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December 7, 2020 18:14
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Jupyter Notebook on Smooth Transitions between Two Functions
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"import seaborn as sns\n", | |
"\n", | |
"from scipy.special import erf\n", | |
"\n", | |
"%matplotlib inline\n", | |
"\n", | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Prototypical Problem\n", | |
"\n", | |
"Consider the problem described [here](https://www.j-raedler.de/2010/10/smooth-transition-between-functions-with-tanh/). You have two functions $f_1(x)$ and $f_2(x)$ that intersect (not required) at a point $x^*$.\n", | |
"\n", | |
"You want to construct a new function $h(x)$ that smoothly transitions between the two, so that,\n", | |
"$$h(x) = \\begin{cases} f_1(x) & x \\ll x^* \\\\ f_2(x) & x \\gg x^* \\\\ \\end{cases}$$\n", | |
"\n", | |
"One such idea is to use a smooth switching function like $\\tanh(x)$ which goes from -1 to +1 as $x$ goes from $-\\infty$ to $+\\infty$. In particular the switching function,\n", | |
"$$s(x) = \\dfrac{1}{2} \\left(1 + \\tanh(\\dfrac{x-x^*}{\\sigma}) \\right),$$\n", | |
"goes from 0 to 1 as $x$ goes from $-\\infty$ to $+\\infty$. The transition is centered around $x^*$, and $\\sigma$ controls the width over which the transition occurs.\n", | |
"\n", | |
"We then define $h(x)$ as a weighted average of the two functions.\n", | |
"\n", | |
"$$h(x) = \\left(1-s(x)\\right) f_1(x) + s(x) f_2(x)$$\n", | |
"\n", | |
"## Example 1\n", | |
"\n", | |
"Let $f_1(x) = 1/x$ and $f_2(x) = x^2$. They intersect at $x^* = 1$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"f1 = lambda x: 1/x\n", | |
"f2 = lambda x: x**2\n", | |
"\n", | |
"xst = 1.0\n", | |
"sigma = 0.1\n", | |
"\n", | |
"def s(x, xst, sigma):\n", | |
" return 0.5*(1.0 + np.tanh((x-xst)/sigma))\n", | |
"\n", | |
"def h(x, xst, sigma):\n", | |
" sx = s(x, xst, sigma)\n", | |
" return (1.0-sx) * f1(x) + sx * f2(x)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, '$x$')" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"xi = np.linspace(0.5, 1.5)\n", | |
"plt.figure(figsize=(9,6))\n", | |
"plt.plot(xi, f1(xi), '--', label=r'$f_1(x)$')\n", | |
"plt.plot(xi, f2(xi), '--', label=r'$f_2(x)$')\n", | |
"\n", | |
"plt.plot(xi, h(xi, xst, sigma), alpha=0.6, label=r'$h(x)$')\n", | |
"plt.plot(xi, s(xi, xst, sigma), label=r'$s(x)$', c='gray', alpha=0.5)\n", | |
"\n", | |
"\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Lengthscale of Transition\n", | |
"\n", | |
"One can change the spread parameter $\\sigma$ to control the lengthscale over which the transition occurs." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, '$x$')" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(9,6))\n", | |
"plt.plot(xi, f1(xi), '--', c='gray')\n", | |
"plt.plot(xi, f2(xi), '--', c='gray')\n", | |
"\n", | |
"plt.plot(xi, h(xi, xst, 0.05), alpha=0.6, label=r'$\\sigma$ = 0.05')\n", | |
"plt.plot(xi, h(xi, xst, 0.1), alpha=0.6, label=r'$\\sigma$ = 0.10')\n", | |
"plt.plot(xi, h(xi, xst, 0.2), alpha=0.6, label=r'$\\sigma$ = 0.20')\n", | |
"\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"As $\\sigma$ increases, $h(x)$ takes its own sweet time to transition from one to the other." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Other Switching Functions\n", | |
"\n", | |
"There are other choices around which \"sigmoid\" switching functions can be built. Other popular choices include the error function erf$(x)$, and the arctangent function $\\tan^{-1}(\\pi x)$.\n", | |
"\n", | |
"$$s_\\text{core}(x) = \\begin{cases} \\text{tanh}(x) \\\\ \\text{erf}(x) \\\\ \\dfrac{2}{\\pi} \\tan^{-1}(x) \\end{cases}$$\n", | |
"\n", | |
"To center it around $x^*$, and transition over a lengthscale $\\sigma$, replace $x$ with $(x-x^*)/\\sigma$ in the equations above. The overall switching function is then,\n", | |
"\n", | |
"$$s(x) = \\dfrac{1}{2} \\left(1 + s_\\text{core}\\left(\\dfrac{x - x^*}{\\sigma}\\right) \\right).$$\n", | |
"\n", | |
"The [logistic](https://en.wikipedia.org/wiki/Sigmoid_function) function also has a sigmoid shape, but goes from 0 to 1, rather than -1 to 1. So it constitutes a switching function by itself.\n", | |
"\n", | |
"$$s(x) = \\dfrac{1}{1 + e^{-x}}.$$\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.legend.Legend at 0x7fa18d4e6550>" | |
] | |
}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"xi = np.linspace(-5, 5,200)\n", | |
"plt.plot(xi, erf(xi), label='erf')\n", | |
"plt.plot(xi, np.tanh(xi), label='tanh')\n", | |
"plt.plot(xi, np.arctan(np.pi*xi) * 2.0/np.pi, label='arctan')\n", | |
"plt.plot(xi, 1.0/(1.0 + np.exp(-xi)), label='logistic')\n", | |
"\n", | |
"plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Let us apply this to the original example, but generalize the underlying switching function. For this, I have to generalize some of my older definitions. The arctan case needs some normalization, so I define it explicitly as a function `tanInv`. I am not using the logistic function here, because it has a slightly different structure." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# generalizing the switching and transition functions from above\n", | |
"def s(x, xst, sigma, s_core=np.tanh):\n", | |
" \"\"\"s_core is the switching function\"\"\"\n", | |
" return 0.5*(1.0 + s_core((x-xst)/sigma))\n", | |
"\n", | |
"def h(x, xst, sigma, s_core=np.tanh):\n", | |
" sx = s(x, xst, sigma)\n", | |
" return (1.0-sx) * f1(x) + sx * f2(x)\n", | |
"\n", | |
