{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "HW 6", "provenance": [], "collapsed_sections": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name":...

1 answer below ยป
Q2 and Q3


{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "HW 6", "provenance": [], "collapsed_sections": [] }, "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": "3.7.3" }, "test_info": { "id": "4adb3d5055da02e7ae8251ca99f4acfa901ab256" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "GTECSaaF2HIz" }, "source": [ "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n", "\n", "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and collaborators below:" ] }, { "cell_type": "code", "metadata": { "id": "FgdGPJGQ2HI0" }, "source": [ "NAME = \"\"\n", "COLLABORATORS = \"\"" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "hdheqpHA2HI4" }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "deletable": false, "editable": false, "nbgrader": { "checksum": "015255c8d63a81a6277731d085451e10", "grade": false, "grade_id": "cell-23f58e80afda25d4", "locked": true, "schema_version": 1, "solution": false }, "id": "q5_8md-x2HI5" }, "source": [ "# Homework 6: Stream Averages and Motion Detection\n", "\n", "## CSE 30 Fall 2020\n", "\n", "Copyright Luca de Alfaro, 2019-20. \n", "License: [CC-BY-NC-ND](https://creativecommons.org/licenses/by-nc-nd/4.0/)." ] }, { "cell_type": "markdown", "metadata": { "deletable": false, "editable": false, "nbgrader": { "checksum": "e42300239388933dcf5ae54de0207866", "grade": false, "grade_id": "cell-ed51b034c970c018", "locked": true, "schema_version": 1, "solution": false }, "id": "HB7EBYTS2HI6" }, "source": [ "For how to work on this homework assignment, please refer to the instructions posted on Canvas. \n", "\n", "## Submission\n", "\n", "* **First, remove the output, or the notebook will be too large:**\n", "\n", " Edit > Clear all outputs\n", " \n", " \n", "* Then, download the .ipynb file:\n", "\n", " File > Download .ipynb\n", " \n", " \n", "* Finally, [submit the .ipynb to this Google Form](https://docs.google.com/forms/d/e/1FAIpQLSfUqr_ibrn1NKW8hKVT3eoomMogY6Q4kOJ7z2HfL0takEvrVw/viewform?usp=sf_link).\n", "\n", "Deadline: Wednesday November 4, 11pm (check on Canvas for updated information)." ] }, { "cell_type": "markdown", "metadata": { "deletable": false, "editable": false, "nbgrader": { "checksum": "2177f64fe3d728669a088c66163e0e5e", "grade": false, "grade_id": "cell-dd3c62597369770a", "locked": true, "schema_version": 1, "solution": false }, "id": "8XIJ_qZs2HI7" }, "source": [ "## About this homework\n", "\n", "This homework notebook has many cells, as it is derived from the chapter, but there are only three questions. \n", "Each question is marked\n", "\n", " ### Question n:\n", " \n", "for $n = 1, 2, 3$. \n", "The questions are: \n", "\n", "* Implementing a sliding window averagerator\n", "* Implementing a class to clean data streams\n", "* Implementing a class to perform motion detection." ] }, { "cell_type": "markdown", "metadata": { "deletable": false, "editable": false, "nbgrader": { "checksum": "232d22754eec312f64dbf32844db108c", "grade": false, "grade_id": "cell-e435450e249172c7", "locked": true, "schema_version": 1, "solution": false }, "id": "5_tJZtWP2HI8" }, "source": [ "Suppose you have a series of numbers, and you need to compute their average and standard deviation. What is a good way for doing this? \n", "The obvious way is to use the [numpy library](https://www.numpy.org), which offers a wealth of functions to operate on matrices, arrays, and much more. \n", "Numpy is one of the fundamental packages of Python, and you would be well advised to browse its documentation and familiarize yourself with what it can do. \n", "With numpy, we can compute average and standard deviation of a list of numbers very simply: \n" ] }, { "cell_type": "code", "metadata": { "deletable": false, "editable": false,
Answered Same DayNov 05, 2021

Answer To: { "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "HW 6", "provenance": [],...

Vicky answered on Nov 06 2021
163 Votes
{
"cells": [
{
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"Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
"\n",
"Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
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"NAME = \"\"\n",
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"---"
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"source": [
"# Homework 6: Stream Averages and Motion Detection\n",
"\n",
"## CSE 30 Fall 2020\n",
"\n",
"Copyright Luca de Alfaro, 2019-20. \n",
"License: [CC-BY-NC-ND](https://creativecommons.org/licenses/by-nc-nd/4.0/)."
]
},
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"For how to work on this homework assignment, please refer to the instructions posted on Canvas. \n",
"\n",
"## Submission\n",
"\n",
"* **First, remove the output, or the notebook will be too large:**\n",
"\n",
" Edit > Clear all outputs\n",
" \n",
" \n",
"* Then, download the .ipynb file:\n",
"\n",
" File > Download .ipynb\n",
" \n",
" \n",
"* Finally, [submit the .ipynb to this Google Form](https://docs.google.com/forms/d/e/1FAIpQLSfUqr_ibrn1NKW8hKVT3eoomMogY6Q4kOJ7z2HfL0takEvrVw/viewform?usp=sf_link).\n",
"\n",
"Deadline: Wednesday November 4, 11pm (check on Canvas for updated information)."
]
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"source": [
"## About this homework\n",
"\n",
"This homework notebook has many cells, as it is derived from the chapter, but there are only three questions. \n",
"Each question is marked\n",
"\n",
" ### Question n:\n",
" \n",
"for $n = 1, 2, 3$. \n",
"The questions are: \n",
"\n",
"* Implementing a sliding window averagerator\n",
"* Implementing a class to clean data streams\n",
"* Implementing a class to perform motion detection."
]
},
{
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"source": [
"Suppose you have a series of numbers, and you need to compute their average and standard deviation. What is a good way for doing this? \n",
"The obvious way is to use the [numpy library](https://www.numpy.org), which offers a wealth of functions to operate on matrices, arrays, and much more. \n",
"Numpy is one of the fundamental packages of Python, and you would be well advised to browse its documentation and familiarize yourself with what it can do. \n",
"With numpy, we can compute average and standard deviation of a list of numbers very simply: \n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"deletable": false,
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"outputs": [
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"name": "stdout",
"output_type": "stream",
"text": [
"avg: 2.5714285714285716\n",
"std: 0.9035079029052513\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"s = [1., 2., 3., 3., 2., 4., 3.]\n",
"print(\"avg:\", np.average(s))\n",
"print(\"std:\", np.std(s))\n"
]
},
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"source": [
"## Stream statistics\n",
"\n",
"Assume now that the numbers do not form a fixed length sequence, but rather, a stream of numbers, with new numbers always arriving. The numbers could represent real-time temperature measurements, or water pressure, or electricity usage, or percentages of utilized CPU cycles, and so forth. \n",
"What do we do in order to compute their average and standard deviation? \n",
"\n",
"There are various choices, and the way one does it depends on the application. \n",
"It is certainly possible to accummulate all numbers, and then compute their overall average and standard deviation; this allows the computation of statistics that apply to the entire time range for which the data was available. \n",
"More commonly, one is interested in knowing the _recent_ aveage and standard deviation, so that one can compare the most recent data with the average of the last day. "
]
},
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"source": [
"## Stream Averagerators\n",
"\n",
"One could implement the code that computes the average of a stream in the same portion of code where one reads the stream, as follows:"
]
},
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"text": [
"avg: 0.26679361599246854\n",
"avg: 0.4613264239066112\n",
"avg: 0.36434457445090196\n",
"avg: 0.5154883464580592\n",
"avg: 0.5057340533820456\n",
"avg: 0.49884149192064453\n",
"avg: 0.5543345011717055\n",
"avg: 0.4956537177840408\n",
"avg: 0.46224197433186365\n",
"avg: 0.5142170482263289\n"
]
}
],
"source": [
"import random # We use random to simulate a stream.\n",
"\n",
"def read_stream():\n",
" \"\"\"Reads and returns one number from the stream.\"\"\"\n",
" return random.random()\n",
"\n",
"def use(x):\n",
" \"\"\"Code to do something with x\"\"\"\n",
" pass\n",
"\n",
"# Here we accummulate the sequence, so we can average it.\n",
"seq = []\n",
"\n",
"while True:\n",
" x = read_stream()\n",
"\n",
" # We add x to the average\n",
" seq.append(x)\n",
" print(\"avg:\", np.average(seq))\n",
" use(x)\n",
"\n",
" # This is an example, and I don't what the code to run forever.\n",
" if len(seq) == 10:\n",
" break\n"
]
},
{
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"deletable": false,
"editable": false,
"id": "_vtHSgqv2HJG",
"nbgrader": {
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"source": [
"However, this approach is horrible in two different ways. One way is that the implementation is horribly inefficient; our sequence seq will have to hold all the data we read from the stream. This is bad, and we will fix it later. \n",
"\n",
"The other way in which this is horrible is that the code to compute the average is intermingled with the code that reads the sequence and passes it to the code that uses it. It would be much better to separate out the code, for two related reasons. \n",
"\n",
"**Separation of concerns.** Separating the code makes it easier both to read and to write, because we separate the concerns: when we write the code to compute the average, we can focus on that, disregarding the details of how the stream is read or used; when we write the code that processes the stream, we can focus on that, simply calling a method to compute the average, but disregarding how the average is computed. \n",
"Separating the concerns, or dividing the overall coding task into smaller, independent units, is key. Each person, at any given time, can keep in mind only a fairly small set of facts; indeed, several studies on software verification point out to the fact that in order to write correct code, programmers usually use no more than a dozen facts about the previous code and input, reflecting what likely is an underlying limitation of our brains. \n",
"By focusing on one task at a time, we can apply our full mental powers to that particular task, making it much easier to write its code. \n",
"The same goes for reading code: it is much easier to understand code that does one specific thing, than code that mixes multiple goals at a time. \n",
"\n",
"**Ease of modification.** As we mentioned, there are various ways of computing a stream average: there are more and less efficient implementations, and we can consider the entirety of the data read from the stream, or only the most recent one. It will be easier to change the implementation if the code for computing the stream average is all in the same place, rather than sprinkled in multiple places that must be tracked and updated. \n",
"\n",
"For these reasons, we introduce _averagerator_ classes that comput running averages and standard deviations. \n",
"The first we write, _FullAveragerator_, is for computing the statistics of complete sequences.\n",
"\n",
"The class has one method, _add_, used to add data to it, and two properties, _avg_ and _std_, which return the average and standard deviation so far. \n",
"\n"
]
},
{
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"source": [
"class FullAveragerator(object):\n",
"\n",
" def __init__(self):\n",
" self.seq = []\n",
"\n",
" def add(self, x):\n",
" self.seq.append(x)\n",
"\n",
" @property\n",
" def avg(self):\n",
" return np.average(self.seq)\n",
"\n",
" @property\n",
" def std(self):\n",
" return np.std(self.seq)\n"
]
},
{
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"source": [
"The previous code can be rewritten like this:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"deletable": false,
"editable": false,
"id": "hferIZPd2HJK",
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"avg: 0.8481248454765221\n",
"avg: 0.504288984206181\n",
"avg: 0.6513735669656283\n",
"avg: 0.5826409775245193\n",
"avg: 0.5891647224299991\n",
"avg: 0.544397207289974\n",
"avg: 0.5019998731524652\n",
"avg: 0.48379177599808726\n",
"avg: 0.43511750176911945\n",
"avg: 0.45041774154479075\n"
]
}
],
"source": [
"averagerator = FullAveragerator()\n",
"\n",
"for _ in range(10):\n",
" x = read_stream()\n",
"\n",
" # We add x to the average\n",
" averagerator.add(x)\n",
" print(\"avg:\", averagerator.avg)\n",
" use(x)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
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}
},
"source": [
"The improvement seems minor, but this is only because our averagerator, as written is very simple. \n",
"Very simple, and very inefficient, as remarked. Let us write it more efficiently."
]
},
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"source": [
"A picture is worth a thousand words, so let's draw one."
]
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{
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"text/plain": [
"
"
]
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],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"averagerator = FullAveragerator()\n",
"\n",
"xs = []\n",
"smooth_xs = []\n",
"for _ in range(200):\n",
" x = read_stream()\n",
" xs.append(x)\n",
" averagerator.add(x)\n",
" smooth_xs.append(averagerator.avg)\n",
"plt.plot(xs, label=\"xs\")\n",
"plt.plot(smooth_xs, label=\"smooth xs\")\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
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"source": [
"### Efficient Stream Averagerator\n",
"\n",
"The idea in computing a more efficient implementation is to avoid storing the entire sequence, summarizing it instead by aggregate statistics. The average $E[X]$ of a sequence of $n$ numbers $x_1, x_2, \\ldots, x_n$ can be computed as $S_n / n$, where \n",
"$$\n",
"S_n = \\sum_{i=1}^n x_i \\; .\n",
"$$\n",
"When $x_{n+1}$ arrives, all we need to do is compute \n",
"$S_{n+1} = x_{n+1} + S_n$, and return the average $S_{n+1} / (n+1)$.\n",
"\n",
"Thus, we do not need to store the complete sequence to compute the average: we need to store only the sequence length ($n$ above), and the sequence sum ($S_n$ above). \n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
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"id": "0My1Jzex2HJS",
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"outputs": [],
"source": [
"class EfficientFullAveragerator(object):\n",
"\n",
" def __init__(self):\n",
" self.sum_x = 0.\n",
" self.n = 0\n",
"\n",
" def add(self, x):\n",
" self.sum_x += x\n",
" self.n += 1\n",
"\n",
" @property\n",
" def avg(self):\n",
" return self.sum_x / self.n\n"
]
},
{
"cell_type": "markdown",
"metadata": {
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"id": "ziXhT6bb2HJV",
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"source": [
"This works, but what about the standard deviation? \n",
"\n",
"The standard deviation is the square root of the variance, and for a series $X = x_1, x_2, \\ldots, x_n$ of numbers, the variance is \n",
"$$\n",
"E[(X - E[X])^2] = E[(X - \\mu)^2]\n",
"$$\n",
"where $\\mu = E[X]$ is the average.\n",
"This equation does not tell us directly what to store. We cannot compute the average of $x_1 - \\mu, x_2 - \\mu, \\ldots, x_n - \\mu$, because $\\mu$ is not known when $x_1$ arrives: $\\mu$ depends on the _entire_ sequence, so when its first element $x_1$ arrives, $\\mu$ is not known yet! \n",
"\n",
"To obtain a form that we can compute on the fly, we need to develop the above equation.\n",
"\n",
"$$\n",
"E[(X - \\mu)^2] = E[X^2 - 2\\mu X + \\mu^2] = E[X^2] - 2 \\mu E[X] + \\mu^2 \n",
"= E[X^2] - \\mu^2 \\; ,\n",
"$$\n",
"\n",
"where we have used that $E[X] = \\mu$. \n",
"The relation\n",
"\n",
"$$\n",
"E[(X - \\mu)^2] = E[X^2] - \\mu^2 \\; ,\n",
"$$\n",
"\n",
"_is_ suitable to be computed on the fly. \n",
"It is just the average of the sequence of squares $x_1^2, x_2^2, \\ldots$ (and we already know how to compute sequence averages), minus $\\mu^2$, which we also already know how to compute.\n",
"\n",
"Using these ideas, here is the complete implementation of our efficient averagerator class."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"deletable": false,
"editable": false,
"id": "LWx6WK-h2HJV",
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},
"outputs": [],
"source": [
"class EfficientFullAveragerator(object):\n",
"\n",
" def __init__(self):\n",
" self.sum_x = 0.\n",
" self.sum_x_sq = 0.\n",
" self.n = 0\n",
"\n",
" def add(self, x):\n",
" # We compute the sum of the x, to compute their average.\n",
" self.sum_x += x\n",
" # Sum of the x^2, so we can later compute the average of the x^2.\n",
" self.sum_x_sq += x * x\n",
" self.n += 1\n",
"\n",
" @property\n",
" def avg(self):\n",
" return self.sum_x / self.n\n",
"\n",
" @property\n",
" def std(self):\n",
" mu = self.avg # To avoid calling self.avg twice.\n",
" return np.sqrt(self.sum_x_sq / self.n - mu * mu)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
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"id": "wxJpGx9N2HJa",
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}
},
"source": [
"Let us play with this implementation."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
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"id": "v1E6AMZo2HJa",
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},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"averagerator = EfficientFullAveragerator()\n",
"\n",
"xs = []\n",
"smooth_xs = []\n",
"stdevs = []\n",
"for _ in range(200):\n",
" x = read_stream()\n",
" xs.append(x)\n",
" averagerator.add(x)\n",
" smooth_xs.append(averagerator.avg)\n",
" stdevs.append(averagerator.std)\n",
"plt.plot(xs, label=\"xs\")\n",
"plt.plot(smooth_xs, label=\"smooth xs\")\n",
"plt.plot(stdevs, label=\"std\")\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "1em618kT2HJd",
"nbgrader": {
"checksum": "81a4ec8f9d39abdd9a7633704ee6dba7",
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"source": [
"This works, and we can see that the average tends to $0.5$, and the standard deviation tends to $1/\\sqrt{12}$. \n",
"This because the input numbers are uniformy distributed between 0 and 1, and:\n",
"$$\n",
"\\int_0^1 x \\: dx = \\frac{1}{2} \\; , \\qquad \\int_0^1 \\left(x - \\frac{1}{2}\\right)^2 \\: dx = \\frac{1}{12} \\; .\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "GLRglx2-2HJd",
"nbgrader": {
"checksum": "8a298bf1414d69a676871e3965256247",
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}
},
"source": [
"### Sliding Windows Averagerators\n",
"\n",
"Often, we are more interested in the recent average than in the average since the start of a stream. \n",
"This is especially true if we plan to use the average and standard deviation to identify outliers (possibly incorrect data) in a data stream. \n",
"\n",
"Consider, for instance, a temperature sensor giving us readings of outside air temperature once per minute. \n",
"If one considers statistics that span more than one year, a location might have an average temperature of 15 (Celsius; all temperatures in the following are in Celsius), and a standard deviation of 15, accommodating Winter temperatures slightly above freezing and Summer ones around 30C. \n",
"\n",
"Yet, if we saw input data: \n",
"$$\n",
" 12.3, 12.3, 12.4, 12.3, 12.4, 12.4, 23.3, 17.5, 12.4, 12.5, 12.6 \n",
"$$\n",
"we should be suspicious: outside air temperature does not change by more than 10C in a minute. \n",
"We do not know what happened --- someone touched the temperature sensor with a finger, perhaps --- but we know that the data is probably not reflective of air temperature. \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "YwyhvPS-2HJd",
"nbgrader": {
"checksum": "75d45d54793cfb992a5e375a409b13fb",
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"grade_id": "cell-f8c96ee944887983",
"locked": true,
"schema_version": 1,
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}
},
"source": [
"As a concrete example, let us simulate a sensor that senses air temperature. Air temperature varies between 5C and 25C, as a sine wave (just to make it easy to draw); the sensor has a noise of $\\pm 1C$ on each measurement. "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"deletable": false,
"editable": false,
"id": "rCh0PbTt2HJe",
"nbgrader": {
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"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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zXRPDaTEgHI3jYJsLy3P0e9Ua/nAU+1q5FL/rl9fhtvOntvcjcF5jGc5rLAPAxXWZgI+kpd+HWJyiqTeZJ8888EngCkQSApIrLKMsQw+2s3xYMf5wNGVI8eK64pxkoABI6Yp3jo1Xy0izaG5osdWAtbPLc36OUpuJxcAzIOyLdQ9zxWabr1+Ejy2ukfScmhTwYX8k0Q42VwghlBtX1OG+DfMTw2F3sU6FKQTCsZRwUy4RPwiYB5iZ5v6kgN+8umGMT04e5oFnRmgf0cUL+DVLayXvGaO5EAqlFC5+EzOXGPU67Pz2R1FqMyVStPa1DmFf69A431lY+COxnFa8ihGnIrIsoMw093lBCHD8RxskmQADANPLbPAEo9jdMpgIqzCSPWKEjpmTad2RLZrzwL2hKGJxmnH24lSpLrKk5Neunl6KvedcoJOdWKBBAuHYiJTLXCH2wIeYBziCXncQZ/t9qCu2SibeAPDJ8xtQV2zBQ2+ckuwcakQo7usaDoKQ3LbuGA3NCbiwjCnOcQglE4vqitDvDcEdYJkRANf9LhSNSxZCMRmSy1G2hE/lQJsL5z+wDS8c6JS81bHNZMDVS2vxQfMA7nl6v2S9rtWGoD3haBwOkyEvLXc1JeCtA368dqQLAFBfKv3wVWFTzRdmAg4gMe5MKs+jQZTN4mK9aFJo7kumrkld/QcAq/j2tC8d7MRWNqUHQOo9mY/wCaCxGPhHH9qOSIwLZ8yuckh+Phv/S/IzAQcA+MOcgEvlgVc5LWh58Fqs+clWDLIsiBTED00pep+ks2pGMo3TpNeUHzhpxIV9wkg6qdHUlRfEGwCqnNI2kQEAGy9UgnAVMsP+CDa/dBQAYJ1k18eJUmozJWLg/7u7DZ9/kg3aFc8XKZO4fBsAaoutiVYVbAXKIRbw9CEYUqEpARdPvMhH/MlmZgIu8Os3T+GVQ1z4SioPXKBUVMp937OH8OZxtoQXi6jUxSMCP//nZQDA+tOAG6Ax1eExk0FTAi7ESIX5iVIj9BdnIRQgGk+6gFLvvpfajSMKSQo9EyggciJK8xBCATiHSa8jrLUsRo6Zy9fMXE0JeDASw6xKO56/e11ezicI1Z1b9uBnrx3PyzmVisWQFG0pU9gAYFalA2f6fDgtKlkORQt7Rql4FZiPEArArXLtJj0TcIzcVL9kbmVezqspAfeFolg3uwK1xdJnoACpnuYf3mnOyzmVijj3W2oP/PPrZ8Jm0uM/t51OHAtFClvAA6JVYD42MQWcFiO8IRZCTB/wsn5uRV7Oq6ksFF84lrfYEzD5EW1aRLzjILWAlzvMuG5ZHV440JE4FozGUAzpc/+VitgDz3UV8ljYzXp4Q4Wb0kkpRTAST4RQfnrTEsTiVPJJPAKa8cAjsTjC0XhOex+PRz4qrdSCWECkDqEAwNVLalLOKeSgFyLdw0Gc5vPAbSY9qovyE38FuM26ph4vTova1xYSLxzoxMLvv45957imdutmV+Czaxvzdn7NCLifX8bl0wMXZ70UOn6RgObjwbZ2dnlKtW2wgEMoF/5sG7af7ENDmRXHJOyBkgmH2YDmfh+ueOidvJ1TSezneyH9dXcbgPyufgANCbiXjwHmK4EeyE+qoloQZ0FI1QtFjFGvwxULqxPvC9kDF7AZ8x/Sy1e+s1IRMt/6vSEQkpvh3dmgGQH3hwQBl+eGKvSZDuJUSnFGipTcvKY+8ZoJOGAx5v/POZ/evhIRZz85zQbo8ywE4/7GCSENhJC3CSHHCSFHCSFf44+XEUK2EkKa+H+nPvRwkrT0+/DEP84CAOwybSya8yRaSkUcj87XhKILZ5Xj2S+tBQAECzyNEAACMjzECn2wg9hxkKMUYSKP7CiAb1BKFwK4EMDdhJBFAO4HsI1SOhfANv593nEHI7jsl9vx9C4uBiWXB26WwftREoFwDI3lNjx55/l5Pa/w4CxUD1wcuvLKUBEp7kRYiMVU4uvvkSEfflzVoZR2UUr38a89AI4DmAZgI4An+Y89CeBGqYwcixf2d6S8lyszJB4vvJsXAHac6cc9T+/HnnNDmFPlwKXz8lPAICAs4QtVwMUesBwCUiPKeAnHCm8VFIzG8h42EZOV20gIaQSwEsBOANWU0i6AE3kAVbk2biK8dqQb86udifdybarIsXxVAn/Z2YqXDnYCkL6JVSaEuG+hFvKkCLgMHvgvb16Oi/milWC48H4HwUgc1XzjvHnV0ndATWfCAk4IcQB4FsC9lFJ3Ft+3iRCyhxCyp6+vbzI2jgqlFMe73Fg1ozTRwCcfGRBiFtUWAeA6IUYK0AMRxkcBye6M+SThgUdjBVnSPeSTt4imxGbCNUtrAQD+SGFd/7/tbceus4OwGPXY+90r8NyX89PCQ8yEBJwQYgQn3k9RSp/jD/cQQmr5r9cC6M30vZTSRymlayilayorc7u87vWEMOSPYEGNE//zxbX4/PqZqMxTBZTAi19Zh/s2zAdQmMv4bpGAy7EPIAj48/s7sPgH/4djnRP2LTSB4IFfsbAa/7PpQllsEMKWhdaV85vPHETroB9mox7lDrMsq/+JZKEQAH8EcJxS+pDoSy8CuJ1/fTuAF3Jv3tgc7+L+WBfUODGnyoHvXrcobxkQAga9DkV87mehhVEopehxhxIFNekd2fKBJTFgmquEOyuayl4IuHgBf+CfluCCWeWy2CC0Dw4UmIALyJG+KTCRM68D8BkAHyGEHOD/uwbAgwCuJIQ0AbiSf59XTnZz3egW1BTl+9QpCDdwocUAh/wRhKNxrJzOTWeRYzaiQa+DQfTQLrSHaK8nBB2BJEO8J4oQtiykax8Wpa3mq+4hE+P6/JTS95Haq0jMR3NrTna0DvpRYjOiOM/lq+kIN3ChxQC7h7nwyarppdh+sg9Oszy/h6goA6jQptUf6RjGnCoHTDK2dRBCKIXkgacUrsnogau6DrbDFcC0kvy0jh0LawHewEByA3PdnApML7PhkjynEGaikGZlUkpxuGMYl82XJQEsgbAPcaRzGC8f6sRPb1oKo8bnZPry3LxtNNQt4EMBzKywy21GMgZYQEtIAOjiPfCaYgtWz5CtEDeBxagrKA+8cziIfm8Yy+qLZbVDaKv8i9dPAgA+cV4DVs8ok9MkyRFnPMkp4Kp9TFJK0eEKoL7UJrcpyRh4gQl4tzsIQvIzQHoiNJbbE7MyC4EzfAtXcR2EHKQXz/V7tf87SBVwZW9iKhKXPwJ/OIZppcoJofgKaDLJK4e68PaJXlQ4zIpYLjvMBpTYRs7K1DLCw6pC5gdougfaNuiXyZL8If5bl7MrqWpDKB2uAAAoIgYuNNDvGg7IbEl+iMTiuPsv+wAAS6fJu3wHgEObr4KeEPzb3w4mMpMKAUHA8zlCLRPpHnhBCLhoEzMiYyM11Qp4wvvI0wDXsSi2GlFiM+LcgPZvXAA41ZMUyXxOfxkNIQ+/1GYaMVxWywz6wtARpAy2kAMjn8opZAO1FoKAi0IoclZgy7/2nSTCBXRYlPEMmlFux1M7W/GzV7U/nf5g23DitdziIabMbsKQP1wwjcUG/WGU2kx5L17LhNgLbxvS/kpUnIUSicl3v6lWwIXOa0qZCDKDn8zxh3ebNS8gh9pdidfuoHI83lKbCXGqLJuk4g/vnMFfdraizC7/ChQAlohCaa4C2IcQe+BydmFUrYD7FCbg4gyULlF/EC3S4w4mdt4vlKl8OxOCmBVCJsrPXjsBAChViIDfdsF0ANzfo1uGroj5xq+QEIoy1G8SCM3r5RrgkM4/r67HG8d6AADNfV5FbK5KhTsYxarppfjlzctT+kHLjSBmWs9E8YhWGEoZrH3dsjpUOszYcWYA/7mtCaFoTNNTqrx8FsqSaUX45lXzZbNDGb/9SeANR2E26BSRwgYAH1tcg13f5joLNPdpu6HScCCCYqsRdSVWRcRfBYRsjEGZW6xKTROf/w0ki6mUwAWzyhOrIDl6k+cTfziKKqcZL99zcUr4KN8oQ/0mgTcYhVMhG5gClU6upWRzn3f8D6sYQcCVRqmds0nr1ZhNoiwgpYQQBYS/Sa0LuDcUVcS1l9+CLKGUglIuBq6U8IkAIQSzKu1o1nhLU6UKeCIGrvEQSnO/DyaDDg/ctBRrZytnDwIAnHxKp0fjG8m97pDsBVSACj3wJ3e04PJfbYc3FJVtAv1YzKqwazqEEozEEI7GUaRAAbca9TAZdJqPgQ94w6iwm/Dx1fWK22spFA9cKY30VCfghzvcODfgR583rJgccDGzKh3oHA5oti+Kmx/aoEQBJ4SgzGbSfAhlyBdGiczVl6MhCPipHo9mp9TH4hTd7iDqSuTfwFedgPd6uE2bjiG/ImJQ6cyqtINS4N1TfXj3VG5ngMpNJBbHt547DEBZBTxiSu0mzW9iDvnDisn/Tkeoiv3hS8fwm22nZbZGGvo8IcTiFHXMA88eoQd1vzesSAEX2ttu+q+9+OwTuzTlhexuGcS2E9zoU6UK+LQSC870ebG/dUhT117MkD+imPzvdMSJBU/vapXREukQ+jDVFTMBz5oed3Jsl9I2MQFgdqUD4sw6r4YmpYtTNpUq4OvnVOBsvw83/W4HXjncJbc5kjDoC6NM5ilUoyF2qgZ92mxrsON0PwAwDzxbgpFYyuBcpaURAlxrzUbRkIkeDVVliuP6RQq89gBSptPsbB6U0RJpiMbiGA4o1wM3iB7y4VgcLQPa2tBv6ffhV1tPwagnaChjAp4Vve7UoblKFZFKRzK9qMed/0G/UiEeGVdulz+FKhONFXbce8VcFFuN+LB5QG5zco6Ld2BKFbqJmU63ggqNckEn3zL6t7etSkwikhNVCXiPJ/VmmFPlkMmSsREPmNWUB873PX7mrrWyD5Iei3uvmId/WT8TTb3elOGzWkBoFKVUDxwA/nzn+Xjk06sBAL0e7TgwADDMtyueXib/JDBAbQKeJoYLa4tksmRs7vvYgkSOaLeWBJwPoSip/8lolDu0WdItZNjIPcRhLC6ZV4n1cysAaMuBAbgNZAAoUYgDozIBT32aNyhgHmYmltYX4x/3fwROi2FE2EfNCAIu5xDXiSJspmmtIrDfy91PSk0jFHCYDbCb9JoKIQKAK8CtgEqsyrj+8gdxsqDXHYTJoEOYX8orqZFSJqqcZk15IIKAW03KF3AhH1lrrU07+GEJSpgFOx7VRZYRYU+14gtF0TLgw7A/ArNBp5i/AVUJeI87iOoiMx777BoYFC7eAFetqKU0wmCEe3BaFNLCdCyEDCWvxgS8fcgPp9mg2DROMVVFZvRpxAO/938OYOuxHtywvE4x4RNAdQIeQrXTggU1yox9p+MwGzQm4DEYdCQlVUypODTak6PDFVCF9w1wHvj+Vtf4H1QBe88NAQDO9HkVEz4B1BYD9wQVMUR3othM+pTRS2pmyBdG21AAVhXEv4FkVzxvSFsx8PahAOpVIuA1xRZ0Dwc1UcwjDM443etVVAaWqgS81x1CVZEy848zYTcb4Atpo6nVmp++iZcOdsKsGgHXqAc+pIwueBOhvtSGcCyuiVRCYeM+FI2jREHhK9UIuC8UhTcURZVTPR64w2yATyN5yDHeixJmYSododWwlgR82B+BJxRVTQilgbezbcgvsyVTRzy6TkkxcHX8NSI5qLZc4elTYmwmg2ZCKAJqSCEEAL2OwGE2aErAzw1yZekzyu3jfFIZNPDFLm2D6hdw8X1f4VBOFEA1Ai70QFFS/Gk8HGY9IjGaSHtk5BenxaCpGHjLACeEjSoRcCHU0zYYkNmSqSOePC/nDMx0VCPgLr+6ekAAyW6JWvLCxf1QlI7mPHB+VJ9SyrjHw2LUo7rIrOoQCqUU9z97CEc73Yljy+qZgGeNMCZLSfGn8RDisFpKJVRTbxGnxYCWAT/+8M6ZlC6WaqVlwI+aIotiikgmQqXTnAh/qhF/OIa/7m5LOaakTWTVCLjQhU1JO8DjIXjgF//ibQx41b8TD3A3tFoothpxvMuNn712Ar99q0luc6bMuQEfGivU4X0L2E3qroVwpbWv/n8bFoAQ5RQRqkbAh3kPXE0xcLs56Sm9fVK949XEebwhFcXz//XKeXjwn5bi6iU1eGpnq6rCP5lo7vclJj6pBYdZ3Rv5LrCqq8EAACAASURBVNGA7C9eMgtfumy2jNaMRDWVmEP+CGwmPcwG9SwfxRODlDh8YqIEo+oUvmX1JVhWXwKLUY/XjnSjaziAWZXKbEE8HgPeEAZ9YcypcsptSlbYVS/gSQ9ciSMcVeOBu/wRVYVPgGQMHFDX5l86agqbZEJoLTugwlhsNBbH5heP4i1+FulchfbAHw272QCviovZxAKuxBYS4z5SCCFPALgOQC+ldAl/bDOALwAQ4gLfppS+KpWRADAcCKNYRRkoQOoT26NiL0T88Pn9p1bJaMnkEKYHqXEf4minG1t2tCTez61Wl4A7zOpuJyG0jwWUWRQ2kUfKFgAbMhz/NaV0Bf+fpOIN8JO4VRT/BgCLKXl51dwVL8C3kX34tlW4emmtzNZkTwXvgfd71eeB94seOg6zQRXDNMTYzQYEIrFEJa/aEHvgSuxBM66AU0rfBSD7dNgBb0jRY6QyUW4341pe8NRcUCKEUKwm5S0hJ4Jw3wyoUMA7XMkimHVzyhWVATERhFWoWltKuPxhWI16vPSV9bhumfKcl6n8RX6FEHKIEPIEIaR0tA8RQjYRQvYQQvb09U0uE4NSiq7hIOqK1eV96HUED39qFUpsRniDUWw/2Ys+FTb2EXK/rUblbeJMBKNehxKbEQM+9V17YYADAFw8t1JGSyaHsJHvV2kc3OWPoMRmxNL6YkU+PCcr4L8HMBvACgBdAH412gcppY9SStdQStdUVk7uBhz0hRGKxlGnoAT6bHCYDXAFIvjcn3bj1sc+lNucrBFi4DYVFZCkU243pYQj1ILggW9YXIMbV06T2ZrsEQRcrbngrkBE0cMzJuVSUUp7hNeEkMcAvJwzizLQ6eLGMtUWq1fAu/j/h9O9XpmtyR4hBq5qAXeYVRkD73AFsG5OOR75zGq5TZkUDr4WQq0bmS5/WNHV35PywAkh4mDQTQCO5MaczHQO83MAVeqBOy2GlFim2hBi4GrpRJiJCodJlVkoXa6gah0XgOvICahXwN2BaGK+qhKZSBrh0wAuA1BBCGkH8AMAlxFCVgCgAFoAfFFCG9HJi19tibpi4AIOsyHxEFIjWgihFFmMikwDG4t4nKLfG0KVUzntS7PFofIQiicYQZGaQyiU0lszHP6jBLaMSqcrAJNBp6pe4GIcFiOoCrOoKKW4+y/70M5vpNkVWIk2UZwW9XUmHA5EEI1TRfWfzhbhnvnu80fwxf/ei+YHrlHkZuBoeIJRRVdRK9cyEXOrnfj46npV/eLFpJfghqNxmFQw2X04EMGrh7sBAEumFak6hOIwGxGIxBCNxRVZUZeJPj7kU6FiD1zoBySMVfOElB2SEBOLU8Xbq4o7+ZY1DXjgpqVymzFp0p/gfSqJxYrj9hfMLJfRkqkj/A7UtJTv50WvUsUeeKnNlDKOrHs4KKM12SHcK0r2wFUh4GonPYbZ41bHTSxk/1Q4zPj8xTNltmZqOFQ45Fh40Fc61Rk6BLgc/I0r6hLv1STgbr6VLPPAC5z0EtwhlTRV6uI3Xl/92npVZ0IAQJEKPXCh6EvNMXAA2HzD4kQbVjUJuPCwL7IyD7ygqS9NbcIv7q+gZDpcAZj0OlTY1S0gABcDB4DD7cMp/c2VTL83DKOeKLqQZCLYTAbce8VcAECXigTcHeT+Tp3MAy9s0vPX1TLeq9MVRE2xBTqdOjePxQhxzPuePYTfvn1aZmsmRr83hAqHWbWb92LMBj3K7SZ0qyR8GIzEWAiFwSGu5CIkdUyTEnH5w/jWc4dwtt+LGpX1nxkNh2gj6v2mfhktmTh9npDqwydiaootibCckvGFoljwvdfxwKvHAbBNzIJH7EE5zYbEeDil8vDbp/H0rjYc6XCjTGU92EfDKU7lVIlD2+8NoVLFKYTpTCuxpjTnUirnBvwAuCHSABRdyMMEPE/8f7euxCOfXoUSm0nxIZSwaO6lkvtAZIM4jhmJqWOuJxdC0cYDFAAaymxoHwqAKryqrXXQl/KeeeAMXL+8DhuW1KLYalR8CCUm+gNT+waagMWYvNU7Fd6XhlLKl9GHNRVCaSi1IhCJKb6pmOCBA1wXS6OCC7+Ua5lGKbEZsf1kH1493CW3KaMiTtIo1ogHLg5j9bhDCCl0UHM8TjHzW6/i238/jFicaiqE0lDGZWO1DvrH+aS8tIgE/K5LlTWFPh0m4HlG8Gi//NQ+mS0ZHfEMTK144ABw+fxKzKywA1BuPvKhjmEAwF93twFQfw64GEHA24eULeCtgz4sqy/G01+4UPEFbEzA84w4vqxUBkWFRiVW7cRg/3TH+bj/6gUAlFuRue14T8p7TQk4Xw/R0q9sAT834MfMCjvWzlb+CDsm4Hmmud83/odkZkiUJaOVTUwBpbc3Pdg+nPJezWX06VhNesytcmB/25DcpoxKOBpHpyuAGWW28T+sAJiA55kfb1ySeK3UikCxB66lEAqQbG+q1AED/WkzU2tU3sIgnTWNZdh7bkixU+rbh/yIU2B6uV1uUyYEE/A8s3Z2Ob5zzUIAyp3UPaRhARdGfCnVAxfP7Sy3m0a0IlY75zWWwhOM4lSPR25TMnKO32BtLGceOGMUhOY4bgXGYUPRGHziTUyNhVASU9LDystCiccpBnzhROuFMpUOMBmLOVUOAEgMCVEa5/gQ53Qm4IzREIpKPEHl5YOnb+45TNryAJUcQnEFIojFKWZVcsv3cg0V8QiU8pW9QwqtRm4bCsBq1KumB7u2/jpVgtAcxx1Qnoj4Q5xn+qONi7F2VrkmGlmJsZuUu4kphE/WzanAe039uGOdslPYJoOwqlBqS+UhfxhldpPis08EmIDLgDMxXEB5HrggbFVOM+ZWO2W2JvfodQRWo16RHriwgbm8vgRnf6au2ZETxWbSw2TQYVChHrjSZ2Cmw0IoMuBU8HQYP7+xquYBxuNhNxvgDSkvBt7Pe6UVDvV4gNlCCEGZzaRYD9wbjKpq45gJuAwI3c3cCvbAbRqLfYtxmJXpgfe6kyPstEyp3YRBn/LufQDwhCLMA2eMjbI9cM4zVZMXki12swEvHuzEY+82y21KCvvbXKgpsmiueCqdMrsRLkWHUNRz/ZmAy4DZoIfZoEspmFEKSQ9cL7Ml0mExcv9vP331uGJ+B5RSfHhmABepoHx7qpTYTNhzbggnu5WTCx6MxBCJxbkQCvPAGeOxsLYIB9pccpsxAj8v4Fr2wMXtZH+zrUlGS5I09Xox4AvjwtnlcpsiOXbeOfjYf7wrsyVJFnzvddz8yAdsE5MxMdbOLsfBNpfiYrFCEY/NrF0PXBise9n8SmzZ0YJzA/L3p9nfyvUHWTOjVGZLpEc8T0NJwx0OtLkQjsUVPQMzHSbgMrF2VjmicYo/f3AO7zX1yW1OAl8oCqOewGzQroAvbygBANx7xTwAwKker5zmAAAOtA2jyGJItLvVMvdtmI/zG8sAAJ989EP0KGzQsZpWn0zAZWLl9BIQAvz89RP4zB93yW1OAl8oqukMFAD4853n4737LkdDKVeyroT+1AfaXFjeUKL5+DcAVBdZcM9H5wAAdp4dxHP7OmS1J72xFguhMMbFaTEm+iMrCV84pioPZDIUW41oKLOhzG6C1aiXvS8HpRRNPR4sqiuS1Y58Il5pyN0ywJ/WVI5loTAmhBKr1DkPXLvhEzGEENSXWmX3wIOROKJxqqnhGeNRJ2qTG4zIW1TlSyvqUpMDwwRcRj6+ul5uEwAAx7vc2H6yF5FYHL5wTNNVmOk0lNnQNiivB+5LVL8WxoMTAHQ6gufvXgdA/s6Q6W2d1RRCUY+lGuTLl81BnyeEJz84h1icQi+DS04pxacf34kBXxi/+Pgy+ELRghKS+lIr9rQMymqDkIlk1/jeQzrLphUDUICA89d/bpUDc6sdiZa3aqCw7hiFodMRTOM30gIReWLP3e4gBvhilmOdbjT1eHDFwuq82yEX5XYz3MEoIrE4jHp5FqTCEr6QHpwAd/9bjDoEZB5sIlz/H25cjItmV8hqS7awEIrMWPmqwIBMXsgh0QzGLTta4A5GNdnGdDRK7dyGlcsvX28OXwE0EBsNm8kguwcubGKqKfYtwARcZoSybrk2cg61u2DQkcSycValHUvri2WxRQ5K+AEDcvbm8BVAA7HRsBr1eGpnK+7cshuhqDx/A2pu4MYEXGaEmyYgk4C3DwVQV2LFdH4K90yVDHPNFaV846ghOT3wkPYbiI2GkPH01olePLJdnuZiwgpAjSGscQWcEPIEIaSXEHJEdKyMELKVENLE/6v9+l+JsJq4X4FcIRR/OAabKTlCakbBCTjngf/45WOyDdoVQiiFkr4pRvz/fLpPnopYNa+AJuKBbwGwIe3Y/QC2UUrnAtjGv2dMAiGEIpcHHuAFXKChzDrGp7WH0Lr1cMcw7vrvvbLY4CuABmKjYRXde3KFsRKbyCp8gI4r4JTSdwGk51ltBPAk//pJADfm2K6CQe5NTF84CrvZkHiAqKkKLRcIHjgAGHX5jSgGIzE8/PbpxAaqlhuIjYbY65VrI9kfjsJs0MEgUxbSVJjsI7+aUtoFAJTSLkJI1WgfJIRsArAJAKZPnz7J02kXuWPggXAMlQ4zPn/xTLzX1IdL5qkrjWqqiFcfVUX5nYTz+HvN+OUbp2A36TXfQGw0dKLeL66APB64NxRVbQaQ5I8cSumjlNI1lNI1lZWVUp9OdcjtgQsx8GX1Jdj//atQ5bTIYodciJtH5bsCT2jd6wvHVBl/zQVC5onZoJPNA+9xh1BiVefKc7IC3kMIqQUA/t/e3JlUWFiETcxIDFv+cRZfynMc1h+OwqZS7yPXpPfEkBq96OFRiPFvAAhFuObgMyvs8ASjiIqbheeBSCyOD5sHcMGssryeN1dMVsBfBHA7//p2AC/kxpzCwyrKA9/80jG8dqQ7r+f3h2OwGQtv6S7mJzcuAZDMB84XOlHrhELMQAGAIO+Bz67k6hCGA/nxwk92e7CnZRB7WobgDUVx6bxRo8CKZtzHPiHkaQCXAagghLQD+AGABwH8LyHkXwC0ArhZSiO1jJwhlHicIhCJFax4CHz6whl4r6kPLf157koomkaj1hjsVBEK2Or5lhJD/gjKHdLvRQjj3JbXF6PEZsS6OeocZTfuXUMpvXWUL300x7YUJAa9Dia9Dn7RJmY0Fs/LjngwGgOlgLVA469iHGZj3j1wn+ihrfVJ9KPRWG7HqR5vov5gOM8bmQfbh/HjG5eoNvuK/eUqAK6hT/KP2R+JoSgPAq7mCrRc4zDr8y/govPVFhfW5rHAL29Zjr0tQyi1Cy0N8r+ROaNMeYNVJor6Eh81SInNhK7hZE9qf54204SHhrXAY+AA4LAY4AtF8zpk15si4IVVQCVQZDHi8gVVqOCn8nTLMB9TTf2/02ECrgDWz63AO6eSg43TG8xLRbKEW703cK5wmI2IxilC0fxlQYgFvKZAPXCBumIrHGYDTnbnv52BWsMnAAuhKIKPLa7BX3a2Jt7nwwO/5Q8fJJbthVgBmI6DvwaeYDTR3kAq3jrRg3dO9rEQigidjmBBjRPHOt2Snyt9lVWkYg9cvZZriPMbU3NQpfbAg5EYdp1Ndkco9DRCgAuhAMDrR7vRUGrFZfOlSyu7c8seAKl9ZwpdwAFgYW0R/r6/A/E4TUmxzDW+tIwvNXvgLISiAKxpaXyffPRDvHSwU7Lzne33pbxnIZTkOLPvPX8En/vT7rycUzyLs6ZAY+BiFtQ64Q1F0Tks7YxSTzB1o9RiVK8MqtdyjZG+jHv47dOSnau5L03AWQgFFc789EGJx1OX74tqi/CFi2cWbCWmGGFSfY87JOl5PMHUFa64nYLaYAKuEKaXp6YymQzS/Wqa0/ouO5l4YEV9SV7O0+FK9S4vnleB71y7KC/nVjqV/EP09SNdI+7RXJLugasZJuAK4be3rsIVC5NxV4OEMUBxCMWk16EiD5VvSkenI/jPT64AIG1a5RlemEx8nj97eCap4gX8sffO4iO/ekey87iD8g5RziVMwBVCY4Udv/vU6sR7KSekC1PoAW6or5QbRmpi44ppuOcjc/gKVWnywYf4oQXP3LUWP964GDevaZDkPGokvYT+dK80KYXpIRQ1wx7/CkIcNpEyH1mcvsY2MFOxmw2glKtSlaI/iZcXj9oSC5Y3NOb856sZfZoj8cGZAcypcub8PCyEwpCcIQnGS8XjFH/Z2YoBXzjxx1LojazSETYT/76/Q5LWpl4+x99pVm/qWr7wSlQPcbDNperMEzHM/VIog77cC/hLhzrx7b8fBgBUF5nR4w4VbBe80RAE/LvPH4E/HMWmS2bn9Of7QlHoiLpT1/KFX4J6iF53EM8f6MQta+pxoM2Fa5bW5vwc+YT99SqMMrsJg74wPMEoIrF4TmPhXcPJPhMLa4vQ4+7DxhV1Ofv5WkD8QBNfr1whjO9Sc+qalFw6rxLvnOqDw2xINFvLJT98+RgA4PPrZ6Gxwp7zn59vmBugMPZ970r8eONiALnvzOYXxb4X1xXh4Pevwm3nszmlYsSdGaVI5fSGoiznewwev30Njv9oA6wmfc49cH84ilcPd+FzFzVqQrwBJuCKRGitOeDLbUGDOPvEYTai2GZknmAa4tg0Qe6vjU/FA3TzgVGvg9Wkh92kz/mIu6YeLygFVk0vzenPlRMm4AqkoZQr6tlxegA9OWyvKQ4JOFTcwEdKxB64FMMFmAc+MWym3IdQTvZwaYnza3Kf2SIXTMAViLC8+9HLx3DBA9sQyVE2RKeoCpAVkGRGLK5SDBdgAj4xbBKEUE51e2Ax6jBdxQMc0mECrkCKrUYY9cnl+/P7O3Lyc8Vl3ExEMiMOb0iRysmFUFjq5njYJNjEbOr1YnalY0S+uZphAq5QIrFkJWAumtyHo/GUCjQWQsmMOC++1xNCKJpbEfGFpCkQ0hp2CTzwHndQc5OPmIArFCHEUeEwT2nMVIcrgHUPvoXDHa6U48wDzwwhBP/2sflYUONEc58Pl/5ie85+9q6zg+hwBVj4agJYJdjE7PeGUek05fRnyg27kxTKM19ai0Ptw3h2b/uUNjKf39+BDlcAD799JuW4mucASs3dl89B64AfJ7o9OZ3ReMsfPgAA5oFPALvJgEAkdwIei1MM+kIot2urcRvzwBXKgpoi3LKmAbXFlikVlAghgY6h1DamUrar1QK52jgWEJflDwe004tDKmxmfUrPnqni8ocRp0gMT9YKzBVQONXFFvS6Q6CUTipn22zgBZzfwHz8s2twus+LmiI2wmss7r9mAfa3uXC234dwND7lB16PJ5nTX1eirTisFNiMBoSiccTiNCebjv1ebkM6X4M78gVzwxRObZEF4Vh80r1RhE04YQL64mlFuOvS2ayAZxyqnBbcsa4RQG48ZiGF80cbF2PTJbOm/PO0jpCp4w1GccefduHD5oEp/bx+L/cAZSEURl6p4YfdTjaMkr4MLbVpawkpJcVWripzKgJOKcWfP2jBiS5u2vpFs8sl7fWuFYQ2x029Hrx9sg/3PL1/Uj/nVI8HZ/t9CQFnm5iMvDKzwgEAON3rxZJpxVl/v3gCt8Wog4VNoJ8wSQGffD74rrOD+P4LRxPvtZbGJhXC3s3/7G4DMPmsqat+/S4A4HvXcWPrtDZ9irkCCmd2pR1mgw5HOoYn9f1iD5x539lRwl8vwQP/zbYmvHmsJ6uf4RJ57yU2I8tAmSBL64thMujwzN52AJhy8dN7TX2ocJhQZNFWH3Ym4ArHoNdhQY0TRzvdWX/vvtahlNih4FEyJoZwve7csgdb/nEWD209hfufO5TVz+gTb14y73vCzK504N8/vizxfqpzSref7MPnLmrU3PhAJuAqYFFdMY52Dmc9p/GffrcDp3q8IAS4YXkd7lw3UyILtUmJ6IG3+SWuj/TcCY74er+pH7E4Tek/M62UCXg2LK8vSbyeTFFPehXthiU1U7ZJaTABVwEzK2xwB6PwZMiL3fziUVz167EneK9oKMFvbl2JW85jA3SzoSjDiiUsyufu94Zwtt+HFw6k9qp5v6kfn/7jTjzyzpmUzedpLH0wK2aUJ5tOuSbRlya9GVmDhppYCbCAnAqocnKZKA+8chyfXduIRXVFia9t2dECAAiEY7COMt+Szb2cHJnyj4WhxJ5gBGt+8mbi+NrZ5bAa9Tjd601Uzp7s9qRU0daVsNz7bCCE4L4N8/H77WcwNInOkOnNyISaCC3BPHAVUMUXH/x1dxtufezDjJ850Z0aIxdXEkai2YVeGEn+dMd5KQ9AIZ/eHUxdDb17qh9ffmofbvrdjsTU8+7hIJp6vYnPsAKe7PnyZXNw16WzEYjEEORL61873IWP/HJ7xkZjlFLE49z9PuTTfsUrE3AVUFWUTH0KR5PCLL6BhU1O4eYVLx8zhV4YE+Py+VVYIBoAIAh4IK1T3jun+rDv3BAA4HQfJ9q7WgbhD0exYTEXe2UCPjmE7Cnhnv7mMwfR3O/D8a6RXTq/8vR+zPr2qwCkaQesNJiAq4BKR3LpXWRNRr06Xcnl+bEuN6KxONb9/C1sfvFoSu6y4BEyJgf/TMT0MhvcwQgOtbvgTdtUO9jmSmQ4NPUkve7L51dh06WzMLfKgTlVjrzZrCVKbdxexKAvDEpp4jofaB0a8dlXDnUB4DxxsYD/4p+XjfisFmAxcBUgFm2nKI+1ddCfeH24fRh3bNmNruEgtuxowbXLahNf8wSZBz4VhADUzAo7Wgf9uOG3/8APb1ic8pnWQX8iZn5aFDZZWFuEVdNLsfXrl+bLXM0hVCN/4c97UoaSHGhzjfYtcAej2Mrn7J/48QbNFrBNScAJIS0APABiAKKU0jW5MIqRirhvSTQWhzsYQZHFiPYhTsAX1hbhsKjQp9xuSgmhfIJln0wJYQ+itji5EtqXwfuL8a66eHj0wtqiEZ9jZIewchGLt9Wox55zI38HAi8c6MD2k30wGbRdfZyLEMrllNIVTLzzQ8uAH8s2vwF/OIp+DycUC2u5GK1BR/D1K+dhwBdG1zB3s2/910tw/4YFstmrBX7+z8vwwxsW44JZZYlj4gfmyuklmb4NADC/WjsDdOXCaTFCSAj6wfWL8PI963HfhvloHwqgTbQKFbO/lfPO/3bX2nyZKQssBq4SXr5nPS6dV5l43z4UQL83hGKrMZFfXOU0J3JnhdL76mKL5qrP8k2Z3YTbL2qE05wMXzX3+RKvZ1c6YE9L1bxlTT2euWstppdrL/dYDoR9iKXTirFkWjEuml0BAHj/dD8ALutq84vJnjPHu9ww6gmW1GXfP0hNTFXAKYA3CCF7CSGbcmEQIzNLphXj4rkVifdX/fpd/NeH51DuMKGK7+1tMeoTxQo7zgxAryNsfFcOGW2OqMNsGFFluWRaMc5rLMv4eUb2rJlRCgCJGoh51Q7MrLDjhy8dxcluDz5sHkjURADAiW4Pqpzad16mKuDrKKWrAFwN4G5CyCXpHyCEbCKE7CGE7Onr65vi6QqbTM2oyu2mRIzWqNdhBi/g7UMBXL2khvX9ziGjdcSzmfQjugyy2Hdueeyza/Dsly5KtJklhGDLHechGIljx5l+tAyMDKVUF2mr82AmpiTglNJO/t9eAH8HcH6GzzxKKV1DKV1TWVmZ/mVGFmQqxym3m1Fm54TdZNCh3GHGw7etwvXL67A5LVOCMTV0ozwM7WYDSmypZffza1jsO5eU2k1YzXvhAtPLbHBaDDjb78OxDM3eaoq1X/k66fU1IcQOQEcp9fCvrwLwo5xZxhjBjAzx1DKHKREDv2Yplzp47bLalDRCRm6YXWXHRbPLsXJ6ScqQaLtJP8I711rbUiVCCMGsCjvO9vvgzjB0o7oAxgZOxQOvBvA+IeQggF0AXqGUvp4bsxiZOK+xDO/dd3nKMT0hqCuxYvd3rsBdl7JRXVJiNujxly9ciBtXTEs5bjMbEvn5q2eU4re3rZTDvIJkZoUd7zX142B7MitICJ0IPYS0zKQFnFLaTCldzv+3mFL601waxshMQ5kNj35mdSJ1zceXdFc6zSzenSeml9sgvtQOswHX8qufH1y/CNctq5PJssKjscIOgFsFCf3Dn797HX79ieX41IXT5TQtL7AUBRVy1eIaVBdZsPHhf2Dl9NLxv4GRU8wGPepLrWgb5HLtbSY9ltYXo+XBa2W2rPC4fnkdWgf9uHPdTCyZVoyb13BFazetrJfZsvzABFylLG8owbv/djkayliDJDn46Y1LsfPsAB5++wwbkyYjsysdeOiWFXKbIRvszlMxrEhEPi6ZV4mV00sQjVEsq9d2sQhDuTABZzAmidNixLeuWSi3GYwChpXSMxgMhkphAs5gMBgqhQk4g8FgqBQm4AwGg6FSmIAzGAyGSmECzmAwGCqFCTiDwWCoFCbgDAaDoVIIpZm6TEt0MkL6AJyb5LdXAOjPoTm5gtmVPUq1jdmVHcyu7JiKXTMopSMGKuRVwKcCIWSPEgcnM7uyR6m2Mbuyg9mVHVLYxUIoDAaDoVKYgDMYDIZKUZOAPyq3AaPA7MoepdrG7MoOZld25Nwu1cTAGQwGg5GKmjxwBoPBYIhgAs5gMBgqRRUCTgjZQAg5SQg5TQi5X2ZbWgghhwkhBwghe/hjZYSQrYSQJv5fyQdVEkKeIIT0EkKOiI6Nagch5Fv89TtJCPlYnu3aTAjp4K/ZAULINTLY1UAIeZsQcpwQcpQQ8jX+uKzXbAy7ZL1mhBALIWQXIeQgb9cP+eNyX6/R7JL9HuPPpSeE7CeEvMy/l/Z6UUoV/R8APYAzAGYBMAE4CGCRjPa0AKhIO/YLAPfzr+8H8PM82HEJgFUAjoxnB4BF/HUzA5jJX099Hu3aDOCbGT6bT7tqAaziXzsBnOLPL+s1G8MuWa8ZAALAwb82AtgJ4EIFXK/R7JL9HuPP93UAfwHwMv9e0uulBg/8fACnKaXNlNIwgL8CVx3DswAAAt9JREFU2CizTelsBPAk//pJADdKfUJK6bsABidox0YAf6WUhiilZwGcBndd82XXaOTTri5K6T7+tQfAcQDTIPM1G8Ou0ciXXZRS6uXfGvn/KOS/XqPZNRp5u8cIIfUArgXweNr5JbteahDwaQDaRO/bMfYNLjUUwBuEkL2EkE38sWpKaRfA/UECqJLJttHsUMI1/Aoh5BAfYhGWkbLYRQhpBLASnPemmGuWZhcg8zXjwwEHAPQC2EopVcT1GsUuQP577D8A3AcgLjom6fVSg4CTDMfkzH1cRyldBeBqAHcTQi6R0ZaJIvc1/D2A2QBWAOgC8Cv+eN7tIoQ4ADwL4F5KqXusj2Y4JpltGeyS/ZpRSmOU0hUA6gGcTwhZMsbH5bZL1utFCLkOQC+ldO9EvyXDsaztUoOAtwNoEL2vB9Apky2glHby//YC+Du4ZU8PIaQWAPh/e2UybzQ7ZL2GlNIe/o8uDuAxJJeKebWLEGIEJ5JPUUqf4w/Lfs0y2aWUa8bb4gKwHcAGKOB6ZbJLAddrHYAbCCEt4MK8HyGE/Dckvl5qEPDdAOYSQmYSQkwAPgngRTkMIYTYCSFO4TWAqwAc4e25nf/Y7QBekMO+Mex4EcAnCSFmQshMAHMB7MqXUcINzHMTuGuWV7sIIQTAHwEcp5Q+JPqSrNdsNLvkvmaEkEpCSAn/2grgCgAnIP/1ymiX3NeLUvotSmk9pbQRnEa9RSn9NKS+XlLtxubyPwDXgNudPwPgOzLaMQvczvFBAEcFWwCUA9gGoIn/tywPtjwNbqkYAfc0/5ex7ADwHf76nQRwdZ7t+i8AhwEc4m/cWhnsWg9uiXoIwAH+v2vkvmZj2CXrNQOwDMB+/vxHAHx/vHtdZrtkv8dE57sMySwUSa8XK6VnMBgMlaKGEAqDwWAwMsAEnMFgMFQKE3AGg8FQKUzAGQwGQ6UwAWcwGAyVwgScwWAwVAoTcAaDwVAp/z99mYeu2Q1LSgAAAABJRU5ErkJggg==\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def noisy_temp(noise=1., d=0.05):\n",
" t = -d # time\n",
" while True:\n",
" t += d # We increment time.\n",
" yield 15. + 10. * np.sin(t) + noise * 2. * (random.random() - 0.5)\n",
"\n",
"# Let's show how this looks.\n",
"xs = []\n",
"for x in noisy_temp():\n",
" xs.append(x)\n",
" if len(xs) == 400:\n",
" break\n",
"plt.plot(xs)\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "ssGleNfZ2HJh",
"nbgrader": {
"checksum": "749ee8adf54454bcff5ea8958e702348",
"grade": false,
"grade_id": "cell-863de9fd6d03582b",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"Let us construct a version of this signal with outliers, where once in 50 readings, about, the sensor has an error that can be up to 10C. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"deletable": false,
"editable": false,
"id": "VJo9baF62HJi",
"nbgrader": {
"checksum": "9843e27c015cb83985d8cc77a52efdac",
"grade": false,
"grade_id": "cell-ca8ffb99d3ee0737",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def noisy_temp_with_outliers(noise=1., d=0.05, outlier_prob=0.02, outlier_size=10.):\n",
" t = -d # time\n",
" while True:\n",
" t += d # We increment time.\n",
" x = 15. + 10. * np.sin(t) + noise * 2. * (random.random() - 0.5)\n",
" # Adds the outlier, with a certain probability.\n",
" if random.random() < outlier_prob:\n",
" x += outlier_size * 2. * (random.random() - 0.5)\n",
" yield x\n",
"\n",
"# Let's show how this looks.\n",
"xs = []\n",
"for x in noisy_temp_with_outliers():\n",
" xs.append(x)\n",
" if len(xs) == 400:\n",
" break\n",
"plt.plot(xs)\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "127--NK02HJl",
"nbgrader": {
"checksum": "8cd1efbf49bb3fc96ee7c50a3880d2d5",
"grade": false,
"grade_id": "cell-4b27edd269fd5ff7",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"Let us compare these outliers, with the average and standard deviation of the whole series. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"deletable": false,
"editable": false,
"id": "Z0pNpWTp2HJm",
"nbgrader": {
"checksum": "76d4503f22b6c9fb7b7886db6cbb2e0e",
"grade": false,
"grade_id": "cell-23a05a2b0d0c3ae9",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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ALRYxRVFME0XxgPHnQuA40NJiIzIzlYZ3VQu8x7tx9Hg3DpAERUQkT/UD3b7qRl6pDt+y96nIu4tf9mZd97oOagfuDr+bTdM38dd9f+Hv4s/DfzxM6KJQ/nvgv5Try6977q3K6cuFdH17I0cuFQDwzC8JJvEGKCitIDVfS0q2ZRvB3uqk5mtNPydlFdPKw5FOAa7o9CJLdyQz+6eDfL8rpRFHWHuGDx9ORUUFUVFRvPLKKzWWk01JSamxnOyECRPqXE62sLCQ0aNHExUVxYABA/joo48AmDRpEv/+97/p3LkzZ8+eZcmSJTz22GP06tXL5K6xBHUqJysIQjDwDxABPA3cDxQA+5Cs9GucaIIgzARmArRu3bprSop1Pxhhr2ygVKcnoqUra2b3AyD4BamIe/J7o1ifmMY9Kx6iSLWO8aFTOJA4BgzOgDSNP/HmcBSKm0+HRFFk3el1vLHlDfam7iXILYjn+zzP1OipOGucLfcCmwk5xeX8kZDKa/87es2+GX2CuZBTwoWcUk5elqyYfS/fhrez7JIyF2sPpxF/IoMP7olm04kMZizdC0BHPxd8Xe158rb2jP9sR7Vzkt8bxUd/nyLQ05G7uraq8bpyOVnzU5dysrWeKwmC4Az8CjwpimIB8DnQFogB0oAPajpPFMXFoih2E0Wxm4+P9aM3rqTSX7tPFEX+PPc/ilTrcNWNZ7DvaybxBiivMJBWoL32xBoQBIFRoaPY/dBu1k1eh5+zH7PWzSLggwBm/D6DdafXUaK7dS3LHu9urFG8Abyd7XC1V3Mqo9C07WT6lZ8PnM+Vw0DrSGpeaTVXyWM/HuDXAxcxGESOXMo3bT+RXkiItxMxge6Miwmodo2f95xnYdxpnv0lwWrjtgYzZ84kJiaGLl26cOeddzYp8a4rtYpCEQRBjSTeP4ii+BuAKIqXq+z/ClhjkRE2kJqKWRkoJVe9hBc37ufThHmoDSH09J7Nf/46dc35KVnFuDuoyS4qp7WX403vJwgCI9qPYHi74ey6uIsv939pWvAEiPaNZmT7kfRq1YsAlwA6eHe4JSx03Q0yqXxc7MgsLKsWEXH/kj1sfW4wZzOLmPLf3bw6uhMP9A2xwkibP6cvF3L7R//w8qgwHurXptq+S3mlLN2RXG1bWx8nBEFgRp8Qfj+Uatr+wm+J1hiu1bGlcrK1iUIRgK+B46Ioflhlu78oipUhBOOBI5YZYsPQVwkj/CMhlZhAd7I08ylV7uW9HetQGwLxLXuTl0ZGMO2bPQB4OKrJLZGiU5KzS1i06Qw7zmZz7t2RtXKngCTkvQJ70SuwF19WfEl8Ujx7U/cSnxTP/O3z0YtSOyUBAVc7VzwdPHG3d6e9V3vCvMMI9Qol0DWQLv5dcNI4WeCdaTp4O2twtb/yUewa5MH+lFwOnM8lz/h3OHW58Hqny1xF5brCtjNZ1wj4sh3JZBeX89zwDszfcBKAtj6SAdHCpX4uK2tGXdg6de2QVhsLvA8wFUgUBKFyafZF4F5BEGIAEUgGHqnTna2AKIomqy6nuJzZPx2kTLWLUvVeXHXjcXYQEYrGosSDqFZXFjLat3BhT7KUXJKcXcyOs9kAXC7U4u9W9wUJO5UdI9qPYET7Ebw64FXytfmczD7JpYJLHMk4QmZJJlklWeRp89iXuo9fjv6CiDRwpaAk2i+a3q160y2gG0PaDKGVa83+yOaKUqHA1eFK5M6nk7vQc14cqXml2KulGPvicj1ZRWWyX7wWVGppTV6nlQcu4udqz21hviYBj2ntDnDD9/Z6Im1vb092djZeXl6yiDcQURTJzs7G3r72+RA3FXBRFLcBNf1lmlzM99VUzb7MKS5Hq0jksuo91IZg3Cum4S+4kC5qmTOsA+6OGtOxVcUkOasYpUJAbxBJziqpl4BfjZu9G91bdoeWMD5s/DX7S3WlJOUlcS73HDsv7GTnxZ0sObSERXsXISDQP6g/kyImMSFsAi2cWjR4PJam4gYp2tN6BdGrjRfp+ZLV6OagxtfVDge1krR8LQHu0vv9R0IqfySkVku2AigoKyBPm4dSUKJSqHDWONv8jOVmKIxCWtO6QV6Jjnu7+1UTa0eNJAM3ir3/69hlhoVfm6ncqlUrLl68SGZmZg1nydQVe3t7WrWqvYFm05mYVWO/DWjJUn+ISvTFr+w9BNSkF2gRBHhskBTLGezlSHJ2iSl7U6kQSMkuwcVeRV6JjpTsYnq19bL4uB3UDnTy6UQnn06MDpUyvSoMFZzIOsGq46v4IfEHHl37KI+te4y7Ot3Fs72eJbZlrMXHVR9EUSTvqmSpqrw5LsJ4nPT7Pd1aIQgC/u72pOaV4qiRLHARPVrFYV74excnshNNM5jC8mtdK0FuQUS0iCDaN5pBIYPoE9gHB7XlQrmaGpU1TfQGEVEU+XpbUrX9Pdt44W40UsZ3rl1E8CPf7efXR3vRNciz2na1Wk1IiLw20VjYtIAbqhh+BarV6BWZ+Ja9j4Iri4aqKj7tdU/0o0xn4InlkqcoyMuR5Oxi3Iwf9uRGjE9WKVREtIggokUEL/d/mSMZR/ju8Hcs3r+YFUdXMCBoAM/2fpaR7UeiEJpOIkbI3HX0a+990+NGRweQXVzOg8aFypbuDqTmaxFVqeSqvqdYGY9ekcX8HQIdvDvQyacTw9oOo6VLSzwdPDGIBioMFeSU5nA08yhHMo7w59k/eXfbu9gp7egd2Jvb2tzGkJAhdAvoZtPlD0p10vqKQRQ5llbA22uPV9vfOdADhUIg4dWhONvXXgJKy5tnsStbxqYFvNICLxfOka9ajqvYF3tDeLVjFFX8do4aFY4aeHV0GG+ugX7tvHln3XEyCssAyZ3SFBAEgUjfSObfPp+X+7/Mfw/8lwW7FjDmpzFEtIjg/dveZ0S7EY3uk9QahWTr6WsTokZF+lez/pztVKaZkCiKlCsT2JT9OYVZh0ClwN7QGY+yh3hh0CSeuT26VvcvLCtk6/mtxJ2LY2PSRl6Kf4mXeAlvR29GtBvB6NDRDGs7DDf72idyNAe0OkloDaJIat61YbCBntJsxM3x2ozhuSM6smxHcrVkn0pKyivMPFKZhmLbAm4QMVBCpuY9lLjQze05zho/l5WFfFQ1RJW0a+HCtw90Z9tVwnMsrQCtTm9aWGsKuNq58nSvp5ndfTbLjy7njS1vMOrHUQwJGcK/b/83nf07N9rYKiNIauLFUWG0dK/u1hBFkbWn1/L2P2+z+9JulKIn7hXTcaoYjArJdXUpp/ar9C52LoxsP5KR7UcCkFGcQdy5ONadWcfa02v57vB3qBQq+rXux+jQ0YwOHU2oV2g9XmnTotIC35ucy97kfdX2udirbvhgf2RAWyJbuTH5q93X7CvUygLe1Gg6c20LYDCIlCoOUKFIxav8ccJ8WzKlh1Su1NVesj6UNwgLDPa+Evfd1seJ8zkldHxlA0dT8697TmOhVqq5L+o+js46ysLhCzmUfoiui7syffV0LhZcbJQx5ZVeW06gTzsv/pkz6Brxjk+Kp/OXnRnz0xjSi9JZOGwREwNX41Zxt0m8AbKK61+ioIVTC+6NvJfvxn9HxrMZbJuxjWd7PUtmSSbP/PUMHRZ1oP0n7Xlqw1PEnYtrtuUQyowCfjXz74xixwuDb3p+VCt32vpcWQgeFu4LSHXbZZoWtm2BiyIGQaqwpjYEc3e3QPq18+bVMZ3o855UQexGhXuqisygDi04myktBp3NLCY8oGlOuzVKDY/3eJxp0dOYt3UeC3cv5Ndjv/JSv5d4utfTVq2YmH+VBb73pdtwdVBhp7oyg0kvSueZv57hx8QfCXEPYem4pUyOnIxaqWa7dxbbT1+xBJ3tVGQXlZllbEqFkj6t+9CndR/m3TaPlLwU1p5ey5pTa/h83+cs2L0AF40Lw9oNY1jbYQwJGUKIR/NYrNNeR8AD3B1wsb95oTVnOxVxzww0lZz45N4utH95LSeyEvn+8HaS85JJyk0iOT+ZovIidHod5fpy9KIeJ7UTbvZuuNm54engSaBrIMHuwXT07kh4i/BbImnNmti0gGcWlmEQJL91nzaSeCsUAnYKpcnyvpEFLggC42IC+P1QKn3aefNf42p+SVnTn0q627vz/u3v82jsozzz1zO8GP8iXx/8mgXDFzCq/Sir+MerRp/cFtYCnyqJIgbRwFf7v+L5jc9TWlHKq/1f5YW+L1SLFukR4mkK4QRo7+tMat6V4lfmJMg9iFmxs5gVO4vi8mLikuJYc2oNa0+vZeWxlQAEuwczOHgwQ9oMYVDwIPxd/C0yloZSeh0Br8ufXBRF3rrLlXWnNjLp16+5aL+R9w8VgjETxM/Zj2D3YDzsPdAoNaiVapSCkqLyIvLL8rlcdJns0mzSi9KrXbeNRxsiW0QS0SKCyBaRRPpG0t6zvU1X8PwjIZUOfi6E+tZc2bQh2LSAJ2UVY6AEhaDg54cHVRMtlUJh/H7jT/V7E6Lo3daLAaE+rJndl9GfbCOjsAyd3oC6GZTdDHYP5td7fuXvs3/zxIYnGPPTGEa0G8GC4Qss7u+trLV+b/fWzB3Z0bT9YNpBHlnzCHtT9zIoeBBfjP6ixrGolArOvjuSNYdTefLnQ8QEupN4MR+DQax1Rmx9cNI4MbbDWMZ2GIsoipzIOkFcUhzxSfH8duI3vjn0DQCdfDqZBH1A0AA8HDwsNqa6ULmICTC1ZxAvjOjIL/su0KvNjUNg9QY98UnxfHv4W/488yeZJVJsd7B7MB6K3vRq2Y/5YycQ7B5c67DMsooyUvJTOJZ5jMTLiRzJPELi5UTWnFpjykbWKDWEeYcR5RtFtG800X7RRPlGNYsch5uRVVTG7J8OAvDXU/3NLuI2L+CiUIKrxvUai7PS8lbcxCxx0CiZGCv5zSNauuGgVvLh36f4flcKe166zTIDtwC3t72dhP9LYNGeRby+5XUiPovgqZ5P8XL/l69b87yhVLpQXhzZERd7NcXlxby++XUW7l6Il6MX34//nsmRk286GxgdFcDoqAC+3pZEhUGkQKurlnhlSQRBIMwnjDCfMP7V/V/oDXoOpR8iPimeuKQ4vjn0jSnBqot/F4aEDGFwyGD6tu7baAlFVV0oXs4anOxU3N/n+u6f09mnWZawjGUJy7hYcBF3e3fGhI5hUPAgBoUMkmYe/9lMawdXwnzqVnnQTmVHqFcooV6h3NHxjitjrNByMuskiRmJJF5OJDEjkbikOL47/J3pGD9nP6J9o03CHuUbRUfvjs3CWr+QU8L9S/ZUaxFoiZ6jNi/gdmotTjWEiVVa3ipl3Sw5TycNl/JKTaGFzQm1Us1TvZ5icuRk5sbNZf6O+Xx3+Dvm3z6fKZFTzOZW+W5nMgNCW5BXWo5SIeBsp+L3E7/z9F9Pk5SbxPSY6Xww9AM8HTxveq2qeDtLop1VVGY1Ab8apUJJ14CudA3oypw+cyjXl7P74m7ik+KJT47no10fMX/HfNQKNT1b9TQJeo9WPdAorTPmqi4UL6ea71lYVsiKoytYmrCUbee3oRAUDGs7jA+GfsDYDmOxV1VP53axV5miUMorDOSWlOPrWv8WePYqe6L9JGu7KlklWSSkJ3D48mESLieQcDmBhbsXmhaUNUoNHbw6EN4inHAf41eLcNp6tG1Ssf2/7LvA2cxi3l57HAe1koTXhlqky5RNCviOs1nEBntKAq7R4mrnes0xtfGB14Srg5pLFvLDWgtfZ1++GfcNj3R9hNnrZzN11VQ+3/c5n4z4hC7+DSutWVxWwSu/H8XF7iTjOgegsb/IhBUTWH1iNREtIoifHs/A4IH1unZl+ndWUTntmsjsWqPU0C+oH/2C+vEar1FcXsz2C9uJOxdHfHI8b2x5g9e3vI6j2pF+rfsxOGQwQ0KGEOMXYxHB+edUJr8duGT63aOKgFcYKohPiueHxB9YeWwlJboSOnh14L0h73Ff1H20dL1+VqaLvdoUhfLEzwdZfySds++OrPP/z83wdvRmSJshDGkzxLRNp9dxMvskCemSoB/NPMrOCzv5+cjPpmPslHamhdJwn3AiWkQQ7hNOiEdIoyS2VV0s7hrkYbEWgTYn4IkX85n81W5m9m/DqfRCVC7aGhM1Kj94N/OBX/FZ3UoAACAASURBVE15xRXrRm8Qzf4BtiY9WvVg10O7WHpoKS9sfIFui7txf8z9zOk9p85T5UoqrbSs8iP8cGYeyeIWUpNceXvQ2zzX57kGTX+9jBZ4ZhOe/ThpnBjadihD2w4FILc0ly0pW0yC/vzG5wHwsPdgYPBABocMZnDIYMK8w8wyA6qsqFmJvUpgS/IWlh9dzspjK8ksycTVzpX7Iu9jRucZ9GjZo1b3dbFXse1MFu+sPcb6I9LCZEGprtoDwlKolWpTFvIUppi2F5YVcjzrOEczjnI0U/ramrKVHxOvlIt1UDkQ5hNWzVoP9wknyD3IosJetdduj5C6zTTrgs0JeGaRlKmz9nAahWUVKNxLcbO71lyrdJ0oFXX7IxZViUDJKynHq5lXx1MICh7o/AATwibw5pY3+WzvZyw5tIQR7Ubwr+7/YkjIkFqHHmYWZ/LVgR9J1yymTHkMVbELHRxnsP2xf+Pl2PAaMq08pLj88znNpzGGh4MHd3S8w+T/TS9Kl9wtRh/6qhNSN3U/Zz+TdT44ZDDB7sF1vldl0TCRCkoV+ylV7mXSHwfI1mbgqHZkdOho7o24l+Hthl/jIrkZlSVqv9p6pa5Kbkm5VQT8erjYudC9ZXepMFwVCsoKOJZ5rJqwxyfFV/OvO6mdahT21m6tG/QgLavQU6St4ExGATohjXLhHAfzNzH2p1PMGzKP8BbhN79IHbA5Ac8uknxllW6OCoprtMAro1DqGkhSXKYHY6nXXBsQ8Erc7d35cNiHzO07ly/2fcGnez9l1I+jcNY4c3ub2xnadigRLSJo59kOpaBEZ5Bif4vLi9lxYQcrjq0gPikeg2hAJbTEo/whnPXDmN493CziDVJ8sq+rHasOXsLHxY6f9pznldGd6NK6aUR/1AY/Zz8mR05mcuRkAJJyk0xiHncuzmQ9ejt609G7Ix29OtLBuwMdvTvS2q01GqXG9KVSqCgsKySrJItLhZfYkXKEDM06yhTHMQhFqBWO3B48nEkRExnVflSDFlVDfV1IvFQ9gS33Bpm2jYmrnSs9W/WkZ6ue1bbnafM4lnmMIxlHTOL+59k/WZawzHSMs8aZTj6daOvRFn9nf/xd/PF39sfP2Q97lT1qpRq1Qo0gCBSWFVJQVkBheSH52nz+OXeC1Yn70SkuUSGkItpLxuS3R5R09O5Idmm22V+rzQn45Sot0NRKgbyKQlw11/rAVYo6WOCiCKkH4fAKNtuvRUMWzpRiWOyA3tkXZcQd0GEktOwGdbTomxo+Tj68MuAVnuvzHH+f+5u1p9ay5vQak6V4Pdp7tmdu37m0cbqNN1YVIRgrEI+JCrjheXWlrY8zO85m89zKwwC8teYYq2b1Mes9rEmIRwgPejzIg10eRBRFjmcdJz4pnsTLiZzIPsH/Tv2PjIMZtb6eSmiFo743norenH55rtkWTt++I4Lbwlrw6A8HTNvySppXpqq7vTu9A3vTO7B3te05pTlXrHXj992XdpNWmEZpRe3XuwSUKBUtUIkB2BvC6eQdwfxxY4ltGW2xapg2J+DpVQQ8zN+VDbn59feB51+ChJ/g8HLIOgVKDV5tB5MheLP0aBGO+jJCy1Ppt/1jhG0fQYtwGDAHwsY1eyG3U9mZ6oN8Jn5Gcl4yJ7JOcC73HCD5JTVKjcnHGNkiEkEQWHM4FYGD/PuuKFKySwgPuPbh2RCu7hrj5WQbMyCQQhYrywhXJac0h5NZJ0ktTDXNfMr15ej0Opw1zng7euPn7Mf6Q3oWbzF1OjRr1IuDRsmQMF86+rng5axh+5nsJmuB1xVPB0/TQnRVRFGkoKyAtKI0Lhddpkxfhk6vQ2fQIYoiLnYuuNq54mrniovGha//yeKbbVfKVrS286R/cM+rb2dWbE/A868scMWGuPBHtg43uxpcKMobRKEYDLBjIWyaB/oyaN0bRs+C8DsQHDww5JfyYUK86fDdT8bgm74Ftn4Iv9wPPmEw8HnodEfd0t+aKIIgEOIRUqtU8iLjImafdt7c3c38VsfV5U89aqioZ2t4OnjSK7DXTY9bsTMRZztVtXUac6JRKdjwZH/yS3REv/lXs7PA64ogCFJZAHs3Onp3vOnx+SXVi9+l5ls+Wq15m4k1UNWF4u8hLXbVFG+svF4mZm4K/HcIbHwdOgyHxw/BA+uh2wwwZtp5XBWDXKhwg5jJ8NhuuPNrEA2SkK+cAdoC8724ZkBlFIpLHepM14U5Qzvy5G3tTb9fL238ViSzsIxWHtJD897ugRa7j4u9CoVw42qTtyIZhdXdt88MtXxlS5uzwC8XaOkR4kmwlxNZhj8BuK3NtRmTqpriwFMPwY/3gE4L47+EqIk1WtD2aiVdgzxwUCvZdiaL4kqLR6GEyLsgfDzs+Bji3oK0w3DPMvCLNP+LbUJsOZXJ9G/2MDY6AEEAJ41lPlpujmqeGNKeBRtPA9XDtW51Mgu1+LjYseHJ/ha9j0Ih4O6oIdfGLfC6kp6vpY23E7OHtGN8Z+v0rbUpC9xgEMkpLqdbsAfv3xXF6hO/0sW/C209215z7DWJPKf/hiUjQamBB/+E6Ek3dH/8+mhvUwOC4qunrAol9H0K7l8DuhL4agic3GCeF9lE+Wn3eQD+OZ2Js0Zl0VolgiDw0cRoHNRKWcCrkFFYRguX+mdH1gV3R7VsgV/F5QItfdt7W028wcYEvECro8Ig4ulkR0peCrsv7eaeTvfUeKyq6iLmyQ3w40TwagMP/g0tapfE4mwnWZnX9TkG9YZHtoJvJ1h+H5xYW/cX1UwoMyY45ZXoLOY+qcr4zq0YGu4rC7gRg0Eks7CMFq7WWdR1d1CT04Da7LZGabmeAm1Fg8oL1AebEvBs4wfK21ljKgF6d/jdNR5baXm3KT8p+ar9IuD+deBa+xKhTnZSKnTxjVpNOfvA1NXgHw0rpsGx32t9/eZCTnE5SVXazdWlz2JDcHNQk5Jdwod/nbTK/ZoyuSXlVBjEa6J0LEVbH2dOpBdgMNS+Q5Itk2WsU+9j5bwQ2xJwYxKPh6OaJYeW0L1ld9p4tLn2QFEktiiePopE/pX+Mjh5w+RfwL5uIW+VFriU3HMDHNxh6ipo2RV+mQFHfqvTfZo69y7eVa3hc22aBpiDymbTH8efobzi1m64m2kUEGu5UGKDPckt0XE2s8gq92vqVAq4t4t1M1NtSsBziqU38XzRIY5mHmVml5k1H7h9AdNT3+IHzTyUYgVM+RVcfOt8PyeTgNcibMveFe77FQK7w68PQuLKOt+vqXLyciFw5YFmLSukqqvGUo0emgsZBUYL0EoWeKyxvsee5Byr3K+pk2U0Hq2dl2BTAl75Jv5+ZhkuGhcmRUy69qALeyHuLU47dWOvIZSvA+eBT/3CfRw1SgQBTmcUEfzCWvYk3eTDbOcCU1ZC616w6v/g/LWNY5sjGpWCRwa04eVRYYT6Oldr3mBJ0qp0Tp+zMuGWtgYryxtby4US7OWIu6OaI5eaXn/YxqCy1V9lwTVrYVMCnlNcjoEi/jj1K/dF3Xdt7YeyIvjtYXBtyY8hb3N3+eucd46q9/0EQcBJo2Llfin7atXBWjQPtnOGST+Ae6C0sJnfOA2HzYVWp6e8woCrvZpJ3Vvz11MDCPKyTiODKT2C8DQWU9qbnMsrq49Y5b5NkcoYZGstYgqCQAdfF06mF1rlfk2V42kF3Pn5DpKypTUg76bmAxcEIVAQhE2CIBwXBOGoIAhPGLd7CoLwtyAIp43fG72iUHZRGUr705Tpy7ir013XHvDni5CbDOO/QK+WutDUtZzs1VQuZAL4udYy89DBAyb9BLpS+HmK9L2ZUmCsEe3qYP2MyHYtnNlXpSuSWyOMoamQUVCGs50KRwvF39dEBz8XDpzPY/o3e0yVEG81Fm06w/6UXH7cfR5nOxX2aus2laiNBV4BPCOKYhjQE3hMEIROwAtAnCiK7YE44++NSnqBFjRnERDoFtCt+s6T6+HAMujzOAT3qXdDh6up9IMDlNwoGuVqWnSEO7+CtAT4/V9SwaxmSIExjM/VSpEnV1M13twGqhbUi4wCLYmX8q3mPqmksr/jllOZJvflrUaIcbZZqK2wuvsEaiHgoiimiaJ4wPhzIXAcaAmMAyrrMC4D7qj5CtbBYBDZk5SDYHeWMJ+w6l14ijLhf7PBNxIGvQRcJxOzPlTR3TonNnQYAYNfhiMrYfuCho2jkcgvlR5ajWn9rnu8H97OdresiAz+YAv7U3LxtrKAh/lf6aWaXVxGdlEZYjM1RMzB9drXWZI6+cAFQQgGOgO7AV9RFNNAEnmgxiZXgiDMFARhnyAI+zIzMxs22htwNLWAnJJyssuPVi/wLoqSeGsLYMJiMDYnUCkr64E3TMDPVYl/ziuth4D0ewbCJ8DGN+DUnw0aS2PQmC6USjoFuNI9xMO0kHQrIYqiKZHM2q+/a5Anr42RKifuPJtN17c3smLfBauOobGpmsRnp7J+T85aC7ggCM7Ar8CToijWukKTKIqLRVHsJopiNx8fn/qM8aZkFGp59If9oLpAQXkO/VtXqQVxNg5OrYchr0oZkUZU9WypdjUORp9XtyCP+qUWCwKM+1SqlfLrQ5DZvJJSrrhQGtf/7OmkMSVy3UpUbS/n72aZmtM3ol97bwC2npYq8W0/Y/6mBU2ZorIKvJw0vDK6k1WKV11NrQRcEAQ1knj/IIpiZRbKZUEQ/I37/YHaV503M19uOUdavpa7ekshTYNCBl3Zeemg9L3r/dXOqbS8FQ10nK5/oh9rZvfF00lT/7RujSNM+lGaHfx0L5TmNmhM1qRSwBt7AdHLyY68Et0tt5hWGYM/Z1gHFkyKsfr9PY1xz2nG0qn2apsKbLspxWUVeDppeLBvCN2CLdf78nrUJgpFAL4Gjoui+GGVXf8Dpht/ng40So64KIos33uB0VH+HM3ZTIh7SPV+ghnHwD1ICt+rgsnybqALPNjbiYiWbg0v7uMeCPd8B3nnYeWDYGgeZVILLFw+trZ4GxeQcm6xCnmVYXyTYgOtHsIGUk0UhQDJWVImrrWjMBqborKKaoEM1qY2j8s+wFRgsCAIh4xfI4H3gNsFQTgN3G783epkFpVRVFZBS+9c/jz7J/fH3F/9gIzjNRanMne1PHdHDXml5Q1bxAnqBaP+I7l9Nr1jvsFZkPxSHXYqRaP/41ZaglmFt5aAn8sqxsNR3Wi9WRUKAQ9HDeXGmU/FLVYbpaisolGNl5veWRTFbVzfTh1i3uHUnQvGDuW7M39CrVAzs2uV9PmKcsg+IzVmuIrKno2Y6fPm5qBGqzMw6D+buS3Ml5dHd7r5STXR9X64uE/q7hPUB9o1+lt8XXR6A7vPZVstfftGdPCTIiK2n8mik5nbuDVlkrOKrZY4dT08qqw/FNxC1SEvF2jJKirD10r1Z2qi2TuszueUYKCEP5OWc0/4Pfg5+13ZeeRXMOiklmhXYe6Y4coY3OTsEv67LclUXrVejJgPPh1h1SNQmG6mEZqfn/deIOFiPs8Nt07q/I1o18KZrkEe/LT3fGMPxaokZxUT4t24Au5ZJXyu0qVmy4iiyHvrT9Dj3Tgu5JRarfpmTTR/Ac8upVS5m2JdIf/X7f+u7Kgohy3vS9Ed7W+3+DjGRAdwb/dA3I09GredzrrJGTdA4wh3L5VS/399qEn6w0VR5IddKUS0dGVstHk7z9eXwR1bcC6zmNLypvd+WQKtTk9qvpbgRrbAO/pdiQc/fbmQE+m23UZww5F0vthy1vS7cxP3gTdpLuSWoLfbTYBLAL0Dq1ja+5dAbhIMftXs5nZxeTG/HP2FSSsnEf5ZOHf/cjdz/n6SvhEX2PysFMJ4LrP4Jle5CS06Sv7w5K2wZb4ZRm1eLuSUciK9kLu6WK/7yM2odOVk3SLx4CnGEr7B3o6NOo45wzrQLUiqpJGWr2X4gq2NOh5LczpDKpp2d1fps9+YAt7se2KeysigQNzDfWGPoBCMzyNtPmx+D0L6m9X6PpB2gHe2vsO60+vQVmjxcfQhtmUsh9IPkVaYxqK9i2jl2ooSTX8u5T8J1FCLvC7ETIHkbdJMonVPaDvo5udYiXRj8+g2Ps43OdJ6VAp4RmEZgZ6NK2qW5HKBlmNpBWiNM4023o37N3CxV7Py0d68uCqRH3fbvgsrp7gcFzsVwUbXVXkjhq42awE3GEQOXN6MXlnOnWF3Xtmx+0sozYHb37qp9V2bNcyi8iKe+/s5vtj3BZ4OnjzU+SHu7HQnfVv3RaWQ3kKdXscfp/7gqwNfsaHgJz49upeHB2yipWvL+r9AQYBRH0DqQamK4iNb69QxyJJUJpBYq/pdbaisQ141ucUW+WzTGZbtTEGjVCAIkv+/KVA1KU6nN6BWNvsJfo3klpTj4aQxrXulVylrbG2a9Tt8IbeEXDbjpvGmb+u+0kadVhLw9kMh4PqJDbV1qmxN2UrU51F8se8LHu/xOGceP8MnIz9hYPBAk3gDqJVqJoRNYP2U9cQ6fUh+eSo9v+5J4uXEBrxCQOMEdy+D8mKpEYS+aSwSZRrLl1q7hdSNuFVcKMVGy7tcbyDQwxEHTdOIva5an92We5XmFEsC3rONFwC3dap7Mxhz0WwFXKvTs/nMMUoUuxgXOgmlwvghTvgJSrKg9+wGXV9v0PNi3IsMWDoAQRD4Z8Y/LBi+AHd795ue28GjF33cFmEQDYz6cRS5Dc2sbNERRi+AlO2w+d2GXctMZBSWoTLGADcVPJ00CILtW+BVO0Dpm1DcdViVxUxb7lifW1KOp6OaQE9HzrwzolEX8ZulgM9bf5yOr2zgmQ1vAPBi/6ekHQYD7FwE/jEQ3K/e1y8sK+SO5Xcwb9s8HuryEAn/l3DFwq8Fnk4a9GVBrJ64mrSiNP5v7f81vEpb9EToMh22ftCoRa+0Oj2JF/PJLCzD29nO7AlRDUGtVODpqDH1h7RVCrQ6gr0kH39M65sbFNZi9pD2vGLMf8ivT2G3ZkJusQ4PY+ikqpHdRM1SwNckpFGk3Ei2uI5Wmjvo4GNcLDy1Xkrc6fN4rSNPrhbWjOIMBi0bxPrT6/ls5GcsHrMYZ03dfIyeThpyisuJbRnLGwPfYMXRFXyb8G2drlEjI94HvyjJH5599ubHW4B//3mSMYu2sSc5p0kk8FyNt7MdWTZugReUVhDi7cSa2X15/876d5QyN2qlgq7GaJR5606YugTZGpIF3jRmns1OwIvKKkjJu0i2eiF2hgiGBz4h7TDoYfM8cG8NYeNqfb2q+p2cl0zfb/pyLPMYqyet5tHYR+s1Ri8nDUVlFZRV6Hm+z/MMCBrAv9b/i+S85Hpdz4TaASZ+D4IClk+F8pKbn2Nmko3lc1OyS6zeQKA2+LnZczG3+XY4qg2FWh2uDmoiWro1aghbTbgbi5rtS8nlnbXHG3k05ker01NSrjdZ4I1NsxPwMxlFlCh3gCDipZtFG29jidp930B6Itz2Bihv/qG+2kBPyk2i/5L+ZJVksXHaRkaHjq73GCvrcuQUl6NUKFl2h9T3Yvb6hvnlAfAIgju/lop0rXnK6p18/NyupA0HuFu/fOnN6OjnwpmMIpuuSligbdz6GzeiMpENQGODUSi5xmJpTWXtp9m9w6cvF1Kq3ImvQ3vUYiBtvZ2hJAfi35bivsPH1+o6QpU4lJS8FAYtG0RReRHx0+OrJwTVA393SeTOGxMtgtyDmNt3LmtOreFA2oEGXRuQ6qMMnAuHf4bdXzT8enWgapbjxNhAq967NnTwc6FcbyApq4GJVE0UURQpKNU1ev316+FSZVyejdBizJK8+ccxHlq2DwBPp6bx/jc7AT+bWUiZ4jTjO93Gsge6c1fXVrDjEyl5Z/h7dc66LNRlMvjbweSX5bNx2kZi/BpeUzncXyqmdDT1SkrxY7GP4WHvwZy/55in7VT/OdBxtNSo+eSGhl+vluQZw8Me7hdCREs3q923tlQWtdqVlNPII7EMWp2BCoPYqB2QbkTVDle2VtJgx9ks0/90U7HAm+Y87AYk5ychCqV0DejCgFAfyfresxjC7wDf8FpfR1ReRk8+Pyc9T5Y2nfhp8XTx72KWMbZwtcfbWcOba46Rll/KS6M64WbvxjuD32HWulksP7qcSRGTGnYThUJqEbdkJKx8AB5YD/7RZhn/jcgv1dGnnRcvjapntUVzIoqQc05KdMo4DnkpdCzJ5XtNOqVrNeSf9MfN3ROcvMHFH3wjwD8K7Fxufu0myAd/nTTNG5uqCwUgoqUrRy4VUGRDha1EUay2tuLZRHzgTfdTcB2S8qXEGJPY7lwkJbn0f67W19h2fhuPbOyH0lEFRSJ/3PsHPVr1MOs4tTrJB/vV1iST2M3sOpOvD37N038+zaj2o3BpqJBonODen+G/Q+DHifBwPLhaNiY1r6Scjn6NWK417wIcXQXnNsGlA6DNk7YLSnBrhdLRi3BvFZeychAy8yCzRMoLMFSKiQBe7SCwuxRq2n4oOHk12supC5/EnzH93FRdKABrZvdj+IJ/bKoyYX6prlr/S3fZAq8fl4qPI6Ai3CdcCqXbsQgi76rW7/JGXC66zN2/3A2AXqxgybgljGg/wuzjfHNcOE+vSCDU90oIolKh5LNRn9Hzvz15Y8sb/Gfofxp+I1d/mLwCvhkmifiM9dd0HzIn+aUV1p++F6bD0dVSeeCLe6RtLcKh0zho2RVadpHK7yqlcTlW6Bn98gae7hzK40PaS5Z60WVIOwxpCZB6AE5tgEM/AIIk5qHDIHRErT9HjU1TdaFU4mqvZndSNr8duMiEJlTwrL5cHdlUdbG2MWk2Al6hN/DAsn2czUvE3b4NdkoNrH1a6iM59O3rnieKIoLRL6436Llv1X3kafM4/H+H6eTT6UoGp5mZ0KUVu8/lsPlU9Vah3Vt2Z2r0VD7b+xlz+87Fy9EM1p9fBNy1BH6aKLlTJv1gEjNzIooi+aXl1vnw6rRwZCUk/CwV9EIE30ipOXX4ePC8fqEwO5USb2c7UvOM/3SCAC5+0lfoUGmbwQDpCVJS1KkNEPem9OUfLSVMRd4N9k23MURTdqEAONurKNRW8PSKBJsQ8MrGMQCu9qomU+elaYyiFqTla9lyKoNyxVl8HcJg+wI4t1n6h3bxq/Gcn4/8jN3bdqw5tQaAedvmsfHcRhaNWESkb6TFxLsSdyc1ucW6axYtn+31LKUVpXx14Cvz3Sx0KIz8D5z+U6ohboGaKSXlenR60RTraxEK0yH+HfgoHH5/TPp94Avw2F54dBv0e+aG4l1JS3d7LuXdIB5coYCAztK1Z26GZ05K75/BIBkGH3SA1Y/Bhb1WD9WsCa2u+oKgr2vjdYGpDVXj082yaN/INEX/NzQjCzyrqJiL9lMwCAV0sG8JG9+QLLFuD9Z4/PeHv2fqqqkArD+9nhZOLXht82tMiZzCA50fsMqYK3sFlpTrqzU+jfSNZEjIEBbtWcQzvZ5BbS5rOfZB0JXCXy9JFvj4L8GMD6l8S3agzzgO2xYYuyhVQIcR0OP/pNDQetRzD3B3MNVtrhUuftD9YYh9SHKx7F8GiSvh0PeSu6b7QxA1SWq20QhU9b8C+DVxAa86QyirMDR6z9SGcjH3igXeVJJ4oBkJ+MmsZAyCFMIzXp8hZSMOfUeypK7ix8Qfmb56OoNDBpNVksXB9INs+X0L/s7+fDryU5NLxdJ4GF0NuSXl13SufqrnU4z+aTQrjq5gStQU8920979AXya5A5QaGLuoxveoruSX6vhuVwpgZusv44SUQXtsNaidpIdQ95ng1bZBlw1wd2DLqcxqLrRaIQhGv3pXGPaO9EDZ+7WUNBX3JnR7QBrfdWZ9luLqiA5lY9eg0eZD5inIPg0FqdIaQ1GGFFBQoWVWZi5TNIXSWJctAmdPsHcHB3dw8ADPEPBqL/2dNY3bUag2XMgtNZXIaCohhNCMBPxczkUAPMtnclfBRslCc6tea/tY5jGe2PAEG89tZGDwQP649w+e3PCkyVWx5t41uNlbL3a58g+dV6KjlUf1fSPajyDcJ5z3tr/HvZH3XmlGYQ76PQN6nSSMggCjF9YqO/VGvPhbImsT0+jZxpP+oT4NH2P2WalRxeEV0j9wv2eh12Pg6NnwayMJeEm5nsyiMlYduMS9PVrXPXLDzkVqMt1lOpzfCTs/lZpN7/gEIu+RxmulRc+qFrjVMxxzk6VG25f2w+UjknAXXdWr1c4NnFtIC+gqB7QKBy6JUkZyG4Medc45KM2TooZ0V5WAcG0pRQb5RUoL0i27gnuQ+RvXNoCLuSVEtnRjy6lMWcDrw/n8SwBEih44lWdB2Jhq+xPSExj87WAEBN4d/C5P9HwCR7UjUb5SsZ+pUVMZFTrKqmOunGotjDvN51O6VKtcphAUzO07l/tW3ceaU2sY22GseW8+4HkQDZJIluZJ6ffq+lvOafmlOGmULJ3RvWHWX8452PJvOLxcmiH0ng19njR7KF9LYzbsG38cY+3hNBSCwMP969khSRAgqLf0lX0Wdn0GB3+Q3CttBkHPR6Hd7WaZ6VyPAu2V8qwWr/9dViS18jsTB2c2Sq0JAVQO0gOr3RDwDgWfDpIV7RpwjWvp818SWJkpGV1rR/clPKCK4VReIn0Osk9LxeeyzkDWKdj7X9hpLIDl4g8hA6DNQGgzwOLhsTeiMga8TztvzmUV0bZF05kxNBsBTy2UBHyYIhmDoETRfqhpX0J6Ard9dxuOake23L+FNh5X/lHHdRjHgbQD5gnZqyOVLpS/j11mT1IOvdt5V9s/MWIir2x6hfe3v29+ARcEGPQiOHrB+ufgu/Fw95J6T/3zS3UM6OBTf19mQZr0MDn4HShUkn+7zxPgYpli+JV1WtYeTgPAXm0mcfVqK3VJGvQS7Ptacq/8eI+0sNr9EYiZbJHolaoulPAAM19fFCXL+sxGSbTP7wKDDtSO0hpEz1kQ1At8PSrMfwAAIABJREFUwmo9k9Oorrzf1yT0aBylyCm/iOrb9Tqpxs/FfVLt+zMbpXIRID0w2gyUvoL7ghVn0jnF5ZSU6wn0cGTDE/2xUzWd2I9mI+CXi9NAVDNOkUi2Zxd8jFPtPZf2MOz7YThrnImfFl9NvAEC3QL5Ztw3jTHkalOtmpIaVAoVs2JnMefvOZzMOkkH7w7mH0SPR6RMxNWPwed9YMxCCKt7oa4CbUX9Fi9zUySLdf8yaXGy6wzo/6zFfcj+btULbRWVmTmt29FTKmfQ50k49jvs+hw2PC+VNmjZRfKVh09o0KynKpUulDnDOjC5e+uGX7AkB87GSyJ5Nl7yYYOUrdprFrQdIvVhVdWv4uTzwzuSU1TOhqPpFJfXMiJKqZbCOP2jpbUQgwEyjkrRZue2wMHvpaxrQQEBXSTLvM1ACOxR73HWhsoIlFYeDtesZTU2TWs0NyBHm44HDnRSXOSo/xR8gPP55xn14yg8HTyJmxZHsHtwYw+zGp5OGibFBvLz3gumKmZXMzlyMs9vfJ5vE77lnSHvWGYgEXdKkRS/PgTLp0g1VEbMv2YN4Ubkl+rqljySlgDbP5ayJgVB8hkPeE5avLICXldFChRqLdQhRqmWEski75Isx5Pr4PgfsPpR+PMl6DIVOk8D73YNuk2h0QCYFBtYvygIUYTMk1LM+6k/4cJuEPXSgmLbwZJgtx1stp6rbg5qnhkayoaj6fV/eCoUkl/cL1JytVWUw8W9kqAnbZGilrZ+ILl2WveUxDykv/QAMGP01WVjA++rjYKmQLMR8OKyVMIpBpwIG3If2gotE5ZPoFxfzrrJ65qceAMIgsDrY8P5ee8FcoprFvAAlwBGth/JVwe+4pUBr2CvslB4WIuOMHOTVHpg8/vwaQ/o+4QUNufgccNTtTo95RWGmy8CVpRLArbvG+kfTOMs+Yd7Pgpu1k3muLpTUKE10rpbdZO+Br8CSf/A3q+kTOHtCyURCp9gTEKq+0Os0gJ3rksCT0mONI5zmyUrO0+KIsIvEvo9De2HSbMFC+VDVFqrxWVmeu9VGgjuI33xEmgLJFdLpYW+8TXpODs36ZiQ/lK5hBadGrQ+UdnhqcENTETR7AuzN/00CILwDTAayBBFMcK47XXgYSDTeNiLoiiuM+vIrkJbkUYAAty/DoVHa96Of5n9aftZPXG1ZVwPZsJercRRoyT3OgIO8HTPpxn87WCWH1nO9JjplhuMUg19n4JOd8CGF6QSvFs/gi7TpGmze81T84IbxX+LImSekNLSDxn7kbq2khKsuj0ohY01MoGeDpazwGtCEIzT+wGS7//oKjj6G8S9IX35x0h+3MAeUhp/LdxJhdoKNEoFdqobiK22AC7tMwraZql0ACJoXCCkn/S3bz+0TjOvhmB2Ab8ae1cpGq2DsRRGYbqUtZu0BZK2SsYESOtAQX2kJud+UZKbyMWv1mJa2WPVqzblcUURSnOlxe7M41J+w+Wj0veJ30kzBTNSm8f5UmARcHVPsI9EUbTKymCFXk+hIZcglOAbzpGMI7y//X2mRU9jXMfad99pLDwcNeRcx4UCMDB4IO0827E0YallBbwSzxCYvBzSj0ghcXu/knyLwX0gdDgE9pQaRzh6gSBUT+Ax6KWwsrRDcHG/1MYu55y0MBk6XAq7azvYYlZdXVg1qzcl5XreWXvcOhZ4Tbj6Sw/HXrMg77xU0+XkOtjzlTQbAunBGdhDshQ920izFQcPKW5aZUdOmcDGY+n4O4pQnA3FmVCYKl0vJ0mKErl8VIroAFCopQfDoBclt0JAlwaHkdYHJ2O0zNVJSBbDxe+KOwukwmfJWyUxT9kOx/935VhHb2kR1aud9H67BUphkI5e4OAprXEoJcHOLCzD00nz/+2dd3hUVfr4P2dKem8kIQmhEzoYSkAFRERcXLGjouiqiG2/yoq67trX+rMt69oQy+IqurqgaxcUVEQh9NBLgDTSe51yfn/cmckkpEySqeF+nmeembm55eVw573vec9b0GOCmhJFQdeXKzOculJlZlN2tPnVUNl8HX2QUqdn8HnKjNTJdPq/KqX8UQiR6vQrd4EDxXkYhYk+uhgMfsHc+NmNhPuH8/x5z3tSLIexJgC0hxCC60Zfx0PrH+JI2REGRvUsicVh4kfCJa/DzAcVt8f+L5VFOCv6YGoCE4nV+POZXy2DvzPCpwXNlf20fsoUNeN2GHahyyJKusu4FMU1FGqpy+FxIlKUfq1T/6i4m07uUnzROb/BsY2w+z9tHhYFrLV++X+t/qjRKw/bmKEw+kpFWadMdmlBM0fRaTX4aTW8tPYQAXotu/Mq+efVzinZ7BARyUpU0Nirle/1FcqDrjBLGfuTWUq2rbWiZTs8YXnxeDs7CK1yragBSg2dqAHKK3YoRKS6NLy0J4/lO4QQ1wGZwJ+klOVt7SSEWAQsAkhJ6d7q+Y58xbKIDe3Pw