVmpaugnycOTnV8ZzfdqUcakfW9OTtLeWbOXfx/9NVWsVTgYnLo24lFVTV7EgdAEOdg7WDnNIrJ7AHRwciI6OtnYYQpyX1pqWlhaamppobGykoaGhN3H35ejoiKurK56engQHB+Pi4oKrqysuLi606TaOtxznaONRiuqLKDxdSHFDMQ0dDQA0tz/W77GNne5E+UXhaHDEweBAQ0cDlS2VFDYX0tp15vGdDc5Eu0cT5RpFuGM4FeVhvH3YubdVX9nUyQObD5GXn8fVCX54e3vj5eWFl5cXjo6je6GJregydZF1KovtJ7b3Jm0HOwcWhS7irpS7WB6xHHdH9/MXZGOsnsCFsEU9ybquro76+noaGxtpbGyku7u7dxt3d3e8vb2JjIzEw8MDNzc3XFxcsLc3f6y6TF0U1Rexr3ofB8sPcrD6IMcbj/fu7+HgQaxPLFdOuZKp3lOJ847jzooGKhvOnbI4zNuV3132u3OWa61pMjZxsvkklS2VnGw5yfHG4+TW5bKjZgctxhaaC+9Dm87sAjOaFO8Um1gQ0sDJkyd7l7u6uuLn50dAQAD+/v69Uy5MRPXt9eys2MmO0h3srNhJU2eTOWmHmZP2JRGX4OHoYe0wR0QSuBCAyWSisbGRurq63kfP9LsODg54eHgQERGBl5cXHh4eeHh49CbqHqfbT7Pr5C4OVpuT9aGaQ7R1tQHg6+zL7IDZXBd7HQm+CcR6xxLkGnRO/+r9V5fzwNuHaDN+/UXh4mDgnqum9Ru3UgpPR088fT2Z5nvmNiZtoqypjKW/PtTvvjVt3fy59c9M85lGtEs0oXahuHS6UFlZSWlpKQBeXl4EBAQQEBCAj48PBoP1hsydj0mbyK3LZVf5LnaW7+Rg9UFM2oSvsy+XRV7G0vClLAhZMCFb2gORBC4uSt3d3dTX11NbW0tdXR2nT5/undTrYL0D/zqmqWm1I9jTiXuvTuDqlDPPAVS3VpNbmUtubS55dXnk1uVS3lwOgEEZmOY7jWunXsvswNnMDphNuHv4kE6G9Yw2GY1RKHbKjkjPSMK8iyivbztnvYdrF95O3nxS+gmNneabbNnb2RPrHctU96mEGkLxNfpSW1RLUVERBoMBf39/QkNDCQ4OPucLzBrq2uv4suJLdpbvZHfFbura6wBI9E3kjll3sCx8GdP9pg97tj9bZ/VL6YUYL21tbZw6dYpTp05RXV3d2x3i4eGBr68vvr6+7K4w8vB7+We0gJ3sFbcsU3j5FZJTl0NebR617bW96yM9IknwTWC633RmB8wmyT8JF3uXcX9/A3nnQP+t+sfWzOS6OWForSlrLiOnNofc2lxy63LJqc2hvqMeMH8hRbhFEO4Yjm+XLwE6gDCHMMqMwWzKbaOqyThuwx2rW6vJrMokoyqDzKpMiurNN1/xcfJhYdhCFoUuYmHoQvxc/MY0jvE20KX0ksDFpGUymaivr+fUqVNUVVXR2GhuZTo7OxMUFERgYCC+vr606TbKmsoobS7lvlc6aGg9t2Wp7E/jHf8bYrxjepN1gm8C03ymTYif5Bc6tlxrTWVLJTl1OeTU5pBXl0debR6n2sx3TuxsSKbz5LfQ+uvRGo728KvrprM2deSDErTW1LTVUFRfRHF9Mfmn89lftZ8TTScAcLV3ZU7gHOYGzWVB6AISfROtekXkWJMELiaNwZJRZ2cn1dXVVFZWcqLqBHWddTTrZkwuJkwuJjrsO2gyNVHdVk1tWy1VLVU0Gb+ejrcp9zH6u3+JAvIevRwnw8Q9qTcaatpqyK/L54d/qRnwi27qjJeI9Ysl1jsWPxc/PBw9cHd0x8PBo/e5g3KgobOB+o56Gjq+/lvTVkNxffEZI3MAvJ28SQ5IJjU4lblBc0nwTcDezvpdOONFJrMSk8LZ3QHl9W3c+88sPir4EEfnbCpaKqjrrqPeVI8R49c7mhvfOBmc8Hfxx9/FnyjPKFKDUgn3CCfCI4Jwj3BurTjByYZz70ka6u1y0SdvwFx3Yf40tr7f73rd5U2gDqS4qpi9J/di1MZ+txuIt5M30V7RXDHlCnNfvPdU8xeBs1zo15/zJnCl1IvAKuCU1nqGZdkvgduBnqtvNmitPxirIMXFrcvURV5dHplVmWz8lxttxjP7lzu7YOshZwLivyLIJYgEvwSifKIIdgvG38WfANcA/Fz8CHAJwN3BfdBEcN/Vbhc0CuRiFert0u+J0TBvV55d+SzHjh2jrKyMdlM7Ll4u+IT44OTpREtXC02dTXSZuvBy8sLbyRsvJy+8nLzwdPS8qFrVo2EotfUS8HvglbOWP6W1fmLUIxIXvfaudg7VHCKzKpP9VfvJqs7qHY7XNsCFLnT5sOc/9oy4lTaao0Ams3uumjbgF52XlxfJyclMnz6dEydOUFJSQm1+Le7u7sTHxxMaHSqt6VEylJsa71BKRY19KOJi1djZSNapLDKqMthftZ8jtUfoMnWhUMT5xHFV2FWE6TB8Wn3Y6ASnz+3hINTbZdSSwnVzwiRhn8dQvugcHR2JjY0lJiaGkydPUlBQwP79+ykoKDAn8lBJ5CM1pJOYlgS+5awulHWYexYzgJ9prU+frxw5iSl61LfX8+8T/+ajYx+xr3IfGo29sifJP4mUoBRm+szEv8Of