{ "cells": [ { "cell_type": "markdown", "id": "96d9caf9", "metadata": {}, "source": [ "# BoolForge Tutorial 5: Example Use Cases of the Random Function Generator\n", "\n", "In this tutorial, we explore example use cases of BoolForge’s random Boolean\n", "function generator. This functionality allows generating large ensembles of\n", "Boolean functions with prescribed structural properties and studying their\n", "statistical and dynamical characteristics.\n", "\n", "## What you will learn\n", "In this tutorial you will learn how to:\n", "\n", "- compute the prevalence of canalization, $k$-canalization, and nested canalization,\n", "- determine distributions of canalizing strength and normalized input redundancy,\n", "- investigate correlations between absolute bias and canalization,\n", "- generate and analyze dynamically distinct nested canalizing functions.\n", "\n", "It is strongly recommended to complete the previous tutorials first.\n", "\n", "---\n", "## 0. Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "0ac80be3", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:40.269335Z", "iopub.status.busy": "2026-01-15T21:43:40.269103Z", "iopub.status.idle": "2026-01-15T21:43:41.365597Z", "shell.execute_reply": "2026-01-15T21:43:41.365371Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "import boolforge\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import scipy.stats as stats" ] }, { "cell_type": "markdown", "id": "59f0552d", "metadata": {}, "source": [ "---\n", "## 1. Prevalence of canalization\n", "\n", "Using random sampling, we estimate how frequently Boolean functions of degree $n$\n", "exhibit a given canalizing depth." ] }, { "cell_type": "code", "execution_count": 2, "id": "ef466ce5", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:41.367007Z", "iopub.status.busy": "2026-01-15T21:43:41.366861Z", "iopub.status.idle": "2026-01-15T21:43:41.812726Z", "shell.execute_reply": "2026-01-15T21:43:41.812512Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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" ], "text/plain": [ " k=0 k=1 k=2 k=3 k=4 k=5 k=6\n", "n=2 0.221 0.000 0.779 0.000 0.000 0.0 0.0\n", "n=3 0.608 0.103 0.000 0.289 0.000 0.0 0.0\n", "n=4 0.952 0.030 0.003 0.000 0.015 0.0 0.0\n", "n=5 1.000 0.000 0.000 0.000 0.000 0.0 0.0\n", "n=6 1.000 0.000 0.000 0.000 0.000 0.0 0.0" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nsim = 1000\n", "ns = np.arange(2, 7)\n", "canalizing_depths = np.arange(max(ns) + 1)\n", "\n", "count_depths = np.zeros((len(ns), max(ns) + 1))\n", "\n", "for _ in range(nsim):\n", " for i, n in enumerate(ns):\n", " f = boolforge.random_function(n)\n", " count_depths[i, f.get_canalizing_depth()] += 1\n", "\n", "count_depths /= nsim\n", "\n", "fig, ax = plt.subplots()\n", "for i, depth in enumerate(canalizing_depths):\n", " ax.bar(\n", " ns,\n", " count_depths[:, i],\n", " bottom=np.sum(count_depths[:, :i], axis=1),\n", " label=str(depth),\n", " )\n", "\n", "ax.legend(\n", " frameon=False,\n", " loc=\"center\",\n", " bbox_to_anchor=(0.5, 1.1),\n", " ncol=8,\n", " title=\"canalizing depth\",\n", ")\n", "ax.set_xticks(ns)\n", "ax.set_xlabel(\"Number of essential variables\")\n", "ax.set_ylabel(\"Proportion of functions\")\n", "plt.show()\n", "\n", "pd.DataFrame(\n", " count_depths,\n", " index=[\"n=\" + str(n) for n in ns],\n", " columns=[\"k=\" + str(k) for k in canalizing_depths],\n", ")" ] }, { "cell_type": "markdown", "id": "8144c1f2", "metadata": {}, "source": [ "We see that hardly any Boolean function with $n\\geq 5$ inputs is canalizing, let alone nested canalizing. \n", "This makes the finding that most Boolean functions in published Boolean gene regulatory network models\n", "are nested canalizing very surprising (Kadelka et al., Science Advances, 2024).\n", "\n", "To zoom in on the few functions that are canalizing for higher $n$, we can simply require `depth=1` and repeat the above analysis." ] }, { "cell_type": "markdown", "id": "01301911", "metadata": {}, "source": [ "### Restricting to canalizing functions" ] }, { "cell_type": "code", "execution_count": 3, "id": "8587bb69", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:41.813974Z", "iopub.status.busy": "2026-01-15T21:43:41.813893Z", "iopub.status.idle": "2026-01-15T21:43:42.289688Z", "shell.execute_reply": "2026-01-15T21:43:42.289445Z" } }, "outputs": [ { "data": { "image/png": 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" ], "text/plain": [ " k=0 k=1 k=2 k=3 k=4 k=5 k=6\n", "n=2 0.0 0.000 1.000 0.000 0.000 0.000 0.0\n", "n=3 0.0 0.195 0.000 0.805 0.000 0.000 0.0\n", "n=4 0.0 0.575 0.113 0.000 0.312 0.000 0.0\n", "n=5 0.0 0.948 0.033 0.005 0.000 0.014 0.0\n", "n=6 0.0 1.000 0.000 0.000 0.000 0.000 0.0" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "count_depths = np.zeros((len(ns), max(ns) + 1))\n", "\n", "for _ in range(nsim):\n", " for i, n in enumerate(ns):\n", " f = boolforge.random_function(n, depth=1)\n", " count_depths[i, f.get_canalizing_depth()] += 1\n", "\n", "count_depths /= nsim\n", "\n", "fig, ax = plt.subplots()\n", "for i, depth in enumerate(canalizing_depths):\n", " ax.bar(\n", " ns,\n", " count_depths[:, i],\n", " bottom=np.sum(count_depths[:, :i], axis=1),\n", " label=str(depth),\n", " )\n", "\n", "ax.legend(\n", " frameon=False,\n", " loc=\"center\",\n", " bbox_to_anchor=(0.5, 1.1),\n", " ncol=8,\n", " title=\"canalizing depth\",\n", ")\n", "ax.set_xticks(ns)\n", "ax.set_xlabel(\"Number of essential variables\")\n", "ax.set_ylabel(\"Proportion of functions\")\n", "plt.show()\n", "\n", "pd.DataFrame(\n", " count_depths,\n", " index=[\"n=\" + str(n) for n in ns],\n", " columns=[\"k=\" + str(k) for k in canalizing_depths],\n", ")" ] }, { "cell_type": "markdown", "id": "42ce7752", "metadata": {}, "source": [ "This analysis reveals that among Boolean functions of degree $n\\geq 5$, \n", "functions with few conditionally canalizing variables are much more abundant than functions with more conditionally canalizing variables, \n", "which is mathematically obvious due to the recursive nature of the definition of k-canalization." ] }, { "cell_type": "markdown", "id": "d93bcf34", "metadata": {}, "source": [ "---\n", "## 2. Collective canalization vs degree\n", "\n", "Using a similar setup, we can investigate if and how the various measures of collective canalization, \n", "specifically canalizing strength (Kadelka et al., Adv in Appl Math, 2023) and the normalized input redundancy (Gates et al., PNAS, 2021), \n", "change when the degree of the functions changes." ] }, { "cell_type": "code", "execution_count": 4, "id": "b5cbe5dc", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:42.291131Z", "iopub.status.busy": "2026-01-15T21:43:42.291042Z", "iopub.status.idle": "2026-01-15T21:43:44.211083Z", "shell.execute_reply": "2026-01-15T21:43:44.210867Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nsim = 100\n", "ns = np.arange(2, 8)\n", "\n", "canalizing_strengths = np.zeros((len(ns), nsim))\n", "input_redundancies = np.zeros((len(ns), nsim))\n", "\n", "for j in range(nsim):\n", " for i, n in enumerate(ns):\n", " f = boolforge.random_function(n)\n", " canalizing_strengths[i, j] = f.get_canalizing_strength()\n", " input_redundancies[i, j] = f.get_input_redundancy()\n", "\n", "width = 0.4\n", "fig, ax = plt.subplots()\n", "\n", "ax.violinplot(\n", " canalizing_strengths.T,\n", " positions=ns - width / 2,\n", " widths=width,\n", " showmeans=True,\n", " showextrema=False,\n", ")\n", "ax.scatter([], [], color=\"C0\", label=\"canalizing strength\")\n", "\n", "ax.violinplot(\n", " input_redundancies.T,\n", " positions=ns + width / 2,\n", " widths=width,\n", " showmeans=True,\n", " showextrema=False,\n", ")\n", "ax.scatter([], [], color=\"C1\", label=\"normalized input redundancy\")\n", "\n", "ax.legend(\n", " loc=\"center\",\n", " bbox_to_anchor=(0.5, 1.05),\n", " frameon=False,\n", " ncol=2,\n", ")\n", "ax.set_xlabel(\"Number of essential variables\")\n", "ax.set_ylabel(\"Value\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c95e2bd0", "metadata": {}, "source": [ "Both measures decrease with increasing degree, but canalizing strength declines more sharply.\n", "\n", "If we stratify this analysis by canalizing depth \n", "(exact canalizing depth using `EXACT_DEPTH=True` or minimal canalizing depth using the default `EXACT_DEPTH=False`),\n", "we can confirm that functions with more conditionally canalizing variables tend to also have higher average collective canalization, \n", "irrespective of how it is measured.\n", "In other words, the various measures of canalization are all highly correlated." ] }, { "cell_type": "markdown", "id": "405e699d", "metadata": {}, "source": [ "### Stratification by canalizing depth" ] }, { "cell_type": "code", "execution_count": 5, "id": "dd645c01", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:44.212366Z", "iopub.status.busy": "2026-01-15T21:43:44.212288Z", "iopub.status.idle": "2026-01-15T21:43:47.930095Z", "shell.execute_reply": "2026-01-15T21:43:47.929878Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nsim = 100\n", "EXACT_DEPTH = False\n", "ns = np.arange(2, 7)\n", "\n", "max_depth = max(ns)\n", "\n", "canalizing_strengths = np.zeros((len(ns), max_depth + 1, nsim))\n", "input_redundancies = np.zeros((len(ns), max_depth + 1, nsim))\n", "\n", "for k in range(nsim):\n", " for i, n in enumerate(ns):\n", " for depth in np.append(np.arange(n - 1), n):\n", " f = boolforge.random_function(n, depth=depth, EXACT_DEPTH=EXACT_DEPTH)\n", " canalizing_strengths[i, depth, k] = f.get_canalizing_strength()\n", " input_redundancies[i, depth, k] = f.get_input_redundancy()\n", "\n", "fig, ax = plt.subplots(2, 1, figsize=(6, 6), sharex=True)\n", "\n", "base_gap = 1.0\n", "intra_gap = 0.3\n", "width = 0.28\n", "\n", "for ii, (data, label) in enumerate(\n", " zip(\n", " [canalizing_strengths, input_redundancies],\n", " [\"canalizing strength\", \"normalized input redundancy\"],\n", " )\n", "):\n", " positions = []\n", " values = []\n", " colors = []\n", " group_centers = []\n", "\n", " current_x = 0.0\n", " for i, n in enumerate(ns):\n", " depths = np.append(np.arange(n - 1), n)\n", " offsets = np.linspace(\n", " -(len(depths) - 1) * intra_gap / 2,\n", " (len(depths) - 1) * intra_gap / 2,\n", " len(depths),\n", " )\n", " group_positions = current_x + offsets\n", " positions.extend(group_positions)\n", " group_centers.append(current_x)\n", "\n", " for d in depths:\n", " values.append(data[i, d, :])\n", " colors.append(\"C\" + str(d))\n", "\n", " group_width = (len(depths) - 1) * intra_gap\n", " current_x += group_width / 2 + base_gap + width + intra_gap\n", "\n", " for pos, val, c in zip(positions, values, colors):\n", " vp = ax[ii].violinplot(val, positions=[pos], widths=width, showmeans=True, showextrema=False)\n", " for body in vp[\"bodies\"]:\n", " body.set_facecolor(c)\n", " body.set_alpha(0.85)\n", " vp[\"cmeans\"].set_color(\"k\")\n", "\n", " ax[ii].set_ylabel(label)\n", " ax[ii].set_ylim([-0.02, 1.02])\n", "\n", "ax[1].set_xlabel(\"Number of essential variables (n)\")\n", "ax[1].set_xticks(group_centers)\n", "ax[1].set_xticklabels(ns)\n", "\n", "depth_handles = [\n", " plt.Line2D([0], [0], color=\"C\" + str(d), lw=5, label=str(d))\n", " for d in range(max_depth + 1)\n", "]\n", "\n", "fig.legend(\n", " handles=depth_handles,\n", " loc=\"upper center\",\n", " ncol=7,\n", " frameon=False,\n", " title=\"exact canalizing depth\" if EXACT_DEPTH else \"minimal canalizing depth\",\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d4f400b6", "metadata": {}, "source": [ "---\n", "### Correlation between canalizing strength and input redundancy\n", "\n", "We can generate all (non-degenerate) Boolean functions of a certain degree $n$ \n", "(only feasible up to $n=4$) and compare canalizing strength and input redundancy." ] }, { "cell_type": "code", "execution_count": 6, "id": "28b56219", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:47.931765Z", "iopub.status.busy": "2026-01-15T21:43:47.931681Z", "iopub.status.idle": "2026-01-15T21:43:48.014810Z", "shell.execute_reply": "2026-01-15T21:43:48.014581Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "SignificanceResult(statistic=np.float64(0.9700304760700043), pvalue=np.float64(1.0759731607818433e-134))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 3\n", "ALLOW_DEGENERATE_FUNCTIONS = False\n", "degenerate = np.zeros(2 ** (2**n), dtype=bool)\n", "strengths = np.zeros(2 ** (2**n))\n", "redundancies = np.zeros(2 ** (2**n))\n", "\n", "for i, fvec in enumerate(boolforge.get_left_side_of_truth_table(2**n)):\n", " bf = boolforge.BooleanFunction(fvec)\n", " strengths[i] = bf.get_canalizing_strength()\n", " redundancies[i] = bf.get_input_redundancy()\n", " if not ALLOW_DEGENERATE_FUNCTIONS:\n", " degenerate[i] = bf.is_degenerate()\n", " \n", "if ALLOW_DEGENERATE_FUNCTIONS:\n", " which = np.ones(2 ** (2**n), dtype=bool)\n", "else:\n", " which = ~degenerate\n", " \n", "\n", "plt.figure(figsize=(5, 4))\n", "plt.scatter(strengths[which], redundancies[which], alpha=0.7)\n", "plt.xlabel(\"Canalizing strength\")\n", "plt.ylabel(\"Normalized input redundancy\")\n", "plt.title(f\"n = {n}\")\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "stats.spearmanr(strengths[which], redundancies[which])" ] }, { "cell_type": "markdown", "id": "53275db9", "metadata": {}, "source": [ "Both measures are highly correlated but markedly not the same.\n", "Some functions possess relatively high canalizing strength but low input redundancy, and vice versa.\n", "It remains an open question what drives this behavior." ] }, { "cell_type": "markdown", "id": "82f8adeb", "metadata": {}, "source": [ "---\n", "## 3. Correlation between canalization and bias\n", "\n", "Basically all metrics used to assess the sensitivity of Boolean functions (canalization, absolute bias, average sensitivity) are correlated. \n", "For example, functions with higher absolute bias are more likely to be canalizing." ] }, { "cell_type": "code", "execution_count": 7, "id": "2ed22a7d", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:48.015985Z", "iopub.status.busy": "2026-01-15T21:43:48.015906Z", "iopub.status.idle": "2026-01-15T21:43:54.002642Z", "shell.execute_reply": "2026-01-15T21:43:54.002390Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = np.arange(2, 6)\n", "nsim = 3000\n", "bias_values = np.linspace(0, 1, 21)\n", "\n", "count_canalizing = np.zeros((len(ns), len(bias_values)), dtype=int)\n", "\n", "for i, n in enumerate(ns):\n", " for _ in range(nsim):\n", " for j, bias in enumerate(bias_values):\n", " f = boolforge.random_function(n, bias=bias, ALLOW_DEGENERATE_FUNCTIONS=True)\n", " if f.is_canalizing():\n", " count_canalizing[i, j] += 1\n", "\n", "fig, ax = plt.subplots()\n", "for i, n in enumerate(ns):\n", " ax.plot(bias_values, count_canalizing[i] / nsim, label=f\"n={n}\")\n", "\n", "xticks = [0, 0.25, 0.5, 0.75, 1]\n", "ax.set_xticks(xticks)\n", "ax.set_xticklabels([f\"{p} ({round(200*abs(p-0.5))}%)\" for p in xticks])\n", "ax.set_xlabel(\"bias (absolute bias)\")\n", "ax.set_ylabel(\"probability canalizing\")\n", "ax.legend(\n", " loc=\"center\",\n", " frameon=False,\n", " bbox_to_anchor=(0.5, 1.05),\n", " ncol=6,\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2330fc97", "metadata": { "lines_to_next_cell": 2 }, "source": [ "### Degeneracy vs bias\n", "\n", "Similarly, the probability that a function is degenerate (i.e., that it does not depend on all its variables) \n", "also increases as the absolute bias increases." ] }, { "cell_type": "code", "execution_count": 8, "id": "f196101b", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:54.003859Z", "iopub.status.busy": "2026-01-15T21:43:54.003784Z", "iopub.status.idle": "2026-01-15T21:43:57.055557Z", "shell.execute_reply": "2026-01-15T21:43:57.055289Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "count_degenerate = np.zeros((len(ns), len(bias_values)), dtype=int)\n", "\n", "for i, n in enumerate(ns):\n", " for _ in range(nsim):\n", " for j, bias in enumerate(bias_values):\n", " f = boolforge.random_function(n, bias=bias, ALLOW_DEGENERATE_FUNCTIONS=True)\n", " if f.is_degenerate():\n", " count_degenerate[i, j] += 1\n", "\n", "fig, ax = plt.subplots()\n", "for i, n in enumerate(ns):\n", " ax.plot(bias_values, count_degenerate[i] / nsim, label=f\"n={n}\")\n", "\n", "ax.set_xticks(xticks)\n", "ax.set_xticklabels([f\"{p} ({round(200*abs(p-0.5))}%)\" for p in xticks])\n", "ax.set_xlabel(\"bias (absolute bias)\")\n", "ax.set_ylabel(\"probability degenerate\")\n", "ax.legend(\n", " loc=\"center\",\n", " frameon=False,\n", " bbox_to_anchor=(0.5, 1.05),\n", " ncol=6,\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9f1cb41b", "metadata": {}, "source": [ "---\n", "## 4. Analyzing functions with specific canalizing layer structure\n", "\n", "The average sensitivity of the Boolean functions governing the updates in a Boolean network, determines the stability of the network to perturbations. \n", "More generally, it determines the dynamical regime of the network (see Tutorial 8). \n", "The ability to generate canalizing functions with a specific canalizing layer structure enables us \n", "to investigate the link between layer structure and average sensitivity, as well as other properties, \n", "such as canalizing strength or effective degree.\n", "\n", "For nested canalizing functions of a given degree $n$, there exists a bijection \n", "between their absolute bias and their canalizing layer structure (Kadelka et al., Physica D, 2017).\n", "The function `boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(degree,hamming_weight)` implements this.\n", "NCFs with the same layer structure have the same dynamical properties. \n", "That is, they have the same average sensitivity, canalizing strength and the same effective degree.\n", "Iterating over all possible absolute biases (parametrized by the possible Hamming weights), \n", "we can thus generate all dynamically different types of n-input NCFs and investigate their average sensitivity, \n", "which we can compute exactly for relatively low degree." ] }, { "cell_type": "code", "execution_count": 9, "id": "7b0dd09e", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:57.057047Z", "iopub.status.busy": "2026-01-15T21:43:57.056963Z", "iopub.status.idle": "2026-01-15T21:43:57.073396Z", "shell.execute_reply": "2026-01-15T21:43:57.073156Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Hamming weight Absolute bias Layer structure Number of layers Average sensitivity Canalizing strength Effective degree\n", "0 1 0.0625 [5] 1 0.3125 1.0000 1.1250\n", "1 3 0.1875 [3, 2] 2 0.6875 0.7705 1.3984\n", "2 5 0.3125 [2, 1, 2] 3 0.9375 0.6369 1.5938\n", "3 7 0.4375 [2, 3] 2 1.0625 0.5993 1.5833\n", "4 9 0.5625 [1, 1, 3] 3 1.1875 0.5033 1.7266\n", "5 11 0.6875 [1, 1, 1, 2] 4 1.3125 0.4657 1.8021\n", "6 13 0.8125 [1, 2, 2] 3 1.3125 0.4657 1.7708\n", "7 15 0.9375 [1, 4] 2 1.1875 0.5033 1.6094\n" ] } ], "source": [ "n = 5\n", "all_hamming = np.arange(1, 2 ** (n - 1), 2)\n", "all_abs_bias = all_hamming / 2 ** (n - 1)\n", "\n", "avg_sens = np.zeros(2 ** (n - 2))\n", "can_strength = np.zeros_like(avg_sens)\n", "eff_degree = np.zeros_like(avg_sens)\n", "layer_structures = []\n", "\n", "for i, w in enumerate(all_hamming):\n", " layer = boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(n, w)\n", " layer_structures.append(layer)\n", " f = boolforge.random_function(n, layer_structure=layer)\n", " avg_sens[i] = f.get_average_sensitivity(EXACT=True, NORMALIZED=False)\n", " can_strength[i] = f.get_canalizing_strength()\n", " eff_degree[i] = f.get_effective_degree()\n", "\n", "df = pd.DataFrame(\n", " {\n", " \"Hamming weight\": all_hamming,\n", " \"Absolute bias\": all_abs_bias,\n", " \"Layer structure\": list(map(str, layer_structures)),\n", " \"Number of layers\": list(map(len, layer_structures)),\n", " \"Average sensitivity\": avg_sens,\n", " \"Canalizing strength\": np.round(can_strength, 4),\n", " \"Effective degree\": np.round(eff_degree, 4),\n", " }\n", ")\n", "\n", "print(df.to_string())" ] }, { "cell_type": "markdown", "id": "b8b5a42e", "metadata": {}, "source": [ "We notice that nested canalizing functions with higher absolute bias tend to be \n", "more sensitive to input changes and also less canalizing. \n", "However, the relationship between absolute bias and these other metrics is far from monotonic. \n", "Further, we notice that there is a perfect correlation between the average sensitivity of a nested canalizing function and its canalizing strength, \n", "and a near perfect correlation between average sensitivity and effective degree.\n", "\n", "To investigate the non-monotonic behavior further, \n", "we can vary the degree and create line plots that reveal a clear pattern, as shown in Kadelka et al., Physica D, 2017." ] }, { "cell_type": "code", "execution_count": 10, "id": "5ce5e7b9", "metadata": { "execution": { "iopub.execute_input": "2026-01-15T21:43:57.074499Z", "iopub.status.busy": "2026-01-15T21:43:57.074433Z", "iopub.status.idle": "2026-01-15T21:43:57.117965Z", "shell.execute_reply": "2026-01-15T21:43:57.117704Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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Y83OdRYlNz1D6nhaorYXl/VOIK9kDFpb2uv9H1sAhov9w4MCBN/aJ2U3vo3fv3vJmDJwtRf/JUD9lUH84FH2EZk93YMA6LSrd0f3o/F3TDMsb4K09BVvOP8KEzZfx/GUdhialXPFt69Io7Kyb+ZTe5p6fi6ezZ8uZRmL2ltuQofio6EfwD/OH5bLNsFq8UZ4X0/cjxPbSTVF0m78N0SvWyvv7PFXwbanIkN4QEeSsOX0fv+68bqhb8S7vlxhu00+XX1tbgQuFlYjOq8DosgNQ6rQZp4oTUZbG2VKUphwH9AMenEbQ3AVA2TAMqgmEu+QG7kTjfitPfD19JXK+TF4Vkrv4a7RaGdgUdbXD2DalUb+4SCfOGPoVtb2HDIVzRQ26zpwF/+u/Y+uPUWh3yQpBizcaCt+JACC/fX7k6tEDlzd5QaTGPatZDN6LN0P1H68xrYhE5G7VCqBVuTxyKGvpv3ex5+ozOYw3v1cVNCjhmuxrlDk2Q4YiV+lofDzvD3T8V40JPVQIvrAFQTseMLAhomyDPTf0VifOzsPPfj4YEvQM5Y6b4fkVe2jMlFAmaOD/cQ20+mGx4dzEs3PaFuwta8XU9HCSx8SP2d9+j9C6fB5dDkkGSdwmfUByu0VLxN29a5hlZOHhAcsiulLm8YHPEON3HhozFZQJagRWL4p6S7e89fnS261nEXKI6tqTMOz7sgFsLZP+TfJ6m7QaDe60bYu423cMr1Ef2Dy8vQv2zqWQw0E3A42IyBSv3wxuKFn3XwRg2ubu2Kt5ISITdLmkxif/2iHhRTSgVsuLf5lLl9543Oyzc3HCPwgnz1WBvZU59n9VX37NTDV5Yu/4406rVsmeb1HUA/H3AnT1elJ4jcaoHSN+TQMjYuFqbyW3NRotvt10EZ0ru+NEyMo3XqMmOhrXK1WW/3dCjjZt4DJsED7f1Q53VMCQfE3RqdEvUJlZZNhrICL6EAxu3iI7BzeJE4Nfv+jf66UrGue6cC4G7xmMc8/OQQMNPB5rMHajAjYvXiXJ6qsQJx7mED9GWy88xuRtV/HoRYzcV61wLkzvUgH5HW2QGXOIoFLJQM2uQQPY1a8nj0WeOIHwHTuTfY2ZyfozD/Dl2vPyfgfPvPi6ZSm4OegCnySvUakUkZBup5UFbrvE4UxBBdbVVcFJC9TLUwsTm89L8jNQaNnSNwI4JiMTkbEx54b+cwFIZe1XhfjEMgFRJ0/K+zOG1MSZWhrkiNRi+MlcKHdcN11bf5F0GjwIrsOGvbp4AnjavgcmbrmCk3eD5Xa+nNb4plUptCrnJitbZiaJF5cUQYt+26p8OXlcBDavHxMyW4BTr7gLulTJj7VnHmCT3yPsvPwU3g090L9uEYTPn5fkNT6eMAGhq1YDMXEokeAGjyNPYA41VtZVYeOTf3FxWVVMe9wcsS9/BsT6Vj4epw3F/7ggJxFlNey5yWb0FyrbunVwNVcMIs6eRun7gEMZGxy0ewHPE+bYU80SjS4poIzS9cConJygfv78jV4M/XP9VaoFlpdoAitzJQbVL4rP6xWBtcWrNU8ya2Dz+n4hpWOZtQfnwoNQfL/lCs7cC5HbA+8dQIdzW+E8dChcvAe/sfZXzk8+gZmri3xN12rnwDV1OIo/1MqfAU0ZD4Spo5Hz2iOElswLz++nI+Lo0Uz9+oko+whjzw0lRySamud2g8LGBpGHj6BAomMLckVjbR1rjLLLgSZ7dT0wgkPnzjDPnTtJnRsRD4seGf12qQuP0K6CGBopibw5X1YNzowS18BJRGxHHT+hW8spmWP6x2ZG5fPnxDqvmth8/hEmb7uGiKhY7KzWHsMGDUpyngx0RCeaGFp6+ZpKzpyFkonOUV6+jZwv74sA526PT4GEBAY2RJTlsOfGlAvu7Z8MKFWy8Js6IlIm0SY8eybP08+i0SiAHVUUOFtEgatFLXG251lcLVceiI+XeSclL15I8vyicu6UHdcxr2dluOfS5dIkqDUwy8AZUJQ8UQDQ98Bt1C/hgsoFc8l90XFqWTxRrMmVmPi1v1a2rC5oUyqxrYpC5tiIPKxuRdohZPVGWXla/zPw8OsxMHdzg+sXw3XVkmVRwTHyuZiPQ0SZ7frNK5KJ5tXIC44IbETJ/oNTELxsqQxsNOZmuFZYLCoJxKsgL2DhVrrAJl4TL/Mt9IGNSKiVzwPIqrn9lpxCn8WncOVxGGbtu2n4lgxsMgexKvDIZiUMgY0w9+BtNJh6QNbKEUGoXtDcuTIgEf/PIpcq3FKLlc2ssKSxAtsf75Q/F+LnQ/wM3P1+DML++QfPfX3xoFsLaPdN0v1sJUnO5s8AEb1J/CE1depUFC9eHJaWlnJtqkmTXi5Tk444LGVi9MMH4oITVasW8n00EiGzfkfQpRw43Sg/HkQ9RIfjWmypo8Sj1qWQc9tVWdHWu2J/nHpyCoXXHId/lxpoNXGx4cJ16EYgvratini1FmZKBfrWLoShWWhtk+xKTBcX/3cvouMxfvNlLBdLObQpgxK71xjyaNbXVhqqGht+Bg4ex556FvijtgadjmjQdeUmxFubwTweCD93D7f8iyJ/l9aIyOT5SERZWqKe9ze81nuamQ0fPhy7du2SAU65cuUQHBwsb+mNw1ImSPyX+n/UEbHXrhlmOa2vo0CCQiEvYjebuuFe34744+IfckaMmC2lT6gVgc3olzNlcmva4NLkGeh8YRuWlWyOJ+2747s2peHhYmfsl0jvSPTWrDp1X64+HhIVj27XdqPXtZ0w7++FPU0tDcX/kvsZ6JinDq4GHELpE5A/NzcKaFHsoRIK9auPDAY2ROnktUWB/3N/GmnQoAHKly8PKysruXq3WNXby8sLEyZMSPVzXb16VT7XpUuXUKJEiQ9uGxOKs5HkitQFzZkjAxuZV6PRQKEEzMtHouBpS1h4xqHdrP265Qj0VXYrwJBQK3psAl7WOLkbFIWFRRrB0lyFjkWdULVvNaO+Vko9MWT4aY2CaFM+D37bcxPqa1oZqK4PKY4Wj8//58/A+Maz8PeLQtistUcslDjaowj6/HwbipfxTc6PPjJ6gUOiLCUuMuVjChVg/rJelQhc1HG6QEZ8rTMCODIDOPQrUO9/QK2h//28Fu+3dt/SpUsxcuRInDhxAseOHUOfPn1Qu3ZtNG3aFC1btsThw4dTfGzBggVx+fJleX/Lli0oUqQItm7dihYtWsg/vJs0aYIpU6YgV65Xw+fpgT03WdzrpfdfbN6MR6NGG45rRF6NGnAqGwbXCrGAOj7FiP/xi2i5GnXx3PaGZNS1Z+7jk6oFYGHGnApTcPNpOCZuvYIT/sHYO7K+ISk8RS//SoxQmuEPBzu0vVsRCduvv1q6okolePy13GhLUxBlORMcUj5WrBnQQ7dYrzQpDxAflfy5BesAff95tT2lCBD1/LXv9eK9em7UanWSAKZatWpo1KgRfv75Zzx8+BDR0dEpPt7c3FwGOILo8VmyZAk8PT3x66+/yucdMWIEHB0dsW/fvlS3jT032Yj+IiIuKubnb6D6LzugrzCzq54Fhue9i8BLdjLnRtFoKFzKROj+EhBeBjhiNs38Q3cw58BteLja4m/vOnLxRlGrplfNQsZ6aZQOiuW2x7J+1XAnKDJJYDN7303ULuqMigUck+3+tqv3P/Qc1R1B2/3g3K4itjb3hPWvS1Dh9FkcnDgEV9qXSdobSERZVvny5ZNs58mTB89ezrQVCcHvSqPRIDY2FsuWLZMJxcLChQtRuXJlXL9+PU2GqlLC4MYEiItJvP9dlJ/wN1QvV0nY38AGvfLeATSAS/c2wJMKupwKkSMhem72T5JdhDucemHStqt4EKKLxK3NVQiNioOTnaVxXxSlG1GjKHHe1Jl7wZi664a8daqUH6NblIDruZlJxvVlcvkWXWDjYvMPuj2ORbPeudBoXwi6rtiL/ff3wdt7KAMbov/yzaO3D0sl9r9br4aiVBa64SkxJCWGqES+QWJfXEyzJpqLWZSJm6VQyEBFSM2wlAiKzMzMDIGNUKpUKfk1ICCAwQ2lUMfmpeCYYFy8dxJ11ECUObC9mhLfud2SgQ1KtAI6zoOL/mQxHVhcrMJjcPD0PXwVdFbuzuNghTGtSqFt+TyZbskESl/ujjboXDk/1p15gPVnH2DHpcdYUjgQFeuPgZl++DJxAcRl7WF1aw/2upRE1bpmKHs3Di1OaxG61Q/wTPrcrIFD9AF5MMd8dIGNPpVA35sqAp3XUwveM78mtUSS8X8NS+mJPJ2EhATcvn0bHh4ect+NGzfkV/3QVXphcJOF14cSF5qYhBgM2zcMRS89hVU8sLmmGVbXA5wj3OBVohvQ5FWGuz4gOhcQgk5HK0OjBSzNlBhY3wOD6ntkyiUTKP255rDC1I8ryMTjCZsvw+9+KD6+3gAFg2zwresTNC2dO2lw0t4HmN8YC+MfQa3NiXBbJRzua+Dw1yEcKvAL6vXS5XxxTSqiD5DcrCj919dSCzJSvlQMS4nk4UqVKqFfv3747bffZO+Pt7e3TExO3JuTHhjcZOE6NtBqYdmyCapu80ezwxpc7eiJ0T+thMPLxE4450ZygwQV8ueUZfvzOVpjTMuSmW7VbjIOT/ec2DCoFjb5PcTP26/h3vMofLPxEuoUc5YFAg0c8sO3Rjf43F4P75BQ9O3bHrt9jiF/QBQcJy/B+fyFkfdaEGvgEH0IWccmmckf+m1xPJNTKpVyxtTQoUNRr1492NraymGtadOmpfv35mypLEr/V7F+1srV9mXQccR4wK3cGzNXyth0gu/B25jXswrsLM0MM6HYU0MpiYxNwJwDt1DM1R4dKur+UhMfFWExCVh5Y6HuZyt/M3gdWSQWLUNCg29x9Lu/4BoUb/iZZGBDRGmJyy9kA4HW8fKrXB9KqUDHoiHAwubA7f1yv0js7FH8c2zye4CeC0/i6K3nckaUHgMbehtbSzP8r3lJQ2Aj/O33CA1+3Y9z94MxqPxgeDWeBrT4RR4zOzAJlad9aQhshFzduxup9USU3Rk1uDl06BDatm2LvHnzyiTWTZs2vfX8DRs2yLE6FxcXGbXVrFkTO3fuRHZz8u8/oP3FV7ehVEKp0SJw5zVAZS6HDCJiE+SwwqKtRXHtak25ZEK/2oXljeh9bTj3UFY53nmkAjYfLIN/bwcB1T8HaogVx5WI3nzYENgItz7ujDgxu4OIKDsFN5GRkahQoQJ8fHzeORgSwc22bdtw5swZNGzYUAZH586dQ3Zx/dQuWH0zQ/7HBefPgRLTO8C5bJisYxOo7ob196zRcOoBOQwVp9agbjFn7PiiLsa1LQ0Hm6TT+4hSY1HvKpjYvgwcrM1x7Uk4us8/gUF/ncH9Kt8g0NIbQeuPyqGown//Da29LTT3H2L9N5/I4SwiooyUaXJuRM/Nxo0b0aFDh1Q9rkyZMujatSvGjRtn8jk3T+5dwcN2nWETq0WoowUqTR0Iy926hdMCNT0QtGY/TjTojAk5a6CQkw3GtimNRiVdObWb0lRIZBx+23MDf50IgFqjxac39qDHlR2vcmyigvHvw+PY/esodDmkxp2Pq6P1D0uM3WwiyuKyTYViMa0sPDz8rWtUiOqI4pb4zclqtWxm7L4BDWLhsHYwasdqEWcGlPx9DCy3644fyDsADT6fCrjNQb3IWHxTvSR61yoESzPm1VDac7S1wPfty6J79YL4fstlaK+qEduzv+7nNfgOgv9oj4IWTig7ciwu3Z0Aq8MnsG/JD2jUZyxm7r0pA6IRTYuzBg4RpZssHdyIJdQjIiLQpUuXFM+ZPHkyvv/+e2TlWjYKhQYLrv2ATzS6dUNsP/4IOfy3AVo11ibUw/yINmjw8lxRrO9zIzefsocSbvZY3r86/JqXgKd+2YaEWFjHPUeumACU2bsBd0uWQcFdl6H+ZQVmvLDB749LYuTLwIY1cIgovWTZ2VIrVqyQQcuaNWvg6uqa4nljxoyRXVj62/3795HZiSBFfOiLD39xEWhYPgZdz19BlyNanG/RDLc6DUPVq10xMb4nvknoD3trC7k+FFFGE0OeidejemRRCIPjv0C8VoWSgTtgUyYfgvPaQaUFGv6xAMNKvkC367tZA4eI0lWWzLlZtWqVrHi4du1atG7dOlXfJyvl3Oj/uhUzoqDR4HSzOhhr094w2dbWUoVJHcqhvaduthmRsT0Lj8HP265BdWE5fjX/Q+4bFdsPbXbvhkuEmjVwiOi9mXSdm5UrV6Jv377ya2oDm8xMrKgsCu8lZqEvT63RyFo2Pau/wGTzRVBBDaUCOPlNE1mHhIENZRau9laY3tUTn3z+DdZa64aLJ1ksxcJG7QyBjfjq1K/fG48VP//i94CI6EMZNbgR+TJ+fn7yJvj7+8v7YrVQ/ZBSr169kgxFiW1Rurl69ep48uSJvIkoLqtTKpSy6qs+wLl85G8EvMxH0Cigq2Wz8Sg6KA+juOqxXBdq4RF/I7eaKHmVCzriUaUvsVldE+YKNUbd3mwIbMTXs20aQ6N+NZSqr6gtfg+IiD6UUT9JTp8+jYoVK8qbMHLkSHlfP6378ePHhkBH+OOPP+QKo2LhLbGUuv42fPhwZHWiorBYKkF8wM/ePh5xg8fATAM8zgkc/rmGoZbN2WdtsX3SQJmUOX33DTn7hCizET+XM/bexv16U/EkuD6Ul9VYVrI5Tn/xEzQKBWwfBGPB8KZvLBUifg+IyDRMmDBBjiy8fhNrTGWbnJuMktlzbuYcmYqKwxYiZxQQagOcndAAg8+uhAJanH7YFLaHLxvyFcQFRAQ4ItAZ1riYsZtOJCX+uUycPLyyRFO5f5j7bYSf85UJ8qvrqrC+joKBDdFrxBCt6MlM7vdC/EGg0Wow2DNz561FRETIW2KNGzdG1apVsWRJ6mtfZZs6N6ZGxJllZu6UgU2UBTC2nwX2XNgoO/Mv5OmMKuMXIHDuXFkbRNAHNKJuCFFmIX4e9QF34JWdhmB8GIBST7egQPC/GN2gM7SK9VBqNHAJMUdF+4+N3WyiTJmqICQOcBL3dKaHBg0aoHz58rCyssKCBQtgYWEBLy8v2QuTWnZ2dvKmd/78eVy5cgW+vknzS9MDg5tMUqhPCAgPwKJSTzD8KvBvaSWe2mvgm2AOL5e6KP/JPDGl7I0ZJuyxocxGFOjTS1Kg78UDNL39M6CORTM3LZ5rtPC8o0WbU3H4+uloFCs3GGNalkR+RxsW+COTFRUfleIxlVIFS5WlIaCJV8fLQEZ8/azcZ1h4cSH+uPgHPi/3OfqU6fOfz2tjbvNebVy6dKlMEzlx4gSOHTuGPn36oHbt2nL5o5YtW+Lw4cMpPrZgwYK4fPlyssdEsFS8eHHUrVsX6Y3BTSYp1CcM2TsElR9pIBb8/qSeN8zd78AHO4GSdeGl4n8VZXEO+YEOc+C7dwTmRt7AeCtXFH38VB4at+covrKyQOMrbTEz/iwK/P0XC/yRSaq+onqKx+rmq4s5TV7NGPzz6p/yqwhoxE1P3D/77CwWt1hs2NdifQuExIYkeb6LvS++VxtFz8348ePl/WLFimH27NnYu3evDG5EgBIdHZ3iY83Nk1/DMCYmBsuXL8fXX3+NjMArppHoAxoR4MTd8cf2Rg6ovO0Ouh7WQPX5p/K47Ig8X1TXNWlmwZwEyvJ8NUHwccwJ75BQdHZ9gLWNK6Ps3odwCgfG7tuPU3kCUMDvNuvgEBlR+fLlk2yLiTvPnj2T9/Ply/dezynq2Inlknr37o2MwODGiMSHtyYyCsELF6LWVt0UWUWr4ijep7vhHH1AI5LHiLI68XMsk4fvXgTO/YWG+a/iz2pOaHEyHkWeAkWe3obT0FeBzdFbQXIV8rL5HIzddKI0caL7ibcOSyV2oMsBw1CUudIc8Zp4OSQlhqheL5uwo9OONGuj+Wu9L2KGk1jLUXjfYSnR49OmTRvkzp0bGYHBjZGpQ3XdiDKwMVOiZI4DwKLmwNCzgKUuEYs9NmQqDLM7ysYDoffh7H8QFarmAM6ogJd1bxxatpBfo+PU+GrteTwJi0HXKu74qnkJONvp8hGIsqrU5MEsu7JMBjb62YT6ZGJzlfkb14X3za9JrfcZlhI17Pbv34/NmzcjozC4MaLoS5fxYv0G3YZKCW2CBoGX7OAy6n+GwIbIJKnMgS7LZCBf7m4RBKn9ZMI8tFrcHzwYRXfskOulVSucC3/7PcKqU/fxz4XHGN6kGHrVLAQLMxb7I9OWXP0n/dfkZlFllHzvMSy1aNEiObQlen0yCj8hjDjt+8FQXcLkXRfg12HxhkJ9gafjjd08ovRnnROBmu4I2uInc2yKbPsHGgd7xN+9h0CfOXC0tcDvn1TEOq+aKJsvB8JjE/DjP1fR4vdD2H9dN/5PZPJDuK8FMPqCr1klVUGj0ciaNmLGlUqVdNgtPbGIn5E8+GIEwnfsQIISGDpIhZ8jn6FGoaYIfF4LQbNmM6GSTJ5+YVj9z/ri8/Mw49ws/O9yEVTZcjPJ74ConbPuzH38uvM6giLi5L5/htVBmbzMxSHKLsJYxC+T2j8ZUKqgqT4MEUeOyF0bailRQRWNGuZOgHMJuHzireuef1moj8hkqTWvAhh1Amrtn4HfcpphSll//OXSCdqEBMOpqsO/oqtGjZZffYXZ+27hyYuYJIGNCH5UYjVZIiIGNxlMZMLvnwTExCOyRQ2E7dmD7dUVWBuqBiIfAeZW8jT22FB2kKRAn8oMJZzLoHPIGayzs8Pup3vR4YI9cvXsCbML83W/Nw2/RQ4rc3zTqpQc1tUTgU6Xecfg3dADnSu7M8ghIubcZKj6o+QHtPrYFIwvdQYjB6jQxakU3CND5H55nCi76rEO3laFYKfWoMypUMTfv4+gr/sZApvEvx9iaqreoqP+CAiOwuj1F9He5whO3Q020gsgosyCwU1Gqz8Kqyp1xL2EcDgoNPj84m4GNkSCQoFc/fZgYIIFljTRfTSFHLqKmKKfv/X346tmJfBd61KwtzTDpYdh+Nj3GIatPIdHoSlPVyUi08bgJp3Xj5Jr5LwU7eeHez17oYn7AIzdF4MfdkfDTmnOwIZIT2WGbr32IyqPGg+cxLRCBZ6uPp5kGEoQv1dyfTZATgvvX7cI9v+vAbpVc5cpa5vPP0LjaQcx98BtI70QIjImBjcZsH6U+CDWajR48tNkRJ06hehR/0O5E2YoKYqWqeOAg1OM3VKiTMP81Hz8LzgE1wrrtqNuBiFi3z7dhlZrmGUlfr8SEwX+Jncsjy1D6qBqIUdEx6sRGq2bWUVE2Qungqcz/QexfdOmCN+9GwpRrE/MEmlXES5TVugCm2RyCoiypZe/D9oG3yCmzjA87dAC0beeQWljgWLHT+H5yPYI2nMXzoP6w2X4lyk+jfhY23bxCeoVd4a9la5i6vUn4XJWVem8xisBQUTvj1PBMxEx80mboMbzl8NTIrCxbFNGF9gI+oBGBDiJt4mym0SBvqL+KFgDcF+1DTdr14AmKg7XPT1FZTNZ7NIlZjZwygGo1EcOZb1OJBy3Lp8nSbDzzcaLOBcQgm7VCuDLZiWQy9Yig18gEWUUDktlAIv8+Q3341WA1YSZyc6igka3tg5RtiR+/l/rwVTa2uDBxAFQi08qjRYKMzO4NHQHooOBf74E/qgP+Ke8iJ9eVJwaeRysxFNg+YkANPh1PxYd8Uc860kRmSQOS6Uz8fberFsP6qAgqBWASgtWHyZ6R2FxYfAZ3gAd9kdDY6aCMkEN5yHecKlmCez7EYgJ1Z1Yqh3Qehpg5/rW5zvpH4wJmy/jyuMwuV3U1Q7j2pRGveIuGfFyiCiDrt/suUlnj8eOlYGNWGbhm6/d4ODtZUgyJqK3i13wlwxsVtdVwus7R9j264mg2T669deGnQOqDgAUSuD+CcBcDGS9nViIc8vQOpjcsZwclrr1LAK9Fp3E/mtcq4ooPezcuRM1atSAvb09XFxc0KlTJ9y9exfpjTk36UgEMC/WrcfpEma44abBgDojkdejrVyuXs72YDViov9Mxs811Bvn8+1B9+U3EH5lOXJ1+yTR789UoEpfIPwJYGmve6BGA9zaDRRrplvK5DWigrHIu2lVLg9m7r2J03eDk/TciN7WxEUCiYxBljpQKZO9Rsg/jtWapFW+MyF/f3+0b98eI0eOxPLly2WPy4gRI9CxY0ecPXs2Xb83g5s0NMdvDpQK5atVXNUanG9fGlNK30BumzxwCwuQuw0/rBzvJ3qntadKHn4I84QbUKo1CAt/Lvfrf398nxyWKyQPRmPd4y6uBTZ+DrhXB1r+AuStmOzTO1ibY2yb0khQa2TAIy4mCVBgsMoT3asVwDPVZqiUKvn7fK9Xb4jx+0LLluq+53lf3ff0HPzGscSfA+IiFHnsOGxr1pCvI/HjstJFioxXSkRIHOAkXnA2PTRo0ADly5eHlZUVFixYAAsLC3h5eWHChAmpfq4zZ85ArVbjxx9/hFKpGyj66quvZMATHx8Pc3PdTMb0wOAmDYkPNB8/H3lffLDZevXDsi3bgHDgadRT+UGpxx4bordLfMEvmKMgtlVRovZVNeJ27IHjoQkwy5VLBgvid87b0/vVA+PCAXNb3VDVHw2Bij2ARuMA+9zJfh8zfb0clRKhM2ehZMnm+F9AU7gXeYhQyy0osP4ECp88abiwrK+tNHxPsR2V6Jj4vdZ/DsjHrTkOmxrV5cXo1JNT8PE4bWhrel+kKHPSREWlfFClgtLS8tVM2/h4+TMivjoPGICg+fPxfK4vnAZ5walfv/98XqWNzXu1cenSpbK35cSJEzh27Bj69OmD2rVro2nTpmjZsiUOH045ib9gwYK4fPmyvF+5cmUZ1CxevFg+R0REBP788080adIkXQMbgQnFaUz/YTu01OdoNv1f+HnmwATXo/CqPORVjw4RpdovJ35G6dFLUfQJoPm8Gw43djUEGW/8boU9AvZMAC6s1m1b2OtmYVX3AsxSngL+ZLYPQmbPxqqyLbG0aGN8en8eepy5iesdq6F2fl2QIvJ/3IYMRaejmiTBif6+uChtG9dXBjb+XWqg1cTFb2wnDmz4h072crVkqRSP2davhwLz5hm2r1WsBG108suI2FStioJ/LjNs36hZC+qQkCTnlLp29b16bkRvS+IAplq1amjUqBF+/vlnPHz4ENEptEkQQYsIcPQOHjyILl264Pnz5/J5a9asiW3btiFnzpzpev1mcJMORIBzbcksDNyuwdOcwLW5Q+FVkR9gRB/q98md0GzpFQTbAd6DVf/9R8P9k8D2UcCjc7rt0u2BLq8uCMnRBx5qlRlU6gRcd3FAgvULKKCA8wstXF9ADkOJrJxgFyss+NZTPq7mzgeou/2BLs9Hq0W0sz3u2ITLx2mhRZGYHLB+FgaFubnuL3EGNtlSVghuypQpAx8f3SiEIIaRnJycsGjRolQ915MnT1CvXj106NAB3bp1Q3h4OMaNGwczMzPsFkVtU5nbxiJ+Rjaw/EDsPq2rZbO7ihkmMbAhShNDv1yJE+sqIFcEUOuGEiWblkREXATsLOySf4B7NaD/PuD8SmDv9wi8kQd4OXwk7Z8MiOHi+qMQ6OODmCtXoY2PkwGIKj4eahWgMlehhEyXe/V3oP4j2SosBqefnpb3T3sCdXbIvxjltnVQOMrIe7ptjTIcMFPKwEY8v2PXrkmTRkURQ1nrZ4w8n/k4pqnE2TMpH1S9Sl0Qih89YhiK0gfFYkhKDFHhZQ6LXtG9e9KsjeavDRmJIEQjEvWBVA1LiQBJBCNTprxaYuivv/6Cu7u7HPISs6jSC4ObdLB6xXeoEKhFjDmwp5wW7ud9OSRFlAb+uLoITysq0eWIBg3PJmDYvmFwsnbC8ErD0c6jncx3eYO4CIi8m7KdgPmLXiVplosGbu8DHpzE47+OIvTwjSQPEwU3zdXAA6dQbKmmhFKhQtWrCah1TQu1UgmVRoOHpUrh1/qfy/Mdlu+CQrsdCQolzLQaPK1RFCvc7rwMhbSodk2L2tc00Cq1QHw8bjVpCvO8eRB3+w5w9whcbP7RFTFkPo5JS00ezPMlS2Rgo+/l0/9ciEDn9V6/982vSS2RZPxfw1J6UVFRhkRiPdXLAE4fLKUXBjfpMCRls2qjvJ/n427oW0OXFyAwwCH68Hy2L3r2g2sNB9wscBvax1sRFB2EsUfHYvW11fi6+teo4FIh+ScwtzJcEGSAUz4aOQu/wP1DrogN0QU2+kKBa2srsLaeCj1PWKHtvggULFUDVd2qImijLufGr8HHKL02FD39duLa7ydRp5gzgv7cjmUlmyPPUG8UPfiTzLHp0KUGWn6/CMtHd0DlazfkY9fXUWLChjiUvh6tC2yUCgRtPgdtqxZwFT1IzMeh1wJc/c9Bkp9fI01MyZcv3zuf27p1a8yYMQMTJ040DEt98803snenYsXkZzGmFQY3afzhu+bAbMy+peuGdvz0U3gVKSLvM8Ahen+JZ0V9Jn6H6gPfiN6Sc/nhe8EX5kpzXHp+CZ9u+xRtirTBF5W+QG7b5GdHJb5ABF14VfjvmbMGrkGQAciBulZolL8O/sQ+lLUrLQOVIByHczMP5K6txO2Y9chbzxGPlE4ouX0lgrZDBjYV+jREaNCXGO3hj18a5pKPCzhTG5Vvh+B2Q0esrxEOM4UZVn+SC78tv4MXt+zkshLC820X8HxXOSAhgYENJSmFkFhWKiXSqFEjrFixQg5LiZuNjY1MKN6xYwesrf+76OaHYEJxGhL1LYr+eQTu/5yDbZ06KLBgvuHY6/UtiOgDakgl4nt2DiLUUXKphk23NsnkXRdrF+zstFMWzEyOOjwcN6pWM2zbtI3BX8HWcg0ru7KR+LzpTCyLe6j7nhp73Bs2VlfLpvFz3ffMmQMaURMn9AV27SmPYK0DxtQdhO1Nn2Pfxe+ghBZeoWEIvGSHyKeWsM0dC5eyEfCt0QNhuQqhQ7EOKD6rJgIvWCEqzBwhEY6wDI7RNcbMDKUuXUyvt5Ioy+JsqQwMbl6vIhl15gyeL14skwWjL15kQiBROhC/d/GPHiLO/y5sa9c2/I5dDrqMwz8Og4d9YTT9YYEhKBJJ/olnZjzz8cHzWbOhUSqgFCuNty6Dk25HUTYuAQXj44Dqg4CWP+tOfnIRuLEj2XYcvfUc424WwW2trqveQ/EQv5ULQLn8Dsk3vHgLwK3cqxXQocDcnPYIvGiPj4+++ih+/S92/nFEBM6WMmYVSZvKleWNCYFE6UilxIuNm+TduPv34TTwcygtLOC65iDq73iEXEM/ksf0BfX+vvU3ZjaaCQ9rd1yc+SMsFq2Xw0/o+zG8N92QOS/V2jWEy5QVrwIPm1y62jgiGBG314ilG6bfuIGRTYujV82C6Lv4FM7dB3Y41UO5eiVTbrv++UXycN0vUW5QHTgdDZV5PnHmCrgkKNEs0WdKsoUKieitGNx8oOQSvJgQSJS+5O+VWoMgHx+onz9H2JatiH/65I3fO9Fjs/r6ajyIeIABf3XEjIVaWMWoZWCzpZ4VfgoN1M1SatdaBjgoJKaJj9J9E9mzAl2Ak1xgs1sX2AxrXEzu2+hdG9N2XcesfbdgaabC0EZFMXTlOTQq6YoOnvmgVCqSBjYvk4edDoYiR+vSsC1wGusd7KFRAKEKJbrMnIUTD4/Bp7hf8oUKiShFHJZKI4mn6LFAF1HGuNe3H6KOHTNsO30+AK4jRyY552HEQ4zc6oU+c26h0DMg1AaYPa4cZrXwRa5j817VuXm9rsxrdWcSm7H7hlyPSh/YvB74qDValMpjD6+/dIsDViyQE+PbloHnrbmG7ye8Xufm7ou7GBJyAgGaWPzwpxo2scDt3wfDq5L3G3VNiLIb5twYKaH4WrnyhgJdJS9eSNPnJqI3aaKjcb1SZVkRWFA5OMC6ahVYlS5t+ONCm5CA+4MGI/LwYUSbAwc8VRj556V0b1tsghqLjtzF7H03ERmnlvs6VcqP0S1KwDWH1Vsf2/7XCpi0KA4qLZCrUTHkrvAC6haToSpYSx5ngT/KjsJScf3mnwJpRHzY6AMb8VV++BBRuhLJ+zKwMdONsKtf6NZGEL2o8ndSq8WTH36UgU2CErCOB8KstDKPJb2JoalBDTyw76sGMqgR1p99gIZTD2DugduIT2Eqr2jbHVcNTpfQfTwH77uJkMM3MG5LD4z6qz78p4zTDYPrF/wkojfwtyMNJM6xET024qv+w5WI0v/3Tkyddh6iS7i1Kl3K8Dt4p207hK5eDRFGmGl0s5DEopciQTcjAhwhdw4rTOtSAZu8a8PTPafsxfnb76FhCYfEEicP99l0GSFldEHR49M58fCpDWwOBiFm0Vr4N80L+77dMqT9RFkRh6U+UErJw0wqJko/7/J7J3pQRel6vcTnJg4iMjJRV6PRYpPfQ+R3tEG1wrnkvph4Ne4HR2Hvk+VvtEl8PJ9qWQ/2d4MMi3VuqKnAqgYq5FUDX1YYjKaVvFK9ACFRVsSp4BnJBKpIEpni753jJ58gyHeeXMjy9bV49MGDqB2TkcSMqY4vh6j0Fh7xlzOvKld4gv5lBiUJtkTQUnXzXlyt4GlYkLPaR+1gvWkzwlQKfKmagyqBJ1EyV0k4WDrIx97r1VtXcHDZ0jdq5DBXh7ILBjcf6G0fEuyxITLe7524kOsDG30eXHIBjrHdehYhZ1edPFcVN6+bI1fCPXSvVkDOxhKCFizQBTYiryghAZ4PCqBshc8QOncBckUpsaGdPyq6VpS9PgXWHEXhk7pVysXrXV9baegNYu0tyk6Yc0NEJicr5cHN6OqJvz6rjuK57RASFY+xmy6h9czDOHb7+Zt5RS9fh5m5NRw+6oCmZxIwe5EKA545YPqWKBRefxqXauaEQ/eu8rwns2fJwKbTUQ2HySlbYc4NEZmUrJoHl6DWYPmJADlE9SI6Ht2u7UavaztTfB1i2YnIf/81TIN/3cYaCnx0/FXPVa7+nyH3V19l4CsiyqZTwQ8dOoS2bdsib968cmx50yZdOfW3OXDgACpVqgRLS0sULVoUS5YsyZC2ElHWz8eRQzKZNA/OTKVE71qFcOCrBnI5BwulFmb9vVJ8Hdaenij89yaRmGM4prY1R7gV5G1LdSXUKsjARghdtRr3+n2GwFm6auqSrJg82RA0yaKCRCbAqDk3kZGRqFChAvr164eOHTv+5/n+/v5o3bo1vLy8sHz5cuzduxf9+/dHnjx50Lx58wxpMxFlblk9D87R1gIT25fF88ZT4GRnadj/685rKJ7bHu0q5E2SVyR6bvS9MwGtK2O0x2n5V+tHRzRQqYF4JWCuATQREYj69195iwu4j3xtnA1LQTAfh0xNphmWEj03GzduRIcOHVI8Z/To0fjnn39w6dKr6qKffPIJQkNDsWNH8qv2vo7DUkSU1Vx6+AJtZx+RI1CVCzpiQtsycNu8PMkw27ZxfVF4zXH4d6mBqm5V5TGxhtb6Okp0OqJG18NaKCzMoI1LkM9pbhcP9/91Qdjz/Jl6uI4oyw1LpdaxY8fQpEmTJPtEj43Yn5LY2Fj5hiS+ERFlJUVd7fBVsxKwsVDhzL0QrBw6XgYkNgMHG1YOFz02IrARAY4+WHHz1vVi7WmcC7Eti8nAxto5VvxZi/gIc9wZv5GBDZmkLDUV/MmTJ8idO3eSfWJbBCzR0dGwtrZ+4zGTJ0/G999/n4GtJCJKW1bmKng3LCqXcZiy4xoUVzVYVrI5toQWx7BDtxFvp5azolr19sK9u7o6NyJYkZPdFQokaBLg2WUQAu8XALQKHGqiRpXVNiLGgcbs5cKdr0lcH4coq8lSPTfvY8yYMbILS3+7f/++sZtERPRe3BysML2rJzrO/B5XmnRGRGwCfA/eQa+Snxvq9hRcttRQwE8Q+4dUHAIcngaXshGwKh+B+w9sZWATrwKUCRr8M7ZPku+jr+CsVJj8JYJMVJbquXFzc8PTp0+T7BPbYuwtuV4bQcyqEjciIlMh8m42Dq6NDecewlylgIONudwvUigfhETDPZdN0gfIWVG65OGYXTfQ8chRHKypgU8DC3Q6okHXtSew81p9NJq3EQvvrzHK0hRE2Ta4qVmzJrZt25Zk3+7du+V+IqLsRCzl0Lly0qUctl96gmErz6FXzUIY3qQYHKzNkwQ2gZftELT+KJxblcbAHHuQ/5kNZtTNizL3olD24jMca1EbfwxUwbvKEAY2lKUZtc8xIiICfn5+8qaf6i3uBwQEGIaUevXqZThfTAG/c+cORo0ahWvXrmHOnDlYs2YNRowYYbTXQESUWYiqxgkaLRYd9UfDqQew4kQANOoEGdig/qhXNYCmroWidHu0iYzCloAHCBvYBrFmgEsYMHmJBgPLff7Gc7MODmUlRg1uTp8+jYoVK8qbMHLkSHl/3Lhxcvvx48eGQEcoXLiwnAouemtEfZxp06ZhwYIFrHFDRATghw5lsbRfNTm7KjgyDt9svIg2F+vihPtnhhpAMnlYqQQ+mgfkrwqbSr0R71EEP3dRQq0ACgRqcbxTsyTPq6+DAxVzcChryDR1bjIK69wQkamLV2vw57F7mLHnBsJjdHVtBjfwwKgWJZOeGBcF36vLDDk2n9xxw+MxY+ShwCpFUO+vfzL9shWUfYSZap0bIiL6b+YqJfrVKSyXcuhRvQDEAuO1PJzfOC9xYONVph9yugfDeZAu18bl9B1cLlOagQ1lSey5ISIycQHPo1DA6dUMqlUnA2BraYYAzUaolCp4lR8ILP8YuLUb2lrDsXPFSRQ4fg9y1SpzM5S6eNGYzSeS2HNDREQGiQObZ+Ex+GHrFQxdeQ4HT1RCHeduusU3y3aSxxX//g5PtzwysBF1cBCfgHu/TzVi64lSj8ENEVE2ksPKHAPre8DKXImTd4PlmlVjNlxAUNGOQP2vEXjJDiGbjsOuW1N886OHXJ8qau5CPJw+zdhNJ3pnDG6IiLLZUg7DGhfDvi8byBXGRWLCypP35dTxHdvVCLqUA85lw+BuvgFzKozAhYo5EWYNhP2xAE9nzTJ284neCYMbIqJsKG9Oa8zsVhFrvWqibL4cclbV0RuBUPXrD5fWFYC4cBTYNAzjC/aGVZzuMfd2bTB2s4neCROKiYiyObVGi3Vn7iMwPBZDGhUDooIRPKsBbOOCYNlrPQ4dPACXn5bJc3N/9x3+ylNNPmZE0+Jyn5guLgoEijo6ROmFCcVERPTOVEoFulYtoAtsBJtcWFxwCtpFjUXnbVp4dvkKNrV0y9w8+XESjvy5ST5GYIE/yoz400hERG/QOhbGdW0BnL4Xgho/7cWFz4bhhbsHFNBi3MklaGJ9nQX+KNNicENERG/4qnkJLO5bFY425igTfxl1drXGrioFEJrLASqNBuj3PwY2ZDrBTe/evXHo0KH0aQ0REWUaDUu44sQ3TVBRdQuOigh8Z7ECmlG9oFFA1sFJUClg3f/V4saC73lfzPGbY7Q2E71XcCMSeZo0aYJixYrhp59+wsOHD/lOEhGZKN+Dt/FHQmusUDeCUqFF4b9+gVKrK/BnptZizZiPEa+J15173lcu56BUcFCAjCvVP4GbNm2SAc2gQYOwevVqFCpUCC1btsS6desQH6/7AScioqxv5t6bmL77BkY2LYEu41bj3JVieHHJBg4V4rFpTltZ4K/mP3dxonUD+PrNfbVOVQXd+lRExvJe4bWLiwtGjhyJ8+fP48SJEyhatCh69uyJvHnzYsSIEbh582bat5SIiIwQ2BSXRf9C5i+A1YVI2FQyR95SgfA+sRvmjWpDA8DJPxg5x8xiYEOZxgf1HT5+/Bi7d++WN5VKhVatWuHixYsoXbo0ZsyYkXatJCKiDCXq2OgDm5c7ZPJwwbnbEGHhDKeoO2gbbYk/m4gFqIAK/lp0f1zojecRM6oCZ83O6OZTNpfqIn5i6Gnz5s1YvHgxdu3ahfLly6N///7o3r27oajOxo0b0a9fP4SEhCCzYRE/IqIP9MgPR1ZMxgC4wcxlHyYtVaPYIy00SgUKL18Om4oV5WmcKk7Gun6bpfbJ8+TJA41Gg27duuHkyZPw9PR845yGDRsiZ86cqX1qIiLKCvJ6YrNnNZg9XILYwKZ48N1A5P2xD2wfheJ2714osfUfvNi6lYENGU2qgxsx3PTxxx/DysoqxXNEYOPv7/+hbSMiokxIzIra/nAJaufqgZ1XywD7foRiSE9E/7IA1i+icatZczlVnIENZZmcm/379yc7KyoyMlIORRERkWnTaDUyedi37deYUfI6BpttRp5LE/BlbzVEnoMIbBTm5gxsKOvk3IjEYZFI7OrqmmR/UFAQ3NzckJCQgMyMOTdERGlHnZCAC9PbomLUv1h1xw0VTiplcT9RA4c9N5Tpc27Ek4o4SNzCw8OTDEup1Wps27btjYCHiIhMm8rMDCUGr8L1fnVR4UI8NtZRYmVdJWbfqw+IBTVF+RAGOJTB3jm4EXk0CoVC3ooX1y1zn5jY//3336d1+4iIKJOLXLYcmgvxyFUZcC/9AoAjFtqdxXd53HQrhjPAocwa3IhcG9Fr06hRI6xfvx65cuUyHLOwsEDBggVlET8iIspmXtbAcencEJ/Mq4c19vFocCgU6sdamLvnh1at1p13cAqgUQMNxxi7xWTi3jm4qV+/vvwqZkEVKFBA9tQQERG5DB1iuG9ethNG3diI8Q1dUPmmGrj/ANalS+sCm/2TgIbfGrWtlD28U3Bz4cIFlC1bFkqlUibyiCrEKRFF/YiIKJv6yBfOf9qiathGnCmbGzXPh+LphDGwbXAdyibfAvVHGbuFlA28U3AjCvU9efJEJgyL+6LXJrlJVmK/SC4mIqLsq1TPaWi7UIlaRefj1nVXxAeGI0TdDk4MbCgzBTdiKEoslqm/T0RE9Da1+k6BZuIiWDvFIeKhNZ5tvwSHEYEwe3kt0S/PIPJ1Eg9rEWVYcCOShfVy58791urEREREysO/QokEPHPVwuYhgOgYPFzwBwqO+faNdaeIjF6hWAxN9e7dW64ELtaYIiIiSiJR8vD5L7/Bbk/dBJT4c0uAuCguqEmZL7hZunQpoqKi0L59e+TLlw9ffPEFTp8+nT6tIyKirCXxrKj6o9Cr0mfY1akQVtdVIv6CGa55VmZgQ5kvuPnoo4+wdu1aPH36FD/99BOuXLmCGjVqyMJ+EydOTJ9WEhFR1iDr2LyaFWWmNMN3dcZhfR0l4lWAVgMoVEoGNpS51pZKjghwevToIaeMZ/bZUlxbiogo4y39qg2qbb0NLbRQQIHH7T9Bo1/GG7tZlIWk5vqd6p4bvZiYGKxZswYdOnRApUqVEBwcjP/973/v+3RERGSiRI6NCGx2VlHJwEZka+b5exVOfv+rsZtG2b1Csd7OnTuxYsUKbNq0CWZmZujcuTN27dqFevXqpU8LiYgoy0qcPKypFoPz3y1AhbtaXM5VCGVWLsJVcw1KfTPa2M0kE/NeOTfR0dFYtmyZLOw3b948BjZERPT2dacGD8bn5T9Hwc8Gyd1FIp/hSsmCsDqzEE8f3DZ2Kym799yIRGJ7e/v0aQ0REZmUxAX67CzscM5DiRq5HWD99AUq2AegsMdT3F7cCbbD9+Mv/9XQaDUY7MlkY8qAnhuRxKMn8o/Fdko3IiKilChVKqwqFy7vhz10RKA2JzzU/pi2rCV8/HygVLx3KihR6npuHB0d8fjxY1nAL2fOnMmuCC6CHq4tRUREb+NVwQszu7xA9KElsH4UjMseg3EpeC7W2UfC27oIvMoPNHYTKbsEN/v27UOuXLnk/f3796d3m4iIyIQNqzcaEz7aiXPWz+CvXQ6toz28Q17Ay/8A8O8soPYwYzeRsludm4CAALi7u7/ReyOe5v79+yhQoAAyM9a5ISIyvieRT9B0XVN5X0wPP1OsP8x3jZXbZ1puRuXq9Y3cQspWdW4KFy6MwMDAN/aLOjfiGBER0X/ZdGuT4b5SrcGnz48ivEI/TFd9hu5bonAuIMSo7aOsLdXBjT635nURERFcLZyIiP6T73lfmTw8tOQALPGrjrk+atx5fBkjbSNxyb0bYhM0GLDsNO4HRxm7qWTqU8FHjhwpv4rAZuzYsbCxsTEcE0nEJ06cgKenZ/q0koiITCqw8fb0xoDyA3Hn+zaIiwQaXNRih+UxfFa2PJ6GVcD9R49xYW5v5Bg0Bw65XIzdbDLVnptz587Jm+i5uXjxomFb3K5du4YKFSpgyZIlqW6Aj48PChUqJHt9qlevjpMnT771/N9++w0lSpSAtbW1zP0ZMWKEXAqCiIgyP1HHRgQ2YtZU0GwfmBdwl/t7XHbE52UGwMJMiUV9qmLp7SmodvYYHvh2QlwsP+MpnXpu9LOk+vbti99//z1NknFXr14te4R8fX1lYCMCl+bNm+P69ety2vnrxLIPX3/9NRYtWoRatWrhxo0b6NOnj+xNmj59+ge3h4iI0leSAn0qJSIPHITCwgKWj56jb2QF2NWvL5dssLoYifiyKpSJO49Tc3qjyvCVUChZA4cycFXw9yUCmqpVq2L27NlyW6PRyN6YoUOHyiDmdUOGDMHVq1exd+9ew74vv/xSDokdOXIk2e8RGxsrb4mzrcX34GwpIqLMs/aUYFunDqwrVkTQrFnY1TQXqrb3QrXDw2Cm0CCmztewajLG2M2lLDJb6p16bjp27CiHnMSTiftvs2HDhndqZFxcHM6cOYMxY179sCqVSjRp0gTHjh1L9jGit+avv/6SQ1fVqlXDnTt3sG3bNvTs2TPF7zN58mR8//3379QmIiLKWGLNKfWLFwhZugyRR47I2z+Nc2BplTD4JeyDfeWxKHf2e1gd+Rlw9QDKdzF2kykLeKc+PhEp6WdIiftvu72roKAgmYicO3fuJPvFtliQMzndu3fHxIkTUadOHZibm8PDwwMNGjTAN998k+L3EcGTiPL0N1GLh4iIMg838UeufshJoUDbH5bB1twWp5+exkrHIGhrDtUd+9sbEdcPGLWtlDW8U8/N4sWLk72f0Q4cOICffvoJc+bMkUNat27dwvDhw/HDDz/IGVzJsbS0lDciIsq8Q1PQaHQBjkaDXKv2Ynr76Ri8dzC23NmC/OW9MKh0e0TcPoE+q25jyuAq8HCxM3azKRNLdXZWdHQ0oqJe1R64d++eTATetWtXqp7H2dkZKpVKrjKemNh2c3NL9jEigBFDUP3790e5cuXw0UcfyWBHDD2JfB0iIsqaOTfOw4ai1JXL8qvYLva3H76r/q08Z+4FX2ws1xZD7abiTLQb+i4+hecRr3IpiT44uGnfvj2WLVsm74eGhsrcl2nTpsn9c+fOfefnsbCwQOXKlZMkB4sARWzXrFkz2ceIoErk5SQmAiTBiHnRRET0gYGNyL0RxFfnoboAp9Ko5ehXpq/c/8PpnzDy49Jwz2WNgOAo/LJwBWKiIoz8CshkgpuzZ8+ibt268v66detkL4vovREBz8yZM1P1XGIa+Pz587F06VI5C2rQoEGIjIyU082FXr16JUk4btu2rQygVq1aBX9/f+zevVv25oj9+iCHiIiyCLUmSWCjl6NFc/k19vp19DiqQsvCLVErby38+3Q3Fvepih9vLYbXuh9xfUALaNRqWRhwjt+cJEFT4CzdLFzKnt65zk3i3hN7e3t5XwxFidlTojelRo0aMshJja5du8p1qsaNGyeTiEWF4x07dhiSjMUinYl7ar777juZ2Cy+Pnz4EC4uLjKwmTRpUmpfBhERGZnL0CHJ7rf08IBd48aI2LsXz+f6YsxPk7Da45msbFxg/QlUvnQZClctLM48x5rP68GnXpgsDPh6bxBlX6muc1O+fHmZ8yLyXcqWLSuDETGMJKZ1t27dOsWZTpkFVwUnIsoa7n7aE9GnT8tE4wKLFuLgtnkovOY4DrTIg/L12+PFht9R+JQlrjZ2R0efXckOc5HpSM31O9XBjRiKElOyxTTuxo0bGxKJRVLvoUOHsH37dmRmDG6IiLIGrUYD//YdEHvzpmHf1kb2WFY9Ggoo0H1/AppfVMMqUmmYacXAxnSl5vqd6pybzp07y+Gi06dPy14bPRHozJgx4/1aTERE9Bqx3EKhdWtl7Ru9huN0uTVaaOEWDF1gI4gZswrAtnp1mW8jp5cLB6cA+ycbHs98nOwh1Tk3gkgifn26tpg1RURElJaeL1wopsMCZmZAQgKezfEBPEQco8DGWkrEmmlQ74oIdbRQaBW41+NTWBYvjtgbN4C7R+Bi8w/QUDelnPk42Ueqe27EbCYxQ0kshVC0aFEUKVIkyY2IiCjNa+Bcugj/LjVkzs0vt6vgfK/z6PS8sAxsVtdVYsAwM8Q6JcjHicDGqrAzgjafQ2BUa6D+KObjZDOp7rkRycQHDx6UxfTy5MljWJaBiIgorbwejIjp3j4ep/HLywAnIKAvqh6/hdudq2F9sbNwtHTC4WZF0fnkLoTetoWNlT/s2tWTAc7z7eWhjY9nYJONpDq4EQnD//zzD2rXrp0+LSIiInqtBo5Gq5HTvVv19kKg2xxEHjuu69EZPBgPzvsiQZOAmjV7wEmzEUprNTbZ2cGhXztU2H5JBjZiWIuBTfaR6tlShQsXlitxlypVClkRZ0sREZkomTw8CevsbfG9sxM6HdGg6+FXS/Pk6tsXuUePMmyL3iARNA32ZNCD7D5bSixSKYruJV5fioiIKDMENiJ5OI9zX/y+K0IGNutrKhDgrDslePFiPPvtN3lfDnP5+UCpSPVlkExxWEqsI3X79m1ZRbhQoUIwNzd/Y3kGIiIiYwQ2Inm4+CUfBJ2xgn25cCgrmuGXinb4cakajpHAc995OB14Dj7Fz8phLq8KXsZuPWWG4KZDhw7p0Q4iIqL3o1EbAhvdtha5vAfD0X4Pvrl7AB9bqzGlZxEMXvgMVvGA5shJeH88jIGNCUt1zk1Wx5wbIqJsIiYMWNQCeHYZEc7lMPzJC3y5LkHU+oPrV1/CqX//JKfLwn9qTYprXpEJ59wIoaGhWLBggVyxOzg42DAcJRazJCIiyhSscgA91iDMoQTaxnngZDHAz0N32bt4bAueRD55Y+o5VMzBMQWp/l+8cOECihcvjl9++QVTp06VgY6wYcMGGewQERFlGg758VuV7ghyOovYwKY433clAlpXRO6jN/DHiKY4H3ieBf5MUKqDm5EjR6JPnz64efMmrKysDPtbtWolF84kIiLKLMSsqLV3FqJlvj5IeN4YF84cgYVnaexskgsfH0qAsv4nDGxMUKoTik+dOoV58+a9sT9fvnx48uRVFx8REZGx6Yv/ieThqvgXLQ/3g93tGFi0mIyEfbNgphGLcAJmndsYu6lkzJ4bS0tLmdTzuhs3bsDFxSWt2kVERPTBRIE+/ayoj5vUwqXc7eR9jyU/GwIbkWB8vX1bxEVHGrm1ZLTgpl27dpg4cSLiRTlr8UOhUCAgIACjR49Gp06d0qxhREREaa3q53Nx4UZphFyyhUP5OKjmjEG8CnAIicOpto2g0byqaEzZKLgRRfwiIiLg6uqK6Oho1K9fX64Obm9vj0mTJqVPK4mIiNJA8B9/wPxsKGyqWCFv6SCUuPQbYr73gghpcj0Iw+Xu/CM9W9e5OXr0KM6fPy8DnUqVKqFJkybICljnhogo+wqcNVtO93bp2Qlhs+shR+wTaAvUxJ6wcsjvu1Wek+fnyVhmXwZqjRYjmhbXPY41cEy/zo0gVgUfPHgwRo0ahSpVqrzv0xAREWUYEZzIWVH2ubG5zO8I01rj7MNo7HbpAOvKleU5d36eit92XYNKKbJxWAMnK0r1/5Sob7N69WrDdpcuXeDk5CRnS4meHCIioqzg03YtsLD4XHSNHIk1F0Oxoee3CCpVEdahzzEk7He0qaJiDZzsMixVuHBhLF++HLVq1cLu3btlcCOCnTVr1sjE4l27diEz47AUERElNmDZKey+8gxi7lQxxUO0ffE3mu7zR4IKMFODgU12GJYStWzc3d3l/a1bt8rgplmzZnJ4StTAISIiykrm96oKM4UGP5gtxjaLMeji7WUIbMRf/7a9uidbHHCO3xyjtJf+W6qDG0dHR9y/f1/e37FjhyGRWHQAqdXq1D4dERGRUc3cexNqLZBTEQFzhRqaCcMNgY3IujnZqj7U6oQkgY2Pnw+UCubgZFap/p/p2LEjunfvjqZNm+L58+do2bKl3H/u3Dk5JZyIiCgrBTbTd9/AiKYlofzIF34XC+HFRSvYeWoR/ctQqBVA7mdx2NOmZpLARl/1mEwkuJkxYwaGDBmC0qVLy5wbOzs7uf/x48dy9hQREVFWCmxGNi2OYY2Lodqx7bC8HAfzshq4l3yMfLf+QuAXneW5Bfwj8GfbMgxsTL3OTVbFhGIiIhJm7L4hp3uLwEZfAyc8XoN8PVpAM78JrBNeAKXaYttFFQqvOymHqaZ8YoElE5LODGYNHBOqc0NERJSViQJ9+sBGEMFJkZHDYJm7OKx7rgJUFsC1f3CvSV74u+ryb0asjcPCg9MMj2ENHBNZFZyIiMjUqd1r4njZH7FTcx4b723FkBlDUHzMZiAgAPf/WgTfnLbodFTDGjiZFIMbIiKi16w5fR/jb1+HpcthfF52EAZWHozILb1x4Mch6Lr2BOL//R1BrIGTabEfjYiI6DUdK+WDg7UKsYFNEfe8MRDsj6BlrfBdMT+5iri5GtCINaoY2JhOcBMaGooFCxZgzJgxCA4OlvvOnj2Lhw8fpnX7iIiIMpylmQo/1P8ScUGNMe/QHURtH4+CD89jwr44GdiI5GKlWoOnU341dlMpLYKbCxcuoHjx4nKNqalTp8pAR9iwYYMMdoiIiExB8zK5UbOIE+ISNBin7o9A/8IoflyLzXWUuJFPd07wokW62VKUtYObkSNHok+fPrh58yasrKwM+1u1aoVDhw6ldfuIiIiMQqFQYFzb0hCLg5tv2ICgE7FwrqSGR6kQLGmiMpwnkooZ4GTx4EasHzVw4MA39otVwcW6U0RERKaiVJ4c6FatAJRaDXZWawfnKSvxUbQGZk7xOFhWTA4HzNzcoOXyQ1k7uLG0tJSFdF5348YNuLi4pFW7iIiIMgVRwfhhh0/RcNIYKPJXhqrTAowODsGKBkrEmAMJT57AslChVw84OAXYP9mYTc72Uh3ctGvXDhMnTkR8fLyh2y4gIACjR49Gp06d0qONRERERuNkZ4klfauhgntO3Y5SbVA1f130jwtFjqbF5a5nU6dBExX1MrCZBChfDVtRFghupk2bhoiICLi6uiI6Ohr169eXC2ba29tj0qRJ6dNKIiKiTCIsJh7osQ69KnqjsO0BmDvbw7ZmTWgPTNMFNg2/BeqPMnYzs7VUF/ET6zqIBTOPHDkiZ06JQKdSpUpo0qRJ+rSQiIgoE0hQa/Drruv469g9bB1WF4UbjoFSqUIRzU+4bH8fTqeioGJgkylw4UwiIqJ31HvRSRy8EYgmpVyxoHdVue/vT4vinLUl3EuH47MRAUnO56Kaxrl+p7rnZubMmcnuF7k3Ymq4GKKqV68eVCqONxIRkWkZ26YUjvwWhD1Xn+HwzUDUfbQYTlo1uh7WYGe0LW5/3BB5vp4Km8qVDYtqiiUaKJP33BQuXBiBgYGIioqCo6Oj3BcSEgIbGxvY2dnh2bNnKFKkCPbv3w93d3dkNuy5ISKiDzFh82Us+fcuvnfYit6xK6CpPwbzli9HgyMJ8rhVASfYte+GoFmzufaUka7fqU4o/umnn1C1alVZxO/58+fyJqaBV69eHb///rucOeXm5oYRI0a80/P5+PigUKFCstdHPMfJkyffer6oiOzt7Y08efLIaemiWvK2bdtS+zKIiIjeyxdNiuF/1n/LwOZc0cFQNvwaNb8Yg001dHVvYgKeM7AxslQHN9999x1mzJgBDw8Pwz4xFCWWYhDLL+TPnx9TpkzB0aNH//O5Vq9eLSsejx8/Xq5NVaFCBTRv3lz2/iQnLi4OTZs2xd27d7Fu3Tpcv34d8+fPlwUEiYiIMkJOGwvUKeKIafGd0fdOQ4RGxcGzbHeENnWFWhffSAxsslBw8/jxYyQk6LreEhP79BWK8+bNi/Dw8P98runTp2PAgAHo27cvSpcuDV9fXzm8tWjRomTPF/vFQp2bNm1C7dq1ZY+PmIougqKUxMbGyq6sxDciIqIPUab7ZOxy7o3YeA3OP3gh93k9rAeVVreopvB43DijtjE7S3Vw07BhQ7n8wrlz5wz7xP1BgwahUaNGcvvixYsyN+dtRC/MmTNnkkwhVyqVcvvYsWPJPmbz5s2oWbOmHJbKnTs3ypYtK4fJ1G8pez158mQ5Rqe/ZcY8ICIiylrMVErM6OqJ/V81QP3iLjJ5OGbRWvg3zYMTL5dlCF2zlmtOZZXgZuHChciVKxcqV64sc17ErUqVKnKfOCaIxGJR7O9tgoKCZFAigpTExHZKa1TduXNHDkeJx4k8m7Fjx8rv8+OPP6b4fcRQmUg+0t/u37+f2pdMRET0htJ5c8DNwSrJrKhGU9ajw2hf3QlKJRfVNJJUTwUXycKiiN+1a9dkIrFQokQJeUvcu5MeNBqNrIz8xx9/yKnmIsB6+PAhfv31V5m3kxx9AEZERJQu1BrEfNoft1t0RQ1rRywyv4QytYqjTM020EREyuN6vud9odFqMNiT+TiZKrjRK1mypLy9L2dnZxmgPH36NMl+sS0CqOSIGVLm5uZJauiUKlVK9vSIYS4LC4v3bg8REdH7OFy7A0auOY8iGy5ixxf1oFQoMaT+HTR12IV8OePx5cebDIGNj58PvD29jd1kk/dewc2DBw9k/ouY9i2CiteThN+FCEREz8vevXvRoUMHQ8+M2B4yJPlKjiKJeMWKFfI8kZ8jiN4jEfQwsCEiImNoWjo3nO0scScoEsuO3YVXXS8EB9/CyoCd8niTS6twTB1qCGy8KngZu8kmL9VF/ETwIVYGF4X6xNCUSOoVU7PF04g1pvbt2/fOzyWmgvfu3Rvz5s1DtWrV8Ntvv2HNmjXyeUXuTa9eveQ0b5EULIh8mTJlysjHDB06VNba6devH4YNG4Zvv/32nb4ni/gREVFaW30qAKPXX4S9lRkOfNVAriT+yZLqyHE1AhX8tfBtpYR3xSEMbDJrET+RoPvVV1/JGVGi8N769etl0CGmZH/88cepeq6uXbvK+jjjxo2Dp6cn/Pz8sGPHDkOSsegZElPP9cRMp507d+LUqVMoX768DGqGDx+Or7/+OrUvg4iIKM10ruyOMnlzIDwmAdN26/JRZ9aeCe9/NGh0QYtSDxUMbDJzz429vb0MQkQRP7H8glgdXPSmnD9/Hu3bt5e9OJkZe26IiCg9nPQPRpd5x6BUAFuH1sWhwBVI+GkmGp/X4t9SCkR98xmGVv3S2M3MstK158bW1taQZyNyXW7fvp1kejcREVF2VK1wLrQunwcaLTBk+y8yx8buE92IRvVrWqw/vlgmFVMmTCiuUaOG7K0Rs5RatWqFL7/8Ug5RbdiwQR4jIiLKrsa0LInToWsQaPaPTB7uU8ELfksOwfL6EzQ/o4FPDh95HoeoMllwI2ZDRUREyPvff/+9vC8Sg4sVK/bOM6WIiIhMUX5HG/Sq6Q6VUjcrKlAsoOlRCeHXt6H9ZSs4efdDglZX90YW91Nr4DI0+RnClEHBjagMLKaBi2Re/RCVWA+KiIiIdLwrvqpjo1UqEb5tG5T29tCEh6PLPTfk7Nw5SVVjSnupyrkRxfOaNWuGkJCQ9GsRERFRFqfRaLHm1H10iSoF64GDZGBjljcvzPLkwd0p4wyBDVcOTx+pTigWdW3EGk9ERESUshUnA3D3eRR88teH89AhSHj0CPc+H4DoRWvxrHUxBjaZKbgRi1SKOjdbt26VNWjE1KzENyIiouxOqVRgfNvS8v7aMw/wuH0PKMzNoVRrEa8CxpW9g4jwV3XcyMh1bvTLHsgHK3TLugviacS2yMvJzFjnhoiIMsqI1X7YeO4hvnpyBI2PbwLMzYH4eBwtqUDYpyUwsvNGYzcxy0jN9TvVs6X279//IW0jIiLKNka3KAn7NcvQ+PJ2PO/SB6UKuuDZr7+i9jUtNmy7jntVD6NgwbrGbqbJSXVwI5ZZICIiov+mWr4I3S5vx7KSzXHAugr2fFwD5suXI/7RI3T8V4v9k4ahzx/njN1Mk5PqnBvh8OHD+PTTT1GrVi08fPhQ7vvzzz9lcT8iIiJ6Sa1BTu8hOFSjHR6/iMHhgDC4jvqfPJSgBAKjY3HsDEuqGD24EQtlNm/eHNbW1jh79ixiY2PlfjEG9tNPP6V5A4mIiLIqUaAvz1BvTOlcHhsH10KLsnlgL66hVSrDTAPkigTuBl0xdjNNznvNlhKF++bPnw9zkRj1Uu3atWWwQ0REREnVLuqMigUc5X0x+cbtm2/EHdS6okV7lz7Gbp7JSXVwc/36ddSrV++N/SKDOTQ0NK3aRUREZJLuB0fhXi535OzcSW4HTp9h7CaZnFQnFLu5ueHWrVsoVKhQkv0i36ZIkSJp2TYiIiKTsuPSEwxbeQ4l89hj3dBh0L5cW+ripZW4eP8wurecY+wmZs+emwEDBmD48OE4ceKE7Fp79OgRli9fLgv7DRo0KH1aSUREZAIqF3SEhZkSFx68wOb7sTDPkwf+C6ei+5mfMOXpIdy5s8dwrlh/Siy8SRkQ3Hz99dfo3r07GjduLFcEF0NU/fv3x8CBAzF0KBcAIyIiSomLvSWGNCoq70/ZcQ3xWkD91zZ8ddQMOcOBKYe/hVajMSysCdV7TWrO9lJdoVgvLi5ODk+JAKd06dKws7NDVsAKxUREZEyxCWo0m3EI955HwbuhB3pf34Xnc+YiQQF8MVCFX55VhO2G01xY8wOu36kOCf/66y9ERUXBwsJCBjXVqlXLMoENERGRsVmaqfBNq1Ly/vzD/ojp8RnM3fPDTAvM9FXLwCbXYC8GNh8g1cHNiBEj4OrqKoemtm3blunXkiIiIspsmpXOjdpFnRCXoMHk7dfgPm8etC8vyhoFsNPjUpLzfc/7Yo4fk43TLbgRK4GvWrVKJhN36dIFefLkgbe3N/7999/UPhUREVG2JK6hY9uUhp2lGUq42SNs+w6IpahlgKMF7H4/gpDg24bAxsfPB0oF82/SPedGEMNTGzduxIoVK7Bnzx7kz58ft2/r/jMyK+bcEBFRZhEeE4+YRfNl8rDIsTkadQklFugWqLZr0hj/DCgrAxtvT294VfBCdhaWnquCJ2ZjYyOXYggJCcG9e/dw9erVD3k6IiKibCVxYCNybDoA2Bn4KQr8fQYRe/YiOGIfvEcMy/aBTWop37fHRtS2adWqFfLly4fffvsNH330ES5fvvw+T0dERJQ9qTUysPFv+Ql6LjyBsJh4NJu8DPs9VfB3BYo/AgaW+/yNh7EGDtK25+aTTz7B1q1bZa+NyLkZO3YsatasmdqnISIiyvZEdWK1RotPZhzE7cBIzNp7E075D2FuSwU6H1Ghy2E1VnzRBD1m7jM8Rl8DRwRFlEbBjUqlwpo1a+RwlLif2KVLl1C2bNnUPiUREVG2pVIq8F2b0ui7+BT+vLYA5kG7ZY5NfI79WI1L6LrrMU41rY3KW/bi+aJFSYaxKI2CGzEclVh4eDhWrlyJBQsW4MyZM5waTkRElEoNS7iiRInjeKTcjXzaDjLHJsqjI9oHNUSrU4D9/WBcq1hJzAJiYPMO3nte2aFDh9C7d285FXzq1Klo1KgRjh8//r5PR0RElK3VLe6E+KCmuHatBg7dCISNnSuGFe2AaR2Vcoq4CGxgZsbAJq2DmydPnuDnn39GsWLF8PHHH8upWLGxsdi0aZPcX7Vq1dQ8HREREb30Xe0v0L14f3n/h61XEK/WoHW979EgQClr4EgJCQic7WPMZppWcNO2bVuUKFECFy5ckLOjxGrgs2bNSt/WERERZSPDGxeDo405bj6LwLaLj/F83h9ocCQBG2soEGmpOydo9myZVExpkHOzfft2DBs2DIMGDZI9N0RERJS2HGzMMaFdGYgRqJpH/0bQLF3ycLjDWqyzfYbeezVQWFvrVgwXs604RPVhPTdHjhyRycOVK1dG9erVMXv2bAQFBb3rw4mIiOgdtPfMhw4V80Gh0dXAEQHMFzk90aluBVgUKgRtdDRsa9eSNXKkg1OA/ZON3eysvfxCZGQkVq9ejUWLFuHkyZNydtT06dPRr18/2NvbI7Pj8gtERJRVRMQmICImAW5+M4H9kxCRuw/iclSDY9euUJiZvQxsJgENvwXqj4IpC0vF9fuD1pa6fv06Fi5ciD///BOhoaFo2rQpNm/ejMyMwQ0REWUF/94KwvDVfijpZo9l/apBcehXGcg8q9Yfl3K6olG8ItsENqm9fn/QEqMiwXjKlCl48OCBrHVDREREaSOfozVeRMXj8M0g7Lv2TAYw/pV6oM3THRh9fRke7/8ZcWWHZYvAJrXSZP10Uam4Q4cOmb7XhoiIKKso6GSLfnUKy/s//nMVcQkaFGozG6Xi4pA7UIGA7a54sNQP2oQEYzfVNIMbIiIiSntDGhWFs50l/IMisfTfu1AcnorRz0NQ57IalpEKxN68hZA1a5I8JpCLajK4ISIiyqzsLM0wqkUJeT9272SZY1O61v9QRKWC5csOm6BpU6B+8SLJoppQZe/Le6rXliIiIqKM07lSfsTt/RmfRq/B7tyfoWmD0WhkYYU/FL746CigjoxF4Jh+UJVtzEU1X8reoR0REVEmp1Qq0LC4E6bFd8b2XL2g0WjhXLkf3DzjcaCsbmGGkH1XGNgkwp4bIiKiTC7fRxPxUZ0IFHGx0+2wtMenRTuhi/Vm1L8E3dpTSiUDm5fYc0NERJQFGAKblyzqjcK8iM9eLaqp0XDNqcwU3Pj4+KBQoUKwsrKSSzuIysfvYtWqVVAoFHIaOhERUXZwPzgK4/6+hMeLViHYdyGch3ij8MYNcB46VA5NBTLAMX5wI5ZyGDlyJMaPH4+zZ8+iQoUKaN68OZ49e/bWx929exdfffUV6tatm2FtJSIiMiaRb9Nz4QnEL16AUJ/Zuhwbb2/c1lzEyIJHENuvIwOczBDciHWpBgwYgL59+6J06dLw9fWFjY2NXLsqJWI9qx49euD7779HkSJF3vr8sbGxsmRz4hsREVFWTS7+oklxKLUarCzTEppP+wEbvfDD0e/g9/wipue/jJy9e71aVBOA73lfzPHLXsGOUYObuLg4nDlzBk2aNHnVIKVSbh87dizFx02cOBGurq747LPP/vN7TJ48Wa5Fob+5u7unWfuJiIgyWnvPvLjSvCuWFWuMKTuuAwVqoEZ0DOpf0ODLSddx7/ZZuAwdYghsfPx8oFQYvS8jQxn11QYFBclemNy5cyfZL7afPHmS7GOOHDkiF+ucP3/+O32PMWPGyEW29Lf79++nSduJiIiMQeSajm9bRt5ff/YBLji1wBfRCjg6xMJCDdgdvYSQgFuGwMbb0xteFbyQnWSpUC48PBw9e/aUgY2zs/M7PcbS0lKuHpr4RkRElJV5uudEx4r55P3vd/hDW6k3xmkCcb2AAiot4DuhfbYNbIwe3IgARSy6+fTp0yT7xbabm9sb59++fVsmErdt2xZmZmbytmzZMrlgp7gvjhMREWUHo1qUhI2FCmfuhWBfjrYwVyjhVDRcHmt0TgMbtVm2DGyMHtxYWFigcuXK2Lt3r2GfRqOR2zVr1nzj/JIlS+LixYvw8/Mz3Nq1a4eGDRvK+8ynISKi7MLNwQojmhTHsEZFUbNSRaBka1wqCjxzAHJEA9UvxcmhqezI6BWKxTTw3r17o0qVKqhWrRp+++03REZGytlTQq9evZAvXz6ZGCzq4JQtWzbJ43PmzCm/vr6fiIjI1A2o92rGsK9bAcyJyYmRnlq4HlSj50VH9DunWx08u/XgGD246dq1KwIDAzFu3DiZROzp6YkdO3YYkowDAgLkDCoiIiJKnkwevrsFn+drjl4/f4ObjZrA/kkYvnLtjql+PtkuwFFotVotshFR50ZMCRczp5hcTEREpmDCoenYezUInjk+xrigo4i7H4Dco0dDlSsX5l2YB41Wg8Geg3XF/dQaw1RxU71+G73nhoiIiD5MZ4/PsHT7EdzXPkJ/+1hYbN6CqxZP8XvlYPg29UU+u3wysNGvHG7qON5DRESUxZXN54CuVXSTalZbW8G5sgb51p1E5W13sOHk4iSBTXZYOZzDUkRERCYgMDwWDacegG3sMxyzHo6zF3PA9pI1xEVerBye1QOb1Fy/2XNDRERkAlzsLTG0UVE8RS7sQQ1ULBNiCGy0SmWWDmxSi8ENERGRiehTuxAKOdnAN6Ypgi/bycBGUGg0eOajmzWVHTC4ISIiMhGWZip827o0Sly9i6BLOWBfOhzRFrpjz2fN1s2WygYY3BAREZkQz/3r0evaLjh93AD5y4fjUWnd/hBXG5lUnB0CHAY3REREpkSjkcnDruN/A2xdUbrAc7k7Z2A0HHv1lHVuTB3r3BAREZkQl0QF+mJazsCF+2aoFLoRkYcOQWlplSUL+KUWgxsiIiITpNFo0X53Dlx/Go7f6ndAw7ZtkKN5c2QHHJYiIiIyQUqlAp9U0xX2m3jHDA8qF8HP56Zh/Y31MHXsuSEiIjJRn9YoiDXHb6NvyEycW3URK5zsUMiuADp4tIdKZbohAHtuiIiITJS5SokS+ZzgoXyEjuEhaH1Oga+m3MGpTfPk8Zl7b2LG7hswNQxuiIiITFgRFzssTmgBG60WNR/HwfUFEPLXchnYTN99AyqlvtSf6WBwQ0REZMKGNS4G1+of44nWERULPYeYCF7oagjWbfkbI5sWl8dNDYMbIiIiEzeufQXss2uLAtZxuFVE11PzWcgekwxsBAY3RERE2cAnXuPw+KIDCimj5Xb5s/cQGvTQcFxULg6cNRumgMENERFRNjD7ZCiua91hccsK4daAVTwQuXGzIbARSzNAZRphgWm8CiIiIkrRzJfJww/7fAvndpVgr+u8wdMlqxA420cGNmLJBpfBg2EKGNwQERFlg8BmZNPi6NGuFVymLIfToEHymHlwEIJmzzapwEZgcENERGTC1BrtG7OiXIcPg8LcHGZaDRJUSpMKbAQGN0RERCZsRDLTvQN/+Ara+HjEqwAztQbXp/0AU8LghoiIKBsJFMnDy/+Bc9kwrPvMAjfzAJr5K+R+U8HghoiIKJsIfDkrynlQf7h4qvFRQCCKPQYSlJD7TSXAYXBDRESUXag1uuTh4V8CFbri34JmCMitgJkGCC1fUB7X8z3vizl+WTPYYXBDRESUTbgMHfIqebi6F1QKLbZU0VUs1tx7gJwD+xsCGx8/HygVWTNMMN31zomIiChlrqXg5VgRcxPO4YWNHXK9UOP46pm4XD6HDGy8Pb3hVcELWVHWDMmIiIjow9UYhEERYbhcTis3g5YuyfKBjcDghoiIKLsq1gwo3R6f9B4pk4pLPtCi2FNVlg5sBAY3RERE2ZVSBXRZhj+dNNhdUYG/a5nhmW2CzLnJyhjcEBERZWO+L5OHbUYNw7B5J1CnXBu5nZUDHCYUExERZfPAxrtsf/QOj0ajlbURoU1Aj5I95H4hKw5RMbghIiLKpjRajS55OF9jBA5siAH2NthX0Bw1Dh+H4yAvqLW6ujeyuJ9aI6eSZwUMboiIiLKpwZ6JFsx0LoKaBwPheUYD6/jrqNihPxzatHlV1XjYUGQVDG6IiIgILl+NQ1xwH+Civdx+tHg+4gICDIFNVlo5nMENERERAR6NkK9ebhyyCIPnGTPg8g0EXb6R5QIbgbOliIiICFAq5ZIMuSqEQ6N4tS+rBTYCgxsiIiLSqfAJyp+zgVJXsBjQaBA4azayGgY3REREJAUu/BOh5ywRUd8ZCgdd7k2Qj49utlQWwuCGiIiIYJgVNXQoqs47jJyt28CqdGnkaNdO7s9KAQ4TiomIiAiijk3i5OHcY8ZAYW4OrVYLi0IF5fGsgsENERER4fUCfef9t+OPM78hb4E6+G7wRGQlmWJYysfHB4UKFYKVlRWqV6+OkydPpnju/PnzUbduXTg6OspbkyZN3no+ERERpZJWi5h9P+BwXCAOXP0HYcePISsxenCzevVqjBw5EuPHj8fZs2dRoUIFNG/eHM+ePUv2/AMHDqBbt27Yv38/jh07Bnd3dzRr1gwPHz7M8LYTERGZJIUCVSt7oXhQAqb9FoUHAwdCExmJrEKhFYNpRiR6aqpWrYrZs3VTzTQajQxYhg4diq+//vo/H69Wq2UPjnh8r1693jgeGxsrb3phYWHy+V+8eIEcOXKk8ashIiIyEXFRmDzfE9X/UiFPCJD311/h0LaN0Zojrt8ODg7vdP02as9NXFwczpw5I4eWDA1SKuW26JV5F1FRUYiPj0euXLmSPT558mT5ZuhvIrAhIiKi/3D0d7S0zoejpXUV/UL/2fLq2MEpwP7JyKyMGtwEBQXJnpfcuXMn2S+2nzx58k7PMXr0aOTNmzdJgJTYmDFjZJSnv92/fz9N2k5ERGTSlCqUDziLG8V1AzyRh49AHRr6MrCZJI9nVll6ttTPP/+MVatWyTwckYycHEtLS3kjIiKiVKg/SvaAVPTzwT0XGxQM1CDc5yvkjF8LNPxWHs+sjNpz4+zsDJVKhadPnybZL7bd3Nze+tipU6fK4GbXrl0oX758OreUiIgoG6o/Cq3yN8DdYmq5GbZrX6YPbIwe3FhYWKBy5crYu3evYZ9IKBbbNWvWTPFxU6ZMwQ8//IAdO3agSpUqGdRaIiKi7KdkxyXo5/xC3o98ZgG150BkdkafCi6mgYvaNUuXLsXVq1cxaNAgREZGom/fvvK4mAEl8mb0fvnlF4wdOxaLFi2StXFEbo64RUREGPFVEBERmahDv8LCJgZ5aoajaJunUPnNQ2Zn9Jybrl27IjAwEOPGjZNBiqenp+yR0ScZBwQEyBlUenPnzpWzrDp37pzkeUSdnAkTJmR4+4mIiEzWwZfJww2/haZ6f2zcPQrNDk5GTnEsEw9NGb3OTWaeJ09ERJRtHXwV2IhApuvWrrjy/ArGO9VA59NrMjz3JjXXb6P33BAREVEmpFEnCWA+O2GLO1fVsEm4hOflOsBJHH9Jrhiu1ryxPlW2zbkhIiKiTKjhmCQ9M0WdSqD+JS0KXwvF84uhuuMvA5ugmbMAVeYJKTJPS4iIiCjTKvLFaBxtpMuHVV+7gVh/f0Ng4zxsKFwGD0ZmwWEpIiIieifWQwfg0bkfkTcEuNO6jajfkukCG4E9N0RERPROmhVshr9rvVx2QaOBwtw80wU2AoMbIiIieicuNi6oHP1qBQFtfLwumTiTYXBDRERE70QEMtX2PYTS2Ulu2zVtInNuMluAw5wbIiIi+k+Jk4eFqFOnkLNTJ1iVKqWbLSV6djLJEBWDGyIiIvpv6jeTh6MTouHSoIHheGbBCsVERESUKvfC7mHs0bEIiQnB5g6boVAokJmu38y5ISIiolRxtnaWSzGEPPLHtePbkNkwuCEiIqJUsTW3xafBJTB/lhovvp+MzIbBDREREaXKHL85eF7YCSLLxuHuc8Q9fWo45nveVx43JgY3RERElCpKhRKbgvfDP48u1+ba9pWGwMbHz0ceNybOliIiIqJU8argJb+e9ZgJj8fAs7074FvRSgY23p7ehuPGwp4bIiIiSjURwNjWrSvvO164B98zszNFYCMwuCEiIqL3MrT77wizBmxigdKPVZkisBEY3BAREdF7WXRlCfyK6PJuyt2Mlzk3mQFzboiIiCjV9MnDY7p0Rl6rynB1vI3f/HzkMWP34DC4ISIiovcKbESOTfeXgcxnAOIdbOR+Ywc4DG6IiIgoVTRaTbLJw/ptcdyYGNwQERFRqgz2TLr6d/yzZwjbvBma6Bh4DR0CY2NCMREREX2QhGeBeDZ1GoIXL4Y2Lg7GxuCGiIiIPohV6VJQOTlBExWFqLPnYGwMboiIiOiDKJRK2L0s6Bdx6BCMjcENERERfZDAWbOhiYmR9yMOHUx6bM4ceTwjMbghIiKiD6NSInzHDkChQNyt24h/+NAQ2ATNnCWPZyTOliIiIqIP4jJYN3tKBjKi9+bwYSQEB8tt52FDDcczikKr1WqRjYSFhcHBwQEvXrxAjhw5jN0cIiIik3Gvbz9EHTum66lRa9I0sEnN9ZvDUkRERJQm8s+aCYW5uQxsxNeM7rHRY3BDREREaSJ42TJo4+NlYCO+ipwbY2BwQ0RERB9MnzwshqJKXrwgv4ptYwQ4TCgmIiKiNAts9ENRrycZZ+QQFYMbIiIi+jApJA8bttUZu5AmZ0sRERFRpsfZUkRERJRtMbghIiIik8LghoiIiEwKgxsiIiIyKQxuiIiIyKQwuCEiIiKTwuCGiIiITEqmCG58fHxQqFAhWFlZoXr16jh58uRbz1+7di1Kliwpzy9Xrhy2bduWYW0lIiKizM3owc3q1asxcuRIjB8/HmfPnkWFChXQvHlzPHv2LNnz//33X3Tr1g2fffYZzp07hw4dOsjbpUuXMrztRERElPkYvUKx6KmpWrUqZs+eLbc1Gg3c3d0xdOhQfP3112+c37VrV0RGRmLr1q2GfTVq1ICnpyd8fX3/8/uxQjEREVHWk5rrt1HXloqLi8OZM2cwZswYwz6lUokmTZrg2LFjyT5G7Bc9PYmJnp5NmzYle35sbKy86Yk3Rf8mERERUdagv26/S5+MUYOboKAgqNVq5M6dO8l+sX3t2rVkH/PkyZNkzxf7kzN58mR8//33b+wXvUNERESUtYSHh8senGy9KrjoFUrc0yOGvYKDg+Hk5ASFQvHBUaQIku7fv88hrgzA9zvj8L3OWHy/Mxbf76z5XoseGxHY5M2b9z/PNWpw4+zsDJVKhadPnybZL7bd3NySfYzYn5rzLS0t5S2xnDlzIi2J/zD+gmQcvt8Zh+91xuL7nbH4fme99/q/emwyxWwpCwsLVK5cGXv37k3SsyK2a9asmexjxP7E5wu7d+9O8XwiIiLKXow+LCWGjHr37o0qVaqgWrVq+O233+RsqL59+8rjvXr1Qr58+WTujDB8+HDUr18f06ZNQ+vWrbFq1SqcPn0af/zxh5FfCREREWUGRg9uxNTuwMBAjBs3TiYFiyndO3bsMCQNBwQEyBlUerVq1cKKFSvw3Xff4ZtvvkGxYsXkTKmyZctmeNvFcJeoz/P6sBelD77fGYfvdcbi+52x+H6b/ntt9Do3RERERCZVoZiIiIgoLTG4ISIiIpPC4IaIiIhMCoMbIiIiMikMbv6Dj48PChUqBCsrK7nI58mTJ996/tq1a1GyZEl5frly5bBt27YMa2t2e7/nz5+PunXrwtHRUd7EmmT/9f9D7/+zrSfKL4jq3h06dEj3Nmbn9zs0NBTe3t7IkyePnGlSvHhxfp6k4/stypCUKFEC1tbWsqLuiBEjEBMTk2HtzaoOHTqEtm3byqrB4nMhpXUeEztw4AAqVaokf66LFi2KJUuWpH3DxGwpSt6qVau0FhYW2kWLFmkvX76sHTBggDZnzpzap0+fJnv+0aNHtSqVSjtlyhTtlStXtN99953W3Nxce/HixQxve3Z4v7t376718fHRnjt3Tnv16lVtnz59tA4ODtoHDx5keNtN/b3W8/f31+bLl09bt25dbfv27TOsvdnt/Y6NjdVWqVJF26pVK+2RI0fk+37gwAGtn59fhrc9O7zfy5cv11paWsqv4r3euXOnNk+ePNoRI0ZkeNuzmm3btmm//fZb7YYNG8TMa+3GjRvfev6dO3e0NjY22pEjR8rr5KxZs+R1c8eOHWnaLgY3b1GtWjWtt7e3YVutVmvz5s2rnTx5crLnd+nSRdu6desk+6pXr64dOHBgurc1O77fr0tISNDa29trly5dmo6tzL7vtXh/a9WqpV2wYIG2d+/eDG7S8f2eO3eutkiRItq4uLgMbGX2fb/FuY0aNUqyT1x8a9eune5tNSV4h+Bm1KhR2jJlyiTZ17VrV23z5s3TtC0clkpBXFwczpw5I4c69EQxQbF97NixZB8j9ic+X2jevHmK59OHvd+vi4qKQnx8PHLlypWOLc2+7/XEiRPh6uqKzz77LINamn3f782bN8slZcSwlChoKoqU/vTTT1Cr1RnY8uzzfovisOIx+qGrO3fuyCHAVq1aZVi7s4tjGXSdNHqF4swqKChIfpDoKyXrie1r164l+xhRYTm588V+Svv3+3WjR4+W476v/+LQh7/XR44cwcKFC+Hn55dBrcze77e4uO7btw89evSQF9lbt25h8ODBMngX1V4pbd/v7t27y8fVqVNHrjydkJAALy8vWQWf0lZK10mxenh0dLTMeUoL7Lkhk/Dzzz/LRNeNGzfKBEJKO+Hh4ejZs6dM4HZ2djZ2c7IFsYCw6CUTa+aJxYXFMjXffvstfH19jd00kyQSXEXP2Jw5c3D27Fls2LAB//zzD3744QdjN43eE3tuUiA+xFUqFZ4+fZpkv9h2c3NL9jFif2rOpw97v/WmTp0qg5s9e/agfPny6dzS7Pde3759G3fv3pUzIhJffAUzMzNcv34dHh4eGdDy7POzLWZImZuby8fplSpVSv7VK4ZdLCws0r3d2en9Hjt2rAzg+/fvL7fFTFexgPPnn38ug8rE6xvSh0npOpkjR44067UR+D+WAvHhIf5i2rt3b5IPdLEtxsKTI/YnPl/YvXt3iufTh73fwpQpU+RfV2KxVbGyPKX9ey1KG1y8eFEOSelv7dq1Q8OGDeV9MW2W0vZnu3bt2nIoSh9ECjdu3JBBDwObtH+/Rb7e6wGMPrDk8otpK8Ouk2manmyC0wnF9MAlS5bIKWuff/65nE745MkTebxnz57ar7/+OslUcDMzM+3UqVPl1OTx48dzKng6vt8///yznO65bt067ePHjw238PBwI74K03yvX8fZUun7fgcEBMiZf0OGDNFev35du3XrVq2rq6v2xx9/NOKrMN33W3xWi/d75cqVcqryrl27tB4eHnIGLL2d+LwV5TjETYQU06dPl/fv3bsnj4v3Wbzfr08F/9///ievk6KcB6eCG4GYg1+gQAF5ERXTC48fP244Vr9+ffkhn9iaNWu0xYsXl+eL6W7//POPEVqdPd7vggULyl+m12/ig4rS/mc7MQY36f9+//vvv7KUhLhIi2nhkyZNktPxKe3f7/j4eO2ECRNkQGNlZaV1d3fXDh48WBsSEmKk1mcd+/fvT/ZzWP/+iq/i/X79MZ6envL/RvxsL168OM3bpRD/pG1fEBEREZHxMOeGiIiITAqDGyIiIjIpDG6IiIjIpDC4ISIiIpPC4IaIiIhMCoMbIiIiMikMboiIiMikMLghIiIik8Lghog+eEVlhUKB0NDQdPseDRo0wBdffJFuz/+h37tQoUL47bffMqxNRPR2DG6I6D8dO3ZMLiTYunVrZAViFXMRcImFPTPCqVOn5ArSRJQ5MLghov+0cOFCDB06FIcOHcKjR4+M3ZxMx8XFBTY2NsZuBhG9xOCGiN4qIiICq1evxqBBg2TPzZIlS5I97+jRoyhfvjysrKxQo0YNXLp0yXDs3r17aNu2LRwdHWFra4syZcpg27ZthuMHDx5EtWrVYGlpiTx58uDrr79GQkJCim0SvTKbNm1Ksi9nzpyGthUuXFh+rVixojxXDC3pLViwAKVKlZLtLFmyJObMmfOf74Foy5AhQ+Dg4ABnZ2eMHTtWLDqc4rDU9OnTUa5cOfla3d3dMXjwYPk+vuv7QUQfhsENEb3VmjVrZBBQokQJfPrpp1i0aFGSC7ve//73P0ybNk0O0YieDHHxjo+Pl8e8vb0RGxsre34uXryIX375BXZ2dvLYw4cP0apVK1StWhXnz5/H3LlzZU/Rjz/++N5tPnnypPy6Z88ePH78GBs2bJDby5cvx7hx4zBp0iRcvXoVP/30kwxUli5d+tbnE8fNzMzk8/7+++8yeBFBUkqUSiVmzpyJy5cvy8fu27cPo0aNMhx/2/tBRGkgzdcZJyKTUqtWLe1vv/0m78fHx2udnZ21+/fvNxwX98VHyapVqwz7nj9/rrW2ttauXr1abpcrV047YcKEZJ//m2++0ZYoUUKr0WgM+3x8fLR2dnZatVott+vXr68dPny44bj4fhs3bkzyPA4ODtrFixfL+/7+/vKcc+fOJTnHw8NDu2LFiiT7fvjhB23NmjVTfP3ie5cqVSpJ+0aPHi336RUsWFA7Y8aMFJ9j7dq1WicnJ8P2294PIvpw7LkhohRdv35d9lZ069ZNbovei65du8qeldfVrFnTcD9Xrlyyp0f0jgjDhg2TPTG1a9fG+PHjceHCBcO54hzxWDF8pCfOE8M4Dx48SLPXEhkZidu3b+Ozzz6TvST6m2iX2P82YpgtcftEe2/evAm1Wp3s+aLHqHHjxsiXLx/s7e3Rs2dPPH/+HFFRUf/5fhDRh2NwQ0QpEkGMyDfJmzevDGzETQwbrV+/Hi9evHjn5+nfvz/u3LkjL/JiGKZKlSqYNWvWe7dLBBqvD43ph8BSos95mT9/vpxFpb+J3KDjx48jLWdqtWnTRuYfiffpzJkz8PHxkcfi4uLS5f0goqQY3BBRskRQs2zZMplHkzgYEHkxIthZuXJlkvMTBwghISG4ceOGTNzVE4m1Xl5eMv/lyy+/lEGGIM4RU80TBysiOVn0eOTPnz/ZtomcHpFLoyd6UfS9IoKFhYX8mrhnJXfu3LLdIqgoWrRokps+ATklJ06ceOO1FitWTE6Pf50IZjQajXzfRI9P8eLFk51hltL7QUQfziwNnoOITNDWrVtlkCKGccQsocQ6deoke3XExVlv4sSJcHJykkHEt99+K2cVdejQQR4TRfBatmwpL/TiOffv328IfMRMIjHTSEw1FzOSxFCYGKoZOXKkTMxNTqNGjTB79mw5PCQCmNGjR8Pc3Nxw3NXVFdbW1tixY4cMkMTMKPEavv/+ezkkJO63aNFCJvWePn1atkl8v5QEBATI4wMHDsTZs2dlL4sIXpIjgiXRiyTOEUnVIlDz9fVNcs7b3g8iSgNpkLdDRCaoTZs22latWiV77MSJEzJh9/z584aE4i1btmjLlCmjtbCw0FarVk0e0xsyZIhM5rW0tNS6uLhoe/bsqQ0KCjIcP3DggLZq1arysW5ubjJhVyQv672eUPzw4UNts2bNtLa2ttpixYppt23bliShWJg/f77W3d1dq1Qq5eP1li9frvX09JTfy9HRUVuvXj3thg0bUnwfxGMHDx6s9fLy0ubIkUM+RiRBJ04wfj2hePr06do8efLIpOrmzZtrly1bJt+jkJCQd3o/iOjDKMQ/aREkEREREWUGzLkhIiIik8LghoiIiEwKgxsiIiIyKQxuiIiIyKQwuCEiIiKTwuCGiIiITAqDGyIiIjIpDG6IiIjIpDC4ISIiIpPC4IaIiIhMCoMbIiIigin5PxYrxgWkBPRkAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = np.arange(5, 9)\n", "fig, ax = plt.subplots()\n", "\n", "for n in ns:\n", " all_hamming = np.arange(1, 2 ** (n - 1), 2)\n", " all_abs_bias = 2 * np.abs(all_hamming/2**n - 0.5)\n", " avg_sens = np.zeros(2 ** (n - 2))\n", "\n", " for i, w in enumerate(all_hamming):\n", " layer = boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(n, w)\n", " f = boolforge.random_function(n, layer_structure=layer)\n", " avg_sens[i] = f.get_average_sensitivity(EXACT=True, NORMALIZED=False)\n", "\n", " ax.plot(all_abs_bias, avg_sens, \"x--\", label=f\"n={n}\")\n", "\n", "ax.legend(frameon=False)\n", "ax.set_xlabel(\"Absolute bias\")\n", "ax.set_ylabel(\"Average sensitivity\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "18a6d53f", "metadata": {}, "source": [ "---\n", "## 5. Summary and outlook\n", "\n", "This tutorial illustrated how ensembles of Boolean functions generated under\n", "explicit constraints reveal systematic relationships between canalization,\n", "bias, redundancy, and sensitivity.\n", "\n", "The key findings include: \n", "\n", "1. Canalization is rare in random functions but common in biology.\n", "2. Canalizing strength and input redundancy both decrease with degree.\n", "3. Functions with high absolute bias are more likely to be highly canalizing.\n", "4. For NCFs, layer structure is uniquely determined by bias.\n", "5. Average sensitivity varies systematically with layer structure.\n", "\n", "These relationships constrain the space of biologically plausible functions\n", "and suggest evolutionary optimization for robustness.\n", "\n", "We now move on to Boolean networks, where Boolean functions serve as node update\n", "rules and give rise to collective dynamical behavior." ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "main_language": "python", "notebook_metadata_filter": "-all" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }