{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# STAT540: Computing in Statistics\n", "# Python Lecture 3: Defining Functions, Plotting with Matplotlib, and Conditional Programming\"\n", "\n", "---\n", "\n", "\n", "## Outline\n", "\n", "1. Making plots with Matplotlib\n", "2. Defining new functions\n", "3. Conditional programming (`if` / `elif` / `else`)\n", "4. Putting it together: piecewise functions\n", "5. Practice\n", "\n", "## Making Plots: Getting Started\n", "\n", "To make plots, we import **matplotlib** --- the most widely used Python plotting library ([matplotlib.org](https://matplotlib.org))." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "x=np.linspace(0,4, 5)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0., 1., 2., 3., 4.])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "x = np.linspace(0, 2*np.pi, 361)\n", "sinx = np.sin(x)\n", "plt.plot(x, sinx)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- `plt.plot(x, y)` draws a line plot\n", "- `plt.show()` displays the figure" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sinx = np.sin(x)\n", "cosx = np.cos(x)\n", "plt.plot(x, sinx)\n", "plt.plot(x, cosx)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding Features and a Legend" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = np.random.random(30) * 2*np.pi\n", "v = 0.8*np.sin(u) + 0.2*np.cos(u) + np.random.normal(0, 1/3, u.size)\n", "\n", "x = np.linspace(0, 2*np.pi, 361)\n", "fx = 0.8*np.sin(x) + 0.2*np.cos(x)\n", "\n", "plt.figure() # start a new, empty figure\n", "plt.plot(u, v, 'bo', label='observations')\n", "plt.plot(x, fx, label='true function')\n", "plt.xlabel(\"x\"); plt.ylabel(\"response\")\n", "plt.title(\"Demo plot\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "A `label=` on each plotted feature builds the legend automatically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Figure/Axes Approach\n", "\n", "The more flexible --- and more common in tutorials --- way to build a plot: set up a **figure** and a set of **axes** first, then add to the axes." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 5))\n", "ax.plot(u, v, 'bo', label='Observations')\n", "ax.plot(x, fx, label='True function', linestyle=\"--\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"Response\")\n", "ax.set_title(\"Demo plot\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi-Panel Figures\n", "\n", "Setting up the figure first lets us build figures with several panels (each panel is an **axes**):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n", "\n", "ax1.plot(u, v, 'bo', label='observations')\n", "ax1.set_title(\"Demo plot\"); ax1.legend()\n", "\n", "ax2.plot(x, fx, 'g', label='true function')\n", "ax2.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A \"mosaic\" arrangement (`plt.subplot_mosaic`) allows even more flexible panel layouts, with panels referenced by name instead of position.\n", "\n", "## Outline\n", "\n", "1. Making plots with Matplotlib\n", "2. **Defining new functions**\n", "3. Conditional programming (`if` / `elif` / `else`)\n", "4. Putting it together: piecewise functions\n", "5. Practice\n", "\n", "## Defining a Simple Function\n", "\n", "A one-liner function:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8414709848078965" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def f(x): return x * np.sin(x)\n", "\n", "f(1) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Key rule: A Python function must return a value explicitly. If you do not write a return statement, Python automatically returns a special value called None." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def print_lyrics():\n", " print(\"I'm a lumberjack, and I'm okay.\")\n", " print(\"I sleep all night and I work all day.\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I'm a lumberjack, and I'm okay.\n", "I sleep all night and I work all day.\n" ] } ], "source": [ "print_lyrics()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining a Python Function\n", "With more than one line, we **indent** the body --- no curly braces as in R. The function ends when the indentation stops." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def hyp(a, b):\n", " csq = a**2 + b**2\n", " c = np.sqrt(csq)\n", " return c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Returning Multiple Values\n", "\n", "List every object to return, separated by commas:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def eucl(r, th):\n", " x = r * np.cos(th)\n", " y = r * np.sin(th)\n", " return x, y\n", "\n", "x, y = eucl(2, np.pi/3)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0000000000000002\n", "1.7320508075688772\n" ] } ], "source": [ "print(x)\n", "print(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python automatically packages multiple return values into a tuple, which we can unpack on the left-hand side --- just as we did with multiple assignment earlier." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Default Argument Values\n", "\n", "Default values work just as they do in R:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def logistic(x, a=0, b=1):\n", " l = a + x*b\n", " val = np.exp(l) / (1 + np.exp(l))\n", " return val\n", "\n", "x = np.linspace(-4, 4, 200)\n", "fx1 = logistic(x) # uses defaults a=0, b=1\n", "fx2 = logistic(x, a=-2, b=3) # override the defaults" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Arguments can be supplied positionally or by name (`a=-2`); naming them makes calls more readable.\n", "\n", "## Outline\n", "\n", "1. Making plots with Matplotlib\n", "2. Defining new functions\n", "3. **Conditional programming (`if` / `elif` / `else`)**\n", "4. Putting it together: piecewise functions\n", "5. Practice\n", "\n", "## `if` / `else`\n", "\n", "The logic of conditional programming is the same in every language --- only the syntax changes." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "#| echo: true\n", "#| eval: true\n", "def rolldice():\n", " r1 = np.random.choice(np.arange(1, 7), 1)\n", " r2 = np.random.choice(np.arange(1, 7), 1)\n", "\n", " if r1 == r2:\n", " print(\"Doubles!\")\n", " else:\n", " print(\"No match.\")\n", "\n", " print(r1, r2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as with functions and loops, the body of an `if`/`else` block is defined by **indentation**, not braces.\n", "\n", "## `elif`: \"Else If\"\n", "\n", "Python spells \"else if\" as a single word, `elif`:\n", "\\small" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def rolldice():\n", " r1 = np.random.choice(np.arange(1, 7), 1)\n", " r2 = np.random.choice(np.arange(1, 7), 1)\n", "\n", " if r1 == r2:\n", " if r1 == 1:\n", " print(\"Snake-eyes!\")\n", " elif r1 == 6:\n", " print(\"Can't beat it!\")\n", " else:\n", " print(\"Doubles!\")\n", " elif (r1 + r2) <= 7:\n", " print(\"Sad rollin'.\")\n", " else:\n", " print(\"Mighty fine!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conditions can be **nested** just like in R.\n", "\n", "## Booleans as Numbers\n", "\n", "The function `bool()` coerces its argument to `True`/`False`:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "bool(1) # True\n", "bool(0) # False" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as in R, a logical value coerces to $0$ or $1$ in arithmetic. This lets us write **piecewise-defined functions** compactly, without an explicit `if` statement, using indicator-style expressions.\n", "\n", "## Outline\n", "\n", "1. Making plots with Matplotlib\n", "2. Defining new functions\n", "3. Conditional programming (`if` / `elif` / `else`)\n", "4. **Putting it together: piecewise functions**\n", "5. Practice\n", "\n", "## Example: Soft-Thresholding\n", "\n", "$$\n", "S(x, \\lambda) = \\begin{cases}\n", "x + \\lambda, & x < -\\lambda \\\\\n", "0, & -\\lambda \\le x \\le \\lambda \\\\\n", "x - \\lambda, & \\lambda < x\n", "\\end{cases}\n", "\\quad (\\lambda > 0)\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def softthresh(x, lam):\n", " return (x + lam)*(x < -lam) + (x - lam)*(x > lam)\n", "\n", "x = np.linspace(-2, 2, 200)\n", "fx = softthresh(x, lam=1)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(x, fx)\n", "ax.axhline(0, linestyle=\"--\", linewidth=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The boolean expressions `(x < -lam)` etc. act as $0/1$ indicators.\n", "\n", "## Result" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| echo: false\n", "#| eval: true\n", "def softthresh(x, lam):\n", " return (x + lam)*(x < -lam) + (x - lam)*(x > lam)\n", "\n", "x = np.linspace(-2, 2, 200)\n", "fx = softthresh(x, lam=1)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 4))\n", "ax.plot(x, fx)\n", "ax.axhline(0, linestyle=\"--\", linewidth=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: A Bivariate Density Surface" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def bivn(z1, z2, rho=0):\n", " r = 1 - rho**2\n", " a = 1 / (2*np.pi*np.sqrt(r))\n", " b = (z1**2 - 2*rho*z1*z2 + z2**2) / r\n", " return a * np.exp(-b/2)\n", "\n", "gs = 50\n", "z = np.linspace(-3, 3, gs)\n", "X, Y = np.meshgrid(z, z) # build a 2-d grid from 1-d grids\n", "Z = bivn(X, Y, rho=-0.5) # evaluate the function on the grid\n", "\n", "fig = plt.figure(figsize=(8, 8))\n", "ax = fig.add_subplot(projection='3d')\n", "ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Result " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "fig-height": 2, "fig-width": 6.4 }, "outputs": [], "source": [ "def bivn(z1, z2, rho=0):\n", " r = 1 - rho**2\n", " a = 1 / (2*np.pi*np.sqrt(r))\n", " b = (z1**2 - 2*rho*z1*z2 + z2**2) / r\n", " return a * np.exp(-b/2)\n", "\n", "gs = 50\n", "z = np.linspace(-3, 3, gs)\n", "X, Y = np.meshgrid(z, z) # build a 2-d grid from 1-d grids\n", "Z = bivn(X, Y, rho=-0.5) # evaluate the function on the grid\n", "\n", "fig = plt.figure(figsize=(8, 8))\n", "ax = fig.add_subplot(projection='3d')\n", "ax.plot_surface(X, Y, Z, cmap=plt.cm.YlGnBu_r)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outline\n", "\n", "1. Making plots with Matplotlib\n", "2. Defining new functions\n", "3. Conditional programming (`if` / `elif` / `else`)\n", "4. Putting it together: piecewise functions\n", "5. **Practice**\n", "\n", "## Practice: Write a function for Bootstrap Median\n", "\\scriptsize" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'estimate': 29.6,\n", " 'ci_lower': 29.4,\n", " 'ci_upper': 29.8,\n", " 'boot_dist': array([29.5, 29.9, 29.7, ..., 29.8, 29.5, 29.5])}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def bootstrap_ci(x, n_boot=2000, seed=42, alpha=0.05):\n", " rng = np.random.default_rng(seed) \n", " x = np.asarray(x, dtype=float)\n", " n = x.size\n", " obs_median = float(np.median(x))\n", " boot_meds = np.empty(n_boot) # pre-allocate storage\n", "\n", " for b in range(n_boot):\n", " idx = rng.integers(0, n, size=n) # 0-based, high exclusive\n", " x_star = x[idx]\n", " boot_meds[b] = np.median(x_star)\n", "\n", " lo, hi = np.quantile(boot_meds, [alpha/2, 1 - alpha/2])\n", " return {\"estimate\": obs_median, \"ci_lower\": float(lo),\n", " \"ci_upper\": float(hi), \"boot_dist\": boot_meds}\n", "bmi = np.round(np.random.default_rng(1).gamma(30.0, 1.0, size=5000), 1)\n", "res = bootstrap_ci(bmi, n_boot=2000, seed=42)\n", "res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Practice: Read Code\n", "\n", "Predict the output of the following code before running it.\n", "\\small" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUoAAAE6CAYAAABwCxvEAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8ekN5oAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA46UlEQVR4nO2dB3RVVfbGN+mkAan03hKa9I6AgIDYO/be0dHRmfnPOOOMTnWKIvZesVcEBAVpAaQJSBJaaKGkQnpP/uvbLzcEBR5J3nv33ve+31qslYS89849Z58v99zznb2b1dTU1AghhJBT4nfq/yKEEAIolIQQ4gQKJSGEOIFCSQghTqBQEkKIEyiUhBDiBAolIYQ4gUJJCCFOoFASQogTKJSEEOIECiUhhDiBQkkIIU6gUBJCiBMolIQQ4gQKJSGEOIFCSQghTqBQEkKIEyiUhBDiBAolIYQ4gUJJCCFOoFASy1BUVimj/7FExvxziX5NiFWgUBLLsDOzUA4eK5H0oyWyK7PQ7OYQUgeFkliG5EP5x78+fPxrQsyGQkksw4KfDtf7+oipbSGkPhRKYgmOFZfL6t05dd8n7cqWvOIKU9tEiAGFkliCxckZUlldI71bR0iv+Aj9enFKhtnNIkShUBJLsLB2qT21b2v95/jZ8aU4IWZCoSSmU1BaISt2ZuvX0/u10X9g+c5sKaRNiFgACiUxnSWpmVJeVS1dY8OkR1y49IwPl64xYVJeWa3/R4jZUCiJZZbd0/q2lmbNmuk/Lr+JlaBQElMpLq+Updsdd43T+jqW3PW/XpqaJSXlVaa1jxBAoSSmsmx7lpRWVEv7Vs2lT9vIup/3bRepPyupqJJlO7j8JuZCoSSmsuBny24DXX73cSy/aT4nZkOhJKZRVllVt1kzrXanuz7Gz5akZOrvEmIWFEpiGitr7T+tI0PkrPYtf/H/Azu0lPjIYCkoq5RVuxz2IULMgEJJTMNYUmOH28/v+LLbAD+rW35v5fKbmAeFkphCRVW1HlsEhhXoZEyt3f1elJyhryHEDCiUxBSQACOvpEJiwoNkaOeoU/7esC5REh0WpL+7Ju140gxCPAmFkpi67J7Sp7X4n2TZbYD/w+/Ufw0hnoZCSTxOFTIDJR+3BTnD+J1F247oawnxNBRK4nHW7c2V7MJyadE8UEZ0jXb6+yO7Revv4jXr9+Z6pI2E1IdCSTzOgq2O89uTE+Ml0N95COJ3JiXEO17L5TcxAQol8SjV1TWycNuZL7sNjN9FAg28ByGehEJJPMqmA8ckI79MwoMDZEyPmDN+HX43LMhfjuSXyo/px9zaRkJ+DoWSeBQjbdo5CXESHOB/xq8LCfSXc2qX30ZaNkI8BYWSeIyampoTkmA0FOM1qNaI9yLEU1AoicfYdihf0o+WSPNAfzm7Z1yDX392r1gJCfSTA7kl+l6EeAoKJfEY82t3u8f3ipXmQWe+7DYIDQqQ8bUCW78GOCHuhkJJPAKWyvUrLTaWaf2On9Lh8pt4Cgol8Qg7MgolLbtIggL8ZGLvhi+7DfDaIH8/Scsqkp2ZhS5tIyGngkJJPIKxVB7XI0YiQgIb/T547dhaWxFTrxFPQaEkHuH4svuXmcwbirF053NK4ikolMTtpGUVSuqRAgnwayaTa72QTQFHH/FeeM892UUuaSMhp4NCSdyO4Z3U5BahjV92G7QMDdL3crw37yqJ+6FQEo8tu+vX7XbV8pundIgnoFASt3Igt1i2HswT5Oad0qfpy26DKYmt9T23pOdJ+tFil70vISeDQkncyje1mYJQ0iEmPNhl7xsbEVxXQoJ3lcTdUCiJW1nghmX3yVKvEeJOKJTEbRzJK5UN+47q1+fW1r1xJYbVaP2+o5KRX+ry9yfEgEJJ3L7sHtSxpbRuEeLy98d7DuzY8oTPIsQdUCiJ2zCsO9P7uX7ZbTC99q6Sp3SIO6FQEreQU1gmP+zJdduy++c2obV7cvQzCXEHFEriFhYlZwhK2/Rr10I6RIW67XPw3n3bRepnLU7OcNvnEN+GQkncmnuyKSnVzhRjR30+d7+Jm6BQEpeTV1whq3fnNLrkQ0MxxDhpV7Z+NiGuhkJJXM7ilAyprK6RXvER0jU23O2f1y02XHrGh+tnfpvC5TdxPRRK4rZKi0Y2ck9gLL8NgzshroRCSVxKYVmlLN+Z7bbTOKfCEOXlO7O0DYS4EgolcSlLUjOlvLJausaE6XLYU2CZ3yUmTD97aWqmxz6X+AYUSuJSFtTb7W7WrJnHPhefxcznxF1QKInLKCmvku+3Z3l82W1g7LAvTc3SthDiKiiUxGUs25EpJRVV0r5VczWBexqY29u1bK5tWLbDIdiEuAIKJXFDSjXPLrsN8JnHU69x+U1cB4WSuISyyir5LiXTZZUWm7r7jbagTYS4AgolcQkrd2arLSc+MlgGdnCkPjODgR1aaRsKyipl1S6HTYmQpkKhJC5ddk/t01r8UMzGJPDZRrYipl4jroJCSZpMRVV1XeYeM5fdBoZNCEcp0TZCmgqFkjSZNWk5kldSIdFhQVpEzGyGdY7SthwrrpC1aY6cmIQ0BQolcdmye0qf1uJv4rLbIMDfr640Ls3nxBVQKEmTqKqukUW19Wo8kVLtTDEeAXyzLUPbSEhToFCSJrFub65kF5ZLi+aBMrJbtFiFkV2jJTIkQLILy2T9Xi6/SdOgUJImYdTUnpQQL4H+1gmnoAA/mZRoLL+5+02ahnUim9iO6uqaOqG00rLbwDhvjlK2aCshjYVCSRrNj+nH5Eh+qYQHB8iYHjFiNcb2iJGwIH85nFcqm9OPmd0cYmMolKTRGHeTE3vHSUigv1gNtGliQvwJbSWkMVAoSaOoqamps95YcdltYLQNzynRZkIaA4WSNIpth/LlQG6JhAT6ydm9YsWqjO8Vq23cn1usbSakMVAoSaMw7ibH94yT0KAAsSpo29k9HULO5TdpLBRK0shl9xGPV1psLNP7GRUaeUqHNA4KJWkwOzMLJS2rSIL8/XQjx+qgjWjr7qwi2ZlRYHZziA2hUJIGY6Qvg/0mIiRQrA7aaNiXaD4njYFCSRqMsYQ10pnZAaOt82urRBLSECiUpEHsyS6S1CMFEuDXTCbXHhG0A5MT4jWzEdq+N7vI7OYQm0GhJI26m0QCjJahQWIXWoUFaaIMwOU3aSgUStIgjp/tNj+TeUMxduhZoZE0FAolOWPSjxbLlvQ8QW5eIzGunZiSiDK6IpvT8+TgsRKzm0NsBIWSNPhucmjnKIkJDxa7ERsRrG0HNJ+ThkChJGdMncncRrvdpzz7zd1v0gAolOSMyMgvlQ37jlqm0mJTbUIb9h+VzPxSs5tDbAKFkpwRSH4LBnVsKa1bhIhdadOiuQzs2FKQSMi4JkKcQaEkDTqNY8fd7tOlXiPkTKBQEqfkFJbJ2j05tjuNcyoMsV+7J1evjRBnUCiJUxYlZwhKzvRtFykdokLF7uAa+rSN1DK2i5MzzG4OsQEUStKA3W77L7sNuPwmDYFCSU5LXnGFJO3K9pplt4Gxc5+0O1vySirMbg6xOBRKclq+TcmQyuoa6RUfId1iw8Vb6B4XLj3jw6Wiqka+S+Hym5weCiU5LcbS1JvuJn9+V8nlN3EGhZKcksKySlm+M8s2JR8a+5xy2Y4svVZCTgWFkpySJamZUl5ZLV1iwnTp7W30bh0hnaND9RqXpmaa3RxiYSiU5JQY6ciw7G6GtDteBq7JWH4zSQY5HRRKclJKyqtkaapj2T3di2xBP2d67SOFpdszpbSiyuzmEItCoSQnBc/tSiqqpH2r5mo091b6tWsh7Vo2l+LyKr1mQk4GhZKcftndxzuX3Scuv43M51x+k5NDoSS/oKyySr5LyfTa3e5T7X5/m5yh107Iz6FQkl+wale2FJRVSnxksAzs0Eq8nUEdW0lcRLBec9IuR/IPQupDoSSnTKl2bp/W4ocCOV4OrhHXWr/KJCH1oVCSE6ioqpbFtUf6vCkJhjOMRwzIJlRZVW12c4jFoFCSE1iblivHiiskOixIhnVxFOLyBYZ1jpKosCA5WlyheSoJqQ+FkpyAsfREOVp/H1h2GwT4+8mUREcJXi6/yc+hUJI6kMjWqCNj5wJijeW4TShD+4IQAwolqWP93lzJLiyXyJAAGdk1WnyNUd1iJCIkQLILy+oqThICKJSkDiPd2KTEeAkK8L3QwDVPTuDym/ySAHEjNTU1eodCrA/G6t21++o2NrIKfLPo1tAuUfLppoPy7pr9ctf4btJMfOc5rZ2JCQ9y6wmyZjWYIW7i5jfWaaouQghxJxN7x8lrNw615x1l8EmWb158bNjW1P9z6etjxL6wPjU1zrXGNneUSIj6n8Xb5cVlafo9apQ8c/Ug6dXa+5LA2hmEwLgnl8qB3BJ57ppBMr2f7+141+frLYflnvc2SseoUFn28HivTgpiR7YfKZD75m6UHRmF+v2dZ3eTByf3dOtzdbfKMBr+u2kJ8vYtwyQmPFgv7II5K+XtNft0chJrsO1QvopkSKCfjO8VK74O+gB3KPtziyX5cL7ZzSG1QDOgHdAQaElsRLBqy2+n9Xb75qNHtjbH9oiVhQ+MlbN7xkpZZbU8+vlPcuc7G+RYMTd6rICRXmx8zzgJDXLr0xhbEBYcUPcHg6nXrAG04o63N6h2QEMwPgvuH6va4gk85gHBHeXrNw6VP5yXIIH+zeSbbRky7ekVsjaN2VrMxrDC+EJKtTPFOOfOCo3msyYtR7ViUXKGasejMxLltRuGqqZ4Cj9PZ2m5dWxX+ezu0Vqw6nBeqVz98hr57+IdTERgEjszCmR3VpEE+fvpziFxMDEhTiflrsxC7SPieaAJ0IaZL69RregaE6baccuYLh7PamWKq7hvuxYy774xcvng9oKTYrO/26mCefBYiRnN8Wnm16ZUG9MDp1ICzW6OZYgMCZQx3WP0a95Vep70o8Vy1UtrVBugEdCKr+4bo9phBn5mPgd68vIB8vRVZ0l4cICs23tUpj21XBZs5YkIM5bdxjlnchwuv81h/tbDMv3pFbJ+31GJCA5QjYBWQDPMwvRzahee1U7mzxorAzq0lPzSSrnr3Y3yu0+3ahVA4l72ZhdJ6pECzRJkHN0jx5mc6MiglHI4X/blFJndHK+npLxK5/7d725ULTirQ0v5etZY1QizMV0oQcfoUPn4zpGOI2PNROb+sF8tAKlHaM1wJ8ad0qhu0dIqLMjs5lgO9ImRHIR3le4Ff4zOn7NS5z404O7x3eSjO0eqNlgBSwglCPT3k99M7S3v3DJc65fszITncpW8tXovPZfurrTIZfcpMfqGQukeMLcxxy98dpVunGHuQwMemdpbNcEqWKcltYzuHqP+qAm9YvVkzx+/2Ca3v71BjhbRc+nqh+Wb0/P0r/eURArlqUACY/TR5gPHuNnoYjCnb3trg85xzHW4LjD3oQFWw3JCCaLDg/WA+x9nJKptBXVM4KNavZueS1dhGKmHdo7SEw7k5MRFhMjQTo6SGDSfuw7MZczpb1MydI7/6fxEefWGITr3rYglhRLgfO3NY7rIZ/eMkq6xYXIkv1RmvrJG/rNoOz2XLsCY9EZNa3Immc/pyGgqmLuYw5jLmNOY25jjN43uYukz9ZYVSoM+bR2eyyuGtNeMIc8s2SVXvrRGl46kcWTml8qG/Y4M3nw+6Ryjj2BXySwoNbs5tuVAbrFc8eJqncOYy1cO6aBzG3Pc6lheKAHOH//rsgHyzNUD1VeFNP24bUeWF9JwUBcHgTqwY0tp06K52c2xPG1bNlerCvoMR29Jw5m35ZBMn71CNu4/pnMYc/mfl/W3TW4BWwilwfkD2sr8+8fqBC8ordRUWL/9ZIsUl1ea3TRbYezgctl95hh9xeV3w8DcxBy9971NOmcxdzGHMZfthK2EEnSICpUP7xgp90xweC7fX3dAzn9mpSQfoufyTMgpLNMkA/VPnhDnGH21Ji1XcunAOCMwJzE3MUcxV++d0F3nLuaw3bCdUAL4qx4+t7e8e8twiY8M1qQOFz23St5YtYeeSyfAQYCzs33aRtoyYM0CxufENpFaxnZxMne/TwfmIObiRc+u0rmJOfrurcPl1+f2spQ3siHYs9W1jFLP5TiZlBCnPqzHvkqW295az7/4p4HL7sZj9BnN56cGc+/WN9frXCyvqta5iTmKUsB2xtZCCaLCguTl64fIY+c7PJffpmTKtKeXS9LubLObZjnySirq+mWaj5d7aAxGn63ala19SU4kaVe2TH1quXyXmqkZx/98QR+dm5ijdsf2Qgngv7pxdBf5/J7R0i02TDLyy+SaV9bKk9+kSgU9l3V8l5IhFVU1WruoW2y42c2xHd3jwqVHXLj24ZJU7n4bYI5hrl3z6lrJLCjTOfj53aPlhlGdLe2N9DmhNEhsG6k5664a2kGtHM8u3a2+Lfi3yPHck1O5idPk5bfRl77OgVpvJOYa5tzVwzroHMRc9Ca8SigBfFn/uLS/zJk5UCJCAmTT/mOa2+6rzYfElyksq5TlO7P0az6fbDzGH5nlO7KkqMy3bWmYU5hbmGOYa8/OHCR/v8Q+3kifFkqDGf3bap7LQfBcllXKfXM3ySMfb/ZZz+XS1Ezd8OocHSq9WS640SS0iZBO0aFa4Grp9kzxRYrLK3UuYU5hbg3u1EqTWZzX33tXKl4rlPU9l/dN7K4+rg/Xp8uMZ1bKtkN54rNnu/u18ZrnRmaAvvPlzOc/HczTOYS5hDCaNbG7fHD7CGnfyrutZl4tlCDA308emtJL3rt1hLSODJG0rCK5+NkkeW2l73guSyuq6u5+uOxuOkYf4i4dfesL1NTUyKsr98glzyXpHMJcwpx6cEovnWPejvdfYS0ju0Xr8gDp/eHv+su8ZLnlzfV6UsXbWbYjS4rLq6Rdy+bSz6TiTN5E//YttC/Rp3hW6e3kFJbJzW+sk8fnObyRmEOYS5hTvoLPCKWR2v+l6wbLXy7soz6vJanwXK5QX5w3YxRsQxYcLrubDvrw3D6+YT7H3Jj69ApZuj1L58zjF/bROeRrpUN8SiiNIL9+ZGf54p7R6omD7+vaV9fKPxd6p+eyrLJKvkvhstvVTOvn6EsknsUmmbeBufCPBak6N7IKynSufHnvaLlupPd4IxuCzwmlQUKbSPny3jEyc3hH9X89//1uueyF1bI/x7s8l0m7cnRnErVIBnVsZXZzvIbBHVtpZnhkxFnlZafAMAcwF15Y5vBGzhzeUedK79be5Y1sCD4rlKB5kL/87eJ+8tw1gyQyJEDroiBn3hc/HhRvrNvt5+d7dwLuAn05tXb5vdCLzOeIfcwBzAXMieevGaRzBHPFl/FpoTSY3q+NLHhgnAzt3EqN2fe//6P8+qPNtjcUY/m0KNlx1I6ZzF2P8ShjUfIR25cnQawj5hH7mAOYC5gTzAnggEJZC3Yx5942Qu4/p4fgxuvjDQ7PJXxjdmVtWq4cK67QpATDOjsKZBHXMaxLlLQKDZSjxRWydk+u2N0biZhH7GMOYC5gThAHFMp6wA/2q8k95b3bRkibFiGyJ7tILn5ulbyyIs2Wnktj2T0lMd4nvG6eBn1qlPo1+tpOVFfXaGwjxhHriHkIJOYA4+VE2BsnYURXh+fy3D7xminmia9T5KY31km2jTyXSDBr1Hfhstt9TK3d/UZfQ3jsAmL55jfXaWwjxhHriPnhXX3HG9kQKJSnoGVokLxw7WB54qK+EhzgJ99vz5KpT62QFbWJJawOCrBhMuCBvN2TplqZ0d1iNCEELDRGZUurgxhGLCOmEduIccQ6Yp6cHArlaYBf7NoRndQagRyOEJ7rXv1B/r4Af4Wt/fDeWApOSoxXozBxD+jbyQnx+vUCi+9+w++J2EUMI5YR04htxLgveiMbAmfQGdCrdYR8cc8YuWZ4R/3+xWVpctnzSbIvp0isCJaAdUkwmHvS7UytV6HRqs+yEauXv5CksQuuHeHwRiK2iXMolGcIfGR/vbifLlFaNA+Uzel5ct7slfL5Jut5LjenH5PDeaUSFuQvY3tw2e1uxvWMldAgfzmUV6pxYTUQo8gbibYhdh2PlPpJSKBveyMbAoWyEXcPqEsMuw38Zg988KM8+KHDe2YVjLvJCb3jOBk8APoYfW213W/EJGITMVpUXqUxiw0bbu41HAplI4C/7L3bhssDkxyey083HpQZs1fIVgvcTWDpd7zSIpfdnjaf44+UFZbfW9KPaUwiNhGjv5rUU+bePkLa0hvZKCiUjQQ+swcm9ZQP7hgpbVuEyN6cYrnk+VXy8vI0U20iyYfzZX9usYQE+sn4XrGmtcPXmNArTneQ9+UUS8rhAtPagdhDDF76fJLGJGITMXr/pB7izyOsjYZC2USGdo7SpTjO/cKP9tf5KXLjG+vULmLmsvvsnrESFux9tUusCvoafW5s6phBZkGp3PD6DxqDiEXc5aKmNmKUNA0KpQuA/+z5awfJXy92eC6RzBW1xZEw19PMr809yWW3eanX5puQoxKxhg2bFTuzdTVhJHtpERro8bZ4IxRKFwEf2jXDO2mpzl7xEZJdWC43vPaD/G1+isfyFe7MKJDdWUUS6N9MJiY4NheI55jYO177fldmoezK9MzyG7GFGEOsIeZQOO6r2vSB9Ea6Dgqli+kZHyFfIMHpiE76/UvL0+SyF5L0LK27MTZxxnSPkcgQ3kl4GlhvRneP8Zj5HDGFZ5GIMXD9yE7yORJSx9Mb6WoolG6yizx+UV958TocCwuULel5tTuQ6W793LrdbqbGMo3pHqrQ+MmGdDkPTouDeRpjjhInfWkHcxMUSjeCuiqaaKBLlPrYHvxws/zqA/d4LnHyIuVwvu5sGkfqiOdB4S2MgboP3JAtv6C0QmPooY9Qo75KYwsxNqU2iTBxDxRKN9OmBTyXI+ShyT11An226aDeCSCDtCsx7mBGdo32ucJPVgJ9P6JrlFvM54gZ5I1EDCGWHqpLCUhvpLuhUHoABPV95/TQQvEwq8Nrh2dLLy7b7TLPZf1Ki8RcptYuv121+40YQf0axAxiBzH04R0jNKbojfQMFEoPMgSey1ljZXq/1lJZXSN/X5Cqvjf435rCwWMleo4Xm5xT+nDZbTbI7YixwB3goWMlLvFGoiIiYua8fm3Utzu4E72RnoRC6WHga3t25iD5xyVISuCnvjf435Zud5SUbYrJfGinKImLCHFha0ljwBgM6dTqhLFpDIiJaU8d90YiZubMHKi768SzUChNAP62q4Z1lHn3oQSow3N50+vr5Il5yVqHu6EYJ0EMwzMxH8Pw3xihRAw8Pi9ZYyKnyOGNRKwgZuiNNAcKpYl0j4tQ39sNIx2ey1dW7tHnUGlZhWf8Hpn5pbJ+nyOzNp9PWgdjLNbty23QoxWMPWLg1ZV79PsbR3XWGEGsEPOgUJoMfG9/vrCvvHz9EK3o99PB/LqKeGeSheabbchWI3JWh5bc/bQQyNIzoENLHRujdtHpwFh/tP5AbeXPfI2FV64fIo9d0IfeSAtAobSQ/w4JDGAtgT8ONZaRRxC+udNxPKUa7yatm3rt9DYhjDHqaT/88RYde1i8EAso40GsAYXSQrRuESLv3jpCfj3F4bn84sdDmkV90ymKVuUWldfVk2YSDOsK5Zq0XDlaVH7S38HYTp+9Qr7cfEjH/OFze8k7tw7XWCDWgUJpMTBZ7p3YQz68Y6T65ZBb8vIXVsvz3//Sc7k4+YiWpU1sEykdo0NNazM5OZ2iwyShTaSO0eLkE5ffGMvnvt+lY3sgt0Tat4I3cqTcM6E7vZEWhEJpUQZ3aqV+ufP6t1H/3D8Xpsr1r/2gmzc/X3bDl0msyfTau8r6p3Qwhte9tlb+tXC7ju2M/oY30mEpItaDQmlh4Jebc/VA+eel/aR5oL+s3JUtU+G5TM2UvJIKWbUr+4STIMR6GJYtjF1+aYUsSc3QMVy1K0fH9F+X9pdnrh7IbE8Wp1mNFQp8EKcgx+F9czdp4guAXdGjxRXSIy5cFj94ttnNI6dh0n+X6fgZYwbwuGT21QOle1y42c0jZwDvKG0CJtRnd4+Sm0Z31u+NCce6zNYHiZzrjxnG8LN7RlEkbQTvKG0Idkhnzd1U9/2/Lusvlw9uz1MbFsPhjUyXRz7ZUvczLLPPH9DW1HaRhsM7Shvy803RRz7eIrPe/1GfgRFrgLHAo5L6Ign8+MfMllAobYix233HuK7yyNReaif5avMhTa6x8RSeS+I5MAYYi3lbDuvYYIxuH9fVLTkqiWegUNqM0ooq3fUG0/u1kbvHd5eP7hypPrz0oyXqy3t26S717hHPgj5H32MMMBYdoprr2GCMMFZgSWqmjiGxFxRKm4GypDjmBjN6//Yt9GeDOjo8l3j2hcn65Dfb5bpX10pGPc8lcS9H8krl2lfWat9jDC4Y0Fa+njVWxwYMaN9C2rYI0bFDOWNiLyiUNsNI24V6PPU3b+DDm33VWfLkZf3Vn5e0O0emPrVcvktxnpCBNA30Meq4r07LkdAgfx2Dp6866wRvJMbq3Lqz356v+02aBoXSRqCG87e1wney3JOYjJcP6SDzZo2RPm0j1Y5yy5vr5bEvt3G55wbQp+hb9DH6Gn2OvJEYg5M5EIzz+ItTMjxW6524BgqljVi1O1sKSislLiJYBtcu6U5Gt9hw+fTuUXLLmC76/RtJe+Xi55LU9Excw67MArno2VXat+DWMV20z7vGntobiSOKsRHBOoZJux2nqog9oFDaiIVbjy+7/ZwkTggO8JdHZyTK6zcOleiwID3Rc/4zK+WDdfvPKM8lOTnou/d/2K95I1OPFGjfoo//MCNR+/x0YAcc9XQAl9/2gkJpEyqrqmVRcsNzT07oHad1n8d0j5GSiir5zSdb5d65m/SsOGkY6LN739skv/10q5RWVGufom/Rx2eKsfxGwmWMKbEHFEqbgLyTeA6G88LDujSsAl9cZIi8dfMw+e203hLg10y+3nJYfX4b9jlyWRLnoK/QZ19vPax9+LtpvbVP0bcNYXiXqLoz3z/U5hIl1odCaRMMo/KUxNYS4N/wYcNS/c6zu8nHd42SjlGhWuL2ihfXyJwlO+m5PA3om2e+26l9hT5D36EP7zi7m9PHHycDY4ds9vUPDhDrQ6G0AUjyatRdaWqlRdTW+XrWGLnwLIfn8t+Ldsg1r6xRHyA5kcN5JTLz5TXyn8U7tK8uOgveyDHah01hWr/jy++fJ2Mm1oRCaQM27D8qWQVlEhESIKO6xTT5/SJCAuWpK8+S/1w+QH1/KFUw9enlv8jC7css2nZEpj29Qh95oI/+e8UAeeqqgdp3TWV0txgdy8yCMh45tQkUShuwoHa3e3JCvAQFuGbI4PO7dHB79f31bRcpx4or5La31sufvvjJpz2XuPY/fvGT3P72Bu0T9A1O2FwyqL3LPgNjOCmBy287QaG0gR3FqOLnjrrd8P19ctcouW2sw3P55up96g/cmVEgvgauGdf+1up9+j365NO7RkuXmDCXf5YxlrAJ0a5lfSiUFmdzep4cyivV5d+4nrFu+Qz4/35/XqK8cdNQiQkPUn/g+XNWytwffMNziWt8b+1+vWZcO/rgzZuHaZ+46g7+55zdM1bHFBtEW9Lz3PIZxHVQKG2y2w2vXkjg6Q3NTWV8rzhNrjG2R4z6BH/36Va5572NklebmdsbwbXd/e5G+b/PHN5IXDv6AELmTjCWE3o5/JdcflsfCqXll921lRY9VEAsLiJE3rxpmPzfdIfncv7WI1p3ev1e7/P8rdubq8ksIFSB/s30mnHt6ANPYDgY8GjFF+7c7QyF0sKkHC6QfTnFEhzgJ+N7ufcOpz7wB94+rps+u+wUbXguV8vs77zDc4lrePrbnXLli6v1sUbn6FC9VlxzY7yRjQV3lBjbvTnFuuQn1oVCaYNlN5aBYcEBHv/8Aeq5HCsXD2wn0Mf/Lt6hvkL4C+3KoWMlcvXLa+R/3+7Qa7pkYDuZN2us9G/fNG9kY8CYGs+dF2xl5nMrQ6G0MMazq6aazJtCeHCA/O/Ks9RHGBbkr75C+AthlrYbeIyBtuPoIK7lf1cOkP9eeZZeo1kY5/b5nNLaUCgtnMYLadHw7Gxib4fnzkzgI8TdJbKqw194x9sb5NHP7eG5RBv/8PlWufOdDZrYAtfguFN2nTeysZyTEK9jvDOzkGnwLAyF0uImc2SoadG86adBXEHnmDD5+M5RdYWy3l6zTy6cs0p2WNhzuf1IgVwwZ6W8s2Z/XUE2XAOuxQpgbEd3d5y2MvyyxHpQKK2+7PbQbveZAl/h/01PUJ9hTHiwbM8o0DyX767dZ6mdW7TlnTX7VCR3ZBRqW5Ht53fTE9zmjWwsXH5bH2tFDFH25RRJ8uF8TfRqZJqxGthgQi5GbEaUVVbL7z/7Se56Z6McKy43u2naBiyz//D5T9o2tHXhA462WpHJia11rLcdypf9OcVmN4ecBAqlBTHuLEZ0jZJWYUFiVVDW4I0bh8rvpyfoc7aF245ozkYz8yyuTcup3WzK0Db94bwEzUCOO0qrEhUWpHkqAet+WxMKpYWFcqrFlt0nA77D28Z11TPR8CPCl3jVS6vlqW93eDSDNz7rf4t3qPXncF6pns9Gm24d29Wj3sjGwuW3taFQWtDnt/nAMUERP6O+ih3o176F+hEvHdRe/YlPfbtTZr68Vs3q7gafAYF8+rud+tloA7IioU12wVF+WOTHA8ds7VP1ViiUFsM4sji0U5THjtK5CvgR/4O8jbXexB/2OsonuHM3F0btaU8tl3V7j+pnop422mCGQb8poKTEkE6OyposPGY9KJQWw5gk7kip5ikuGthOM4EPaN9CfYt3vrNRfq9JJ1znuSwpr9JEFne9u1HySyv1FNH8WWPlwrPaiV0xHrVw+W09KJQWIrOgVNbVFvyys1CCTtFh8tGdo7ROD3h37X616sDX2FRSj+TreyE1GtBaQHeOlI7RoWJnjDFHsg7EArEOFEoLgZ1aWBFxd9S2ZXOxO/ArovLj27cM0x1y+BkhcDCqN8Zzide8vXqvXDBnlZ5kwXu+c8tw/YzARhRcsxrtWjbXu3B0zaLaGknEGtg/urwI41leQ+p224GxPRyeS2RAgq8RRx9xBLIhnsujReVanuHRL7ZJeWW1TOgVKwtRr7xH02sIWXH5zeeU1oJCaREgBCjy5Y1CCeBjfO2GofLojET1Ny5KzlC/45q0HKevxe/gd1H8DK/Fe7x241CJtrA3srEYY786LUdjglgDCqVFgAggT2Jim0h9vueNwM94y5gu8tndo6VrTJj6HZG2DenbTua5xM/+u2i7Wn+O5Jfqa/BavAeKo3kjOIOe0CZSY2FxCpffVoFCaRGMExneeDf5c/q2ayFf3TdGLh/s8FwiIfBVL62R9KPHj+/h6ytfWiOzl+zSZ3ZXDGmvr8FrvR0jBrj8tg7NaqyUycBHgYVmyBOLpaKqRr59cJx0j4sQX+GLHw/qOfHCskqJDAmQf1zaX4Xxt59ukYLSSokIDpAnLu5ra9tPY6pBTv7fcn3MsOHRyRLpglripGnYy5XrpSxJzVCR7B4X7lMiCSCAAzu0klnvb9JTKSj0ZTCwY0uZfdVA6RBlb9tPQ+kRHyHdYsNkd1aRLEnJVF8qMRcuvS2Ue9IXlt0nA/7Hxy/s+4uf42e+JpIGRno9JsmwBhRKkykqq5RlO7IsmXvSE+DJz5tJe+XSF5J+8X+XPJ8kb63ea6k8l57CKP+B2CgurzS7OT4PhdJkvt+epd5CVDtMaONby+7conK57a318qcvHd7Iib3jZMMfJuk/fI2f/fGLbXLbWxt8zioD90PHqFCtNY4YIeZCoTSZ+bVLKxxf81bLy8lI2p2tNbW/TcmUIH8/eez8RHn1hiHqjcQ/fP2n8xP1/75NcXguV+927rn0FhALxqOY+azQaDoUShNBkoilqZk+teyuqKqWf3+zXa55Za1k5JdJ19gw+eyeUXLj6BO9kfj6ptFd9P/wO/BRznxljfxn0XaP5rm0wtlvxIgdirh5MxRKE1muz5+qpG2LED3j6+0cyC2WK19cLXOWOryRVw7poHkj+7Q99bXj//A7+F285pklu+SKF1fre3k7A9q3lDYtQqSovEpW7Mw2uzk+DYXSRAxD8bk+sOz+avMhmT57hWzcf0wiQgJkzsyB8s/L+ktokHOHGn4Hv/vM1QPVV4n3wHvN23JIvBmcZEJCX8Ddb3OhUJoENiqMI2rT+3nvshs7tr/5eIvcN3eTGsjhjUTeyBn92zb4vc4f0Fbm3z9W3wPvde97m+S3n2zx6l1hIza+Tc7QmCHmQKE0cTMDkx2pwgZ3dGS29ja2HcqTGc+slA/WH9AyB/dO6C4f3jGySd5IvBbvgffCe76/7oCWy00+lC/eyOBOrTShCJITI1EGMQcKpckmc9TFsUPxq4YA3+Prq/bIxc8mSVpWkcRHBsu7tw6XX5/byyV5I/EeeC+8J94bJ1guenaVvLFqj9d5LlHG1qidhLIXxBwolCaAXdtFycZpHO9aducUlsktb66XP3+VLOVV1TIpIU4W3D9ORnVzfd5IvCfeG5+Bz3rsq2S59c316s/0JowYQWo6X9nxtxoUShNA3eujxRXSKjSwrp6zN5C0C97IFbIkNVOzm//5gj7y8vVDtG61u8B74zPwWfjM71IzZepTy7Ut3sLwrlHSMjRQ/wCgYBvxPBRKEzCKR01JbC0BXlDCAN7Ify1MlWteXSuZBWWa3OOLe0bLDaM6e2Q3H5+Bz/r87tGaTAJtQFue/CZV22Z38KhhSqJj+c3Ua+Zg/1lqM6qra2ThttpKi7Xnee0M/IyXv7Banvt+t/ocrx7WUb66d4wmn/U0iW0jNWfl1cMcnstnl+72Gs+lsfyGUCKGiGehUHqYDfuPSlZBmXoJR7vhuZ2nc0mibjfSoyGX5HPXDJK/X9JPmgf5m9YmeC7/fkl/eXbmIO3jTfBcPr1Cvtxsb8/lqO7R6iHF3fLG/UfNbo7PQaE0abd7UkK8PlOza8ajhz/aLPe//6MUlFXKkE6t1N9oJT/oef3baEEz2GvQxllzN2mb7eq5DA7wl3MS4vRr1v32PPacqTYF1pVvjGW3TXNP/nQwT32LH21IF7iaZp3TQ96/fYS0b2W9vJFo0we3j5BZEx2eS7QZvk5cg90rNHqbDcrqUCg9yJb0PDl4rERCg/zl7J6xYicwMV9duUcueS5J0rKLpHVkiLx32wh5cHJPS29IoW0PTukl7906QtsMXyeuAddiN7FBzDQP9NcY2mpTsbcr1o1wL8RYMk3oHSchgeY9x2so2YVlcvMb6+TxeQ5v5OTEeF3WjugaLXZhZLdobTPajmvAteCa4Pu0C3j2izydgMtvz0Kh9BC4e1low0qLK3c6vJFLt2fpM9XHL+wjL103WFq50RvpLtBmtB3XgGvBNU19eoWsspHn0nhkg1M6drsjtjMUSg+RcrhA9uYUS3CAn0zo5bgrsDLwH/5jQapc99pa3aXvERcuX947Wq4b6RlvpLtA23ENuBZcE67t2lfX6rXawXOJ1QhEHrGUeqTA7Ob4DBRKD2HcTY7rGSthwdYufrkvp0gue2G1vLDM4Y2cObyjfHnvGOnd2vPeSHeBa8E14dpwjbhWXPP+HGt7LsODA2RcD8fzbS6/PQeF0kMYQW31ZTe8kefNXimba72RL1w7SP52sbneSHeBa8K1PX/NIL1WXDPyXKIPrIwRQ8YfX+J+KJQeYFdmoezMLNSC9uckOI6iWY3Cskp56EOHNxJfD+3cShY8MK7OkuLNTOvXRq8V14xrRx/8+qPN6he1IvDgIpZ2ZBTK7qxCs5vjE1AoPYDxl3909xhp0TxQrMbWdIc38pONDm/k/ef0kLm3jZB2LZuLr4BrxTXj2tEHH1vYc9kiNLAuGxPPfnsGCqUHmL/VmstunBl+ZUWaXPL8KtmTXaS1e96/faT8yuLeSHeBa8a1QzBRqwZ9cvFzq7SPrHa+mhUaPYvvzQYPg82B5MP5moB1cqJ1hBK7vTe9sU6e+DpFKqpqNDksjiEO86K0b41leFeH5xJ9gr5BH9385jr1k1oF+EFx57vtUL7lN6C8AQqlmzGKQiHvpDvzMja0+iO8kct2ZKld6YmL+soL1w6WlqHWaJ8VQF+gT9A36KPv4bl8aoWs2JklVgC1z4d3cRj+F27jXaW7oVD60G43ilP9fX6KXP/aD3p31Cs+Qi0y147oZGtvpLtAn6Bv0Ec948O1z6579QftQysU+ppWm6aPNiH3Q6F0I4fzSjQFGTTIKDtqFnuz4Y1MkheXp+n3143oJF/cO1p6tY4wtV12AH3k+IPSUb9HH6Iv0admgphCbCGVHGKNuA8KpRsxdiSRhiwuMsS0dny2KV3Om71Ck3Jg1x1Lyscv6mur8+Zmg7564qJ+2nfoQ/Ql+vTzTeZ5LuMjQ+oqeH7Du0q3QqH0QO5Js7yI8AQ++MGP8qsPNktReZVu1GCTwq4p3qwA+g59OKxzlPbpAx/8qH2MvjarPWA+hdKtUCjdRGZBqazb5ygEZYYwbUk/pnc8n246qLujD9baXtr6kDfSXaAP594+Qn41qaf2Lfp4ht6xH/N4W4zYWrc3V50MxD1QKN3Eom0ZeoZ4QPsWHjVuw+/30vLdmnNxX06xfvYHd4zUBLuwKBHXgL68f1IP7Vv4T5Gk4tLnk+Tl5Z71XCI5cf/2LTTWjBLIxPVQKN38fBLH4zx5F3vD6z/I3+anSmV1je60z581VoZ2pjfSXaBvUVscfQ3P5V/np+gYYCzMKDxG3AOF0g0cLSqX1Wk5HrUFfb89U4tordiZLSGBflrkC8W+cNyNuBf0MfoaCTbgucQYTK/1qXoCI8aSdudo7BHXQ6F0A4uTM6SqukZLtnaKDnPrZ8HP99evk+XG13FypFx6t47QcrEoG0tvpOdAXyNlG8rlYgwwFje8hrt793suO8eE6Wci5hanZLj1s3wVCqUbT+O4+24SZ5H1udiKPfr9DSM7yef3jJYe8fRGmkXP+Agdg+tHdtLvX1qepmOEsXInXH67Fwqli8kvrZCVtaUF3CWUKAHwyQaHNxJFplqGBmqJgz9fSG+kFcAY/OXCvjomGBuMEcYKY+buUzoo3VFQWuG2z/FVKJQuZklKpj7U7xYb5pY7O0yCX33wozykNaqrZERXhzdyisknf8gvwZhgbHDOH2OFMcPYuUPIUNaia2yYFk5bkprp8vf3dSiUblp2T3fDbjeOQyL7+Oc/HlJ7yq+n9JR3b0VKMHojrQrGBmV9H5rcU8fsM3gun3FkkHf1M9Lptctv46ADcR0USheCjNjIMuNqkzl8eVrT5fkk2Z/r8EZ+eMcIuXcivZF2AGN03zk95IPbHcmQ4W/Fc0uMqSs9l0bMfb8jU4rLrZmd3a5QKF0IRLKsslo6RoVKYhvXFOLKzC/VbD+oEghv5Hn92mjeyMGd6I20G0M6R6mvFWOIscSYqucy3zWeyz5tI6VDVHMpraiu+4NNXAOF0k273a6w5ixNzdS609gcgjfyn5f2kzkzB1qynAQ5c88lxvAfl/TTMV1RVze96c8VEXPG7jdTr7kWCqWLKK2oUmFzxbK7rLJKHp+XrBnIc4sc3sh5942RK4fSG+kNYAyvGtZRxxRjm1NULje9vk7HHGPfFIzYW5KSoTFJXAOF0kXgzgDZZHDu96wOLRv9Pqiqh3Par650eCNvHNVZfXnd4+iN9DYwphhbjDHAmGPs05pQWfGs9i213g9iEVYh4hoolC5edp/byGU3vJEfrj8gM2av1DoorUID5ZXrh8hjF/ShN9KLwdhijDHWGHOMPXbFP1p/QGOiofj5NatLEs3lt+ugULoAHFHDsUVgPCNqqEkdtaQf+XiLlFRUyUgtbjVOJiVaswY4cT0Ya4w5fLHwXD788RaNicZ4Lo2DDouTj1iiZIU3QKF0AUm7cRqiUmLCg2VwJ0fG6TNl4/6jemrjy80Ob+TD5/aSd24dLq1bmJcRnZgDxhy+WMQAYgExMX32Ctm0/2iDd9djwoMkv7SyLjkLaRoUShdgnK9FedMz9TXCP/fs0l1y+Qur5UBuibRv1Vw+unOk3DOhO72RPgzGHjHw4R0j1XOJ2ECMPPf9rjP2XOI9jJNaC2sfCZGmQaFsIpVV1bKogcvujPxSue61tfLkN9s148uM/g5v5KDa+ieEYGWCmDivv8Nz+a+F2zVmztRzaSy/kUAaMUaaBoWyifywN1ctPHgQP7yrcxP4dykZ6ptbtStHmgf6y78u7S/PXD1QIkPojSQnAr/snKsHaowgVhAz8NUuSXWeSm1E12hNyAHr0Q97HCVJSOOhULpo2T05MV4C/U/dnfDHPfblNrnlzfUqrDi5M2/WGLliaAd6I8kpQWwgRpDnEvlNETs3v7Fe/vzVttN6LhGLkxMcm4FcfjcdCmUTwDOjupIPp1l278oslIufTZI3kvbq9zeN7iyf3TNKusWGe6ytxN50jwuXz+4epbEDXl+1V2MKvltnqddgE/JkHR9vhELZBLBjnVlQJhHBATKqe/Qv/h8+uA/W7Zfzn1kpyYfzJSosSF67cYj86fw+EhxAbyRpuOcSsfPqDUM0lhBT8N1+uO7knsvR3WM0NhGjmw40bOecnAiFsgkYht5zEuJ+IXx5JRVy39xN8ptPtqo3cnT3aFl4/1iZ2JveSNI0zkmA53KsjOoWrbH1yCdbNNbgx60PYnJiQpx+zdRrTYNC2UjwF/xUlRY37HN4I+dtOSwBfs3kN1N7y9s3D5e4SHojiWuIjwyRt28ZLo9MdXguEWsoaIZVTn3qJ8lozEkf4oBC2UiQ3v/gsRIJDfKXs3vG6s9gw5izZKdc8eJqST9aoimv4I28a3w3PVpGiCuBQN49vrvGGGINMQfPJfy5hiUIsYkdc8TqTwfzzW6ybaFQNpL5tUuZCb3i9NnRkbxSufaVtfLvRTs0SC8Y0Fa+njVWBtIbSdwM/LeItfMHtNXYgz8XsYiYbB7kLxN6O/6Qz+fud6NpVsP78QaDLpvw7+9lb06xeiDxF/vhjzfL0eIKvcNEYalLB7Wj7Yd4PC4/3pAuf/pym54Xh7f3ycsGSHFFlcyau0m6xITJkofOZlw2goDGvMjXST1SoCKJ1TSK3CM4jQzTEM6utP0QE4AAXj6kgwzq1EqFEZmIbn1rvVw2uL3GKkrmbs8okN6tXZN935fg0rsJu914DGSI5K1jusind4+iSBLTgT8XsXjLmC76PWLUsFFy97txUCgbQf2TDtFhQfL6TUPlDzMS6Y0klgGx+OiMRHn9xqEaowaGU4M0DAplA0F1ux0ZjtMQY3vEyIIHxuqGDiFWZELvOPVcjukeo99j6V1SzhIRDYWbOQ0E3YXjY9i0uWJIB9p+iC3AEUZk0Mcmz821S3Jy5lAoCSHECVx6E0KIEyiUhBDiBAolIYQ4gUJJCCFOoFASQogTKJSEEOIECiUhhDiBQkkIIU6gUBJCiBMolIQQ4gQKJSGEOIFCSQghTqBQEkKIEyiUhBDiBAolIYQ4gUJJCCFOoFASQogTKJSEEOIECiUhhDiBQkkIIU6gUBJCiJye/wfB+F7O76vISwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| echo: true\n", "#| eval: false\n", "def star(p, s):\n", " th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n", " x = np.cos(th[::s])\n", " y = np.sin(th[::s])\n", " return x, y\n", "\n", "x, y = star(5, 2)\n", "\n", "fig, ax = plt.subplots(figsize=(4, 4))\n", "ax.set_aspect('equal')\n", "ax.axis('off')\n", "ax.plot(x, y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.57079633 2.82743339 4.08407045 5.34070751 6.59734457 7.85398163\n", " 9.1106187 10.36725576 11.62389282 12.88052988 14.13716694]\n" ] }, { "data": { "text/plain": [ "array([ 1.57079633, 4.08407045, 6.59734457, 9.1106187 , 11.62389282,\n", " 14.13716694])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p=5\n", "s=2\n", "th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n", "print(th)\n", "th.size\n", "th[::s]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Result" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def star(p, s):\n", " th = np.linspace(np.pi/2, np.pi/2 + 2*np.pi*s, s*p + 1)\n", " x = np.cos(th[::s])\n", " y = np.sin(th[::s])\n", " return x, y\n", "\n", "x, y = star(5, 2)\n", "\n", "fig, ax = plt.subplots(figsize=(4, 4))\n", "ax.set_aspect('equal')\n", "ax.axis('off')\n", "ax.plot(x, y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.patches import FancyArrowPatch\n", "\n", "GARNET, BLUE = \"#73000A\", \"#1B5E9E\"\n", "INK, MUTED, FAINT = \"#1A1A1A\", \"#9AA0A6\", \"#DDE1E5\"\n", "\n", "plt.rcParams.update({\n", " \"font.family\": \"DejaVu Sans\",\n", " \"font.size\": 9,\n", " \"axes.titlesize\": 10,\n", " \"figure.facecolor\": \"white\",\n", " \"axes.facecolor\": \"white\",\n", "})\n", "\n", "\n", "def angles(p, s):\n", " \"\"\"The angle array the original star() builds, before and after th[::s].\"\"\"\n", " th = np.linspace(np.pi / 2, np.pi / 2 + 2 * np.pi * s, s * p + 1)\n", " return th, th[::s]\n", "\n", "\n", "def frame(ax, lim=1.42):\n", " ax.set_aspect(\"equal\")\n", " ax.set_xlim(-lim, lim)\n", " ax.set_ylim(-lim, lim)\n", " ax.axis(\"off\")\n", "\n", "\n", "def guide_circle(ax, r=1.0):\n", " t = np.linspace(0, 2 * np.pi, 400)\n", " ax.plot(r * np.cos(t), r * np.sin(t), color=FAINT, lw=1, zorder=0)\n", "\n", "\n", "def caption(ax, text, y=-1.33):\n", " ax.text(0, y, text, ha=\"center\", va=\"top\", fontsize=8.5, color=MUTED)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "all 11 angles (deg from start): [ 0. 72. 144. 216. 288. 360. 432. 504. 576. 648. 720.]\n", "spacing: 72.0 deg\n", "\n", "after th[::2]: [ 0. 144. 288. 432. 576. 720.]\n", "spacing: 144.0 deg\n", "\n", "vertex index visited at each step: [0, 2, 4, 1, 3, 0]\n" ] } ], "source": [ "th_all, th_sub = angles(5, 2)\n", "\n", "deg = np.degrees(th_all) - 90 # measured from the starting angle\n", "print(\"all 11 angles (deg from start):\", np.round(deg, 1))\n", "print(\"spacing:\", round(deg[1] - deg[0], 1), \"deg\")\n", "print()\n", "\n", "deg_sub = np.degrees(th_sub) - 90\n", "print(\"after th[::2]:\", np.round(deg_sub, 1))\n", "print(\"spacing:\", round(deg_sub[1] - deg_sub[0], 1), \"deg\")\n", "print()\n", "\n", "print(\"vertex index visited at each step:\",\n", " [int(round(d / 72)) % 5 for d in deg_sub])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14, 4.6))\n", "gs = fig.add_gridspec(1, 4, wspace=0.12, top=0.86, bottom=0.12)\n", "\n", "th_all, th_sub = angles(5, 2)\n", "r_ramp = np.linspace(0.70, 1.12, len(th_all))\n", "xs, ys = r_ramp * np.cos(th_all), r_ramp * np.sin(th_all)\n", "\n", "# --- 1. the raw angles ---------------------------------------------------\n", "ax = fig.add_subplot(gs[0]); frame(ax); guide_circle(ax)\n", "ax.plot(xs, ys, color=BLUE, lw=1.6, alpha=0.65, zorder=1)\n", "ax.scatter(xs, ys, s=46, color=BLUE, zorder=3, edgecolor=\"white\", linewidth=1.2)\n", "for i in range(len(th_all)):\n", " rr = r_ramp[i] + 0.13\n", " ax.text(rr*np.cos(th_all[i]), rr*np.sin(th_all[i]), str(i),\n", " ha=\"center\", va=\"center\", fontsize=8, color=BLUE)\n", "ax.set_title(\"1. 11 angles, 72° apart\", color=INK, pad=12)\n", "caption(ax, \"Two full laps (2π·s with s=2).\")\n", "\n", "# --- 2. the subsample ----------------------------------------------------\n", "ax = fig.add_subplot(gs[1]); frame(ax); guide_circle(ax)\n", "keep = np.zeros(len(th_all), dtype=bool); keep[::2] = True\n", "ax.plot(xs, ys, color=FAINT, lw=1.4, zorder=1)\n", "ax.scatter(xs[~keep], ys[~keep], s=42, facecolor=\"white\",\n", " edgecolor=MUTED, linewidth=1.4, zorder=3)\n", "ax.scatter(xs[keep], ys[keep], s=52, color=GARNET, zorder=4,\n", " edgecolor=\"white\", linewidth=1.2)\n", "for i in range(len(th_all)):\n", " rr = r_ramp[i] + 0.13\n", " ax.text(rr*np.cos(th_all[i]), rr*np.sin(th_all[i]), str(i),\n", " ha=\"center\", va=\"center\", fontsize=8,\n", " color=GARNET if keep[i] else MUTED,\n", " fontweight=\"bold\" if keep[i] else \"normal\")\n", "ax.set_title(\"2. th[::2] keeps every other one\", color=INK, pad=12)\n", "caption(ax, \"Six survive, now 2 × 72° = 144° apart.\")\n", "\n", "# --- 3. the visit order --------------------------------------------------\n", "ax = fig.add_subplot(gs[2]); frame(ax); guide_circle(ax)\n", "vx, vy = np.cos(th_sub), np.sin(th_sub)\n", "for k in range(5):\n", " ax.add_patch(FancyArrowPatch((vx[k], vy[k]), (vx[k+1], vy[k+1]),\n", " arrowstyle=\"-|>\", mutation_scale=13, lw=1.8, color=GARNET,\n", " shrinkA=9, shrinkB=11, zorder=2, alpha=0.45 + 0.11*k))\n", "ax.scatter(vx[:5], vy[:5], s=58, color=INK, zorder=4,\n", " edgecolor=\"white\", linewidth=1.2)\n", "for step, vert in enumerate([0, 2, 4, 1, 3]):\n", " a = np.pi/2 + vert * 2*np.pi/5\n", " ax.text(1.24*np.cos(a), 1.24*np.sin(a), f\"v{vert}\", ha=\"center\",\n", " va=\"center\", fontsize=9, color=INK, fontweight=\"bold\")\n", " ax.text(0.44*np.cos(a), 0.44*np.sin(a), f\"step {step}\", ha=\"center\",\n", " va=\"center\", fontsize=7, color=GARNET, zorder=5,\n", " bbox=dict(boxstyle=\"round,pad=0.22\", facecolor=\"white\",\n", " edgecolor=FAINT, linewidth=0.8))\n", "ax.set_title(\"3. Each 144° step skips a vertex\", color=INK, pad=12)\n", "caption(ax, \"v0 → v2 → v4 → v1 → v3 → v0.\")\n", "\n", "# --- 4. the result -------------------------------------------------------\n", "ax = fig.add_subplot(gs[3]); frame(ax); guide_circle(ax)\n", "ax.plot(vx, vy, color=GARNET, lw=2.2, zorder=2)\n", "ax.scatter(vx[:5], vy[:5], s=46, color=GARNET, zorder=3,\n", " edgecolor=\"white\", linewidth=1.2)\n", "ax.set_title(\"4. ax.plot joins them — a pentagram\", color=INK, pad=12)\n", "caption(ax, \"5 × 144° = 720°, so the path closes.\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, y = star(7, 3)\n", "\n", "fig, ax = plt.subplots(figsize=(4, 4))\n", "ax.set_aspect('equal')\n", "ax.axis('off')\n", "ax.plot(x, y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# 1. Generate data\n", "x = np.linspace(0, 10, 100)\n", "y = np.sin(x)\n", "\n", "# 2. Create the figure and axes objects\n", "fig, ax = plt.subplots()\n", "\n", "# 3. Plot data on the specific axes\n", "ax.plot(x, y, label=\"Sine Wave\")\n", "\n", "# 4. Customize the specific axes\n", "ax.set_title(\"Simple Line Plot\")\n", "ax.set_xlabel(\"X Axis\")\n", "ax.set_ylabel(\"Y Axis\")\n", "ax.legend()\n", "\n", "# 5. Display the window\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python (genomics-cnn)", "language": "python", "name": "genomics-cnn" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.25" } }, "nbformat": 4, "nbformat_minor": 4 }