+sfZnPeZj687ENigmI6OdI7iAz2I6+8ngaDqd0wvBvH38jjPz7Ost+W8fc5f3evgOEWl8fMh5SokcI9UHEcY2k2G3/dih8GJOEkx6UQmHi5YsHHj1YsRp33JDW0R2iAvkUqtFeg82v2mWfcrmxrrFYs6uoCxbprqARTI9/uOkF2USWLzhmB0Ac21zcP76tYjl4w22mPJktru6e/2g/AY79vJDrEQ71UAyPsfOh2NNZAZa4ys6krVV71ZcpsU0pWbTmBn1bDJen9lJmR/SsoCkITPfY76K4CfxXleSQt788DbRYYkVK+AbwBkJ6e3q2qNgfzdgJwMqwPT//8NDeNu4krRlzRnVN5hLAAHT8W1bDwrc18eEtGm/skhiYyf+R8VmxfwaMzHiUiwEO+48h+ygs4WljNLT/9aPvTDxdMJzLGe5IYHCXMWyzwzvAPVRpOJLTsNP/PHRsJTtRyy1nO9Z96goOFNWR4SoG3h3+IssjPsBab9+ZX8evRUt6S2UxIiuKSaT3v1uVsumXbSykLpZQmKaUZWA5MdK5YLcnP2wjAk/nrGBk3kpfOf8mVl3M61hjw3zpp83X35LupNdTy5rY33SFWp1h7eloJ8/ISpu2huFDcuIjpRExmycGT1aQleG9p24646cyWETcHC6s9JEnX+demYzz2+V5yy+t7HoHiIrqlwIUQ9sGiFwNZzhGnbX4o+UG5rlbH6itXE+wDxW/s+fMc5cnet5Mu7uMSxjEjdQbLfluGweR5hXOirKUC95YuJF0lNEBPTaPRJ8uaHjhZTb3BxHAfVeB/nTuccSnNs8kDPqTA7WXt76Uzz04VuBDiA2ATMFQIkSuEuBF4VgixWwixC5gB3O1KIX/X7wKmBA1mw/Ub3LfA50TSEsK4fkqqLRyvI+6efDc5VTms3r/aDZJ1zImyOjQCbjl7AOvvme75CnjdJDRAh1lCrQ822f3hgNIQ5KzBvrHe0xb2SVVHulLi14NIqcx8rIxO8r4G3uBYFMpVbWxe4QJZ2uXv16505+VcQnignupGI0aTuUVRq9b8bsjvSA5L5t2d73rcz59TVsfQ+DD+fEGaR+XoKdbpb0FFPYP7+FZD4+/3FzE6KZw4L6//3RH2DRCKLDHV3k5eRX2LB/4QL71vvKcqSy/H2obscHENpTXt38QaoeGaUdfwzeFvKKotanc/d1BY3UB8mHf6/rrCyL6K9bQrt7KTPb0Ls1mSlVfJxFTnlNj1FFHByj2k1QhOVjb4hCsrK6/lveItLdRa451S9UKsWYznv/QTE59cd0qLLHsWjF6ASZpYlbXKXeK1SXmtwatqH3eXgbEhBPkpcci+QE2jkStf38TafYU0Gs0MjPN8THdPsLpQ0hJCqTeYfKJb/dp9RYQF6PjhnulsvP8cT4vTLqoCdxP2jYBNZsnx0vbjkkfEjWBc/DhW7vKs66iirslnFy7t0WoEIxPD2ZnbccKGt7Anr5LfsstYtHIroDyAfBmrC8W6EGstDuWtmMyS7/cXMWNYHP1jgjsNPvAkqgJ3E+GBLRVhdknHiznXj72ezPxMtuZvdaVY7dJkNFPbZLLVNPd1hiWEcqiwxiem76ZWMg6I9c4ICEcZnhhGWICOqZZ6+N6uwEtqGimrbSLdB1xXqgJ3E60LQR0pru1w/4VjFhKsD+Yfm//hSrHapcJSuyXCixq49oQBMcHUNBptleW8GfsGCDqNOKU0rq+RlhDGrkdmMzZZCSc8WendCtxavCrOS2O/7VEVuJuwd6HEhfqTXdKxAg8PCGfhmIV8kPWBRxYzy+uUkMfeYoH3t7ghjnby4PQGrMWffj8mkb/NG+m2JtyuxtoM29sjUawP+RhvyxhtA1WBuwmrBd4vOoj+McEc60SBA9wx8Q6aTE0s37rc1eKdgrUBRW9YxATFAgfILqnlqa/2ce4LGzwsUftYFfhDFw5nvjO673gJAXotgfqOSyt7A6oFrnIKeq2Gt65P5z+LM4gJ9W+3Q489abFpTE+dzortKzBLsxukVJo3pN7/Bc9+rRQfiuglFnjfiED8dBqOFNXw+oajHPbihBJr3ZYQL2vf5QzCA/W28sTeSolqgau0xTnD+hAXGkBYgN7hUKpF4xeRXZHNV4e+crF0ClbrY9sJJWKjt1jgGo1gbFIEPx0qsW0zm71zQbO20YheK7yqea6z8AUFXlzdSIi/jkA/763yaKX33SE+QFigzuGb+LLhl5ESnsJTPz/lYqkUWtct7y0KHODCMQkt6lvUdRCL70lqGo0E++t6je/bHl9Q4CU1TcQ40n3HC1AVuAcIC9DTZDR3mMxjRa/Vc9eku9iYs5FdhbtcLpu9Ag/y0/qEFeIoF4xKaFHPxWWtvnrAlmNlfLojv1e6TwDCLAo8u6SWQ15a2Kq4usFrqw+2RlXgHsDa3b3KwRKn1465Fr1Gz7s73nWlWECz/w8gOTLI5ddzJ9Eh/i2KQnljjfDLX9tEZb2h1yrw8EA9VfUGZjy3nlkv/tj5AR6gqKpRVeAq7WOtq11V75gCiQmKYe6Quby3+z2Xl5kttbPAk6O8NwOtu8yf0BzV4Y0WuBVvrb3RU7zdhSKlJK+i3quzL+3pnXeJl9NVCxyUzMyi2iK+Pvy1q8QCWrpQknqZBQ5w/sh4/vUHpf+IK5rtzvvnRqY+/X2Pz1Ps5bHS3SU8UN+iyp/R5J7oKkcpq22i0WgmUVXgKu1hjQl3pD64lTmD5hAfEu/yzEx7F4qvduDpjGjLApUrXCg7cirIq6jv1rH2af5F1d6drdhdwgNb3lMlNd4VE55foYy7qsBV2iUswGqBO65ArIuZ3x39jm0F21wlGqV2P6hAv96pwEP9lfH3NhdKtZ08Xhrh2GPCW+UVeFtdlLwKpcic6kJRaZcwixXSVV/g4vTFhPmH8ezGZ10hFgCltY0Miw/l7CGxXDkh2WXX8STB/kpkTU2j0SVulO5SZvfwfG3BeA9K4jpa1wTyPgWuyKMqcJV2sVrgD67J4pJXNjoUTghKfZTFZyzmP3v/w5GyIy6RrbCqkTFJEfzrDxNbdFLpTYRYXEMfbD7ByIe/8ZpwNusC8js3TOD8kQmd7O2bDItv2duz0Mt8/Xnl9QTqtT6TgawqcA8QoG+Ord52ouKU7h8dcdfku9BpdDy/6Xmny2UwmSmpaaRPuO+273IEf50WvVaw39LzMKe8/drs7sTaqSk62DdC2LpDYkQgq2+bwp9mDUEjoNDLKhMeLKxmUFyIzyRRqQrcQ/zjqnG8c8MEAHZ2odVXQmgC146+lrd3vE1JXUnnBzhIfkU91674DSkhoZcrcGhZZ8Ro8g6HszUCKMpHsgC7y7iUSO6cOZiUqCCOdlIX3138cKCIvflV7C2osjWe8AVUBe4hLhyTyPShcfQJ82d3FzvF3D35bhqMDbye+brT5Hl9wxF+PVoGQPxpoMCD7RS4t7T4soYO+nr9b0cZGh/K/gLvcF/d8PYWLlj2E2W1TaQleGcD47ZQFbiHGdU3nL0FVV06ZkTcCGYPnM3LW16m0egcH2K0XeW1eB/ugO4o04bE2j53JZzTleRXNhAT4tfCxdabGRYfRnZpLfVNnq1J0zqYIE21wFUcJSbE39Y8oSvcPfluTtacdFrfTLNdDPLp4EL527yRfHr7VKBrCVWuJL+i3mfij51BWkIoUsKhIs9a4a1r849NifCQJF1HVeAeJixQT3U3FMh5A89jYt+JPLrhURqMPV8Isk/rbx3q1RsRQjAmOYIQf53DJQ1cTX5FPYnhp48CH2DpktRZdypXcry0luvf3gzApP5RfH3XWfjrfGcGpCpwDxMWoKPBYKbR2LVppBCCJ895ktyqXF7LfK3Hclit0NevPcNnVuCdQViAjrc2ZpP+t7VkHivzmBxSytPOArd2vPFk2YD3N5+wzYDf/cPEU8IcvZ1OFbgQ4i0hRJEQIstuW5QQ4jshxCHLe6Rrxey9WOuidCete+aAmczsP5Mnf3qS6saeTUOr6g0Miw9l9oj4Hp3HW2kyNbVZCCzUEpNfUtPIhoPF7hbLxv6T1dQ2mUiM6P3uKyvhgXr8dBr2n6wm10OhnH52RcN8ce3BkVzpd4CXgX/ZbbsfWCelfFoIcb/l+33OF6/3Y0urrzd0q4XTE+c8weQVk3np15d4cNqD3ZKhoq6JwqoGmyy+iJSSrKIsfj7xM1lFWewp3kN2RTbVjdXUNNVgMBsQCOKC40gMTWRw9GCm95tOnTkUSQQC4bHysk1GM3P+/hPgOzU4nIEQgtgQfz7emsuu3Aq+vXua22Uor2vCX6fhp3tnuP3azqBTBS6l/FEIkdpq80XAdMvnd4H1qAq8W1jT6p/9+gBPXjKqy9mPk5ImMW/YPJ7b9By3TbiN6KDoLssw9rHvADg3rU+Xj/UkTaYmvjvyHWv2r+Grw1+RV50HQJh/GCNiRzCt3zTC/cMJ8QshxC8Eg9lAfnU+edV5/JLzCx/t+QgAbUAUAabR7Cq5DCmHO8WFJKV0+DzWRbyBscFMHxrbyd69i7gwf/Iq6jlcVEODweR2K7i81kBSZCBxPhp51d1qRX2klAUAUsoCIURcezsKIRYBiwBSUnpPh21nYbV6v95zkiB/LS9cMbbL53h8xuN8uv9Tnt34LM/Meqb7sgR6f/Eqk9nEj8d/5IOsD/hk3yeU1ZcR5h/GrAGzmDNoDjMHzKRfeL9OlaeUkiPlR5jywt+pFbuo125jdc56xrz2OkunLGX+yPnotd2fkZglaB18DuzJU8JIl1+XTlAvLSDWHtb73yzhSHENIxLD3Xr9stomny4Z4fK7RUr5BvAGQHp6unekvHkRYXYRH03G7tVGHhk3kgWjF7Bs8zLunHQnSWFJDh9rv3ga7MXKI6soi7e2v8WqrFUU1BQQrA9m3rB5zB85n/MGnoeftms/QiEEg6IGES7nEGQ8n5FxQRSb1lEr13Ddmut44PsHWDJ5CbdOuJUAXdetM6PZjFbjmDW5J7+SYD8tqdHBXb6Or2NfTOxwkfsVeHldEylRvlv3vrtRKIVCiAQAy3uR80Q6vQi1q7kd2oP624/NeAyApd8tdfiYw0XV3Ptxc5/NCi9JaLFS3VjNm9veJGNFBqNeHcXLm19mUtIkPrzsQ4qWFvHeJe8xd8jcLitvez66JYN7zx9Kn9AQYjSz2X3rbr64+gsGRQ1iybdLSPtnGmv2r3HoXPZd7k1dqAebebycEX3D0WhOn+gfK/ZJPD8eLGkxhu6grLbJpxt3d1eBfwYstHxeCHzqHHFOP+wXDhsM5m5npaVGpHLf1PtYlbWKDcc2dLp/XZORc1/4kU935Nu2ldZ4vjKclJJfc3/lps9uIuH5BG7+381UNVbxwnkvkLckj9VXruaKEVcQpHeO1TQuJZLbpg8iJEBHdYMRIQQXDL6AHxb+wNpr1xLiF8LFH17MvFXzyKnM6fBcBnPzDMrooCLKKatjT34V56a164Xs1Tx72WguHteXS8b15ZNtuXy/3322oJSS8romInuzC0UI8QHKgmWMECIXeBh4GvhICHEjcAK43JVC9maC7Lq+r96ex+rteRx7+nfdOtd9U+/j3Z3vcuNnN7J10VbCA9qfju7Nb5m+nxAewEMXDu/WdZ1BSV0JK3euZMX2Fewp3kOwPpgrR1zJTeNvYnLSZJfHpocG6E5JqJo5YCbbFm3jpV9f4uH1D5P2zzT+ds7fuGPiHeg0p/507K1uUycFssxmiRDw7d5CAOb0wvKx9YZ6SupKKG8ox2Q2oREatBotGqHBT+tHdGA0wxPDefHKsVQ1GPjv9jy3JvXUNBoxmCRRwb4bfeVIFMpV7fxpppNlOS1pSzF1d2ElUB/Iexe/x7R3pnHXN3fx9kVvt7vv0VY/lH/fNMmWGecupJSsP7aeN7a9wX/3/ZcmUxOT+k5i+YXLuXLElYT6u6+oUGiAnuoG4ynRI3qtnqVTl3LZ8Mu4/cvbufubu1m5ayVvzH2DMxLPaHEOg53S7swCP+f59YxIDCciSE9UsB/JPuqHlVKSXZFNVlEWB0sPtngV1BR0erxeo2dYzDBG9xlNrZ8/v+RN5pK68G5FU3WV8lrlgR3hwy4U7121Oo34+/yxvPDdQY6XKskMT325jwcuSOvW1G5qylTunXovT/38FPNHzGf2oNlt7pddUoteK2xKx501qItqi3hnxzss37acw2WHiQyIZPEZi7n5jJsZGTfSbXLYExqgw2iWHCutQ68VpzR07h/Zny+u/oKP937MH7/+IxPfnMidE+/k8RmP2x40Jgd94IeLajhWWsex0jpmDovzmeJhUkpyqnLIzM9s8SpvKLftExMUw9DooZw/6HwGRg4kLjiOqMAodBodJmnCLM2YpZkGYwOldaWcrDnJnuI9bDi+gRJtLu8cfIt/PbeYs/udzWVpl3Fx2sUkhia65N9jTR7yle47baEqcC/gorF92XSk1KbA/7M1lz5hAdwze2i3zvfQtIdYvX81iz5fRNatWW1astnFtaREBXGkWLHEXR1CKKXkpxM/8fLml1mzfw0Gs4GzUs7i4WkPc2napQTqPfsjsmZkznhuPUCbbiwhBJePuJxZA2fxwLoHWPbbMj7Z9wkvz3mZi4Zd1KLDutHcfkTR57ua1x1yyutIjvRO67umqYYteVvYlLuJTbmb2Jy3maJaxUet0+gYGTeSS9MuJT0xnTHxYxgSPYSowKhuX2/OP76iXh4lfWgeXx5ewx1f3cGdX91JRnIGl6VdxiVpl9Avop+z/nlklyr3fmqM70b/qArcS6hrtXipczSIuA0CdAGs+P0KznzrTO759h5ev/DUuuHZJbX0jwmxKXBX+ZjrDfV8kPUBy35bxs7CnUQGRHLHxDu4efzNpMWmueSa3SGsVQRQR0klEQERvPK7V7h29LXc8vktzPtwHvOGzeOBKc29SjuywAsqmouPHSysYUJq95Wes5BScrT8qKKscxSFvatwFyap3JdDo4cyZ9AcJiROID0xndF9Rjv9ods3LIa1+8wcy0/l2NNPsrd4L5/s/YRP9n3Ckm+XsOTbJaQnpnNZ2mVcPepqksN71rP1WEkt/joNCT4yA2oLVYF7CdYFtHvOG8Jz3x7scY3kKclTWDplKc/+8iwT+k7gpvE32f4mpeREWR1TB8Ww7k/TXNLW6kTlCV7d8irLty2ntL6UUXGjeGPuG1wz+hqnRZA4k9YhnAdOVjMmueOyohnJGWxdtJUXf32RR9Y/wndH1qLVXUCgeTxGc/tp4dWNLRdLPVG+t85QR2Z+pk1Zb8rdZLOuQ/xCmNR3En8+889kJGcwOWlyjyxrR2ldSmJ47HCGTxvOg9Me5HDZYZsyv3/d/fx53Z+ZNXAWN4y9gXnD5nU5Vv/BNVms/PU4g+NCfDp8U1XgXsIV6cn8cKCYy9OTeeeXY1Q7oVv6EzOfYEfhDm774jbSYtKYmqLUv66sN1BvUAonDYwNYaCTFi+tbpJlvy1j9f7VAMwbNo8/TvwjZ/c726urHPaNaPlQ2ZVX2akCB2WR896p93L58Mu5Yc1iNpz4iCo+4pYvf+K1C19iUNSgU46pqjcytE8oByzNlBNcXEJWSsnxyuP8kvOLTWHvLNyJ0azcY4OjBnP+oPPJSMogIymDkXEjHU5Ccib294fJLNHaKdZBUYO478z7uO/M+zhafpR3drzDuzvf5apPriIiIIKrR17NDeNu4IyEzqtpNhpNrPz1OACFVd7Vk7OrqArcS5gzKsHmdw3x11HjhMJKOo2OVZeuYtKbk7j4w4tZf/16hscOJ98yhXeW4qgz1PH+7vd5efPL7CzcSVRgFEunLOXW9Fud6rN0JYPjWj7EjhR1rVdj/8j+vHHBx8x88X/U6L7hl9xPGP7P4SxOX8xfzvoLfUKa68xUNxiIDw8gOSqQtfuK6OPkKXy9oZ6tBVtbWNcna04CEKQPYmLfiSydspSMJMW6jg32jvor9lnBNY3GduvSD4gcwGMzHuOR6Y/wffb3vL3jbd7a8RavZL7CyLiR3DD2BhaMXkBccNux9ZuOlAKg1QgenOv60Fnr4m9MUIzTZ5+qAvdCQgJ0LVKMe0JkYCSfX/05096ZxuQ3J7NszjKS/c8HIKGHpUuzy7N5ZcsrrNi+gvKGckb3Gc2bF77JVaOu8ko3SUfYT6ND/HWUdCOpyWiSaAkn3HgFb1/xAB8eeJFXtrzCW9vf4rox13Hz+JsZlzCOqgYjyVFBPHf5GD7bmc/kAd13T0gpOVF5gl9zf7Up6+0F2zGYFTfNgMgBzOw/kynJU8hIymBUn1FtxrB7A/fOHsbPh0ooqm6kusHQaWMRjdBw7oBzOXfAuVQ0VLAqaxVv73ibP337J+5bex9zh8zlhrE3MGfQnBZ1bXbmKE3E9zw626nFs4xmI0fLj7KveB97i/eyr2Sf8ireR62hlm8XfMusgbOcdj1QFbhX4iwL3MqQ6CH8euOvLFyzkBs+vYEz4s7DxHXd6v6XNMNjAAATB0lEQVQipWTt0bW8vOVl/nfgf2iEhkvSLuHOiXdyZsqZXu0m6Yz3bpzER5k55FXU89OhEh5YvZvHfj8CndaxhGX7yJPIgD68Nvc1lmQs4YmfnuDtHW/zauarjE8YT3HdFAYwDa1mFFekd20hLr863xa+tyV/C5n5mZTUlQAQqAtkQt8JLMlYYrOu7S1/byc+PIBHfz+CW/+9TemS1IUuAxEBESxOX8zi9MXsKdrDOzveYeWulazZv4ZQv1DO7nc201OnMy5+HIdLdMSF+ndLeZulmbyqPA6VHeJg6UEOlR6yfT5aftT24ARICksiLSaNG8fdSFpsmksW7YWU7qs9kJ6eLjMzM912PV/lpnczyauo56v/O8up5/3vthy2lK7k/216BLNZy81nXMfCsQuZnDQZjWhfSTWZmth4YiNfH/6aNQfWcLD0IHHBcSwav4hb0m/pUvEsX2Dxyq18vUdxObx/8ySmDIxx6LhtJ8q55JVfAPjk1gzO6NdsWZfXl/P+7vdZvm05Owt3AuCv9WdUn1GMjx/P0JihxAXHEe4fTp2hjpqmGmoNtZTUlXCi8gQ5VTnsK95nS47RCA0jYkfYokIm9J3AmD5jelRB0Rv4+VAJC1b8xoeLJjNpQM+SeQwmA98c+YYvDn7Buux1HCo7ZPtbgCaGGQMmkBqRSkxQDGH+YWiFFq1Gi1Yo2aIVDRUU1xUrr9pi8qrzOFJ2hHpjve08gbpABkUNYnD0YAZHDSYtRlHUw2KGEebvvO4+QoitUsr01ttVC9wLCQ3QUdNowPpwdVZ96iUf7QLGMH/YB3ybs5x3d77LG9veICksiUvTLmVU3CjiQ+Lx0/pR2VhJdnk2G3M2si57HTVNNeg1es5MOZO/nvVXrhhxBf469yX/uJOY0OYEqnX7ihxW4Eb7TMxWqfSRgZHcPvF2/jD2FgY9/Bbnja0jNiqfbQXb+M/e/7RIhrFHIzQkhiaSEp7CuQPOJT0xnfTEdMbGj/U5N5UjWPMRnNFcQ6/VM3fIXOYOmQtAcW0xOwt3svjD/6L1P0FedQ5b8rdQWleKpG1DNlgfTFxwHLHBsQyIHMDsgbMZHDWYwdGDGRI9hMTQxA6NH1ejKnAvxOpCWbRyK9HBfjx96egen7PK7gfx8/4AFp7xDH+9MJX/HfwfH+35iFczX6XJ1HTKcSnhKVwz6hrmDJrDOf3PcWt6u6ewD2f7xbLg5Qj2LpT24sCrG43oZV/OSRnBtRmpgPJwrWyspKi2iKrGKoL1wQT7BRPiF0KYf5jX+qxdgTWhqqrBQE5ZnVNLDLzwTQEmcyy6ugu5dnQ//vI7ZQHTZDZRb6zHZDZhkibbe7h/uMcTzDrj9LkzfAjrIuau3AqC/Z3zX1RR16ycwwP13D1rCOEBgSwYvYAFoxfQaGzkZM1JCmoKMJlNhPiFkBKeQmTg6dfu1F6Bl9U6vphpdKAWitWyDLWrQimEICIggoiAzsMWezvWePzXNxxlyUc7+fzOMxnZt+c1ws1myQebm6tJ2reu02q0hPi5tw6Qs1AVuBcS4q/DYJIUVjWi0zRhMJnRO7iQ1h7WztsrFqYzfWhcixhbAH+dP/0i+vlM2J8r8dM1j3VlF2qkO1ILpcpyPl/ofuQJrArcGiN/pLjGKQr8YFHLpt+9pfeo55w3Ku1inxVoNEue+Wo/Zz7zPT1ZcC63WOARQX6nKG+VlsSEKD7wiCA9DQYzDQbHsmINps7rgbdlgas046/T4m/3AK1yUpORzdllLb6f0a93zCxVBe6FhLRym7z5cza55fU0drPlGjS7UCKDVMXRGTOGxvGvP0zkT7OGAI5b4Y5Y4AWVSgRDtA83EXA19g+33Ip6Vm46Zqsc2F0OFra0wFun7fsqqgL3QtrLzKvtQXKPtfaxL7ePchdCCM4eEmsr51tR55gCNzigwLccKycySH9a9r90lLjQZuX6cWYuD366h0f/t7dH5zxRVs+IxDD8dRpumz6wpyJ6DaojzgtJT22e3gXqtdRbpvA1jUaiu2k5VNQ1IUTLJsoqHRMRqChwqwV+/ye7GJUUzjWT2l4nMJnbLidbVNXA+5tPUNNg5OOtuZybFufTBZRczcy0OPYWKB2jSmuVmWN3MmPtOVFay4jEcL74o3NzKzyNaoF7If46LcGWVmujkpoXcHqSXl9ep6Qmq/5vx4mwuJsq6prYfqKcVVty+MvqrHb3t+/IY2+BP/r5Xl5ae4g3f84GYNoQ76g94q3MGt4ye9RPq2H7iQru+3hXt9aBTGZJbnm9z3Y96gjVAvdSfrhnOsdK61i9Pc+2AFNVb+SbPSeZNiS2y2nA5XW+3X3bE1hrcVTUG9hwsNi2Pa+ivs0uLvZK234R8+DJZv/r3+eP5cLRrukw01sYnRTB+zdNwmiWbD9RQWJEAEs/3sWHmTlcN6UfIxK7FpWSX1GP0SzpF937FLhqgXspcWEBTOwfxcDYZl/ppiMl3LJyK+c8t77LlkhZbZO6gNlFrBZ4ZZ2Bk5UNtvDCXw6XtLm/fUeedzYeI/X+LzhaXMMhu8qGF45OVN0nDjBlUAxnD4nl/84dzJxRCSzMUNxWa/d2vWv9rlyleFVvXHdQFbiXMzyhuZ7CMUvLtfzKBltct6MUVDaQ0EtiX92FNRroiS/3sW5/EWekRKLXilMaQluxt7qtPtzM40qK/GsLxpP16GxVeXeDEH8dj140knEpEaw/2HUFvvyno6REBTEhtXeEDtqjKnAvJ2NgNG9ep9SwsQ+lai8+tsFgIv1v3/GNpRgTKFloeRX1JKkKvEu0rkETHaJ0j/9ubyFf7j6143rr+iegtO0CZUbVOjxUpWtMTI1iT14VdU2OrwVV1hvYkVPBlROSHa4q6Uv0vn9RL0MIwSRLvei8iuYqaO3FJp8oq6Okpomnvtxn21Za20ST0dxrss/cyeYHZto+Rwb5kRodzOGiGm779zabG6u8tonKOkObyTsHCxX3SZS6/tBjxqVE0mQyM/yhb9htcYtYeX3DEX7Yf6p1ftLSLrA3+r9BXcT0CYL9lP+mwqrmUKr2FHhJtbKPv05Z5JRS8u1exRpva+FNpWPiwgKICfGjpEZZQ7A3yqvqjYQH6Rn3+HcIAfMnpKARYK/HD1tSuKNCVAXeU8anNNeK2XikxBahJaXkqa/2A7D6tikcKqqx1VnPtyROeaLvqDtQLXAfQKMRtrBCK+0p8HyLxWFdcPvvtjxb6JtqgXcP68MwIsivhZV9oLCaJ75QEkykVBaZpw5qWXr2WGkdeq0gVHWf9Ji4sACWzh4KwNHi5oVh+9/Cxa/8wr0f77J9t1rg8S7uO+opVAXuI1irElr9qFUNzTdteW0Tqfd/wZe7CzhpsTj8dBqklLy24Yhtv76RvfMmdjV6rWJ2RwbruXXaQJIs4/j453tZ/lO2bb9jpXWcNfjU2uFRwX4+3anIm7h9xiCmDopmv11opr1r0Updk5Gy2iYKKhsQomV2Z2+iR2aBEOIYUA2YAGNbHSNUnENIgI6i6kZSooLYW1BFZb2B6gYDvx0ts6V8//OHw7ZO6rWNRk5WNXCoqIarJqbQLzqo0x6DKm1jXfyKCFIWMT+6JYMpT3/fZkdz+y48VqKCe6fy8BTD4sN479fjts71eeWnKvDzXvyR3PJ6xiZHEBvi3+Nqnt6KM+Z1M6SUbQfGqjgNq+XdJ8yfw0UaKusN3PH+djYcLOb6KamAEoFinTKW1TbZrJSLx/VlYv/uN8493dFZQv+sD8DYUH80AoqqT03vTo0OQqsRLZJ61MJVziU1OohGo5ni6ka+2F1gc6HMG5vImh35AORalPqOnArGJPW8HK230jsfS70Q6xQwNEBPWKCefQXVtuzAd345BkCDwWwLNSyva2J/gaLAh/bp/V10XIk1giHQkv2q12qIbWdKHhXsh7aVuyTQz3mdz1Wwjf26/YU8/vlelq07hF4rePHKsay5feop+w/vYuamL9FTBS6Bb4UQW4UQi9raQQixSAiRKYTILC4ubmsXFQe4ckIKAMfL6ggP1LH1mJJeb3WZABTXNHK4qMbWEGLr8TISwgMIVzMwe8Szl47hmUtHMSy++UHY3oKwEAKzJbzwmkkpXDK+L5ef0buaPnua2FAlomRnToVt2/CEMIQQJEY0R5ukWGqf3HRWf/cK6EZ6qsCnSinHA3OA24UQZ7feQUr5hpQyXUqZHhurFvHpLjOHxTF/QjL3zR5KeKCe2ialQuGUgc2du5uMZswSzrMUA1q7r4jxvaRwvScJD9Jz5YSUFguRA2Lab8GVYrHYh8aH8sIVYzlvRLzLZTydsM5Gd+YoseDr75nOqkUZAETbrTf8+6ZJrFiYzsBY32yX5gg9UuBSynzLexGwGpjoDKFUTkWjETx96WimDIohwpIU4q/TMC751D6K8yemoNMIRvUN5/GLRrpb1NOCgXFKXY2zBsew77HzgWbFYn2oOlpHXKVrWF0oBwqrCfbT0i86yOamsq+2mRwVxMy0Pm2eo7fQ7UVMIUQwoJFSVls+nwc85jTJVNpldFI43+8vIjRAb7P2QEk1PntIDBP7R3Hwb3PUuhsuxGqBV9YbCPTT8sylo8gYoIQQLp42kJ8OlXDBKNXydgUBei2hATqqG4wkRASeEqI5Z2R8i99Fb6YnUSh9gNWWwdMB70spv3aKVCodctbgWF5ae4iSmkaSIptv1I8WZ9g+q8rbtfSPUSxwq5VtXaMASIoMYsPSGR6R63QhLtRfUeBtZFi+uuAMD0jkGbqtwKWUR4ExTpRFxUGsYVEXjIpXCyR5iP4xwUxMjeKuWYM9LcppSWyoP0eKa0/78hDqr98H0Wk1bHtwFkEWv9/b109Q0+TdjJ9O02LGo+JebjxzAMmRQVyb0XZ7u9MF0Z0WRd0lPT1dZmZmuu16KioqKr0BIcTWtjLd1UQeFRUVFR9FVeAqKioqPoqqwFVUVFR8FFWBq6ioqPgoqgJXUVFR8VFUBa6ioqLio6gKXEVFRcVHURW4ioqKio/i1kQeIUQxcLybh8cA3tj5R5Wr63irbKpcXUOVq2v0RK5+UspT6nG7VYH3BCFEpjf23FTl6jreKpsqV9dQ5eoarpBLdaGoqKio+CiqAldRUVHxUXxJgb/haQHaQZWr63irbKpcXUOVq2s4XS6f8YGrqKioqLTElyxwFRUVFRU7VAWuoqKi4qP4hAIXQpwvhDgghDgshLjfw7IcE0LsFkLsEEJkWrZFCSG+E0IcsrxHukGOt4QQRUKILLtt7cohhPizZfwOCCFmu1muR4QQeZYx2yGEuMADciULIX4QQuwTQuwRQvyfZbtHx6wDuTw6ZkKIACHEZiHETotcj1q2e3q82pPL4/eY5VpaIcR2IcTnlu+uHS8ppVe/AC1wBBgA+AE7geEelOcYENNq27PA/ZbP9wPPuEGOs4HxQFZncgDDLePmD/S3jKfWjXI9AtzTxr7ulCsBGG/5HAoctFzfo2PWgVweHTNAACGWz3rgN2CyF4xXe3J5/B6zXG8J8D7wueW7S8fLFyzwicBhKeVRKWUTsAq4yMMyteYi4F3L53eBea6+oJTyR6DMQTkuAlZJKRullNnAYZRxdZdc7eFOuQqklNssn6uBfUBfPDxmHcjVHu6SS0opayxf9ZaXxPPj1Z5c7eG2e0wIkQT8Dniz1fVdNl6+oMD7Ajl233Pp+AZ3NRL4VgixVQixyLKtj5SyAJQfJBDnIdnak8MbxvAOIcQui4vFOo30iFxCiFRgHIr15jVj1kou8PCYWdwBO4Ai4DsppVeMVztygefvsZeAewGz3TaXjpcvKHDRxjZPxj5OlVKOB+YAtwshzvagLI7i6TF8FRgIjAUKgOct290ulxAiBPgEuEtKWdXRrm1sc5lsbcjl8TGTUpqklGOBJGCiEGJkB7t7Wi6PjpcQYi5QJKXc6ughbWzrsly+oMBzgWS770lAvodkQUqZb3kvAlajTHsKhRAJAJb3Ig+J154cHh1DKWWh5UdnBpbTPFV0q1xCCD2Kkvy3lPK/ls0eH7O25PKWMbPIUgGsB87HC8arLbm8YLymAr8XQhxDcfOeI4R4DxePly8o8C3AYCFEfyGEHzAf+MwTggghgoUQodbPwHlAlkWehZbdFgKfekK+DuT4DJgvhPAXQvQHBgOb3SWU9Qa2cDHKmLlVLiGEAFYA+6SUL9j9yaNj1p5cnh4zIUSsECLC8jkQOBfYj+fHq025PD1eUso/SymTpJSpKDrqeynlAlw9Xq5ajXXmC7gAZXX+CPAXD8oxAGXleCewxyoLEA2sAw5Z3qPcIMsHKFNFA8rT/MaO5AD+Yhm/A8AcN8u1EtgN7LLcuAkekOtMlCnqLmCH5XWBp8esA7k8OmbAaGC75fpZwEOd3eselsvj95jd9abTHIXi0vFSU+lVVFRUfBRfcKGoqKioqLSBqsBVVFRUfBRVgauoqKj4KKoCV1FRUfFRVAWuoqKi4qOoClxFRUXFR1EVuIqKioqP8v8BVFX902OXFF4AAAAASUVORK5CYII=\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xs = []\n",
"avgs = []\n",
"stds = []\n",
"a = EfficientFullAveragerator()\n",
"for x in noisy_temp_with_outliers():\n",
" xs.append(x)\n",
" a.add(x)\n",
" avgs.append(a.avg)\n",
" stds.append(a.std)\n",
" if len(xs) == 400:\n",
" break\n",
"plt.plot(xs, label='x')\n",
"plt.plot(avgs, label='average')\n",
"# Let's move to numpy to compute average plus and minus standard deviation.\n",
"a_avg = np.array(avgs)\n",
"a_std = np.array(stds)\n",
"plt.plot(a_avg + a_std, label='avg + std', color='g')\n",
"plt.plot(a_avg - a_std, label='avg - std', color='g')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "1brrurLG2HJp",
"nbgrader": {
"checksum": "03188cb49f18c8f5712e6abdc5227c07",
"grade": false,
"grade_id": "cell-ef48cf79a4bf29fd",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"As we see: \n",
"* The temperature, even when read without outliers, often differs from the average by more than the overall standard deviation, and this simply due to the daily temperature variations. \n",
"* The outlier themselves, even though quite visible to our eye, often differ from the average by _less_ than the standard deviation, just because the standard deviation is really rather large, as it is influenced not only by sensor noise, but also by the daily temperature cycle. "
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "Zpoje5vk2HJp",
"nbgrader": {
"checksum": "a70a435f302d76b46c05733d511c32b6",
"grade": false,
"grade_id": "cell-7a0c92b48dd4c3e9",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"To detect these outliers, and change in conditions, it is far more useful to have the average and standard deviation of _recent_ data only, rather than computed over the whole series. \n",
"A _sliding window averagerator_ considers, in the computation of averages and standard deviations, only the most recent $N$ data values, for a specified $N$."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "FMsgh34Z2HJq",
"nbgrader": {
"checksum": "30447b31dee3a88564971af6abe81ba1",
"grade": false,
"grade_id": "cell-7afb9f34eac8298e",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"**Exercise:** Complete the code below, defining a sliding window averagerator. The class should have methods:\n",
"\n",
"* `__init__(self, window_size)` to initialize;\n",
"* `add(self, x)`, to add a value\n",
"\n",
"as well as properties `avg` and `std`, as in the previous averagerator classes. "
]
},
{
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"### Question 1: Implement a `SlidingWindowAveragerator`\n",
"\n",
"class SlidingWindowAveragerator(object):\n",
"\n",
" # YOUR CODE HERE\n",
" def __init__(self, window_size):\n",
" self.window_size = window_size\n",
" self.values = []\n",
" \n",
" def add(self, x):\n",
" self.values.append(x)\n",
" \n",
" def getavg(self):\n",
" if len(self.values) < self.window_size:\n",
" L = self.values\n",
" else:\n",
" L = self.values[-self.window_size:] #get only last window_size elements\n",
" return sum(L)/len(L)\n",
" \n",
" def getstd(self):\n",
" if len(self.values) < self.window_size:\n",
" L = self.values\n",
" else:\n",
" L = self.values[-self.window_size:] #get only last window_size elements\n",
" m = self.getavg()\n",
" n = len(L)\n",
" s = 0\n",
" for v in L:\n",
" s += (v-m)**2\n",
" \n",
" s /= n\n",
" return s**0.5\n",
"\n",
" avg = property(getavg)\n",
" std = property(getstd)\n"
]
},
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"source": [
"### 5 points: Tests for `SlidingWindowAveragerator`\n",
"\n",
"# First some simple cases.\n",
"sa = SlidingWindowAveragerator(20)\n",
"for _ in range(10):\n",
" sa.add(10)\n",
" assert sa.avg == 10\n",
" assert sa.std == 0\n",
"\n",
"sa = SlidingWindowAveragerator(10)\n",
"for _ in range(10):\n",
" sa.add(4)\n",
"assert sa.avg == 4\n",
"for _ in range(10):\n",
" sa.add(8)\n",
"assert sa.avg == 8\n",
"assert sa.std == 0\n",
"\n"
]
},
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"source": [
"### 10 points: Now for slightly more complex tests.\n",
"\n",
"sa = SlidingWindowAveragerator(10)\n",
"for i in range(10):\n",
" sa.add(i)\n",
"assert sa.avg == 4.5\n",
"assert abs(sa.std - 2.87) < 0.1\n",
"for i in range(10):\n",
" sa.add(i)\n",
"assert sa.avg == 4.5\n",
"assert abs(sa.std - 2.87) < 0.1\n",
"for _ in range(10):\n",
" sa.add(1)\n",
"assert sa.avg == 1\n",
"assert sa.std == 0\n",
"\n"
]
},
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"source": [
"### Duck Typing\n",
"\n",
"You may wonder: should we have not defined an abstract _Averagerator_ class, and make all these classes, such as _FullAveragaerator_, _EfficientFullAveragerator_, _SlidingWindowAveragerator_, subclasses of the superclass? \n",
"\n",
"If we were in a strongly typed language, such as Java, the answer would be a resounding Yes. In Java, a superclass serves as the common type of all objects belonging to the more specialized classes. One can then define a method accepting a superclass, say, an _Averagerator_, and then pass to it objects of any of its subclasses. \n",
"\n",
"In Python, objects are rarely tested for the class to which they belong. The more common pattern in Python is simply the one of calling methods of objects, assuming the methods do the proper thing. This approach to type checking (or the lack of it) is sometimes called _duck typing:_ [if it quacks like a duck, and it waddles like a duck](https://www.youtube.com/watch?v=R6kizqah-Po), it is a duck --- meaning, if the object's methods do the right thing, that suffices for us. \n",
"\n",
"Thus, in Python, except in special cases, the subclass relationship is useful especially if there is non-trivial shared code between a subclass and its superclass. This not being the case for the Averagerator classes we have defined so far, we have preferred the simpler approach of defining each class individually, which has the advantage of keeping all the class code in the same place."
]
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"source": [
"### Discounting Averagerators"
]
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"A sliding window abruptly truncates the past: the stream values go from being considered fully considered as part of the average, to being disregarded, in one step. \n",
"A consequence of this is that to implement a sliding window average of size $N$, we actually need to store $N$ values: otherwise, we would not know how to remove a value from the sliding window when the value \"falls off\" the window. \n",
"Can we do better? Can we obtain something similar to a sliding window average, but that forgets past values in a smoother way, rather than with an abrupt threshold, and such that the amount of data to remember is independent on window size? \n",
"\n",
"The answer is Yes. Given a data stream $x_0, x_1, \\ldots, x_n$, the idea is to give to the most recent value $x_n$ a weight of 1, to $x_{n-1}$ a weight of $\\alpha$ for $\\alpha < 1$, to $x_{n-2}$ weight $\\alpha^2$, and so forth: a value that ocurred $k$ \"times\" ago has weight $\\alpha^k$. \n",
"This approach is known as _discounting:_ it is as if the value of the past accumulated experience decreased by a factor of $\\alpha$ upon the arrival of a new data value. \n",
"\n",
"Aside from being a smoother way to average (the effect of past values slowly decays, rather than abruptly dropping out of a fixed size window), discounted averages are also far more efficient to implement. \n",
"The idea, for the average, consists in keeping the running sum of values $S$, and the running sum of weights $W$. \n",
"The average is simply the sum divided by the total weight, or $S/W$. \n",
"When a new value $x$ arrives, $S$ and $W$ are updated by first discounting their current values by $\\alpha$, and then adding the contribution of the last value:\n",
"\n",
"$$\n",
" S := \\alpha S + x \\qquad W := \\alpha W + 1 \\; .\n",
"$$\n",
"\n",
"For the computation of the variance, we proceed in similar fashion.\n",
"The implementation is below.\n"
]
},
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"class DiscountedAveragerator:\n",
"\n",
" def __init__(self, alpha):\n",
" \"\"\"Creates an averagerator with a specified discounting factor alpha.\"\"\"\n",
" self.alpha = alpha\n",
" self.w = 0.\n",
" self.sum_x = 0.\n",
" self.sum_x_sq = 0.\n",
"\n",
" def add(self, x):\n",
" self.w = self.alpha * self.w + 1.\n",
" self.sum_x = self.alpha * self.sum_x + x\n",
" self.sum_x_sq = self.alpha * self.sum_x_sq + x * x\n",
"\n",
" @property\n",
" def avg(self):\n",
" return self.sum_x / self.w\n",
"\n",
" @property\n",
" def std(self):\n",
" mu = self.avg\n",
" # The np.maximum is purely for safety.\n",
" return np.sqrt(np.maximum(0., self.sum_x_sq / self.w - mu * mu))\n"
]
},
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"source": [
"### Data Smoothing\n",
"\n",
"Running averages can be used for smoothing data. \n",
"If you have some background in digital signal theory, a discounted average is a digital filtering operation, whose behavior in the frequency domain can be modeled also with the help of its [_z-transform_](https://en.wikipedia.org/wiki/Z-transform) $1/(1-\\alpha/z)$. \n",
"We will be content here with watching it at work. \n",
"Let's build a stream where there is a sinusoidal signal, with superimposed noise. Here, an iterator comes in handy."
]
},
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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def noisy_sin(noise=1.):\n",
" d = 0.05 # Time increment.\n",
" t = -d # time\n",
" while True:\n",
" t += d # We increment time.\n",
" yield np.sin(t) + noise * (random.random() - 0.5)\n",
"\n",
"\n",
"# Let's display it.\n",
"xs = []\n",
"for x in noisy_sin():\n",
" xs.append(x)\n",
" if len(xs) == 200:\n",
" break\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(xs)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "hRi8rOiL2HJ6",
"nbgrader": {
"checksum": "e2ab2805ee7be3f331a9a6e8c18482bb",
"grade": false,
"grade_id": "cell-589d81cc2e61ef6d",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"Let's apply now our smoothing average with $\\alpha=0.9$, and compare raw and smoothed data."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"deletable": false,
"editable": false,
"id": "ITGZr5IL2HJ6",
"nbgrader": {
"checksum": "6811f5fad91db1a9e8002b4f3e382d72",
"grade": false,
"grade_id": "cell-5c608ba821577fae",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xs = []\n",
"smooth_xs = []\n",
"a = DiscountedAveragerator(0.9)\n",
"for x in noisy_sin():\n",
" xs.append(x)\n",
" a.add(x)\n",
" smooth_xs.append(a.avg)\n",
" if len(xs) == 200:\n",
" break\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(xs)\n",
"plt.plot(smooth_xs)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "iwGE14mo2HJ8",
"nbgrader": {
"checksum": "7e11486e8eea0816dfb4e74329903337",
"grade": false,
"grade_id": "cell-9ceff0cf237004f",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"We see that the output is a smoother, time-delayed, and somewhat contracted (multiplied by a factor smaller than 1) verson of the input. The time delay and contraction are due to the fact that the average mixes present with past of the sine wave, and would be present even in absence of noise. "
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"deletable": false,
"editable": false,
"id": "zXTiMvaq2HJ9",
"nbgrader": {
"checksum": "a08294f5920855efb7f4bc82f14fb743",
"grade": false,
"grade_id": "cell-97ee2f08ea2fb3bc",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xs = []\n",
"smooth_xs = []\n",
"a = DiscountedAveragerator(0.9)\n",
"for x in noisy_sin(noise=0.):\n",
" xs.append(x)\n",
" a.add(x)\n",
" smooth_xs.append(a.avg)\n",
" if len(xs) == 200:\n",
" break\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(xs)\n",
"plt.plot(smooth_xs)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "2rdjia932HKA",
"nbgrader": {
"checksum": "10c16406ce3c2c5222417366c8a120de",
"grade": false,
"grade_id": "cell-3bbf35ea38c5b0da",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"### Outlier Detection\n",
"\n",
"Let us return to our noisy temperature sensor. How can we detect the outlier errors? \n",
"One simple idea consists in calling an outlier any point that differs from the average by more than, say, two standard deviations. \n",
"Let us see how this approach would work. "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"deletable": false,
"editable": false,
"id": "zaB5nQAU2HKA",
"nbgrader": {
"checksum": "197310cb1b34ebd4ffb1c2b1008061a8",
"grade": false,
"grade_id": "cell-db17683da37a7a39",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"a = DiscountedAveragerator(0.9)\n",
"\n",
"xs = []\n",
"avgs = []\n",
"stds = []\n",
"for x in noisy_temp_with_outliers(d=0.02):\n",
" xs.append(x)\n",
" a.add(x)\n",
" avgs.append(a.avg)\n",
" stds.append(a.std)\n",
" if len(xs) == 400:\n",
" break\n",
"plt.plot(xs, label='x')\n",
"plt.plot(avgs, label='average')\n",
"# Let's move to numpy to compute average plus and minus standard deviation.\n",
"a_avg = np.array(avgs)\n",
"a_std = np.array(stds)\n",
"plt.plot(a_avg + 2. * a_std, label='avg + 2 std', color='g')\n",
"plt.plot(a_avg - 2. * a_std, label='avg - 2 std', color='g')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "NecrBatW2HKG",
"nbgrader": {
"checksum": "7a6d3e01bfc4f7f913c7a17bf06de7b9",
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"grade_id": "cell-9665661ba601ee40",
"locked": true,
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}
},
"source": [
"Indeed, this approach would be able to detect most of the large outliers. We can use this idea to define a cleaned version of the data: when a reading is further away than two standard deviations from the average, we replace the reading with the last valid data. Let us define a _CleanData_ class that does it for us."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "6rZokSz-2HKG",
"nbgrader": {
"checksum": "869a112d4ea901ed13bef4d9c0ff4d7c",
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"grade_id": "cell-dc25d824b2455ef4",
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}
},
"source": [
"**Exercise:** Use the averagerator to write a class that counts how many spikes there are in the last `n` time units, where `n` is a parameter."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "9RwwYZbt2HKH",
"nbgrader": {
"checksum": "19db6e436014776478bf175f5ab7dbaa",
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}
},
"source": [
"**Exercise:** Complete the following implementation, in which an averagerator is used in order to replace values that are more than num_stds away from the average, with the average itself.\n",
"\n",
"The `CleanData` class is initialized by passing a discount factor for its averagerator. \n",
"Every piece `x` of data is then filtered via a call to `filter(x, num_stdevs)`; this call returns:\n",
"\n",
"* `x` if the value of `x` is closer than `num_stdevs` standard deviations from the running average,\n",
"* the running average if the value of `x` differs from the running average by more than `num_stdevs` standard deviations."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"deletable": false,
"id": "Ys8h_yQB2HKH",
"nbgrader": {
"checksum": "75ed989c3bb662937c19c59326d5dae8",
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"grade_id": "cell-b174c6e7b3a85ef0",
"locked": false,
"schema_version": 1,
"solution": true
}
},
"outputs": [],
"source": [
"### Question 2: Implement the `CleanData` class\n",
"\n",
"class CleanData(object):\n",
"\n",
" def __init__(self, discount_factor):\n",
" \"\"\"\n",
" @param discount_factor: discount factor for the averagerator.\n",
" \"\"\"\n",
" # YOUR CODE HERE\n",
" self.discount_factor = discount_factor\n",
" self.sum_x = 0.\n",
" self.sum_x_sq = 0.\n",
" self.w = 0.\n",
"\n",
" def filter(self, x, num_stdevs=2.):\n",
" \"\"\"Returns a filtered value for x.\n",
" @param x: the value to be filtered.\n",
" @param num_stdevs: number of standard deviations from the average\n",
" beyond which data is rejected.\n",
" It can be done in 5 lines of code.\n",
" \"\"\"\n",
" # YOUR CODE HERE\n",
" self.w = self.discount_factor * self.w + 1.\n",
" self.sum_x = self.discount_factor * self.sum_x + x\n",
" self.sum_x_sq = self.discount_factor * self.sum_x_sq + x * x\n",
" self.avg = self.sum_x / self.w\n",
" mu = self.avg\n",
" self.std = np.sqrt(np.maximum(0., self.sum_x_sq / self.w - mu * mu))\n",
" \n",
" if x < self.avg + num_stdevs*self.std and x > self.avg - num_stdevs*self.std:\n",
" return x\n",
" else:\n",
" return self.avg"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "9EJxEmTX2HKK",
"nbgrader": {
"checksum": "30489db5ee60a54e15436b2db1ee239a",
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"grade_id": "cell-a946fe6eec1d8d6b",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"Let us see how it works, visually:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"deletable": false,
"editable": false,
"id": "6NCbIhoU2HKK",
"nbgrader": {
"checksum": "4b77094345b06ebaadcde76fb653c8d6",
"grade": false,
"grade_id": "cell-363a0840585a6825",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"a = DiscountedAveragerator(0.9)\n",
"xs = []\n",
"clean_xs = []\n",
"avgs = []\n",
"stds = []\n",
"cleaner = CleanData(0.9)\n",
"for x in noisy_temp_with_outliers(d=0.02):\n",
" xs.append(x)\n",
" a.add(x)\n",
" avgs.append(a.avg)\n",
" stds.append(a.std)\n",
" clean_xs.append(cleaner.filter(x, num_stdevs=2))\n",
" if len(xs) == 400:\n",
" break\n",
"plt.plot(xs, label='noisy x')\n",
"plt.plot(clean_xs, label='clean x')\n",
"# Let's move to numpy to compute average plus and minus standard deviation.\n",
"a_avg = np.array(avgs)\n",
"a_std = np.array(stds)\n",
"plt.plot(a_avg + 2. * a_std, label='avg + 2 std', color='g')\n",
"plt.plot(a_avg - 2. * a_std, label='avg - 2 std', color='g')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "zqq5ODtQ2HKM",
"nbgrader": {
"checksum": "4171f7331e970c457e7dffc270b8234e",
"grade": false,
"grade_id": "cell-94ad8f3c30436d28",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"And let us put it through some tests."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"deletable": false,
"editable": false,
"id": "NgRSqo7K2HKN",
"nbgrader": {
"checksum": "4cf7b9b83cd6c4039e2cfa70648b52f7",
"grade": true,
"grade_id": "cell-b665ab18291fc64e",
"locked": true,
"points": 10,
"schema_version": 1,
"solution": false
}
},
"outputs": [],
"source": [
"### 10 points: Tests for `CleanData`\n",
"\n",
"a = np.zeros(10)\n",
"a[3] = 1\n",
"a[8] = 10\n",
"c = CleanData(0.9)\n",
"aa = [c.filter(x) for x in a]\n",
"assert max(aa) < 2.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "BfL77RbZ2HKP",
"nbgrader": {
"checksum": "47910a33ff83d437046941474e45e201",
"grade": false,
"grade_id": "cell-b8a95de09a387db7",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"source": [
"An alternative idea that seems promising at first thought is to include in the computation of the running average and standard deviation only points that are not outliers. Let us play with the approach."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"deletable": false,
"editable": false,
"id": "jC3sTI0b2HKQ",
"nbgrader": {
"checksum": "293c8bbece8d447185eca4ef85fdd1a6",
"grade": false,
"grade_id": "cell-4af68a53daf8ff9c",
"locked": true,
"schema_version": 1,
"solution": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"a = DiscountedAveragerator(0.9)\n",
"\n",
"xs = []\n",
"avgs = []\n",
"stds = []\n",
"for x in noisy_temp_with_outliers(d=0.02):\n",
" xs.append(x)\n",
" if len(xs) >= 20:\n",
" # We need enough data to be able to rely on the statistics.\n",
" a_avg, a_std = a.avg, a.std\n",
" x_min, x_max = a_avg - 2 * a_std, a_avg + 2. * a_std\n",
" if x_min < x < x_max:\n",
" # The data is good.\n",
" a.add(x)\n",
" else:\n",
" # We add all data until we have reliable statistics.\n",
" a.add(x)\n",
" avgs.append(a.avg)\n",
" stds.append(a.std)\n",
" if len(xs) == 400:\n",
" break\n",
"\n",
"plt.plot(xs, label='x')\n",
"plt.plot(avgs, label='average')\n",
"# Let's move to numpy to compute average plus and minus standard deviation.\n",
"a_avg = np.array(avgs)\n",
"a_std = np.array(stds)\n",
"plt.plot(a_avg + 2. * a_std, label='avg + 2 std', color='g')\n",
"plt.plot(a_avg - 2. * a_std, label='avg - 2 std', color='g')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "UZl3LrYg2HKT",
"nbgrader": {
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"source": [
"We see that the problem with this approach is that, should the signal change behavior or become more noisy, or drift from its previous range, we risk disregarding all future data. Better play it safe and include in the statistics all input, in case what we think of as an outlier is really the first in a series of data with higher noise or drift in them.\n",
"\n",
"This is one more case in point supporting the author's motto: _when in doubt, be stupid._ \n",
"\n",
"It is often better to take a simpler, more robust approach (in this case, averaging all data) than to try to be smart without understanding all the facets of a problem (in this case, trusting our simple outlier detection to the point of letting it screen even the data we feed to it)."
]
},
{
"cell_type": "markdown",
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},
"source": [
"## Motion Detection"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "InMUo4Cz2HKU",
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"source": [
"We can use our averagerators to perform motion detection in a sequence of images captured by a webcam. \n",
"The idea is this. Each image will be represented as a H x W x 3 3-d array; H and W are the image height and width, respectively, and 3 is the number of color channels of a RGB image. \n",
"\n",
"We will compute the discounted average and standard deviations of _every single color pixel_ in the image. If a pixel has a value that is outside the interval $[\\mu - k\\sigma, \\mu + k\\sigma]$, where $\\mu$ is the pixel average $\\sigma$ is the pixel standard deviation, we detect motion. \n",
"Here, $k$ is a sensitivity threshold that specifies how many standard deviations must separate the value of a pixel from its average for us to detect motion. "
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "VvmseDZy2HKU",
"nbgrader": {
"checksum": "46530b240d7aa29f8d4c42fe5f29b26c",
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},
"source": [
"Computing mean and standard deviation of every pixel sounds like a crazy idea, until we realize that our DiscountedAveragerator essentially does it for us already. \n",
"So far, we have used the DiscountedAveragerator by passing to it a scalar, that is, a floating point number. \n",
"If we pass to it a value of _x_ which is a Numpy array, everything works: Numpy will re-interpret our $+$, $-$, $*$ operators as operators betwen arrays, and compute mean and standard deviation as _arrays_, one entry per color pixel, rather than scalars. "
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "g3YrD3002HKV",
"nbgrader": {
"checksum": "075b198ea9b9634e8b2fe2ee9bd5d61e",
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}
},
"source": [
"To experiment with motion detection, let us get a series of images captured by a webcam, and convert each image to a numpy matrix. \n",
"We will obtain a list of numpy matrices. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
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"editable": false,
"id": "hK2x5rcV2HKW",
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"grade_id": "cell-6e5346fce4837cd9",
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}
},
"outputs": [],
"source": [
"from PIL import Image\n",
"import requests\n",
"from zipfile import ZipFile\n",
"from io import BytesIO\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"deletable": false,
"editable": false,
"id": "y7yrVPzi2HKY",
"nbgrader": {
"checksum": "e3078e7c4d84b5afd03fbdec33827706",
"grade": false,
"grade_id": "cell-1cecc7149be7b8d4",
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}
},
"outputs": [],
"source": [
"# Gets the zip file.\n",
"ZIP_URL = \"https://storage.googleapis.com/lucadealfaro-share/GardenSequence.zip\"\n",
"r = requests.get(ZIP_URL)\n",
"# List of images, represented as numpy arrays.\n",
"images_as_arrays = []\n",
"# Makes a file object of the result.\n",
"with ZipFile(BytesIO(r.content)) as myzip:\n",
" for fn in myzip.namelist():\n",
" with myzip.open(fn) as my_image_file:\n",
" img = Image.open(my_image_file)\n",
" # Converts the image to a numpy matrix, and adds it to the list.\n",
" images_as_arrays.append(np.array(img).astype(np.float32))\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "MQCElwNh2HKa",
"nbgrader": {
"checksum": "e07efc4d95cd7285ce737f2eeaf786e4",
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}
},
"source": [
"Each numpy 3-d array has shape (Y, X, 3), where Y and X are the dimensions of the image (480 x 640 in our case), and 3 correspons to the three color channels."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"deletable": false,
"editable": false,
"id": "50lWf8zM2HKb",
"nbgrader": {
"checksum": "286ae65cf3ddc5ff26406403f2073b88",
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"grade_id": "cell-47dfa8b2a3588965",
"locked": true,
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}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(480, 640, 3)\n"
]
}
],
"source": [
"print(images_as_arrays[0].shape)\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"deletable": false,
"editable": false,
"id": "EBJuLDGX2HKe",
"nbgrader": {
"checksum": "f828e0ad449205838ebec6bdb78d28e2",
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"grade_id": "cell-36fc9c93eb570522",
"locked": true,
"schema_version": 1,
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}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"255.0\n"
]
}
],
"source": [
"print(images_as_arrays[0][10, 20, 2])\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": false,
"editable": false,
"id": "cvH-5K6I2HKh",
"nbgrader": {
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}
},
"source": [
"We can then construct a `MotionDetection` class. \n",
"Internally, it will initialize a discounted averagerator. \n",
"\n",
"We will feed images to `MotionDetection`, one by one; the images will be of size $h \\times w \\times c$, where $h$ is the height, $w$ the width, and $c$ the color depth: in our case, $480 \\times 640 \\times 3$ (but please, write you class without hardcoding $h$ and $w$). \n",
"\n",
"As we feed each image, `MotionDetection` computes which pixels of the image have one of the 3 color channels that are outside the $\\mu \\pm \\kappa \\sigma$ interval, where $\\mu$ is the average, $\\sigma$ is the standard deviation, and $\\kappa$ is a parameter; we will use $\\kappa = 4$ in our experiments, thus detecting motion if values deviate from the average by more than 4 standard deviations. The result is a $h \\times w \\times c$ boolean matrix filled with True/False values. \n",
"\n",
"To perform the above check, you can use a trick: if `a` and `b` are Numpy arrays of the same size, then `a > b` returns an array of the same size, filled with True and False:\n",
"\n"
]
},
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"text": [
"a: [[[0.58988724 0.98257164 0.65310724]\n",
" [0.17528772 0.72969077 0.1010652 ]\n",
" [0.90133345 0.50192711 0.03034517]\n",
" [0.01710612 0.82449776 0.36166953]\n",
" [0.58229081 0.78706916 0.27968468]]\n",
"\n",
" [[0.82254115 0.22839682 0.32881489]\n",
" [0.9333283 0.77659965 0.38511686]\n",
" [0.3742577 0.36388454 0.85904747]\n",
" [0.60655272 0.52103594 0.84577722]\n",
" [0.50827484 0.6277686 0.07708527]]\n",
"\n",
" [[0.61111599 0.7266579 0.55036741]\n",
" [0.26173502 0.93227912 0.56840452]\n",
" [0.80121556 0.89832329 0.58971133]\n",
" [0.87044045 0.56113117 0.61842375]\n",
" [0.02243503 0.29402925 0.73645772]]\n",
"\n",
" [[0.79541709 0.19178147 0.70087627]\n",
" [0.66369074 0.01589839 0.65296235]\n",
" [0.08858225 0.60549936 0.6470015 ]\n",
" [0.05171335 0.22675509 0.65375004]\n",
" [0.26636199 0.7828988 0.73146332]]]\n",
"b: [[[0.12316287 0.77813984 0.12399989]\n",
" [0.35647038 0.73345791 0.5070159 ]\n",
" [0.07673366 0.29047574 0.64102057]\n",
" [0.00455623 0.85792226 0.77562966]\n",
" [0.43420941 0.94829584 0.18574847]]\n",
"\n",
" [[0.20712861 0.50931562 0.45514622]\n",
" [0.62857408 0.69992506 0.48534169]\n",
" [0.38674344 0.23880634 0.91401087]\n",
" [0.82350658 0.71876304 0.86420415]\n",
" [0.90322959 0.43077208 0.7263074 ]]\n",
"\n",
" [[0.17241489 0.1919637 0.04482737]\n",
" [0.93460231 0.9132634 0.11102496]\n",
" [0.59754146 0.83956064 0.67582432]\n",
" [0.07331473 0.03653652 0.58847148]\n",
" [0.5666586 0.13717583 0.24138978]]\n",
"\n",
" [[0.66801439 0.6211336 0.62416392]\n",
" [0.08466707 0.17559581 0.69477133]\n",
" [0.84374102 0.19496068 0.37426721]\n",
" [0.22238644 0.47545646 0.03210523]\n",
" [0.66333275 0.79471338 0.17922195]]]\n",
"a > b: [[[ True True True]\n",
" [False False False]\n",
" [ True True False]\n",
" [ True False False]\n",
" [ True False True]]\n",
"\n",
" [[ True False False]\n",
" [ True True False]\n",
" [False True False]\n",
" [False False False]\n",
" [False True False]]\n",
"\n",
" [[ True True True]\n",
" [False True True]\n",
" [ True True False]\n",
" [ True True True]\n",
" [False True True]]\n",
"\n",
" [[ True False True]\n",
" [ True False False]\n",
" [False True True]\n",
" [False False True]\n",
" [False False True]]]\n"
]
}
],
"source": [
"a = np.random.random((4, 5, 3))\n",
"b = np.random.random((4, 5, 3))\n",
"print(\"a:\", a)\n",
"print(\"b:\", b)\n",
"print(\"a > b:\", a > b)\n"
]
},
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"source": [
"Moreover, if you have two arrays of the same size, you can compute their _or_ via `np.logical_or`: "
]
},
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{
"data": {
"text/plain": [
"array([[False, True, False, True, True],\n",
" [False, False, True, True, False],\n",
" [False, False, True, False, False],\n",
" [ True, False, True, True, False]])"
]
},
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"metadata": {},
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}
],
"source": [
"a = np.random.random((4, 5)) > 0.7\n",
"b = np.random.random((4, 5)) > 0.7\n",
"np.logical_or(a, b)\n"
]
},
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"source": [
"Finally, we take the union of the motion detections over the three color channels, obtaining a boolean 2-d array of size $h \\times w$. \n",
"This array will contain the motion detection for each image. \n",
"To take the union, you can use `np.max`, specifying the max to be taken over axis 2, which is the one for color: \n"
]
},
{
"cell_type": "code",
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"id": "rLEaCTLw2HKp",
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{
"name": "stdout",
"output_type": "stream",
"text": [
"aa shape: (4, 5, 3)\n",
"b shape: (4, 5)\n",
"b: [[False False False False False]\n",
" [False False False False False]\n",
" [ True True False True False]\n",
" [ True True True True True]]\n"
]
}
],
"source": [
"a = np.random.random((4, 5, 3))\n",
"aa = a > 0.8\n",
"print(\"aa shape:\", aa.shape)\n",
"b = np.max(aa, axis=2)\n",
"print(\"b shape:\", b.shape)\n",
"print(\"b:\", b)\n"
]
},
{
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},
"source": [
"We let you build the class `MotionDetection`."
]
},
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"source": [
"### Question 3: Implement the `MotionDetection` class\n",
"\n",
"class MotionDetection(object):\n",
"\n",
" def __init__(self, num_sigmas=4., discount=0.96):\n",
" \"\"\"Motion detection implemented via averagerator.\n",
" @param num_sigmas: by how many standard deviations should a pixel\n",
" differ from the average for motion to be detected. This is\n",
" the \\kappa of the above explanation.\n",
" @param discount: discount factor for the averagerator.\n",
" \"\"\"\n",
" # YOUR CODE HERE\n",
" self.discount = discount\n",
" self.num_sigmas = num_sigmas\n",
" self.w = 0.\n",
" self.sum_x = 0.\n",
" self.sum_x_sq = 0.\n",
"\n",
" def detect_motion(self, img):\n",
" \"\"\"Detects motion.\n",
" @param img: an h x w x 3 image.\n",
" @returns: an h x w boolean matrix, indicating where motion occurred.\n",
" A pixel is considered a motion pixel if one of its color bands deviates\n",
" by more than num_sigmas standard deviations from the average.\"\"\"\n",
" # YOUR CODE HERE\n",
" self.w = self.discount * self.w + 1.\n",
" self.sum_x = self.discount * self.sum_x + img\n",
" self.sum_x_sq = self.discount * self.sum_x_sq + img * img\n",
" avg = self.sum_x / self.w\n",
" std = np.sqrt(np.maximum(0., self.sum_x_sq / self.w - avg * avg))\n",
" \n",
" maxima = avg + self.num_sigmas * std\n",
" minima = avg - self.num_sigmas * std\n",
" b = np.logical_or(img > maxima, img < minima)\n",
" return np.max(b, axis=2)\n",
" "
]
},
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"source": [
"Let's write a `detect_motion` function to facilitate our experiments. It will take a list of images, and compute the motion detection of each. If the motion detection contains more than 500 motion pixels, it puts the detection, and the index of the image, into a list of results. "
]
},
{
"cell_type": "code",
"execution_count": 38,
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"id": "qUTrjxdp2HKw",
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"outputs": [],
"source": [
"def detect_motion(image_list, num_sigmas=4., discount=0.96):\n",
" \"\"\"Takes as input:\n",
" @param image_list: a list of images, all of the same size.\n",
" @param num_sigmas: a parameter specifying how many standard deviations a\n",
" pixel should be to count as detected motion.\n",
" @param discount: the discount factor for the averagerator.\n",
" \"\"\"\n",
" detector = MotionDetection(num_sigmas=num_sigmas, discount=discount)\n",
" detected_motion = []\n",
" for i, img in enumerate(image_list):\n",
" motion = detector.detect_motion(img)\n",
" if np.sum(motion) > 500:\n",
" detected_motion.append((i, motion))\n",
" return detected_motion\n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
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"editable": false,
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"outputs": [],
"source": [
"# Compute the motion detections.\n",
"motions = detect_motion(images_as_arrays[:60])\n"
]
},
{
"cell_type": "markdown",
"metadata": {
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"id": "yT6HnmF52HK2",
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"source": [
"We can finally visualize the detected motions. "
]
},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Motion at image 1 : 548 ------------------------------------\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
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},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
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\n",
"text/plain": [
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Motion at image 10 : 550 ------------------------------------\n"
]
},
{
"data": {
"image/png":...
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