diff --git a/01-g-h-filter.ipynb b/01-g-h-filter.ipynb index 6c50ea1..d9f296a 100644 --- a/01-g-h-filter.ipynb +++ b/01-g-h-filter.ipynb @@ -272,7 +272,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Before we start, be sure you understand how to use Jupyter Notebooks, and are familiar with the SciPy, NumPy, and Matplotlib packages, as they are used throughout this book. The Preface contains an introduction to these packages." + "Before we start, be sure you understand how to use [Jupyter Notebooks](http://jupyter.org/), and are familiar with the [SciPy](https://scipy.org), [NumPy](http://www.numpy.org/), and [Matplotlib](https://matplotlib.org/) packages, as they are used throughout this book. The Preface contains an introduction to these packages." ] }, { @@ -294,7 +294,7 @@ "\n", "\"I never said it was accurate,\" she replies.\n", "\n", - "Sensors are inaccurate. This is the motivation behind a huge body of work in filtering, and solving this problem is the topic of this book. I could just provide the solutions that have been developed over the last half century, but these solutions were developed by asking very basic, fundamental questions into the nature of what we know and how we know it. Before we attempt the math, let's follow that journey of discovery, and see if it does not inform our intuition about filtering. " + "Sensors are inaccurate. This is the motivation behind a huge body of work in filtering, and solving this problem is the topic of this book. I could just provide the solutions that have been developed over the last half century, but these solutions were developed by asking very basic, fundamental questions into the nature of what we know and how we know it. Before we attempt the math, let's follow that journey of discovery, and see if it informs our intuition about filtering. " ] }, { @@ -309,29 +309,31 @@ "\n", "* We could choose to only believe A, and assign 160lbs to our weight estimate.\n", "* We could choose to only believe B, and assign 170lbs to our weight.\n", - "* We could choose a number less than either A or B.\n", - "* We could choose a number greater than either A or B.\n", + "* We could choose a number less than both A and B.\n", + "* We could choose a number greater than both A and B.\n", "* We could choose a number between A and B.\n", "\n", - "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not probably the answer is somewhere between A and B. \n", + "The first two choices are plausible, but we have no reason to favor one scale over the other. Why would we choose to believe A instead of B? We have no reason for such a belief. The third and fourth choices are irrational. The scales are admittedly not very accurate, but there is no reason at all to choose a number outside of the range of what they both measured. The final choice is the only reasonable one. If both scales are inaccurate, and as likely to give a result above my actual weight as below it, more often than not the answer is somewhere between A and B. \n", "\n", "In mathematics this concept is formalized as [*expected value*](https://en.wikipedia.org/wiki/Expected_value), and we will cover it in depth later. For now ask yourself what would be the 'usual' thing to happen if we took one million readings. Some of the times both scales will read too low, sometimes both will read too high, and the rest of the time they will straddle the actual weight. If they straddle the actual weight then certainly we should choose a number between A and B. If they don't straddle then we don't know if they are both too high or low, but by choosing a number between A and B we at least mitigate the effect of the worst measurement. For example, suppose our actual weight is 180 lbs. 160 lbs is a big error. But if we choose a weight between 160 lbs and 170 lbs our estimate will be better than 160 lbs. The same argument holds if both scales returned a value greater than the actual weight.\n", "\n", "We will deal with this more formally later, but for now I hope it is clear that our best estimate is the average of A and B. $\\frac{160+170}{2} = 165$.\n", "\n", - "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The measurements falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 pounds. However, if we look at how they overlap we can further constrain the estimate." + "We can look at this graphically. I have plotted the measurements of A and B with an assumed error of $\\pm$ 8 lbs. The measurements falls between 160 and 170 so the only weight that makes sense must lie within 160 and 170 lbs. " ] }, { "cell_type": "code", "execution_count": 2, - "metadata": {}, + "metadata": { + "scrolled": false + }, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -340,22 +342,30 @@ ], "source": [ "import kf_book.book_plots as book_plots\n", - "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], \n", - " xlims=(150, 180))" + "from kf_book.book_plots import plot_errorbars\n", + "plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "> A word on how I generated this plot. I import code from the module book_plots in the `kf_book` subdirectory. Generating this plot takes a lot of boilerplate Python that isn't interesting to read. I take this tack often in the book. When the cell is run `plot_errorbars()` gets called and the plot is inserted into the book." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 171 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n", + "A word on how I generated this plot. I import code from the module book_plots in the `kf_book` subdirectory. Generating this plot takes a lot of boilerplate Python that isn't interesting to read. I take this tack often in the book. When the cell is run `plot_errorbars()` gets called and the plot is inserted into the book.\n", + "\n", + "If this is your first time using [Jupyter Notebook](http://jupyter.org/), the code above is in a *cell*. The text \"In [2]:\" labels this as a cell where you can enter input, and the number in the bracket denotes that this cell was run second. To run the cell, click on it with your mouse so that it has focus, then press CTRL+ENTER on the keyboard. As we continue you will be able to alter the code inside the cells and rerun them. Try changing the values \"160\", \"170\", and \"10000\" to some other value and run the cell. The printed output should change depending on what you entered.\n", + "\n", + "If you want to view the code for plot_errorbars, either open it in an editor, or create a new cell and type the function name followed by two question marks. Press Ctrl+Enter, and your browser will open a window displaying the source code. This is a feature of Jupyter Notebooks. If you want to just view the documentation for the function, do the same but with one question mark.\n", + "\n", + "```Python\n", + "\n", + " plot_errorbars??\n", + "```\n", + "or\n", + "```Python\n", + " plot_errorbars?\n", + "```\n", + "\n", + "So 165 lbs looks like a reasonable estimate, but there is more information here that we might be able to take advantage of. The only weights that are possible lie in the intersection between the error bars of A and B. For example, a weight of 161 lbs is impossible because scale B could not give a reading of 170 lbs with a maximum error of 8 pounds. Likewise a weight of 169 lbs is impossible because scale A could not give a reading of 160 lbs with a maximum error of 8 lbs. In this example the only possible weights lie in the range of 162 to 168 lbs.\n", "\n", "That doesn't yet allow us to find a better weight estimate, but let's play 'what if' some more. What if we are now told that A is three times more accurate than B? Consider the 5 options we listed above. It still makes no sense to choose a number outside the range of A and B, so we will not consider those. It perhaps seems more compelling to choose A as our estimate - after all, we know it is more accurate, why not use it instead of B? Can B possibly improve our knowledge over A alone?\n", "\n", @@ -369,9 +379,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -379,8 +389,7 @@ } ], "source": [ - "book_plots.plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], \n", - " xlims=(150, 180))" + "plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))" ] }, { @@ -399,9 +408,9 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -409,8 +418,7 @@ } ], "source": [ - "book_plots.plot_errorbars([(160, 1, 'A'), (170, 9, 'B')],\n", - " xlims=(150, 180))" + "plot_errorbars([(160, 1, 'A'), (170, 9, 'B')], xlims=(150, 180))" ] }, { @@ -419,11 +427,11 @@ "source": [ "Here we can see that the only possible weight is 161 lbs. This is an important result. With two relatively inaccurate sensors we are able to deduce an extremely accurate result.\n", "\n", - "So two sensors, even if one is less accurate than the other, is better than one.\n", + "**So two sensors, even if one is less accurate than the other, is better than one.** I will harp on this for the remainder of the book. We never throw information away, no matter how poor it is. We will be developing math and algorithms that allow us to include all possible sources of information to form the best estimate possible.\n", "\n", "However, we have strayed from our problem. No customer is going to want to buy multiple scales, and besides, we initially started with an assumption that all scales were equally (in)accurate. This insight of using all measurements regardless of accuracy will play a large role later, so don't forget it.\n", "\n", - "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's write a simulation for now." + "What if I have one scale, but I weigh myself many times? We concluded that if we had two scales of equal accuracy we should average the results of their measurements. What if I weigh myself 10,000 times with one scale? We have already stated that the scale is equally likely to return a number too large as it is to return one that is too small. It is not that hard to prove that the average of a large number of weights will be very close to the actual weight, but let's write a simulation for now. I will use NumPy, part of the [SciPy](https://scipy.org/) ecosystem for numerical computation." ] }, { @@ -435,15 +443,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "Average of measurements is 165.0079\n" + "Average of measurements is 164.9961\n" ] } ], "source": [ "import numpy as np\n", "measurements = np.random.uniform(160, 170, size=10000)\n", - "print('Average of measurements is {:.4f}'.format(\n", - " measurements.mean()))" + "mean = measurements.mean()\n", + "print('Average of measurements is {:.4f}'.format(mean))" ] }, { @@ -452,9 +460,7 @@ "source": [ "The exact number printed depends on your random number generator, but it should be very close to 165.\n", "\n", - "If this is your first time using Jupyter Notebook, the code below is in a *cell*. The text \"In [2]:\" labels this as a cell where you can enter input, and the number in the bracket denotes that this cell was run second. To run the cell, click on it with your mouse so that it has focus, then press CTRL+ENTER on the keyboard. As we continue you will be able to alter the code inside the cells and rerun them. Try changing the values \"160\", \"170\", and \"10000\" to some other value and run the cell. The printed output should change depending on what you entered.\n", - "\n", - "This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements very similar to how a real scale would." + "This code makes one assumption that probably isn't true - that the scale is as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `numpy.random.normal()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements similar to how a real scale works." ] }, { @@ -466,25 +472,24 @@ "name": "stdout", "output_type": "stream", "text": [ - "Average of measurements is 164.9937\n" + "Average of measurements is 165.0258\n" ] } ], "source": [ - "measurements = np.random.normal(165, 5, size=10000)\n", - "print('Average of measurements is {:.4f}'.format(\n", - " measurements.mean()))" + "mean = np.random.normal(165, 5, size=10000).mean()\n", + "print('Average of measurements is {:.4f}'.format(mean))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The answer again is very close to 165. \n", + "Again the answer is very close to 165. \n", "\n", "Okay, great, we have an answer to our sensor problem! But it is not a very practical answer. No one has the patience to weigh themselves ten thousand, or even a dozen times. \n", "\n", - "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n", + "So, let's play 'what if'. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n", "\n", "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the measurements along with the error bars, and then some possible weight gain/losses that could be explained by those measurements in dotted green lines." ] @@ -496,9 +501,9 @@ "outputs": [ { "data": { - "image/png": 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SF6JAkwJCCJFjmjs1Z06nOQBM3DmRzec3K5xR7lOpVHSs0pGtvlsJez+Mdxu+\ni4WpBf/c+oePd3wsTyKEyKJtl7ZRY04NJu2cROTDSGYdnEXzRc1xnO7ImK1j+CvyL/ToCbsbZtin\ndJHSfNjsQyoWr6hg5kIUfHmmD4QQomAY5jqM47eOM/+f+QTsCaBT1U6oVCql01KEi4MLC7os4Ku2\nX/HzPz/jYOWAxiRtsqQUXQoT/5zIoAaDZPQXIf7jzL0z+AT7kKpPJSImgsqzKpOif/r07o3yb+Bd\n05seLj1wKuqkYKZCFE5SQAghctwsj1kUsyjGhGYTCm3x8CwHawcmtZyUbt3aM2v59u9v+fbvb/Go\n4oG/uz9vVnpTzpco1K4+uMrSE0v54cAPxCbH0sKpBYu6LiI6IZp4bTw+Lj541fSSSRyFUJgUEEKI\nHGdmYsb/3vyf0mnkaZWKV6Jr9a5sOLeBLRe3sOXiFmo51GKs+1j61emX6SgzQhQ0ETERhISHEHIm\nhMM3DhvWO9k6EdorFHNTczb22Wh4eieEUJ70gRBCGJVer+enIz8xeVfWJn0qLFzLurKu9zrOjz7P\naLfRWGusCbsXxrsb38VpphO3H91WOkUhjGrtmbU0/qUxlX6sxIQdE9IVDxamFqz2WU0Jq7SJX6V4\nECJvkQJCCGFUh28cZuTvI/li7xesDlutdDp5ThW7Kvzo8SPXx13n+/bf41TUiap2VSldpLQhRooJ\nURBcvH+Re/H3DMuPkh9x9OZR1Co1bZzbMM59HABqlZq1vdbSxLGJUqkKIV5CmjAJIYyqiWMTxjcd\nz/cHvmfQ+kFUt69OvdL1lE4rzylmUYwP3vgAP3c/7jy6Y1h/P+E+lX+sjLujO2ObjMWzmucLZ+AV\nIi85H32e4LBgQs6EcOL2Cb558xsmNJsAwNvV32a+53y61+xOSeuSADQo04DYpFjeqvKWkmkLIV5C\nCgghhNFNe3Ma/979l22XttE1qCtHhx01NE0Q6ZmqTdNNTLf36l6SUpLYGbGTnRE7qWpXFb8mfgys\nP7DAz/Yt8qezUWcNRcO/d/41rDdRmXAj9oZhuahFUYY3Gp5uX9+6vrmWpxDi1cnXWEIIozNRmxDU\nI4gqdlW4+vAqPsE+aFO1SqeVL3Sr0Y3Lfpf58I0PKWpelAv3LzBqyygcZzjy0faP0jUJEUJpCdoE\nXBe48vnuz/n3zr+Yqk3pWLkjC7ss5M74O8zymJUu/lbcLbxXe0szPSHyGSkghBC5orhlcdb1WkcR\nsyLsvrKbD7Z9oHRK+YZTUSe+bf8t18ddZ7bHbKrYVeFB4gNmHJyBVieFmMh9er2e03dPM3nXZHqs\n7mFYb6mxpGv1rnhU8WDR24sJ2GayAAAgAElEQVS4M/4OW323MqThEOyt7NMdI0GbQLffurHmzBre\nWfdObr8FIcRrkCZMQohcU6tkLX7t/is9VvegvG159Hq9zHuQDUXMijDKbRTvN36fzec3cybqDGVt\nyhq2j982niblmtC9ZndM1XJ5FzlLr9dz6u4pQ/Oks1FnDdvORp01TIi4wmvFS3+v9Xo9g9YP4vCN\nw9hZ2jG301yj5i6EyFnyF0YIkau61ujK+dHnqVS8ktKp5FtqlZou1bvQpXoXw7qwu2H8cOAHACoU\nrcBot9EMaTiEYhbFlEpTFCAh4SFM3DmR89HnDevMTMx4q8pbeNf0ppzN0347WflSYMqeKfwW9hsa\ntYbQnqFUsatilLyFEMYhTZiEELnu2eIhLiku3ahD4tWUtC7JZy0/o4RVCa4+vMr47eMpP6M8Y7aM\n4dL9S0qnJ/IRvV7PsVvHuPbwmmGdRq3hfPR5zE3M6VajGyu8VnDvw3us772e/vX6Y2Nuk+XjB50O\nYsqeKQDM7zyfVs6tcvw9CCGMSwoIIYRiLsdcpmlgU7oGdSUxJVHpdPI1B2sHvmjzBZFjI1nYZSG1\nHGrxKPkRsw/Ppursqmy/tF3pFEUeptfrOXrzKB9t/4gqs6vgusCVn//52bC9Y5WOrPRayb0P77G2\n11r61umLrblttl/n0PVDDFw3EIDxTcczuMHgnHoLQohcJE2YhBCK0ev13Iy7SUxiDCM2j2DR24uk\nT8RrstRYMqThEAY3GMyOyzuYcXAGx28fp0WFFoaY89HncS7mjJmJmYKZCqXp9XqO3Dxi6NNw5cEV\nwzZLU0sStAmGZQtTC/rU6fPar1nCqgSVileiqn1Vpr057bWPJ4RQhhQQQgjFVLarzGqf1XT8tSNL\nTiyhQekGjGkyRum0CgSVSkX7yu1pX7k9DxMfYmFqAYBOr8NzpSfxyfGMbDyS4Y2Gy5wchVSKLgWP\nFR7cT7gPgJXGCs+qnvi4+NCpaiejzDNS2a4yB4YcQK1SY6I2yfHjCyFyhzRhEqIA+PDDCkqn8Mre\nrPQm37f/HoBxf4xjZ8ROhTMqeIpaFDX8OyImgvjkeG49usWkXZMoP6M8wzcO58y9MwpmKIxJp9fx\n97W/8d/qT4vFLdDr9QBoTDT41vGlV61ehPiEcO/De6z2WY1PLZ8cLR5SdakcvnHYsFzUomi2+kwI\nIfIeKSCEKAD+/jt//zEe6z6W/nX7k6pPpWdwTyJiIpROqcCqbFeZK2OvsLz7chqWaUhiSiILji3A\n5ScXPFZ48M/Nf5ROUeQAnV7Hvsh9+G3xw2mGE80WNWPmoZnsi9zH0ZtHDXGzPGYR5B1ED5ceWGms\njJLLJ39+QtPApsw9LEO1ClFQSAEhhFCcSqXi584/06hsI6ITohmxeYTSKRVoZiZm+Nb15ei7R9kz\ncA/da3RHhYqtF7cSr41XOj3xmrbd2IbjdEdaLG7Bj4d/5EbcDWzMbOhXpx/req2jTqk6uZbL4uOL\n+e7v79DpddhZ2uXa6wohjEv6QAgh8gRLjSVre61l5O8jmec5T+l0CgWVSkXLCi1pWaEll2MuExwW\nTAunp52tv9jzBcmpyYxsPJIyNmUUzFRkJlWXyl+Rf1GmyNP/n+Jmxbn16BZFzYvStUZXvGt606Fy\nB8xNzXM1tz1X9jB803AAPm/5eY50whZC5A1SQAgh8gxHW0fW916vdBqFUqXilfio+UeG5dikWL7/\n+3vikuP4dv+39K7dG393fxqUaaBglgLSOj/vvbqX4LBgQs+Gcjf+btrEgWWHANCwREN+7/s7bSu2\nzfWi4YlL9y/htdoLrU5Lz1o9mdx6siJ5CCGMQwoIIUSe9dvp37A2s6Zztc5Kp1LoWGmsWNx1MTMO\nzmD/tf0s/3c5y/9dTqsKrfB396dztc7MmmnC9OnZO65WW9Pwb40me/uOG5f2Uxjp9Dp2RuwkOCyY\ntWfXcu/xPcO24hbF0/VfMFGZ4FHVQ4k0AXiQ+IDOqzpzP+E+jcs2ZknXJahV0mJaiIJECgghRJ60\n4dwGeq/pjY2ZDYeGHqKmQ82X7yRyjKnalB4uPejh0oPDNw4z8+BMgsOD2XN1D3uu7mFqm6mkxE7i\nxo3sHvnV556IjX3lXfMlvV6fbl6UQesHcT32OgB2lnZ0r9EdHxcf2lZsi8ZEw8mTJ5VKNZ0V/67g\nbNRZwxNFS42l0ikJIXKYFBBCiDzJo4oHLSu0ZO/VvXQN6srhdw9TzKKY0mkVSm7l3FjZYyXftv+W\nOYfnEHg8kP51+7PmKJQrB9qi51ClWGIa7/TC4+j1cPNm2r8dHLSYmWXvEYRt9ic+zne0qVr+jPiT\nkPAQ9l/bz6kRpzBVm6JWqXm34btcj72Oj4sPrZ1bozHJ5iOcXPJ+4/dJ1afSwqlFgeo78+GHFfjr\nL6WzECJvUOmfDAitkLi4OKZOncqJEyc4fvw4UVFRTJ48mYCAgHRxL5qdtnr16pw9ezbdutmzZzN3\n7lwiIiIoW7YsAwcO5NNPP0Xzn2fmOp2OuLi4dOtsbGxQq+Vxa045efIkWq0WjUZDvXr1lE6nwIiP\nhyJF0v6tVutJTS14Mzjfjb9LowWNuBZ7DY8qHmzsszFXJp+Sz+yLaVO16W5e3171Nr9f+J0eLj3w\nd/fH3dE9w/2e/cweOHAKd/fcGw0oL0tOTWbH5R0Ehwez/ux6YhJjDNt29N9Bu0rtsnQcpT+3/31i\nUhAUhuuskpT+zBZEuXVfq/hdcnR0NAsWLCApKYlu3bplGnfgwIHnfmbOnAlA9+7d08V+9dVX+Pn5\n4eXlxR9//MH777/P119/zciRI436XoTITampT/+t16dfLihKWpdkXe91WJpasuXiFibtnKR0SgLS\nFQ/aVC0JKQmk6lNZHbaapoFNcV/ozm+nfyNFl6JglvlDcFgwJb8riedKT5acWEJMYgylrEsxotEI\ndg7YSWvn1kqnmCXbLm2jy6ouPEx8qHQqQohcoHgTpgoVKhATE4NKpSIqKoqFCxdmGOfu/vw3Wj//\n/DMqlYohQ4YY1kVHR/Pll1/y7rvv8vXXXwPQunVrtFotkyZNYuzYsbi4uBjnzQiRS0JDYcyYp8t6\nvQpnZ5g1C7y8FEvLKBqWaUjg24H0De3LtP3TqF+6Pr1q91I6LfH/NCYatvffzsnbJ5l5aCYrT63k\n0I1D9F7Tm/Lby/Nl2y8ZUG+A0mnmCYkpiWy7tA1HW0calmkIpE3s9zDpIaWLlKZHzR74uPjQ3Kl5\nrjxpyyln7p3BJ9jHMHLX1LZTlU5JCGFkij+BUKlUr/TIMy4ujuDgYFq1akWVKlUM67du3UpiYiKD\nBg1KFz9o0CD0ej3r1q177ZyFUFJoKHh781zn1Rs30taHhiqTlzH1qdOHj5qlDTEadi9M4WxERuqV\nrsfirouJHBvJ5FaTcbBy4FrsNeKTC/fEdAnaBNadXUe/0H6U/K4kXYO68uOhHw3bG5RuwP7B+7nu\nf505nebQyrlVvioeoh5H0XlVZ2KTYmnh1IJJLeUpoRCFgeJPIF5VUFAQ8fHxDB06NN3606dPA1Cn\nTvq2tWXKlKFEiRKG7ULkR6mp4OeX1mTpv/R6UKn0+PnpedMjARMTMFGbYGFqYYh50c2cWqVON1pK\ndmIfax+TWXcqlUqVbojJ7MQmaBPQ6XUAfNr8U5qXb06bim0MuVmbWWcYm5FnYxNTEknVZa3N18ti\nrTRWhi9BklKSXthsJzuxlhpLw9CXyanJaFO1ORJrYWphuEHNTqw2VUtyanKmseam5piqTSlVpBQT\nW0xktNtogsOC8arpZfj/WnB8KfTdBAfGodeXBNLmNEhKScr0uGYmZoYmU9mJTdWlkpiSmGmsxkSD\nmYlZtmN1eh0J2oQXxmrUGtaeXcvqsNVsvrCZR8mPDNvL2pSldJHSxCfHY6o2xdzUnDfKv4Fer3/h\n79yTWEjra/BY+/i5mISUBLQpWnTq9L8HLzru61wjYhJi6BbUjcsxl3Eu5szy7stJ0aWQkpyiyDUi\nI697jYhPBjSA1jrT/YQojBTvRP2sqKgoHBwcMuxE/V/u7u6cO3eOW7duYWHx9OI3bNgwli1bRmLi\n838MqlevjrOzM3/88YdhXUadTSIjI9HpMr/IiOzRap/eoPy3E7vIniNHrHn33SovD3ynNVTcQ/NS\nzZnTdI5htftGdxJTM75RcrV3JbBFoGG5ze9tiEmOyTDWpZgLK1uvNCx7/OHBrYRbGcZWsqlEaLun\nj0W8/vTictzlDGPLWJZhS8cthuW+u/sS/iA8w9himmJs99iORp32mRry1xD+if4nw1gLEwsOdjlo\nWB51YBT77uzLMBbgiOcRw78/Of4JO27uyDT2QOcDWJqm3Sh99s9nbLy2MdPYnR47sTO3A+Drk1+z\nOmJ1prGb22+mnHU5AKafns6yi8syjQ1pG0IV27TPxbwz8/j53M+Zxv7a6ldqF68NwJILS5gZNjPT\n2F+a/UJjh8YABF0OYtq/0zKN/dH9R1qWbgnA+qvrmXz8xROHVS1Snf7V+mGqMuXTfz7NNG5Kgyl0\nrdAVgL239zLm4JhMYz+u+zG9K/UG4Mi9I7y7/91MY8fWGsvAqgMBOB1zGt89vpnGDq8+nBE1RwBw\nMfYi3ju9M40dUGUA42qPe+Hn/ImeFXvyab20934/6T5tt7TNNLZL+S5MdU1rGpSQkkDTTU0zjW1X\nuh0/uP9gWK6/rn6msa96jdDr9TTZ2IRkXcZFZV64RhQ3K86uTrsMy691jQjQo1brOXbs3wz3F69G\n7g9ynlqtxskp/Yh4xuhEnS+fQISFhXHo0CFGjhyZrnh44kVNorLSXColJYXUgtgjNQ949mIhsu/O\nnSxeAB6lDZ2o1+mzfM71+vSxejL/buG/sdk67ku+s8hqbFxKHN+e/JYJtSdk/7i6rH9v8rJYrVaL\nqT7tUvqibzcBUrQpaNVpebzsS4qUlBRDzkaLTX1xbGpqqiH2ZdfE1JSsx5JixoVH5/j82OcUMS2S\n9RxSXpJDNvLVpeoMsSkpL+7srdNlP7aHUw8uxF5g3bXMm82mO672JcfVP43Vprz8dy/Lv5+veI1Y\ncXlFpsXDf2Ozc9wnyy+S1Vg9r3HcTH7v5W+Y8ci5zRkmJrnTBDJfPoEYN24cM2bM4Pjx49Svn/6b\nlU8++YRp06YRHx+PlZVVum0ODg60b9+elSuffisiTyCMT75hyDlZfQIxd344DRvFolapMTcxN6xP\nSMm86YVKpcLCxCLHYwHDN/TZjU1MTczwj/7+O/sZf2Q8AJPrT6a7c/dMYzM6blJq0gtv9p8UBAA6\nte6FsRYmFoYvJpJTk0nVZ37jmp1YcxNzQ7MkrU77wuZO2Yk1MzHDRGWS47EatQZTtekLYxMSVLRt\nWxs0jxg2/0vW3vyNe4lpMyo3L9mc79y+e24fU7Wp4SlTii4FrS7zm4xnY1P1qS9scvWqsY+0j9h5\ncyc7b+3kwN0DJOmeNqn6tvG3tCnTxhCr0+tISs28yZWJysTQNEqv12f6zX9WY59ca9UqNUUsnhZm\nL/qde9VrxLmH5xhzYAz9KvfDp6LPC2NfdlzI+WvE68Y+uUYYPrNaa3kCYQRyf5Dz5AlEJpKTk1m+\nfDmurq7PFQ/wtO/DqVOnaNKkiWH97du3iYqKonbt2i99jVq1ask8EDlIxnnOObVrw5QpaR2mM/o7\nqFKBoyMMH+pCLn0JoQh33EkoksBnuz7j63+/pkPDDrxR/o0cO758Zo0jPh7QAlprBlUdxpy+0wkO\nD2bGwRl81vYz3CunjbZ3M+4mJ2+fpGOVjobCKC9YE74G302+6fpLVCpeCR8XH3xcfGhYpqGi8yDk\n5ue2HvXo6NYRW3PbAjf3w7NiY0n7zJJ2za1du16BvrbmNrnW5ryMvhg3hrxzZc6iDRs2EBUVlW7o\n1me99dZbWFhYsGTJknTrlyxZgkqleuFcE0LkdSYmaUO1Qlqx8KwnyzNnUij+wE1sMZEeNXug1Wnp\nsboHN2JvvHwnkadoTDT0rdOXw0MP075Se8P62Ydm02llJ2r/VJufj/6cYYdhY3uY+JBf//2VPVf2\nGNbVLVWXxJREqthV4ZPmn3Bs2DEujr7ItDen4VrWtUDfSAPcfnSbg9ef9hMoalG0QL/n0FB4dtT3\nJ8NlF8SR7oTIrjzxBGLLli3Ex8cbKqbw8HBCQkIA6NSpU7qmSIGBgVhaWtK3b98Mj2VnZ8ekSZP4\n7LPPsLOzo0OHDhw5coSAgACGDh0qc0CIfM/LC0JC0uaBeHYoV0fHtOKhoM0DkRmVSsWSbks4H32e\nU3dP0f237uwdtDfdiDIif/jvTailxhIbMxvORJ3hvc3vMXHnRIa7Dmek20jK2pQ1Wh4PEh+w4dwG\ngsOD2XZpG8mpyXSr0Y1Wzq0AqGpflfD3w6lRokaBvnHOSII2ga5BXTlx+wS/ef9GtxoF+8u4J8Nl\n//dJ75PhskNCCs+1VoiM5Ik+EM7Ozly9ejXDbRERETg7OwNw7do1nJ2d8fX1ZenSpS885o8//sjc\nuXO5cuUKpUuXZtCgQUycOPG5Nna5NeV3YSaPKI0jNhaKFk37t0qlR6tVFYonD/91OeYyjX9pzP2E\n+7zf6H3mes597WPKZ9Y44uOhyP83zT9w4BTu7nUyjY1NimXR8UX8eOhHIh5EAGn9LIY0GMK8zvNy\nLCe9Xs+yk8tYHb6a7Ze2p+tjUaNEDfrX7c+nLTIfJSovMdbnVq/X0ze0L0GngyhuUZxDQw9R1b5q\njh0/r0lNBWdnuH494+1PmopGRBSOp73GJNfanJdb97V54gnElStXshRXvnz5LI+ONGbMGMaMyXy4\nPyHyu2f/cKlUhfcPWaXilVjtvRr/P/wZ6z5W6XREDrE1t2Ws+1hGu41m/bn1zDg4g32R+wwdtSHt\nxlan12V74rX45HjDmP8qlYr5/8w3NM1xcXAx9GmoVbJWzr2hfOyLPV8QdDoIU7Upob1CC3TxAPDX\nX5kXD5D2VOLatbS41q1zLS0h8pQ8UUAIIcTraFepHceHH89XM/iKrDFRm+BV0wuvml4cvXmUktYl\nDdsOXD9A/7X9GeM2hsENBmNjbpPpcaIeR7Hu7DpCwkP4K/Ivrvtfp7hlcQBGu43Go4oH3i7euDhI\nM9dn/Xb6NwL2BAAwz3MerZ1bK5pPbriV8XQVrxwnREEkBYQQokB4tnjYcXkHlYpXolLxSgpmJHJa\no7KN0i0v+GcBl2MuM/aPsXy++3OGNhjK6CajcS7mDMC9+HusPbuWkPAQdkbsTDds7q4ru/CqmdaI\nvW+djPvUFXaHbxxm4PqBAHzQ9AOGNhyqbEK5pEyZnI0ToiCSAkIIUaCsOrUK37W+1HKoxd9D/qaI\n2YsnKhP510+eP+Hu6M7MgzM5F32O6QenM/PQTLxqetGwdEM+2/VZuqKhQekGeLt44+3iTTX7agpm\nnj8sObGExJREOlfrzDdvfqN0OrmmRYu0Pg4vGy67RYvcz02IvCJHC4hr164RFhZG48aNsbe3z8lD\nCyFElrSs0JKS1iU5dfcUA9cNJNgnuNCNmFNYWGmseK/Re7xd/W2++usr9kfu5+Sdk4SEh3Do+iH0\n6GlYpiE+Lj54u3hTxe7lkzCKp+Z0mkN1++oMbjC4UDUPfDJctrd3WrHwbBFR2IbLFiIzr9wle9Kk\nSfj7+xuWd+zYQbVq1fD09KRatWqEhYXlSIJCCJEd5WzLEdozFDMTM9acWcNXf32ldErCCG7F3WLO\n4Tm0XtIax+mO/HTkJ+yt7Pn3vX8ZXH8wnzT/hGv+1/hn2D+MazqOTec3EZMQo3TaeZ5OrzPM1qxW\nqfFz93th35KC6slw2WX/M2qwo6MM4SoEvEYBsWbNmnRzKkyaNIm6deuydu1aKlSowJdffpkjCQoh\nRHY1Ld+Unzr9BMBnuz5jw7kNCmckcsq8I/NosbgF5aaXY/SW0ey5ugc9etzKudG5amfqlKpDYNdA\nRjQeYZgz4rfTv+H/hz+OMxwZuXkk56PPK/wu8q5PdnxC39C+JGgTlE5FcV5eEB7+dFml0hMRIcWD\nEPAaTZhu3LhBlSppj4Ojo6M5cuQIv//+Ox07diQxMZEPPvggx5IUQojsGtJwCMdvH2fukbn4hvpy\naOghajrUVDotkU134++mG3lp3bl17IvcB4C7ozs+Lj70qNmDCsUqZHoMO0s76paqy793/uWnoz8x\n7+g8PKt54u/uTxvnNtLE7f8tObGEb//+FgDfOr54VvNUOCPlyXDZQmTslZ9A6PV6dDodAPv378fE\nxISWLVsCUKZMGaKionImQyHES73xRtzLgwqhGR1n0KpCK+KS41h1epXS6YgsinwYyfQD02ka2JQy\nP5ThRuzTKddHu41mRscZRI6N5MCQA4xrOu6FxQOAZzVPTgw/wZ8D/qRztc7o0bPp/CbaLWtH/Z/r\nE5ckvz97r+5l2MZhAExqMUmKByHEC73yE4jKlSuzadMm2rVrR1BQEG5ublhaWgJw69YtihcvnmNJ\nCiFe7LvvrgKZz+pbWGlMNAT7BLP+3HqGNBiidDriBa48uEJIeAjB4cEcvnHYsF6Fin2R++hVuxcA\nnat1fqXjq1Qq2lZsS9uKbTkffZ5ZB2ex5OQS7C3t07Xxf6x9jJXG6vXeTD5z6f4lvH7zQqvT4u3i\nzZQ2U5ROSQiRx71yATF8+HBGjhzJsmXLePDgAYsWLTJs279/f7r+EUIIoRQHa4d049fr9XppspLH\nbDq/iS6ruhiWVahoUaEFPi4+eNX0MvRlyCnV7Ksx13MuX7b9kqjHT5+W33l0h+pzquPt4s1Y97HU\nLlk7R183L3qY+JAuq7oQnRBNo7KNWNptKWrVKzdOEEIUEq9cQIwYMYLixYvz999/4+bmhq+vr2Fb\nQkICAwcOzIn8hBAixzxMfEjf0L741vGlT50+SqdTOBW/BC4h/HFTj/v/PzVr4dQCS1NL3B3d8Xbx\nxqumF6WLlDZ+KpbFDbNRA6w9u5aHSQ8JPB5I4PFA2ldqz1j3sbxV5a0Ce1Pdf21/zkSdoZxNOdb3\nXl/onr4IIV7Na80D0bt3b3r37v3c+gULFrzOYYUQwih+OfYLv1/4nZ0RO6leojoNyzRUOqVC4UL0\nBYLDg1l9OgT8jgPw29VaTOZjAIpaFOX2+NvYmtsqmSbDXYdTp2QdZh6aSeiZULZf3s72y9upUaIG\nfk38eKfeO1hqLBXNMaeNf2M8J++cZG2vtTn+pEcIUXC99kRy169fZ+/evURHR2Nvb0/Lli1xdHTM\nidyEECJH+bv7szNiJ1subqFbUDeODjuaboQfkbOmH5jOspPLOHnn5NOVOhOIaEvXLk3TNSdTuniA\ntH4SzZya0cypGVceXGH2odksPL6Qs1Fn8f/Dnx41exS4AqJlhZZcGH0BMxMzpVMRQuQjr/xMVqfT\nMWbMGCpWrIivry9+fn74+vpSsWJFRo8ebRihSQgh8goTtQkre6ykmn01rsVewyfYB22qVum0CoyL\n9y+mWz5w/QAn75zERGVCh8odmNPhF/j+NizfRtfy3nm6L4pzMWd+6PgD1/yvMbPjTD5q9hEO1g6G\n7VP3TOXozaMKZvjqdkXsIuzu08lepXgQQmTXKxcQAQEBzJkzh8GDB7Nr1y7OnDnDrl27GDRoEHPn\nziUgICAH0xRCiJxRzKIY63uvx9bclr1X9zJ261ilU8rXwu6GEbA7gFo/1aLq7KqcjTpr2DbabTSB\nbwdyZ/wd/vD9g4F1h8LjEgpmm3225rb4ufsR0DrAsO6fm//w+e7PafxLY1osbkHomVBSdanKJZkN\nZ6PO0v237jQNbMqxW8eUTidfkeGyhXjqlZswLVq0CD8/P2bMmGFYV716dVq1aoWVlRWLFi3iiy++\nyJEkhRAiJ9UoUYMVXit4e9Xb/HT0J+qXrs+7ru8qnVa+oNfrOX33NMHhwYSEh3Am6oxhm0at4dit\nY9QoUQNIax7TskJLpVI1GltzW3zr+hJ0Ooh9kfvYF7mPisUqMqbJGAY3GJwnmmNlJPpxNJ1XduZh\n0kOalW9GLYdaSqeUr8hw2UI89cpPIO7fv4+nZ8YTzXh6enL//v1XTkoIIYytc7XOfNn2S8rblse1\nrKvS6eQb2y9vp+78ukzdO5UzUWcwMzGjS7UuLO22lLsf3qVvnb5Kp2h0Ve2rsrz7cq6OvcqnzT/F\nztKOiAcR+P/hj+N0xzz5zX5yajJeq724FHMJ52LOrO21FnNTc6XTEkLkU6/8BKJevXqcP3+eN998\n87lt58+fp3btgj9+thAif/uk+SeMaDQi3VCeIo1er+fE7RMEhwdT1qYso9xGAWlPFRysHHij/Bt4\nu3jTpVoXiloUVThbZZS1KctX7b5iYsuJ/Prvr8w8OJPYpFjqlHz6LfWdR3coaV1S0f4eer2eEZtG\nsPfqXmzMbNjUZ1O6/hxCCJFdr1xAfPfdd/Tp04cKFSqkexKxceNGpk2bxsqVK3MkQSGEMBaVSpWu\neDhx+wTV7asrmJGy9Ho9x24dMzRPuhRzCUibeG1k45GoVCosTC24Pu66dLx9hpXGimGuwxjacCjX\nHl5DY6IBIEWXgttCN0pal8Tf3R8fFx/Dttz0w4EfWHRiEWqVmt+8f6NWSWm6JIR4PdkqIOrWrZtu\nOTExkbfffhsbGxtKlSrFnTt3iIuLw87OjlGjRnHy5MlMjiSEEHlL0OkgBq4biE8tHz6o+IHS6eS6\n//31PxYeX8jlmMuGdZamlnSq2glvF2/06FGR9i26FA8ZU6vUVChWwbB84vYJ7jy6Q+TDSPqF9mPC\n9gmMchvFMNdh2Fna5UpOqbpU/rj0BwDTO0zHo6pHrryuEKJgy1YBYWdnl+4xrL29fbrtZcvKJDRC\niPyppHVJUnQp/Prvr5TSlaJ3hecnySwo9Ho9/9z6B9cyroZr+sX7F7kccxlLU0s8q3ni4+JDp6qd\nKGJWROFs869GZRsR6ZfOSDYAACAASURBVB/Jz0d/Zu6RudyIu8Enf37C1L1TeafeO0xoNgHnYs5G\nzcFEbcLvfX8nODyYPrVl9nUhRM7IVgGxe/duI6UhhBDKaluxLdM7Tsdvqx8zTs+golVFmpdtrnRa\nOUan13Ho+iFCwkMIORNC5MNIDg09hFs5NwBGuY3Co6oHHlU8sDazVjjbgqOkdUk+a/UZE5pNIOh0\nEDMOzuDknZPMOzqPgfUHGq2AeKx9jJXGCgCNiaZQdG4XQuSebBUQkZGR2Tq4k5NTtuKFEEJJo91G\nc/z2cZacWMKnxz9lRdEV1KOe0mm9Mp1ex4FrBwgOD2bNmTVcj71u2FbErAgXoi8YCogGZRrQoEwD\npVIt8MxNzXmn/jsMqDeA3Vd2s/XiVsO5B/h2/7eUsCpB3zp9sTC1eK3XSkxNpM3SNriVdWPGWzMw\nVb9yd0chhMhQtq4qzs7O2RpJIjU1f0ysI4QQkNapep7nPI5ePcrpmNOMPTiWVq6tsDG3UTq1V7Iv\nch+tlrQyLNuY2dClehd8XHzoWLkjlhpLBbMrnFQqFW0qtqFNxTaGddGPownYHUBCSgKf/Jk2MtiI\nRiMoVaRUto+v1+sJOBbA4RuHuRB9gfFvjE/XL0MIIXJCtgqIRYsWKToUnRBCGJuFqQXT3abTZ3cf\nLsVdYv7R+XzY7EOl03qhVF0q+yL3ERwejIOVA5NbTwagWflmVLOvhls5N3xcfOhQucNrf7stcp6Z\niRlTWk9h9uHZXIu9xpQ9U/jfvv/Rr04//N39qVMq65OXLbywkK03tmKqNiW0V6gUD0IIo8hWATFw\n4ECjJBEXF8fUqVM5ceIEx48fJyoqismTJxMQEPBcrFarZfbs2SxevJiLFy9ibm6Oi4sL33//f+3d\nd1gUV9sG8HuXXXpRBEUsYLCgiNjFWKNBiY0iRtQYKxp7i8YYjcQWY6xBzSe2ECOiYC9oEltMsSQK\nsSYWUDSigCi4gizsfH/wupEIuMAus7vcv+vikp09M/PM4RHm2Zk5ZynefPNNAEBiYiLq1KlT6L62\nbduG4GDjfTiSiMquqkVVfNniS5x9dBbT3tTPEZnyVHn46fZPiL4SjV1Xd+GB4gEAoLp1dczpNAdS\niRQmUhNcG3eNH/zoORszG0xvNx1T2k7Bzis7seL0Cpy5dwab4zZjc9xmbOi9ASOaj3jtdo7cPYLw\n6+EAgK97fo3Orp11HDkRVVR6cWNkWloawsPD4eXlBX9/f2zYsKHQdnl5eQgICMDPP/+MGTNm4M03\n34RCocAff/wBhULxSvsJEyZg4MCCD47Vq1dPJ8dARMbFs7InmldtDqlEKnYor/jsxGdY+/taPFQ8\nVC+rZF4J/u7+CGoYBEEQ8L8RV1k8GBCZVIb+jfujf+P+OH33NFacXoH9f+1Hj3o91G1uP74NB0uH\nVx50P3vvLD49/ykAYLDbYIxsPrJcYyeiikUvCggXFxekp6dDIpEgNTW1yAIiLCwMsbGx+OWXX+Dt\n7a1e/vJEdi+rXbt2gXZERKWRpczC5MOTMbHNxHKfhCtXlYsTiSfQ2bWz+mHYJ8+f4KHiIewt7OHf\nwB/9PPqhS50unJ/BiHjX9Mb2oO1Iz0ovMNlhyP4Q/P7P7xjVYhTGtx6PmrY18Uz5DAHbA/Bc9Rzt\nq7bH5MaTRYyciCoCvfhoTSKRaPQp2apVq9CxY0cWBURUrj768SOEnw+H/3Z/pGel63x/yjwljtw4\ngpH7RsJpqRN8tvjgROIJ9fsftPwAR947guRpydjotxG+dX1ZPBipl4uHzOeZSHicgPTsdHzxyxeo\ns6oOBu4ciMsPL+Prnl+jiX0TLGi2ACYSExEjJqKKQC8KCE0kJSUhMTERnp6emDVrFqpVqwaZTAYP\nDw9EREQUus7ixYthamoKS0tLtG/fHvv27SvnqInIGHza6VO4VnLFjUc3ELwzGLmqXK3vIycvB4dv\nHMaIvSPgtMwJvlt9sfHCRqRlpcHB0gEPnj5Qt61fpT66uXWD3ESu9ThIf9mY2eDauGvY038POrl0\nQq4qF9subUPrDa3xxS9fYEyDMbCScQ4PItI9vbiFSRP37t0DAERERKBmzZpYvXo17OzssH79egwd\nOhQ5OTkICQkBAJiZmSEkJAQ+Pj6oXr067ty5g7CwMPj5+WH9+vUYObL4e0MvX74MlUql82OqKJRK\npfrf+Ph4kaMxHllZUgD5o7Owb7WrsJz9otkXGPLTEHx/83uM2DYCUxtP1eo+rz6+igEn/p0p2N7M\nHl2rd4VPDR80r9IcMkFm8D9j5qx2uMIVq5qtwgr5CiQpkvBT8k/4NelXdK3cFbBn32oTc1a3eH6g\nfVKptFzmYTOYAuLFCX12djYOHToEF5f8oel8fHzQsmVLzJs3T11AVK9eHeHh4QXW79evH9q0aYOZ\nM2di6NChkMmKPvTc3FzOYaEjL35ZUNkpldL/vGbf6sKLfn3D8g182uRTzLowC9/e+BZ1revinRrv\nlHh7OXk5OJN6BkfvH4W13BofenwIAHCzdINXZS/Us62Ht6u/jab2TdW3ogh5ApR5hv/zZc5qz/6k\n/Yi4EQF7U3tEdojE0eSj6O7cXf3+zls78XfG3wiuE4yaljVFjNSwMWfLD/tWO0xMyucWRoMpIKpU\nqQIAcHd3VxcPQP7zE927d8fnn3+Ohw8fomrVqoWuL5fL0b9/f8ycORPXr19Hw4YNi9yXTCaDVGow\nd3fpvZd/KcjlvOVCW3JzC+Yo+1Z7isrZHi49cENxA5v+3oSFfy5E3Up10ahSo9du73nec/z68Ff8\neO9HnEw+iae5TwEA1jJrfNjkQ8il+fuI6FT47ZjGgjmrHedTz2PRxUUAgEDXQNS3r4/69vXVeZsn\n5OGbm98gSZGEHYk78Fb1t/Ce23toVqUZR+UqIeasbvH8QPvK6/zVYAoINzc3WFpaFvqeIAgAXt9p\nmrbz8PBgAaFF8fHxUCqVkMvl8PLyEjsco/HyyMX5fav5ZFNUvOJyNtwzHMlRyThz9wxquNaAl0vx\nOf3J0U/w1dmv8DTnqXqZs40zghoGoZ9HPzSvpZ9DxeoCc7bsbqXfwvQj05Er5CKoURDWBa1T58+L\nvDWTm2G9/3qsOL0CR24ewbH7x3Ds/jG0qN4CU7ynoJ9HPz50ryHmrG7x/ED7VCoVMjMzdb4fgykg\nZDIZ/Pz8EBMTg8TERLi6ugLILwoOHz4MNzc3ODg4FLm+UqnE9u3b4eDggLp165ZT1ERkbEykJogM\njER6djpcK7kWeO+Z8hlir8finXrvwFKe/4GH3ESOpzlPUdO2JoIaBiGoURDa1mpbYYoG0p4n2U/Q\nK7IX0rLS0KJ6C0T4RxSaRxKJBN3rdkf3ut1xJeUKVp5eiS1/bsEf9//Ae7vfw9GEo9jkt0mEIyAi\nY6E3BURsbCwUCoW6arpy5QpiYmIAAD169IClpSXmz5+P2NhY+Pr6IjQ0FLa2ttiwYQPi4+OxY8cO\n9bamTp0KpVKJdu3awcnJCUlJSQgLC0NcXBw2b95cbveHEZFxsjO3g525HQBAkaNA5MVI/HDrBxy8\nfhDPlM+w892dCGwYCAAY0WwEurt1R5uabVg0UKnlqnLRP6Y/rqZehbONM/YG71UXqcVp5NgI4b3D\nsajrIvzf7/+HNefWYGjToer3/8n8BxnPM+Du4K7D6InI2OhNATFmzBjcvn1b/To6OhrR0dEAgISE\nBLi6usLNzQ2nTp3CzJkzMWrUKCiVSjRt2hT79u1Dr1691Os2btwY69atQ2RkJDIyMmBjY4PWrVvj\nyJEj6NatW7kfGxEZl2fKZ9j/137EXI3Bvmv7kKPKUb/nYueC7Nxs9etadrVQy66WGGGSEXmc/Rgp\nz1JgIbPAvuB9qGFbo0TrO1g6YHbH2ZjRbob6mRsA+PKXL7HyzEq8U/cdTPGegrffeJvPSRDRa+lN\nAZGYmKhRu8aNG+PAgQPFthk+fDiGDx+uhaiIiPIJgqA+sfon8x8E7wwu8L5UIsW6XuswotkInoCR\n1jlYOuCnoT8hLjkOLZxblHo7/332IS0rDRJIEHsjFrE3YtG4amNMbjMZg5oMgrnMvKxhE5GR4vV0\nIqIiPFU+xdY/tyJgewAG7RqkXl7Xvi4CGwZiZruZ+D3kd/T36A+VoMInxz7B3Yy7IkZMxib1War6\neytTK7Sr3U6r2/824Fv8PeFvTGg9AVZyK1x6eAkj949E7RW1sfTXpVrdFxEZD725AkFEpA+eZD/B\ngTsHcOTuEZxOPQ2lKn+YQTMTMzzNeQprU2sAwM53d6rX2dhnI66lXkP8g3j4b/fHz8N+hoXcQpT4\nyXhcS72GthvbYor3FMzpOEdnV7bq2tfFV+98hXlvzcPG8xvx1dmvcOfJnQKznxMRvYxXIIiI/mfm\njzPh+KUjZp+fjVMPT0GpUqJBlQaY3WE2zoachZXcqtD1rEytsCd4DxwsHXD+/nmE7A9RDxtNVBpp\nz9LQK7IXHmc/xvc3v1cXsrpUybwSpr05DTcn3sSOoB2Y2Gai+r1jCcfwVsRb2P/XfqgElc5jISL9\nxgKCiCqkR1mPsPnCZjzKeqReVtWqKpQqJd6weQMj641ETJcYXB13FfO7zEeTak2K/QTYtZIrovtF\nw0Rigq0XtyLyYmR5HAYZoZy8HPTd0Rc302/CtZIrdvffXa7zNsikMvTz6Ffg4f9VZ1bhROIJ9Inq\nA/fV7lhzdk2BuU2IqGLhLUxEVGGkPUvDnmt7EH0lGkcTjiJXlYvNks3qYS0HNxmM7m7dkXs/Vz25\nUUluG+ns2hkrfVfiaspV9PPop6OjIGMmCALGHhyLk7dPwsbUBgcGHICjlaPYYWH1O6vhXsUd4efD\ncf3RdYyPHY/Zx2djVPNRGN96PEcaI6pgWEAQkVHLfJ6JqEtRiLkag6O3jiJPyFO/51nVExayf59V\ncLRyhKOVI+Lvx5d6f+Nbjy9TvFSxrTi9AhsvbIRUIsX2oO3wqOohdkgA8ocj/sLnC8zpNAcRcRFY\neWYlbjy6gSW/LsHB6wdxccxFjj5GVIGwgCAio5OnyoOJNH/CSIVSgdEHRkNA/jMJXtW80K9RPwQ1\nCkIDhwY6jSNXlYulvy7FuFbjYGNmo9N9keG7lnoN03+YDgBY1m0Z3qn3jsgRvcra1BrjWo/DmFZj\ncPDvg1hxegX6NeqnLh6ylFk4eP0g/N39IZPyFIPIWPF/NxEZhQdPH2DX1V2IuRoDmVSGI+8dAQA4\nWTthVItRcLFzQVCjINSrUq/cYhq+dzi2/LkFp++exq7+uzgTNRXL3cEdG3pvwPn75zGpzSSxwymW\nVCJF7wa90btB7wIDBnz353cYdSD//9uE1hMwovkIVDKvJGKkRKQLLCCIyGAlP03Gzis7EXM1Bj/d\n/kk9OoyJxATpWemobFEZAPB/vf5PlPjGtx6PHZd3YO9fezHv5DyEdg4VJQ4yHMOaDcOwZsPEDqNE\nXr51SSWo4GDpgNtPbuPDHz5E6MlQDGs6DJPaTIKbvZuIURKRNvHjMCIySDN+mAHnZc4YHzseJxJP\nQCWo0Mq5FZa8vQTXJ1xXFw9ial2jNdb1WgcA+OzkZ9h9dbfIEemP6dNdxA5BL2TnZmPCoQlIUaSI\nHYpWjG45Gncm38GG3hvg4eiBpzlPEXY2DPXC6iFgewCUebofjpaIdI8FBBHpvbsZd/HVma/wT+Y/\n6mX1q9SHAAFtarTBUp+lSJyUiLMhZzG93XTUqVxHxGgLGtJ0iPp2lMG7B+PSw0siR6Qffv2Vz4QI\ngoDhe4dj9bnVeGfrO0Yzd4iF3AIjmo/AxTEX8f173+Oduu9AgIDnuc8hN5Gr23E+CSLDxVuYiEgv\nJT1JQsyVGMRcjcGvSb8CyD/hmuSdfzL+rse76ObWDbXtaosZpkaWdluKiw8v4ljCMfhF+eFcyDnY\nW9iLHRaJbMFPC7Dt0jbIpDJ86fOl0Y1iJJFI4OPmAx83H1xNuVpgBLS7GXfRblM7jGo+CqNbjoaD\npYOIkRJRSbGAICK9kfE8A+v/WI+YqzE4ffd0gffa1WqHmrY11a9tzWxha2Zb3iGWikwqw/ag7Wi1\nvhUePH2Aiw8uopNrJ7HDIhHtuLwDn574FACwtsdavFXnLZEj0q2Gjg0LvN54fiPuPLmD2cdnY8Gp\nBXi/yfuY7D35lXZEpJ9YQBCRqJ4pn8FSbgkg/wrDrGOzkJOXAwkkaF+7Pfo16ofAhoGoYVtD5EjL\nxsHSAfuC9wEAPKt5ihwNiencvXMYsmcIAGCK9xSEtAgROaLy93GHj+Fm74YVp1fg/P3zCD8fjvDz\n4fCt64vJbSajm1s3o7siQ2RMWEAQUbm7lX4L0ZejEXM1BgBwLuQcAMDO3A7T35wOJ2snBDYMhLON\ns5hhat1/C4ecvByYmpiKFA2J4W7GXfhF+SE7Nxs96/XElz5fih2SKExNTPFek/cwyHMQTt05hRWn\nV2Dvtb04fOMwTt0+hbtT73L4VyI9xgKCiMrFjUc31EXD+fvn1ctNJCZIfpoMJ2snAMCCLgvECrFc\n/XznZ7y36z1E94tGqxqtxA6Hykl2bjasTa3RuGpjRPaNVE94WFFJJBJ0dOmIji4dcfPRTYSdDYOl\n3FJdPAiCgLXn1iKwYSCq21QXOVoieoEFBBHp3PTvp2Ppb0vVr6USKd5yfQv9GvWDv7s/qllXEzE6\ncaw4vQK3n9xGwPYA/D7qd3UBRcatrn1dnB55GoochcE8w1Ne3OzdsNJ3ZYFlv939DeNjx2PKkSkI\nbhyMKd5T0Kx6M5EiJKIXOIwrEWnVtdRrWPDTAtx4dEO9rFWNVjCRmKCbWzeE9wpH8rRk/Pj+jxjd\ncnSFLB4AYFOfTWhQpQHuZd5D0I4g5OTliB0S6dDNRzfV39tb2KOWXS0RozEcEkjQrlY7KFVKbPlz\nC5qHN0fnbzpj77W9yFPlvX4DRKQTLCCIqMyupFzBvJPz4Pm1JxquaYg5x+cg6lKU+v0+DfrgwYcP\ncOS9IwhpEQJHK0cRo9UPduZ22Bu8F3Zmdvgl6ReMPzTeaOYBKEreS+d7glDwtTGLiItAg9UN8PW5\nr8UOxeC0rdUWPw//GWdGnsGAxgMgk8pw8vZJ+G/3R4PVDZCQniB2iEQVEgsIIiqVJ9lPEHoiFB5r\nPeCx1gNzT8zFpYeXIJfK8U7dd+BVzUvd1lxmjiqWVUSMVj81cGiAyL6RkECC9efX4/9+/z+xQ9KZ\nXbuARo3+fS0IEri65i83Zj/f+Rkh+0OQJ+ThXuY9scMxWK1rtEZk30gkTErAR+0+QmXzylAJqgLz\nwGQps0SMkKhiYQFBRBoRBAEpihT1azOZGZb/thxXUq5ALpWjZ72e+MbvGzz48AEODTqE3g16ixit\n4ehRrwcWdV0EAJh4eOIr818Yg127gKAg4N5/zp/v3ctfbqxFxK30WwjYHgClSomgRkGY99Y8sUMy\neDVta2Lx24uRNCUJe4L3qB9Cf577HA1WN0D/mP5G+X+ISN/wIWoiKpIgCIh/EI/oy9GIvhINAPhr\n/F+QSCQwl5njs86fwcHSAb0b9OaQi2XwUbuPEJccBwECPKsa1xwReXnApEn5tyz9lyAAEgkweTLg\n5weYGNGARE+yn6D3tt5IfZaKFtVbIMI/AlIJP7PTFitTKzSp1kT9+njicSRlJCHpchJ2XN6BNjXa\nYIr3FPRt1BcyKU91iLSN/6uIqABBEHAh+YJ6yNWXH4Y2MzHDnSd34FLJBQAwpe0UscI0KhKJBBH+\nETA1MTW6ybNOnQLu3i36fUEAkpLy23XuXG5h6VSuKhfBO4NxJeUKnG2csTd4r3qyRNIN37q+iBsd\nh5VnViLyYiTO3DuD4J3BqPVDLUxoPQEhLUL4IQeRFvHjECIq4KMfP0KL8BZY/Mti3Hh0A+YycwS4\nByAyMBIPpz9UFw+kXWYyM3XxIAgCdl/dbRQPVd+/r912hiD6cjQO3zgMC5kF9gXvM/hZ1A2Fl5MX\nNvttxp3JdzC301w4WjoiKSMJM36cgduPb4sdHpFR4RUIogpKEASc++ccoi9HY1CTQWjq1BQA0KVO\nF6w+uxo96vVAv0b90LN+T1ibWoscbcUhCAIG7RqEbZe2YcnbSzC93XSxQyqT6hrO/aVpO0MQ3DgY\nSRlJcKvshhbOLcQOp8KpZl0NoZ1DMbP9TERejMS5e+fg5fTvoA6rz66Gh6MHOrt2NrorfkTlRS+u\nQGRmZmLGjBno1q0bHB0dIZFIEBoaWmhbpVKJ5cuXw9PTExYWFqhUqRLefPNN/Prrr6+0++yzz+Dq\n6gozMzO4u7sjLCysHI6GSH8JgoDTd09j2pFpcF3lijYb2mDpb0ux9c+t6jZvv/E2UqanIObdGPRv\n3J/FQzmTSPLHvQfyrwYdvnFY5IjKpkMHoGbN/GcdCiORALVq5bczFhKJBDPazUDfRn3FDqVCM5eZ\nY3iz4fi617/D5yY/Tca076ehy7dd0Dy8OSLiIvA897mIURIZJr0oINLS0hAeHo7nz5/D39+/yHZ5\neXkICAjAvHnzMGDAAMTGxmLr1q3w9fWFQqEo0Hbs2LH4/PPPMW7cOBw5cgQBAQGYNGkSFi1apOvD\nIdI7mc8zMfXIVLisdEHbjW2x/PRy3HlyB1ZyK/T36A8fNx91W5lUBitTKxGjpbGtxmJEsxEQICA4\nJhjX066LHVKpmZgAq1blf//fIuLF65UrDf8B6r9S/8KgXYOQ+TxT7FCoGIIgYESzEbCQWSAuOQ5D\n9w6F6ypXzD85v8Aoc0RUPL24hcnFxQXp6emQSCRITU3Fhg0bCm0XFhaG2NhY/PLLL/D29lYv79mz\nZ4F2ly9fxsaNG7Fw4UJMn55/+b9z585IS0vDggUL8MEHH8De3l53B0QkMpWgwp0nd+BayRUAYCm3\nxNaLW/FQ8RDWptboXb83+jXqB9+6vrCQW4gbLL1CIpFgTY81uJJyBb/d/Q1+UX44PfI0bM1sxQ6t\nVAIDgZgYYOLEgkO51qyZXzwEBooXmzakPUtDr229cOPRDVjILLChT+F/w0h81W2qY23PtVjQZQHC\n/whH2Nkw/JP5Dz498SkW/bwI0f2i0at+L7HDJNJ7enEFQiKRaHQf4qpVq9CxY8cCxUNh9uzZA0EQ\nMGzYsALLhw0bhqysLBw+bNi3BBAVJk+Vh59u/4SJsRNRa0UtvLnxTagEFQDARGqCL97+Anv670HK\n9BRE9o1EQMMAFg96zExmhp3v7oSzjTOupl7F4N2D1T9PQxQYCFy58u9riURAQoLhFw85eTkIig7C\njUc34FrJVT2nB+k3ewt7zGw/E4mTErE1cCtaOrcEALSp0UbdJkWRYhQDGRDpgl4UEJpISkpCYmIi\nPD09MWvWLFSrVg0ymQweHh6IiIgo0PbSpUtwdHSEk5NTgeVNmjRRv09kFCR5gOsJfHllIWquqIlO\n33RSf6KmUCpw89FNddOhTYfCz90P5jJzEQOmkqhuUx27+++GmYkZYq/H4vz982KHVCYv36YkkRj+\nbUuCIGDcwXE4kXgCNqY22D9gP6paVRU7LCoBuYkcAz0H4uzIs7g05hIcrRzV7/Xd0RctN3sALcIB\nGWe5JnqZXtzCpIl7/7vuHRERgZo1a2L16tWws7PD+vXrMXToUOTk5CAkJARA/jMVhd2iZGVlBVNT\nU6SlpRW7r8uXL0OlMtxP+vSNUqlU/xsfHy9yNPpryxYHbNni+PqG/yMIEqDLXKDD59iVlL9M8twO\nZgl9YHYzEKZJXdF+hRmAnELXHzw4BYMHp2ohcuOjTzlrBjPMazYPVS2qQp4iR3yK4f4fysqSAvh3\nojyx+7asttzYgg2XNkAKKRY1X4S8+3mIvy/eMelT3hqq+KT8fkvJTsH5f85DkasAeo8Gav4GpXIC\n+1XLmLPaJ5VKUbt2bZ3vx2AKiBcn9NnZ2Th06BBcXPLHovfx8UHLli0xb948dQEBoNhbol53u1Ru\nbi7y8vK0EDX914tfFvSqjAwJHj40LdlKf/cCWv4fcM0fuBIE4dbbyM4zRbaG++PP4/X0oY+6VOsC\nQD9iKQulUvqf14Z7PKcenMLyS8sBAJMaTYJ3FW+9Oh59isUQVTKphANdDmDnrf1YfW4X8McoAOxX\nXWLfaodJOV3aNZgCokqVKgAAd3d3dfEA5BcD3bt3x+eff46HDx+iatWqqFKlCuLi4l7ZhkKhQE5O\nzmsfoJbJZJBKDebuLr338i8FuVwuYiT6zdZWQNWqhV8tKIrwvDkQcQcS1f8KjypAUVccCtsffx6F\n0+ec/fvJ31h2aRm+aPUFKpka1sy6ubkFf6/qW9+WhJO1ExzMHdDRqSPer/e+XswnoM95a4gqyytj\nkNtQrB68BBBMAJxnv2oZc1b7yuv81WAKCDc3N1haWhb63ouHnF50mqenJ6KiopCcnFzgOYiLFy8C\nABo3blzsvjw8PFhAaFF8fDyUSiXkcjm8vLxev0IF5eUFLF1asnXK1rc1/vdF/6WvOasSVBj8f4Nx\nMeUi5l+dj8PvHYZMajC/xvGf0bb1qm9LygteeKvFW6hiUQVyE/048dHXvDVkCgWA/z1Hnd+vnsW2\np5JhzmqfSqVCZqbuh5M2mLNkmUwGPz8/XL16FYmJierlgiDg8OHDcHNzg4ODAwDAz88PEonklYer\nv/nmG1hYWMDX17c8Qyci0gqpRIqtgVthJbfC0YSjmPHDDLFDqlCyc7Px54M/1a+drJ30pnggIipP\nevPRVWxsLBQKhbpqunLlCmJiYgAAPXr0gKWlJebPn4/Y2Fj4+voiNDQUtra22LBhA+Lj47Fjxw71\ntjw8PDBixAjMnTsXJiYmaNWqFb7//nuEh4djwYIFnAOCiAyWZzVPRPhHICg6CCtOr0BTp6Z43+t9\nscMyeoIgYMS+Edh1dRe2Bm5FYEMDH3+WiKgM9KaAGDNmDG7fvq1+HR0djejoaABAQkICXF1d4ebm\nhlOnTmHmzJkYiOdTzgAAHa1JREFUNWoUlEolmjZtin379qFXr4ITv6xduxY1atRAWFgYkpOT4erq\nilWrVmHChAnlelxERNrWt1FfzOk4B/N/mo9R+0fB3cEdrWu0Fjsso7bw1EJEXoyETCpDJXPDevaE\niEjb9KaAePm2pOI0btwYBw4ceG07uVyO0NBQhIaGli0wIiI9FNo5FPEP4rHvr30I2B6A30N+R3Wb\n6mKHpbE338wEYBgza0dfjsac43MAAGt6rEGXOl1EjoiISFx6U0AQEZHmpBIptgRsgfcGb9SwrQEz\nmZnYIZXIl1/exstzQuir3//5HUP2DAEATG4zGaNajBI5IiqL5cvzvzT18kTUffq4w7SEI21PnZr/\nRWRsWEAQERkoWzNbHH3/KBytHA1qNCZDcTfjLvps64Os3Cz0qNcDS7uVcJg00jsZGcD/5qUtsZSU\nkj8wn5FRun0R6Tv+xSEiMmD/vW3pSsoVNHJsJFI0xiXsTBjuP72PxlUbY1vfbTCRls8ETaQ7trZA\njRKOXq1U/ju3jlxesksQtoZxlx5RibGAICIyArmqXIw/NB4bL2zEj4N/RCfXTmKHZPAWdV0EC7kF\nhjYdClszngkag9LcUhQff5VzFRD9h8HMA0FEREUzkZgg43kGclW5CIoOwu3Ht1+/EhXLRGqC0M6h\ncK3kKnYoRER6hQUEEZERkEgk2NBnA5o5NUPqs1T4b/fHM+UzscMyON/Gf4she4bgee5zsUMhItJb\nLCCIiIyEpdwSe4L3wNHSEXHJcRi+dziEl4eRoWL9fOdnhOwPwbfx3+KbuG/EDoeISG+xgCAiMiK1\n7Woj5t0YyKQybL+8HUt+WSJ2SAYhIT0BAdsDkJOXg74N+yKkRYjYIRER6S0WEERERqajS0d85fsV\nAGD28dlISE8QOSL9lvE8A7239Ubqs1Q0r94cEf4RkEr455GIqCgchYmIyAh90PID3Hh0A13qdEGd\nynXEDkdv5apyERwTjMspl+Fs44x9wftgZWoldlhERHqNBQQRkRGSSCRY1n2Z2GHovRk/zEDsjVhY\nyCywL3gfatiWcJIAIqIKiNdoiYgqgIT0BEw7Mg0qQSV2KHqlV/1esLewx7cB36KFcwuxwyEiMgi8\nAkFEZOSyc7PRYXMH3Mu8Bwu5BRZ0WSB2SHqjS50uuDnxJiqZVxI7FCIig8ErEERERs5cZo7Pu34O\nAFh4aiFirsSIHJG4/k77G9dSr6lfs3ggIioZFhBERBXAYK/BmOo9FQAwZM8Q/PngT5EjEsejrEfo\nFdkL3hu88WvSr2KHQ0RkkFhAEBFVEF/4fAGfN3zwTPkMflF+SH2WKnZI5UqZp0TQjiBcf3QdduZ2\ncKvsJnZIREQGiQUEEVEFIZPKEBUUhTcqv4HEx4noH9MfuapcscMqF4IgYNyhcTieeBzWptY4MOAA\nqllXEzssIiKDxAKCiKgCsbewx97gvbCSWyHjeQYeZz8WO6RysfL0Sqw/vx5SiRRRfaPgWc1T7JCI\niAwWR2EiIqpgGldtjGNDjqFJtSYwl5mLHY7OHfz7IKZ9Pw0AsNRnKXrW7ylyREREho1XIIiIKqDW\nNVoXKB6eZD8RMRrd+vr3ryFAQEjzEEz2nix2OEREBo8FBBFRBaYSVJh9bDY81nrgn8x/xA5HJ3a+\nuxNf+nyJNT3WQCKRiB0OEZHBYwFBRFSBPVM+w+5ru3Ev8x767uiL57nPxQ5JK/JUeervzWRm+PDN\nDyE3kYsYERGR8WABQURUgVmbWmNv8F5UMq+E03dPY+zBsRAEQeywykQQBLy/531MOzKtQCFBRETa\nwQKCiKiCq2tfF9uDtkMqkWJT3CasObdG7JDKZOGphYi8GIlVZ1YhLjlO7HCIiIwOCwgiIkI3t274\n4u0vAACTD0/G8YTjIkdUOtGXozHn+BwAwJoea9DCuYXIERERGR+9KCAyMzMxY8YMdOvWDY6OjpBI\nJAgNDX2l3dChQyGRSF75cnd3L9AuMTGx0HYSiQRRUVHldFRERIZlWttpGOQ5CHlCHt6NeRfpWeli\nh1Qiv//zO4bsGQIAmNRmEka3HC1yRERExkkv5oFIS0tDeHg4vLy84O/vjw0bNhTZ1sLCAseOHXtl\nWWEmTJiAgQMHFlhWr169sgdMRGSEJBIJ1vdej8THiRjdYjQqW1QWOySN3c24iz7b+iArNwvv1H0H\ny7otEzskIiKjpRcFhIuLC9LT0yGRSJCamlpsASGVSuHt7a3RdmvXrq1xWyIiAizkFvhp2E+QSvTi\nArVG8lR58I/yx/2n9+Hh6IGooCiYSE3EDouIyGjpxV+IF7cXERGR+F4uHh48fYCtf24VMZrXM5Ga\n4OP2H8PFzgX7B+yHrZmt2CERERk1vSggSiIrKwtOTk4wMTFBzZo1MX78eDx69KjQtosXL4apqSks\nLS3Rvn177Nu3r5yjJSIyXKnPUtFyfUsM3j0YB/8+KHY4xerbqC/+Gv8X6lSuI3YoRERGTy9uYdKU\nl5cXvLy80LhxYwDAyZMnsWLFChw9ehTnzp2DtbU1AMDMzAwhISHw8fFB9erVcefOHYSFhcHPzw/r\n16/HyJEji93P5cuXoVKpdH48FYVSqVT/Gx8fL3I0xoV9qxvs139523sjJiMGwdHB2NJpC+rYlP4E\nPStLCsATgHb69uT9k3Cv5I5qFtXKtB1jwbzVDfar7rBvtU8qlaJ27do6349E0LMZg1JTU+Ho6Ii5\nc+cWOhLTf+3cuRNBQUFYvnw5pkyZUmQ7pVKJNm3a4M6dO0hOToZMll87qVQqZGZmFmh769Yt5OVx\n8iEiIqVKibGnxyIuPQ4uVi74pt03sJZbl2pbWVlSdOzYHADw00/nYWFR+g9q4h7FYeyZsbCV22Lz\nm5tR3bJ6qbdFRGQsTExM8MYbbxRYZmNjA6lUuzcdGdQViMIEBATAysoKp0+fLradXC5H//79MXPm\nTFy/fh0NGzYssq1MJtN6R1dkLz5hAPJ/DqQ97FvdYL/+Sw45lrVZhoEnB+K24jY+jf8UK71XwkRS\n8oeUc3ML/l4tbd/eU9zDjD9mQKlSwsveCzVtaxrUQ9+6wrzVDfar7rBvta+8zl8NvoAAAEEQNOqw\nFxdbXtfWw8ODBYQWxcfHQ6lUQi6Xw8vLS+xwjAr7VjfYr686WOsg2m9uj1MPTiEmLQaLui4q8TYU\nin+/z+9bzxJvI+N5BgZtHIT0nHQ0c2qGfUP3wcrUqsTbMUbMW91gv+oO+1b7CruzRhcM/iw5JiYG\nz549e+1wrUqlEtu3b4eDgwPq1q1bTtERERmHFs4tsKF3/hDbu67ugiJH8Zo1tC9XlYvgmGBcTrmM\n6tbVsW8AiwciIjHozRWI2NhYKBQKddV05coVxMTEAAB69OiBlJQUDBw4EMHBwahbty4kEglOnjyJ\nlStXwsPDo8CD0VOnToVSqUS7du3g5OSEpKQkhIWFIS4uDps3b4aJCccHJyIqqUFNBkGpUiLAPUCU\nE/cPv/8QsTdiYS4zx97gvahpW7PcYyAiIj0qIMaMGYPbt2+rX0dHRyM6OhoAkJCQADs7O1SrVg3L\nly/HgwcPkJeXBxcXF0ycOBGzZs2CldW/f8waN26MdevWITIyEhkZGbCxsUHr1q1x5MgRdOvWrdyP\njYjIWAxtOrTAa5WgKpfnDxQ5ChxPPA4A+Nb/W7Sq0Urn+yQiosLpTQGRmJj42ja7du3SaFvDhw/H\n8OHDyxgREREVRRAEfHXmKxy8fhAHBx6E3ES3D0BamVrhl+G/IPZ6LPp59NPpvoiIqHgG/wwEERGV\nv3uZ9zD7+Gz8cOsHTPt+ms72k6XMUn9vbWrN4oGISA+wgCAiohKraVsTWwK2AADCzoZh04VNWt/H\no6xHaLquKRb/vBh6NmUREVGFxgKCiIhKxd/dH6GdQgEAYw6OwW9Jv2lt28o8JYJ2BOHvtL/x9e9f\n48nzJ1rbNhERlQ0LCCIiKrU5neYgwD0AOXk5CNwRiHsZ98q8TUEQMO7QOBxPPA5rU2scGHAAlcwr\naSFaIiLSBhYQRERUalKJFBH+EfBw9EDy02QE7ghETl5Omba58vRKrD+/HhJIsK3vNnhWK/mEc0RE\npDssIIiIqExszGywN3gvHC0dMaDxAMilpR+R6eDfB9UPZS/tthS96vfSVphERKQlejOMKxERGS43\nezfcmHgDtma2pd7G/cz7CN4ZDAECRjYbiSneU7QYIRERaQuvQBARkVa8XDxkPM/A+fvnS7R+dZvq\nWOqzFN3cumFNzzWQSCTaDpGIiLSABQQREWlV0pMktNnQBj5bfJCQnlCidUe3HI3YQbEwNTHVUXRE\nRFRWLCCIiEirHCwdYG1qjUdZj+C/3R+KHEWRbQVBwJJfliDtWZp6mVTCP01ERPqMv6WJiEirLOQW\n2N1/N6pZVcOfD/7E0L1Di5wI7vOfP8dHP36E9pvbl3n0JiIiKh8sIIiISOtq2tbEznd3Qi6VI+ZK\nDBadWvRKm51XduKTY58AACa1mcTbloiIDAQLCCIi0ol2tdthTY81AIA5x+fg0M396veuPbmCwbsH\nAwAmtp6ID1p+IEqMRERUciwgiIhIZ0JahGBMyzEQIODTn2YCkjzA5h6mX5iIrNws+Nb1xbLuy8QO\nk4iISoDzQBARkU6t9F0JMxMzTGj+EdymZgMD+iD1+UM0cmyEqL5RkEn5p4iIyJDwtzYREemUqYkp\nVviugEIBwCoBMH+MSvLKODDgAOzM7cQOj4iISogFBBERlZ/HdYANZ7Bi11HUqVxH7GiIiKgU+AwE\nERGVr2cOcLdrJHYURERUSiwgiIiIiIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiI\niIhIYxzGlYiISmX58vwvTQnCv9/36eMOU9OS7W/q1PwvIiISFwsIIiIqlYwM4N690q2bkiIv1f6I\niEh8LCCIiKhUbG2BGjVKto5SmaP+Xi4v2SUIW9uS7YuIiHRDLwqIzMxMzJ8/H3Fxcbhw4QJSU1Mx\nd+5chIaGFmg3dOhQREREvLJ+gwYNcO3atQLLlEolFi1ahM2bN+P+/fuoU6cOxo0bhwkTJujyUIiI\nKozS3FIUH38VSqUScrkcXl5eugmMiIh0Si8KiLS0NISHh8PLywv+/v7YsGFDkW0tLCxw7NixV5b9\n19ixY7FlyxbMnz8frVq1wpEjRzBp0iRkZmZi1qxZWj8GIiIiIqKKQC8KCBcXF6Snp0MikSA1NbXY\nAkIqlcLb27vY7V2+fBkbN27EwoULMX36dABA586dkZaWhgULFuCDDz6Avb29Vo+BiIiIiKgi0IsC\nQiKRaHV7e/bsgSAIGDZsWIHlw4YNw/r163H48GEMHDgQACC8PCzI/6hUKq3GU9FJpVKYmJhAKpWy\nb7WMfasb7FfdYd/qDvtWN9ivusO+1b7C+rGwc92y0osCoiSysrLg5OSElJQUVK9eHf7+/pg3b16B\nKwqXLl2Co6MjnJycCqzbpEkT9fsvFNapCoVCR9FXTLVr11Z/n5mZKWIkxod9qxvsV91h3+oO+1Y3\n2K+6w74tHxW+gPDy8oKXlxcaN24MADh58iRWrFiBo0eP4ty5c7C2tgaQ/0xFYbcoWVlZwdTUFGlp\naeUaNxERERGRsTCoAmLKlCkFXvv4+KBZs2YICgrC+vXrC7xf3G1R2r5lioiIiIioopCKHUBZBQQE\nwMrKCqdPn1Yvq1KlSqFXGRQKBXJycvgANRERERFRKRnUFYiiCIIAqfTfWsjT0xNRUVFITk4u8BzE\nxYsXAUB9CxSQ/wCPlZVVge1JJBJepSAiIiIigyIIwivPPLx8jqwtBl9AxMTE4NmzZwWGdvXz88Ps\n2bMRERGBjz76SL38m2++gYWFBXx9fdXLpFKpTjqWiIiIiMgY6c2Zc2xsLGJiYrB//34AwJUrVxAT\nE6MuEG7fvo127dohLCwMsbGxOHz4MD7++GMMGTIEHh4eGDlypHpbHh4eGDFiBObOnYuFCxciKCgI\n1tbWWLduHezs7PD9999rFNPDhw8xdOhQODg4wNLSEm3btsXRo0d1cvyG6OnTp5g8eTKcnZ1hbm6O\npk2bIioq6rXrffPNN+qrPP/9Sk5OLofI9VtmZiZmzJiBbt26wdHRERKJ5JVZ2YvDvC1aWfqWeVu0\nY8eOYfjw4XB3d4eVlRVq1KgBPz8//PHHHxqtz5wtWln6ljlbtLi4OPTs2RO1a9eGhYUF7O3t0bZt\nW3z33Xcarc+cLVpZ+pY5WzIbNmyARCJRDyL0OtrMW725AjFmzBjcvn1b/To6OhrR0dEAgISEBNjZ\n2aFatWpYvnw5Hjx4gLy8PLi4uGDixImYNWvWK7chrV27FjVq1MCCBQuQnZ2NatWqYdiwYcjOzsaA\nAQOgUqnUc0EU5vnz5+jatSseP36MVatWoWrVqlizZg18fX3x448/olOnTrrpCAMSGBiIc+fOYfHi\nxahfvz4iIyM16tsXNm/eDHd39wLLqlSpoqtwDUZJZmb/L+Zt8crSty8wb1/19ddfIy0tDZMmTUKj\nRo2QkpKCZcuWwdvbG0eOHEGXLl2KXJc5W7yy9O0LzNlXPX78GLVq1cKAAQNQo0YNKBQKbN26FYMH\nD0ZiYiJmz55d5LrM2eKVpW9fYM6+3r179/Dhhx/C2dkZT548eW17reetYMQOHjwoABAiIyMLLPfx\n8RGcnZ2F3NzcItdds2aNAED49ddf1cuUSqXQqFEjoXXr1jqL2VCUpW83b94sABDOnTun6zANkkql\nElQqlSAIgpCSkiIAEObOnavRuszb4pWlb5m3RXvw4MEryzIzM4Vq1aoJXbt2LXZd5mzxytK3zNmS\na9OmjVCrVq1i2zBnS0eTvmXOaq5Xr15C7969hSFDhghWVlavba/tvNWbW5h0Yffu3bC2tka/fv0K\nLB82bBj++ecfnDlzpth1GzRogLZt26qXyWQyvPfeezh79izu3buns7gNQVn6lopXlof4mbfF4wAJ\nulG1atVXlllbW6NRo0ZISkoqdl3mbPHK0rdUcg4ODpDJir85gzlbOpr0LWnmu+++w8mTJ7F27VqN\n19F23hp1AXHp0iU0bNjwlYQtbEbqwtZ90a6wdS9fvqzFSA1PWfr2hV69esHExAT29vYIDAzUaB0q\nHvNW95i3mnny5AnOnz8PDw+PYtsxZ0tO0759gTlbNJVKhdzcXKSkpGDt2rU4cuRIgcFXCsOc1Uxp\n+vYF5mzRHj58iMmTJ2Px4sWoWbOmxutpO2+NuhRMS0vDG2+88cryF/NAFDcjdVGzWWuybkVQlr51\ncnLCJ598Am9vb9ja2uLixYtYvHgxvL298csvv8DLy0tncRs75q3uMG9LZty4cVAoFPjkk0+Kbcec\nLTlN+5Y5+3pjx47FunXrAACmpqb46quvMHr06GLXYc5qpjR9y5x9vbFjx6JBgwYYM2ZMidbTdt4a\ndQEBlG1Gas5mXbzS9o+vr2+BoXQ7duyInj17wtPTE59++in27t2r1TgrGuatbjBvNTdnzhxs3boV\nYWFhaNGixWvbM2c1V5K+Zc6+3qxZszBy5Eg8fPgQ+/fvx/jx46FQKPDhhx8Wux5z9vVK07fM2eLt\n3LkT+/fvx4ULF0qVZ9rMW6MuIIqakfrRo0cAUOyM1GVZtyLQdv+4urqiffv2BWYUp5Jj3pYv5u2r\nPvvsMyxYsAALFy7E+PHjX9ueOau5kvZtYZizBdWuXRu1a9cGAPTo0QMA1EPEOzo6FroOc1Yzpenb\nwjBn8z19+hTjxo3DhAkT4OzsjMePHwMAcnJyAOSPfiWXy18ZlfQFbeetUT8D4enpiatXryI3N7fA\n8sJmpC5s3RftSrpuRVCWvi2K8J8ZxankmLflj3n7r88++wyhoaEIDQ3FrFmzNFqHOauZ0vRtUZiz\nRWvdujVyc3Nx69atItswZ0tHk74tCnMWSE1NxYMHD7Bs2TJUrlxZ/bVt2zYoFApUrlwZgwYNKnJ9\nredticdtMiCHDh0SAAhRUVEFlvv6+r52qNG1a9cKAITTp0+rlymVSsHDw0No06aNzmI2FGXp28Lc\nunVLsLa2Fvz9/bUZpsEr6VCjzFvNlbRvC8O8/de8efMEAMLs2bNLtB5z9vVK27eFYc4Wb/DgwYJU\nKhUePnxYZBvmbOlo0reFYc7my8rKEo4fP/7KV/fu3QVzc3Ph+PHjwsWLF4tcX9t5a9QFhCDkz0tQ\nuXJlITw8XDh27JgQEhIiABC+++47dZvhw4cLJiYmQmJionpZdna24OHhIdSqVUvYunWr8MMPPwgB\nAQGCTCYTTpw4Icah6J3S9m3Xrl2Fzz77TNi9e7dw9OhRYeXKlYKzs7NgY2NTbPJXJIcOHRKio6OF\nTZs2CQCEfv36CdHR0UJ0dLSgUCgEQWDellZp+5Z5W7SlS5cKAARfX1/ht99+e+XrBeZsyZWlb5mz\nRQsJCRGmTZsmbN++XThx4oQQExMj9O/fXwAgTJ8+Xd2OOVtyZelb5mzJFTYPRHnkrdEXEJmZmcLE\niRMFJycnwdTUVGjSpImwbdu2Am2GDBkiABASEhIKLE9OThbef/99wd7eXjA3Nxe8vb2FH374oRyj\n12+l7dvJkycLjRo1EmxsbASZTCY4OzsL7733nvDXX3+V8xHoLxcXFwFAoV8v+pJ5Wzql7VvmbdE6\ndepUZJ++fKGbOVtyZelb5mzRNm3aJHTo0EFwcHAQZDKZUKlSJaFTp07Cli1bCrRjzpZcWfqWOVty\nhRUQ5ZG3EkEQhJLd9ERERERERBVVxX4ihYiIiIiISoQFBBERERERaYwFBBERERERaYwFBBERERER\naYwFBBERERERaYwFBBERERERaYwFBBERERERaYwFBBERERERaYwFBBERaV1oaCgkEonYYRARkQ6w\ngCAiIiIiIo2xgCAiIiIiIo2xgCAiojI5ePAgmjZtCjMzM9SpUwdLly59pc2aNWvQsWNHVK1aFVZW\nVvD09MSSJUugVCrVbebPnw+ZTIakpKRX1h8+fDiqVKmC7OxsnR4LERG9nkzsAIiIyHAdPXoUfn5+\naNu2LaKiopCXl4clS5bgwYMHBdrdvHkTAwcORJ06dWBqaor4+HgsXLgQ165dw6ZNmwAAo0ePxsKF\nC7Fu3TosWLBAve6jR48QFRWF8ePHw9zcvFyPj4iIXiURBEEQOwgiIjJM3t7eSEpKws2bN9Un95mZ\nmXB1dcWjR49Q2J8YlUoFlUqFbdu2YdiwYUhJSUHlypUBAEOHDkVsbCySkpJgamoKAFiyZAk+/vhj\n3Lx5E66uruV2bEREVDjewkRERKWiUChw7tw5BAYGFrgyYGNjg969exdoe+HCBfTp0wdVqlSBiYkJ\n5HI53n//feTl5eHvv/9Wt5s0aRIePnyI6OhoAPnFxtdff42ePXuyeCAi0hMsIIiIqFTS09OhUqng\n5OT0ynsvL7tz5w46dOiAe/fuYdWqVTh16hTOnTuHNWvWAACysrLUbZs1a4YOHTqo3ztw4AASExMx\nfvx4HR8NERFpis9AEBFRqVSuXBkSiQTJycmvvPfysj179kChUGDXrl1wcXFRL4+Liyt0uxMnTkS/\nfv1w/vx5rF69GvXr14ePj4/2D4CIiEqFVyCIiKhUrKys0Lp1a+zatavA6EiZmZnYv3+/+vWLCeXM\nzMzUywRBwPr16wvdbkBAAGrXro1p06bhxx9/xNixYzkpHRGRHmEBQUREpTZ//nwkJyfDx8cHe/bs\nwc6dO9G1a1dYWVmp2/j4+MDU1BQDBgxAbGwsdu/eje7duyM9Pb3QbZqYmGDcuHE4ceIELC0tMXTo\n0HI6GiIi0gQLCCIiKrUXhUNGRgb69++PqVOnom/fvhg+fLi6jbu7O3bu3In09HQEBgZiwoQJaNq0\nKb766qsit9u/f38AwODBg2FnZ6fz4yAiIs1xGFciItI7YWFhmDhxIi5dugQPDw+xwyEiopewgCAi\nIr1x4cIFJCQkYPTo0WjXrh327NkjdkhERPQfLCCIiEhvuLq6Ijk5GR06dMCWLVsKHSKWiIjExQKC\niIiIiIg0xoeoiYiIiIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiI\niIhIYywgiIiIiIhIYywgiIiIiIhIYywgiIiIiIhIY/8Ptgmcy50clGYAAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -513,7 +518,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a humans' weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n", + "As we can see there is an extreme range of weight changes that could be explained by these three measurements. In fact, there are an infinite number of choices. Shall we give up? Not me! Recall that we are talking about measuring a human's weight. There is no reasonable way for a human to weigh 180 lbs on day 1 and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). \n", + "\n", + "The behavior of the physical system we are measuring should influence how we interpret the measurements. If we were weighing a rock each day we'd attribute all of the variance to noise. If we were weighing a cistern fed by rain and used for household chores we might believe such weight changes are real.\n", " \n", "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based solely on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, merely one that is reasonable and could be explained by the measurement." ] @@ -525,9 +532,9 @@ "outputs": [ { "data": { - "image/png": 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5RQkJCZo1a1a1NBA1o1cv17g6XyfZLUs691xXHBoO8l5ez56Vm50BDYcJuecz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\nmDFjbEn2Sy+9VBu7DT8ZOXK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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -552,9 +559,9 @@ "outputs": [ { "data": { - "image/png": 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q3LmzlyIDEEw8TgrCw8P15ptvatasWdqxY4eys7MVGxur2267TQkJCc52/fv3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\nv5dfflnXXHONFi1apKysLLV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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -569,7 +576,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that surely looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n", + "Does it 'seem' likely that I lost weight and this is just really noisy data? Not really. Does it seem likely that I held the same weight? Again, no. This data trends upwards over time; not evenly, but definitely upwards. We can't be sure, but that looks like a weight gain, and a significant weight gain at that. Let's test this assumption with some more plots. It is often easier to 'eyeball' data in a chart versus a table.\n", "\n", "So let's look at two hypotheses. First, let's assume our weight did not change. To get that number we agreed that we should average the measurements. Let's look at that.\n" ] @@ -581,9 +588,9 @@ "outputs": [ { "data": { - "image/png": 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//RZ/+9vf0K9fPyQkJOCPP/5AZGQk2rZti5s3b2Lt2rVQKpUYNGhQjccuLi7G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\nyRPt379fNTU18vLy0tKlS1VcXEzAGUH/9l5JUkh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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -600,7 +607,7 @@ "source": [ "That doesn't look very convincing. In fact, we can see that there is no horizontal line that we could draw that is inside all of the error bars.\n", "\n", - "Now, let's assume we gained weight. How much? I don't know, but NumPy does! We want to draw a line through the measurements that looks 'about' right. NumPy has functions that will do this according to a rule called \"least squares fit\". Let's not worry about the details of that computation, or why we are writing our own filter if NumPy provides one, and plot the results." + "Now, let's assume we gained weight. How much? I don't know, but NumPy does! We want to draw a line through the measurements that looks 'about' right. NumPy has functions that will do this according to a rule called \"least squares fit\". Let's not worry about the details of that computation (I use [polyfit()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html) if you are interested), and just plot the results." ] }, { @@ -610,9 +617,9 @@ "outputs": [ { "data": { - "image/png": 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LxMbGok+fPnqlNxMSEiAIAo4fP45x48ZhwIABAIAnnngCM2fOxNChQ9GpU6cW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\nAAAASUVORK5CYII=\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -631,7 +638,7 @@ "\n", "\"But is it impossible?\" pipes up a co-worker.\n", "\n", - "Let's try something crazy. Let's assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, assume I know it is approximately correct. Maybe I am eating a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. Let's see if we can make use of such information if it was available without worrying about the source of that information yet.\n", + "Let's try something crazy. Let's assume that I know I am gaining about one lb a day. It doesn't matter how I know that right now, assume I know it is approximately correct. Maybe I am on a 6000 calorie a day diet, which would result in such a weight gain. Or maybe there is another way to estimate the weight gain. This is a thought experiment, the details are not important. Let's see if we can make use of such information if it was available.\n", "\n", "The first measurement was 158. We have no way of knowing any different, so let's accept that as our estimate. If our weight today is 158, what will it be tomorrow? Well, we think we are gaining weight at 1 lb/day, so our prediction is 159, like so:" ] @@ -643,9 +650,9 @@ "outputs": [ { "data": { - "image/png": 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mTNulUNdfD97e3T1StyarTgkhhBBCiP7t3Dllx8LRkrGdCQqyFRZpaTBpkhQW3UwKDSGE\nEEII4drOnrUVFRkZUFCgPkZwMMyaZetYTJrUL5eUdSXy6gohhBBCCNdSXKzsWJw+rT5GSIitsEhL\ngwkTpLDoZfJqa9iFCxcwGAx4enoyZMiQvh6O6AWSc+2RnGuP5Fx7+kXOi4qUHYuiIvUxQkNh9mzb\nqlATJoCnZ7cO01W4S86l0NCwsrIy6xrMrvwmFd1Hcq49knPtkZxrj9vl3GSyFRaW4qK4WH2cAQPM\nhYWlYzF+fL8tLOy5S86l0BBCCCGEED3HZDJf+tS6Y3H2rPo4YWG2bsWcOTBunGYKC3clhYaGjRgx\nApPJhK6f3vZetCU51x7JufZIzrXH5XJuMsGpU8o5FufOqY8THm4uKCzFRUoKyC0BABfMeTvkPhq9\nSO6jIYQQQoh+x2QyLy/bumNx/rz6OBERyo5FcrIUFi5G7qMhhBBCCCF6jskE+fm2oiIjAy5cUB8n\nMtJWVKSlQVKSFBb9jBQaQgghhBCifSYT5OUpOxZlZerjDBpkm7g9Z465sHDxS3/EtZFCQ8Oampqs\n1/f5+vr29XBEL5Cca4/kXHsk59rT7Tk3meD4ceUci/Jy9XGGDFF2LMaMkcKim7jL51wKDQ3Ly8uz\nLo2Wmpra18MRvUByrj2Sc+2RnGvPNefcaDQXFpaiIjMTKirUx4mKUnYsRo+WwqKHuMvnXAoNIYQQ\nQggtMRohJ0fZsaiqUh8nJkbZsRg1SgoLoSCFhoaFhYWh1+vx8pK3gVZIzrVHcq49knPt6TTnRiMc\nO6bsWFy8qP4HDR1q61ikpcHIkVJY9BF3+ZzL8ra9SJa3FUIIIUSPMxjg6FFbx2LPHqiuVh8nNlbZ\nsRgxQgoLjZPlbYUQQgghtMRggOxs21KzX38Nly6pjzN8uK2oSEsz/12IayCFhhBCCCGEO9Hr4cgR\n26VQX38NNTXq44wYYetYzJkjhYXodlJoCCGEEEK4Mr0eDh+2dSz27oXLl9XHiY9X3nk7NrabByqE\n0jUVGkajkcbGRgICArprPKIXnTx50jqRKCEhoa+HI3qB5Fx7JOfaIznvB1pa4NAh2xyLvXvB7rp4\np4wapexYDBvW3SMVfcRdPueqCo3GxkY+/vhjPv/8c7755hvKy8sxmUz4+voyduxY5s2bx1133eXS\n6/kKm/r6eusazEIbJOfaIznXHsm5G2ppgYMHbR2Lb76B2lrVYRrj4vC76SZbcRET090jFS7CXT7n\nTi131NDQwPr164mOjub+++/n+PHjpKen8/DDD/PUU09xzz33EB4ezttvv82kSZOYNWsW+/btc3oQ\nV65cYcWKFdx0001ERkai0+lYt25dm+fde++96HS6Nn8SExPbPPfUqVPcfffdxMbG4u/vT3x8PI8+\n+ihVTqwT3d7PsfzJysrq0piEEEIIIWhuhm+/heeeg5tvhrAwmDYNfvc7+Oc/nS8yxoyB//N/KH7u\nObK/+IL87dvhrbdg+XIpMoRLcKqjkZCQQGBgIE8//TR33XUXgwcPdvg8k8nE7t27+etf/8rcuXP5\n85//zK9+9atO41dVVfHWW2+RmprK4sWLeeedd9p9rr+/P7t27WrzWGsVFRVMnTqVkJAQNm7cSGxs\nLIcPH2bt2rXs3r2bgwcPdrik7OrVq/n1r3/d5vGFCxfi6+vL5MmTVY/JFUnnSXsk59ojOdceybkL\nam6G77+3XQr17bdQX68+TlKSco7FkCEAxF39I7TDXT7nThUaGzZs4J577sHT07PD5+l0OubNm8e8\nefNYv349Z86ccWoQcXFxVFdXo9PpqKys7LDQ8PDwYOrUqR3G2759O1VVVXzyySekp6cDMHfuXJqa\nmli5ciXZ2dlMnDix3f3j4+OJj49XPJaZmUllZSVPP/10m9fBmTEJIYQQQiOamsyFhWVVqG+/hYYG\n9XHGjrUtNTt7NrTzi14hXJVThcZ9992nOvDIkSMZOXKkU8/VdfPNXyzXq4WGhioeHzBgAAB+fn6q\nY7777rvodLouvRZCCCGE6McaG+G772wdi337zI+plZJi61jMng2DBnX3SIXoVd2yvG1jYyNFRUUk\nJCR02vW4Vg0NDQwZMoSKigqioqJYvHgxGzZsYODAgdbnLF68mNjYWB577DHeeOMN4uLiOHToEJs2\nbWLhwoUkJSWp+pk1NTVs3bqV9PR0RowY0aUxCSGEEKKfaGyErCxbx2LfPnMXQ61x42wdi1mzIDKy\nmwcqRN9SXWj86U9/4tKlS6xevRqAgwcPsmDBAi5evMjw4cPJyMhgWA8tn5aamkpqaiopKSmA+XKm\nV199lZ07d7J//36CgoIAcycjKyuLpUuXWp8LsGzZMj744APVP/ejjz6ioaGB+++/v8tjak9ubi5x\ncXGEhIRYH2tqaiIvLw+AsLAwYu3WuT558iT1V6/ttL9Gr7KykpKSEgBiY2MJCwuzbjMYDOTk5ADm\n28WHhIRgNBrx8PAgIiKCwsJCLl9dlzs5ORkvL9vb49KlSxQXFwMQHR1NpN3J8OjRo5hMJvz9/Rk9\nerRi29mzZ7l48SIAY8aMUXSUamtrKSgoAGDQoEFERUUp9j1+/Lh1VYWxY8cqtpWWllJeXg6YL3dr\n/Vo3NjaSn58PwMCBA9u8J0+cOEFDQwM6nY7x48crtlVUVHD+/HnAfFmfpRMGoNfryc3NBSAkJKRN\n4Xn69GmuXF2CMCUlRVF4V1dXWy8njImJISIiQrFvdnY2AAEBAW2Wqjtz5gzV1dUAJCYm4uvra912\n+fJlCgsLARg8eDBDrl6za5Gbm4ter8fX15eIiAhFzs+fP09FRQUAo0aNIjAw0LpffX09J0+eBCA8\nPJyhQ4cq4ubn59PY2Iinp6ficwZQXl5OaWkpAMOHD1d0F5ubm/nhhx8A82d1uN0NogoKCqi9OhFy\n3LhxivlUVVVVnDt3DoChQ4cSHh5u3WY0Gjl27BgAQUFBbS5/LCoqoubqDa2SkpLw8fGxbqupqaGo\nqAiAqKgoBtn9FjEnJweDwYCfnx9jxoxRbDt37px1kYmEhATFct91dXWcOnUKgMjISKKjoxX75uXl\n0dTUhJeXF8nJyYptFy5coKysDIARI0Z0+RwRExOjyLmac4R9V1rOEWaufo4YNGgQnp6e1pyrOUfY\nL2Qi5wizmgsXqPx//4/AAwcYeOwYPocOdamwMI4bh8fcudbCos7f33aOaGkh2u75zp4jBg4ciK+v\nrzXnvfU9Qs4RfXeOCAkJITAw0Jpz6J3vEfa56YzqQuOdd95RTPB+8sknGThwIKtXr+a1117jmWee\n4T//8z/VhnXKI488ovj7/PnzmThxInfccQdvv/22dXt1dTW33XYb9fX1bN68mWHDhpGTk8PGjRtZ\ntGgRn3/+ueLN35l3332X8PBwlixZ0uUxtUev12MymRSPmUwmWlparNsd7WPZbs9oNFq3GY3GNttb\nxy0pKbF++CIiIhRx7cfUOq7BYHAY12QyOVxmzWAwXFPc9o61dVz7Y239GjqKazlWR5ftORu3J3PT\nUdyO3i/tvYZ6vR4PD482Oe8oN87EbWlpcbito7itj1Vtzp19DR3t33pM9jo71ubmZoxGo8OObXe8\nho5eI2fjdvZ+sc95T70P5RzRNm5fnSPKysrQ6/XWnKs5R3R0rJo6R9TXm++2fbVjEfLdd4Q2Nzv8\nme3S6SA1lcuTJlE+dixXJkxg9NSpimLNVFvbLeeIyspKDAaDw5y7yr9Vco5oG/daclNdXU1VVZU1\n55ZjdSbutXyPUEt1oXHmzBnrbzyuXLnCnj17+Pjjj7n99tsJCwtjzZo1qgdxLZYsWUJgYKBiydnn\nn3+eI0eOUFxcbK1sZ82aRWJiIvPmzWPz5s3cc889TsU/evQoBw4c4OGHH1ZUf2rH1B4vL682b1Kd\nTmf9oDkqiLy8vNpdN9nDw8O6zdEbwtm49mNqHdfRly1vb29MJpPDuJ6entcUt/V/24trf6ytX0NH\ncS3H6ugE4WxcV8lNZ8dqOU5vb2+a7H4D11FunIlrMBgcbusobutjbS/utb6Gnb1f7HV2rD4+PtZ/\nxDuK25XX0Gg0qv7cuOL7UM4RbeP2VW7sv0SoOUfY08w5oq6OwG+/JWjPHoIOHMA7N9d8bwvLsTr8\naUomnY6mpCT8Fiwwz7OYNQvCwrh87hx1VVV4ODjW7jpH2H+ZdYX3oZwjevYc4agI7I3vEWrpTI7K\n5A4EBATwxRdfkJaWxr/+9S9uueUWLl68SEhICF9//TU33XQTDV1ZWeGqyspKIiMjWbt2rcN7adgz\nGo0EBwezaNEiPvroIwAWLFhAfn6+tQ1kUVtbS3BwMI8//jgvvviiU+N5+OGH+eMf/8ixY8fatH7V\njMny+BW7O3sGBwd3qULsDtXV1dZLKlq3RkX/JTnXHsm59kjOnVBba14JyjLH4vvvwcFvgTvk4QGT\nJtkmb8+cCa0ukelNknPt6aucq/0uq7qjERsby9dff01aWhrbt29nwoQJ1muHKyoqFNcR94atW7dS\nX1+vWF42OjqanTt3UlJSQkyrG9ZYbiJofx1pe5qamvjwww+ZMmWK00VGe2NyRXIy0h7JufZIzrVH\ncu7AlSvmu21bVoU6cKBrhcV119nuYTFzJtitbtlXJOfa4y45V11o/PznP2f9+vX84x//IDs7m5de\nesm67cCBA6oniVh8+eWX1NXVWauk48ePs3XrVgBuueUWKioqWL58OXfeeSejRo1Cp9ORmZnJa6+9\nRnJysmLeyIMPPsjmzZuZP38+Tz31lHWOxjPPPMPgwYO56667rM/dsGEDGzZsYOfOncyZM0cxpn/8\n4x9cvHix3ZsOFhcXOz0mIYQQQvSSy5fNhUVGhvnPwYPg4NrzDnl62gqLtDSYMQN6+ZepQrg71YXG\nqlWr8PLy4ttvv2XJkiX8+7//u3VbTk4OS5cu7dJAHnjgAetqBABbtmxhy5YtgHkVg9DQUAYPHswr\nr7xCWVkZBoOBuLg4fvvb37Jy5UrF5KrrrruOrKwsNm7cyKpVq6ioqCAmJoZFixaxZs0axUoeRqMR\ng8HgcKLVu+++S2BgIHfeeafDMYeEhDg9JiGEEEL0kJoa2LvX1rE4eBAcXMPeIU9PmDzZ1rGYMQOC\ng3titEJohuo5GqLrXG2ORuuVBXr6/ifCNUjOtUdyrj2ayPmlS+bCwjLH4tAh9YWFl5etsEhLg+nT\noZMl6V2VJnIuFPoq5z0+R8OisbGRQ4cOUVVVRXh4OJMmTerSHbdF38nJybEue2m/jrbonyTn2iM5\n155+mfPqavNys5aOxeHDoPb3pN7eMGWKrWMxfTr0kysP+mXORYfcJeddKjReeeUVNm7cyOXLlzGZ\nTOh0OoKDg1m9ejWPPfZYd49RCCGEEFpy8aLiPhYcOdK1wuKGG2wdi2nToNUNNYUQPa9LdwZ//PHH\nmT9/PsuXL2fIkCFcuHCBzZs3s2LFCry9vfntb3/bE2MV3Sw4OBi9Xq/q5oXCvUnOtUdyrj1umfOq\nKtizx9axOHpUfWHh4wNTp9o6FlOnaqawcMuci2viLjlXPUcjPj6eGTNm8Le//a3Ntp///Ofs27fP\neit4oeRqczSEEEKIPlFZaS4sLKtCHTumPoavr7lLYbmPxQ03gL9/Nw9UCNFaj8/ROH/+vGJ52Nbu\nvvtu/v73v6sNKYQQQoj+rLzcVlhkZkJOjvoYfn7mwsLSsbjhBvNjQgiXpbrQGD16NGVlZQ63lZaW\nMmrUqGselBBCCCHcWFmZsmNx/Lj6GP7+5gnblo7FlCnmLoYQwm2oLjTWr1/PI488wqRJkxR3yz56\n9Cjr16/nlVde6dYBCiGEEMLFXbhgm1+RmQk//KA+RkCAubCwdCwmT5bCQgg351ShsWjRIsXf9Xo9\nEyZMIDk52ToZPDc3l+joaP7rv/6LJUuW9MhgRfcqLCy0TiQaMWJEXw9H9ALJufZIzrWnV3JeWmor\nLDIyID9ffYyAAJg509axuP5684RuoZp8zrXHXXLuVKFx9OhRdDqdbScvL4YNG8bly5e5fPkyAMOG\nDQPgWFcmdIk+cfnyZesazEIbJOfaIznXnh7JeUmJsmNx4oT6GIGB5sLC0rG4/nrzErTimsnnXHvc\nJedOFRpFRUU9PAwhhBBCuIxz55Qdi1On1McICoJZs2wdi0mTpLAQQmNUL28rus7VlrfV6/XWGy66\n+jrMontIzrVHcq49Xcr52bOKIcVRAAAgAElEQVS2oiIzE7qyTH1wsLmwsNwgb+JEkPdcr5DPufb0\nVc57fHlb0X/IyUh7JOfaIznXHqdyXlxsKyoyMqCwUP0PCgmB2bNtHYsJE6Sw6CPyOdced8m5U6P0\n8PBQzNHoiE6nQ6/XX9OghBBCCNGNioqUHYuuXBI9YICyY5GaCp6e3TlKIUQ/41ShsWbNGqcLDSGE\nEEL0IZPJ3KFo3bE4c0Z9nLAwZcdi/HgpLIQQqsgcjV7kanM0Ll26hNFoxMPDgwEDBvTJGETvkpxr\nj+RcA0wmOH3a2rEw7t6NR0mJ+jgDB5oLC0vHYtw46KN/n4Q68jnXnr7KuczREE4rLi62Lo0mJyZt\nkJxrj+S8HzKZzKtAte5YtCosnC4NwsPN3QpLxyIlRQoLNyWfc+1xl5w7VWh8+umn/OQnP1EV+Pz5\n8xQWFjJjxowuDUwIIYQQmAuLkyeVcyzOn1cfJyLCVlSkpcHYsVJYCCF6lFOFxoMPPsizzz7LQw89\nxE9+8hNCQkLafe7Bgwd57733+K//+i9efPFFKTRcWHR0NAaDAU+55lYzJOfaIzl3QyaT+U7brTsW\nFy6oDmOMiMBj7lzbDfLGjgWZb9kvyedce9wl507N0aipqWHdunW89dZbGAwGJk6cyKRJkxg0aBB+\nfn5cvHiRgoICsrKyKC0tJSUlhRdeeIGbb765N47BbbjaHA0hhBAuwGSCvDxlx6KsTH2cwYNtRUVa\nGiQmSmEhhOhWar/LqpoMXl1dzV//+le++OILsrKyqK+vt24bOXIkaWlp3HXXXcydO7eLw+/fpNAQ\nQgiByQTHj9uKisxMKC9XH2fIENtlUHPmwJgxUlgIIXpUjxYa9mpqamhoaCA8PBxvb++uhtEMKTSE\nEEKDjEbIzbVdBpWZCZWV6uNERys7FgkJUlgIIXpVr646FRoaSmho6LWEEEIIIfoXoxFycpQdi6oq\n9XFiYpQdi1GjpLAQQrgVWd5Ww44ePWpdGm38+PF9PRzRCyTn2iM57wVGIxw9autY7NkDFy+qjzN0\nKMyda+tYjBzZpcJCcq49knPtcZecS6GhYSaTyfpHaIPkXHsk5z3AYDAXFpaOxZ49UF2tPk5srLJj\nMWJEt3QsJOfaIznXHnfJuRQaGubv74+3tzdeXvI20ArJufZIzruBwQBHjig7FjU16uMMH668j8Xw\n4d06TAvJufZIzrXHXXJ+TZPBhToyGVwIIdyAXm8uLCwdi6+/7lphMXKkrbCYMwfi4rp7pEII0avU\nfpd1iW+4V65cYcWKFdx0001ERkai0+lYt25dm+fde++96HS6Nn8SExPbPPfUqVPcfffdxMbG4u/v\nT3x8PI8++ihVTkzIy8jIcPhzdDodWVlZbZ6/Y8cOpk2bRkBAABEREdx7772Ud2WpQiGEEL1Pr4fv\nv4cXX4Rbb4WBA2HyZHjiCfjsM+eLjPh4uP9++NvfoLgYCgrgvffgF7+QIkMIoUmq+y0jR45k27Zt\npKamttmWk5PDokWLOH36tKqYVVVVvPXWW6SmprJ48WLeeeeddp/r7+/Prl272jzWWkVFBVOnTiUk\nJISNGzcSGxvL4cOHWbt2Lbt37+bgwYNOdRGeffbZNvcESUlJUfw9MzOTH/3oR9x6661s376d8vJy\nnnzySdLT0zlw4AC+vr6d/hwhhBC9qKUFDh2y3SBv716orVUfJyFB2bEYOrSbByqEEO5NdaFRVFRE\nU1OTw22NjY0UFxerHkRcXBzV1dXodDoqKys7LDQ8PDyYOnVqh/G2b99OVVUVn3zyCenp6QDMnTuX\npqYmVq5cSXZ2NhMnTux0XAkJCZ3+rCeeeILRo0ezdetW63VyI0aMYMaMGbz33ns88MADnf4cIYQQ\nPailBQ4csM2x2LsX6urUxxk92lZUzJljXn5WCCFEu7o0g0TXzqoYp0+fJjg4uNvidZXl5oH29/gY\nMGAAAH5+ft3yc0pKSti/fz/PPfecYjLO9OnTGT16NNu2bXPpQuPs2bMYDAY8PT0ZNmxYXw9H9ALJ\nufZoMufNzebCwtKx+PbbrhUWiYnKjkVUVDcPtGdoMucaJznXHnfJuVOFxvvvv8/7779v/fsDDzxA\nSEiI4jkNDQ1kZ2czZ86c7h2hnYaGBoYMGUJFRQVRUVEsXryYDRs2MHDgQOtzFi9eTGxsLI899hhv\nvPEGcXFxHDp0iE2bNrFw4UKSkpKc+lkPPvggd955JwEBAUybNo3Vq1czc+ZM6/acnBwAh+sXjx8/\nnm+++eYaj7ZnXbx40boGsyu/SUX3kZxrjyZy3tQE+/fbOhbffAMNDerjJCUpOxZDhnT3SHuFJnIu\nFCTn2uMuOXeq0Kivr6eiogIwdx8uXbrU5vIpX19ffvrTn7J+/fruH+VVqamppKamWudJZGZm8uqr\nr7Jz5072799PUFAQYO5kZGVlsXTpUsWcimXLlvHBBx90+nNCQ0N5+OGHSUtLIzw8nFOnTvHiiy+S\nlpbG559/zs033wxgnVjeusixGDhwoFMTz3Nzc4mLi1MUbk1NTeTl5QEQFhZGbGysYp+TJ09SX19v\nfU1aq6yspKSkBIDY2FjCwsKs2wwGg7U4ctR5Kiws5PLlywAkJycrujSXLl2yXhYXHR1NZGSkYt+j\nR49iMpnw9/dn9OjRim1nz57l4tWbV40ZM0bRUaqtraWgoACAQYMGEWX3G8Pjx49bP0hjx45VbCst\nLbVOuo+Pj7fmH8yX8eXn5wPmXNh/CE+cOEFDQwM6na5NoVhRUcH58+cB82V9lk4YgF6vJzc3F4CQ\nkBBGjBih2Pf06dPW1RhSUlLw9PS0bquurubMmTMAxMTEEBERodg3OzsbgICAABISEhTbzpw5Q/XV\ndfoTExMVc38uX75MYWEhAIMHD2aI3Zej3Nxc9Hq9w/lC58+ft362R40aRWBgoHVbfX09J0+eBCA8\nPJyhdtef5+fn09jYiKenZ5u5S+Xl5ZSWlgIwfPhwRXexubmZH374ATB/1obbLfFZUFBA7dXr5ceN\nG6eYT1VVVcW5c+cAGDp0KOHh4dZtRqORY8eOARAUFER8fLwiblFRETVXJ/UmJSXh4+Nj3VZTU0NR\nUREAUVFRDBo0SLFvTk4OBoMBPz8/xowZo9h27tw562c9ISGBgIAA67a6ujpOnToFQGRkJNHR0Yp9\n8/LyaGpqwsvLi+TkZMW2CxcuUFZWBpgvx+zqOcKemnPEyJEjFfu6zDmiqck8eTsjg7rPP8c/OxuP\nxkaHx9uRhvh46q67DtLSiLj9dhg82LrtxIkTNJSVueU5wn4xSTXnCPvFVeQcYebq5wij0ajY1lvf\nI1z2HNFKf/0eYZ9z6J3vEfa56YxThcYDDzxgvQRoxIgR/P3vf3c4GbynPfLII4q/z58/n4kTJ3LH\nHXfw9ttvW7dXV1dz2223UV9fz+bNmxk2bBg5OTls3LiRRYsW8fnnn3e47vDEiRMVczhmzZrFkiVL\nGDduHCtWrLAWGhbtXfrlzCVher2+zT8KJpOJlpYW63ZH+1i22zMajdZtjt6EreOOGTMGk8lkHWfr\nuPZjah3XYDA4jGsymayXrbVmMBiuKW57x9o6rv2xtn4NHcW1HKujHDkbtydz01Hcjt4v7b2Ger0e\nDw+PNjnvKDfOxG1paXG4raO4rY9Vbc6dfQ0d7d96TPY6O9bm5maMRqPihO8obldfQ0evkbNxO3u/\npKSkKHLeU+/DnjxH6GtrCczJIeDkSfMk7n374GphEdgmWgdSUqwdi4bJk8m9+gU6IiKCiFZFRutj\ndcdzREJCAj4+PtaxqzlHdHSsco5w3XNEXFwcQUFBDnPuKv9WyfeItnGvJTdRUVEMHDhQ8fN743uE\nWqrnaFgqHlexZMkSAgMDFcvOPv/88xw5coTi4mJrZTtr1iwSExOZN28emzdv5p577lH1cwYMGMCP\nf/xj3nzzTRoaGvD397f+psRR5+LixYsOOx32vLy82rxJdTqd9YPmqCDy8vJy+EEE82R5yzZHb4jW\nce3nqrSOaz+m1nEdnUi9vb0xmUwOx+vp6XlNcVv/t7249sfa+jV0FNdyrI5OEM7G7cncdBS3o/dL\ne6+h5Tn2Oe8oN87EtVwfaq+juK2Ptb241/oadvZ+sdfZsfr4+GAwGDqN25XX0Gg0qv7cqHkf2ue8\np96H3XqOaGyErCzIyCBw504mfv89Hs3NbfbrTEtSEpcmTKDu+uuJuP12glr9ZlzX2Ij3pUvtjted\nzxF+fn6K31aqOUfYk3ME1jG68jnC19dXsQKnK7wP5XtEz54j7HPe+hh78nuEWl2+YV95eTnFxcU0\nOLgOdvbs2V0JCZhbdpGRkaxdu9bhvTTsGY1GgoODWbRoER999BEACxYsID8/v01RVFtbS3BwMI8/\n/jgvvvii6rH9+te/5j//8z9paGjAz8+PkpIShg4dyqZNm3jyyScVz01MTCQ2NpZ//etfirHKDfuE\nEMJOQ4O5S2G5QV5WlnlCtxo6HYwfb7vr9qxZ0OqyGSGEENdO7XdZ1R2N0tJS7r77bnbv3t1mm6U9\n76jt0lO2bt1KfX29Yhna6Ohodu7cSUlJCTGtlh/ct28fQJvrSJ1RXV3NZ599xoQJE6y/IYyJiWHK\nlCl8+OGHPP7449YqMCsri/z8fP7jP/7jWg5NCCH6p/p680pQlsnb33/ftcJiwgTbqlCzZplvtCeE\nEMJlqO5oLF26lIyMDH73u98xfvx4hxNMu7Ly1JdffkldXR1XrlzhvvvuY9myZfzkJz8B4JZbbqGi\nooLly5dz5513MmrUKHQ6HZmZmbz22mvEx8fz3XffWSepHTx4kOnTpxMfH89TTz1lnaPxzDPPoNPp\nyMnJsU6y27BhAxs2bGDnzp3WcS9fvpzY2Fiuv/56IiIiOHnyJC+//DIFBQV8+eWX3HjjjdZxZ2Rk\nMH/+fBYuXMhvfvMbysvLeeqppwgNDW1zwz5X62jU1tZiNBrx8PBQTIAS/ZfkXHtcIud1debCwtKx\n+P57870t1PDwMBcWlo7FzJnQapKqsHGJnIteJTnXnr7KeY93NDIzM3nppZf45S9/2bURtuOBBx5Q\n3Oxvy5YtbNmyBTDPCwkNDWXw4MG88sorlJWVYTAYiIuL47e//S0rV65UrIRx3XXXkZWVxcaNG1m1\nahUVFRXExMSwaNEi1qxZo1jJw2g0YjAYFBNjxo8fzyeffMKbb75JbW0tAwcOZObMmXzwwQdMnjxZ\nMe60tDS++OIL1qxZw8KFCwkICODHP/4xL774osvfFbygoMC6EkNfTO4XvU9yrj19kvPaWvMSs5aO\nxf794GByYoc8PGDSJFvHYuZMaLVyi2iffM61R3KuPe6Sc9UdjcjISD766CPFb/WFc1yto5Gdne0W\nb1LRfSTn2tMrOb9yxVxYWDoWBw50rbC4utQsaWkwYwbY3XRVOEc+59ojOdeevsp5j3c0li1bxmef\nfSaFRj8waNCgdlcEEf2T5Fx7eiTnly/D3r22jsXBg6B2bp6nJ1x/va1jMWMG2N0IVnSNfM61R3Ku\nPe6Sc6c6GocOHbL+/+XLl/m3f/s3fvSjH7Fw4ULFzXAsJk2a1L2j7CdcraMhhBBOqakxFxaWjsXB\ng+Bgff0OeXmZCwtLx2L6dHBw41AhhBCuS+13WacKDQ8PD8Wau5Zd7Nfh7YtVp9yJFBpCCLdw6ZKt\nsMjIgMOHu1ZYTJlivUEe06eDTFIVQgi31iOXTv31r3+99pEJIYRwTdXV8PXXto7F4cOg9hZL3t62\nwiItDaZNg0BV9+0WQgjRz3T5hn1CPeloCCFcwsWLsGePbY5Fdrb6wsLHB264wdaxmDYNAgJ6YrRC\nCCFcRI9PBhf9x/Hjx60rFowdO7avhyN6geRce44fP46xooLQ7GyGFRSYi4ujR7tWWEydautYTJ0K\n/v49MWRxjeRzrj2Sc+1xl5yrLjTuu+++drd5eHgwYMAAJk+ezJIlS/Dx8bmmwYme1dLSQovam2YJ\ntyY514iKCmvHYsT//i/+J0+qj+Hra+5SWDoWN9wghYWbkM+59kjOtcddcq660Ni9ezc1NTVcunQJ\nLy8vwsPDqaqqQq/XM2DAAEwmE6+88gpjxowhIyODwYMH98S4RTfw9vZW/Ff0f5Lzfqq83FxYWOZY\n5ORYNzldGvj52QqLtDTzfAs/v+4fq+hx8jnXHsm59rhLzlXP0Th06BBLlizhhRde4I477sDT0xOD\nwcCWLVt48skn2bJlC3q9nttvv51bb72Vd999t6fG7nZkjoYQoluUlZkLCssci+PH1cfw9zevBGXp\nWEyZYu5iCCGEEO3okeVtW0tLS2Pp0qX8+7//e5ttf/jDH9iyZQt79+7l1Vdf5aWXXqKkpERN+H5N\nCg0hRJdcuGArKjIz4Ycf1McICDDfFM9yg7zJk83zLoQQQggn9fhk8P3797N69WqH21JSUli5ciUA\nEyZMoLKyUm14IYQQ588rOxb5+epjBAaaCwtLx+L666WwEEII0atUFxohISHs3r2b9PT0Ntt27dpF\nSEgIAA0NDQTLXV+FEKJzJSXKjsWJE+pjBAXBzJm2jsV115nvbSGEEEL0EdWFxvLly3n++ecxmUws\nW7aMwYMHU1ZWxieffMLLL7/Mww8/DMDBgwdJSkrq9gGL7lNaWorBYMDT05OoqKi+Ho7oBZJzF3H2\nrLKwOHVKfYzgYHNhYelYTJrksLCQnGuP5Fx7JOfa4y45V11oPPfcc5SWlvLcc8+xadMm6+Mmk4mf\n/exnPPvsswBMmzaNm2++uftGKrpdeXm5dQ1mV36Tiu4jOe8jZ87YCouMDDh9Wn2MkBCYNcvWsZg4\nEbw6P4VLzrVHcq49knPtcZecqy40fHx8+O///m9Wr15NZmYmVVVVhIeHM3v2bMUNQ2688cZuHagQ\nQriN4mJbUZGZCYWF6mOEhMDs2baOxYQJThUWQgghhKtQveqU6DpXW3WqtrYWo9GIh4cHQUFBfTIG\n0bsk5z3AZIKiImXHorhYfZwBA8yFhaVjkZoKnp7XPDzJufZIzrVHcq49fZXzHl/eVnSdqxUaQogu\nMJnMHQpLtyIjw3xplFphYcqOxfjx3VJYCCGEED2lR5a39fT0ZN++fUyZMgUPDw90Ol27z9XpdOj1\nehVDFkIIF2YyQUGBsmNx7pz6OAMHmgsKS8di3DiQXzIIIYTox5wqNNasWcPQoUOt/99RoSGEEG7N\nZDKvAtW6Y9GVG4+Gh9uKirQ0SE6WwkIIIYSmyKVTvcjVLp1qbGzEZDKh0+nw8/PrkzGI3iU5d8Bk\nMt+3onVhUVqqPk5EhO0yqLQ0GDvWJQoLybn2SM61R3KuPX2V8x6/M7joP/Lz861Lo6Wmpvb1cEQv\nkJxjLizy85WrQl24oD7OoEHKjkVSErhgt1dyrj2Sc+2RnGuPu+S8S4VGXl4e69evJyMjg6qqKrKy\nspg0aRLr169n9uzZzJ07t7vHKYQQXWMywQ8/2IqKzEwoK1MfZ/BgZcciMdElCwshhBDCVaguNI4c\nOcKsWbMIDg4mLS2NTz/91LqttraWN998UwoNNzFw4EDrXSWFNmgi5yYTHD+u7FhUVKiPExWl7FiM\nHu2WhYUmci4UJOfaIznXHnfJueo5GgsWLODKlSt89dVX+Pj44OPjw4EDB5g0aRJbtmzhySef5HRX\n7nqrAa42R0OIfsFohNxcZceislJ9nOhoZcciIcEtCwshhBCip/T4HI1vvvmGDz/8kICAAAwGg2Lb\n4MGDudCVa52FEMJZRiPk5Ng6Fnv2QFWV+jgxMbZuRVoaxMdLYSGEEEJ0I9WFhslkwsfHx+G26upq\nfH19r3lQQghhZTTC0aO2jsWePXDxovo4w4YpOxYjR0phIYQQQvQg1dfsjB8/nm3btjnc9r//+79c\nd911qgdx5coVVqxYwU033URkZCQ6nY5169a1ed69996LTqdr8ycxMbHNc0+dOsXdd99NbGws/v7+\nxMfH8+ijj1LlxG8+d+3axX333UdiYiKBgYHExMRw2223cfDgwWsakxDCCQYDHD4Mr74Kt91mXjZ2\n4kR45BH4xz+cLzJiY+Gee+C99+D0aSguhr/9De6/X7oXQgghRC9Q3dF4+OGHWb58OYGBgdx9990A\nnDlzhl27dvHee++xdetW1YOoqqrirbfeIjU1lcWLF/POO++0+1x/f3927drV5rHWKioqmDp1KiEh\nIWzcuJHY2FgOHz7M2rVr2b17NwcPHuxwXsRf/vIXqqqqePjhhxk7diwVFRW8/PLLTJ06lX/+85/M\nmzdP9Zhc0YkTJ9Dr9Xh5eTF69Oi+Ho7oBS6Zc4MBjhxRdixqatTHGT7cdhnUnDnmvwvXzLnoUZJz\n7ZGca4+75Fx1ofHTn/6UgoIC1q1bxx//+EcAli5dipeXF+vXr2fhwoWqBxEXF0d1dTU6nY7KysoO\nCw0PDw+mTp3aYbzt27dTVVXFJ598Qnp6OgBz586lqamJlStXkp2dzcSJE9vd//XXX2fQoEGKxxYs\nWMCoUaN49tln2xQazozJFTU0NFjXYBba4BI51+vNHQvLzfG+/houX1YfZ+RI22VQc+ZAXFx3j7Rf\ncImci14lOdceybn2uEvOu3QfjZUrV/KLX/yCf/7zn5SVlREREcHNN99MXBf/odd18yUMlhc9NDRU\n8fiAAQMAOr2Don2RARAUFMTYsWM5e/ZsN42y77W+1EtoQ5/kXK+HQ4dsHYuvvwa7FSucEh+v7FgM\nG9bNA+2f5HOuPZJz7ZGca4+75LzLdwYfOnQo999/f3eOxSkNDQ0MGTKEiooKoqKiWLx4MRs2bGDg\nwIHW5yxevJjY2Fgee+wx3njjDeLi4jh06BCbNm1i4cKFJCUlqf65NTU1HDp0qE03w9kxuaLx48f3\n9RBEL+uVnLe0wMGDto7F3r1QW6s+TkKCsmMxdGh3j1QT5HOuPZJz7ZGca4+75Fx1oTF58mTmz59P\neno6M2fO7NVVplJTU0lNTSUlJQWAzMxMXn31VXbu3Mn+/fsJCgoCzJ2MrKwsli5dan0uwLJly/jg\ngw+69LMffPBB6urqWLVqVZfG1J7c3Fzi4uIICQmxPtbU1EReXh4AYWFhxMbGKvY5efIk9fX11p/f\nWmVlJSUlJQDExsYSFhZm3WYwGMjJyQHMax6PHDlSsW9hYSGXr17CkpycjJeX7e1x6dIliouLAYiO\njiYyMlKx79GjRzGZTPj7+7e5VvDs2bNcvDqBd8yYMYqOUm1tLQUFBYC5kxQVFaXY9/jx49bW4Nix\nYxXbSktLKS8vByA+Pl7xWjc2NpKfnw+Yb2ozzO633ydOnKChoQGdTtfmw1pRUcH58+cB82V9lk4Y\ngF6vJzc3F4CQkBBGjBih2Pf06dPW9aVTUlIUN9Kprq7mzJkzAMTExBAREaHYNzs7G4CAgAASEhIU\n286cOUN1dTUAiYmJis/d5cuXKSwsBMxLTA8ZMkSxb25uLnq9Hl9f3zaLFJw/f56KqzezGzVqFIGB\ngdZt9fX1nDx5EoDw8HCG2n3Rz8/Pp7GxEU+jkZTGRlvHYu9eqKtDtdGjIS2NsqQkKpOT0Q8axLhx\n4xTzqaqqqjh37hxg/mVHeHi4dZvRaOTYsWOAuQMZHx+vCF9UVETN1bkfSUlJitXzampqKCoqAiAq\nKqpNVzMnJweDwYCfnx9jxoxRbDt37px1kYmEhAQCAgKs2+rq6jh16hQAkZGRREdHK/bNy8ujqakJ\nLy8vkpOTFdsuXLhA2dU7mI8YMULOEcg5wm3PEZ6ein+LAcrLyyktLQVg+PDhiisQmpub+eGHHwDz\nv+fD7eZbFRQUUHv1lxdyjpBzhJwjbHrjHKF2PojqQiMqKoo33niDTZs24efnx4wZM7jxxhu58cYb\nu7TilBqPPPKI4u/z589n4sSJ3HHHHbz99tvW7dXV1dx2223U19ezefNmhg0bRk5ODhs3bmTRokV8\n/vnnijd/Z1avXs3mzZv505/+1OYYnR1Te/R6Pfb3TDSZTLS0tFi3O9rHst2e0Wi0bjMajW22OxvX\nfkyt49rfP8US12QyObxW0GAwXFPc9o61dVz7Y239GjqKazlWRy1HZ+O6Sm46O9aWlhb0er3DBRA6\nyk27cZubYf9+Bnz6KX7ffUdQdjY0Njo85o40DB9O87RphC5aZO5YXP3HoTovj4baWnNnxI6zr6Gj\nHLQ+VnudvYbNzc0YjUaHd2Dt0mvYaryWz05X47rK+1DOEW3jukpuev0c0SpuS0uLw20dxbXs21lc\nR+Qc0Tauq7wP5RzRNq6r5OZazhGdUV1o/M///A8Gg4HvvvuOHTt2sHPnTtasWcPKlSsJCwtj3rx5\nfPrpp6oH0lVLliwhMDCQrKws62PPP/88R44cobi42FrZzpo1i8TERObNm8fmzZu55557nIq/fv16\nnnnmGX7/+9/z0EMPdXlM7fHy8mrzJtXpdNYPmqOCyMvLq93JPx4eHtZtjt4Qzsa1H1PruI5OpN7e\n3phMJodxPT09rylu6/+2F9f+WFu/ho7iWo7V0QnC2biukpvOjtVynJ29hu3F1TU343/wIHzwgblj\n8c030NDAYIdH2YGkJEhLQz9zJvmDB6OPiCA0NJRQu99Went7X/Nr2Nmx2uvsNfTx8cFgMHT5NWwv\nrre3N0ajUfXnxhXfh3KOaBvXVXLT0+eIjuIaDAaH2zqKa9m3o7hyjpBzhJq4rf/bXlw5R3TtHNEZ\nnclRmazS999/z5o1a/jXv/6FTqdzWA05q7KyksjISNauXevwXhr2jEYjwcHBLFq0iI8++ggwrxCV\nn59vbQNZ1NbWEhwczOOPP86LL77Yaez169ezbt061q1bx9q1a50+Bkdjsjyu5rbtPa2iosL6j4B9\nC1P0T07lvKkJvvvONsdi3z5oaFD/w5KTbfMrZs+GwapLE9EN5HOuPZJz7ZGca09f5Vztd9kuTQa/\ncOECO3bs4KuvvmLnzj2q9wYAAB9DSURBVJ2UlpYybNgwfvnLX3LjjTd2JWSXbd26lfr6esXystHR\n0ezcuZOSkhJiYmKsj+/btw+gzXWkjmzcuJF169bx9NNPqyoy2huTKzp//rz1ukU5MWmDw5w3NpoL\nC8sci337unQpFOPG2SZvz54N8p5yCfI51x7JufZIzrXHXXKuutAYN24cx48fJywsjLS0NJ5++mnS\n09PbTDpR68svv6Surs5aJR0/ftx6879bbrmFiooKli9fzp133smoUaPQ6XRkZmby2muvkZyczK9+\n9StrrAcffJDNmzczf/58nnrqKescjWeeeYbBgwdz1113WZ+7YcMGNmzYwM6dO5kzZw4AL7/8MmvW\nrGHBggXceuutbS6BshQQxcXFTo9JCFeha2wk8MgR2LbNXFxkZZm7GGqNH6/sWNhNShNCCCGEtqm+\ndMrDwwN/f3/uvvtuFixYwLx58xQrHXTV8OHDrasR2CssLCQ0NJT777+fw4cPU1ZWhsFgIC4ujiVL\nlrBy5co298w4fPgwGzduZP/+/VRUVBATE8O8efNYs2aNYuWAdevWsX79enbv3k1aWhoAaWlpZGZm\ntjtWy0tWXV2takyudunUpUuXMBqNeHh4KFZEEP1Mfb25mMjIQL9jB54HD6JrblYXQ6eD1FRbx2LW\nLGi1motwXfI51x7JufZIzrWnr3Ku9rus6kLj0KFD7Nixgx07drB37170ej3XX3898+fPZ/78+Uyb\nNs3hRBLheoWG6Kfq6+Hbb21zLL77zuEKTh3S6WDCBFvHYtYscPH7wgghhBCiZ/V4odFaU1MTe/fu\n5auvvuKrr77iyJEjBAUFWdehFkpSaIgeUVdnLiwyMsx/9u9XX1h4eMDEibaOxcyZ0GrtdCGEEEKI\nXpkMbnHhwgWKioooLi7m7NmzmEwm6rpyoy4hhPNqa81LzFo6Fvv3g4M1szvk4QGTJtk6FjNngrTb\nhRBCCNGNVBcaf//7362XTp0+fRqTycTo0aP5yU9+Qnp6OvPmzeuJcYoeYLlZoE6nU3UDQ9HLrlwx\nFxaWjsWBA6B2CWlPT7juOoyzZmGcPRtmzMBL5lhognzOtUdyrj2Sc+1xl5x3aTJ4VFQU6enppKen\nc+ONNyqWkBXtc7VLp7Kzs61Lo6WmpvbJGIQDly/D3r22jsXBg10rLK6/3taxmDEDQkIk5xokOdce\nybn2SM61p69y3uOXTuXk5DB27NiujU4I0VZNjbmwsHQsDh0Co1FdDC8vmDzZNsdi+nQIDu6BwQoh\nhBBCOEd1oSFFRv8REhKCXq936ZZbv3TpEnz9te0GeYcPd62wmDLF1rGYPh2CgjrdTXKuPZJz7ZGc\na4/kXHvcJefXtOqUUMfVLp0SvaS62lZYZGTAkSOg9mPn7Q033GDrWEybBoGBPTBYIYQQQgjHenXV\nKSGEAxcvwp49to5Fdrb6wsLHx1xYWDoW06ZBQEBPjFYIIYQQokdIoSHEtaqqshUWGRlw7FjXCotp\n02wdi6lTwd+/BwYrhBBCCNE7pNAQQq2KCmXH4tgx9TF8fc2FhaVjccMNUlgIIYQQol+RQkPDTp8+\nbZ1INHLkyL4ejusqL1d2LHJz1cfw8zNP2LZ0LKZMMT/WyyTn2iM51x7JufZIzrXHXXIuhYaGXbly\nxboGs2ilrMx2D4vMTDh+XH0Mf39zYZGWZv4zebK5i9HHJOfaIznXHsm59kjOtcddci6FhhClpeaC\nwlJc5OWpjxEQYL4pnuVSqMmTzfMuhBBCCCE0Spa37UWutrytodXdpj09PftkDH3i/HllxyI/X32M\nwEBbYZGWBtdd5xaFhWZzrmGSc+2RnGuP5Fx7+irnsrytcJpmTkYlJbaiIiMDTp5UHyMoCGbOtHUs\nrrvOfG8LN6OZnAsrybn2SM61R3KuPe6Scyk0RP9z9qyyY3HqlPoYwcG2wiItDSZNMt+NWwghhBBC\nOEW+OQn3d+aMsmNx+rT6GCEhMGuWbVWoiROlsBBCCCGEuAbyTUrDqqurMRqNeHh4EBYW1tfDcV5R\nkbJjUVioPkZoqLmwsHQsJkwAN2lDXgu3zbnoMsm59kjOtUdyrj3uknMpNDTszJkz1qXRXPZNajKZ\nC4vWHYviYvVxBgyA2bNtcyxSUzVRWNhzi5yLbiU51x7JufZIzrXHXXIuhYZwLSaTuUNhuTleZqb5\n0ii1wsLMBYXlUqhx4zRZWAghhBBC9BUpNDQsJibG2nbrMyYTFBQoOxbnzqmPM3CgraiYM8dcWPTl\ncbkol8i56FWSc+2RnGuP5Fx73CXnch+NXuRq99HoEyaTeXlZS1GRkWG+r4VaERHKjkVyshQWQggh\nhBA9SO6jIVyLyQQnTig7FqWl6uNERio7FmPHSmEhhBBCCOHCpNAQ3ctkgrw85apQFy6ojzNokK2o\nSEuDpCTQ6bp5sEIIIYQQoqdIoSGujckEP/yg7FiUl6uPM3iwbanZOXMgMVEKCyGEEEIIN9bn155c\nuXKFFStWcNNNNxEZGYlOp2PdunVtnnfvvfei0+na/ElMTGzz3FOnTnH33XcTGxuLv78/8fHxPPro\no1RVVTk1ptraWv7jP/6D6Oho/Pz8mDBhAh9//LHD5x46dIgbb7yRoKAgBgwYwO23387prtwwrg9k\nZ2dz4MABsrOznd/JaIScHHj9dVi2zFwgJCfDgw/Cp586X2RERcHPfgZvvmnugJSWwscfw69/Ld2L\nHtSlnAu3JjnXHsm59kjOtcddct7nHY2qqireeustUlNTWbx4Me+88067z/X392fXrl1tHmutoqKC\nqVOnEhISwsaNG4mNjeXw4cOsXbuW3bt3c/DgwU4nX99+++3s37+fTZs2MXr0aP77v/+bn/3sZxiN\nRpYvX259Xl5eHmlpaUyYMIFPP/2UxsZG1qxZw6xZszhy5AiRkZFdeEV6V6dLARiNkJtr61hkZkJl\npfofFB2t7FgkJEgxIYQQQgjRj/V5oREXF0d1dTU6nY7KysoOCw0PDw+mTp3aYbzt27dTVVXFJ598\nQnp6OgBz586lqamJlStXkp2dzcSJE9vd/4svvuCrr76yFheW/YuLi3niiSf46U9/iufV+zGsWbMG\nX19fPvvsM0JCQgC47rrrSEhI4KWXXuL5559X9Vr0litXYNUq+L//dywtLeDtDbffDr//PQQHX33S\nyZOwejXs2AFOdoIUhg5VzrGIj5fCwgUEBASg1+vx8urzj77oJZJz7ZGca4/kXHvcJed9PjpdN3/5\n9Pb2BiA0NFTx+IABAwDw8/PrcP9t27YRFBTEsmXLFI//8pe/ZPny5Xz33XdMnz4dvV7PZ599xi9+\n8QtrkQHmwmnu3Lls27bNJQuNK1dg2jTztAqj0dv6+Ouvw65dsG8fBPu1wKxZUFbmfOBhw2wdi7Q0\nGDFCCgsXlJCQ0NdDEL1Mcq49knPtkZxrj7vkvM/naKjR0NDAkCFD8PT0ZOjQoTz00ENcvHhR8ZzF\nixcTGxvLY489Rm5uLrW1tezZs4dNmzaxcOFCkpKSOvwZOTk5JCUltakQx48fb90OUFBQQENDg/Vx\n++eeOnWKxsbGazncHrFqlaXIUD5uNJoff/ppzHfi7qzIiIuDe+6B996D06ehuBj+9je47z4YOVKK\nDCGEEEIIjevzjoazUlNTSU1NJSUlBYDMzExeffVVdu7cyf79+wkKCgLMnYysrCyWLl1qfS7AsmXL\n+OCDDzr9OVVVVYwcObLN4wMHDrRub/1fy+P2zzWZTFRXVxMVFdXhz8vNzSUuLk7RFWlqaiIvLw+A\nsLAwYmNjFfucPHmS+vp6wPy6tFZZWUlJSQnA/2/v3oOiKvs4gH8Xdhd0QSMUbUXBJC+hhvYqWa9p\nFlo2yWCZmqWCmY3hdp3UsrKAyds0ajqmNjaOGE6G0MV4R1Sspsy8YIV5C1HwghIXZVFkd8/z/kF7\nYtkFYfcsu8D3M8M4nnOeZ37n/HYfzo9zedCrVy8EBQXJ6ywWC9LTzZAkP4exSBLw5Zc3kRBficHD\nh0P166//tg0Lw9V77oHxP/+Bbvx4BN97r03b33//HUIIdOjQAX379rVZV1RUJBeE/fr1s7mqZDQa\nkZ+fDwAICQmxO15//vknTCYTNBoN7r77bpt1ly5dwpV/Hj7v06eP/BkAgOrqapw8eRJAbT569uxp\n0/bUqVO4ceMGVCqVXbFYUlKCi/9MIhgWFiZfDQMAs9mMY8eOAQA6deqE3r1727Q9c+aMPJHNwIED\n5dvsAKC8vByFhYUAamf07NKli01b6wNdHTt2tPtLRWFhIcrLywEA/fv3h5/fvzm8du0aCgoKAADd\nunVD9+7dbdoeO3YMZrMZfn5+di9PuHjxIkpKSgAAERER0Ol08rrr16/j9OnTAIDg4GCEhobatD15\n8iSqq6vh6+tr810DgCtXruDSP/OlhIeH21xhrKmpwfHjxwHUfl/Dw8Nt2ubn58NoNAIABg0aZPNM\nVWlpKc7/M3N8aGgogoOD5XWSJOGPP/4AAAQEBKBPnz42/Z49exZXr14FAAwYMABarVZed/XqVZw9\nexYAcMcddyAkJMSmbV5eHiwWC/z9/dGvXz+bdefPn5fHg7vuugsdO3aU11VVVeGvv/4CAHTt2hV6\nvd6m7YkTJ3Dz5k2o1WpERkbarCsuLsblfwr+3r17t9gYYf1jSmBgoN1YWFBQgGvXrgEAIiMjbf4g\nU1FRgXPnzgEA9Hq93TNqHCNqcYyoxTGiFseIf3GMqOXtY0T93NxKqyk0Xn31VZv/x8TEYMiQIXjq\nqaewceNGeX15eTliY2Nx/fp1bN26FT179kReXh6SkpIwYcIE7Ny585b3szV2O1f9dc3Z1hGz2Yz6\nk7MLIWAymeT1jtpY19cnSZK8Tqp32UIIwGRqPCaTSYUakxnmXbug+d//aquP++/H1cBA+W1aoT16\nOGhnghBCvnWtLovFIsdUf1/rxmuxWBz229C+1u3Xfl9Fo/1aj6GjHDW1XyVzA6DJ/Tb2eWnoGJrN\nZocvQWgsN03p12QyOVzXWL/Wtrfq15GmHkNH7evGVN+t9rWmpgaSJNkM+I76dfYYOjpGTe3XWz6H\nTfkuc4zgGNGUfq1tb9WvIxwj7Pv1ls8hxwj7fr0lN66MEbfSagoNR+Li4qDT6fDLL7/Iy5YuXYqj\nR4/i3LlzclU7cuRI9O/fH2PGjMHWrVsxY8aMBvsMDg52+BpcayVtvYJh/StJQ9uqVCqbCrYharXa\nYfFi/aI5KorUarXDLyJQ+8C8dV39D4RKBWg0jb9mSqMR0Go1UOl0wOTJ//ZbUSH362gg1Wg0EEI4\njNfX11duW39f68bbUL91/22oX/t9VTXar/UYOhogmtqvkrkB0OR+G/u8NHQMrdsUFhbKD4/16tWr\n0dw0pV+LxeJwXWP91t3Xhvp19Rje6vNS3632VavVwmKx3LJfZ46hJEnN/t4053NYP+fu+hw25bvM\nMaJlxohLly7Jx7pXr17NGiMa21eOEd47RpSUlKC0tNRhzr3ldxXHCPt+XclNeXk5jEajnPO6++jO\n84jmUglHZbKH/P333+jatSvee+89h3Np1CdJEgIDAzFhwgSkpaUBAB599FGcPHlSvgRkZTQaERgY\niDfeeAPLly9vsM8XXngBaWlpKC8vt0nUtm3bMHXqVPz000/yw+CdOnXCjBkzsG7dOps+Hn30UZw5\ncwanTp2yi9d6OcwqMDDQqQrRWQZD7YPfDgph+PgAiYnAqlUtFg61sN9++02+hFz/cjm1Tcx5+8Oc\ntz/MefvjqZw391y2VT0MXt+XX36J69ev27zyVq/X4/z58/L9hVb79+8HALt7SOuLi4uD0WhEenq6\nzfLNmzdDr9cjOjoaQG1l+MQTT2DHjh02B7ywsBA5OTmYOHGiS/vmLikptfPh1f88+PjULk9O9kxc\nRERERNS2eMUVjaysLFRVVaGyshIJCQmYNGkSnn76aQDA+PHjUVJSgmeeeQZTpkxBREQEVCoVvv/+\ne6xcuRJ9+vTBgQMH5AfUDh8+jPvvvx99+vTBggUL5Gc0kpOToVKpkJeXJz8888EHH+CDDz7Anj17\nMGrUKDmesWPH4tChQ1i6dCkiIiKQlpaGjRs3IjU1FdOmTZO3O3HiBIYNG4ahQ4diwYIF8oR9ZWVl\nDifs84YrGkDtK24XLQK++kqCyaSCRiMQG+uD5OQ682hQm3Tz5k0IIaBSqWweBKO2izlvf5jz9oc5\nb388lfPmnst6RaERHh4uv4mgvoKCAnTu3BmzZs1Cbm4uLl++DIvFgrCwMMTFxeGtt96ymzMjNzcX\nSUlJOHjwIEpKStCjRw+MGTMG7777rs1bAxYvXoz3338fOTk5GD16tLzcaDTi7bffxhdffIGysjL0\n798fCxcuxJQpU+ziO3z4MObPn4/9+/dDrVZjzJgxWLFihd3bLADvKTTqEoJvoiUiIiKiW2uVhUZ7\n4Y2FBhERERFRU7SrZzSIiIiIiMg7terX27Y2ji4eOXoPckupW5EG8uGMdoE5b3+Y8/aHOW9/mPP2\nx1M5d3Te2tjNUbx1qgWZzWZUVVV5OgwiIiIiIkXodLoGJ8PmrVNERERERKQ4FhpERERERKQ4FhpE\nRERERKQ4PqPRgiRJsnuIRqVSQcWJLIiIiIjIywkh7B7+9vHx4TwaRERERETUcnjrVBtkNBrxyiuv\nQK/Xw9/fH1FRUdi2bVuT2l65cgUzZ85Ely5d0LFjR4wYMQJ79uxxc8TkKmdzvmPHDkydOhURERHo\n0KEDwsPDMW3aNJw+fboFoiZXuPI9r2vRokVQqVQYOHCgG6IkJbma86+++gqjRo1Cp06doNPpEBkZ\niQ0bNrgxYnKVKznPyclBTEwMQkJCEBAQgMGDB2P16tWwWCxujppcUVlZiTfffBNjx45F165doVKp\nsHjx4ia397rzOEFtTkxMjLjtttvEJ598Ivbu3Suef/55AUBs3bq10XbV1dVi4MCBIjQ0VKSmpopd\nu3aJ2NhYoVarxb59+1ooenKGszkfPny4mDBhgti0aZPYt2+f2LJlixgwYIAICAgQeXl5LRQ9OcPZ\nnNeVm5sr/Pz8RLdu3URkZKQboyUluJLzDz/8UPj4+Ii5c+eKrKwssXv3brFmzRrx8ccft0Dk5Cxn\nc56dnS18fHzE6NGjRWZmpsjOzhbz5s0TAITBYGih6MkZBQUFonPnzuLBBx+U8/3ee+81qa03nsex\n0Ghjdu7cKQCIzz//3GZ5TEyM0Ov1wmw2N9h27dq1AoD4+eef5WUmk0ncfffdYvjw4W6LmVzjSs4v\nX75st+zChQtCo9GIWbNmKR4rKcOVnFuZTCYRFRUlDAaDGDVqFAsNL+dKzg8dOiR8fHzE0qVL3R0m\nKciVnE+bNk34+fkJo9Fos3zs2LGiU6dObomXlCFJkpAkSQghRElJSbMKDW88j+OtU21MRkYGAgIC\nMGnSJJvl8fHxuHjxIg4cONBo2379+mHEiBHyMrVajWeffRa//vorLly44La4yXmu5DwkJMRumV6v\nR2hoKIqKihSPlZThSs6tlixZgrKyMqSkpLgrTFKQKzlfs2YN/Pz8MG/ePHeHSQpyJecajQZarRYd\nOnSwWX7bbbfB39/fLfGSMlx5SZA3nsex0Ghj8vLyMGDAALsZGgcPHiyvb6ytdTtHbY8dO6ZgpKQU\nV3LuyJkzZ3Du3DlERkYqFiMpy9Wc//nnn0hOTsa6desQEBDgtjhJOa7k/IcffsCAAQOQnp6Ofv36\nwdfXF6GhoViwYAFqamrcGjc5z5Wcv/jii6ipqYHBYMDFixdRUVGBLVu2ICMjA2+++aZb4ybP8cbz\nOBYabUxpaSluv/12u+XWZaWlpW5pS56jZN7MZjNmzZqFgIAAvPrqq4rFSMpyJeeSJCEhIQETJ07E\n+PHj3RYjKcuVnF+4cAGnT5+GwWCAwWDA7t27MXPmTKxYsQLx8fFui5lc40rOo6OjsXfvXmRkZKBH\njx4ICgpCfHw8UlJS8Prrr7stZvIsbzyPU996E2ptGrvkdqvLca60Jc9RIm9CCMyaNQs//vgj0tPT\n0bNnT6XCIzdwNucfffQRTp8+ja+//todYZEbOZtzSZJQWVmJtLQ0TJkyBQDw0EMPoaqqCitXrsT7\n77+PiIgIxeMl1zmb88OHDyMuLg7R0dFYv349dDod9u7di0WLFqG6uhrvvPOOO8IlL+Bt53EsNNqY\n4OBghxVrWVkZADisdJVoS56jRN6EEHj++eeRmpqKzZs3IzY2VvE4STnO5rywsBDvvvsulixZAq1W\ni4qKCgC1V7IkSUJFRQX8/Pzs7usmz3N1bC8uLsa4ceNslj/22GNYuXIljhw5wkLDC7mS85deegnd\nunVDRkYGfH19AdQWlz4+Pli8eDGmTZuGO++80z2Bk8d443kcb51qYwYNGoTjx4/DbDbbLP/jjz8A\noNF35Q8aNEjerrltyXNcyTnwb5Hx2Wef4dNPP8Wzzz7rtlhJGc7m/MyZM7hx4wZefvllBAUFyT8/\n/fQTjh8/jqCgICxcuNDt8VPzufI9d3TPNgB5dt+GZvQlz3Il50ePHsW9994rFxlWw4YNgyRJOH78\nuPIBk8d543kcR5c2Ji4uDkajEenp6TbLN2/eDL1ej+jo6EbbnjhxwuZNFmazGampqYiOjoZer3db\n3OQ8V3IuhMDs2bPx2WefYf369bxfu5VwNudRUVHIycmx+7nnnnsQHh6OnJwcJCYmtsQuUDO58j1/\n8sknAQBZWVk2y7/77jv4+Phg2LBhygdMLnMl53q9HocOHbKbnG///v0AgNDQUOUDJo/zyvM4j7xU\nl9wqJiZGBAUFiQ0bNoi9e/eK2bNnCwAiNTVV3iYhIUH4+vqKs2fPysuqq6tFZGSk6Nmzp9i6davI\nzs4WcXFxnLCvFXA254mJiQKASEhIEPv377f5OXLkiCd2hZrI2Zw7wnk0Wgdnc15TUyOGDh0qOnfu\nLFatWiWys7PF/Pnzha+vr0hMTPTErlATOZvz1atXCwDiscceE5mZmWLXrl1i/vz5Qq1Wi0ceecQT\nu0LN8N1334nt27eLTZs2CQBi0qRJYvv27WL79u2iqqpKCNF6zuNYaLRBlZWVwmAwiO7duwutVisG\nDx4s0tLSbLaZMWOGACAKCgpslhcXF4vp06eL22+/Xfj7+4v77rtPZGdnt2D05Axncx4WFiYAOPwJ\nCwtr2Z2gZnHle14fC43WwZWcl5aWijlz5ohu3boJjUYj+vbtK5YvXy4sFksL7gE1lys5T09PF//9\n739Fly5dhE6nE5GRkSIpKcluEj/yPo39brbmubWcx6mE+OcmTSIiIiIiIoXwGQ0iIiIiIlIcCw0i\nIiIiIlIcCw0iIiIiIlIcCw0iIiIiIlIcCw0iIiIiIlIcCw0iIiIiIlIcCw0iIiIiIlIcCw0iIiIi\nIlIcCw0iImqVFi9eDJVK5ekwiIioASw0iIiIiIhIcSw0iIiIiIhIcSw0iIjI6+3cuRNRUVHw8/ND\n7969sWLFCrtt1q5diwcffBAhISHQ6XQYNGgQli1bBpPJJG+TlJQEtVqNoqIiu/YJCQkIDg5GdXW1\nW/eFiKi9UHs6ACIiosbs2bMHsbGxGDFiBLZt2waLxYJly5bh8uXLNtvl5+fjmWeeQe/evaHVavHb\nb78hJSUFJ06cwKZNmwAAc+bMQUpKCtavX4/k5GS5bVlZGbZt24bExET4+/u36P4REbVVKiGE8HQQ\nREREDbnvvvtQVFSE/Px8uQiorKxEeHg4ysrK4OjXmCRJkCQJaWlpiI+PR0lJCYKCggAAM2fORFZW\nFoqKiqDVagEAy5Ytw8KFC5Gfn4/w8PAW2zcioraMt04REZHXqqqqwsGDBzFx4kSbKw2BgYF44okn\nbLbNzc3FhAkTEBwcDF9fX2g0GkyfPh0WiwWnTp2St3v55Zdx5coVbN++HUBtUbJu3To8/vjjLDKI\niBTEQoOIiLxWeXk5JElC9+7d7dbVXVZYWIiRI0fiwoULWLVqFX788UccPHgQa9euBQDcuHFD3nbI\nkCEYOXKkvO7bb7/F2bNnkZiY6Oa9ISJqX/iMBhERea2goCCoVCoUFxfbrau7LDMzE1VVVdixYwfC\nwsLk5UePHnXYr8FgwKRJk3DkyBGsWbMGffv2RUxMjPI7QETUjvGKBhEReS2dTofhw4djx44dNm+D\nqqysxDfffCP/3zpxn5+fn7xMCIGNGzc67DcuLg69evXC66+/jt27d2Pu3Lmc/I+ISGEsNIiIyKsl\nJSWhuLgYMTExyMzMRHp6Oh5++GHodDp5m5iYGGi1WkydOhVZWVnIyMjAuHHjUF5e7rBPX19fvPTS\nS9i3bx86duyImTNnttDeEBG1Hyw0iIjIq1kLjGvXrmHy5Ml47bXX8OSTTyIhIUHepn///khPT0d5\neTkmTpyIefPmISoqCqtXr26w38mTJwMAnnvuOXTu3Nnt+0FE1N7w9bZERNQuffzxxzAYDMjLy0Nk\nZKSnwyEianNYaBARUbuSm5uLgoICzJkzBw888AAyMzM9HRIRUZvEQoOIiNqV8PBwFBcXY+TIkdiy\nZYvDV+cSEZHrWGgQEREREZHi+DA4EREREREpjoUGEREREREpjoUGEREREREpjoUGEREREREpjoUG\nEREREREpjoUGEREREREpjoUGEREREREpjoUGEREREREpjoUGEREREREp7v+/vcnve87OiwAAAABJ\nRU5ErkJggg==\n", 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\n", 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+Wloajh8/jg0bNti0vuzsbMTGxppdRaurq8Phw4cBSGNau3fvblbn2LFjqK6u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\nREREREREZIH/D7RD2bRQGB5wAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -687,11 +694,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. \n", + "We have a problem. Our prediction doesn't match our measurement. But, that is what we expected, right? If the prediction was always exactly the same as the measurement, it would not be capable of adding any information to the filter. And, of course, there would be no reason to ever measure since our predictions are perfect.\n", "\n", - "> The key insight to this entire book is in the next paragraph. Read it carefully!\n", + "> **The key insight to this entire book is in the next paragraph. Read it carefully!**\n", "\n", - "So what do we do? If we only take data from the measurement then the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italicized the key point)." + "So what do we do? If we only form estimates from the measurement then the prediction will not affect the result. If we only form estimates from the prediction then the measurement will be ignored. If this is to work we need to take some kind of **blend of the prediction and measurement** (I've bolded the key point)." ] }, { @@ -700,19 +707,25 @@ "source": [ "Blending two values - this sounds a lot like the two scale problem earlier. Using the same reasoning as before we can see that the only thing that makes sense is to choose a number between the prediction and the measurement. For example, an estimate of 165 makes no sense, nor does 157. Our estimates should lie between 159 (the prediction) and 164.2 (the measurement).\n", "\n", - "Should it be half way? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart." + "One more time, this is so important. We agreed that when presented two values with errors, we should form an estimate part way between the two values. It does not matter how those values were generated. In the start of the chapter we had two measurements, but now we have one measurement and one prediction. The reasoning, and hence the math is the same in both cases. We *never* throw information away. I mean it. I see so much commercial software that throws away noisy data. Don't do it! Our prediction of a weight gain might not be very accurate, but so long as there is some information we should use it.\n", + "\n", + "I have to insist you stop and really think about this. All I have done is replaced an inaccurate scale with an inaccurate weight prediction based on human physiology. It is still data. Math doesn't know if the data came from a scale or a prediction. We have two pieces of data with a certain amount of noise, and we want to combine them. In the remainder of this book we are going to develop some fairly complicated math to perform this computation, but the math never cares where the data come from, it only makes computations based on the value and accuracy of those values. \n", + "\n", + "Should the estimate be half way between the measurement and prediction? Maybe, but in general it seems like we might know that our prediction is more or less accurate compared to the measurements. Probably the accuracy of our prediction differs from the accuracy of the scale. Recall what we did when scale A was much more accurate than scale B - we scaled the answer to be closer to A than B. Let's look at that in a chart." ] }, { "cell_type": "code", "execution_count": 14, - "metadata": {}, + "metadata": { + "scrolled": true + }, "outputs": [ { "data": { - "image/png": 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IDg7GypUrMX78eJSVleGZZ56xOX9iYiLOnDmDb775xq7lHT16FNHR0aqrZKWl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\nEZEW/w/EmKk6xB4sQwAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -729,7 +742,7 @@ "source": [ "Now let's try a randomly chosen number to scale our estimate: $\\frac{4}{10}$. Our estimate will be four tenths the measurement and the rest will be from the prediction. In other words, we are expressing a belief here, a belief that the prediction is somewhat more likely to be correct than the measurement. We compute that as\n", "\n", - "$$\\mathtt{new\\_estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\n", + "$$\\mathtt{estimate} = \\mathtt{prediction} + \\frac{4}{10}(\\mathtt{measurement} - \\mathtt{prediction})$$\n", "\n", "The difference between the measurement and prediction is called the *residual*, which is depicted by the black vertical line in the plot above. This will become an important value to use later on, as it is an exact computation of the difference between measurements and the filter's output. Smaller residuals imply better performance.\n", "\n", @@ -743,9 +756,7 @@ { "cell_type": "code", "execution_count": 15, - "metadata": { - "scrolled": false - }, + "metadata": {}, "outputs": [ { "name": "stdout", @@ -764,16 +775,6 @@ "previous: 169.65, prediction: 170.65 estimate 170.87\n", "previous: 170.87, prediction: 171.87 estimate 172.16\n" ] - }, - { - "data": { - "image/png": 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z+fjjjwHo0qULw4YN09e1atWKLVu20Ldv30K37LlfbPLDgy2g0BGwUtm4EcaM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qOj6d69O+np6Tp133jjDWbOnMmoUaP4/vvvCQoKYuzYsXz44YdlfToVys4TV3hudixTY6/z2a+3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\n4eGF6oWEhKDRaArdGjVqVGS7J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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ @@ -787,865 +788,44 @@ "time_step = 1.0 # day\n", "scale_factor = 4.0/10\n", "\n", - "def predict_using_gain_guess(weight, gain_rate, do_print=True, sim_rate=0): \n", - " \"\"\" sim_rate allows for interactive plots in the notebook\"\"\"\n", - " \n", - " with figsize(y=4):\n", - " # store the filtered results\n", - " estimates, predictions = [weight], []\n", + "def predict_using_gain_guess(weight, gain_rate, do_print=False): \n", + " # store the filtered results\n", + " estimates, predictions = [weight], []\n", "\n", - " # most filter literature uses 'z' for measurements\n", - " for z in weights: \n", - " # predict new position\n", - " prediction = weight + gain_rate * time_step\n", + " # most filter literature uses 'z' for measurements\n", + " for z in weights: \n", + " # predict new position\n", + " prediction = weight + gain_rate * time_step\n", "\n", - " # update filter \n", - " weight = prediction + scale_factor * (z - prediction)\n", + " # update filter \n", + " weight = prediction + scale_factor * (z - prediction)\n", "\n", - " # save\n", - " estimates.append(weight)\n", - " predictions.append(prediction)\n", - " if do_print:\n", - " gh.print_results(estimates, prediction, weight)\n", + " # save\n", + " estimates.append(weight)\n", + " predictions.append(prediction)\n", + " if do_print:\n", + " gh.print_results(estimates, prediction, weight)\n", "\n", - " # plot results\n", - " gh.plot_gh_results(weights, estimates, predictions, sim_rate)\n", + " return estimates, predictions\n", "\n", "initial_guess = 160.\n", - "predict_using_gain_guess(weight=initial_guess, gain_rate=1) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is pretty good! There is a lot of data here, so let's talk about how to interpret it. The thick blue line shows the estimate from the filter. It starts at day 0 with the initial guess of 160 lbs. The red line shows the prediction that is made from the previous day's weight. So, on day one the previous weight was 160 lbs, the weight gain is 1 lb, and so the first prediction is 161 lbs. The estimate on day one is then part way between the prediction and measurement at 159.8 lbs. Below the chart is a print out of the previous weight, predicted weight, and new estimate for each day. Finally, the thin black line shows the actual weight gain of the person being weighed. \n", "\n", - "The estimates are not a straight line, but they are straighter than the measurements and somewhat close to the trend line we created. Also, it seems to get better over time. \n", - "\n", - "Before I go on, let me show this plot interactively so you get a better feel for how the filter works. First I need to write some boilerplate code to enable plotting interactively. The magic `%matplotlib notebook` enables the interactive plotting module, and the magic `%matplotlib inline` returns us to the non-interactive plotting. Unfortunately `%matplotlib notebook` permanently alters the plot sizes, so I reset it to the book's default with `reset_figsize()`." + "estimates, predictions = predict_using_gain_guess(\n", + " weight=initial_guess, gain_rate=1, do_print=True) " ] }, { "cell_type": "code", "execution_count": 16, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from contextlib import contextmanager\n", - "from kf_book.book_plots import reset_figsize\n", - "\n", - "@contextmanager\n", - "def interactive_plot():\n", - " %matplotlib notebook\n", - " yield\n", - " %matplotlib inline\n", - " reset_figsize()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we can run the plot interactively. Put your cursor inside the next cell and press CTRL+Enter to execute the cell. This will cause the plot to be drawn slowly, step by step." - ] - }, - { - "cell_type": "code", - "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $('
');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - " $(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " if (mpl.ratio != 1) {\n", - " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", - " }\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " fig.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " '
');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var backingStore = this.context.backingStorePixelRatio ||\n", - "\tthis.context.webkitBackingStorePixelRatio ||\n", - "\tthis.context.mozBackingStorePixelRatio ||\n", - "\tthis.context.msBackingStorePixelRatio ||\n", - "\tthis.context.oBackingStorePixelRatio ||\n", - "\tthis.context.backingStorePixelRatio || 1;\n", - "\n", - " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width * mpl.ratio);\n", - " canvas.attr('height', height * mpl.ratio);\n", - " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('');\n", - " button.click(method_name, toolbar_event);\n", - " button.mouseover(tooltip, toolbar_mouse_event);\n", - " nav_element.append(button);\n", - " }\n", - "\n", - " // Add the status bar.\n", - " var status_bar = $('');\n", - " nav_element.append(status_bar);\n", - " this.message = status_bar[0];\n", - "\n", - " // Add the close button to the window.\n", - " var buttongrp = $('
');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], + "image/png": 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\n", "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2467,46 +867,15 @@ } ], "source": [ - "import time\n", - "with interactive_plot():\n", - " for x in range(2, 6):\n", - " plt.plot([0, 1], [1, x])\n", - " plt.gcf().canvas.draw()\n", - " time.sleep(0.5)" + "e, p = predict_using_gain_guess(initial_guess, -1.)\n", + "gh.plot_gh_results(weights, e, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Back to filtering. The results of the filter may strike you as quite silly; of course the data will look good if we assume the conclusion, that our weight gain is around 1 lb/day! Let's see what the filter does if our initial guess is bad. Let's predict that there is a weight loss of 1 lb a day:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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vZeG20/h7ezClX2Puq1cJpRQVS3kwYdlOY1dmGU9Gdw6he6NicAD8wYPGyJi7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\naKFNr+et8O3hUfDvX1HKiEE/7r/vYyGXbnM3MytXW0p6JpODjrPi0KV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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "predict_using_gain_guess(initial_guess, -1., do_print=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is not so impressive. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was correct, the filter will fail as soon as that rate of change changes. If I stop overeating the filter will have extreme difficulty in adjusting to that change. \n", + "That is not so impressive. The estimates quickly divert from the measurements. Clearly a filter that requires us to correctly guess a rate of change is not very useful. Even if our initial guess was correct, the filter will fail as soon as that rate of change changes. If I stop overeating the filter will have extreme difficulty in adjusting to that change. Note that it is adjusting! The estimates are climbing even though we tell it we are losing 1 lb a day. It just can't adjust fast enough.\n", "\n", "But, 'what if'? What if instead of leaving the weight gain at the initial guess of 1 lb (or whatever), we compute it from the existing measurements and estimates. On day one our estimate for the weight is:\n", "\n", @@ -2516,7 +885,9 @@ "\n", "On the next day we measure 164.2, which implies a weight gain of 4.4 lbs (since 164.2 - 159.8 = 4.4), not 1. Can we use this information somehow? It seems plausible. After all, the weight measurement itself is based on a real world measurement of our weight, so there is useful information. Our estimate of our weight gain may not be perfect, but it is surely better than just guessing our gain is 1 lb. Data is better than a guess, even if it is noisy.\n", "\n", - "So, should we set the new gain/day to 4.4 lbs? Yesterday we though the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Hmm, sounds like our same problem again. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n", + "People really balk at this point, so make sure you are in agreement. Two noisy measurements of weight give us an implied weight gain/loss. That estimate is going to be very inaccurate if the measurements are inaccurate, but there is still information in this computation. Imagine weighing a cow with a scale accurate to 1 lb, and it shows that the cow gained 10 lbs. The cow might have gained 8 lbs up to 12 lbs, depending on the errors, but we know it gained weight, and roughly how much. This is information. What do we do with information? Never throw it away!\n", + "\n", + "Back to my diet. Should we set the new gain/day to 4.4 lbs? Yesterday we thought the weight gain was 1 lb, today we think it is 4.4 lbs. We have two numbers, and want to combine them somehow. Hmm, sounds like our same problem again. Let's use our same tool, and the only tool we have so far - pick a value part way between the two. This time I will use another arbitrarily chosen number, $\\frac{1}{3}$. The equation is identical as for the weight estimate except we have to incorporate time because this is a rate (gain/day):\n", "\n", "$$\\text{new gain} = \\text{old gain} + \\frac{1}{3}\\frac{\\text{measurement - predicted weight}}{1 \\text{ day}}\n", "$$" @@ -2524,798 +895,16 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 18, "metadata": { "scrolled": false }, "outputs": [ { "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. 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');\n", - " var titletext = $(\n", - " '
');\n", - " titlebar.append(titletext)\n", - " this.root.append(titlebar);\n", - " this.header = titletext[0];\n", - "}\n", - "\n", - "\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._init_canvas = function() {\n", - " var fig = this;\n", - "\n", - " var canvas_div = $('
');\n", - "\n", - " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", - "\n", - " function canvas_keyboard_event(event) {\n", - " return fig.key_event(event, event['data']);\n", - " }\n", - "\n", - " canvas_div.keydown('key_press', canvas_keyboard_event);\n", - " canvas_div.keyup('key_release', canvas_keyboard_event);\n", - " this.canvas_div = canvas_div\n", - " this._canvas_extra_style(canvas_div)\n", - " this.root.append(canvas_div);\n", - "\n", - " var canvas = $('');\n", - " canvas.addClass('mpl-canvas');\n", - " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", - "\n", - " this.canvas = canvas[0];\n", - " this.context = canvas[0].getContext(\"2d\");\n", - "\n", - " var backingStore = this.context.backingStorePixelRatio ||\n", - "\tthis.context.webkitBackingStorePixelRatio ||\n", - "\tthis.context.mozBackingStorePixelRatio ||\n", - "\tthis.context.msBackingStorePixelRatio ||\n", - "\tthis.context.oBackingStorePixelRatio ||\n", - "\tthis.context.backingStorePixelRatio || 1;\n", - "\n", - " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", - "\n", - " var rubberband = $('');\n", - " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", - "\n", - " var pass_mouse_events = true;\n", - "\n", - " canvas_div.resizable({\n", - " start: function(event, ui) {\n", - " pass_mouse_events = false;\n", - " },\n", - " resize: function(event, ui) {\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " stop: function(event, ui) {\n", - " pass_mouse_events = true;\n", - " fig.request_resize(ui.size.width, ui.size.height);\n", - " },\n", - " });\n", - "\n", - " function mouse_event_fn(event) {\n", - " if (pass_mouse_events)\n", - " return fig.mouse_event(event, event['data']);\n", - " }\n", - "\n", - " rubberband.mousedown('button_press', mouse_event_fn);\n", - " rubberband.mouseup('button_release', mouse_event_fn);\n", - " // Throttle sequential mouse events to 1 every 20ms.\n", - " rubberband.mousemove('motion_notify', mouse_event_fn);\n", - "\n", - " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", - " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", - "\n", - " canvas_div.on(\"wheel\", function (event) {\n", - " event = event.originalEvent;\n", - " event['data'] = 'scroll'\n", - " if (event.deltaY < 0) {\n", - " event.step = 1;\n", - " } else {\n", - " event.step = -1;\n", - " }\n", - " mouse_event_fn(event);\n", - " });\n", - "\n", - " canvas_div.append(canvas);\n", - " canvas_div.append(rubberband);\n", - "\n", - " this.rubberband = rubberband;\n", - " this.rubberband_canvas = rubberband[0];\n", - " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", - " this.rubberband_context.strokeStyle = \"#000000\";\n", - "\n", - " this._resize_canvas = function(width, height) {\n", - " // Keep the size of the canvas, canvas container, and rubber band\n", - " // canvas in synch.\n", - " canvas_div.css('width', width)\n", - " canvas_div.css('height', height)\n", - "\n", - " canvas.attr('width', width * mpl.ratio);\n", - " canvas.attr('height', height * mpl.ratio);\n", - " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", - "\n", - " rubberband.attr('width', width);\n", - " rubberband.attr('height', height);\n", - " }\n", - "\n", - " // Set the figure to an initial 600x600px, this will subsequently be updated\n", - " // upon first draw.\n", - " this._resize_canvas(600, 600);\n", - "\n", - " // Disable right mouse context menu.\n", - " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", - " return false;\n", - " });\n", - "\n", - " function set_focus () {\n", - " canvas.focus();\n", - " canvas_div.focus();\n", - " }\n", - "\n", - " window.setTimeout(set_focus, 100);\n", - "}\n", - "\n", - "mpl.figure.prototype._init_toolbar = function() {\n", - " var fig = this;\n", - "\n", - " var nav_element = $('
')\n", - " nav_element.attr('style', 'width: 100%');\n", - " this.root.append(nav_element);\n", - "\n", - " // Define a callback function for later on.\n", - " function toolbar_event(event) {\n", - " return fig.toolbar_button_onclick(event['data']);\n", - " }\n", - " function toolbar_mouse_event(event) {\n", - " return fig.toolbar_button_onmouseover(event['data']);\n", - " }\n", - "\n", - " for(var toolbar_ind in mpl.toolbar_items) {\n", - " var name = mpl.toolbar_items[toolbar_ind][0];\n", - " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", - " var image = mpl.toolbar_items[toolbar_ind][2];\n", - " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", - "\n", - " if (!name) {\n", - " // put a spacer in here.\n", - " continue;\n", - " }\n", - " var button = $('