{ "cells": [ { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "# Computing Bounds for Clamped Means #\n", "\n", "Sometimes, the settings for private algorithms can inadvertently reveal private information.\n", "\n", "Consider computing average energy use for a rural zip code. The largest energy consumer here may not consume very much energy, and the noise needed for differential privacy would not be very high, say $\\pm1,000$kWh.\n", "\n", "Imagine, then, that a wealthy environmentalist moves into the neighborhood. This person's house, while proclaimed an efficiency engineering masterpiece, happens to consume much more electricity than expected, much more than neighboring houses (perhaps our environmentalist couldn't resist running a bitcoin rig in the basement).\n", "\n", "Now, because of the increased range of the dataset, obscuring this zip code's total energy use requires more noise; instead of $\\pm1,000$ kWh it would be $\\pm10,000$ kWh. If we use the exact upper and lower bound of the dataset to scale DP noise, the confidence interval published alongside it would reveal our environmentalist's embarassingly high energy usage almost exactly. Oops!\n", "\n", "The solution to this problem is to _privately_ compute the required scale of noise before computing the private mean. In this notebook, we employ a method that focuses on ease of implementation and high accuracy that does not minimize the privacy budget consumed. \n", "\n", "By the end, we'll have made sure not to have inadvertently publicly shamed our high-profile environmentalist.\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T23:06:22.324Z", "iopub.status.busy": "2020-09-28T23:06:22.318Z", "iopub.status.idle": "2020-09-28T23:06:22.333Z", "shell.execute_reply": "2020-09-28T23:06:22.340Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [], "source": [ "# Preamble: imports and figure settings\n", "\n", "from eeprivacy import (\n", " PrivateClampedMean,\n", " PrivateQuantile,\n", " laplace_mechanism,\n", ")\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib as mpl\n", "from scipy import stats\n", "\n", "np.random.seed(1234) # Fix seed for deterministic documentation\n", "\n", "mpl.style.use(\"seaborn-white\")\n", "\n", "MD = 28\n", "LG = 36\n", "plt.rcParams.update({\n", " \"figure.figsize\": [25, 7],\n", " \"legend.fontsize\": MD,\n", " \"axes.labelsize\": LG,\n", " \"axes.titlesize\": LG,\n", " \"xtick.labelsize\": LG,\n", " \"ytick.labelsize\": LG,\n", "})" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "## Dataset ##\n", "\n", "For this example, we consider a dataset of one year of hourly energy consumption readings from 20,000 homes. In total, there are 20,000 \\* 365 \\* 24 = 175,200,000 data points, with each home contributing 8,760 each.\n", "\n", "From experience, we know this sort of dataset follows a power law distribution." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T22:59:42.890Z", "iopub.status.busy": "2020-09-28T22:59:42.883Z", "iopub.status.idle": "2020-09-28T22:59:52.682Z", "shell.execute_reply": "2020-09-28T22:59:52.724Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "data": { "image/png": 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fysoKtWrVgqWlJSIjI/H8+XNxbAEBAejXrx9OnjwJKysrANk730eOHMH58+eVXre0tESzZs2yfCy3bt3C0aNHIZfLYWhoiIYNG6Jo0aIICQmBh4cHEhMTERMTgwULFiA6OloydoOuFShQQJyXCxcuiABIw4YNxfmoUaNGlrb56tUrODo6SoIbRYsWRZ06dVCgQAEEBgbC29sbycnJiIiIwIwZMxAYGJhhhWCawMBADBo0CKGhodDT00Pt2rVRtmxZxMTEwMvLS+wvICAAQ4YMgZubW7ZaxIeGhsLR0REvX74Ur1lYWKB+/fowNzdHcHAw7ty5g4SEBMTGxmLFihV4+vQp/vjjDxGIVzy/L1++FC1vraysJC2Os3qO02zcuBGrVq0S8yYmJqhXrx6KFi2KqKgo+Pj44N27d5DL5Thy5AieP3+OXbt2wcTEJMNtyuVyTJw4EWfPngUA2NjYoFatWjA2NsazZ8/EsyYhIQFz5sxBmTJl0KRJE5XbOnLkCGbMmCECiIaGhqhbty5KliyJuLg4PHr0SFSoXLp0CX369MG+ffvEdZuR+fPnq6xobNGihSTf/rRp03D8+HExb2pqioYNG8LCwgIvX77EvXv3EBMTg+nTp2dYUZo/f3506tQJBw8eBJAaFM8sCH/s2DEx3blzZ7XnW52//voLy5YtE/N6enqoVasWypYti4iICPj6+opr9vDhwwgLC8PGjRuVKoJ2796N+fPni3mZTIaaNWuiXLlySExMhK+vr6hwf/DgAX744Qf89ddfqF27ttryZedZnubPP//E+vXrxXzJkiVRvXp1mJmZITQ0FH5+fggKChJlc3Z2hpubm0aVSbqyadMmnDx5EkBqj7I6derA3NwcDx8+FGn8goKCMHXqVAwcOBCTJk2CXC5H0aJFUa9ePRgaGsLHx0d81kNCQjBx4kRx7jJy4MABsYyRkREaN26MIkWKICAgAPfu3UNKSgo+f/6MESNGYNmyZbC3txfr5sR3jHv37mHgwIFiW0BqQ5Dq1avDyMhIVD7J5XKEhITAxcUFs2fPxk8//aR2u/fv38fKlSsRFxcnuUdERETAw8NDBJh9fHwwZswY/P3331kqd3qXL1/GyJEjkZiYCCD1uqpTpw7Kli2L8PBweHh4ICoqCitXrpT0EM3IqlWrsHHjRjFvZmaGunXrokiRIpDL5QgODsb9+/fFeQsMDMTQoUPh5uYmvrdq8yzWxX6JiP4rGIQnIiKdmTp1KgYNGiR+ULx79w4rV67EypUrUaZMGTRo0AANGjRAvXr1NPpBkaZHjx5Yu3YtUlJS8ObNG9y9e1dtt3LFwIO6rveHDx+Gnp4eXFxcMHjwYEmr/devX2PkyJHih+327dsxZMgQEcSoW7euSBejGIQfP358hkH/NGkBeCcnJ4wdO1YSrAkJCcGIESNEgGn9+vVwcnJS6lEQGRmJ0aNHiwB8jRo1sGDBAqVW1wEBAZg5cyY8PT0RExODcePG4ejRoyLFiK2tLebNmwcAuHbtmviRNHDgQLWpdDISERGBcePGiQB80aJFsXjxYjRt2lSy3KlTpzB16lTEx8cjKCgICxculAR5NOXv7y/KD6T+Xf744w/J3yA0NBQzZ86Eu7u7CKJoIyUlRVLG4cOHY8yYMUqtKs+fP48JEyYgLi4OERER2Lx5s6gkyM75TgvAOzs7Y9CgQTA3N4evry+CgoJgYJD1r3RpLYK/++47LFy4EMWKFZO8N3nyZBGsXbNmDRo3bpylFElZYWlpKc7Ly5cvxQ9/BweHTNM5qBIXF4fBgweLgHiBAgUwe/ZsdO/eXRIYfPv2LWbNmoVr164BADZv3ozy5cuje/fuGW770qVLAIAGDRpg/vz5kgrGhIQErFy5Etu2bQOQWhFw4sQJ9OrVK8vHAKQGokeOHCkC8IaGhpgwYQKcnZ0lf/PQ0FAsWrRIBHrd3NxQvnx5uLi4AJCe38OHD4u/q+LnUVvu7u4iAC+TyTBw4EC4uLgopfdJq8CKjIzEgwcPMGvWLJF2RZWoqCicPXsWBQsWxJw5c9C5c2fJ3+7mzZsYO3YsIiIiIJfLsX79epVB+LR9pQXgv//+e0yZMgVFihSRLHfjxg1MmzYNwcHBeP36NcaNG4fdu3er7Yl0/vx55MuXD1OmTIG9vT2Sk5Nx8+ZNSfD+4MGDkgD8jz/+iClTpkiCT0+fPsWECRPw9OlTce9XxcHBQQTh79y5g+DgYMl1q0gul+PEiRNiXpvrKG0/in8nOzs7LFy4UPK5j4+Px7p167BlyxYAqenRDh48KKkkuHr1KhYsWCDm69SpgwULFqBChQqS/V24cAEzZsxAaGgoIiMjMWrUKBw5ckTp76UoO89yIPWzlhaAl8lkmDVrliQNHpB6/z948CB+++03pKSk4PXr19i/fz8GDBiQ2SnUmZMnT0Imk+HXX3/FgAEDJJV7immM7t27h/Hjx0NPTw+TJk1Cv379xHMq7VpZu3YtAODhw4fw8vKCnZ1dhvtNC8C3bNkSCxYskHy+nzx5gvHjx8Pf3x9JSUmYPXs2GjZsKP5euv6O8eHDBwwbNkxsx8rKCgsWLEDLli0lyz19+hTTpk2Dr68vUlJS8Pvvv6NcuXJq93nq1CkAQMeOHTFjxgxJKrbo6GjMnj0bbm5uAFJTUd26dQuNGzfO8jEAqb2bpkyZIr4vlytXDitXrpR8h4uOjsaSJUtw4MABBAYGqt3e48ePxfUHAP3798eECROUUvFERUVh2bJl2L9/P4DUZ+CpU6fEtZrVZ7Gu9ktE9F/BgVmJiEhnGjZsiKVLl6psbffq1SscPHgQU6ZMQfv27dGqVStMmzYN58+fV+o+nl6JEiUkP5wUAwvpBQUFiTzCBQoUyLT7/dixYzF69GilIHepUqWwevVqEYCJjY1VmdJCWwMHDsTs2bMlAXggNWi9YsUKsd+YmBiVqWa2bt2K169fAwCqVauG3bt3q0x7UrZsWWzbtg3169cHkBqs27x5s86OI72dO3eKNAOmpqbYs2ePUgAeAOzt7TF37lwxf/LkSYSEhGR5fxs3bhSfH1tbW2zbtk2pEqRQoUJYu3atVq3FFfn7+4ucuqVKlcL48eNVpjVo164dJkyYIOYvXLiQrf0q+uGHHzBz5kyUKFECpqamaNy4sdYBXiD1mt28ebNSIK948eL466+/UL16dQCpAagVK1Zkq+y56e+//xZBC0NDQ2zbtg09evRQaplbokQJbN68WRLAWbJkiSQ9jyqVK1fGX3/9pdTDx8jICFOmTJFUEqYF7bVx5swZ3L17V8wvX74cAwcOVKp0KVSoEJYtWyZaMAKp14Y211RWJCUlSVo2jxs3DlOmTFGZX9/e3h47d+4UwRk3NzeRKiUjMpkMGzZsgL29vdLfrkmTJpg0aZKY9/LyQmRkpNI2FixYIAJdP/74I5YtW6YyoNu0aVPs379f9Mi5c+cO/v33X7XlA1Jbwzs6OsLCwgKFCxdG165dxfMqISFB9OJK2/+8efOUWn9WqlQJf//9N0qVKqV2X2np2YDUazItIKiKl5eXqHQsU6aMeAZk1apVq0QKnRo1amDHjh1Kn3tjY2NMmDBBEqTbvn27mE5JScHSpUvFoMC1atXCzp07lQLwQOqYAHv27BHn6P3795JWthnJzrPcy8tLVBw3atRIKQAPpLZS/uGHHySpudzd3TMtl665uLhg6NChSr1rhgwZIkl9lZKSgpEjR2LgwIGS55RMJsPIkSNRqVIl8ZqXl1em+23WrBk2bNig1DukSpUq+Pvvv8Xrnz9/xsqVK7U6Nk1s2LBBpEQyNzfH3r17lQLwQOo1tXv3btGzJDk5GfPnz890YOpmzZph1apVSmOhFChQAIsWLZJ8v8jOvX3nzp2iEYWlpSV27dql9B2uQIECmDdvnkZp0vbu3SsqGhs2bIjp06erzIVvamqKuXPnSvZ1+/ZtrY8jr/ZLRPS1YhCeiIh0yt7eHsePH0fr1q3V5iR+9+4dDh8+jJEjR6JFixb466+/RKBEFcUW7adPn5bkQ1V04sQJ8SPL3t5ebU56c3Nzta3YbG1tJTkr04Le2WViYqKyO3yasmXLSgYvTJ93OiEhAfv27RPzU6ZMUZtmwMjISAzoBwCHDh3KNMioLcWc1cOGDVMbVOrevbtID2NmZqYyt6s6CQkJkiDIxIkTMzwP+vr6+O2337KVJ1ux63tSUlKGn0EA6NatG8aPH48VK1Zg5cqVmf7w19Qvv/yik+0AqcGY33//PcMB0oyNjTFjxgwx7+HhIUmJ8iXbs2ePmHZ2dkadOnUyXNbAwAALFiwQQa1Pnz5JWi6rMnToULVpKBQr/7Jz31A8jo4dO2ZaqThjxgwRDEtISMDevXu13rcmzp07JxnscciQIWqXr1atmuRernh8qnz33Xdqg8ft27cX13RKSoooSxofHx94e3sDSL3vKt4HVSlevDgGDRqkcfmKFSuGrl27Zvj+7du3Rc8nMzMzTJkyJcNlCxYsKEmrlRHFMU7UVUhr2iNMnbSxBtLMmjVLbWqlYcOGAUi9t0RHR4sKWQ8PDzx9+lQsN3/+fLXXT7ly5SR5sF1dXREVFZXh8tl9live29OP9ZGeo6MjJk6ciNWrV0vuj7mhQIECGV5jMpkMDRs2FPP58+dH//79M1xWsVdTZpV1hoaGWLBgQYY9rgoXLiypeD5z5kymjSu0ERcXJ3qCAKkVL+p6VZqYmGDhwoVi/unTp7hx44bafYwaNSrD3i9GRkaS3PLZubcrflcaPny42tRX06ZNyzSVlLGxsUiNp0nvDMXPSvpxHrIir/ZLRPS1YhCeiIh0rlSpUti0aRPOnz+PSZMmoUGDBhkG+oDUbrlprTjTD4aVpkOHDjA1NRXLp6WPSE8x8JBZ9/s6depkms9VsdWT4g/17LCzs8t0wFrF4HX61p0+Pj6IiIgAkPpDW/FHTUZq164tBhGLi4tT2bo+u16+fCnyoQOpaR/U0dPTw99//43bt2/j9u3bGg+clubOnTtiwDkTExOVreEUlS5dWm0ao8yULVtWfI7fvXuHMWPGiPzF6VlaWmL48OHo0qULateurZNBMq2srLI1tkJ6DRo0yHR7dnZ2kmvg5s2bOtt/TlHssQBAo+7uVlZWaNeunZi/fv262uUzyj2eRhf3jejoaMl1qslxGBsbS4K0mR1Hdl29elVMf/fddxoNXq14nWfWEjKzVA8WFhbiuQBAaQBKxfLVq1dPsqwm5bt3757aoKydnZ3aa1uxkrBDhw6Z5j9u0aJFhmOJpOnRo4cIEj558kRlTvqEhAScOXMGQOp9Vt3g5OpcuHBBVCCWLl1abWUWkHqPPHXqFLy9vXH58mUULlwYgPRzWKdOHVSuXDnTfffu3Vvcb+Pj49W21s7us1wxQO/t7Y1Zs2aJypP0ypQpgyFDhqBTp046HXRbE3Xr1lX73SHtfAOpFV7qPu+KY7Bkdo9q06ZNhmmP0tjb24u/QVRUlEh5pUuenp4iuG9oaKjR57pq1aqSMQXU3RNNTEwyHX9AF/f2V69eSRpXKObQV8XU1FTyfFJl5syZcHV1xa1bt9C2bdtMy2Bubi6m1TWAyUxe7ZeI6GvFnPBERJRjSpYsicGDB2Pw4MGIjY3FvXv34OHhgdu3b8PHx0fpC/jDhw8xePBg/PPPP0rdWfPnz4/OnTvD1dUVQGoLwFatWkmWefDggQgCly1bNtOAq2LX7Ywo/ohN63KbXZmlHAAg+aGd/jzdv39fTMtkMsyZM0ej/Sq2xvbz89M6l2lGXrx4IaatrKwy/dEOINP8+eqk5fgFUtODqKvoSVOrVi2Nut6rYm5ujh49eojPoLu7O9zd3VG+fHk0bdoUTZs2RcOGDTUK9GlDVeqG7NC0QqJmzZp48+YNAKjNV/2lePz4sZi2sLBAuXLlNFrPzs5O5ARW1yvD1NRUEuxSRTHYqq7HhDrPnj0T1376lqvq2NnZ4c8//wSQei7kcrlOKoFU8fHxEdO+vr6YPXt2puukVSACqXmBP3/+rDJ9DQCNKp1MTU3FgInp79GK5Xvz5o1G5VP8eyUkJODly5cZBlszuyYV959ZcA/4/8CM6tLglChRAo0bNxYtek+cOKE0mPCFCxdE5W2TJk20HpD6+fPnYrpmzZoarVO+fHml1xSvJ00/x6ampqhUqZK45zx8+DDDitbsPssrVKiApk2binP6zz//wNXVFdWqVUPTpk3RpEkT2NnZ5eogrKpkNpaOYkv19OlU1C2bWU+tBg0aZFo2Y2NjVK5cWXw/efr0abZTwKWneG+vVKmSxs9aOzs7US519/ZSpUqpHQMCkH6OtL23K353sbKyyrTiDUj97pJZD62MyOVyvH//Hs+fP8eTJ0/g7e0t6RGQlm5K1/Jqv0REXzIG4YmIKFfkz58fTZo0ES1Io6KicOXKFezatUukCwBSW/bt3LkTQ4cOVdqGg4ODJAAaHR0tCXYp/kDRZBA6TX7AKf4g01VKEcWWQJpIv9+0wSaB1JZYigPDaionugErlkuTH5V5sT8bG5ts7XPGjBl4/fq1JKfwixcv8OLFC+zevRsGBgaoU6cOWrdujc6dO2d7f4rSjx+QXZkFadIontvQ0FCdliEnKJYxK8FHxUojdceZ1fuGthTLYGZmpnHASfGYk5KSEBkZqfPPThrFnksPHz7UqpImPDw8wyB8du/RiuULCAhQSu2libS8zapkdl4V96/pPUqTyksHBwcRzHJzc8P48eMlFS1ZfRZmJC2dDJC9e7riOczKNVm8eHHxmdLlNanqWf7HH39g4MCBIkAql8vFZ/rPP/+EsbExGjRogDZt2qBTp06ZVsTlhKx8d1CVl1tbmQX/0yh+RjLq1Zgd38q9PSe/u8jlcnh6euLKlSvw8/PDmzdvEBQUlGmapezKq/0SEX1tmI6GiIjyhKmpKezt7bF//34sXLhQ0irr0KFDKtexs7MTLSNjY2Nx/vx58V5SUhJOnjwJQPPu95qkTsgJGeVV1VRaq8/sSJ+2QRcUA/u50WJQsUWtpgGHzNJBZCZ//vzYsWMHFi9ejLp16yq1ME5KSsKdO3ewbNkytGvXDtOmTZOUM7v71qXMcsyq2u/X8INaMXe0pseYftm0QRpVya37hrbHkf5zou5Ysktdnm5NqbsXZTfgldPly+yaVAw+a3pP1ORvrZieLSgoSNK7JywsDFeuXAGQGrRt3769RvtVRVf3dF18lnP6mixcuDAOHTqEGTNmqEyXEx8fj2vXrmHevHlo2bIlFi9enCN5z9XJ7ncHbWlaAaj4GdHF95T0vpV7u+J3Ak2vK02+u3h7e+P777+Hs7Mz/vzzT1y5cgX+/v6S53a+fPnw3XfficGjdSGv9ktE9DViS3giIsq29+/f48qVKwgNDcXnz58lA3RpolevXnjx4gW2bt0KILXFYlRUlMoffj169MCqVasApHbD7969O4DUPJ9prfa+++47jVv5fo0Uf7TVrl0b//zzTx6W5v8Uy5VTA78qUhwgUNNAoy6CJjKZDA4ODnBwcMD79+9x7do13Lx5Ex4eHggODhbLpaSk4PDhw3j27Bn27t2rdkDDvKBpQF0x721We3Gkp6uUTuooBlyykrNXMdiq6woPbejiOICcPZZ8+fKJwNicOXPw008/5di+tKF4TxoyZAgmTpyYq/s3NjYWKYU0/Rtqci/Lly+fUnq2tAFsT506JfZpb2+frRbRurqnfy3XpKGhIfr164d+/frh9evXuHr1Km7dugVPT09JC+rExERs374dgYGB2LBhQ7b2mRv3xOzS9Lmp+LfNib/X1/I5ykxOfHe5efMmhg4dKlnOxsYG1apVQ/ny5cXgxJUqVYKhoSFWr16d6Zgcmsir/RIRfa0YhCciomzz9/fHjBkzxHzfvn2znIajY8eOIggPpP5oyigIv2bNGqSkpODmzZuIjIyEubm5GIQOyF73+6+B4oBqit2a85qFhYWYzmhQu/QSEhJgYGCgVYtXxS7misFvdXR9vqytrdGzZ0/xmXvx4gUuXryIf/75Rwza+uDBAxw7dkyjgTVzk6bpAhTPrZWVleQ9xZ4AmgSTdNEyOTNpAxADqQPoaiooKEhMFylSRKdl0obicXz+/DnDisn0FAelNTY2znbFiTqWlpbib6qYuuRLoXivzIvyWVlZifOj6T1K03unYnq2c+fO4bfffoOenp5On4WK93RN7xfx8fFKgX9tr0nFz3L6e09OK1WqFBwdHeHo6Ai5XI7Hjx/D3d0dBw4cEOfC3d0dN27cQNOmTVVuQ5N7Yk60GNc1bZ4VukzFlkYX9/bc/hypos13F3X3r8TEREydOlUEwsuVK4fFixerHYcibcyI7Mir/RIRfc2YjoaIiLIt/UBsFy5cyPI2FLtZGxgYSIIniooXLy4GFE1KSsLFixeRkpKCS5cuAUjN0duuXbss7/9rUq1aNTEdFBSkcWD56NGjuHz5Mp4/f54jaUUUy/XhwweNgknbt29HrVq10L59e9HDQVNVq1YV035+fhq1KMvuwKLh4eHw9vbO8Idz+fLlMXjwYBw+fFhyXSjmkP9SPHnyJNNlUlJScO/ePTGf/se1Yvd9Tc7/69evNS+glqpXry6mw8PDJQMGq3P37l0xrWpwydxWpUoVcV+Uy+WS8qmjmJrE1tY2xwZlBaTXvOLnRJ03b97g6NGj8PT0xNu3b3U21oYq2pQvPDwcBw8exM2bN/H69etstVSuVauWmPb19dVonQcPHmi0nGJ6tk+fPuHu3buIjIwUn5Py5ctrNBisOornT9Pyu7i4oG7duujatSvOnTsHQHpNavo5/vz5s2Rg2Jy+Jj9+/AhPT0+VYwDIZDJUq1YNo0ePxqFDhyT54NO36lX8LpPZPVEul0sCxF8qTT6TMTExePr0qZivUaOGzsuh+Dl6+vSpxpW6ip85TQfqzkmK311CQ0MRGBiY6Trqrr8rV66I7yQymQzr16/P9NpXfBZrew/Oq/0SEX3NGIQnIqJss7KykgQbtm3bluUWr9evXxfTdevWVZu6w8HBQUy7u7vj/v37oqt4ly5dcj3tR04GuVSpX78+DA0NxfzBgwczXcfLywtTpkzB0KFD0aVLF3h4eCgtk93jqFixoqSl2qlTpzJd59KlS0hMTERgYGCWcrwCQIMGDUSe1ISEBLi5ualdPjQ0FNeuXcvSPhSNHj0ajRo1Qt++fbFt2za1y5qamqJly5ZiXlVe6dz+3KR3/fr1TFulXblyRVSmGBgYKOVzVcxTq9hqVZXY2FjcuXMn03Jl97yUK1dO0tIwrbWwOp8+fcLFixfFfEYtW3OTiYmJ5L6qyXHEx8fjxIkTYj6njyNtoG0gNS1BZp8BANi0aROmTJmCn3/+GT/++GOOBmIUy+fv769RAHjfvn2YMWMGBgwYAHt7+2zl1G/VqpWYPn/+fKYpXe7cuYM3b95ovH3FsU/c3d1x5coVJCUlAdBNj7CGDRuK6YCAADx69Ejt8lFRUbhz5w5iYmLw7Nkz0epY8e9w//59MfipOocPHxbHYmBggAYNGmhzCBrp2bMnvvvuO/z888+SQW1VKVq0qEj9Ayj37lG8J2bWWtvLyytHxmfRtdOnT4sURxk5ceKEWMbS0lJlMDa79/a6deuKXhaJiYk4cuRIpus8efJEEsD+Eu7t5cqVQ5kyZcT84cOH1S6fmJgo6eGSnr+/v5i2tLTMtKIhNDRUUnmUUUVjZn+vnNovEdG3jEF4IiLSiaFDh4rpt2/fYvjw4Rp3s37y5An+/PNPMf/zzz+rXV5xULqrV6/i9OnT4r28SEWj2PItsx+qumBmZiZy4QPA5s2b8ezZswyXT0hIwIIFC8S8jY2NJCiSJrvHIZPJ8OOPP4r5jRs3qm0Nf/XqVREU09fXR7du3bK0v3z58klSvKxcuVLt/hYuXJitnPB169YV025ubpm29FdsdW9ra6v0fm5/btKLiYnBwoULM3w/IiIC8+fPF/OdO3dW6sqf1hIXAB49eiT5UZ7e6tWrNaqcU6xg0va8ODk5iem///5bbSvolJQUzJo1S3w2TExM0LVrV632q2uK98J///0XZ8+eVbv80qVLReoIPT099O7dO0fL161bN5HuJikpCTNmzBCBU1W8vb0lAadevXple/BVdZo1ayb5jP72229qg56BgYGSZ1GnTp00HpRSlXbt2olrJjIyEitWrMhw2fj4eMl9WhM9evQQ58/d3V30QtPX15c8I7RVqVIl2NnZifmFCxeq/ftu3rxZVDTY2tqKQGyTJk0kLdlnzpyptkIiMDAQa9euFfOdOnVCwYIFtT6OzCje2w8cOKA233hSUpKkEiF94FHx83b69OkMz1diYiKWLl2qZYlz14cPH7B+/foM3w8JCZH0ZPvxxx8l9/E02X3mmZqaSiqe1qxZo7YVeVxcHGbOnCnmixcvjubNm2d5vzlB8d6+fft2SS+C9NatW6c2JZBiw5PQ0FC1303SUsgoXn8Z/S0yexbn1H6JiL5lDMITEZFOtG/fXhJE9fT0RMeOHbFnzx6V3buB1CDfli1b8PPPP4sWua1bt0anTp3U7itfvnywt7cHkBpI3Lt3L4DUgEHNmjV1cThZophzObvpTjQ1atQoka83JiYGP//8s8oAnb+/PwYPHiwp18SJEyU/htPo4jj69+8vBsUNDw+Hs7MzfHx8lJa7cOECfv31VzH/448/onjx4lne3+jRo1GiRAkAqa2Zf/75Z6Wu81FRUZgxY4akhbA2evbsKVo5fvr0CcOHD1d5nhISErBkyRLR4ktfX19lPvi8+Nykd+TIEcycOVMpOP7s2TM4OzuLruPm5uYYN26c0vqNGjUS50Qul2Ps2LFK6RXCw8Mxd+5cbN++XaMymZmZiWltz4ujo6MIhiUmJmLQoEE4duyYUqvrkJAQuLi4wN3dXbw2e/ZsSS7svNSpUyfUq1dPzE+YMAE7duxQCuxFRERg+vTp+Pvvv8VrI0eOzPEUHqamppLPxY0bN/DLL78oBcbkcjlOnTqFYcOGidaPVlZWGDRoUI6WT09PD1OnThUtOp8+fQonJyeVLbqvX7+OAQMGiCC9iYkJxowZk639GxkZYdKkSWJ+586dWLhwoVLr+jdv3uCXX37JtKV5esWLFxcVqq9evcK///4LAGjevLnOcl9PmDBBpJ3y9PSEi4sLQkJCJMskJiZiy5YtkgqMsWPHivMuk8kwZcoUMe/j44MBAwaoTBV15coVODo6ikr8IkWKYNq0aTo5low4OjqKY3zx4gVGjRolxvRQFBUVhalTpyIgIABA6ue/S5cukmXatGkjpt+9e4cpU6YoVfy8fPkSAwYMwP3793V8JDln48aNWLFihVJFto+PD37++WfRG7FYsWIYPHiwym3o4pnn4uIi0hVGRkbC0dERly9fVlruxYsXGDBggPg+oKenh0WLFqn87pMXnJycRMqeuLg4DBgwQNIjFEj9LrFq1Sps2rRJ7bYUK8qA1O94qtIU+vj4qDxfGVU6ZfYszqn9EhF9y76MpxAREX0T0loapwWDP336hHnz5mHBggWoWrUqihUrhoIFCyIqKgpBQUF49OgRUlJSxPr169fHH3/8odG+HBwc8M8//wD4f2saxTQ1uals2bJi0KxZs2bh0qVL0NPTw48//qj0I0VXihcvjpUrV8LFxQWxsbEIDw/HmDFjYGNjg1q1asHIyAiBgYHw8fGRdPlNS7GQ0XGkBczXrl2LR48ewcTEBG3bttU4z76lpSVWrVqFX375BTExMQgICECfPn1QrVo1VKxYEUBqblPF4EutWrUwceJErc6Dqakpli1bhmHDhiEqKgqvXr1Cnz59ULt2bZQrVw4RERG4ffu2CDLb2dlJcmZnhYWFBWbNmoWpU6cCSP1R2rNnT1SrVg2lSpWCmZmZyM0cEREh1hs9erTKbtq6ON/ZUb9+fdy5cweurq44deoUGjZsCEtLSwQGBuLu3bvi2jQyMsKyZctQsmRJpW0YGxtj2LBhooXv06dP0bFjRzRo0ABFixbFhw8fcOfOHcTFxUEmk2HIkCHYsmWL2nIptiQ9cOAA3r9/j0KFCqF27dqSnhbqmJqaYt26dejXrx9CQ0MRHR2NyZMnY8WKFahTpw5MTEzw5s0beHt7S1rj9evXL8/uI6ro6+tj9erVcHJyQmBgIBITE7Fo0SJs2rQJ9evXh5mZGd6/fy/OcZr27dvDxcUlV8ro5OQEPz8/HDhwAEDq+AedOnVCrVq1UKZMGURHR+PJkyeSXMAmJiZYs2ZNjg4am6Z169YYN24cVq5cCQB4/PgxHBwcUK1aNVSoUAEJCQl4/vy5JP+4gYEBFi9ejFKlSmV7/927d8fNmzdF6oydO3fi8OHDaNiwIQoWLIigoCB4eXkhKSkJhoaGKFCgAMLDwwFIx1zIiIODgwjepX2WddkjzM7ODlOnThWt9C9fvoy2bduiXr16sLGxQUxMDLy8vCQtdR0dHdG5c2fJdlq2bIkJEyaIZ7y3tze6dOmCWrVqwdbWFklJSfD19RUBbiD1Ol65cmWOD5Rcvnx5uLi4iNb3169fR+fOnVG9enXY2NjAxMQEISEhuHv3rggcymQyzJo1S6nCrl69emjWrJlIfebm5oarV6/Czs4OZmZmCAwMxL179yCXy1GwYEHY29tj3759OXp82WVqaoqoqChs3rwZ//zzDxo2bAgTExO8ePFCUsluamqKtWvXSoK3inTxzCtWrBhWrVqFESNGICYmBh8+fMDQoUNRpkwZ1KhRA0ZGRnj58iV8fHzEM0xPTw+TJ09W2QMwr+jr62Pp0qUYMGAA3r9/j0+fPmHQoEGoUqUKqlSpgri4OHh4eIjKjbTntSo1atRAq1atxNhIt2/fRrt27VC3bl0ULVoUkZGRePHiheTaMjc3F41fMhr0NbNncU7tl4joW8YgPBER6YyRkRHWrFkDV1dXrFu3TgzYlJycDF9f3wwHljIxMcHgwYMxbNgwjVsp1atXD2XLlhVf7g0MDPD999/r5DiyatCgQbh79y7kcjliYmJEi+ty5crlWBAeSM1tunfvXkyZMkV0ZQ4KClI50Fu+fPkwZswY/PLLLxlur1+/fiL3q2IOUgMDgywFhevVq4d9+/ZhwoQJIrD16NEjla08O3bsiAULFkjy6GZV/fr1sXfvXowYMQJBQUGQy+W4d++eJAWJnp4exo8fDxMTE62D8EBqwCspKQkLFy4UwZiMjq1AgQIYO3Ys+vfvr3Jbujrf2uratSvatm2L5cuXIzo6WpITPU2JEiWwdOlStfmYhw4dik+fPmHXrl2Qy+VITEzEjRs3JMsUKFAAs2fPRrVq1TINwv/www/Ys2eP+KGeVq7g4GCNg/BA6hgFhw4dwqRJk0TwIjg4WGVuXTMzM8yZM+eLSUOjyNraGq6urpgxYwbOnz8PAAgLCxODXioyMjLCr7/+igEDBuTqmAPz5s1DuXLlsGbNGkRHRyM5ORne3t7w9vZWWrZcuXJYtmxZjgzcmJHhw4fDxsYGCxcuFEGtjK7bokWLYuHChWjWrJnO9p92j9uzZw/kcjk+f/4s6X0BpAanli5dik2bNol7V1r+a3Xat28PMzMz0XLcwsICrVu31lnZgdR7VeHChTFv3jyEh4cjMTFRaUBSIPXeNWLECIwcOVLldoYMGQIbGxv8/vvvCA0NhVwux/3791W2CK9duzaWL1+uk4oQTYwaNQp6enrYsGEDEhMTkZycDB8fH5U9uYoUKYLp06crtYJPs3LlSowcOVKMvRIREaE0YH2ZMmWwfPnyr6I1vLOzMz59+oR//vkHYWFhKnvdVapUCX/88QcqV66c4XZ09cxr3Lgx9u3bh0mTJonvPq9evVLZe8HKygpLly79InLBp1e+fHn8888/GDFiBB4/fgwgNT1j+kHTnZyc0Lx5c7Vjqvzxxx8YPny4WCY2NlbpOZymW7duGDNmDNq3bw8gtbfaq1evJHnqAc2exTmxXyKibxmD8EREpHN9+vRBjx49cOPGDVy9ehWPHj3CmzdvEBERgcTERBQsWBBFihRBhQoV0K5dO7Rs2VKrvLsODg6idWOLFi1yvLVcRtq1a4ctW7Zg69atePLkCaKiomBqaprpIHy6UK1aNRw7dgznz5+Hu7s77t27h48fPyIuLg5mZmYoX748mjZtit69e4s0MRmpWbMm9u7diw0bNuD+/fuIjIyEiYmJ2hzAGalSpQqOHz+O06dP49y5c3jw4IEIulhbW8POzg69evXS2WB7lStXxunTp3Hw4EGcOXMGT548QWxsLKysrGBnZwdnZ2fUrl1bkq5DW3369EHLli1x9OhR3Lx5E8+ePUNkZCTkcjkKFy6MMmXKoFWrVujWrZvaz6Quz7e2Bg0ahEaNGmH37t3w8PDA+/fvYWZmhgoVKqBDhw7o06cP8uXLp3YbMpkM06dPR7du3eDq6opbt24hJCQEhoaGKFGiBFq3bo2+ffuiePHiavPepilRogQOHDiAdevWwcPDA2FhYTA2NtZqAM8SJUpgz549uH79Ok6fPi1a7MbGxqJgwYKoXLkyWrZsiZ49e+ZKq2xtWVhYYP369fDx8cHx48fh4eGBkJAQfP78WVznzZs3R69evWBtbZ0nZRwwYAC6d++OQ4cO4caNG3j27BnCw8Mhk8lQpEgR1KhRAx06dECHDh1yffBsIDUA1LZtWxw5cgRXr16Fn58fQkNDkZKSAktLS1StWhVt27ZF165dszxIdGb09fUxa9Ys9OjRA4cOHRLXCJA6Rkfr1q3Rv39/FClSBKtXrxbrafKZzJcvHzp37ix6hnXr1i1Hzm+XLl3QsmVLHDx4EJcvXxZ/X2NjY5QsWRJNmzbFTz/9hNKlS6vdjr29PVq1aoUjR47g8uXL8PPzQ1hYGORyOYoXL47atWuLfeX24NUuLi7o1q0bDh8+DE9PT/j7+yMyMhL6+vooXLgwKlasKO7t6r6zmJubY/fu3fj3339x4sQJ+Pj44NOnTzA3N0fZsmVhb2+PXr16IX/+/F9FEF5fXx+///47OnfujL179+LevXsIDw+Hubk5atWqhW7duqFTp06Z9tzIie8Y//77L86fPy+++yQmJsLS0hLVqlVDu3bt0K1bt0yfYXmpePHiOHToEE6cOAE3Nzf4+voiKioKlpaWqFWrFn766Sc0a9ZMZSW5IjMzM+zevRtubm44efIkHj58KO6/5ubmKF26NGrWrInu3bujevXqAFIrutI+f4cPH8b48eMl29TkWZwT+yUi+pbJ5Nr8oiEiIvoCLF68WOSZXr9+fa60HiYiIsoprVq1wrt37wAAW7ZsQcuWLTNdZ/To0SIf/NGjR1G1atUcLSN9+6ZOnSpSKI0aNQqjR4/O4xIRERF9/dgSnoiIvkrJyclwc3MDkNrduFWrVnlbICIiIgXe3t64evUqSpUqhapVq6JKlSpql3/79q1I4wZAbWqPNBERESInc/Xq1RmAJyIiIvpCMQhPRERfpYsXL4qB4Hr37q1xLnkiIqLcEBkZifXr1wNIrSy+dOmS2mfVunXrRKqHChUqoFixYpnu48iRI0hISAAA/PTTTzooNRERERHlBL28LgAREVFWvXv3DosXLwaQOnCdk5NTHpeIiIhIqkGDBiK//IcPHzBlyhR8+vRJabmYmBjMnz8fhw4dEq8NGjQo0+37+flh48aNAFKD/Hk1ODkRERERZY7NBomI6IsXFRWFkSNHwsbGBhEREbhx4wZiYmIAACNGjICVlVUel5CIiEjKxMQEY8eOxaJFiwAAbm5uOHv2LOrWrYuiRYvC0NAQISEh8Pb2Fs80IHVw1V69eilt78WLF1i0aBGsra3x4cMH3Lx5E4mJiQCAyZMnw9jYOHcOjIiIiIiyjEF4IiL64pmamuLRo0e4deuW5PXWrVtjyJAheVQqIiIi9QYMGAAAWLVqFWJjY5GYmAgPDw+VyxoaGmLIkCEZDoJpbW2Nq1evKr3et29ftoInIiIi+sIxCE9ERF+F9u3bw93dHXFxcShdujR69uwJZ2dn5oInIqIv2oABA2Bvb4+jR4/ixo0beP78OcLDwwEAZmZmKFeuHJo0aYKePXuiRIkSGW7HzMwMzZo1w71795CSkoJy5crB0dFRZat5IiIiIvqyyORpo/8QEREREREREREREZFOcWBWIiIiIiIiIiIiIqIcwiA8EREREREREREREVEOYRCeiIiIiIiIiIiIiCiHMAhPRERERERERERERJRDDPK6AERERLnNx8cHV65cwa1btxAcHIxPnz4hMTERBQsWRJkyZVCrVi20b98e9erVg0wmy+viEgEAbt68ib1798LX1xcfP36Evr4+LC0t0atXL4waNUqjbbx58wZt27YV835+fjlV3K8Sz8+XRZO/R+XKlcW0u7s7SpYsmStl+9oFBARgx44duHHjBj58+CCegdWrV8eWLVvyunhaiYqKwtGjR3HlyhU8efIE4eHh0NPTQ6FChVCjRg20adMGXbt2hYGBZj+BU1JS8O+//+LYsWPw9fVFWFgYTE1NUaJECbRp0wa9e/dGsWLFcuRYrl27hkOHDuHevXv4+PEj8ufPj6JFi6J58+bo3bs3ypUr901tLyNTp07FkSNHAACjRo3C6NGjdbJdIiKivMAgPBER/Wd4eHhgxYoV8Pb2Vvn+x48f8fHjR3h5eWH79u2oXLkyxo4dKwkCEeWF3bt3Y8GCBZDL5ZLXY2Njoa+vn0elIqKv0d27dzFkyBBERUVJXv/48SMSExPzqFTZc+bMGfz2228IDw9Xei8oKAhBQUE4e/YsNmzYgFWrVqFatWpqt/fp0yeMGTMGd+7ckbweFhaGsLAwPHz4ENu2bcOsWbPg4OCgs+OIiYnB5MmTce7cOcnrCQkJiIiIwNOnT7Fr1y6MGTMGQ4cO/eq3R0RE9F/CIDwREX3zUlJSsGTJEuzYsUPyer58+VCrVi1YW1vDyMgIHz58EK3dgNRWly4uLujatSt+//13mJiY5EHp6b8uODgYS5cuFQF4ExMTNG7cGBYWFggLC0PDhg3zuIRE9DWZNWuWCMDLZDI0atQIJUqUQFRUFBo3bpzHpcu6gwcPYsaMGWJeX18ftWrVQtmyZZGUlIQnT57g2bNnAIBXr17B0dERu3btQq1atVRuLyoqCs7Oznjx4oV4rWbNmqhQoQLCw8Nx69YtxMbGIjo6GlOnToWenh66d++e7eNISkrCsGHD4OHhIV6rVKkSqlatiri4ONy6dQsRERFITEzE8uXLkZSUBBcXl692e0RERP81DMITEdE3LSkpCaNGjcLFixfFa7a2thg9ejTatWsHY2NjyfLJycm4fv061q1bh/v37wMA3Nzc8Pr1a2zduhVmZma5Wn6iW7duISEhAQBgZmYGNze3HEuBQETftrdv3+L58+difsOGDWjTpk0elih7AgICMGfOHDFfr149LFmyBKVLl5Ysd/v2bUyZMgXv3r1DbGwsxowZgzNnziBfvnxK21ywYIEIwBcqVAhr1qxBgwYNxPsRERGYPn06zp8/DwCYOXMm6tWrh1KlSmXrWDZt2iQC3Pnz58fSpUvRoUMH8X5cXBwWLlyIAwcOAADWrFmDRo0awc7O7qvcHhER0X8NB2YlIqJv2rJlyyQBeEdHR5w4cQJdunRRCsADqS3oWrRogf3792PMmDHi9fv372PixIlISUnJlXITpXn//r2YbtCgAQPwRAr8/PzEP+aDz9yHDx/EtKmp6VcdgAeAdevWiRQ6lSpVwrZt25QC8ADQqFEj7NixQ/Roe/fuHfbv36+03NOnT0UOcgBYu3atJAAPAAULFsTq1avRqFEjAKmpWNatW5et4wgNDcVff/0l5ufNmycJcAOpvffmzZsnWt3L5XKsXLnyq9weERHRfxGD8ERE9M26fPmyJAXNL7/8gt9++w2GhoaZrqunp4eRI0fi119/Fa9dunQJrq6uOVFUogyltYIHUoM/RETaio+PF9Nf+/0kLi4O7u7uYn7cuHHInz9/hsuXLVsWP/74o5hPn9ccAPbt2ydSf7Vu3Rr169dXuS0DAwP89ttvYv7kyZOIiIjI8jGkOXz4MGJjYwGkViZ069Ytw2WnT58ujtPT01Ok2vmatkdERPRfxCA8ERF9s1avXi2m69atiwkTJmR5G0OHDhWt3QBg1apVkiAGUU5LPxgrEZG2vqX7iZ+fH2JiYgAAhoaGaNasWabrKLZqV8z5nkYxqG9vb692W+XLl0f16tUBAImJiSI9jTYU17W3t4dMJstwWQsLC7Ro0ULMnz59+qvbHhER0X8Rc8ITEdE36ebNm3j48KGYHzZsGPT19bO8HZlMhgkTJuCHH34AkNol+8SJE+jdu7dkualTp4ou7EePHkXVqlXx8uVLuLq64urVqwgODkZCQgKsra3RsGFD9OrVC/Xq1dO4HBcvXsTZs2fh7e2NDx8+IDk5GYULF0aNGjXQvn172Nvba3V8ad6+fYu2bduKdDtbtmxBy5YtM11v6dKl2Lp1KwCgZ8+eWLRokcrlPD094ebmBk9PT7x//x7x8fEoVKgQqlSpgtatW8PBwUFleiBVPn/+jOPHj8PDwwNPnjxBeHg4oqKiYGJiAgsLC9SsWRMtWrRAly5dMuz1cPjwYUybNg0AMG3aNAwYMACurq7YsWMHAgMDUbBgQVSuXBk//PADOnbsqFG5VLlz5w6OHz8OLy8vhISEID4+HpaWlqhQoQKaN2+O3r17qxxn4Pbt2+jXr5/S60eOHJGkSli0aBF69uypdfmA1IGL3dzccPLkSTx69AhhYWGwsLBA6dKl0blzZzg4OMDU1FSjbQUGBsLV1RW3b99GYGAgoqKiYGZmhpIlS6Jp06bo2bMnypQpk+H6b968Qdu2bcW8n5+f2v1psnzlypUBAFWqVMGxY8fw5MkTrFixAnfu3IG+vj5KlCiBpk2bZlpJN2DAANy8eRMA0LlzZ6xatUrt8gDw/PlzdOnSBUDqgLrXr1/P0gDPisfXtm1bbNiwAR4eHli7di0ePHgAY2NjlC5dGm3atMGIESOU1v/w4QMOHjyIq1evIjAwEOHh4TA1NYWNjQ2aNm2KPn36qEzdoYpcLseVK1dw5coVeHt74/3794iIiIC+vj7Mzc1RpkwZNGrUCH369EHRokU12ubly5dx+PBh3Lt3D58+fYKZmRkqVqwIBwcHjQe6TPv7AqkB1PQpadL//YHUgOLx48fh6+uLjx8/In/+/ChVqhRatWoFR0dHFCpUKEvlv3//Pj5+/IgCBQqgTJky6NixI3766SeYmJjgl19+wbVr1wAAu3btklTqppHL5bh48SJOnz4NHx8fvH//HklJSbCwsECpUqXQuHFj9OjRQ+O/lSqK5ylNUFCQ5HUHBwcsXrxYabnIyEgcOnQI165dg5+fH8LDw5E/f35YWVmhQYMG6NKlS6YDRDs7O4t84p6enkhOTsbKlStx7tw5xMbGwtraGnZ2dhg5cqTGaYVkMhk6duyIkJAQyOVyjZ4his/J6OhoyXuvXr1CSEiImG/SpEmm22vQoIH4rnHjxg306tVLo7Irio+Px4MHD7K03/r16+Ps2bNiv4rp87707WXX69evsXfvXly7dg1BQUGQy+WwtrZG/fr10bt3b9StW1ej7SQlJeHMmTM4f/48fHx8EBoaCgAoXLgwatasibZt22b63Wrt2rUiFdGmTZvQunVrvHnzBgcOHMClS5fw9u1bAEDx4sXRqlUrODk5oXjx4mL90NBQ7N+/H//++y/evHmDxMREFC9eHM2aNcOgQYNQokQJjY5FV9+xwsPDcfToUVy5cgV+fn6IiIiAsbExLC0tUb16dTRr1gzff/+9xt/XiIhIikF4IiL6Jim2ZitatChatWql9bZq166NSpUq4enTpwBSW3WlD8Knt2PHDixfvlySSgRIDVIGBgbi4MGD6N27N+bNm6f2B97r168xceJE3Lt3T+m9oKAgBAUF4ezZs9iwYQOWL1+OatWqZf0AAZQoUQKNGjUSQcYTJ05kGoRPC96mURUMDg0NxdSpU3H58mWl94KDgxEcHIxLly5h48aNWLhwIb777ju1+9yxYwfWrVuHz58/K70XGRmJyMhIBAYG4uTJk1i/fj02bNiAihUrqt0mkDqA3Pr168X8hw8f8OHDB63zJb99+xbTpk3DrVu3lN4LCQlBSEgIrl+/jo0bN2Ly5MmZfp5ySlBQEEaPHi2psAL+f/xeXl7YsWMHVq9ejRo1amS4ndjYWCxbtgz79u1TGjchNDQUoaGh8PHxwV9//QUnJydMmjRJo7RQuvbkyRM4OjpKgm+RkZEwMDCAgYH6r8UODg7i+rh48SKioqIyrZxIC/oCQKdOnbIUgFfl2rVrGDZsGJKSkgCknvfw8HBJUCfN1q1bsW7dOtFSOE1YWBjCwsLg6+uL7du3o1+/fpgwYYLa+9Djx48xZcqUDCtFYmNjERISAg8PD2zevBmTJk1SWYmUJjQ0FJMmTRLBacXXb9++jdu3b8PV1RXTp0/PcBvaCA8Px8SJE3H16lXJ6/Hx8QgPD8eDBw+wfft2LF26VFK5o2n5w8PDER4ejvv372PPnj2S3lgZ+fDhA0aPHg1vb2+l996/f4/379/Dy8sLmzdvRv/+/TFp0iS1rZB1bf/+/Vi6dKlSwDoxMRGRkZF48eIF9u/fj2bNmmHJkiUoUqRIptuMjo7GkCFDJGlKXr16hbdv32Lq1Kkal61WrVpYs2aN5gcDSO516cuqWJ6CBQvCysoq0+1VqFBBTGdWaZgRf39/cU2n36Y2+/3St5cdW7duxapVq5S+WwUEBCAgIAAHDx5Ev379MG3aNOjpZdzp39PTE9OmTcPr16+V3nvz5g3evHmD06dPY926dVi6dClq166tUfkOHjyI+fPni9Q9aZ49e4Znz57B1dUVmzZtQt26dXHjxg1MmjQJHz9+lCz78uVLvHz5EkePHsWmTZsyTIkE6PY7lru7O6ZOnYrIyEjJ64mJiYiKisLr169x5swZrFmzBkuXLtWoMoaIiKQYhCciom9SWos7IDUVTXaDFi1atBBBeE9PTyQmJmYYRNy1axcOHz4MADA3N4ednR0sLS3x7t07eHp6ih+zBw8ehLW1NcaOHatyO48fP8bAgQMRFhYmXqtatSoqVqwImUyGgIAAPHjwACkpKfD394eTkxM2bdqksqWlJhSDjO7u7oiJiVEbNLx165ZoNVi6dGmlH4rv3r2Ds7Oz5EduuXLlUK1aNRgaGuLNmze4d+8eEhMTERwcjKFDh2LJkiXo2rWryv2tWrUKGzduFPNmZmaoW7cuihQpArlcjuDgYNy/f18EHQMDAzF06FC4ubmhQIECGR6Hh4cHLly4oPS6gYEBOnfunOF6GXn16hUcHR0lP6yLFi2KOnXqoECBAggMDIS3tzeSk5MRERGBGTNmIDAwUDL+gLW1tchd7OvrKwJHZcuWlfx9bW1ts1w+RX379hUDv1aoUAGVK1eGnp4eHjx4gICAAACpAQkXFxe4ubnB3NxcaRtxcXEYNGgQ7t69K14rUKAAGjRogEKFCiE0NBSenp6Ijo5GUlISdu7ciSdPnuCvv/6CkZFRtsqfFQkJCRg/frxSMBGA2vzGaTp06IB58+YhKioKcXFxOHfuHBwcHDJcXi6X48SJE2JemxayisLCwjBp0iRJMCzN999/L5mfOXOmZPyKggULol69eihUqBAiIiJw9+5dhIaGIjExEVu3boW/vz/Wr1+vMhD/6NEjODs7IyoqCkDqeBk1atRAmTJlYGxsjMjISPj6+ooWnwkJCViwYAFsbGxUBrI/f/6Mfv36SQKeJUqUQN26daGnpwdfX1+8fPkSXl5eGD9+vHYnS4X4+HgMHz5cBLttbW1RvXp1yGQyPHr0SKQmiYqKwtixY3Hs2DGUL19eaTuRkZHo37+/eB4Aqa1c69WrBz09PTx8+BD+/v4ICgrCoEGDYGFhkWGZEhISMGTIEDx+/BhAaivtmjVronTp0jAwMEBwcDC8vb0RGxuLpKQkbN26Ffr6+lqlVku7n7x//14MVm5iYiL57KdvQbx48WJs375dzBsYGKBu3booVaoUYmJicPfuXXH/uHbtGnr37o1du3Zl2mJ//vz5KvOEt2jRIkfz1CclJYlnMwDUqVNH8v6bN2/EtKat8RV7fSiunxWK61lYWGjU80hxvzExMQgNDRU9OL707Wnrn3/+EZ+3/Pnzw87ODtbW1nj//j08PT1FqsBdu3ahaNGiGDx4sMrtnD9/HmPGjEFycrJ4rVKlSqhUqRJkMhn8/PzE9R0QEICff/4Zq1atUlsxBwDHjx/HqVOnAKR+P7Gzs0OhQoXw8uVLcd8JDw/HhAkTsGDBAgwfPhzx8fGwsLBAw4YNYWJigidPnuDJkycAUu+V48ePx/nz51W2PNfld6y7d+9i9OjR4pwULFgQdevWReHChRETE4NXr17h0aNHAFLvIUOHDoWrqyuqVKmi9pwQEZEUg/BERPTNiYuLkwRIatasme1tKm4jPj4er169yrA12OHDh6GnpwcXFxcMHjxYMlDc69evMXLkSNEybPv27RgyZIhSsDsyMhKjR48WAfgaNWpgwYIFSj94AgICMHPmTHh6eiImJgbjxo3D0aNHNU4HoUgxyBgTEwN3d3e1wUnFVr49evSQVHQkJiZi7Nix4sdhmTJlMH/+fKWUBSEhIZg/fz7+/fdfJCUlYcaMGahQoYLScT5+/BhbtmwR8/3798eECROUfphGRUVh2bJl2L9/P4DUFumnTp1Cnz59MjyOtF4TnTt3xpgxY1CsWDE8e/YM9+7dy3LQIC4uDoMHDxYB+AIFCmD27Nno3r275Py8ffsWs2bNEi1pN2/ejPLly4sUHLa2tpg3bx6A1O7uaUH4unXritd14f379yhevDgWLVokadUml8uxf/9+zJ07F3K5HCEhIdi1axdGjRqltI0ZM2ZIAvBDhw6Fi4uL5HMfExODtWvXYtu2bQBS0+3MnTsXCxYs0NmxZMbf3x9AanBt9uzZaNCgAcLCwnDq1CmRMkad/Pnzo1OnTjh48CCA1N4i6oLwt2/fxrt37wCorqTKqrRzXK1aNcyYMQPVq1dHcHAwTp48Kcm/vGvXLhGANzQ0xJgxY9C/f3/JtZKcnIz9+/dj8eLFSEhIwMWLF7FmzRqloLdcLsesWbNEAL5SpUpYu3YtypYtq7Tc+fPnMWXKFFHJ8ddff6kMWi1cuFAEYA0MDDBjxgz89NNPkuvj7NmzmDZtGgIDA7U9XUpevnwJIDVgvmDBAqUWoW5ubpg2bRoSEhKQmJiILVu2YMmSJUrbmT9/vni+GBoaYvr06UrlP3/+PKZNmyZ652Tk2LFjIgBfvHhxbNu2DeXKlZMsExoaihkzZoiKwh07dqBfv34atdJWlHbfuH37tgjCW1paZng/OXDggCQA36pVK8yZM0fS60Iul+Pw4cP4/fffERsbi3fv3mHkyJFwdXVFvnz5MizL+fPnkS9fPkyZMgX29vZITk7GzZs3s3xMWbV9+3ZJQDl9znfFitPChQtrtE3FZ0RsbCzi4uLUHrsq2d0vkFpJl/bal749baUF4J2cnDB27FhJhU1ISAhGjBghnpXr16+Hk5OT0kC9T548wfjx40Ww2dbWFosWLVKqgPLy8sLUqVMRGBiIhIQETJw4EQcPHlRZMZcmLQDv7OyM8ePHSyr/3dzcROVZWgVdSkoKfvnlF4wZM0bymTl06JDoBfT+/XucPXtWqaJV19+xli1bJs6Jg4MD5s6dq/T96u7du3BxcUFYWBgSEhKwevVqScMIIiLKHAdmJSKib05oaKhk8Dld/LC3sbGRzGfW4m3s2LEYPXq00g/AUqVKYfXq1aKbdGxsrMqUJVu3bhU/rqpVq4bdu3erbHFUtmxZbNu2TQT4QkNDsXnzZs0PTEFakDGNYive9GJjY/Hvv/8CSG0Zmz4YeeTIEdy/fx9AanBp7969KnMGFy1aFGvWrBFB0Li4OKxcuVJpub1794ofiA0bNsT06dNVtgwzNTXF3LlzJefq9u3bGR5HmmbNmmHlypUoV64cTExMULt2bfTv3z/T9dL7+++/ReDQ0NAQ27ZtU6qgAFJb/m7evFmS8mfJkiWIi4vL8j6zw8zMDPv371fqVi6TyfDTTz9JfvjfuHFDaX0fHx9JSqKpU6diwoQJSp97ExMTTJkyRdLa/+DBg/D19dXVoWjEyMgIO3bsQMuWLWFiYgIbGxsMGTJE43uE4uf81q1b+PDhQ4bLHj9+XOV62VGkSBHs2LED9evXR/78+WFra4tRo0aJHgURERGS62fRokUYOnSo0rWir68PJycnkcsYSL3nKObDBgBvb2/xNzIwMFAZgAdSPy/t27eX5H2+d++eypQRR48eFfNz5syBo6Oj0vXRsWNHbNq0SW06CW3kz58fO3bsUJmSoWvXrhg0aJCYv3TpktIyfn5+kr/r4sWLVZa/Xbt22LZtW6YplxTT2YwbN04pAA+kBjNXrVoFa2trAKmt59On09G16OhoSSqdtm3bYuPGjUppj2QyGXr16oU///xTpHN6+vQp9u7dm+k+5s+fD0dHR1hYWKBw4cLo2rWr1r24NOHl5SU5purVq6Ndu3aSZRR7yWgaSE9fgZ5WYZUV2uw3fe8uxf1+6dvLjoEDB2L27NlKPSaKFi2KFStWiHtGTEyMyjR+K1asEPclGxsb7Nu3T2UOeTs7O+zfvx/FihUT21u2bFmm5evRowdmzpypdPxdu3ZF48aNxXxKSgp69eqFyZMnK53TXr16SVIoenl5Ke1Hl9+xYmNjRSVvvnz5MG/ePJXfr+rVqyepOL9+/brofUBERJphEJ6IiL454eHhknlVA19mVfru16pSWqQxNzfHgAEDMnzf1tZWkqc8fU7ShIQE7Nu3T8xPmTJFbVoYIyMjTJ48WcwfOnRI62CuYrDw+vXrYqCy9M6fPy/SvjRu3Fhp8LCdO3eK6dGjR6vNEyyTyTBlyhSRCuPSpUtKlRzGxsaoVasWLC0t1Z7bNIo/RtN/HlQZNGiQTvIs79mzR0w7OzsrpTtQZGBggAULFogA6qdPnyQBvtwwYMAAEWRQRTEdz6tXr5TeVzzeGjVqZPq3GTp0qGTcAsWWtrmhQ4cOKFWqlNbr169fXwwsm5ycjJMnT6pcLj4+XgxKqKqSSlu9e/dWm67D1dVVXJcNGjTINM1Oy5Yt0bx5cwCpLSv/+ecfyfuhoaFo3LgxSpYsiXbt2qkMwCtSDKKmpKQotQI/e/asGDOgSpUqanuoNGzYUKn1Z3Z9//33ao9BcRDm8PBwpbEn3NzcRAVvkyZNMkydBaT2nnJ2dlZbHsW80eqCWcbGxpgxYwZ+++03/PXXX+JvllPOnDmDT58+iX3Pnz9fbYVIgwYN4OjoKOZ37NihdvvFihVTe+50zc/PDy4uLkhMTASQ+sycN2+e0j1fsdJI04En01e0qEoXlRlt9pt+DIu0Y/satqctExOTDNP3AamNEqpWrSrm01KqpXn9+rUkd/qsWbNgaWmZ4fYKFy6MWbNmifmLFy+KHjWqyGQyteVTDMIDwPDhwzNc1s7OTkynrxwFdPsdS/E+JJfL1d6LWrZsiXHjxmHJkiXYvn17ro5PQUT0LWAQnoiIvjnpByLMatdwVdIPNqnY0j69OnXqZLpPxXyz6cvr4+ODiIgIAKktN1W1bkqvdu3aoqt3XFycyhZgmlAMMiYlJeH06dMql1NMRZN+QNZ3797h+fPnYl4xVUZGihYtKvnxnL71elqO61u3bmWalxWAJHd5Zj/+9fX1VbaEyyp/f3+RFxuA2gBjGisrK0lrzOvXr2e7HFmRWTBPMWCd9plUpFjePn36ZPqDXCaT4YcffhDzaWMQ5JYGDRpkexs9evQQ0xn1FnF3dxctP5s0aaJy4FRtZJbSRrGFtCbXHQC0bt1aTKe/7tq1a4edO3fC3d1do0FG01d4pr/2FFuXp08FooriudaF9EGw9NLnAU9/b1Yc8FuTsmV2D1CsjF22bBmOHTum1HsgTadOneDo6IjmzZvneNoWxeu6Xbt2GqUR6du3r5gOCQmRPAPSs7Ozy7Xg3ZMnTzBw4EBJZezMmTNVDjStWNGgbqBiXdP1fr/07WnLzs5OqZdVeorPrPSVgIqfa2tr60wHnweANm3aiF4ogOoeYWnKli2r1CBBkWKgvFixYmrHTlAcSyJ9ow9df8cqVKiQSDMUHx+PYcOGiTRZ6RkYGGDEiBHo0aMH7OzscnVcFyKibwFzwhMR0Tcnfat1dTl5NZV+G+oGJksLYqujuL7i4GAARBdjIDVoOWfOHI3KqFgx4Ofnl2nAKSMODg5YtWoVgNQgo5OTk+T9jx8/ih+iZmZmaN++veR9xfIDqTnNNaEYJEnLma8JuVyO9+/f4/nz53jy5Am8vb0lP5TTV6CkZ2Njo7angaYUf7RaWFioTC2hip2dncglmzbwWW7JrFW4YmVS+oDqhw8fJOlYNK3IUGzh9+nTJwQHB6ttja9LGY3jkBUODg5Yu3YtUlJSxCCi6QfIVayk0lUreEAatFXFx8dHTF+9elWjgSIVK46yct0BqSkmXr58iadPn8LHx0cpQJX+2lPcfvXq1TPdfs2aNSGTydRWemZFZi3509/XFVs1R0dHi8FbgdSKz8yUK1cOFhYWGfbG+fHHH7F7927Ex8fj8+fPmDx5MubMmYNGjRqhSZMmaNq0aaZ/85ygeB/S9LouX748LC0txTgmDx8+zPB608V1qIk7d+5g+PDhkh4NLi4uYpDa9BQDvJq2aE9/X9QmKKnNftMvp7jfL3172tKkF5NiWdP/bRQ/13Xq1NEo3ZWenh7q1q0rejape0ZnNiCxYgVGZuP2pO9JoCgnvmM5OzuL731eXl7o0aMHbGxs0KxZMzRu3BiNGzfOdk5/IiJiEJ6IiL5B6QN6GaVUyYr0uZ/VtXZSF6BPo/jjL32ASXEQtJiYGBw4cEDTYgqapGDJSI8ePbBmzRqkpKTA29sbr1+/lvz4dXNzExUH9vb2Sq3+FcsPQKfll8vl8PT0xJUrV+Dn54c3b94gKCgoW3lJ1aX3yArFz1lWWj4rfl518VnNCsUeA1mVvqzqrglF6c9NaGhorgXhFVsXaqt48eJo3LixCDifOHFCkgs9NDRU5PpWVUmVHeo+q9HR0ZKW2x4eHvDw8MjS9j9//ozk5GSVrV2DgoJw7tw5PHjwAAEBAXjz5k2m9xnFe1tcXJykRadi69KMmJqaomDBgtm6n6Xfnjrpg3KK5U//DNCk/EDq9Z1R+UuXLo0//vgDkydPFikhYmJicPHiRTF4qrW1NZo3b46OHTviu+++Uxuc05W0QDqQ9XtZ2rqK20hPV/dcdU6cOIHp06dLeha4uLioTReiWBmbvhdERtIvlz4XuCa02W/61tGK+/3St6etrD6v0n+3ys7nOo26Z3RWyqdpWh9VcuI71rBhw/D8+XPJGC9BQUE4cOAADhw4AJlMhurVq6N169bo3Lmz2gFqiYgoY0xHQ0RE3xwLCwtJQPDBgwfZ3qZiehdDQ0O1LSqz2107fR5ibajLWZ+ZtCBjmvQpNxTzlqdPRQPkXPm9vb3x/fffw9nZGX/++SeuXLkCf39/SQA+X758+O6777I0wF9m3ds1pTjwXFZa1isuq5ibNTdkJ6CXfqA9TY85/fnWNKijC7pITQVIW7crBi0A4OTJk6IVqKpKquxQ91nVxcCHcrlc6e8RFRWFadOmoV27dli0aBHc3Nzg6+urFMSpWLGi2vQr6dMZaTvAY3ZkZ6DX9ME3bQfuTK9Dhw5wc3ND3759VVYSvX//HocOHcLQoUPRoUMHnD9/XuMya0vxs5SV86/4+VR3XevqnpuRtWvXYuLEiSIAn5YTW10AHoAkP7i6SgRFip8LMzMzrYKr2d0vIB2A/kvfnrayWwGl7TNa8fOq7hmdGxVkQM58x9LT08Py5cuxceNGNG3aVOlY5HI5fH19sXbtWtjb22PEiBF49+5dtstBRPRfw5bwRET0Tfruu+/g6uoKIDX3pVwuz1YO2lu3bonphg0b5mgeTMXgTu3atZUGS8wNDg4Okpa+Li4uAIAXL17g4cOHAFJTLagaeFTxB2uRIkV0kuf85s2bGDp0qKRVo42NDapVq4by5cuLwW4rVaoEQ0NDrF69Wim/dU7TprUgIP0xnNPBKV1KH5yLiYnRaBDk9D/+s5MKKLNUQzmlQ4cOmDt3LqKiovDq1Svcv39fpCdRTEXTq1evXCtT+qDwn3/+qXFe+IzExsbCyckJT548Ea+ZmJigZs2aqFChAmxtbVGhQgVUrVoVFhYWeP36tbjvppd+AEtNr5GMcqTntvTnNzY2VqNeT5pUrJUsWRJz587F7Nmz4e3tjevXr+P27dvw8fGRpNQICgrC6NGjsWrVKskgsrpmYmIiUrBlpUJXcVldpPjKqsTEREybNk1ScWxoaIiFCxdqNMivYuve4OBgjfapuJyNjU0WSqt6v58+fUJiYqLS9aJuv+bm5pJW2F/69vLKt/KMzonvWGnatGmDNm3aIDw8HDdu3MCNGzfg4eGhNDD7hQsX8OzZM7i6uqod3JaIiKQYhCciom9S165dRTAoKCgIFy9eRJs2bbTalre3twg8A6kD5OUkxR806bsd5xbFIKO/vz+ePn2KSpUqSQZqzSjXtWJrzoiICCQlJWWrhVhiYiKmTp0qgnHlypXD4sWL1eZk1sU4AFmlmC81Ky3EgoKCxLTiwG1fuvQ/vN++fYvKlStnup5iDnJAeszpK8oySo2SRhctArWRL18+dO7cWdxjzpw5g9q1ayMoKEj0vClfvrxGecN1xdzcHAYGBqIV/qdPn7K9zXXr1okAvIGBAaZNm4Yffvghw0pIVYP3prG0tES+fPkQFxcHIHXwzipVqqjdf1JSks5S0WRX+pa8wcHBGuU2f//+vcb70NfXR/369cUAvDExMbh16xZOnTqFU6dOITk5GSkpKViyZAnatWuXY4NkFipUSNxDNb2XyeVyybK5fS+Li4vDyJEjRSooIPWaWLt2rcbjoyjm3w8ODkZUVFSmFS2KA2RWqlQpi6VOVbp0aRgZGSEhIQHJycnw9/fP9F6quN/04wZ86dvLK9o+oxWfWTk9KLImdP0dK6N92NvbiwG0g4KCcOnSJbi6uorxb16/fo0dO3Zg/PjxOt03EdG3jOloiIjom9S4cWNJgGfNmjVatahMSUnBypUrxbyFhYVGLeqyo1q1amI6KChI40D80aNHcfnyZTx//jxbOdKB/wcZ06SlQLhw4QKA1GBR9+7dVa6rWP7ExERJBYY6Z8+ehbu7O548eSJpeXblyhXRqk4mk2H9+vWZBjdfv34tpnU1qGNmFAeaDA8PlwziqM7du3fF9NeUZ7Vo0aKSgITicaijuJy5ubkkt3b6QEJmrYgV/865TbESyt3dHQBEHu/07+cGmUwmCYwpptBSx8/PDydOnMDdu3cREhIiee/gwYNi+pdffsHPP/+sthdQ+r+H4rUnk8kk92Rvb+9My/b06VOlwRXzipWVlSSPtK+vb6brBAUFqa0MSUpKwsuXL+Hp6anyfRMTE7Rp0wZ//PEH5s6dK9luTn72Fe9lml7Xz58/l1R+5ua9LCEhASNGjJAE4EuUKIF9+/ZlaYDyokWLilR2crkcXl5ema5z584dMd2wYcMslPr/9PX1Jc+07O73S99eXlH8XHt7e2vUkyolJUUyEKqmA67nJF1/xwJSU/U8ePAAL1++VLmujY0NnJyc4OrqKvl75naPQyKirx2D8ERE9M2aOnWqmH78+DEWLlyY5W1s2LBB8iNj7NixOs3xrEr9+vUlXb0VA2EZ8fLywpQpUzB06FB06dIlywMyqqIYRDx//jxCQkLw6NEjAECzZs1QtGhRletVrFhREpzVpPxBQUH49ddf4eLigu7du0vSCfj7+4tpS0vLTH8Eh4aGSv5maYPI5rRy5cpJBnDLKC2Hok+fPkkCt02bNs2RsuUUxQCXq6trphUecrkchw4dEvNNmjSRvJ8+xU36VvPpXb16VdOi6pydnZ0YG+LVq1d4+vSp+Fuqq6TKSYqfn9OnT2uUcmHx4sWYOHEifvrpJ8kAs58+fZK0Qrezs8t0W4o9ZQDldEEtW7YU08ePHxet9jOSfjyKvKZYfk3KppiaKL2HDx+iTp066NSpE/r3759pi/+0FqlpdDEGQEYUr0t3d3eNBoxWvN8VKlRIo14xujJz5kyRPg1IfQbt379fo54K6Sn2dMvsb/zs2TMRADUwMECrVq2yvL80ipXeme03LCwMV65cEfPt2rX76raXFxSfVx8+fMClS5cyXefChQuShhBfwjNa19+xFi1aBDs7O/Tu3Rt//PGH2u0YGhpKUmFlZ/whIqL/IgbhiYjom9WkSRP0799fzO/btw+zZs3KNPADpAYLV65cibVr14rXvvvuO/Tt2zdHyqrIzMxMEsDbvHkznj17luHyCQkJWLBggZi3sbFRCm5qQzHI+PDhQ+zbt08EWVUNyJpGJpPB0dFRzB86dAg3b97McHm5XI558+aJv4upqankB79iy9vQ0FC16R3SUtekpbxIey23ODk5iem///5bbWvklJQUzJo1S/TQMDExQdeuXXO6iDr1888/i+mHDx9i+/btapffvn27pNXeDz/8IHnf1NRUksYi/aCnih49eoSjR49mscS61aNHDzF97NgxUfnTvHlzSQv/3NK3b1/RmyAiIgK///672uVPnz4tCV727t1bTKdv8a6YF16VEydO4OzZs5LX0l97vXv3FnmZg4KCsG7dugy39/TpU+zZs0ftPnPbTz/9JKavXbumdpDUwMBA/PXXXxm+X6lSJXEukpOTsXPnTrX7Vrxu9PX11Q4Onl1dunQRKS/i4+Mxc+ZMta2G7927h71794r5Pn36ZGsQ3Kw4evSopLKjUqVK2L17d4aVxJnp3r27SIt18uRJyXgwihITEzFv3jwx3759+2ylKunUqZPI9X337l2197YFCxaIZ1ytWrVQo0aNr257eaFs2bJo1qyZmJ8/f77agWbDwsIkjTfq1q2rdcohXdL1d6x69eqJ6atXr0pSCamieC+ytbXNcvmJiP7LGIQnIqJv2uTJkyUt2/755x907doVZ8+eVZmeJikpCVevXkWvXr2wadMm8XrVqlWxatWqXAssjBo1SgRBYmJi8PPPPysFuIDUVuKDBw+W/CiaOHGizvKDKraGTwsoWVhYZJpfv1+/fihdujSA1ADT8OHDsX//fqVW6cHBwRg3bpykRdrw4cNRsGBBMZ++Be7EiRNVpujx8fGBo6MjLl++LHk9KwOwZZejo6MIjiUmJmLQoEE4duyYUgvxkJAQuLi4iDQmADB79mxJrtevQZ06ddClSxcxv3TpUqxYsUIpjUxcXBxWrlyJJUuWiNd69uwpCYikUfxsbdu2DSdPnpS8n5KSglOnTqF///4aVajlpB49eoh7ws6dO0XQObdT0aQpWbKkpOLx8OHDGD9+PD58+CBZLjExEfv27cOUKVPEa5UqVZKU28zMTBJw2rRpk8qA5KdPn7BkyRJMmjRJ6b301561tbUkf/DGjRvxxx9/KN2Lb926hYEDB2Y7rZauValSRVJR8euvv+LQoUNK17enpyecnZ3VthI1NDSUBPU3btyILVu2SCoQ0zx8+FDSs8ve3l6jQWG1ZWJiIvk7ubu7w8XFRWmwUrlcjuPHj2PQoEHis1+hQgWMGDEix8qmKDo6GosWLRLzFhYW2LJlS7YGiqxSpQr69OkDIPVeM2rUKMl9Gkit4Bo7dqzocWZkZISxY8dmuM02bdqgcuXKqFy5MpydnVUuU7hwYQwfPlzMz5w5U6l3UVxcHGbPni1aMctkMkycOPGr3F5emThxIoyNjQGkVgQ6OjqqrCy/f/8+HB0dxZgt+fPnx/z583OzqGrp8jtW27ZtxaDC8fHxGDZsmMp7fUpKCnbs2IEjR46I13KjYQoR0beEA7MSEdE3zcDAACtXroSNjQ22b9+OlJQUvHz5EmPGjIGJiQlq1aoFKysr6Onp4ePHj/D19VUaXLBdu3ZYsmRJjgY90itevDhWrlwJFxcXxMbGIjw8HGPGjIGNjQ1q1aoFIyMjBAYGwsfHR/Kja8CAAUppC7KjR48eWL16NVJSUkSQpWvXrmrzQgOpLa3Wrl2LAQMGICwsDHFxcfjtt9+wdu1a1KtXDwUKFEBQUBDu3bsnCcB16NABgwcPlmyrRo0aaNWqlfgRefv2bbRr1w5169ZF0aJFERkZiRcvXiAgIECsY25uLvIT62KASk2Zmppi3bp16NevH0JDQxEdHY3JkydjxYoVqFOnDkxMTPDmzRt4e3tLWgn369cvzwK32TV//ny8fv0aPj4+kMvl2Lx5M/7++280bNgQhQoVQmhoKDw9PSXpM+rWrYvZs2er3N7QoUNx/PhxxMXFITExEb/++is2btyIypUrIyEhAQ8fPhSBkZYtWyIkJCTTVto5pXjx4mjSpAmuX78u/p6aVFLlpF9//RXPnz8XlVGnTp3CuXPnUK9ePdjY2CAsLAyPHj2S5H8vXLgw1qxZo1R5N3LkSBFcjImJQf/+/VGtWjXY2tpCJpPh7du38PHxEZUhBgYGMDIyEsF3Vdfezz//jDt37ohKxT///BOurq5o1KgR8ufPj6dPn4q0V5UrV0ZQUFCOpl7JqqlTp+LBgwfw8/NDfHw8pk+fjvXr16NOnTowNDSEn5+fGLiwSJEikgrD9AOpjhgxAu7u7nj27BnkcjmWL1+OrVu3omrVqihevDiSkpLw/PlzcT6A1J5Oqio8dK1v377w8/MTLdwvXryIq1evol69eihZsiRiY2Nx7949yQCXVlZWWL16tWgxndP2798vSeNTrFgxbNy4MUvbUGzNnmbChAnw9PTEy5cv8fnzZ7i4uKBy5cqoWrUqIiMjcevWLUkF06xZs3TSInjQoEG4cuUKvLy8kJiYiJkzZ+LPP/9ErVq1kJCQgNu3b0uOd9iwYWjUqNFXu728ULVqVSxYsABTp05FUlIS/P398eOPP6Jy5cqoVKkSZDIZnj59KnmmGBoaYuHChVqlN8opuvyOZWBggAULFmDw4MFISkrCmzdv0L9/f5QvXx5ly5aFpaUlIiIicO/ePUmFbp8+fb6I9DxERF8TBuGJiOibp6enh8mTJ6Ndu3ZYvny5GDAsJiYmw67mQGrL0FGjRknyX+ampk2bYu/evZgyZQqePn0KILXlVloAUlG+fPkwZswY/PLLLzotQ7FixUSQMY26VDSKqlSpgoMHD2LSpElicL+PHz/i33//VVpWX18f/fv3x8SJE0UqAEV//PEHhg8fLv52sbGxkjQairp164YxY8agffv2AFIHSX316hXKlCmjUbmzq2LFijh06BAmTZokyhscHIwzZ84oLWtmZoY5c+Z8dWloFJmYmGD37t2YP38+Dh06hJSUFERHR0ty3afR09PDL7/8gnHjxmXYW6NUqVLYtGkTxo8fL1IFPHv2TCklU9euXfH7779LUuLkBQcHB8n10a1bt0wrqXKSgYEBNm7ciJUrV2LHjh1ITExEYmJihgPo1alTB8uWLROtKhV16tQJkyZNwooVK0Rl36NHjyRB4TRly5bFokWLsGXLFvG3v3fvHlq3bi1ZTk9PD6tWrcKyZcuwfft2yOVyhIeHK/X0qVChAjZu3Kjx/Sa3mJmZYfv27Rg/frw4p6ruy7a2tli7dq3k2k5rgZsmX7582LlzJ8aNGydaVYeHh2eYWqJhw4ZYuHCh1qlWsuq3336Dra0tVq1ahejoaCQlJcHDw0PlmCMtW7bE4sWLUahQoVwpG5BawaToyZMnWa6QUxWEt7CwwO7duzFmzBjx7PLz84Ofn59kuXz58mH69OlKabW0ZWRkhD///BOTJk0Sre9fvXqFV69eSZbT19fHiBEjMHr06K96e3mlW7dusLKywvTp08V1q+rvC6Te11auXCkZDPVLocvvWE2aNMG6deswffp0MQbEixcvVA4wb2hoiEGDBmHcuHG6PSAiov8ABuGJiOg/o169etizZw8ePXqEs2fPwtvbG/7+/oiIiIBcLoeZmRlsbW1Ru3ZttG3bFvXr18/rIqNatWo4duwYzp8/D3d3d9y7dw8fP35EXFwczMzMUL58eTRt2hS9e/fOscCMYpCxcuXKqF69usbrlixZEvv27cONGzdw5swZeHl54f3794iJiUGBAgVQpkwZNGrUCL1791ab49jMzAy7d++Gm5sbTp48iYcPHyI8PBwymQzm5uYoXbo0atasie7du4vy1a5dG/fv3wfw/7QcuaVEiRLYs2cPrl+/jtOnT8PLywsfPnxAbGwsChYsiMqVK6Nly5bo2bMnzM3Nc61cOSVfvnyYP38+Bg4ciMOHD+PWrVsICgrC58+fkS9fPpQrVw5NmzZFz549NaoMadKkCf7991/s27cPFy5cQEBAAGJiYmBlZYW6deuid+/eOhn3QBfat28PU1NT0Vr7Swga6+vrY+LEiXBychL5gl+9eoXw8HAYGBjA2toatWrVQpcuXdCyZUu1abYGDx6MZs2aYe/evfD09ERwcDASEhJgYmKCokWLolKlSmjVqhU6d+4MQ0NDtGzZUgThjx8/jtGjRytVuOjp6WHKlCno1q0b9u3bh1u3buHdu3fInz8/SpcuDXt7ezg5OeX4INjaKly4MHbt2oVz587Bzc0NPj4++PTpE4yNjVG+fHnY29ujb9++Sul0VF3rhQsXxu7du3HlyhWcPn0avr6+ePfuHWJjY8UYCXZ2dujQoYPK9E05rV+/fujWrRsOHjyIa9eu4cWLF+JzVKJECdSvXx/dunVDgwYNcr1sqgKEumJlZYW9e/fizJkzOHnyJB48eIBPnz7B0NAQpUuXRtOmTeHk5ISSJUvqdL8FChTAhg0bcPXqVRw7dgx3797Fx48foaenh+LFi6NRo0ZwdHTUODf5l769vNK4cWOcPXsWbm5uuHjxInx9fREaGoqkpCRYW1ujRo0a6NixIzp27Kiz9H45QVffsQCgdevWOHv2LI4fP46rV6/Cz88P4eHhSEpKgqWlJUqWLIkWLVqga9euKFWqVO4cIBHRN0YmT5/EkIiIiEhBWitnAJg2bRoGDBiQtwUi+oKEh4ejWbNmSExMRJUqVSSDRNJ/2+vXr9GuXTsx7+3tLQZjpf8Wf39/dO7cGe3bt1c7IDERERF9u77cal0iIiL6IqQFFY2MjPD999/ncWmIviwnT54U+eDTBnSkb9OxY8cQEhKCkiVLol69eihWrJja5b28vMR06dKlGYD/D3v9+jUAZPqZISIiom8Xg/BERESUocePH+PBgwcAUvND52a+X6KvgaurK4DU3Pjdu3fP49JQTnr69Cn++usvAEDHjh2xZs2aDJeNi4sTywLIk1Qy9OU4cOAAAKBt27Z5XBIiIiLKKxkngCQiIqL/tIiICMyePVvMDxw4MA9LQ/Tl2bRpEx4/fgwA6N27N8zMzPK4RJSTWrRoIab//fdfbN26VSnvO5A6EPOQIUPEYMKGhoZwdnbOtXLSl0Mul4uBTJs3b45GjRrldZGIiIgojzAnPBEREQlDhgxBkSJFEBMTg1u3biE8PBxAapqNtLzwRP9V27Ztw4MHD2BsbIxHjx7Bz88PAFCkSBG4ubnB0tIyj0tIOc3FxQXu7u5i3sLCAjVq1IC1tTWSk5MRGBgIHx8fJCcnAwBkMhnmzp2LH3/8Ma+KTHls/vz5iIyMxKxZs1hRR0RE9B/GIDwREREJPXr0EC1709SsWRM7duyAqalpHpWK6Muwc+dOLFy4UPKaiYkJNmzYgCZNmuRRqSg3xcfHY86cOThy5Agy+xllaWmJOXPmoFOnTrlUOvoSyeVyyGSyvC4GERER5TEG4b9QcXFx8PX1hZWVFfT19fO6OERE9B+xfft2uLm5ITo6GtbW1mjdujX69u2L/Pnz53XRiPLco0ePsHTpUgQHB8PU1BQ1a9bEzz//jPLly+d10SiXvXjxAufPn8eDBw/w5s0bxMTEQE9PD5aWlrC1tUXjxo3Rrl07DsZKRERE9B+RnJyMDx8+oEaNGsiXL5/S+wzCf6Hu3LkDJyenvC4GEREREREREREREWlgz549qF+/vtLrBnlQFtKAlZUVgNQ/XLFixfK4NERERERERERERESkSnBwMJycnERMNz0G4b9QaSloihUrhpIlS+ZxaYiIiIiIiIiIiIhInYzSiuvlcjmIiIiIiIiIiIiIiP4zGIQnIiIiIiIiIiIiIsohDMITEREREREREREREeUQBuGJiIiIiIiIiIiIiHIIg/BERERERERERERERDmEQXgiIiIiIiIiIiIiohzCIDwRERERERERERERUQ5hEJ6IiIiIiIiIiIiIKIcwCE9ERERERERERERElEMYhCciIiIiIiIiIiIiyiEMwhMRERERERERERER5RAG4YmIiIiIiIiIiIiIcgiD8EREREREREREREREOYRBeCIiIiIiIiIiIiKiHGKQ1wUgykjZqSdzfB8Bi7vk+D6IiIiIiIiIiIjov4st4YmIiIiIiIiIiIiIcgiD8EREREREREREREREOYRBeCIiIiIiIiIiIiKiHMIgPBERERERERERERFRDmEQnoiIiIiIiIiIiIgohzAIT0RERERERERERESUQxiEJyIiIiIiIiIiIiLKIQzCExERERERERERERHlEAbhiYiIiIiIiIiIiIhyCIPwREREREREREREREQ5hEF4IiIiIiIiIiIiIqIcwiA8EREREREREREREVEOYRCeiIiIiIiIiIiIiCiHMAhPRERERERERERERJRDGIQnIiIiIiIiIiIiIsohDMITEREREREREREREeUQBuGJiIiIiIiIiIiIiHIIg/BERERERERERERERDmEQXgiIiIiIiIiIiIiohzCIDwRERERERERERERUQ5hEJ6IiIiIiIiIiIiIKIcwCE9ERERERERERERElEMYhCciIiIiIiIiIiIiyiEMwhMRERERERERERER5RAG4YmIiIiIiIiIiIiIcgiD8EREREREREREREREOYRBeCIiIiIiIiIiIiKiHMIgPBERERERERERERFRDjHI6wJ8q5ydneHh4aHx8n5+fjlYGiIiIiIiIiIiIiLKCwzC55BKlSohKSlJ7TL37t1DSkoKypQpk0ulIiIiIiIiIiIiIqLcxCB8Dpk1a5ba9/fs2YO7d+/C1NQUW7ZsyaVSEREREREREREREVFuYk74PPDkyRMsWbIEAPD777+jbNmyeVsgIiIiIiIiIiIiIsoRDMLnspSUFEyfPh3x8fHo3Lkz7O3t87pIRERERERERERERJRDGITPZYcOHcLDhw9RoEABzJgxI6+LQ0REREREREREREQ5iEH4XBQdHY1Vq1YBAIYPHw4rK6u8LRARERERERERERER5SgG4XPRwYMH8fHjR1hYWMDJySmvi0NEREREREREREREOYxB+FySnJyMXbt2AQCcnZ1RoECBPC4REREREREREREREeU0BuFzyYULF/DmzRuYmJigX79+eV0cIiIiIiIiIiIiIsoFDMLnkpMnTwIA2rZtC3Nz8zwuDRERERERERERERHlBgNdbCQiIgK+vr4IDAxEcHAwoqOjER8fj3z58qFAgQKwsbGBra0tqlSpAlNTU13s8quSkJCAy5cvAwC6du2ax6UhIiIiIiIiIiIiotyidRDe19cXZ86cwcWLF+Hv76/ROvr6+qhatSpatmyJ77//HqVLl9Z291+VGzduICYmBhYWFvjuu+/yujhERERERERERERElEuyFISXy+U4ceIEdu/eDV9fX8nrmkhKSoKvry98fX2xfv162NnZYeDAgWjbtm3WSv2V8fLyAgDUr18fhoaGeVwaIiIiIiIiIiIiIsotGgfhT506hbVr1yIgIACAcuC9QIECKFOmDMzMzGBmZgYTExPEx8cjNjYWwcHBePfuHT5//ixZz8vLC15eXihXrhzGjRuH9u3b6+aovjAPHjwAANSuXTuPS0JEREREREREREREuSnTILy/vz/mzp0LDw8PAP8PvleoUAHNmzdHgwYNUKlSJZQsWTLTnQUFBcHX1xe3bt3C1atX8ebNG7GPMWPGoG7dupg3bx4qVKiQnWP64jx69AgAULly5TwuCRERERERERERERHlJrVB+G3btmHVqlVITEyEXC6HtbU1HBwc0Lt3b5QqVSrLO7OxsYGNjQ06duwIIDWv/LFjx3D8+HFERETg7t27cHBwwIgRIzBixAjIZDLtjuoLEhcXh4iICABAwYIF87g0RERERERERERERJSbMgzCDxo0CDdv3oRcLkepUqUwcuRIdOvWDfr6+jrbeY0aNVCjRg38+uuvOHLkCLZu3YqgoCCsXbsWt2/fxs6dO7O1/djYWHTu3Bnv3r3DokWL0LNnzyytf+3aNRw6dAj37t3Dx48fkT9/fhQtWhTNmzdH7969Ua5cuUy3ERoaKqbNzMyyfAxERERERERERERE9PXKMAh/48YNFCxYECNHjoSjoyMMDLI0hmuW5M+fH46OjujTpw/++ecfrF+/XqS/yY4FCxbg3bt3WV4vJiYGkydPxrlz5ySvJyQkICIiAk+fPsWuXbswZswYDB06VO22SpQoAT8/vyyXgYiIiIiIiIiIiIi+fhlG1h0dHTF27NhcTaFiaGgIJycndOvWDWvWrMnWtrZs2QJXV9csr5eUlIRhw4ZJKgEqVaqEqlWrIi4uDrdu3UJERAQSExOxfPlyJCUlwcXFJVtlJSIiIiIiIiIiIqJvU4ZB+NmzZ+dmOSTMzc0xc+ZMrdaVy+VYt24d1q1bp9X6mzZtEgH4/PnzY+nSpejQoYN4Py4uDgsXLsSBAwcAAGvWrEGjRo1gZ2en1f6IiIiIiIiIiIiI6Null9cF0KXw8HAMGzZM6wB8aGgo/vrrLzE/b948SQAeAPLly4d58+ahe/fuAFKD/itXrtS+0ERERERERERERET0zfomgvByuRxHjx7F999/j8uXL4vX8+fPn6XtHD58GLGxsQBSU9B069Ytw2WnT58utu/p6Ylnz55pUXIiIiIiIiIiIiIi+pbpNAgfFBSECxcu4PDhw9i9e7d4PSkpCQEBAbrclRAfH4+ePXtiypQpCAkJAZDaWn3p0qWoWbNmlrZ1/vx5MW1vbw+ZTJbhshYWFmjRooWYP336dBZLTkRERERERERERETfumwH4ePi4rB9+3a0a9cO7dq1w8iRIzFjxgwsXLhQLPPmzRt07twZzs7O8PHxye4uJeLj4/Ho0SMxb2dnh6NHj4p0MVnZzoMHD8R8kyZNMl2nfv36YvrGjRtZ2h8RERERERERERERffsyHJhVEy9evMCoUaNEK3e5XC7eU2xFHhQUBLlcjjt37sDR0RFTp07Fzz//nJ1dKylVqhTGjRuHLl26qG3BnhF/f38kJSWJ+QoVKmS6juIyfn5+Wd4nEREREREREREREX3btA7CBwUFwdnZGWFhYSL4LpPJYGhoiISEBMmyb9++FdNJSUlYsGABLCws0LVrV213LxgZGWHVqlXo0KED9PX1td7OmzdvxLSFhQVMTU0zXado0aJiOiYmBqGhoShUqJDWZSAiIiIiIiIiIiKib4vW6WgmTJiA0NBQAEDZsmWxYsUKeHl5wcHBQWlZBwcHLF26FMWKFQOQ2mL+999/R2RkpLa7F/Lly4fOnTtnKwAPAB8/fhTThQsX1mid9AH3sLCwbJWBiIiIiIiIiIiIiL4tWgXhL168iHv37kEmk6FixYo4ePAg7O3tYWJionJ5AwMDfP/99zh8+DAqV64MAIiMjMTRo0e1LriuRUdHi+l8+fJptE6BAgUk81FRUTotExERERERERERERF93bQKwp85c0ZML1q0SKPULQB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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 20000\n", "hourly_consumption_kwh = np.random.pareto(4, N*365*24)\n", "\n", "fig, ax = plt.subplots()\n", "ax.hist(hourly_consumption_kwh, bins=50)\n", "ax.set_yscale(\"log\")\n", "plt.title(f\"Synthetic distribution of energy consumption data \\n One year of hourly readings for {N:,} homes\")\n", "plt.xlabel(\"Hourly Energy Consumption (kWh)\")\n", "plt.ylabel(\"Count (log scale)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "## Background Theory ##\n", "\n", "To compute a differentially private mean, noise is drawn from the Laplace distribution at $b=\\Delta/\\epsilon$ where $b$ is the scale of the Laplace distribution, $\\Delta$ is the sensitivity, and $\\epsilon$ is the privacy parameter.\n", "\n", "The unknown parameter in this case is the sensitivity $\\Delta$. For private means, the sensitivity is:\n", "\n", "$$\n", "\\Delta = \\frac{B - A}{N}\n", "$$\n", "\n", "Where $B$ is largest value in the dataset, $A$ is the smallest, and $N$ is the number of elements in the dataset. Intuitively, the sensitivity is the maximum amount that any single element in the dataset can affect the computed mean.\n", "\n", "For datasets where the range of data is known up front, the values of $A$ and $B$ are known exactly.\n", "\n", "However, for datasets where the range of data can vary considerably, the values of $A$ and $B$ must be computed with a private query to avoid leaking information about the largest and smallest values in the dataset.\n", "\n", "## Approach to Privately Finding Bounds ##\n", "\n", "First, we define a criteria for a good choice of upper bound. The eventual use for building science requires private means to be accurate within +/-0.1 kWh. Since the error term for the clamping procedure is difficult to derive exactly, we will target error from the clamping procedure as small enough to be neglible compared to the required accuracy. Therefore, we target +/-0.01 kWh.\n", "\n", "To find the upper bound for this level of accuracy, we simulate clamping random samples from our synthetic dataset. We find that a clamping cutoff that includes 99% of all consumption values reaches this target error:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T22:59:52.702Z", "iopub.status.busy": "2020-09-28T22:59:52.694Z", "iopub.status.idle": "2020-09-28T23:00:00.892Z", "shell.execute_reply": "2020-09-28T23:00:00.925Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The cutoff includes 99.05% percent of consumption readings\n" ] } ], "source": [ "def simulate_clamping_error(number_of_sites, cutoff):\n", " NS = number_of_sites \n", " HY = 8760 # hours per year\n", " trials = []\n", " for t in range(100):\n", " sample = np.random.choice(hourly_consumption_kwh, NS * HY)\n", " true_mean = np.mean(sample)\n", " clipped_mean = np.mean(np.clip(sample, 0, cutoff))\n", " trials.append(true_mean - clipped_mean)\n", "\n", " plt.hist(trials)\n", " plt.title(\"Error from clamping procedure\")\n", " plt.xlabel(\"Error (Average kWh)\")\n", " plt.ylabel(\"Count\")\n", " plt.show()\n", "\n", "\n", "cutoff = 2.2 \n", "simulate_clamping_error(number_of_sites=200, cutoff=cutoff)\n", "\n", "percent_included = np.sum(hourly_consumption_kwh <= cutoff) / len(hourly_consumption_kwh)\n", "print(f\"The cutoff includes {percent_included:.2%} percent of consumption readings\")" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "If we were able to query for the distribution of data exactly, we would ask for the 99th percentile directly." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T23:00:00.913Z", "iopub.status.busy": "2020-09-28T23:00:00.905Z", "iopub.status.idle": "2020-09-28T23:00:08.766Z", "shell.execute_reply": "2020-09-28T23:00:08.807Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The 99% cutoff is 2.2 kWh\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cutoff = np.quantile(hourly_consumption_kwh, 0.99)\n", "\n", "print(f\"The 99% cutoff is {cutoff:.1f} kWh\")\n", "\n", "plt.hist(hourly_consumption_kwh, bins=200)\n", "plt.axvline(cutoff, color=\"r\", linewidth=5)\n", "plt.title(\"Cutoff to include 99% of data points\")\n", "plt.ylabel(\"Count\")\n", "plt.show()\n", "\n", "fig, ax = plt.subplots()\n", "ax.hist(hourly_consumption_kwh, bins=50)\n", "ax.set_yscale(\"log\")\n", "plt.axvline(cutoff, color=\"r\", linewidth=5)\n", "plt.xlabel(\"Hourly Energy Consumption (kWh)\")\n", "plt.ylabel(\"Count (log scale)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "However, this query must be done privately to avoid leaking information. Fortunately, there is a mechanism that can be used to answer this question directly: `eeprivacy.private_quantile`." ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "## Private Quantiles ##\n", "\n", "Under the hood, `eeprivacy.PrivateQuantile` uses a \"private noisy max\" mechanism to score a set of possible outputs. In this case, the outputs are choices for quantiles.\n", "\n", "The following code finds the 99th percentile:\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T23:04:04.267Z", "iopub.status.busy": "2020-09-28T23:04:04.257Z", "iopub.status.idle": "2020-09-28T23:04:58.721Z", "shell.execute_reply": "2020-09-28T23:04:58.738Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Private 99th percentile is 2.24 kWh\n" ] } ], "source": [ "result = PrivateQuantile(\n", " options=np.linspace(0, 5, num=200),\n", " max_individual_contribution=8760\n", ").execute(\n", " values=hourly_consumption_kwh,\n", " quantile=0.99,\n", " epsilon=0.1,\n", ")\n", "\n", "print(f\"Private 99th percentile is {result:.2f} kWh\")" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "## Private Quantile Accuracy ##\n", "\n", "An appropriate choice of $\\epsilon$ is required for `private_quantile`. Too high, and too much privacy budget is spent. Too low, and a poor clipping bound risks introducing error to all further analyses.\n", "\n", "For this demonstration, we show that a choice of $\\epsilon$=0.1 provides a distribution of results that are within acceptable boundaries based on the earlier accuracy simulation." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T23:06:26.416Z", "iopub.status.busy": "2020-09-28T23:06:26.406Z", "iopub.status.idle": "2020-09-28T23:07:18.607Z", "shell.execute_reply": "2020-09-28T23:07:18.618Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Unroll the implementation of `private_quantile` for performance reasons:\n", "# computing `scores` is quite heavy and only needs to be done once.\n", "\n", "values = hourly_consumption_kwh\n", "options = np.linspace(0, 5, num=200)\n", "quantile = 0.99\n", "epsilon = 0.1\n", "sensitivity=8760\n", "\n", "N = len(values)\n", "\n", "def score(values, option):\n", " count = np.sum(values < option)\n", " return -np.abs(count - N * quantile)\n", "\n", "scores = [score(values, option) for option in options]\n", "\n", "trials = []\n", "\n", "for t in range(100):\n", " noisy_scores = laplace_mechanism(\n", " values=scores, epsilon=epsilon, sensitivity=sensitivity\n", " )\n", " max_idx = np.argmax(noisy_scores)\n", " result = options[max_idx]\n", " trials.append(result)\n", " \n", "plt.hist(trials)\n", "plt.title(f\"Distribution of private 99th percentile at ε={epsilon}\")\n", "plt.xlabel(\"99th percentile result\")\n", "plt.ylabel(\"Count\")\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "This choice of privacy parameter is not optimal; it could be further reduced and still meet accuracy needs. In the work that this demo was based on, there was enough privacy budget allocated that $\\epsilon$=0.1 did not hamper further analysis." ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "## Results ##\n", "\n", "In our example, the final computed clamping bound was 2.16 kWh. There was some error introduced in choosing the clamping boundaries with the private quantile mechanism.\n", "\n", "To get a feel for this error, we use our original accuracy simulation for the upper and lower bounds of results from the private quantile function, comparing it to an exact mean computation:\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2020-09-28T23:07:26.166Z", "iopub.status.busy": "2020-09-28T23:07:26.159Z", "iopub.status.idle": "2020-09-28T23:07:42.465Z", "shell.execute_reply": "2020-09-28T23:07:42.477Z" }, "jupyter": { "outputs_hidden": true, "source_hidden": false }, "nteract": { "transient": { "deleting": false } } }, "outputs": [ { "data": { "image/png": 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\n", 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vLV68WFu2bDHeK1mypBo2bKiuXbtaXbXJ6D4tWd41Hx4erqCgIOXLl88p/UnS448/rtatWxs1ZkeNGqUcOXLYPHa+evVqTZs2zVjv3bu3zf4t70oICwtLNTYp/u6GO3fuGOt8sTuXM86hzN6no/tLz3lr+aSLZH3eXrlyxeo9e+7oTFxOKyAgIE3HGGnDOHD+OLA0fvx4PfPMM8qRI4dd/SJzMA4ydxzY66effjKW/fz87PoZgvRjHDw44+Do0aOaPXu28bdX9uzZNWzYsDT3g7RhDGT+GDh58qRmzZolKT6/wHme9RgHmTMOAgMDdfv2bUnxN0WsW7dOCxYsSPJmN5PJpOeee05Dhw61qSwB52AcOH8cnD59WnFxcZJklew/fPiwfv75Z+3cuVPXr1+Xm5ubihcvrqeeekrdu3dP1w1Aj1TC/9atW8ayPQercePGqlKlip588knjta+++squu3XTu09JNoMjODjYeM3R/SX44IMPdOPGDe3evVt3795Vnz59VK5cOVWqVMmoP3vhwgVJ8Y+a9+7dO8lyDCVLljSWw8PD5e/vr/Lly6cYn7+/vzEBsmQ7OOBYzjqHMnOfju7P8rw9d+6cQkNDlTdv3hT7s6zJLFmft5bxeXp62vVDJkeOHPL29lZ4eLgRH5yHcWDbn6PHgSV7HlVE5mMc2PbnzHFgj4MHD1pNbtqqVSu7n5ZE+jAObPvLzHHwxRdf6NixY7p48aLOnDljvO7j46OpU6eqZs2advWD9GMM2PbnzDEQFRWloUOHKjo6Wm5ubvroo4/k7e1tV8xwHsaBbX/OGAeWd/ffvXtXH3/8cbJ9mc1m/fLLL9q1a5fmzp1L+Z9MwDiw7c/R4+Dy5cvGcoECBRQREaGpU6dq2bJlMpvNVtsdP35cx48f1w8//KAPPvggxcmHk/JIlfSxrIHq6elp1zY5c+a0Wrd8nCMr9umsz5ArVy59//33mjhxotH+1KlTWr16tdasWWMk+319fbV06dJkSxk9/vjjKlq0qLH+zTffpBrfokWLrNbv37+f6jZIP8aBbX916tQx+omNjdX333+fan+JZ1u3PG/TE1/iGKnZ7FyMA9v+HD0O8OBjHNj2l5XjICgoSO+++65x14+Xl5d69+6drr5gP8aBbX+ZOQ5+/PFHbd682SrZ7+XlpbFjx9o1yTUyjjFg258zx8Cnn35qlLB94403uKj1gGAc2PbnjHGQuGyhh4eHXnvtNa1atUr79+/Xvn37tGTJEnXo0MG44eHGjRvq3bs3lSAyAePAtj9HjwPLvt3d3fXOO+/oxx9/lNlslp+fn/773/+qQ4cOqlWrltzc3IzPNHToUKungO3xSCX8o6KijGV7ywq4u1s/BJFQvz6r9umszxAbG6sFCxZo+vTpKSYag4OD1bNnT82bN8/4gzSxV1991VhevXq1TULf0i+//KKVK1davWZZbwuOxziw7c/T01MdO3Y01ufOnWs1s3tic+fOtZnMxfK8TU98iWNM6zFG2jAObPtz9DjAg49xYNtfVo2Du3fvqnfv3lYl4YYOHaqCBQumuS+kDePAtr/MGgfR0dFWd+IliIiI0Lvvvqv27dtbXQiAczAGbPtz1hjYtWuXvvvuO0lShQoVNGDAALtihfMxDmz7c8Y4OHnypLHs6+urZcuWadSoUapcubJy5sypXLlyqXbt2poyZYpmzZplJDxv3rypDz/80K7PhPRjHNj25+hxkFDRQZI2bdqkrVu3ysPDQ++//762bt2qzz77TFOmTNHSpUv1yy+/qHLlypLin3iZMGGCzUWzlDxSCf+EiWklGV8cD9s+nfEZoqKi1KdPH33yyScKDg6Wu7u7unfvrlWrVunQoUPGVdYXXnhBJpNJ9+7d0/Tp063uQrPUpUsX46SUpA8//FADBw7U3r17de/ePUVGRurIkSN6//33NXToUJnNZqvaVdmzZ3fI50LSGAdJ69evn4oUKSIp/gt5wIABGjt2rA4fPqzIyEjdu3dPe/fu1YABA/Tpp5/K3d3dqq6y5XmbFccYacM4SJojxwEefIyDpGX2OAgNDdUbb7yhI0eOGK8999xz6tatm0M+D1LGOEhaZowDs9msxYsXa9++fTp06JBWr16t7t27G5/hxIkTeuWVV3Tp0iWHfCYkjTGQNEePgbCwMI0YMUJms1keHh6aNm0avzc9QBgHSXP0OBg4cKBmzZqloUOHas6cOVZ5o8T++9//Wj3p+Mcff+js2bMO+VxIGuMgaY4cB5YJ/+joaJlMJs2YMUOvvPKKTbxlypTRDz/8YJQVio6O1syZM+2O+5Gq4W85U7K9d18lbpfWH8qO3qczPsPnn3+uv//+23hv3rx5atCggVWb2rVrq3bt2nrqqaf03nvvKS4uTr/++quqVKmiN99806ptjhw59OWXX6pnz57GF/LGjRu1cePGJOMbMGCA7ty5Y5QNSksJFKQd48C2Pym+btucOXP05ptv6saNG4qLi9OyZcu0bNkym77c3d01YcIE/fnnn8akMJbnbXriS9yWPwCci3Fg25/k2HGABx/jwLY/KXPHQWBgoN58802jvIMkNWzYUFOmTLG7D2QM48C2PylzxkH27NlVq1YtY71ixYoaM2aMGjdurH79+ikmJkbBwcH64IMPtGDBArs+F9KOMWDbn+T4MTBhwgRdvXpVUnzSM7V57pC5GAe2/UmOHwdly5ZV2bJl7YpNknr27Kmvv/7auOP6r7/+StOcmkgbxoFtf5Jjx0Hivp955hk988wzycaWK1cuDR06VP3795ckbdu2Tbdv37ZrfoJH6g5/y8lwLK+qpCRxeZvEtZ0ye5+O7i8sLEwLFy401gcPHmyT7LfUunVrq6usc+fOVUREhE27woULa9myZerSpYvN4zEJSpUqpfnz56t///5Ws12nZYIPpB3jwLa/BOXLl9eKFSvUunXrZCdJrFy5spYuXaoXX3xRd+7cMV63PG8t+7Y3vsQxpvUYI20YB7b9JXDUOMCDj3Fg21+CzBgHJ06cUKdOnayS/Y0aNdJXX33FRd9MxDiw7S9BVv08eOqpp9SrVy9jffv27bp48WK6+0PKGAO2/SVw1Bj47bfftHbtWklSrVq1bG6YQ9ZjHNj2lyAr/zbIkyePqlSpYqxblgSC4zEObPtL4KhxkHiS9nbt2qUa39NPP21cNDCbzdqzZ0+q20iP2B3+vr6+xnJwcLBd2wQFBVmt+/n5Zek+Hd3frl27jIR9jhw51KVLl1T7e+ONN/T1118rJiZGd+7c0e7du/XUU0/ZtMudO7fGjx+v/v376++//9b58+cVGRmpQoUKqXr16qpTp47RNuHKlyTq1ToZ48C2P0uFChXSjBkzNGTIEP3999+6fPmyYmNjVbhwYdWr93/t3XdUVNf6N/DvIKOiiFiwoQaDgmDDiC2WiHqV2AJiiUaN0Wi4NxpL4NpjEnuLNxHUaCyRqMTeiRFFY4sFFBW7WIBYkKJSdAB5/5h39u8cpusMWL6ftbLWOcw5++yBeQI+e+9nN4Onp6e4VlprWfq5lfYvIyMDKpXKaPLm2bNnsl9I5n6PyTyMA+32pCwRB/TqYxxotydlzTiIiorC2LFjZf/f79y5M+bPn89kfyFjHGi3J1VUvw/69++PJUuWiPPo6GixpJ0sizGg3Z7Uy8bAgwcPMHXqVADqRM+cOXNkJSfo1cA40G5Pqij/bVClShW9/SXLYhxotydliTgoU6aMrM06deoY7Z9SqYSLi4sY8DJ1A+u3KuEvXfqTkpKCnJwcKJVKg/fcu3dPHDs4OMDBwaFIn2np9qSzZVxdXWXLX/RxcHDAu+++K2akxcfH60z4a1SsWBH+/v4G25SO1HKJlnUxDkx7D87Ozvj444/1vv748WPZ/8SlfXJxcYGNjY3Y4+L+/fuoUaOGwefdvXtX6/lkPYwD68cBvfoYB0UTB7/99htmzJgh2wdp4MCBmDhxIpNARYBx8Gr+PqhUqRIcHR2Rnp4OQL1hI1kHY8C6MXDkyBHxOc7KyjJYuqEgadmfESNGcJNfK2IcvJq/CwD1jGYNY++HXg7jwPpxUHDygqn7DEhztaauXHir/lVRs2ZNMWsqLy8P8fHxRu+5fv26ODZl5MXaz7R0e3l5eeLYnH9kSpehmLsLd0FxcXFiuUvx4sXh5ub2Uu2RYYyDF3sPBf3999/i2NnZWbZMq2TJkrIE/7Vr18zqX5UqVcz+RUnmYRxYPw7o1cc4KPw4+OmnnzBt2jSR7FcoFBg3bhwmT57MZH8RYRxYPw4ePnyIbdu2ISQkxKz9KaRL5kuUKPHSfSTdGAP8m4gYB7raexGG4uD+/fvYtm0bVqxYgXnz5plcX106m5mria2LcWD9OHBzc5P9zW/qbH1piaCyZcuadM9b9S+LYsWKoVGjRuI8Ojra6D2nT58Wx82aNSvyZ1q6PelGD5rlKKaQjlYVXO4SEhKCUaNGYcCAAbh06ZLRtvbt2yeOmzdvzj/orYxxoPs9TJ8+HSNHjkS/fv2QkpJitD3p57ZNmzZarzdu3Nii/SPLYhwUThzQq41xULhx8OOPPyI0NFScFy9eHP/73/8wZMgQo88g62EcWD8O7ty5g3HjxmHRokVYvXq11qpGXVJSUsSsaIArH62JMWDdGKhVqxb69u1r0n/dunWTtSl9TVrHnCyPcWD93wV3797FuHHjMHfuXPzyyy+4ePGi0faysrJk10n/jU2WxziwfhyULFkSdevWFefSwQF9MjMzcevWLXFu6qDEW5XwB4APP/xQHO/cudPgtWlpafjrr7/EeceOHV+JZ1qyvSZNmojjR48e4fDhwwbbA9TBIF1WK20DAC5evIg//vgDp06dQlRUlMG2srKyEB4eLs5N2bCCXh7jQLu9U6dO4c8//0RMTAyOHDlisL27d+8iIiJCnOv63Er7FxERYXAGg0qlwp49ewz2jyyPcWD9OKBXH+OgcOJg06ZNWLx4sTi3t7fHypUr4evra7B9KhyMA+vGgYeHh2x18NatWw22p7lGU8ZBqVSiZcuWRu+hF8cYsF4MNG7cGN9//71J/40ZM0bWrvQ1Hx8fg32gl8c4sO7vgrp168p+FxjrHwBs3LgRz549A6Be6WWolDRZBuPA+v82kA7ubtu2DSqVymCbu3fvFpOzy5QpAy8vL4PXa7x1CX9fX19R+ygmJgbbtm3Te+2MGTPw9OlTAEDDhg1feFTd0s+0ZHsuLi6yUdKZM2ciIyNDb3tZWVmYNm2aOG/SpAlq1qwpu6Zdu3biODw83GB9qe+//15spFGjRg1ZYJL1MA6025N+bn/99VdZbWWpvLw8TJgwQZSy8vb21hr0AoBWrVqJ1S9JSUlYunSp3v6FhoaKpVyVK1dG+/bt9V5LlsM4sH4c0KuPcWD9OLhx4wamT58uzu3t7bF69Wo0bdpUbz+pcDEOrBsHdnZ2ssGtlStXGpzlf+3aNdkAmZ+fH+zt7fVeTy+PMcC/iYhxYO04KFmyJLp06SLOw8PDxb6Quty4cQP/+9//xHmvXr1YKqsQMA6s//ugR48eYvArISEBCxcu1Nu/Bw8eaMWBqXtZvHUJ/woVKiAwMFCcT548GRs3bpRtBPL06VN88803YiRIoVAgKChIZ3sDBw6Eu7s73N3d9SbpLP1MS7c3fvx42Nqq92++ffs2+vbti9jYWK3rrl69igEDBogNdpVKJcaPH691XdeuXUWi8/79+/jyyy9lm2AA6l2wx44dK2b4KBQKfPvtt9yEpZAwDrT17dsXJUuWBKDeVyI4OFi2lBxQJ+6HDh2K48ePA1DPMpg6darO9pRKJcaNGyfOQ0JCsGTJElnZrNzcXISEhMgGA8aOHcs4KCSMA22WjgN69TEOtFk6DmbMmIHs7GxxvmDBAjRo0EDntVQ0GAfaLB0Ho0aNQunSpQEAT548weDBgxEXF6d1XWRkJAYMGIDMzEwA6tKho0eP1tkmWQ5jQBv/Jnr7MA60WToOvvrqK5HoVKlUGDJkiLhPav/+/fjkk0/E5NFq1aph7NixOtsky2IcaLN0HDg5Ock+zytXrsTUqVPx6NEj2XWXLl3CwIEDRRmhatWqYcSIETrb1EWRL33HbwmVSoXBgwfLajm98847aNiwIVQqFU6cOCH74QUGBmotr9MYOHAgTp48CUBdW/LAgQNWf6Y12tu0aROmTJkiG6mqU6cO6tSpg+LFi+PGjRu4cOGCCBAbGxvMmjULfn5+Otvbv38/RowYIdqzs7NDo0aNULVqVTx48ACnTp2SLVuZMGECBg8erLd/ZHmMA21r167F999/L84dHBzQsGFDVKxYEf/88w+io6NFwt7W1hbz5883uipl9OjRsiVdlStXhre3NwD10rAHDx6I17p164YFCxYYbI8si3GgzRpxoM/48ePFwO+IESMwcuTIF2qHXg7jQJul4uD8+fPo1auXOC9fvjz+9a9/6X2uLp999hlq1apl1j1kPsaBNkv/Pvjrr7/wn//8R8x8UygUaNiwIVxdXaFSqRAbG4uEhARxvaOjI1auXIl69erpbZMshzGgrTD/JgKAxMREdOjQQZxfuXLlhduiF8M40GbpODh06BD+85//yEre1q1bF3Xr1kVubi7Onz+P27dvi9cqVKiAsLAwuLq66m2TLItxoM3ScZCfn48pU6Zg48aN4mulSpVCkyZN4OTkhFu3buHs2bOynOqyZcvM2ifhrUz4A+pND4KDg7F//3691xQrVgz//ve/DSYgTP3wWvKZ1mrv0KFDmDRpkqw+vy6VK1fGrFmz0KpVK4PXRUREYNKkSWKGji7lypXDN998I1vaRYWHcaBtzZo1mDt3rvjHqC7Ozs6YMWOGSfVkc3Nz8d1332mNKBfUt29ffPPNN2K1DRUexoE2S8eBPkz4vzoYB9osEQdz5szBypUrjT7LWD+aN2/+Um2QaRgH2iz9+yA6OhrBwcFISkoyeF3jxo0xb9481KhRw2ibZDmMAW2F9TcRwIT/q4JxoM3ScXDq1CkEBwcb3cTd29sbM2bMgIuLi9E2ybIYB9qs8ftg2bJlWLx4sWw1cEHVqlVDaGgoPD09TWpT461N+GscPnwY27dvR0xMDB4+fAgbGxtUrVoVzZs3R//+/eHm5mbwfnM+vJZ6pjXbe/bsGbZv346DBw/i4sWLor5++fLl4enpiXbt2uGjjz5C8eLFTWovOTkZ69evx6FDh3D79m1kZ2ejTJkycHd3h4+PD3r27AkHBwez3i9ZHuNALiEhAWvXrsXRo0eRmJiInJwcODo6wsPDA506dUL37t3Fki5TnT17Fps3b8bJkyfx4MED5OXloVKlSvD29kbfvn1le2lQ0WAcyFkjDgpiwv/VwziQe9k4GD58OA4dOmRW/wtiwr/wMQ7kLP37QKVSYceOHYiMjERcXBzS0tJQvHhxODk54b333kOXLl3Qpk0bs94vWRZjQK4w/iYCmPB/1TAO5Kz1u+DAgQOIi4tDamoqlEolnJyc0KhRI3z44Ydo164dFAqFWe+ZLItxIGeN3wd3797Fli1bcOjQISQmJuLRo0ewt7eHu7s7OnXqhICAALEngTne+oQ/EREREREREREREdGb4K3btJeIiIiIiIiIiIiI6E3EhD8RERERERERERER0RuACX8iIiIiIiIiIiIiojcAE/5ERERERERERERERG8AJvyJiIiIiIiIiIiIiN4ATPgTEREREREREREREb0BmPAnIiIiIiIiIiIiInoDMOFPRERERERERERERPQGYMKfiIiIiIiIiIiIiOgNwIQ/EREREREREREREdEbwLaoO0BEREREpktMTESHDh0s0taIESMwcuRIi7T1Nnj69CkCAgJw/fp1fP311xg+fLhJ9+3atQtff/21OG/Tpg1++eUXa3WTXkPu7u7ieP/+/ahevbpZ9/v7++PixYsAgE6dOmHRokUm3bdo0SKEhISI8ypVquDQoUMm3btjxw4EBwcDAGxsbHDs2DGUK1cOwMu/H6mMjAz4+voiOTkZs2fPhr+//wu3RURERPQ24Ax/IiIiIiITzJ49G9evX4eLiwsGDx5s8n1btmyRnR89ehQJCQkW7h29zVq0aCGOz5w5Y/J9hw8flp3fu3cP165dM+ne06dPi2NPT0+R7Lc0e3t7jB07FgAwbdo0xg4RERGREZzhT0RERPQa8/HxQaVKlV7o3vr161u4N2+uY8eOYf369QCA4OBgFC9e3KT7/vnnHxw/fhwAoFQqkZOTg+fPn2PDhg2yWf9EL6Nly5ZYuXIlACA5ORkJCQmoUaOGwXvS09Nx/vx5ra8fPnwYderUMfrMU6dOiePWrVub2WPz+Pn54bfffkNcXBwmTJiAsLAwKBQKqz6TiIiI6HXFhD8RERHRa+yzzz5D8+bNi7obbzSVSoXvvvsOANC0aVN07NjR5Hu3bt2K58+fAwD69u2L3377DQCwefNmfPXVV1AqlZbvML11mjZtKgaUACA6Otpowv/YsWPis+nm5oarV68CUCf8hwwZYvDe1NRUxMfHi/P333//ZbpvlI2NDYKDgzF48GCcOnUKW7ZsQUBAgFWfSURERPS6YkkfIiIiIiIDVq9ejVu3bgEARo8ebfJ9+fn52Lp1qzjv06cP3n33XQBASkoK9u3bZ8lu0lvMzs4OXl5e4jwmJsboPdJyPoGBgShWrBgAdame7Oxsg/dKZ/eXKlUKjRs3NrPH5mvZsqUY3Jw3bx4yMjKs/kwiIiKi1xET/kREREREejx58kRssNugQQN4e3ubfO/JkydFvXEnJye4ubmhS5cu4nVNiSAiSzC3jv+RI0cAqEtNtWvXDg0bNgSgXtFy4sQJg/dKE/5NmzY1ucTVyxo6dCgAIC0tDb/++muhPJOIiIjodcOEPxERERGRHmvWrMGjR48AqGfom0O6WW+HDh2gUCjQrVs38bWTJ0/KyqIQvQxpWZ1r167h8ePHeq+9fPkyHjx4AABo1KgRSpcuLavDrxkM0Cc6Oloct2rV6kW7bLY2bdqgatWqAIBVq1Zxlj8RERGRDqzhT0RERETC+PHjRRmabdu2wcXFBaGhodixYwfS09NRsWJFeHl5YdiwYfDw8DD7eqnc3Fz88ccfiIyMxLlz55CamgoAqFChAho0aIAOHTqgS5cuotSILosWLUJISAgAIDQ0FD4+PlixYgU2bNiA+/fvo3z58qhXrx4GDRokmwFtitzcXISHhwMASpYsia5du5p8b0ZGBvbu3SvOO3fuDACoVasWGjVqhNjYWADA77//jgkTJuhsIzs7G61atUJmZiYAYMGCBbIBA32WLl2KhQsXAgDee+89vSsJ7ty5g82bN+Po0aNISkrCkydP4ODggHfeeQetW7dGnz594OTkpPc5iYmJ6NChAwD1gMbixYtx8uRJLFq0COfPn0eJEiVQs2ZNtG/fHv/+979l9+bl5eHPP//EsWPHcPbsWaSkpODx48dQKpUoW7YsateujZYtWyIgIACOjo5G3/Pz588RERGBnTt34sKFC0hPT0eZMmVQu3ZtdO3aFQEBAVAqlfD19cXNmzcBAPv370f16tX1tpmcnIxNmzbh8OHDuHPnDtLT02Fvbw9nZ2e8//776N27N2rWrGm0b5by+PFjfPrpp7h48SIAdSmdZcuWoWnTpgCAhg0bonTp0sjMzER+fj7OnDmDDz74QGdb0oS+JmH//vvvY9GiRQDk5X4KysjIwOXLl7XuN+bAgQPYvn07YmNjkZKSgjJlyqBatWr417/+hYCAAFSsWNFoGzY2NvD398fixYvx5MkTbN++HZ988olJzyciIiJ6WzDhT0REREQ65ebmIjAwEH///bf4WlJSEpKSkrQSuOZef+rUKUyYMEGUvJFKTExEYmIiIiIiEBISgrlz56JRo0Ym9XnixInYtm2bOL937x7u3btn9ux8QJ2g1MyCbt68OUqXLm3yvREREaIOeuXKlWWDDX5+fiLhv23bNowdOxYlSpTQasPOzg6+vr7YvHkzAGDXrl0mJfx37twpjnv27Kn1el5eHubPn4+wsDCxyatGSkoKUlJSEBMTg+XLl2PUqFH47LPPTHjH6iTyF198gdzcXADqAYv09HQxI1vj+PHjmDJlis6ffU5ODrKysnD37l0cPnwYoaGhmDlzJnx9ffU+NyEhAaNGjUJcXJzs66mpqTh58iROnjyJdevWITQ01KT3AQArVqxASEgIsrKyZF9PS0tDWloaLly4gFWrVmHQoEH4+uuvDQ5KWUJGRgaGDh0qS/YvX75cVmLK1tYWzZo1Q1RUFAB1HX99CX9pQl8zs79Ro0ZwcHDA48ePcevWLSQkJOjc+Dc6Olps9lu5cmXUrl3bYN8fP36MIUOG4OjRo7Kvaz5r58+fx6pVqzB//nzZKgN9fHx8sHjxYgDAunXrmPAnIiIiKoAlfYiIiIhIp6VLl8qS9xp169ZFnTp1Xvj6yMhIfPrpp7KEr5ubG7p164bu3bvDzc1NfP3WrVsYMGAA9u/fb7S/W7dulSX7NcqVK2dSIrGgiIgIcdy2bVuz7tUk6QHgo48+go3N//3Z3a1bN1HzPD09XfacgqQJ+yNHjiAtLc3gc+Pi4nD9+nUA6lUJH374oez1nJwcBAYGYuXKlSLZX7FiRTHLul27drC3twegTtjPnj0b3333ndH3m5aWhuDgYJHsl+rRo4c4PnToEIYNGyZ+9kqlEt7e3vDz80OvXr3g4+Mjm+mdmZmJsWPHaiXzNf755x/0799f9nqtWrXQvXt3dO3aFdWqVQMAXLlyBQMHDjRY5kZj8uTJmDt3rkj2ly1bFj4+PggICEDHjh1Rvnx5AOrv5YoVK/Dll18iLy/PaLsvKisrC8OGDcO5c+cAAKVLl8aKFSt07ichHVjSt3FvVlaWKMnj6OiI+vXrAwCKFSsmu/+vv/7Seb+0fr8ps/u/+OILkeyvXr06OnfuDD8/P9StW1dck5aWhpEjR+ocBCqoQYMG4mdw/fp18XknIiIiIjXO8CciIiIinSIjI2FjY4MRI0agT58+KFGiBKKjo3UmdU29/vLlyxgzZoxIkNaqVQuzZs1C48aNZW1FR0dj/PjxuHPnDlQqFYKCgrBp0ya4uroa7C8ADBw4EEOGDIGDgwMuXLiApKQk2Nqa92dvbm4uDh06JM7N2aw3Pj5etmmqn5+f7HUHBwd07NgRe/bsAQCEh4drXSN9bs2aNXHnzh3k5OTgjz/+QL9+/fQ+e8eOHeK4Y8eOInmvMX/+fJHILVWqFCZOnIiePXvKZqg/ffoUy5cvR2hoKPLz87Fu3Tp4eHgYXCWhSS57enpi0qRJqFevHu7du4fdu3eLwZLs7GxMnTpVDDQ0a9YMCxYsQKVKlWRt5eXlYdOmTfj++++Rm5uLvLw8MQO8oP/+979iFYa9vT1mzZqFTp06idfz8/NFW3fv3tXbf401a9Zg48aNANSDEV999RU+/fRT2QqMvLw8hIeHY/bs2VCpVIiKisJPP/2EMWPGGG3fXE+fPkVgYKD4/trb22PFihXw8vLSeX3Lli3F8fnz55Gbm6v12T9x4oT4Gbz//vuywahWrVrhzz//BKBeBaBr9vzp06dl1xvz4MEDODg4YNq0aejcuTMUCoV4LTIyEmPGjIFKpUJWVhYWL16MWbNmGWxPoVCgSZMm2LdvHwD1ShxjqwyIiIiI3iZM+BMRERG9xlatWoXdu3ebfV/Lli21Zn/rMmrUKAQGBopzHx+fl7r+hx9+gEqlAgA4Oztj/fr1KFeunFY7TZo0QXh4OHr27Il79+4hKysL8+bNw9KlSw0+v0+fPpg8ebI4N7duv8aVK1dE7XylUol3333X5Hulm/U2atRI5yCFv7+/SPifOXMGly9fls14lvLz88NPP/0EQF3WR1/C//nz57LPQsFBhPj4ePz6668A1LO5C5aE0ShZsiRGjhyJihUr4ttvvwUALFy4ED169EDJkiX1vGv1SoHVq1ejbNmyANSDOSNGjBCvR0ZGiqR72bJlsWjRIp31+YsVK4a+ffvi2rVrCAsLA6De4LiggwcPitnmxYoVw88//6z1fhQKBXr37o1y5crhyy+/1Nt3AHj06JHY+wAAZs2ahe7du+vs3yeffILq1atj+PDhANQlgPr374/KlSsbfIY5VCoVRowYgRMnTgAAypQpg5UrV6Jhw4Z673F3d0fFihXx8OFDZGdn4+LFi1rX66rfr+v8xIkTUKlUYjUKoB6AuHDhAgD191a6UbA+tra2WL16NerVq6f1WseOHfH555+LEj3Hjh0z2h6gXhGkSfjrW8lARERE9LZiSR8iIiKi11hUVBR+//13s/8zJUmmVCoxcOBAk/ti7PqEhATZrPkpU6boTPZrVKhQAVOmTBHnUVFRYsNVfYYOHWpyfw05f/68OK5Vq5Ys6WlIXl4etm/fLs71zdxv1aqVbGa7ZnNgXfz8/MSs6OjoaPzzzz86rzt+/DiSk5MBAJUqVdJKxoaFhSE/Px8A0L17d6OrFj7++GMxWJGamioGKPTp1auXSPbrkp2djaZNm6Jq1aombcYrHaxJT0/Xel26msHf39/g++nYsaPYOFmfjRs3ijI+TZs21Znsl/rggw/Qpk0bAOryPhs2bDB4vTlycnIwatQoUWvfwcEBq1atMpjs1zBW1kdX/X6NGjVq4J133gGgLv1T8P6zZ8+K1QEeHh6itI4hPXr00Jns15AOPN67dw/Pnj0z2qa7u7s41gxAEBEREZEaE/5EREREpFO9evXM2qjW2PXSTTsrVaqkd0NRqfbt28sS44ZmADs5OcHFxcW0zhpx+/ZtcaxJgJri8OHDosRM8eLF9W6yW6xYMdlgwM6dO7U2iNVwdnZGs2bNAKhL1OzatUvnddIEeI8ePbQ2kpUmek3Zk0ChUMh+RpqZ5voYG0Do06cPfvvtNxw8eBDjxo0z+vwyZcqI44KbC+fk5MhqzPv7+xttr3fv3gZfN/f7A8hXsBj7/pjq+fPn+Prrr3HgwAEA6tUQq1evRoMGDUy6X1rWp2DCPiEhQXy2a9eujSpVqmjdL53lXzDepOV8TJndD0AMiuhTcGPgR48eGW1TGpPJyclig2wiIiIiYkkfIiIiotfamjVr0Lx5c6u0bW5dbGPXX7x4URx7eXnJaofrY2Njg8aNG2Pv3r1abZj7fHNI6707ODiYfJ+0nE+HDh0M3uvv749ly5YBADIyMrBr1y69dfJ79uwpEsq7du0SpWQ0nj59KkqcaK6XSk1NlW2IunPnTpMS1NeuXRPHV65cMXitro2czZGeno74+HhcvXoVsbGxsgGi58+fy669efMmnjx5AkA9eKLZeNYQLy8vKBQKscqhIM2muIA6+Z+YmGi0TelqC2PfH1NNmTJFtvl1+fLlzfpsG0r4SwdJ9G1k3apVK6xbtw6A9iCGdMNeUzfCrl69usHX7ezsZOcFB3d0KRhXd+/eNavsFhEREdGbjAl/IiIiItLJUHmWF7k+LS1NHFetWtXkdqWzkFNTU1/4+ebQ1O8H5DPNDUlNTRWzsgF1WSBDG+wC6vrmmk2Nw8PD9Sb8O3XqhO+++w5ZWVm4cuUKrl27Jkuw79+/X/S5QYMGWvsGPHz4UHYeFRVl0nuS0lVWR8qc7/+NGzcQGRmJuLg43LlzBwkJCcjIyDD5fk3pIkD98zG0t4D0Ont7ezFQIJWZmSlbYXHy5Emd+wYY8uTJE+Tl5WmtrDCXNNkPqAc3Fi1ahKCgIJPud3Z2Fhs9JycnIyEhQcyil65i0LfhbosWLcTn8sKFC8jMzETp0qWRk5OD2NhYAOp9Hpo0aWJSf8yNS30DMlIFY1Iar0RERERvO5b0ISIiIiKdCs68fdnrpQndUqVKvVC7hkp3mNtfQzQbC5vT7s6dO2WzkxMTExETE2PwP02yHwDi4uJks8ylSpUqBV9fX9mzpArWsy9IV5LbXMaSqqZ8n+7fv4/AwEB06dIFP/zwA/bu3YtLly7JPhs2NjaoV6+e3nJIgHzgx5Rkv4a+z505gw365Ofn6y3LZK6yZcvK9hBYuXKlbF8JY3TN8s/JyREz9kuUKCHKRBVkb2+PRo0aAQByc3MRHR0NQP351MSft7e3yftavOwAiC4Ff46m1P0nIiIieltwhj8RERERFQppks6cxKg00WzJpL4h0iSyNPlviLScz4sKDw/XuzGrv7+/eMauXbswZswYKBQKpKam4siRIwDUGyd37dpV696C37c9e/ZorQKwtocPH6Jv376yckmOjo6oX78+XF1dUatWLdSpUwd169aFvb09jh8/rne/AunPx5z67fquLThosHz5cpPr+Fuao6MjVq1ahdq1ayMuLg7x8fHIy8vDxIkTsWXLFiiVSqNttGzZEr///jsAIDY2Fh999BFiYmJE3DVp0sTgQEnr1q1Fov/EiRNo27btC5XzsZaCCf7C+v8CERER0euACX8iIiIiKhTly5cXx9KkrzHSOulOTk4W7ZM+9vb24tiUwYm4uDhcvnxZnK9fvx7vvfeeSc8KCgoSM/b37NmDCRMm6Cwj1LRpU9SoUQMJCQlISkpCbGwsvLy8EBERIVYK+Pj4wNHRUevecuXKyc5TUlIKPeE/ffp08XMvVaoUpk+fDl9fX70zwB8/fqy3Lenn4PHjx6LsjCFZWVl6Z/I7ODjIyiulpKQYbMuaQkND4enpCQCYNm0aBgwYgPz8fFy9ehVLlizBV199ZbSNFi1aiP0KLly4AEBej99Ywr5169b48ccfAfzf3gaaAQDA9A17raXgwI05m4sTERERvelY0oeIiIiICkW9evXE8ZkzZ7Q2YtXl+fPnom44gELbmFO6x8D9+/eNXi+d3V+9enWTk/0AEBAQII6zs7Oxfft2ndcpFAr4+fmJc80mvbt37xZfk74uVbVqVVnS/+zZsyb1LSYmBnv27MG5c+cM7p9gTHp6umxT4fHjx6Nr164Gy71INxkG5LXdPTw8xEz3/Px8g5s5a1y4cEHvZ06hUMDd3V2cm/r9uXLlCnbu3ImYmBiTPiemkO5Z4e3tLdvXYdmyZbKBJX3KlSsHDw8PAMClS5eQk5Mjm6Gvr36/Rv369cXA0dWrV5Gfn48zZ84AUA+2SL9XReHevXvi2MbGxqw9QYiIiIjedEz4ExEREVGhaNGihThOTk7GwYMHjd5z4MAB2YazhTWzuFatWuJYusJAF5VKJSs9Y6j2vC4tWrRAtWrVxLmmFIsufn5+UCgUANQb9d6/f1/UaK9QoQI++OADvfdK67pv3brV6IBLXl4eJk2ahDFjxqB3796YPn26Se9Hlzt37sj2KzC24Wt+fj727t2r1R+NEiVKyD5PBfc00EXfQIqG9LMVERFh0sqO2bNnIygoCP369TNp5v2LCAoKEisacnJyMHHiRNn3Uh/N90elUuHixYtipr6TkxPq1q1r8F4bGxtxf3p6Oo4fPy42bS7q2f2APCarVq2KEiVKFGFviIiIiF4tTPgTERERUaFwcXGRlRKZPn060tLS9F6flpaGmTNnivPGjRvDzc3Nqn3UkK5GuHHjhsE6/pGRkSIZCgA9evQw61kFZ+5fvXoVp0+f1nlt9erV0bRpUwDAzZs3sXz5cjHzvVu3brC11V+x85NPPhHH8fHxCA0NNdivVatWIT4+Xpz37t3b6HvRp+AGr8Zmqf/8889aGxhLN0QGgP79+4vjzZs3G9zUNiYmBlu3bjX4zI8//lh8/x49eoRp06YZvD4iIgLHjh0T57169TJ4/YtycHDA5MmTxXlcXBx++eUXo/dJE/Ph4eF4+vQpAOOz+zWksbphwwZxbOr91iT9/EhjlYiIiIiY8CciIiKiQhQUFCRm4yYlJaF///46y6fExsaif//+SEpKAqDelPNlZpiby93dXZQ0ycnJwdWrV/VeKy3n4+np+UK18f39/cXMfUCdoDV0rca6det0fl0Xb29v+Pr6ivOQkBBMnz4dT548kV2XnZ2N0NBQLFiwQHytbdu2shUC5nJ1dUXZsmXF+Zw5c3Qm/ZOSkjB+/HgsXLhQ67WCM+7bt28vktq5ubn4/PPPERUVpXXfvn37MHz4cNkKAV2qV6+OTz/9VJxv2bIFY8aMQXJysuy6nJwcrF+/HuPGjRNfc3NzM/r9fxm+vr5o3769OA8NDcWNGzcM3uPt7S3KHklXoJi64a40sR8ZGQlAPTj1Kszw1+xLAMhXDhERERERN+0lIiIieq2tWrVKVsPdXGPGjNHa0NWaPDw8MGPGDIwfPx65ubmIj49H37594e7uDjc3NygUCly9elWWDFYqlZg5cyZq165daP1UKBRo3bq1SJQeP34c9evX17ru/v37OHr0qDjv3r37Cz2vZs2a8Pb2FnXW9+7di0mTJun82XTu3BnTpk1DVlaWSGK7u7uLmu2GzJgxAwkJCYiLiwMAhIWFYdOmTWjSpAkqVaqE5ORknD9/XrZiwcXFBXPmzHmh96WhVCrxxRdfYO7cuQCABw8ewM/PD15eXqhevTpyc3ORmJiICxcuiBULpUqVgkqlkm2kW6FCBa33069fP9y7dw/p6ekIDAzEu+++K2Z9nz9/Hrdu3QIAVKxYUVYeStdqiLFjx+L69es4dOgQAPUmyvv27cN7770HZ2dnpKWl4eLFi7J6/RUqVMBPP/1kcHWFJUydOhUnTpxAZmYmVCoVJkyYgPDwcNjY6J7DZWdnBy8vL5w6dUqsUFEoFCbP0K9WrRpq1aqFmzdvitUVbm5uhbZxtj65ubmyFTBt27Ytwt4QERERvXqY8CciIiJ6jema0WyO4cOHF2rCH1AnxZ2cnDBx4kQxg//KlSu4cuWK1rUuLi5YuHAhPD09C7WPgLo0jybhf/jwYQwbNkzrGmktfBsbG3Tt2vWFn+fv7y8S/iqVClu2bMHQoUO1ritdujQ6d+4sK1Fj6uxye3t7rF27FtOmTRN9z87OxpEjR3Re/8EHH2D27NkoX778C7wjuSFDhuDu3bsICwsDALERrGYzWKkGDRpgzpw5GD16tFhdERsbq1XSqVq1avj1118xevRoXLp0CYC6XJG0FBEAeHl5ITg4WFbWqGCZIUA9CLBkyRIsXLgQq1evRk5ODnJycnDixAmd78nLywvz5s1DzZo1zfhOvJgqVapg7NixotRQbGwsVq9ejSFDhui9p2XLlrLNej09Pc36WbZu3Ro3b94U569COZ8zZ84gIyMDgLrMV40aNYq4R0RERESvFpb0ISIiIqJC16JFC+zduxezZ89G586d4ezsDDs7OyiVSjg7O6Nz58744YcfsHv37iJJ9gPqZGflypUBAKdPn5bNDteQJt2bNWsmrn8Rvr6+KFWqlDjfsGGDmO1ekDTBb2tra9bKAjs7O8ycORO7du3CsGHD0LBhQ5QvXx62trYoVaoUateujd69eyMsLAzLli2zSLIfUM8unzx5MtauXYuPPvoINWvWRMmSJWFrawtHR0d4eHigZ8+eWLJkCTZu3AhXV1fZJsSbN2/W2a6Liws2b96MOXPmoF27dqhcuTKUSiXKlSuHli1bYvbs2Vi/fj3s7e1lfSlTpozO9ooVK4agoCDs27cPI0eOhLe3N5ycnKBUKmFnZ4d33nkH3bt3x9KlS7F+/fpCSfZr9O/fH15eXuL8xx9/xO3bt/VeX7AMk7kJ+4Llf16FhH9ERIQ4DggIKMKeEBEREb2aFPn6/hVBRERERPSWW7ZsmahlP2HCBAwePLhoO0Qv7Pjx4+LnV758eRw/frxoO0Rmy8nJQdu2bZGamooKFSogKipK7AlCRERERGqc4U9EREREpEe/fv3ETPDw8HC9M+6p8IWFhWHFihX4888/kZqaavT6mJgYcezu7m7NrpGV/PHHH+JnPWjQICb7iYiIiHRgwp+IiIiISI8yZcpg+PDhAICbN2/ir7/+KuIekUZ0dDTmzp2LkSNHYvny5QavTUtLw9q1a8V5wVI19HpYs2YNAPUGzIMGDSri3hARERG9mpjwJyIiIiIyYNCgQahWrRoAYMmSJUXcG9Jo27atOA4LC8O2bduQl5endd2NGzcwaNAgpKSkAAAcHR1Z+/01dOTIEZw7dw4AMHLkSNl+F0RERET0f1jDn4iIiIjIiKioKAQGBgIAfv75Z7Rr165oO0TIzc1Fnz59EBcXJ75WqVIleHh4oGLFinj27Bni4+Nx6dIlUYpJqVQiNDRUthkwvR569+6Nc+fOoXHjxli/fj0UCkVRd4mIiIjolcSEPxERERGRCYKDg7Fjxw64urpi+/btUCqVRd2lt96jR4/w3//+FwcPHjR6rbOzM2bNmoXmzZtbv2NkUTt37kRQUBDs7OywefNmuLq6FnWXiIiIiF5ZTPgTEREREZkgMzMTAQEBuHnzJoKCgjBs2LCi7hL9f9HR0di1axfOnj2LxMREZGZmwtbWFpUqVYKnpyfat2+PLl26oHjx4kXdVTJTRkYGfH19kZycjOnTp6N3795F3SUiIiKiVxoT/kREREREREREREREbwBu2ktERERERERERERE9AZgwp+IiIiIiIiIiIiI6A3AhD8RERERERERERER0RuACX8iIiIiIiIiIiIiojcAE/5ERERERERERERERG8AJvyJiIiIiIiIiIiIiN4A/w/xWCqS6cA2XQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def simulate_clamping_error(number_of_sites, cutoff):\n", " NS = number_of_sites \n", " HY = 8760 # hours per year\n", " trials = []\n", " for t in range(100):\n", " sample = np.random.choice(hourly_consumption_kwh, NS * HY)\n", " true_mean = np.mean(sample)\n", " clipped_mean = np.mean(np.clip(sample, 0, cutoff))\n", " trials.append(true_mean - clipped_mean)\n", "\n", " plt.hist(trials)\n", " plt.title(f\"Error from clamping procedure (cutoff={cutoff})\")\n", " plt.xlabel(\"Error (Average kWh)\")\n", " plt.ylabel(\"Count\")\n", " plt.show()\n", "\n", "simulate_clamping_error(number_of_sites=200, cutoff=2.05)\n", "simulate_clamping_error(number_of_sites=200, cutoff=2.30)" ] }, { "cell_type": "markdown", "metadata": { "nteract": { "transient": { "deleting": false } } }, "source": [ "The resulting error is within $\\pm0.01$ kWh in all cases. This is well-suited for the statistics that will be prepared with these data, which can tolerate at least +/- 0.1 kWh of error, an order of magnitude more." ] } ], "metadata": { "kernel_info": { "name": "python3" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.8" }, "nteract": { "version": "0.24.1" } }, "nbformat": 4, "nbformat_minor": 4 }