0ydP09LSgsFgIDg4mEONzmzcfpw249fzi/QdEidsl8lk6k3kzc3NeHh4EBcXJ4l8CEY0CqWfBB4E1AAa+F8gRGu9foB97wDuAIiMjJx7/Pjx/jYTF4FWYyuflH7Ch8c+ZHf5brp0F1GeUVwZdSXzgueR5JdE8+lmTpw4QVVVFVprfH19mTJlyhkXjsh0qxPb2Ync09OTpKQk/P39rR2azRrVBD7UdWeTFvjFp7O7ky/Kv+DDYx/yeenntHe3E+QaxIroFayIXkGibyJtbW2UlpZy4sQJ2tvbcXR0JCIigsjISNzdbX+MtRgek8lERUUFeXl5tLW1ERISwvTp03F1tY2bJdiSUR1GqJQK0Vr3zIDzTeDwSIITk0uXqYu9lXv58NiHbD++nSZjEz5OPlwbey0rolcwJ3AO2qSpqqpiz549vVMJBwQEkJSURFBQkE3PuSFGh52dHeHh4YSEhFBcXExhYSFVVVXExsYydepUm7hU39YNZRjha8AlgL9Sqgx4GLhEKZWMuQulBPj+GMYoJogjNUd4p+gdPj7+MXXtdbg5uHFZ5GWsiF7BvJB5ONg50N7eTmFBIcePH6ejowNnZ2fi4+OJiIiQltdFymAwEB8fT3h4OLm5uRQUFFBaWsr06dMJCQmR/vFByJWYYkQ6uzvZWrKV1/Je41DNIZwMTiwNX8rK6JUsCV/Se/FLQ0MDx44do7y8HJPJRGBgIFFRUQQEBGBnNzknGhLDU1NTw5EjR2hsbCQwMJBZs2bh4mI7c8tYg1xKL0ZVZUslbxa8yVsFb1HXXkeUZxTfTvg2q6eu7p1jWWtzN8nRo0epra3FYDAQERFBdHS09G2LQZlMJkpKSsjLy0MpRVJSEhERERdta1wupRcjprUmsyqTf+T9g09OfIJJm1gWvoybEm5ifuj83ik7u7q6KC0t5dixY7S0tODs7ExiYiKRkZGT9o4vYnTZ2dkRExNDUFAQWVlZHDx4kJMnT0pr/CzSAhfA4EPzWo2tfHDsA17Le42C0wV4OnqyJm4Na6etJcIjoreM1tZWSkpKOH78OF1dXfj4+BAdHU1ISIh0k4hh01pTUlJCbm7uRdsaly4UMaCB5ov++cpQ6uy3srloM02dTcT7xHNzws2sjFl5xnzX9fX1FBUVUVlZCUBISAjR0dH4+vqO+3sRk1dLSwtZWVnU1dURFBREcnLyRfOLThK4GNCijZ/0OzGRsj+NV/wTXD7lcm5KuImUwJQzWj11dXUUFBRQXV2Ng4MDkZGRREdHy09cMWa01hw7doycnBycnZ1JSUm5KBoK0gcuBlTRT/IG89SgW7+1lSC3oK+XaU1NTQ2FhYXU1tbi6OhIQkICUVFRODg49FuOEKNFKUVMTAy+vr5kZGSwe/duEhMTiYmJuai6VHpIAheEeDtTUd9+zvIwb9fe5N0zoqSwsJD6+nqcnZ1JSkoiMjJSLrgQ487b25ulS5eSlZVFTk4OdXV1zJ49+6LpUukhn7yL3IFTB7D3+wAaFoP++j9/z9SgJpOJyspKCgsLaWxsxMXFhZkzZxIRESFXSwqrcnR0JC0tjaNHj5Kbm8uOHTtITU3F29vb2qGNG+kDv0g1dTbxdObTvFHwBiFuIVzqcy/v7bPrHYXy8yviSA2EoqIimpubcXNzIy4ujrCwMBlRImxOXV0dmZmZdHZ2kpycTFjY5JrcTE5iCsDcFbL9xHZ+vefX1LbX8p3E7/Dj5B/j6mC+jL27u5uysjKKiopobW3F09OT2NhYGQoobF5HRwcZGRnU1dURHx9PfHz8pOkXl5OYgsqWSn6959d8WvopCb4J/O7S35HknwSYr3wrLy+noKCA1tZWvL29eyeWmiwfAjG5OTk5MX/+fLKzs3unqk1OTp7UXX2SwC8C3aZuNuVv4rf7f4tJm/jZ3J9xy/RbsLezR2tNZWUl+fn5NDU14enpSXp6OoGBgZK4xYRjMBhITk7G3d29d5ra1NRUnJ2drR3amJAEPsnl1+XzyJePkF2TzaLQRfxi/i8I9wgHoLq6mry8POrr63Fzc2Pu3Lky+5uY8JRSxMXF4ebmxoEDB9i5cyfp6el4enpaO7RRJwl8kjJ2G/lz9p/5y6G/4OnkycYlG1kZvRKlFKdPnyYvL4+amhqcnZ2ZPXs24eHh0sctJpXQ0FBcXV3Zu3cvu3fvJj09fdJd9CMJfBLKr8vnwZ0Pkn86n2tiruHetHvxdvamsbGRvLw8qqqqcHR0JCkpiSlTpkzqPlPZxQ8AABK5SURBVEJxcfP29mbx4sV89dVXfPXVV6SlpREQEGDtsEaNJPBJxGgy8pdDf+HPB/+Ml5MXzyx/huWRy2lpaWH//v2Ul5djb2/PtGnTiImJkQtwxEXB1dWVhQsXsmfPHvbu3UtKSgohISHWDmtUyCd4kig6XcSDux4kpzaHFVEr2DBvA07aiezsbE6cOIFSiqlTpxIbG3vRXa0mhLOzMwsWLGDv3r1kZmYye/ZsIiIizr+jjZMEPsF1m7p56chL/CHrD7g7uPObZb/h0vBLKS4upqioCK01U6ZMITY2ViaZEhc1R0dH5s+fz759+8jKyqKrq4vo6GhrhzUiksAnsGMNx/jFrl+QXZ3N5ZGXsyF9A221bXzyySd0dHQQGhpKQkICbm5u1g5VCJtgb29Peno6mZmZHD58mO7ubmJjY60d1rAN5abGLwKrgFNa6xmWZb7AJiAK802N12qtT49dmKIvkzbxt5y/8cyBZ3AyOPF/S/6PNI80cjJyaGxsxNvbm9TU1El3xl2I0WAwGEhNTeXAgQPk5uZiMBgmbEt8KOPGXgKuPmvZ/cB2rXUcsN3yWoyD0sZS/vOj/+TxjMeZHzKfv1/+d/xr/Pnqq68wGo2kpKSwePFiSd5CDMLOzo45c+YQHBzM4cOHOX78uLVDGpbztsC11juUUlFnLb4WuMTy/GXgM+C+UYxLnEVrzZsFb/JExhPYK3t+Oe+XxBvjObznMAaDgYSEBGJiYmRIoBBDZGdnR0pKCvv27SM7OxuDwUB4eLi1w7ogw+0DD9JanwTQWp9USgUOtKFS6g7gDoDIyMhhHu7i1tDRwMO7H2b7ie0sCFnA9yK+R11JHSXGEqZMmUJ8fPykvVRYiLFkMBhIS0tj7969HDhwADs7O0JDQ60d1pCN+UlMrfVzwHNgno1wrI832WRWZXL/F/dT01bDHdPuILElkaqiKvz9/UlKSpqUlwcLMZ56kvhXX33F/v37sbOzIzg42NphDclwr52uUkqFAFj+nhq9kASYhwc+e/BZ1m9djwED94TdQ1R1FAY7A+np6cyfP1+StxCjxN7ennnz5uHl5UVmZia1tbXWDmlIhpvA3wVutTy/FfjX6IQjwDzt6/c+/h5/zPoj873mc5vjbfgZ/Zg5cybLli2TKV6FGAMODg7MmzcPFxcX9u3bR3Nzs7VDOq/zJnCl1GvAl8A0pVSZUuo2YCNwhVKqELjC8lqMgk9PfMr1717P4erD3OhxI9cYriEpNonly5cTFRUlE04JMYYcHR2ZN28eSin27NlDe/u594q1JXJHHhvR0d3BbzJ+w2t5rxHuGM5al7UkBicyY8YM3N3drR2eEBeV06dP8+WXX+Lu7s7ChQutPm+Q3JHHhh1tOMrPP/s5hfWFLHJaxLW+15I8M5ng4GDpKhHCCnx8fHqHGGZmZpKWlmaTv34lgVuR1pq3C9/msT2PYa/tWee5jpUJK4mLi7P6N74QF7vg4GBmzpzJoUOHOHz4MDNnzrS5BpVkCStp6mziF5//gk8qPiHGPoYfTPkBi5MXS3eJEDYkKiqKtrY2ioqKcHd3JyYmxtohnUESuBVklGdw7+f3UmusZaXnSn4y7yeEhYTZ3Le7EAISEhJobm4mJycHDw8Pm7ohhO116kxiXd1dPP7549y27TaM3UYemf4Ij17zKOGh4ZK8hbBRSimSk5Nxc3MjMzOT1tZWa4fUS1rgY+ydA+U8vjWfivo2HByaUQHZLAibw2PLHyPEd3LcFUSIyc7BwYG0tDS++OIL9u3bx6JFi2ziPJW0wMfQOwfKuf/tbMrr29BAp9EdU9Varo36X0neQkww7u7upKSk0NjYyMGDBxnPIdgDkQQ+RkwmE79+/zDtRtMZy43ddjzx70IrRSWEGImgoCASEhKoqKiguLjY2uFIF8pYaGhoYPPezZxq9gfO7duuqG8b/6CEEKMiNjaWhoYGcnNz8fLysupJTWmBj6Kuri6yDmdx/0f382TFk9g7NPW7Xai33JtSiImq56Smu7s7Bw4csOrl9pLAR0l1dTUvffwSPz3wU3a272RN7BoevXYeLg5n3mDBxcHAPVdNs1KUQojRYG9vz9y5czEajWRlZVmtP1y6UEaoo6ODA4cO8HLxy+xq30WgSyDPL3me+SHzAXAyOPWOQgn1duGeq6Zx3ZwwK0cthBgpT09PZsyYQXZ2NkVFRcTFxY17DJLAh0lrTWlpKR9kfcCmhk3UmGq4Ie4Gfpb2M9wcvr4L/HVzwiRhCzFJRUZGUlNTQ35+Pn5+fuN+L1pJ4MPQ3NxMRlYGm8o3sat9F0GuQTy/+OtWtxDi4qCUYtasWdTX15OZmcmyZctwdHQct+NLAr8A3d3dFBcXsy1nG282v0lNdw03xN/Az1LPbHULIS4eDg4OpKSksGvXLrKyskhLSxu3K6slgQ9RXV0dGVkZbK7ezK72XQS7BkurWwgBmKefTUxMJCcnhxMnTjBlypRxOa4k8PMwGo3k5uayo2gHb7e+TXV3NWvj1/Lfqf8trW4hRK+YmBiqqqo4cuQI/v7+uLmNfX6QBD4ArTWVlZXsz97Plvot5la3WzDPL5JWtxDiXD3jwz///HMOHjzIggULxrwrZUQJXClVAjQB3UBXf7f8mYja2to4dOgQe8v2srltM6e6TkmrWwhxXq6uriQlJXHw4EGOHTs25vOHj0YLfLnWumYUyrG6nqGBBw4f4KOmj9jVvosQtxCev1Ra3UKIoYmIiKCyspLc3FwCAgLw8PAYs2PJlZgWra2t7Nmzh3cz3uWZ+mfY2b6TG+Jv4O1r35bkLYQYsp6hhQaDgaysLEwm0/l3GqaRtsA18LFSSgN/1lo/d/YGSqk7gDvAPOjd1mitOX78OAdzDrK1eSs723aaW93LpdUthBgeZ2dnZs6cyf79+ykqKiI+Pn5MjjPSBL5Ia12hlAoE/q2UytNa7+i7gSWpPweQmppq/Ql0+2hpaSE7O5vMk5lsbt/MKaP0dQshRkdYWBiVlZUUFhYSGho6Jve7HVEC11pXWP6eUkptBtKBHYPvZX1aa0pKSjiYc5CPWz6WVrcQYkwkJSVRXV1Ndnb2mIxKGXYCV0q5AXZa6ybL8yuBR0YtsjHS0tJCVlYWn578lI87PuZ012lpdQshxoSzszOJiYlkZ2dTWlo66t3II2mBBwGbLd8o9sA/tNYfjUpUY0BrzbFjx9h+aDvvtbzHMeMxEnwSeGreU8wNmmvt8IQQk1RkZCRlZWXk5OQQFBSEk5PTqJU97ASutT4KzB61SMZQc3MzOzN38ubJN9nXsQ8vJy8eWvAQa2LXYLAznL8AIYQYpp5RKTt27ODIkSOkpKSMWtmT+kpMk8lEQVEBr2S/wrbWbXTQwc2JN/OD2T/Ay8nL2uEJIS4SHh4exMbGUlBQQHh4OIGBgaNS7qRN4E1NTby++3Ver36dU92nSA9KZ8P8DUz1nmrt0IQQF6HY2FjKy8vJzs7mkksuwd5+5Ol30iVwk8nE7iO7+f3h33Ok8wjBLsE8Pe9pLo28dNymeBRCiLMZDAZmzZrFl19+SVFREQkJCSMuc1Il8Kq6Kp744gm21W/DTtnxw5k/ZP3s9TgZRu+kgRBCDJe/vz+hoaEUFxcTEREx4hkLJ0UC7+7u5qU9L/HX4r/SYGpgefByNizeQLBbsLVDE0KIM0yfPp2qqipycnJIS0sbUVkTPoFnlGbwq12/orijmCnOU/jNot8wL3yetcMSQoh+ubi4EBsbS35+PtXV1QQEBAy7rAmbwGvbann080fZVrUNVztXfjr9p9w691YZFiiEsHlTp06ltLSUI0eOsHTpUuzshjev4IRL4EaTkVcPvcqfsv9Eh6mDy30v54FlDxDgOfxvMSGEGE8Gg4GkpCT27dtHSUnJsOcNn1AJfHf5bh7d/SgnWk8Q7xjPT5N/yqKERTK6RAgx4QQFBREQEEBBQQFhYWHDukJzQswHnl+Xz/c//j7f3/Z9mtub+WHID3ll9SssTlwsyVsIMSEppUhKSqKrq4uCgoJhlWHTLfDy5nL+cOAPbDm6BWflzArXFayfs55pU6dJ4hZCTHgeHh5MmTKF48ePEx0dfcFTztpkAj/dfprnDz3P63mvg4Ylzku4JvAaFqUuGtPbEwkhxHiLi4ujtLSUvLw8UlMv7LbCNpXAW42t/D3377x4+EVaja2kuaax3HE5qQmpxMXFDftMrRBC2CpnZ2emTp1KQUEBdXV1+Pr6Dnlfm0jgXaYuNhdt5tmsZ6luq2au11wWs5gYzxjmzJmDj4+PtUMUQogxM3XqVI4fP05ubi4LFy4cchexVRL4OwfKeXxrPhX1bfi4g2vQNhoctzHTdyY3e9xMUFcQ0dHRJCQkjMqEL0IIYcvs7e2Jj4/n0KFDVFVVERw8tKvIxz07vnOgnAfePkSbsRuAumY43bqMbyXPZxmuONs7k5yaPKKrk4QQYqKJjIzk6NGj5ObmEhgYOKQu43HvVH58a35v8u6hTQ5sP+JGeHg4l1xyiSRvIcRFx87OjoSEBJqbmykrKxvaPmMc0zkq6tv6XV7foZgzZw4ODg7jHJEQQtiGkJAQvL29KSgooLu7+7zbjyiBK6WuVkrlK6WKlFL3D2WfUG+XC1ouhBAXC6UU06ZNo62tjdLS0vNuP+wErpQyAH8AVgDTgZuUUtPPt9/6VD8czzqqi4OBe66aNtxQhBBi0ggICMDHx4fCwsLztsJH0gJPB4q01ke11p3A68C1g+3Q0tJCYNsJvpfsSoiXEwoI83bhsTUzuW5O2AhCEUKIyaGnFd7e3s6JEycG3XYko1DCgL5t/DJg0Im4u7q6SEpKYlV0NPfKpfBCCNEvf39/fH19KSoqIjIycsDtRtIC7y8D63M2UuoOpVSGUiqjs7OTmJgYmcdECCEGMdRW+EgSeBkQ0ed1OFBx9kZa6+e01qla61QZHiiEEEPj7++Pn58fhYWFA24zkgS+D4hTSkUrpRyBbwPvjqA8IYQQfcTHx9PR0THgeqX1Ob0eQ6aUWgk8DRiAF7XWj55n+yYgf9gHHDv+QI21g+iHrcYFthubxHVhbDUusN3YrBHXFK31OV0YI0rgF0oplaG1vrD5EseBxHXhbDU2ievC2GpcYLux2VJcMj+rEEJMUJLAhRBighrvBP7cOB9vqCSuC2ersUlcF8ZW4wLbjc1m4hrXPnAhhBCjR7pQhBBighqXBD6cWQvHi1KqRCl1SCmVpZTKsGIcLyqlTimlDvdZ5quU+rdSqtDyd9zvLTdAXL9USpVb6izLMpx0vOOKUEp9qpTKVUodUUrdZVlu1TobJC5bqDNnpdRepdRBS2z/Y1lu7TobKC6r15klDoNS6oBSaovltdU/l72xjXUXimXWwgLgCsxXb+4DbtJa54zpgYdIKVUCpGqtrTreVCm1FGgGXtFaz7As+39AndZ6o+WLz0drfZ8NxPVLoFlr/cR4xnJWXCFAiNZ6v1LKA8gErgPWYcU6GySutVi/zhTgprVuVko5ADuBu4A1WLfOBorraqxcZ5b4/htIBTy11qts4XPZYzxa4Bc8a+HFSGu9A6g7a/G1wMuW5y9jTgTjaoC4rE5rfVJrvd/yvAnIxTzBmlXrbJC4rE6bNVteOlgeGuvX2UBxWZ1SKhz4BvBCn8VW/1z2GI8E3t+shTbxH9pCAx8rpTKVUndYO5izBGmtT4I5MQCBVo6nrx8rpbItXSxW+wkJoJSKAuYAe7ChOjsrLrCBOrN0B2QBp4B/a61tos4GiAusX2dPA/cCpj7LrF5fPcYjgQ9p1kIrWqS1TsF8Y4ofWboMxOCeBaYCycBJ4DfWCkQp5Q78E7hba91orTjO1k9cNlFnWuturXUy5snn0pVSM6wRx9kGiMuqdaaUWgWc0lpnjudxL8R4JPAhzVpoLVrrCsvfU8BmzF0+tqLK0qfa07d6ysrxAKC1rrJ84EzA81ipziz9pf8E/q61ftuy2Op11l9ctlJnPbTW9cBnmPuZrV5n/cVlA3W2CFhtOU/2OnCpUupv2FB9jUcCt9lZC5VSbpYTTSil3IArgcOD7zWu3gVutTy/FfiXFWPp1fOf1+KbWKHOLCe+/gLkaq2f7LPKqnU2UFw2UmcBSilvy3MX4HIgD+vXWb9xWbvOtNYPaK3DtdZRmPPWJ1rrW7Clz6XWeswfwErMI1GKgQfH45hDjCsGOGh5HLFmbMBrmH8mGjH/arkN8AO2A4WWv742EterwCEgG/N/5hArxLUYc1dcNpBleay0dp0NEpct1Nks4IAlhsPAQ5bl1q6zgeKyep31ifESYIst1Fffh1yJKYQQE5RciSmEEBOUJHAhhJigJIELIcQEJQlcCCEmKEngQggxQUkCF0KICUoSuBBCTFCSwIUQYoL6/wGBttDv1Dxc7AAAAABJRU5ErkJggg==\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"execution_count": 229
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-15T06:36:29.252994Z",
"start_time": "2024-11-15T06:36:16.201297Z"
}
},
"cell_type": "code",
"source": [
"from functools import partial\n",
"def reg_l2_loss_fn(net, outputs, targets):\n",
" loss1 = nn.MSELoss()(outputs, targets)\n",
" loss2 = sum(p.pow(2).sum() for p in net.parameters())\n",
" return loss1 + 0.1 * loss2\n",
"train(fc_net, partial(reg_l2_loss_fn, fc_net), fc_net.parameters(), iters=6000)"
],
"id": "8aa6078691f66ae5",
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"execution_count": 230
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2024-11-15T06:37:07.788027Z",
"start_time": "2024-11-15T06:36:54.845781Z"
}
},
"cell_type": "code",
"source": [
"from functools import partial\n",
"mu = torch.nn.Parameter(torch.zeros(1, requires_grad=True))\n",
"def pinn_loss_fn(net, s_train_hat, s_train):\n",
" lambda1 = 1\n",
" \n",
" data_loss = nn.MSELoss()(s_train_hat, s_train)\n",
" \n",
" s_phys_hat = net(t_phys_torch)\n",
"\n",
" v_x, = torch.autograd.grad(s_phys_hat[:, 0], t_phys_torch, torch.ones_like(s_phys_hat[:, 0]), create_graph=True)\n",
" v_y, = torch.autograd.grad(s_phys_hat[:, 1], t_phys_torch, torch.ones_like(s_phys_hat[:, 1]), create_graph=True)\n",
" a_x, = torch.autograd.grad(v_x, t_phys_torch, torch.ones_like(v_x), create_graph=True)\n",
" a_y, = torch.autograd.grad(v_y, t_phys_torch, torch.ones_like(v_y), create_graph=True)\n",
"\n",
" v = torch.concat([v_x, v_y], dim=1)\n",
" a = torch.concat([a_x, a_y], dim=1)\n",
"\n",
" v.stop_gradient = True # v and a are just \"computations\" of the pose derivatives, we don't want to optimize through them\n",
"\n",
" speed = torch.norm(v, 2, dim=1, keepdim=True)\n",
" g = torch.tensor([[0.0, 9.81]], dtype=torch.float32)\n",
"\n",
" phys_loss = nn.MSELoss()(-mu * speed * v - g, a)\n",
" \n",
" return data_loss + lambda1 * phys_loss\n",
"\n",
"fc_net = Net(1, 2, 32, 3)\n",
"train(fc_net, partial(pinn_loss_fn, fc_net), list(fc_net.parameters()) + [mu], iters=2000)\n",
"print(mu.detach().numpy()[0])"
],
"id": "f87650d66c9de83c",
"outputs": [
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<Figure size 432x180 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.033664506\n"
]
}
],
"execution_count": 231
},
{
"metadata": {},
"cell_type": "code",
"outputs": [],
"execution_count": null,
"source": "",
"id": "1928b7abab9c932a"
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"language": "python",
"display_name": "Python 3"
}
},
"nbformat": 5,
"nbformat_minor": 9
}
\documentclass{beamer}
\usepackage{listings}
\lstset{language={[LaTeX]TeX}, basicstyle=\small}
\usepackage{multimedia}
\definecolor{links}{HTML}{302080}
\hypersetup{colorlinks,linkcolor=links,urlcolor=links}
\usepackage[utf8]{inputenc}
\usepackage{xspace}
\usetheme{Madrid}
\usepackage[overridenote]{pdfpc}
\mode<presentation>
\title[Physical Intuition in DNNs]{Physical Intuition in Deep Neural Networks}
\author[Martin Pecka]{Martin Pecka}
\institute[CTU FEE]{Czech Technical University in Prague, Faculty of Electrical Engineering}
\begin{document}
\begin{frame}{PINN: Example: Ballistic Curve}
\begin{center}
The curve is defined by a differential equation and initial conditions:
$$\vec{a} = -\mu \|\vec{v}\| \vec{v} - \vec{g}$$
$$\mu = 0.03; \vec{s_0} = (0, 0); \vec{v_0} = (200, 200) $$
\includegraphics[width=\linewidth]{gt.png}
\end{center}
\end{frame}
\begin{frame}{PINN: Example: Ballistic Curve}
\begin{center}
There is no closed-form solution for $\vec{s_t}$, numerical integration is needed.\\
\includegraphics[width=\linewidth]{gt.png}
\end{center}
\end{frame}
\begin{frame}{PINN: Example: Ballistic Curve: Black-box NN}
\begin{center}
$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 $$
\href{run:train-dumb.mp4?autostart&loop}
{\includegraphics[width=\linewidth]{train-dumb.png}}
\end{center}
\end{frame}
\begin{frame}{PINN: Example: Ballistic Curve: Black-box NN with L2 Regularizer}
\begin{center}
$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 + \sum \| \vec{w} \|^2 $$
\href{run:train-l2.mp4?autostart&loop}
{\includegraphics[width=\linewidth]{train-l2.png}}
\end{center}
\end{frame}
\begin{frame}{PINN: Example: Ballistic Curve: Gray-box NN}
\begin{center}
Add the error in the differential equation to the loss. $\vec{v}$ an $\vec{a}$ are actually already computed by the net - they are the gradients (and 2nd order gradients).