"tanInv = lambda x: np.arctan(np.pi*xi) * 2.0/np.pi" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"xi = np.linspace(0.5, 1.5)\n", | |
"\n", | |
"xst = 1.0\n", | |
"sigma = 0.1\n", | |
"\n", | |
"plt.figure(figsize=(9,6))\n", | |
"plt.plot(xi, f1(xi), '--', c='gray')\n", | |
"plt.plot(xi, f2(xi), '--', c='gray')\n", | |
"\n", | |
"plt.plot(xi, h(xi, xst, sigma, s_core=np.tanh), alpha=0.6, label='tanh')\n", | |
"plt.plot(xi, h(xi, xst, sigma, s_core=erf), alpha=0.6, label='erf')\n", | |
"plt.plot(xi, h(xi, xst, sigma, s_core=tanInv), alpha=0.6, label='arctan')\n", | |
"\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The three switching functions seem to effectively overlap, and on the face of it there doesn't seem to be any reason to pick one over the other.\n", | |
"\n", | |
"We note the $h(x)$ lies below $f_1(x)$ for $x < x^*$, and below $f_2(x)$ for $x > x^*$ before asymptotically merging into the respective functions. This is because the weight or switching function $s(x)$ is designed to be between 0 and 1, and is forced to **interpolate between $f_1(x)$ and $f_2(x)$ at any point $x$**. That is,\n", | |
"\n", | |
"$$f_1(x) \\leq h(x) \\leq f_2(x).$$\n", | |
"\n", | |
"This explains the \"sag\" in $h(x)$ close to $x^*$. We can control the range of the sag by $\\sigma$. But we can't simultaneously control the sag, and the visual smoothness of $h(x)$." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Product of Functions\n", | |
"\n", | |
"Instead of a weighted sum, the transition function may also be defined as a product of the underlying functions. This was done for example in Baba and Masubuchi to stitch different regimes of MSD evolution.\n", | |
"\n", | |
"The basic idea is to posit:\n", | |
"\n", | |
"$$h(x) = f_1(x)^{[1-s(x)]} \\cdot f_2(x)^{s(x)}$$\n", | |
"\n", | |
"where the switching function is defined more or less as before. Note that asymptotically, it does what we expect.\n", | |
"\n", | |
"Let's consider this for our example." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def hprod(x, xst, sigma, s_core=np.tanh):\n", | |
" sx = s(x, xst, sigma)\n", | |
" return f1(x)**(1.0-sx) * f2(x)**sx" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, '$x$')" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(9,6))\n", | |
"plt.plot(xi, f1(xi), '--', c='gray')\n", | |
"plt.plot(xi, f2(xi), '--', c='gray')\n", | |
"\n", | |
"plt.plot(xi, h(xi, xst, sigma, s_core=np.tanh), alpha=0.6, label='h(x)')\n", | |
"plt.plot(xi, hprod(xi, xst, sigma, s_core=np.tanh), alpha=0.6, label='h_p(x)')\n", | |
"\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For this example, there is basically no difference between the two approaches. The sag persists. This is not surprisingly, since the product is still an interpolation in log space." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Blanket Smooth Transition" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Suppose we want the transition function $h(x)$ to blanket $f_1(x)$ and $f_2(x)$ from above. That is, we'd like to get rid of the sag. Note that in this case, we don't really have to:\n", | |
"* don't specify $s(x)$, because we want to avoid interpolation\n", | |
"* specify $x^*$ because the stitching is controlled by magnitude of the functions\n", | |
"\n", | |
"One idea is described [here](https://math.stackexchange.com/questions/2931665/smooth-transition-between-any-two-functions).\n", | |
"\n", | |
"The idea is to define a sufficiently high $q$-norm,\n", | |
"$$h_\\max(x) = \\left(f_1(x)^q + f_2(x)^q \\right)^{1/q}$$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def hblanket_max(x, q):\n", | |
" return (f1(x)**q + f2(x)**q)**(1.0/q)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, '$x$')" | |
] | |
}, | |
"execution_count": 13, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(9,6))\n", | |
"plt.plot(xi, f1(xi), '--', c='gray')\n", | |
"plt.plot(xi, f2(xi), '--', c='gray')\n", | |
"\n", | |
"plt.plot(xi, h(xi, xst, sigma, s_core=np.tanh), alpha=0.6, label='h(x)')\n", | |
"plt.plot(xi, hblanket_max(xi, 2), alpha=0.6, label='q=2')\n", | |
"plt.plot(xi, hblanket_max(xi, 4), alpha=0.6, label='q=4')\n", | |
"plt.plot(xi, hblanket_max(xi, 10), alpha=0.6, label='q=10')\n", | |
"\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that by definition $h(x) \\geq f_1(x)$ and $h(x) \\geq f_2(x)$.\n", | |
"\n", | |
"For a minima in $h(x)$, so that $h(x) \\leq f_i(x)$, we can use:\n", | |
"\n", | |
"$$h_\\min(x) = \\left(f_1(x)^{-q} + f_2(x)^{-q} \\right)^{-1/q}$$\n", | |
"\n", | |
"**Note that this is the same as the maximum blanket with a -ve $q$.** So strictly speaking, I don't need a separate function." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 108, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def hblanket(x, q, setting='max'):\n", | |
" if setting == 'min':\n", | |
" q = -q\n", | |
" return (f1(x)**q + f2(x)**q)**(1.0/q)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 119, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 0, '$x$')" | |
] | |
}, | |
"execution_count": 119, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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SQoi6tIat/wcb/1ATC+0JD69gWEicaWmJptXo2UatVXucbXRFZw/AWzOM4gXQfmEUz36XoF6jTU5MCCFM5HTCmp/BrpdrYlGD4MHlEBBhXl7iurSK2UaiCUUPhodXgLexhLUqz8Pj3bspPL7T5MSEEMIk9mr0x4vqFC7n/RJxPrJSCpd2SIqXtqrrMHjoY2wWHwD8dZlRwKTvNjkxIYRoYVWl6PfuRR1a7g6l0Js14Y9js8hy/+2RFC9tWewI8qa/TDXGTtQBuhSPpbMpOrnf5MSEEKKFlF5Av3kHKn2jO7SbQSQnfI8HHl6At7e3icmJ5iLFSxsXOXIWedP+XauAKcHy1kyKT3fo2eVCiI4gLx29eAoqu2bW5WZGc6rfM9x7/wN4enqamJxoTlK8tANRY+aSO+UFbK7JY4G6CN68k5Izh03OTAghmsmZvejFU1GFNavmrmIKpcOf4e45c7Ba65v4KtoLKV7aieib7+fCpOewu2aqd3IW4nz9dkqzUk3OTAghmtixtcatooo8AGx48AEz8Bv3Xe644w4sFvnR1t7J/+F2pOv4h8me8Dd3ARPkLMDx2q2UnEo2OTMhhGgie5fAe/ej7BUAlOPDW8wlbtpTTJ48GaWUyQmKliDFSzsTe8sCssf9BYfrf22QsxDr23dBjvTACCHaMK1h859h1fdAOwAosgTzhrqf4bO/y5gxY0xOULSkxqywK9qI2MmPk6ksRH71Uzyx42cvgjdug4c/gaiBZqcnhBCN47DDZz+AfW/VxCIHou9czK0VFnr16mVebsIU0vPSTsVOWkjurS+hPf2MQHkeLLkTMmUdGCFEG1JdDh88WLdw6XkLPPo5wTGJUrh0UFK8tGNRY+ehHlkJPkFGoLII3ppJ1dF15iYmhBANUXoB3rwDjq2piQ28Dx74ELwDzctLmE6Kl/YudgTMXw1+4cZ7WxmW9+8j+6t6N/gWQojWIecYLJ4CZ/e5Q9vVKE4P+wV4eJmYmGgNpHjpCKIGwqNfYPc19vfwxE7njc+Ste7Fa5wohBAmyNiOfm0q1FrD5TMm8W2XuwkNCzM5OdEaSPHSUUT0puSejyhSwQBYcRK1/RecWf0/JicmhBC1HPwI/fYsVGUhANV48D4zudB9BgsWLCAgIMDkBEVrIMVLBxLScwg8toZ8i3ELyYImZs8fyVz+G5MzE0J0eFrDV/8HHy9COaoBKMGfN7kXa9LtPPzww/j4+JicpGgtpHjpYIJik/D6znpyrVHuWOy3z3P6zSfQTqeJmQkhOiyHzVi/ZeN/uUMXCOM17id6+O3cc889eHjIyh6ihhQvHVBAlx74fncD5z27uWPdMj7gzL9m4rRVmZiZEKLDqSqBd++tMxX6JLG8zr0MnniXLPcv6iV/Ijoo/7CuBD2zmTO+fd2x2LyvOP/cLdhK803MTAjRYRSfhddvg/QN7lAySbyj5jDlzjlMnDhRlvsX9ZLipQPz6RRG5A82cTJknDsWVZaC8/XboeS8iZkJIdq97GR4dTKc/9YdOhP/AKusdzBn3n0MHz7cxOREa6e01mbn0CSGDx+u9+zZY3YabZJ2Okl//XESziyrCQZ3h4c+hvAE8xITQrRPRz+H5QvBVm68t3jAXc/DkIcoKCggJCTE3PxEq6CU2qu1rreKlZ4XgbJYSFj0Gnk3/ScoY0dqCk/Ba1NlOwEhRNPRGr5+Ad5/oKZw8Q6CB5fBkIcApHARDSLFi3ALm/oDuO9d8PA1AhX56CV3cmGrrMYrhLhBDhus+j58+SvA6PEvtoZiW/AFxN9ibm6izZHiRdSVOB0WrAY/YxVLZa8kfMP3yVr5R5MTE0K0WRUFsHQO7Kv5Reg00bzsmMdXh8+ZmJhoq6R4EZeLGQ4L11Hm1RkwFrPruu9/OPP6o2iH3eTkhBBtSv4JWDwVTm5xh5JJ4i3mEttnCOPHjzcxOdFWSfEi6hcWj33+55z36OoOxZz+mHPPT8JeJlOphRANcOprY0ZR3nF3aCNj+YTpDB4+innz5uHp6WligqKtkuJFXFFQ1150euYrTvsNcMeiipMpfm4MZVlHTMxMCNHqJb8PS2ZAhfHLjg0rH3EHW9VoJk2eLIvPiRsif3LEVfkGhdP1h5s43uVOdyzUdg61eBL5Bz4zMTMhRKvkdMC638KK74DTBkApfixhHketScycOZNx48bJ4nPihkjxIq7J6uFJwpNLOT7gx9gxplL76XKCPnmIc2v+anJ2QohWo7IY3rsftj/nDp0njMU8wAWvbtx///0MHjzYxARFe9Gg4kUpFaOUekEp9Y1SqlwppZVScQ08N8PV/tLHrHraPq6UOqqUqlJKpSqlnmzc1xHNRSlFrzm/5uzUlynDDwArTiJ3/J6CD58xftsSQnRceemweAocX+sOnfZJ4nXuwx4QxYIFC0hIkEUvRdNoaM9LAjAPKAC2XsfnrAXGXPLYUruBUupx4GVgOTAd+Ah4USn11HV8nmgm3W66h4qHPyfX2sUdCzn8lrHoVFWJiZkJIUxzYjO8OglyU2tiNz1L2NNf0r13fxYuXEh0dLRp6Yn2p0HbAyilLFprp+v1IuBVoIfWOqMB52YA27TWD12ljQdwFvhCaz2/Vvx1YAYQpbW2Xe1zZHuAllVWcJ6iN+YRXXygJti5L9z/HoTEmZaXEKIFaQ27XoU1PwPt6n21esPMf8LAeebmJtq8G94e4GLh0ozGABHA0kvibwNhwM3N/PmikfxDuhD97Ea46fs1wQuH0S9PoGjvsiufKIRoH+zVxoq5X/zEXbhUe4fCo19I4SKaXUsN2L3LNVamSim1o57xLv1cz4cuiae4nvs2b3riulisMPX3MOslsHoBoCoL6bRqIdnvfR+czV3zCiFMUZYLb82ss2JuFl34Z9Ucjpb6m5iY6ChaonhZBTwDTAMeBCqBFUqp2reRQl3PBZecm3/J8TqUUk8opfYopfbk5OQ0YcqiUQY/AI9+gc3PGAejgKjUNzn//C3YS3LNzU0I0bTOfQuv3AKnv3aHDtKHN5lHiQqkuLjYxORER9HsxYvW+hmt9Vta661a62XAZGAP8KcmuPYrWuvhWuvhERERN5yruAExwym5fxVZnj3doS5FByh/bgSlad+YmJgQoskc/MhY6r/oNGBsr7iem1nBbeDpy7x58xg5cqS5OYoOocXXedFaOzBmEsUopaJc4Ys9LpfuhX6xx0XWo28DQmMTifjRdlIjbnPHOjny8V56JznrXzAxMyHEDXHYYc0v4ONFYK8AoApP3mcm29VI/Pz9mT9/PklJSSYnKjoKsxepuzjV6eLYln6XHL841uVwy6QjbpSXjx+9v/seqYN/RRXGOBhP7ERs+xXnXnsQbas0OUMhRKOU5sDbs2DHv9yhXEJYzAMcU/GEhoaycOFCYmJiTExSdDQtXry4pkXfC5zWWl/cC/0bIBdjTExtD2H0umxvuQzFjVJKkTjrJ+TM/ohcS7g7Hpm5mvy/jaE696SJ2QkhGixrH7wyETJqlvc6SjyLeYBcFUZMTAwLFy4kNLTeYYlCNBuPhjZUSs11vRzmer5NKZUD5Gitt7ja2IElWuuFrvf3AzOBz4FMoAvwNDAUuP/itbXWNqXUrzEWpcsC1gOTgMeAZ7TW1df/FYVZYgZNpLjrNk68di89K5IBCKs4QdVLN8O81yBxuskZCiGuaP87sPoH4KgCQKP4ynITm50jQCmSkpKYPXu27AotTNHg4gVjnEptL7qetwATXa+trsdFJ4HOwP9ijF8pwxisO11rvbZWO7TW/1ZKaeBHwE+A08B/aK1fRLRZncKj8PvhBlKWPEvSmXewoPF2lMJ798Kop2Dq78DD2+w0hRAX2ath7c9h9+KamHcQas6rhNtiYNkyxo4dy5QpU2RzRWGaBq2w2xbICrut37H1S4jb8194Vdaa1h45EO55E8LiTctLCOFSch4+fAQyd9TEIpLgvnfcf0fPnTtHZGSkSQmKjuSGV9gVoin0njIfr+/tgt41s5E4dxDHSzdTuOXf5iUmhICMbfDyuDqFS1XC7bBofZ1fLqRwEa2BFC+iZfmFGvsfTf+Le1Veq72c4E3/j9xX56Jlc0chWpbTCdv+DkvugtLzAGgsrGMcr+SPodwhPyZE6yN/KkXLUwpGP4leuI4ij5rZSOFZ6yj961CqMnabmJwQHUhFAbx/P6z/T3BtYVdpDeBtZvO1GkF+QQGbNm0yN0ch6iHFizCNih6MfeFGUn2HuWOB1RewvjmNwjV/kr2RhGhOWfvg5fFwbI07dN4rjhcd93NSdQcgMTGRqVOnmpWhEFckxYswVVhUd+J/9CXJPZ+iGmPKpQcOgnf8mYIXbsFZcNrkDIVoZ7Q2ZhK9Pg0Ka/5+7fEawyvVMylRgQCMGjWKefPm4eXlZVamQlyRFC/CdB4eHgx65M+cvm0p51QXdzyk4AC2f4yg7Js3jH9whRA3pqoUli+Cz34EDmP5LIenP8s9ZvOZbQxOZUUpxW233cb06dOxWORHhGid5E+maDUSRk3H+7tfcTBwknvfCG9dif/aZyl+bTaU5ZmanxBt2oWj8OokOLTMHSoLjOdF+70ccvQAwMvLiwceeEA2VxStnhQvolUJiYik/w+Wkzz0zxQQ5I53OrMJXhwNqWuucrYQ4jJaw/6l8OotkJvqDhf0nMFzJbeTTzAAwcHBLFy4kISEBLMyFaLBpHgRrY7FYmHwjKeoXLCBQz4jag6UXTBW5l35DMiUaiGurbIIli+ET58GW7kR8/CFWf8m6KElxPfpD0BMTAyLFi2ic+fOJiYrRMPJCruiVbPZbFjSN2Bd/T33GhQA9sAYmPUSHvHjTcxOiFbszB5Y9hgUnqqJhfc2VrTu0g+A6upqtm3bxvjx4/HwaMxuMUI0P1lhV7RZnp6eWPtMh+/ugL6z3HGPkjNY355B6UdPG4MQhRAGpxO2/s01m6imcCnvcw/ORRvdhQsYY1wmTZokhYtoc6R4EW2DXyjc8yb67sVUWXwBUGgCUpZS8bfBOFK/NDlBIVqBknOwdDZs+B047UbMO4iMEb/lb2lxfLl5u7n5CdFEpHgRbYdSMGAuxyYvIV31cId9q3KwvncPZUsfkhlJouM6vg5euglObHaHdMwIvur33yzZU4LD4WDnzp3s27fPvByFaCJSvIg2RSnFgJumEfrMRrZGPEI5Pu5j/mmrqPr7YOwH3pd1YUTHYa+CNb+Ad+ZCea4rqLCP/QEf+C1g0/50d9POnTvTs2dPc/IUoglJ8SLapJDQUG7+7j84NvUdUix93XFvezEen3yH8tdnQNEZEzMUogWc+xZeuQV2/KsmFhhFyd3v8EpaZ1KP1xQuiYmJPPbYYwQHB5uQqBBNS4oX0WYppRh80xS6fu8LNkY+SRGB7mN+mV9h/8dw2PWq7JEk2h+nwxiU+8otcCGlJt57Opl3vs9La1LIyclxh2+66SbuvfdevL29TUhWiKYnU6VFu6C1Jnn3dhxrf80wxyX39GNGwO3/B9GDzUlOiKaUlw6fPAWZO2tiHr4w9ffs8xjGZ59/jtNVsFutVu666y4GDRpkUrJCXD+ZKi3aPaUUg0feTK/vf8qXMT+i2Duq5uCZ3cbqop/9GCoKzEtSiBuhNex+Df59c93CpetweHIbXzv6s2r1anfh4u/vz/z586VwEe2SFC+iXenUqRNTF/4avx/sgfE/BatrR1zthN2vYvv7YPS+t+VWkmhbirONAbmf/bBmpVyLB0z6FTy2FsIT6NOnD76+xjICXbp04fHHHyc2NtbEpIVoPnLbSLRvuWnwxU8gfWOdsC1yKJ4zn4Mo+a1UtHKHlsPqH0JlYU0sog/MfvmyW6EZGRns2bOHGTNm4OXl1cKJCtG0rnbbSIoX0f5pzaFlfyY25V8EUbMnksaCHv4Ylsm/Bl+ZgSFamdIL8PlP4PAntYIKxjwNk35NaZWdgIAA09ITornJmBfRsSlF75k/Ys+oF9nGSByuP/YKJ5Y9i3E8P9jYdVduJYnW4OIu0P8cUbdwCe4GC1ajb/0DX+/ex/PPP8/p06fNy1MIE0nPi+hQsrOz2bridYZd+IB4TtU55ujcD+v0P0HPCSZlJzq8/BOw6lk4uaVufMjDMI//92QAACAASURBVO2/sXv4sWrVKg4ePAgYg3Iff/xxgoKCTEhWiOYlPS9CuERFRTH3yZ+TO/0VPvaYRRE13e7WCynw1gz0O/MgJ9XELEWH47DD9ufhxbF1C5eQOHj4E5j5T0psijfffNNduACEhoZitVpbPl8hTCY9L6LDKi4uZt1nKwhPfYex7MUTe81BZYVhC2DizyEgwrQcRQeQnQwrnzGeL1IWY2zLxF+Alx9nzpzhgw8+oLS0Zgf1IUOGcPvtt8uO0KLdkgG7QlzF8ePH2frZ+wwt/JxBHEFR6++EVyCM+yGMfgo8fc1LUrQ/tgrY/Gf4+gXQjpp4lwEw8wWIHgJAcnIyq1atwuEw2iilmDZtGiNHjkQpZUbmQrQIKV6EuAa73c6BAwcYGuWBZd2vIGNrneM6KAY1+bfQfy5Y5G6ruEGpa2DNz6DgZE3M6g0TfwZjnwGrJ06nk3Xr1rFjxw53E19fX+bOnSubK4oOQYoXIRpDazi2Ftb9GnKP1T3WuR/c8gvocwfIb72isXLTYO3P4fiXdePdb4a7nofwBMDY7uLdd98lLS3N3SQiIoL777+fkJCQlsxYCNPc8IBdpVSMUuoFpdQ3SqlypZRWSsU14LzeSqnnlVIHlVKlSqlspdRKpdRlK4MppTa7rnvp49mG5ChEk1EKEqejn9zO18FzKKPW7aILKfDBg/DKRDi+zih0hLiWqhJY91t4cXTdwsUnyCha5q9yFy5g3BpKTEx0v09MTGThwoVSuAjh0tCRXgnAPGAvsBW4tYHn3QrcAiwB9gHBwE+BHUqpm7XWey9pfxD4ziWxjAZ+lhBNSls8UKMe5+VNsYyo/ppR7McLm3Ew+4CxXHvMSGOJdpleLeqjNXz7Eaz7DZRk1zqgYOgjMPk34B9e76nDhg0jOzubwMBAJkyYIONbhKilQbeNlFIWrbXT9XoR8CrQQ2udcY3zwoE8XetDlFJBGAXJKq31I7XimwEPrfXNjf8acttINJ+SkhI2bNjA8QPfcDO7Gc4BPHHUbRQ3zihiuo02J0nR+mQnw+c/hcwddeMxI+H2/3EPyAVwOp1UVFTg7+9fp6nWWooW0WFd7bZRg3peLhYujaW1zq0nVqSUOgZ0vZ5rCtHSAgMDmTVrFmdHjmTt2rV8fWoY49jJML7FiuuvRsZWeH0axE82Bl3GjjQ3aWGe0hzY/N+w901jQ9CLArrA1N/DgHl1Bn1XVFSwbNkyysvLeeyxx/D09HQfk8JFiPq1+AIBSqlQoD/wRj2HhyiligA/4AjwvNb6tZbMT4griY6OZsGCBRw5coT162P5On8E49nBYFKwXJxenb7BeHQbCzf/AHpNlYG9HUVlEWz/B+x4CWxlNXGLpzHVfvxPwKdTnVPOnz/P+++/T2GhseniypUrufvuu6VoEeIazFjd6AVAAc9dEv8KeAc4hjE25hFgsVIqSmv9h/oupJR6AngCoFu3bs2WsBAXKaXo27cvvXv3ZteuXXz5VQTbq0ayqFcevsdX1fymffprePdrY3bSzc9Cv7vBKouJtUvV5bDrFdj297o7P4PRE3fbXyC812WnpaSk8Omnn2Kz2dyx0NDQ5s5WiHah0VOlGzPmpZ5zfw78N7BQa/16A9qvAKYDEVrr0qu1lTEvwgzl5eWkp6czYMAAyDkG25+Dgx+A0163YXA3GPMMDHkIvPzMSVY0LYcN9r0FW/4HSs/VPda5nzEYt/e0y3renE4n69ev55tvvnHHvLy8mD17Nn369GmJzIVoE5p0nZfrLV6UUk8CLwG/0lr/sYHnzAM+AMZqrb+5WlspXkSrUXSGs8t/Sfjp1XhxSRHjFwajnoQRi8BPfstuk5xOOLQcNv2x7iJzYOxFdMsvr7iYYVlZGcuWLSMjI8MdCw0N5b777iMiQrahEKK2Gx6w2wQJPAy8CPy1oYXLJWQxDdFmVHqH83ZOXxRRjOAAo9iPH5XGwfI844fe1r/BgLlGERM92NyERcM4HXB0tdHTcv5Q3WMBkTDhp8b0Z6tnvadnZWXx4YcfUlxc7I717t2b2bNn4+Pj05yZC9HuNHvxopSajTE4d7HW+seNPP1BoAL4tskTE6KZeHt7M2PGDDZs2MBXeb58o4czhEOMYQ/BlBiN7BWw/23jETPCKGL6zgJP+SHW6tgq4MA78M2/IP9E3WM+wcbA7JFPXPV2YGZmJkuWLHHvTwQwceJExo8fL4NzhbgODS5elFJzXS+HuZ5vU0rlADla6y2uNnZgidZ6oev9eOA9IBl4UylVexGMKq31fle7ccDPgI8x1oAJAuYDM4Cfaa1rDd0XonVTSpGUlERiYiL79+9ny5Yt7CoZwh49kP6kMoa9RJJTc8KZ3cZj7S+M39yHP2aMkRHmKsuD3Yth18tGj1ltnn4w+rvGPkS+wde8VHR0NDExMZw6dQofHx/uvvtuevW6fBCvEKJhGjzmRSl1pYZbtNYTa7VZorVe4Hr/n8Bvr3DeKa11nKtdAsYspIFAOGDDWG33Ba31ew3JT8a8iNbKZrOxc+dOtm3bRlVVFWhNDNmM4AD9OI710gXvlAV6TTN6Y+JvAYvVnMQ7qvyTRi/L/qVGD1ltPkEwfKEx9Tmgc6MuW1paysqVK5k+fbrMKhKiAWRjRiFagYqKCrZt28auXbuw242BvLePH8EI62HY8wYUn7n8pIBIY2zMwHshcoCsGdNctDZ6v775FxxZWXdxOYCgWKOnZejD4B14zctlZ2cTGRkpt4SEuAFSvAjRipSUlLB161aOHTvG008/bayo6rDD8bXGbYr0jfWfGJEEg+6FAfdAUEzLJt1elZyHg+/D/ncgN/Xy45EDYOz3od+sKw7ErU1rzfbt29m4cSMTJkxgwgTZ80qI6yXFixCtkN1ux8Oj7rCzc+fO8dG//8zk4FMkViVjrcir50wFcTcbvTF9Zxi3MkTD2auNQnH/UtfO4I7L28RPgrHfg54TG9zbVVlZySeffEJqak0R9OCDD5KQkHCVs4QQV2L6VGkhxOUuLVwANm3aRL4K4aOiEJQeyM3RNkb5ZuB/ehPYyl2ttLGXUsZW+PzH0GMCJE6H3tOhU3TLfom25NwhY9bQwQ8uH4AL4OkP/WbDqO9A1MDGXfrcOT788EMKCgrcsdjYWLp06XKjWQsh6iHFixCthNPpxNfXF6UUWmu0srA125utJJLQbQK3xlYTfnYD6uSWmjEZ9kqjF+H4WuAHEDXIKGJ6T4eowfUulNZhOJ1wLhmOrYWjn8G5g/W3634TDH4Q+s4E74BGf8yBAwf47LPP3OOYAEaPHs2UKVOwWmWwtRDNQW4bCdHK5ObmsmXLFlJSUrj072dsbCy3DE8irmQ36uCHcP4qSyAFRELvW6H3bdBjXIMGmrZ5VSVwYrNRsBz/EkrP19+uU1cYdD8MfgDC4q/ro+x2O1988QX79u1zx7y8vJgxYwb9+vW7rmsKIWrImBch2qC8vDy2bdtGcnLyZUVMdHQ08+fPx6v0jPGDOvULOLX98j2VLlIW6NIfuo2G2FHGc3sY9Ku1sUT/sS+N3qeMbeCorr+t1Rv63AFDHoSeNzYFvaCggI8++ojs7Gx3LCIignnz5hEeHn7d1xVC1JDiRYg2rKCggO3bt7N//36cTuN2UUJCAg8++GDdhpVFxkyl1DVGr0NF/tUv3KlrTSETO8ooblr7ztdluZC1D87uh7Ou5yv1rgD4hkKvW40eqPjJDVpQ7lq01rz++uucOVMztb1///7cddddeHl53fD1hRAGKV6EaAeKi4vZvn07+/bt4+GHH6Zbt7qr8J49e5aIiAhj6rXTYaxbkvoFpG1w7cVzjb/rVm8I7QnhvYxHWC8I7w3hCS0/o8npgJJzkHe8VrGyH4oyr31ulwGu22XToeuwZlnk78KFCyxevBiHw8G0adMYMWKErOkiRBOT4kWIdqSiogJfX986MbvdzvPPP4/D4WDkyJGMHDkSP79ae+1UFhnFzOmdkLkDzuwFWyN23fDvbBQyoT3AP9zY08c3pP6Hp68xvVhrowhx2sBhM25pOWw178vzjYX5irKg2PUoyoLis1CSXf8U5vp4BRhTx3tPM3pZWuh22OHDhwkMDCQ2NrZFPk+IjkaKFyHaub1797J69Wr3e09PT4YMGcKYMWMIDq7nVonDbgz2zdwFp3dA5k6jeGgKFtdibk5b01yvNg8fiBwI0UOg61DjOaxXs86qysjIoKysTAbhCtHCZJ0XIdo5b29vgoODKSwsBIz9lHbt2sXu3bvp378/Y8eOJTIysuYEq4fxgz96iLGuCRi9M7lpxq2a3GOQexzy0ozHlQbB1qepiha/cAiONaZ/Rw81ipWIPg1a6bYpaK3Ztm0bmzZtwsPDg4iICDp3btx+RkKI5iE9L0K0E06nk5SUFLZv387585cPYu3RowejR4+mV69ejRuf4XRA4WmjiCk8BRUFUFHoer70df4lhY4yig2Lp1EwWb1qXnsHQVBXY+Bwp2jjdk+nrkYsMBo8fW78P8p1Ki8vZ8WKFaSlpblj3bt3Z8GCBablJERHI7eNhOhAtNakp6ezfft2MjIyLjt+1113MXTo0Ob6cGPhPHfR0vYWacvMzGTZsmUUFxe7Y926dWPOnDl06tTJxMyE6FjktpEQHYhSioSEBBISEsjKyuLrr7/myJEjaK3x9vZu3rEbShkDdtsgrTU7duxg/fr17inpADfddBOTJk3C0pFXKxailZHiRYh2rGvXrtxzzz0UFhaya9cuvL298fb2rtMmKyuLXbt2MXr0aKKiokzK1FwVFRWsXLmSo0ePumM+Pj7Mnj2b3r17m5iZEKI+UrwI0QEEBwdz66231ntsx44dHDp0iIMHDxIbG8vIkSNJSkrqMPvynDlzhmXLllFUVOSOde3alblz59Y/U0sIYTopXoTowEpLS0lJSXG/z8zMJDMzk4CAAIYNG8bw4cMJCGj8ZoVtic1mq1O4jBw5kltvvbXDFG9CtEUyYFeIDi4rK4udO3eSkpJSZ6wHgMVioW/fvowcOZKYmJh2u4rspk2b2LVrFzNmzCApKcnsdIQQyGwjIUQDlJSUsG/fPvbs2UNpaellx6Ojo3n00Ufx8GjbHbbV1dWX7UHkdDopLS2V2URCtCJXK15k+LwQAoDAwEAmTJjAs88+y5w5cy5b9t7Pz69NFy5aa7Zu3co///lPSkpK6hyzWCxSuAjRhrTdf4mEEM3CarXSv39/+vfvT3Z2Nrt27eLQoUOMHDnysrb79+/H09Oz1Q/wLS0tZcWKFZw4cQKAFStW8NBDD8n0ZyHaKClehBBXFBUVxcyZM5k6deplm0E6HA42bNhAWVkZfn5+DBkyhGHDhhESEmJStvU7ceIEK1asqHMrzOFwUFVVddl3EkK0DVK8CCGuqc4O1S5Hjx6lrMzYmbq8vJzt27ezfft24uPjGTZsGL179za1N8bhcLBp0ya2b99eJz5u3DgmTpwovS5CtGFSvAghrku3bt2YOHEi+/btq7OUfnp6Ounp6fj5+TFo0CCGDh1KeHh4i+ZWUFDA8uXLycqq2Snb39+f2bNnEx8f36K5CCGansw2EkLcEKfTyfHjx9m7dy/Hjx+vt82QIUOYMWNGi+Rz6NAhVq9eTVVVlTsWHx/PrFmz2v2aNUK0J7K3kRCi2VgsFhITE0lMTKSwsJB9+/Zx4MCBOjN6IiMjWySXM2fOsHz58jq5TZo0ibFjx7bbNWqE6IikeBFCNJng4GAmTZrExIkTSU9PZ//+/aSnpzNgwIA67bTWLFu2jOjoaAYOHEhgYGCTfH5MTAyDBg0iOTmZkJAQ5syZQ9euXZvk2kKI1qNBxYtSKgb4f8BwYBDgC/TQWmc04FyL69zvAJFAKvB7rfXyeto+DvwI6AFkAH/XWv+7ITkKIVoPi8VCr1696NWrV72Lwp09e5bDhw9z+PBhNmzYQHx8PIMGDaJPnz43vJbM7bffjp+fHxMmTLhsE0ohRPvQ0H8lEoB5wF5gK1D/Dm/1+y/gx8AvXeffB3yklLpTa/35xUauwuVl4E/AemAy8KJSSmmtX2rE5wkhWpFLCxeAAwcOuF9rrUlLSyMtLQ1vb2/69+/PoEGDrrkdQVlZGZs3b2bKlCl1ihQvL68rbkIphGgfGjRgVyll0Vo7Xa8XAa/SgJ4XpVRnIBP4s9b6t7XiG4AIrfVA13sP4CzwhdZ6fq12rwMzgCitte1qnyUDdoVoO6qqqjh8+DDJycmcOnWq3jZhYWEMHDiQQYMGERQUVOdYeno6n3zyCaWlpQwaNIhZs2a1RNpCiBZ0wwN2LxYu12Ea4AUsvSS+FHhdKdVDa30SGANE1NPubeBR4GZg03XmIIRoZby9vRkyZAhDhgyhoKCAgwcPkpycTEFBgbtNXl4emzZtwm63M2nSJADsdjsbNmxgx44d7nbJycmMGjWKqKioFv8eQghzNPeA3X5AFZB2STzF9dwXOOlqB3DoKu2keBGiHQoJCWHChAmMHz+e06dPk5ycTEpKCtXV1QAMHDgQgJycHJYvX8758+fd5/r7+zNr1iwpXIToYJq7eAkFCvXl96byax2v/VxwjXZCiHZKKUX37t3p3r07t912G0eOHCErK4uwsDB2797Nl19+id1ud7e3WCzExcVhtVpxOp2yYq4QHUibniqtlHoCeAKM1T6FEO2Dp6cnAwcOJD4+nvfff59jx465j1ksFpxOJ06nk5SUFFJSUggICKBfv37079+frl27ypouQrRzzV28FADBrhlDtXtfLvak5NdqBxACZF+lXR1a61eAV8AYsNskGQshWoWCggJef/31Ohsqdu7cmaSkJL799lvy82v+WSgtLWXnzp3s3LmT4OBg+vXrR79+/YiMjJRCRoh2qLmLlxTAG4in7riXvq7nw7XagTH2Jfsq7YQQHURwcDCdO3d2Fy+jRo1iypQpeHh4MGHCBLKysvj2229JSUlxbxAJUFhY6N4kcty4ce7BvkKI9qO5i5c1gA14EPhdrfhDwCHXTCOAb4BcV7v1l7TLB+puCyuEaPeUUsyaNYu3336bW2+9lYSEhDrHYmJiiImJYdq0aWRkZHDo0CGOHDlCZWWlu13Pnj0vu25xcTGdOnVqke8ghGgeDS5elFJzXS+HuZ5vU0rlADla6y2uNnZgidZ6IYDW+oJS6m/Az5VSJcA+4F5gEsb6Lbja2ZRSv8ZYlC4Lo4CZBDwGPKO1rr6RLymEaN2cTicHDhxg0KBBWK1WdzwwMJCnnnrqqrd+LBYLPXv2pGfPntxxxx2kp6eTkpJCVlbWZWPhKisref755wkLC6Nv37707duXiIgIubUkRBvTmJ6Xjy55/6LreQsw0fXa6nrU9kugFPg+NdsDzNNar67dSGv9b6WUxtge4CfAaeA/tNYvIoRotwoLC1mxYgWnT5+msLDwsts8jSksrFYrvXv3pnfv3mitLzs3NTUVp9NJTk4OW7ZsYcuWLYSHh5OUlES/fv3o3LmzFDJCtAENWmG3LZAVdoVoW7TWJCcn88UXX7jXdFFKsWjRIqKjo5vlM7dv387mzZvrTLmuLTQ0lKSkJPr06SOzloQw2dVW2JXiRQjR4srLy/nss884fLhmLL5SivHjxzN+/PhmXbOlurqatLQ0Dh8+zLFjx7DZ6t95ZNiwYdx5553NlocQ4upueHsAIYRoKmlpaaxcuZKSkhJ3LDQ0lNmzZxMTE9Psn+/l5eUe72Kz2eoUMhd7gAB69Ohx2bnZ2dmEh4fj6enZ7HkKIa5MihchRIuorq7myy+/ZO/evXXiQ4cOZdq0afXuPt3cPD09SUpKIikpCbvdzokTJzhy5Ajp6el1ZjcBOBwO3nrrLRwOB/Hx8e6xNf7+/i2etxAdnRQvQohml5+fz9KlS+tsvOjn58eMGTNITEw0MbMaHh4eVx3se+rUKfc07KNHj3L06FEAYmNjSUxMJDExkbCwMBknI0QLkOJFCNHsgoKC6vSsJCUlcccdd7TaXov6ChCbzUZ4eDi5ubl14pmZmWRmZrJ+/XpCQ0NJTEykT58+smWJEM1IBuwKIVrE+fPn3QvODRgwoM32UOTl5ZGamkpqaiqZmZnU929ojx49eOSRR0zIToj2Q2YbCSFajNPp5NChQ/UWKDabrV0Ndi0vL+fYsWMcO3aMtLQ098yladOmMXr06Dptd+3aRXV1Nb1795aF8YRoAJltJIRoEbm5uXzyySdkZWVRVVXFiBEj6hxvT4ULGON2Bg8ezODBg7Hb7Zw8eZLU1NTLxvFordmxYwcFBQVs2LCBoKAgevXqRe/evYmLi2t3/12EaG5SvAghbpjT6WTnzp1s3LjRvQDcunXrSEhIICQkxOTsWoaHhwe9evWiV69elx3Ly8urM1i5qKiIPXv2sGfPHqxWK3FxcSQkJJCQkCCDfoVoAClehBA3JC8vj08//ZTMzEx3zGKxMG7cOIKCgkzMrPUIDAxk1qxZHD9+nLS0NKqqqtzHHA4H6enppKens3btWoKDg3nyySfx9vY2MWMhWjcpXoQQ10Vrzc6dO9mwYUOd5fYjIyOZOXMmkZGRJmZXw+nUFFXYqLA5sDs0NqfTeHY4sTs1dvezRqPx8bTi62nFx9OKj6el1msrVsv19Yh4e3szaNAgBg0ahMPhIDMz0z1OJicnp05bT0/PywqXkpISysrK6NKli/TKCIEUL0KI65Cfn8/KlSs5deqUO3axt2XcuHF1doZuLtV2J6fzyziZW05uaRV5pVXkllaTX1ZNXlkVeaXV5JUZ7x3OppmY4OVhFDMhfp6EBXgT6u9FeIAXof5ehPl7ExZgPIf6exEZ5EOIn+dlxcbF20RxcXHceuutFBUVkZaWRlpaGidOnLhscTyAAwcOsHHjRvz9/enZsyfx8fH07NmTwMDAJvleQrQ1MttICNEoJ0+e5L333quzJ1Dnzp2ZNWsWUVFRTf55heXVpOeUkn6hzHjOKSU9p4zT+eVNVpQ0F19PK11DfOka7EtMiG+t137EhPgSEeCNpVZvjsPhwGaz4ePjU+c6S5YsISMj47Lrd+7cmfj4eOLj4+nWrZsM/BXtisw2EkI0mejoaHx9fbHZbCiluPnmm5kwYUKT9LaUVtnZf7qAvaeMx+GzxeSVVV/7xGsI8PYgwNsDD6vC02rBw6LwsFrwtCr3aw+LQimotDmpqHZQaXdQWe2g0l7zvrG/61XYHKRdKCXtQmm9x708LPQI86dHuD89Iy4+B9Az3EKIv7Gon9aaoKAg/Pz8KC8vr3P+hQsXuHDhAt988w1Wq5Vu3bpxyy23EBsbe13/nYRoK6R4EUI0ire3NzNnzmTt2rXMnDmT6Ojo67qO1pozBRXuQmXPqQJSzxXTmM6UrsG+9IzwJ7KTD2EB3oT5exm3bmq9DvX3wtvjxgsrrTVVdifl1Q7yXbej8kqryC2rJr+05lZVbmkVeWXVZBdWUFbtuOo1q+1OUs+XkHq+5LJjIX6e7mKmV+cBDL9rDCGWSkrOn+bEiROcPn0ap9Ppbu9wODh58iSTJk267FoFBQUEBwfLeBnRbshtIyHEFeXl5XH48GHGjRt32TGn04nFYmnU9QrKqtmUeoGNRy+wOyOf88VV1zzHx9NCz/AA4jsHEB/hT3xEAD0j/OkZHoCvV/OPrbleWhsDhc8UVJBVWGE8F1SQVVhOVqHxuqDcdu0LXSLQ24PekYHEh/sR7lmNZ3kuttxTVBRcwNvbm5/+9Kd1/r+Ulpby17/+lcDAQHr27ElcXBw9evSQmWCi1ZPbRkKIRnE6nezYsYNNmzZht9vp3LnzZQuvNaRw0VqTdqGU9UcusOHIefadLrhqz4pFQZ/ITgzrHsLwuBCGxIYQE+JbZ1xIW6GUItjPi2A/L/p3rb9QKKqwcTK3jJO5pZzIKeNEbhkncoz3lTZnveeUVNndvVU1uhHqF0/PAC/+siaVvtGdSIrqRM9wf06ePGmcV1JCcnIyycnJAISEhLgLmbi4OBn8K9oU6XkRQtRx4cIFVq5cSVZWljsWFBTEM88806BxLdV2J7tO5rP+yHk2Hr3A6fzyK7YN8PZgSLdghnUPYVj3EAbHBhPoI4NOnU7N+ZJKTuQYg5SPnS/h2LlSjp4rprjSfu0LuHh5WIgJsOBVfoEgXUqoKifMUo6nurwwCgsLY+DAgYwfP74pv4oQ1016XoQQ1+RwONi2bRtfffVVnbEUkZGRzJgx46qFi9Op2XEij4/3Z7H20DlKqur/AasUDO0WwqQ+nZmYGEGfyE7XvXZKe2axKKKCfIkK8uWmhHB3XGvNhZIqUs+VcOx8ifv52PlSKmyXj6+ptjs5UegEQl0PUGg6WaoIU2XuYibMUk5eXh5FRUWXXSM3Nxdvb2/pmRGtihQvQgiys7P59NNPOX/+vDtmtVqZMGECY8eOvWLhcux8CR/vy+LTA1lkF1XW28bfy8r43hFMTurCLYkRhAXIyrHXSylFl04+dOnkw/jeEe6406k5lV/O4bPFHMku5nB2MYfPFnOu+PL/JxpFkdOHInw4QZg7HqCqSM0M4PSmNPp3DWJA1yBC/b1Yu3YtaWlphIaG0r17d+Li4ujevbuMmRGmkttGQnRgNpuNLVu28PXXX1P734KuXbsyc+ZMIiIiLjsnp6SKlclnWbH/DIeyiuu9bkyIL1OSujA5qTMje4Q2yWwf0Xj5ZdUcyXYVNGeLSTlbzPH/396dx1dZ3nkf//yyQkISAkkIZGNfZRUVNxAUcauOHe3i1haUamvFPsVHbfsoVp2htdrOtOMobUetjtUuKlWpKCqKFhAEQfYQIIQQkkAgZE9OzvX8cQ6QhAQOJOTkJN/365VXcq57u85NSL657mspKgt4RFdaz+5Ele8jkTKSwirpHVZBN/O18PTs2ZPMzEwyMzPJysrSmkzS5k702EjhRaQLW7RoEatWrTr6OiIigmnT1r3seQAAIABJREFUpnHeeec16pBbV+/lvU2F/GV1Hh9n7292crhesVFcO7Yf149PY0x6gn6RdVBVtfVs2XeYDXsPs2lvKRvyD7N1Xxm19c13EG6qh/keOSWFVZIUVkHvsEqirZ6YmBhmzpxJ7969T34SkQCoz4uINOviiy9m/fr11NTUkJWVxVe+8pVGv3yKyqp55bM8/ndlbrPDmqPCw7hsZApfHZ/OlGHJRIaf2tBpaX/do8IZn5nI+Mxjq33XerxkF5WxMf8wX+aX8mV+KZsKDlPrOT7QlLtoyl00ud5eR8virJrkuiriNxxkbAaM6hdPXLdIKioqWLVqFZmZmaSnpxMVFdUu71E6P7W8iHQhzc3Nsm7dOjweDxMmTMDMcM7xee5B/rg8l39sKKCu/vifEef0T+T68elcPbovCTEaHdQZ1dV7yS4s58v8Q75As6eUzQWBtdCYwcCkWDLjoCJvM0lWQVJ4FWmpKWRkZJCZmUlGRob6zcgJ6bGRSBdXVlbGokWLSExM5PLLL292n6raehZ+kc8fl+eyqeD4vixJPaL45rmZ3Hh2Bpm9Y850laUDqvV42VZYdrR15ss9pWzZd7jZgNuU4ehpVUf7ziSFVZKVEMHArAzS09MZMGAAKSkp7fAuJFTosZFIF+WcY82aNbz33nvU1NRgZpx11lmNpvTfe6iK5z7dyaur8pqdQ+TsrERuOz+LK85KVcfbLi4qIoyz0hI4Ky2Bb/rLajz1bN1Xxvo9vjCzPr+UbYVlx/WLchgHXQwH62PIrvcN/w4r8pJYXEXvNZuZ0L+IW66azNA+cURF+FoHPR4PERH6NSXH03eFSCdVXFzM22+/TW5u7tEy5xw5OTn069eP7MIynvloBwu/yMfT5BdNt8gwrhubxq3nZ7U4O6wIQHREOGPSezImvefRsuq6ejbuPcyXew6x3t9Cs72onKbtM17COOBiOVAfy7YceOU3nxAVEcaIvvGMTounIm8LPWoPMKZ/ClkZ6aSlpZGamtomi4BKaNNjI5FOxuPxsGzZMj755JNGk8316tWLa665hv2WwLMf5bBkc9Fxx2b2iuHWSVncODGdnjHqXCltp7zGw0b/46b1e0pZt+cQuQdann25oXDq6RVWRZJVkBxRzYg+sb5Ak+l75JSQoNFtnVGr+7yYWQbwK2A6YMAS4F7n3O6THDcPeLiFzTXOuW4N9t0FZDWz3/XOuTdOVkeFFxHYuXMnb731FiUlJUfLzIxJ55+Pt89IfvdpbpM1cXzO7d+L2ZMHMm14SkiuIyShqbSy7lj/mfxDrN9Typ6DVQEd2zDQ9Otez+wbruDsIWlEaMRbp9Gq8GJmMcA6oAb4KeCAx4AYYIxzruIEx6YD6U2KY4F3gNedc19rsO8uYAswr8n+W51zx/+0bULhRbqy2tpaFi1adHTRvSP6pqUTPnASr3yxn+yi8uOOmz6yD3dOGcTZWYnHbRMJhpKKWr7ML2VDfinr8g6xbncJheWBrb7dLTKMkX3jGZ2WwKDe0ZTlbmT8wFQyM9JJTU1V/5kQ09oOu3cAA4Fhzrnt/hOuB7KB7wJPtXSgc24PsKdJZW71X/eFZg7Z75xbEUCdRKSBiIgI9u/ff+x1VDfCBp3PCzs85G/f1WjfyHDj+vFpzJ48iMEpPdq5piIn1is2iilDk5nSYPmD4rIaNvhbaL7IPcD6PYfYX3n8Wk7VdV7W7D7Emt2H/CWRhH9ZTKLlkhRexcCeEYxO78mEQX3JykgjOTlZ/WdCVCAtL+8D3ZxzFzYp/wjAOTfllC5otgQ4C0h3znkalO8CPnHO3XIq5ztCLS/S1RUWFvL0MwsoSz6L5YfiKGgyqVyP6AhuOi+TmRcOIDWhWwtnEQkNRwLN+j2H+GJ3CZv3VTS7llNzwvDS06pIjqhmQEIEk4al8bUZFxITpZaZjqS1j432AQudc99tUv40cKNz7vjFT1o+VwawC/i1c+5HTbbtAhKBSCAcWAvMD6S/Cyi8SNdRV1fHmjVrOOecc45OOFfjqefPq/fw2/e3UVhW22j/XrFRzLpoALdMyiKhuyaUk86ruKyGDXtL2bCnlNU7iti49zD7qwJb9iDMYGByD87qF8+ofgkkuDL6dfcytH8aSUlJx03uKGdeax8b9QKa63NSgi9snIpbgDCaf2T0JrAK2An0Ae4GXjezW51zLzV3MjObDcwGyMzMPMWqiISe7Oxs/vGPf3DwoO+/5LizJ/LnVXk8vTTnuFWde8dGMXvyQG6ZlEVstP6ilM4vOS6aqcNSmDosBS4dAsCB8ho27D3MF7kH+HxHEZv3lVNcdfwf7V4H24vK2V5Uzhtf7D1aHms7SQqvJis+jBGpcZw9MIXRg9JJSUnRI6cgCqTlpRZ4yjn3QJPyx4AHnHMB/1Q0s81AlXNuQgD7hgMrgFTnXMbJ9lfLi3Rmhw8f5p133mHz5s0A1DtjB6lkRw44rqUlqcex0KJmcJHjlVbWsbGglLW79rNmRxE7D3nYVVIV8Grb0XjoHV5FRg9jSEoMV04azbnDM7W2VxtrbcvLQZpvYWmpRaalSpwLDAfuDWR/51y9mf0F+LmZ9XXOFQR6LZHOwuv1snLlSpYuXUptbS1eBzn1vVlXn0aZNwqqjwWXpB5RfHfyIG6elKnQInICCTGRXDAoiQsGJcGlwwGorPWwuaCMTXt9HYM/27aXvLJ66t3xUwfUEMHe+jj2lsLKUngpeyOR4ZsYkhLHiL7xjOwXj5XmM2FAH4b2TyMmRstptLVAfsJtBEY1Uz4S2HQK1/oWUAe8fArHHNE5ZtITOQV5eXm8/fbbFBYW4hzsrE/kC08/Sl33Rvsl9YjmzikDufm8LLpHqRlb5HTEREVwdlZig2kDxlJX72V7UTlrdhb5HjntPczOUg/V9ccHmrp6x6aCw2wqOMzf1vgLl5USa1+SEllHVs8IhqfGMa5/MhOGZJCc1FsT67VCII+N7gV+CQx1zu3wl/XHN1T6Aefckye9iFkUUIBvNNF1AVXMLAJYCSQ555qbvK4RPTaSzqKyspIlS5awdu1anIM8bwJr69IocY3/eusVG8VdUwZxyySFFpH24pxjz8Eq1uws5vOcfWzZV0Z+ZRj5hwKbXA8gHC+9wqpJ6wFDkmP46rTzGJ4aT2KsZrVuqLWjjWLxTVJXxbFJ6h4F4vBNUlfu3y8LyAF+5pz7WZNzfBX4G/CvzrnXmrnGN4HrgEVAHr4Ou98HLgK+6Zx75WRvUuFFOouPPvqIpUuXsrc+jjV1aRS7xnOxxEVHcMfkgcy8aAA91BFXpEMoraxj877DbC44zOqcQtbn7mdvBdQTeOtKn/hohqXGkxYLPTyljMlKZuLQdFKTu2YrTav6vDjnKsxsGr7lAV7EtzzA+/iWB2g4ZafhG+LcXI+lb+EbnfRWC5fZCaQAT+DrS1MBrAaucM4tPlkdRTqTmIyRvFdfxJ7axi0t3SPD+c6F/Zk9eaDWHRLpYBJiIpk0sDeTBvbmOxcOAPA9diosY/X2vXyxq5itheXkltZT5mm+Y2/h4RoKDxcfK/gyH2MPCWE19ItxDOgVzYi+CYwb0IdxQ9LpERvbHm+tQ9LCjCJBVFFRQX19PfHx8WwvKuOJxVtZvLGw0T5R4WHcPCmT710ymOS46CDVVETaSklFLWt3FLI6p4DdpfXkHvaQXVhOjSewOWkAIqinV0Qtw/smcPHoQQxNjWN4ahwpcdGdppWm1QszhgKFFwklXq+X1atX8+GHH5LQtz853YfztzV7Gg3VDA8zvjYxnR9MG0K/nt1bPpmIhLx6r2PXgQq2FJTx6cadbMo/xO7DHkpqT60/W0L3SHpH1pEUWcugpFhGpScyYVBfhmaG3tpOCi8iHUheXh6LFi1iV8F+1ntS2eJJob7J09ZrxvTlR5cPY0BS120WFhGoqPGwblcRq7cXsCn/IDsOVJFf7qioP7VQE42H5GgPGfHhDEqKZWR6IhMG9WNwekqHDTUKLyIdQFlZGUuWLOHzdRvY6OnDBk8qdTT+ATR5aDL/d8YwzkpLCFItRSQUFB+uYk1OAXvKHduLK9lWWMa2fWWU1XhOfnAD8dHhDOsbz+CUOIak9GBInx70Cq9lWGafoIcahReRIPJ4PKxYsYKlH3/Chqp4vqjrRzWN1xgam9GT+68Y5ps0S0TkNDjnyD9Yyapte1ifW8y2fWXkltZRWGXUuVOb/TeSepKiPPTrEcaA3t0Z1rcnY/onM2ZgGt27tU/fO4UXkSBwzrFt2zYWL36Xz4sdazxplLnGqzkPSo7lvhnDmTGqT6fpZCciHYtzjl3Fh1mdvZcvd+8nu7CMvNI6iqrDqD3FUBOGl8SIOvrGGv17dePySWMZ1ieOYalxbV5vhReRICgsLOSh//pfVtelc8A17rvSN6EbP7xsKF+dkEaE1kMRkSBwzlFQWk12UTnZhWVsLypnfW4xOcUV1LjA+9QMT43jnXsnt3n9Wru2kYicog35pfz8nV0sqx3WqDyheyR3Tx3Mredn0S1Ss+KKSPCYGf16dqdfz+5MGZp8tNw5R35JOWu272Vjnq+lJvdgDfsqocJ7fGwYnNLjuLIzTeFFpA14vV5KSkqosO788t1tvLlub6Pt0RFhzLxoAHdOGURC98gWziIiEnxmRnrvONJ7D+Pa8xr/AXawvJq1OQWszy2ioMJxoDaccwf0avc6KryItNKuXbt4bdF7fFjUjc21vfE0mKwlzOBrEzO497KhpCZ0O8FZREQ6vsQe3Zg2dgDTxg4Iaj0UXkROU0lJCW+98x6vbTrMBk8fPITTcAH0GaP6cN+MYQxOafuObCIiXZnCi8gpqq6u5oOlH/HiP3eytjaVavo12n5O/0QeuHIEZ2clBqmGIiKdm8KLSIC8Xi+rP/+c3y1ew4qKJMpcRqPtg5Ji+PHVI5k2PEXDnkVEziCFF5EA5OTk8OzCj1lSHEuJS2+0rU+PSO67ciTXj08jPEyhRUTkTFN4ETmJNbv2c8/zn7OnLqVReVxUGD+4bCi3nd9fw55FRNqRwotIC3YUl/Pku9t4+8sC4Ngkc1FhMPOiAdw1dYiGPYuIBIHCi0gDtbW1/POLTSzeE86fV+dR32TY81fHpXLflaPoE69hzyIiwaLwIoKvM+4nn63h14s3sa4qkXoaT9l/1ehUfnT5MAYlt/9MkiIi0pjCi3R5G7Zs44k3PmP5oThq6d1o2wWDenP/FcMZm9EzSLUTEZGmFF6ky9qdl88Tr33C+wVRVNJ4TpaBiZHMu34cFw9J1rBnEZEORuFFupz9Bw7wq79+zN93eSlzjR8D9YkxHrj6LK4bn0GYhj2LiHRICi/SZdTX1/PLl9/h1c2VlHhjGm2Lj3TMuWwot100mMjwsBbOICIiHYHCi3QJK3Yc4InFW/k8F+BYcOke7ph1QSbfmz6SmCj9dxARCQX6aS2d2ob8Un6xeCsfbytuVB5pjm9M6MPca8ZprhYRkRCj8CKdjtfrZdGna/mvj3axubzxfCyR4cb1o5OZe9VoUjRXi4hISFJ4kU7DOceHqzbw5OLNbKyIAY6FkzCD68enc+9lQ8joFdPySUREpMNTeJFOYcX6bfz8rXV8cbg7rsFU/gAzRvVh7uXDGNInLki1ExGRtqTwIiFt3bZd/Psbn/NZSRReGreojE4K4+Gvns3EgSktHC0iIqFI4UVC0rbcfB7/22d8UhROPY37rgzrafz0X8Zx8fB+QaqdiIicSQGFFzPLAH4FTAcMWALc65zbHcCxroVN451zXzTYLwy4H/gukApsBX7mnPtbIHWUruFQZS3PfpTD7z/Ops5FNdrWP87x42tGc/nYrCDVTkRE2sNJw4uZxQAfADXAtwAHPAZ8aGZjnHMVAVzneeDZJmXbmrx+FJgL/AT4HPgG8Bczu8Y5tyiAa0gnVlpZx+8/2cFzn+6ivMYDhB/dlhbj5b4rRnDdOYM0lb+ISBcQSMvLHcBAYJhzbjuAma0HsvG1kjwVwDnynXMrWtpoZin4gst859wv/cUfmtlgYD6g8NJF7d63n98s/pJ3dtRSVuNptC21u2POtIF846IRCi0iIl1IIOHlWmDFkeAC4JzbaWafAtcRWHg5mRlAFPBSk/KXgP8xswHOuZ1tcB0JEflFJfzbX5fz3m4PtU2+TQen9GDOpUO4enRfrT8kItIFBRJeRgELmynfCNwY4HXuMrP7gHpgBfCwc25Zk2vUANubHLfR/3kkoPDSBRTsP8i//205i3fWUUMEDb9FBybHMufSIVwzph/hCi0iIl1WIOGlF3CwmfISIDGA418C3gL2AlnAfcAHZjbdObe0wTUOOeeadu4tabD9OGY2G5gNkJmZGUBVpKPaU1TC/L+t4N3cOn9Ly7FvzV6RHu68KJNZ08cptIiIyJkfKu2cu7XBy2VmthDYgK/T70WtPPcCYAHAxIkTWxrVJB1YXuEB/u1vK1iyu546wmn4LZkY6WH2BRncPn0skRHhLZ9ERES6lEDCy0Gab2FpqUXmhJxzZWb2NjCryTV6mpk1aX050uJSgnQqJRW1/NeSzfxxea4/tBwLJ4kRHmZO6sedV0xQaBERkeMEEl424uuT0tRIYFMrrt0wpGwEooFBNO73MtL/uTXXkQ5kf3kNv1u2gxeX51JZW0/D0NIr0sPt56dzx+XjFFpERKRFgYSXvwO/NLOBzrkdAGbWH7gQeOBUL2hm8cA1wGcNit8B6oCbgUcalN8CbNBIo9C3JbeA3y3bydtbS6mu8zbalhTlYfaFGcy8bBwR4WFBqqGIiISKQMLL74C7gYVm9lN8LSaPAnk0mHjOzLKAHHyz4v7MXzYXGAZ8yLEOu3PxzaB785FjnXNFZvYU8KCZlQFrgK8D0/AN1ZYQtWbbbn7x5lo+Kw7DS+NgMjw1jh9MG8IVo/oQrtAiIiIBOml4cc5VmNk0fMsDvIhveYD38S0PUN5gV8P3DKDhb6GtwPX+jwTgMPApMMs517DlBXwz65YDczi2PMDXnHNvncb7kiBbtn47T/5jA+sORuCafJuN7BvPPZcO4fKRfTRPi4iInDI7fnRyaJo4caJbvXp1sKvR5b2zajP/8e4WNpdFHbcto7uHH1w6hBsv1Iy4IiJyYmb2uXNuYnPbtKq0tJrX6+W1Tzbw9NIcdlRG4Zss+ZjBcR7mXDaMa84dptAiIiKtpvAip83rdby7aR9PLvqS7JI6moaWUT3rmXvlWUwdOzA4FRQRkU5J4UVOWY2nntfX5LPg4x3s2N94UXHDMSHJcd8145g0PCNINRQRkc5M4UUCVnyojCffWMmSPC/7K+oabYsIg0l94P5rJzJ6QGqQaigiIl2Bwouc1I69+/nFwlV8kFtHLY0nj4uLjuCW87P4zoX9SYnrFqQaiohIV6LwIi1asWkXv37nS1YVQT1hNJwNNyk2kjsmD+Km8zKJ6xYZvEqKiEiXo/AijXi9Xl7/50aeXZrDtvJIaDKxXK+IOm6akML3rj6HmGiFFhERaX8KLwJAraeeZ97+jP/9fB+FtVFA42CS1q2WWRdk8q1Lx2s2XBERCSqFly7ucHUdr36Wx/98upOC0moaD3d2jEqo53vThnGV5mgREZEOQuGli8opLOXlVfm8uiqP8hpPo23heLmgbxg/uno84wanBamGIiIizVN46UK8Xi9vrtjMgo+y2VQagaNxS0rv2Cguy4pkztXj6dc7IUi1FBEROTGFly6gorqWBf9YzStrC5vtzzIoOZY7Lh7Iv4xPo1tkePMnERER6SAUXjqx3MISfvX31by7o4pKF0HT6ftHJsJ9/3IOU4Yka3VnEREJGQovndD7a7N59oMtrC4GL2E0/GcOx8ukVOOeK8Zw3vDM4FVSRETkNCm8dBK1Hi+Lvizgv9/fxNb9tTSdn6VHWB1XDe3BvV85l36944NTSRERkTag8BLi9pVW8/LKXF7+LI/95TXHbU/rVstNE/sx6/IJdIvSpHIiIi2prq6muLiY6upqPB7PyQ+Q0xIZGUlKSgrx8af/h7TCSwjyer28tXIzv/94OxsPRVDvGm+PMBjX28vsqcO4/OyhwamkiEgIKS0tpbCwkOTkZFJTU4mIiNDcVmeAc46qqiry8/MBTjvAKLyEkAOHK3jmH5/zxoYDFNdF0fSfLzW+G7dMyuTr52SSHBcdnEqKiISg/fv3k56eTkxMTLCr0qmZGTExMaSlpbF3716Fl85s2Zc7eGbJJj4r9FJHOE1HDZ3bvyffuXAg00f2IUJT94uInLLa2lq6d+8e7Gp0Gd27d6euru60j1d46aDKKqv5/eI1/PWLQvJrogCj4arOEdRzXmoY359+FheM6h+saoqIdBp6TNR+WnuvFV46mB3F5bzw6Q5eWbmTmmbmZukdWcu1I3tx1xUTSEmMC04lRUREgkjhpQOorqtn8cZ9/Omz3azYUeIvPfZPE4aXsb0c37l4MNecN5ywMD0aEhGRrkvhJYiWb9rFgvc38lmRUVHnjtueEF7HlUPj+N6VE8hMSQxCDUVEpCvq378/l1xyCc8//3ywq9IshZd2drCskt8tXsPCDcXkVx95JHQsuIQZTBveh5vPy2DykGTC1QFXRETa2euvv96qeVjONIWXduD1evngixye+2hriyOGUntEcMsFA7nh7AxSE7oFp6IiIiLA+PHjg12FE9Kf9WfQrn0l/OSPH3Duwwu5/c/b+LTQ/MHFJwwvYxI9/OKqDD59cDp3Txui4CIiIm1i3rx5mBlbtmxhxowZxMbGkpmZyXPPPQfAiy++yPDhw+nRowdTp04lJyfn6LH9+/fn29/+9tHXzz//PGbGihUruPnmm4mPj6dfv37cc889VFdXt/dbU8tLW6v1ePlwaxF/Wb2H9zfvw2E0bWXpFVHHlUPjufOK8WSoL4uIiJxBN954I3fccQdz587l6aefZubMmWRnZ7N06VLmz59PXV0dc+bM4aabbmLlypUnPNett97KN7/5TV577TWWL1/OvHnzSExM5JFHHmmnd+Oj8NJG1u8+wML1hbyxNp8DFbX+0mPj2COoZ3yScdtFg7n63GEaMSQiEgL6P/B2sKtw1K75V5/Wcffddx+33XYbABMnTuTNN9/k2WefZefOnUf7tRQUFDBnzhxyc3PJyspq8Vw33XTT0aBy2WWXsXLlSv70pz91zPBiZhnAr4Dp+H4jLwHudc7tPslxE4HZwGQgE9gPLAN+6pzb2WTfXUBzd+x659wbgdSzve0uOsjv3/uCd7ceYl9tVLP7ZHav4ytnJTNz+jh6x8e2cw1FRKSru/LKK49+nZiYSEpKCuPHj2/UIXf48OEA5OXlnTC8XH114wA1evRolixZ0sY1PrmThhcziwE+AGqAb+EbGvMY8KGZjXHOVZzg8G8Ao4D/BDYCacD/A1ab2TjnXF6T/RcD85qUbQ3gfbSbsspqXvxgHQvXFbCtLKLZx0Kp8d3417PTuOHsDAYkKbCIiEjwJCY27p4QFRXVbBlw0v4rvXr1avQ6OjqampqaNqjlqQmk5eUOYCAwzDm3HcDM1gPZwHeBp05w7M+dc8UNC8zsU2Cn/7wPNdl/v3NuRYB1bzf19V7e+mwLf1qew5oiRy3hQGSjfcLxcn5mLHdcNpqLBicRHqZppkVEQt3pPqqRMyuQ8HItsOJIcAFwzu30h5DrOEF4aRpc/GW5ZlaMrxWmQ8spLuc3b67k/e1llHkjaW5wVka3Wq4alcR3Lh1Laq+OOyZeRESkswgkvIwCFjZTvhG48VQvaGYjgBRgczObv2JmlfhWIFwLzA9Wf5f8Q1Vc+uRH/leNW1l6htcxdUAsMy89i9ED+rZ/5URERLqwQMJLL+BgM+UlwCmN8zWzCOAZoBj4Q5PNbwKr8D1S6gPcDbxuZrc6515q4Xyz8XUIJjMz81SqclJpPbszIbMna3YfAiDaPJybGsFNFwxixtlDNVpIREQkSMy549fUabSDWS3wlHPugSbljwEPOOcCHm5tZs8As4CrnXPvnmTfcGAFkOqcyzjZuSdOnOhWr14daFUC8uqq3by/uYgL+0Vw48WjiImOPPlBIiIScjZv3syIESOCXY0u5WT33Mw+d85NbG5bIMHjIM23sLTUItNSJebjayX51smCC4Bzrt7M/gL83Mz6OucKAr1WW/n6OZl8/Zy2bdERERGR1gkkvGzE1++lqZHApkAuYmY/Ae4HfuCcezHw6h114uYhERER6TIC6bjxd2CSmQ08UmBm/YEL/dtOyMzuwTcvzE+cc78NtGL+/jFfB3Y75/YFepyIiIh0boGEl98Bu4CFZnadmV2Lb/RRHvDskZ3MLMvMPGb2UIOybwC/Bt4BPjCzSQ0+RjbY75tm9oqZ3WZmU/3HfQhMwNdiIyIiIgIE8NjIOVdhZtPwLQ/wIr7lAd7HtzxAeYNdDd8Q54aB6Ap/+RX+j4Y+Ai7xf70T3/DpJ/D1pakAVgNXOOcWn9pbEhERkc4soJFC/jWM/vUk++yi4UqEvrJvA98O4PwrgGmB1EVERES6Nk1WIiIiIiFF4UVERERCisKLiIiIhBSFFxEREQkpCi8iIiISUhReREREJKQovIiIiEhIUXgRERHphObNm4eZsWXLFmbMmEFsbCyZmZk899xzALz44osMHz6cHj16MHXqVHJyco4e+8orrzBt2jSSk5Pp0aMH48eP54UXXmh0/j/84Q+YGW+88cbRsvr6eqZMmcKgQYM4fPjwGXtvAU1SJyIiIqHpxhtv5I477mDu3Lk8/fTTzJw5k+zsbJYuXcr8+fOpq6tjzpw53HTTTaxcuRKAHTt2cMMNN/DAAw8QFhbGxx9/zO23305VVRV33nknALNmzWLx4sXcfvvtnHPOOaSlpfHoo4/yz3/+k08++YT4+Pgz9p4UXkRERFoyLyHYNThmXulpHXbfffdx2223ATBx4kTefPNNnn32WXbu3HnJqB7CAAALvUlEQVQ0YBQUFDBnzhxyc3PJysrixz/+8dHjvV4vl1xyCQUFBfz3f//30fACsGDBAsaOHcutt97Kww8/zGOPPcajjz7Keeed14o3enIKLyIiIp3YlVdeefTrxMREUlJSGD9+fKOWkeHDhwOQl5dHVlYW2dnZPPTQQ3z88cfs27cPr9cLQHR0dKNz9+zZk5dffpkpU6YwY8YMJk+ezP33n/n1lNXnRUREpBNLTExs9DoqKqrZMoDq6mrKy8uZPn0669atY/78+SxbtoxVq1Yxc+ZMampqjjv/pEmTGDZsGDU1Ndxzzz2EhZ35aKGWFxERkZac5qOaULZ8+XJyc3NZtmwZF1100dFyj8fT7P6PPPII2dnZjBkzhh/+8IdMnTqVhIQz+7hNLS8iIiJyVGVlJQCRkZFHyw4ePMjChQuP23fZsmU8/vjjPP7447z55pscOnSIu+6664zXUeFFREREjrrggguIj4/n+9//Pm+//TZ//vOfmTJlCklJSY32O3jwIDfffDOXXnopc+fOJTMzkwULFvCnP/3puGHVbU3hRURERI5KTk7m9ddfp76+nhtuuIEHH3yQ22+/nVtuuaXRfrNnz6aqqooXXngBMwN8w7JnzZrF3Xffzfbt289YHc05d8ZO3p4mTpzoVq9eHexqiIhICNq8eTMjRowIdjW6lJPdczP73Dk3sbltankRERGRkKLwIiIiIiFF4UVERERCisKLiIiIhBSFFxEREQkpCi8iIiJAZxl9Gwpae68VXkREpMuLioqiqqoq2NXoMqqqqhrN4HuqFF5ERKTLS0pKYs+ePZSUlFBXV6dWmDPEOUdlZSX5+fmkpKSc9nm0MKOIiHR5CQkJREdHU1xczIEDB1pchFBaLzIykj59+hAfH3/a51B4ERERAbp160ZGRkawqyEBCOixkZllmNlfzazUzA6b2Wtmlhngsd3M7AkzKzCzKjNbbmaTm9kvzMweNLNdZlZtZuvM7F9P9Q2JiIhI53bS8GJmMcAHwHDgW8CtwBDgQzOLDeAafwDuAB4CrgEKgMVmNq7Jfo8C84DfAlcCK4C/mNlVAb0TERER6RICeWx0BzAQGOac2w5gZuuBbOC7wFMtHWhmY4GbgJnOuef8ZR8BG4GfAdf6y1KAucB859wv/Yd/aGaDgfnAolN/ayIiItIZBfLY6FpgxZHgAuCc2wl8ClwXwLF1wKsNjvUArwAzzCzaXzwDiAJeanL8S8BoMxsQQD1FRESkCwgkvIwCNjRTvhEYGcCxO51zlc0cGwUMbrBfDbC9mf0I4DoiIiLSRQQSXnoBB5spLwESW3Hske1HPh9yxw+sb7qfiIiIdHEhPVTazGYDs/0vy81sazDr08EkAfuDXYkuRPe7/ehetx/d6/al+91YVksbAgkvB2m+haWlVpWmxzZ38SMtKSUN9utpZtak9aXpfo045xYAC05Shy7JzFY75yYGux5dhe53+9G9bj+61+1L9ztwgTw22oivT0pTI4FNARw7wD/cuumxtRzr47IRiAYGNbMfAVxHREREuohAwsvfgUlmNvBIgZn1By70bzuRN4FI4MYGx0YAXwfedc7V+IvfwTcq6eYmx98CbPCPbhIREREJ6LHR74C7gYVm9lPA4ZtQLg949shOZpYF5AA/c879DMA5t9bMXgV+bWaRwE7gLmAADYKKc67IzJ4CHjSzMmANvoAzDf9cMHLK9Ditfel+tx/d6/aje92+dL8DZIGsnOlfCuBXwHTAgPeBe51zuxrs0x9fOHnEOTevQXl34HF8k9X1BNYB9zvnlja5RjjwIL5J8VKBrfiC0F9P872JiIhIJxRQeBERERHpKAJamFE6jtYskuk/foSZ/cXM9vsXytxqZnPOZJ1DVSsXJM00sxfMbLf/Pm8zs8cCXA+syzGzdDP7jX/h1kozc/7W3ECO1aKup+B077WZDTWz/zCz9WZW7l9s9+/+ZWCkBa353m5ynm/4j93T9rUMPQovIaS1i2Sa2URgJb6RXbcDVwFPAuFnqs6hqjX32r99CTAZ+H/47vPvgR8B/3MGqx3KBgNfwzdtwrJTPFaLup6a073XlwNTgReArwDfA5KBFWZ2dltXshNpzfc2AGbWE/g1sK8N6xXanHP6CJEPYA5QDwxuUDYA8AD/5yTHhuEbcv56sN9HKHy08l5fjq9j++VNyuf7j48J9vvraB9AWIOvb/ffv/4BHJeCb2mRR5qUvw+sD/b76ogfrbjXSfi7GjQoS8D3S/mPwX5fHfXjdO93k3MsABYDzwN7gv2eOsKHWl5CS2sWybwEGMEJVgGXRlpzr6P8nw83KT+EL0RaW1Wys3DOeU/zUC3qeopO91475/Y7/2/SBmWlwDYgrS3q1hm14nsbADO7EN+0Id9vmxp1DgovoaU1i2Re5P/czcxWmFmdmRWZ2X/6R4RJY62510uAbODnZjbSzHqY2TR8rTnPOOcq2raqXZoWdQ0iM+sFnAVsDnZdOiP/FCMLgCca/iElCi+hpjWLZPbzf34VeBffsPdf4GvGfLmtKtiJnPa9ds5V4wuLYfh+iZbhe4zxFr45k6TtaFHX4PoNvpbEXwe7Ip3U/fj6KP57sCvS0YT0woxySo4E1Zeccw/5v17qn19nvpmNcM7pr6c2YGbd8IXEFHwdfXcD5wIP4evzclfwaifSNszsQXzzd81Sq0DbM7PBwE+A6/1/EEkDCi+hpTWLZB7wf36vSfm7+DqSjkdNvw215l7PwtfHaLBzLsdf9rGZlQILzOwZ59y6Nqtp13Zai7pK65jZncC/AT91zmkE3Znxn/hGPK7wjzYCX/8u87+ucc5VBa12QabwElpau0jmibSqU1kn1Jp7PRo42CC4HPGZ//MIfDNNS+s1XNS14V//WtT1DDGzW4GngSedc48Huz6d2Eggi+b/WDoI/Adwb7vWqANRn5fQ0ppFMv+Br2PjjCblV/g/r26bKnYarbnX+4BEf7NvQ+f5P+e3UR1Fi7q2KzO7HngO+L1zbm6w69PJfQPfvDoNPxYD+/1f/zZ4VQs+LQ8QQvyTn60DqoCGi2TGAWOcc+X+/Y5bJNNf/jC+SdN+ga85ciLwMPCqc+7b7fdOOr7W3Gt/yFmPL8Q8jq/Py0R8934bcG5rh092RmZ2g//LS4E78U2CVgwUO+c+8u/jAV5wzs1qcNx8fH+B/phji7p+F7jWOfdW+72D0HE699rMJuN7zLwR+AGNW2trnHNr26n6Ied0v7ebOc/zwGXOufQzW+OOT4+NQohzrsI/5PZXwIs0XiSzvMGuhm/W3KYtaz/DN/Lle8BcoAB4At8vZWmgNffaObfLzCbhm/X1MXyTe+XhG/L4uIJLi/7S5PXT/s8f4etDBL573XRG6J8A5fiGoh9Z1PVrCi4ndDr3ehq+R3QT8M131FAu0L9Na9i5nO73trRALS8iIiISUtTnRUREREKKwouIiIiEFIUXERERCSkKLyIiIhJSFF5EREQkpCi8iIiISEhReBEREZGQovAiIiIiIUXhRUREREKKwouIiIiEFIUXERERCSkKLyIiIhJStKq0iHR4ZnY2cAvg8K1efDvwXaAnkAY87JzLCVoFRaRdKbyISIdmZkOAbwP3OOecmT0PrPCXGbAMWAs8GaQqikg7U3gRkY7uh8B9zjnnfx0LHHTO/dPMMoCngOeDVTkRaX927OeBiEjHY2ZZzrncBq/zgeedcz8JYrVEJIjUYVdEOrQmwWUE0A/4MHg1EpFgU3gRkVByKVAL/PNIgZkNDF51RCQYFF5EpMMys+5m9gszG+0vmg6sd85V+reHAXODVkERCQp12BWRjuwqfOFkjZnVAQOB0gbbfwK8GIyKiUjwqMOuiHRYZpYE/AI44C+aBzwNVON7fPR359x7wamdiASLwouIiIiEFPV5ERERkZCi8CIiIiIhReFFREREQorCi4iIiIQUhRcREREJKQovIiIiElIUXkRERCSkKLyIiIhISFF4ERERkZCi8CIiIiIh5f8Djp4Tmhrg8UwAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<Figure size 648x432 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(9,6))\n", | |
"xi = np.linspace(0.5, 1.5)\n", | |
"\n", | |
"plt.plot(xi, f1(xi), '--', c='gray')\n", | |
"plt.plot(xi, f2(xi), '--', c='gray')\n", | |
"plt.plot(xi, hblanket(xi, 5, setting='min'), label='min')\n", | |
"plt.plot(xi, hblanket(xi, 5, setting='max'), label='max')\n", | |
"\n", | |
"plt.ylim(0, 2.0)\n", | |
"plt.legend()\n", | |
"plt.xlabel(r'$x$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Some Tricks\n", | |
"\n", | |
"The switching function example works over the infinite domain $x \\in (-infty, \\infty)$. The blanket function example doesn't care about the domain.\n", | |
"\n", | |
"If we want to work with a semi-infinite domain $t \\in [0, \\infty)$, we can map the switching function $s(x)$ to $s(t)$ using something like $x = \\log t$. It might be better to define a linear map via $t = a \\exp(-b x)$, where $a$ and $b$ can perhaps be adjusted (or regressed)." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Links\n", | |
"\n", | |
"1. [Original Example in Gnuplot](https://www.j-raedler.de/2010/10/smooth-transition-between-functions-with-tanh/)\n", | |
"2. [StackExchange Discussion](https://math.stackexchange.com/questions/45321/smooth-transition-between-two-lines-2d)\n", | |
"3. [Maximum of Two Functions](https://math.stackexchange.com/questions/2931665/smooth-transition-between-any-two-functions)\n", | |
"4. [Smooth step function](https://math.stackexchange.com/questions/3877887/smooth-transition-function-with-fixed-start-end-points)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.9" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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