$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 + \sum \| \vec{a} - (-\mu \|\vec{v}\| \vec{v} - \vec{g}) \|^2 $$
\href{run:train-pinn.mp4?autostart&loop}
{\includegraphics[width=\linewidth]{train-pinn.png}}
\end{center}
\end{frame}
\end{document}
% This file is part of pdfpc.
% Copyright (C) 2023 Evgeny Stambulchik
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License along
% with this program; if not, write to the Free Software Foundation, Inc.,
% 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
% -------------------------------------------------------------------------------------------
%
% Allow for defining some meta data and simple textual notes for use
% with the pdfpc presentation application <https://pdfpc.github.io>.
%
% -------------------------------------------------------------------------------------------
%
% Inspired by Carsten Brandt's <https://github.com/cebe/pdfpc-latex-notes>.
%
% -------------------------------------------------------------------------------------------
%
% Please report bugs and other problems as well as suggestions for improvements
% to the issue tracker at github <https://github.com/pdfpc/pdfpc/>
%
% -------------------------------------------------------------------------------------------
%
\ProvidesPackage{pdfpc}[2023/10/21 v0.7.1 PDFPC]
\NeedsTeXFormat{LaTeX2e}
%
% Require additional packages needed by \sty{pdfpc}:
\RequirePackage{kvoptions}
\RequirePackage{xstring}
\RequirePackage{iftex}
\RequirePackage{hyperxmp}
\ifLuaTeX
\RequirePackage{stringenc}
\RequirePackage{pdftexcmds}
\fi
%
\SetupKeyvalOptions{
family=PDFPC,
prefix=PDFPC@
}
%
\DeclareStringOption{duration}
\DeclareStringOption{starttime}
\DeclareStringOption{endtime}
\DeclareStringOption{enduserslide}
\DeclareStringOption{lastminutes}
\DeclareBoolOption{hidenotes}
\DeclareBoolOption{overridenote}
\DeclareStringOption{notesposition}
\DeclareBoolOption[false]{disablemarkdown}
\DeclareStringOption{defaulttransition}
\DeclareDefaultOption{\@unknownoptionerror}
%
\ProcessKeyvalOptions*
%
\ifx\PDFPC@duration\@empty
\else
\IfInteger{\PDFPC@duration}{}
{\PackageWarningNoLine{pdfpc}{`duration' should be an integer}}%
\fi
%
\ifx\PDFPC@enduserslide\@empty
\else
\IfInteger{\PDFPC@enduserslide}{}
{\PackageWarningNoLine{pdfpc}{`enduserslide' should be an integer}}%
\fi
%
\ifx\PDFPC@lastminutes\@empty
\else
\IfInteger{\PDFPC@lastminutes}{}
{\PackageWarningNoLine{pdfpc}{`lastminutes' should be an integer}}%
\fi
%
\ifPDFPC@overridenote
\renewcommand<>{\note}[2][]{%
\IfStrEq{#1}{item}%
% Imitate a bullet
{\pdfpcnote#3{* #2}}%
{\pdfpcnote#3{#2}}%
}%
\fi
%
\def\pdfpc@notespositionauto{auto}%
\ifx\PDFPC@notesposition\@empty%
\def\PDFPC@notesposition{auto}%
\fi%
%
\def\pdfpcsetup{\kvsetkeys{PDFPC}}%
% Guesswork for beamer/pgfpages notes
\ifx\PDFPC@notesposition\pdfpc@notespositionauto%
\def\PDFPC@notesposition{none}%
\def\pdfpc@onepaperheight{\paperheight}%
\def\pdfpc@twopaperheight{2\paperheight}%
\def\pdfpc@onepaperwidth{\paperwidth}%
\def\pdfpc@twopaperwidth{2\paperwidth}%
\def\pdfpc@pagecenter{\pgfpoint{.5\paperwidth}{.5\paperheight}}%
\ifx\pgfpageoptiontwoheight\pdfpc@onepaperheight%
\ifx\pgfpageoptiontwowidth\pdfpc@twopaperwidth%
\ifx\pgfpageoptionfirstcenter\pdfpc@pagecenter%
\def\PDFPC@notesposition{right}%
\else%
\def\PDFPC@notesposition{left}%
\fi%
\fi%
\fi%
\ifx\pgfpageoptiontwoheight\pdfpc@twopaperheight%
\ifx\pgfpageoptiontwowidth\pdfpc@onepaperwidth%
\ifx\pgfpageoptionfirstcenter\pdfpc@pagecenter%
\def\PDFPC@notesposition{top}%
\else%
\def\PDFPC@notesposition{bottom}%
\fi%
\fi%
\fi%
\fi%
%
% Our schema
\newcommand*{\pdfpc@schema}{%
\hyxmp@add@to@xml{%
______<rdf:Description xmlns:pdfpc="https://github.com/pdfpc/pdfpc">^^J%
}%
\hyxmp@add@simple{pdfpc:Duration}{\PDFPC@duration}%
\hyxmp@add@simple{pdfpc:StartTime}{\PDFPC@starttime}%
\hyxmp@add@simple{pdfpc:EndTime}{\PDFPC@endtime}%
\hyxmp@add@simple{pdfpc:EndUserSlide}{\PDFPC@enduserslide}%
\hyxmp@add@simple{pdfpc:LastMinutes}{\PDFPC@lastminutes}%
\hyxmp@add@simple{pdfpc:NotesPosition}{\PDFPC@notesposition}%
\ifPDFPC@disablemarkdown%
\hyxmp@add@simple{pdfpc:DisableMarkdown}{true}%
\else%
\hyxmp@add@simple{pdfpc:DisableMarkdown}{false}%
\fi
\hyxmp@add@simple{pdfpc:DefaultTransition}{\PDFPC@defaulttransition}%
\hyxmp@add@to@xml{%
______</rdf:Description>^^J%
}%
}
%
% Piggybacking on the hyperxmp schema...
\let\oldhyxmp@pdf@schema\hyxmp@pdf@schema
\renewcommand{\hyxmp@pdf@schema}{{\oldhyxmp@pdf@schema}{\pdfpc@schema}}
%
% Note command
\ifPDFPC@hidenotes%
\newcommand<>{\pdfpcnote}[1]{}%
\else%
\ifXeTeX%
\newcommand<>{\pdfpcnote}[1]{%
\only#2{%
\edef\\{\string\n}%
\special{pdf: ann width 0pt height 0pt depth 0pt%
<<%
/Subtype /Text%
/Contents (#1)%
/F 6%
>>%
}%
}%
\relax%
}%
\else%
\ifLuaTeX%
\protected\def\pdfannot {\pdfextension annot }%
\newcommand<>{\pdfpcnote}[1]{%
\only#2{%
\edef\tmp@a{\pdf@escapehexnative{#1}}
\expandafter\SE@ConvertFrom\expandafter\tmp@a\expandafter{\tmp@a}{utf8}
{%
\edef\\{\string\n}%
\pdfannot width 0pt height 0pt depth 0pt {%
/Subtype /Text%
/Contents <FEFF\tmp@a>%
/F 6%
}%
}%
}%
\relax%
}%
\else%
\newcommand<>{\pdfpcnote}[1]{%
\only#2{%
\edef\\{\string\n}%
\pdfannot width 0pt height 0pt depth 0pt {%
/Subtype /Text%
/Contents (#1)%
/F 6%
}%
}%
\relax%
}%
\fi%
\fi%
\fi%
%
\endinput
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment