{ "cells": [ { "cell_type": "markdown", "id": "ecf1b815", "metadata": {}, "source": [ "# Ensemble experiments with random Boolean functions\n", "\n", "In this tutorial, we explore how BoolForge’s random Boolean function generator \n", "can be used to generate large ensembles of Boolean functions with prescribed structural properties,\n", "whose statistical and dynamical characteristics can then be studied.\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", "## Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "67e01cc4", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:29.354641Z", "iopub.status.busy": "2026-03-31T06:05:29.354331Z", "iopub.status.idle": "2026-03-31T06:05:33.282689Z", "shell.execute_reply": "2026-03-31T06:05:33.281759Z" }, "lines_to_next_cell": 2 }, "outputs": [], "source": [ "import boolforge as bf\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": "afd89651", "metadata": {}, "source": [ "## 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": "07205ec1", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:33.287573Z", "iopub.status.busy": "2026-03-31T06:05:33.287023Z", "iopub.status.idle": "2026-03-31T06:05:33.810360Z", "shell.execute_reply": "2026-03-31T06:05:33.810120Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " k=0 k=1 k=2 k=3 k=4 k=5 k=6\n", "n=2 0.187 0.000 0.813 0.000 0.000 0.0 0.0\n", "n=3 0.590 0.109 0.000 0.301 0.000 0.0 0.0\n", "n=4 0.946 0.035 0.002 0.000 0.017 0.0 0.0\n", "n=5 0.999 0.001 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\n" ] } ], "source": [ "n_simulations = 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(n_simulations):\n", " for i, n in enumerate(ns):\n", " f = bf.random_function(n)\n", " count_depths[i, f.get_canalizing_depth()] += 1\n", "\n", "count_depths /= n_simulations\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", "out = 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", ")\n", "\n", "print(out.to_string())" ] }, { "cell_type": "markdown", "id": "49bdefbe", "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 [@kadelka2024meta]." ] }, { "cell_type": "markdown", "id": "d05b07b7", "metadata": {}, "source": [ "### Restricting to canalizing functions\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": "code", "execution_count": 3, "id": "a9c4ea51", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:33.811670Z", "iopub.status.busy": "2026-03-31T06:05:33.811590Z", "iopub.status.idle": "2026-03-31T06:05:34.431480Z", "shell.execute_reply": "2026-03-31T06:05:34.431220Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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0yLN//vx5ufXWW83Fy5cvn89f7+4Fd/v8nIFqy2NbfHauA7Xr+Oxcga7C9m0+O9fMARt8dq5A99SUxj4715v/eMRn5wp0/eZ97LuTjbu5L1yrDPvF56fUio7SpUtL3rx5b/pcWSr8FCtWTE6ePOl1TPc1xKRU66N0VJhuSelzMiL8ZA/N7vNzBipfXv882bnuTlz30ODcPjtXoPPldc+VM6fPzhXofPp7PoSuEmmWAd+vbr7ospKlwk9kZKSsWrXK69iXX35pjgOALeY98B+ni5BlDHa6APBLjg51//PPP82Qdd3cQ9n19rFjxzxNVl26dPE8vlevXnLkyBF5/vnnZf/+/fL222/LRx99JAMHDnTsPQAAgKzF0fCzbds2qVmzptmU9s3R28OHDzf7x48f9wQhVa5cOTPUXWt7dH6giRMnyuzZs82ILwAAAL9v9mrSpIkZupaalGZv1ufs3Lkzg0sGAAACFWt7AQAAqxB+AACAVQg/AADAKoQfAABglSw1zw8AQGTP0f+NggWQftT8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVHA8/06ZNk7Jly0quXLmkXr16snXr1us+fsqUKVKhQgUJDQ2V0qVLy8CBA+Xy5cuZVl4AAJC1ORp+Fi1aJIMGDZIRI0bIjh07JCIiQlq2bCmnTp1K8fELFiyQoUOHmsfv27dP3n33XXOOF154IdPLDgAAsiZHw8+kSZOkZ8+e0q1bN6lcubLMmDFDwsLCZM6cOSk+ftOmTdKgQQN57LHHTG1RixYtpFOnTn9ZWwQAAOB4+Lly5Yps375dmjdv/r/CZMtm9jdv3pzic+rXr2+e4w47R44ckVWrVskDDzyQ6uvExcVJTEyM1wYAAOyVw6kXPnPmjMTHx0t4eLjXcd3fv39/is/RGh993j333CMul0uuXbsmvXr1um6z17hx42TUqFE+Lz8AAMiaHO/wnB7r16+XV155Rd5++23TR+iTTz6RlStXyujRo1N9zrBhw+T8+fOeLTo6OlPLDAAA/ItjNT+FCxeW7Nmzy8mTJ72O636xYsVSfM5LL70kTzzxhDz55JNmv1q1ahIbGytPPfWU/Otf/zLNZkmFhISYDQAAwNGan+DgYKldu7asXbvWcywhIcHsR0ZGpvicixcvJgs4GqCUNoMBAAD4bc2P0mHuXbt2lTp16kjdunXNHD5ak6Ojv1SXLl2kZMmSpt+OatOmjRkhVrNmTTMn0KFDh0xtkB53hyAAAAC/DT8dO3aU06dPy/Dhw+XEiRNSo0YNWb16tacT9LFjx7xqel588UUJCgoy///111+lSJEiJviMHTvWwXcBAACyEkfDj+rbt6/ZUuvgnFiOHDnMBIe6AQAABPxoLwAAgCxf8wMg65oR2d/pImQZfWSP00UA8P9R8wMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxy0+EnJiZGli1bJvv27fNNiQAAAPwp/HTo0EHeeustc/vSpUtSp04dc6x69eqyZMmSjCgjAACAc+Hn66+/loYNG5rbS5cuFZfLJefOnZM33nhDxowZ47uSAQAAZIAc6X3C+fPnpWDBgub26tWrpX379hIWFiatW7eW5557LiPKCMBP7Tl6zOkiAEDG1/yULl1aNm/eLLGxsSb8tGjRwhw/e/as5MqVK/0lAAAA8OeanwEDBkjnzp0lT548UqZMGWnSpImnOaxatWoZUUYAAADnws/TTz8tdevWlejoaLnvvvskW7b/Vh7ddttt9PkBAACBF36UjvDSLTHt8wMAABBw4Sc+Pl7mzZsna9eulVOnTklCQoLX/evWrfNl+QAAAJwNP/379zfhR2t6qlatKkFBQb4tEQAAgD+Fn4ULF8pHH30kDzzwQMaUCAAAwJ+GugcHB0v58uUzpjQAAAD+Fn4GDx4sU6dONTM7AwAABHyz18aNGyUqKko+//xzqVKliuTMmdPr/k8++cSX5QMAAHA2/BQoUEAeeugh35YCAADAX8PP3LlzM6YkAAAA/jrJoTp9+rQcOHDA3K5QoYIUKVLEl+UCAADwjw7PuqBp9+7dpXjx4tKoUSOzlShRQnr06CEXL17MmFICAAA4FX4GDRokGzZskM8++0zOnTtntk8//dQc05FgAAAAAdXstWTJElm8eLFnNXelEx6GhoZKhw4dZPr06b4uIwAAgHM1P9q0FR4enux40aJFafYCAACBF34iIyNlxIgRcvnyZc+xS5cuyahRo8x9AAAAAdXspbM7t2zZUkqVKiURERHm2O7duyVXrlyyZs2ajCgjAACAc+FHV3I/ePCgzJ8/X/bv32+OderUSTp37mz6/QAAAATcPD9hYWHSs2dP35cGAADAH8LP8uXLpVWrVmYdL719PQ8++KCvygYAAOBM+GnXrp2cOHHCjOjS26kJCgqS+Ph4X5YPAAAg88NPQkJCircBAAACfqj7+++/L3FxccmOX7lyxdwHAAAQUOGnW7ducv78+WTHL1y4YO4DAAAIqPDjcrlM356kfvnlF8mfP7+vygUAAODsUPeaNWua0KNbs2bNJEeO/z1VOzkfPXpU7r///owpJQAAQGaHH/cor127dpkZnvPkyeO5Lzg4WMqWLSvt27f3VbkAAACcDT+6npfSkPPoo49KSEhIxpQIAADAn/r8VK5c2dT+JPXdd9/Jtm3bfFUuAAAA/wg/ffr0kejo6GTHf/31V3MfAABAQIWfH3/8UWrVqpVih2i9L72mTZtmmtJ0Vfh69erJ1q1br/v4c+fOmZBVvHhx0/R25513yqpVq9L9ugAAwE7pDj8aOE6ePJns+PHjx71GgKXFokWLZNCgQaY/0Y4dOyQiIsJ0pj516lSKj9eJFO+77z75+eefZfHixXLgwAGZNWuWlCxZMr1vAwAAWCrd4adFixYybNgwr4kOtTbmhRdeMMEkPSZNmmRWh9fJEbUv0YwZM8yK8XPmzEnx8Xr8jz/+kGXLlkmDBg1MjVHjxo1NaAIAAMiQ8PP666+bPj9lypSRe++912zlypUzC59OnDgxzefRWpzt27dL8+bN/1eYbNnM/ubNm1N8jq4oHxkZaZq9wsPDpWrVqvLKK69cdzFVXYojJibGawMAAPZKXzuViGli+ve//y3z58+X3bt3S2hoqKm56dSpk+TMmTPN5zlz5owJLRpiEtP9/fv3p/icI0eOyLp166Rz586mn8+hQ4fk6aeflqtXr3qG4ic1btw4GTVqVDrfJQAACFTpDj8qd+7c8tRTT0lm0xXlixYtKjNnzpTs2bNL7dq1zSiz1157LdXwo0102q/ITWt+SpcunYmlBgAAWT78HDx4UKKiokzHZA0kiQ0fPjxN5yhcuLAJMEk7T+t+sWLFUnyOjvDS2iV9nlulSpVMk5s2o+lM0yl10GZCRgAAcMPhR0dX9e7d24QXDSmJFznV22kNPxpUtOZm7dq1nqUzNEjpft++fVN8jnZyXrBggXmc9g9SP/30kwlFKQUfAACAmw4/Y8aMkbFjx8qQIUPkZmlzVNeuXaVOnTpSt25dmTJlisTGxpo+RKpLly6mj5H221Eaut566y3p37+/9OvXz9RAaYfnZ5555qbLAgAA7JDu8HP27Fl55JFHfPLiHTt2lNOnT5vaIm26qlGjhqxevdrTCfrYsWOeGh6lfXXWrFkjAwcOlOrVq5tgpEHIF0EMAADYId3hR4PPF198Ib169fJJAbSJK7VmrvXr1yc7pkPdt2zZ4pPXBgAA9kl3+Clfvry89NJLJoBUq1Yt2fB2mqAAAEBAhR8dZp4nTx7ZsGGD2RLTDs+EHwAAEFDh5+jRoxlTEgAAAH9c3gIAAMCqmp/u3btf9/7UFiUFAADIskPdE9N1tfbu3WtWdm/atKkvywYAAOB8+Fm6dGmyYzrjsk5AePvtt/uqXAAAAP7b50cnItTZmidPnuyL0wEAAPh/h+fDhw/LtWvXfHU6AAAA/2j20hqexFwulxw/flxWrlxp1ukCAAAIqPCzY8cOr5XctcmrSJEiMnHixL8cCQYAAJAlws/y5culVatWZimLlNbbAgAACKg+Pw899JAZyq6yZ88up06dyuhyAQAAOBd+tFnLvZK69vFJ3OwFAAAQcM1evXr1krZt25rQo1uxYsVSfWx8fLwvywcAAJD54WfkyJHy6KOPyqFDh+TBBx+UuXPnSoECBXxbEgAAAH8a7VWxYkWzjRgxQh555BEJCwvL2JIBAAD4w1B3DT8AAABZlc9meAYAAMgKCD8AAMAqhB8AAGCVNIWfggULypkzZ8xtXcLiwoULGV0uAAAA58LPlStXJCYmxtx+77335PLlyxlTGgAAAH8Y7RUZGSnt2rWT2rVrmxmen3nmGQkNDU3xsXPmzPF1GQEAADI3/Pzf//2fTJ48WQ4fPmxmeD5//jy1PwAAIHDDT3h4uIwfP97cLleunHzwwQdSqFChjC4bAACA85McHj161PelAAAA8Oeh7hs2bJA2bdpI+fLlzabrfX3zzTe+Lx0AAIDT4Uf7/zRv3tys7aUdn92dn5s1ayYLFizwdfkAAACcbfYaO3asvPrqqzJw4EDPMQ1AkyZNktGjR8tjjz3m2xICAAA4WfNz5MgR0+SVlDZ90R8IAAAEXPgpXbq0rF27Ntnxr776ytwHAAAQUM1egwcPNs1cu3btkvr165tj3377rcybN0+mTp2aEWUEAABwLvz07t1bihUrJhMnTpSPPvrIHKtUqZIsWrRI2rZt67uSAQAA+EP4UQ899JDZAAAArJjnBwAAIKsi/AAAAKsQfgAAgFUIPwAAwCqEHwAAYJV0j/aKj483c/roRIenTp2ShIQEr/vXrVvny/IBAAA4G3769+9vwk/r1q2latWqEhQU5NsSAQAA+FP4WbhwoZnc8IEHHsiYEgEAAPhTn5/g4GApX758xpQGAADA38KPru2la3i5XK6MKREAAIA/NXtt3LhRoqKi5PPPP5cqVapIzpw5ve7/5JNPfFk+AAAAZ8NPgQIFWNcLAADYE37mzp2bMSUBAADw11Xd1enTp+XAgQPmdoUKFaRIkSK+LBcAAIB/dHiOjY2V7t27S/HixaVRo0ZmK1GihPTo0UMuXryYMaUEAABwKvwMGjRINmzYIJ999pmcO3fObJ9++qk5piPBAAAAAqrZa8mSJbJ48WJp0qSJ55hOeBgaGiodOnSQ6dOn+7qMAAAAztX8aNNWeHh4suNFixal2QsAAARe+ImMjJQRI0bI5cuXPccuXboko0aNMvcBAAAEVLOXzu7csmVLKVWqlERERJhju3fvlly5csmaNWsyoowAAADOhR9dyf3gwYMyf/582b9/vznWqVMn6dy5s+n3AwAAEHDz/ISFhUnPnj19XxoAAAB/CD/Lly+XVq1amXW89Pb1PPjgg74qGwAAgDPhp127dnLixAkzoktvpyYoKEji4+N9WT4AAIDMDz8JCQkp3gYAAAj4oe7vv/++xMXFJTt+5coVcx8AAEBAhZ9u3brJ+fPnkx2/cOGCuQ8AACCgwo/L5TJ9e5L65ZdfJH/+/L4qFwAAgLPhp2bNmlKrVi0TfJo1a2Zuuzed7LBhw4bSvHnzGyrEtGnTpGzZsmaixHr16snWrVvT9LyFCxea8lyvEzYAAMANzfPjDhi7du0yMzznyZPHc19wcLAJL+3bt5f0WrRokVkpfsaMGSb4TJkyxZz/wIEDZnRZan7++Wd59tlnTegCAADwefjR9bx0GLuGnBYtWkjx4sXFFyZNmmQmTHT3F9IQtHLlSpkzZ44MHTo0xedoOXRGaV1P7JtvvpFz5875pCwAACDwpavPT/bs2eWf//yn16KmN0NHiG3fvt2ruSxbtmxmf/Pmzak+7+WXXza1Qj169PjL19CRaTExMV4bAACwV7YbWdvryJEjPnnxM2fOmFqc8PBwr+O6r5MqpmTjxo3y7rvvyqxZs9L0GuPGjTMdsd1b6dKlfVJ2AABgSfgZM2aM6WuzYsUKOX78eKbWquhw+ieeeMIEn8KFC6fpOcOGDTND891bdHR0hpYRAAAE2MKmDzzwgGcNr8RD3t1D4NOzvIUGGG1KO3nypNdx3S9WrFiyxx8+fNh0dG7Tpk2yGadz5MhhOknffvvtXs8JCQkxGwAAwA2Fn6ioKJ9dOR0lVrt2bVm7dq1nNJmGGd3v27dvssdXrFhR9uzZ43XsxRdfNDVCU6dOpUkLAAD4Pvw0btxYfEmHuXft2lXq1KkjdevWNUPdY2NjPaO/unTpIiVLljR9d3QeIO1zlFiBAgXM/5MeBwAA8En4UTq0XDsd79u3z+xXqVJFunfvfkMzPHfs2FFOnz4tw4cPN52ca9SoIatXr/Z0gj527JgZAQYAAOBI+Nm2bZuZhDA0NNTU1Ljn6hk7dqx88cUXZsbn9NImrpSaudT69euv+9x58+al+/UAAIC90h1+Bg4caDo764gr7WSsrl27Jk8++aQMGDBAvv7664woJwAAgHM1P4mDjzlJjhzy/PPPm347AAAA/izdnWny5ctn+uEkpfPn5M2b11flAgAA8I/wox2UdVkJXZBUA49uurq6Nnt16tQpY0oJAADgVLPX66+/biYz1CHo2tdH5cyZU3r37i3jx4/3VbkAAAD8I/zoxIQ6oaDOu6MzLiudVTksLCwjygcAAOD8PD9Kw457gkGCDwAACNg+P9rU9dJLL5kJDcuWLWs2va3LTFy9ejVjSgkAAOBUzU+/fv3kk08+kVdffVUiIyPNsc2bN8vIkSPl999/l+nTp/uqbAAAAM6HnwULFpjRXa1atfIcq169ullUVEd7EX4AAEBANXuFhISYpq6kypUrZzpDAwAABFT40TW4Ro8eLXFxcZ5jelvX9kptfS4AAIAs2+y1c+dOWbt2rZQqVUoiIiLMsd27d8uVK1ekWbNm8vDDD3seq32DAAAAsnT40eHt7du39zqm/X0AAAACMvzMnTs3Y0oCAADgz5Mcnj59Wg4cOGBuV6hQQYoUKeLLcgEAAPhHh+fY2Fjp3r27FC9eXBo1amS2EiVKmMVOL168mDGlBAAAcCr8DBo0SDZs2CCfffaZnDt3zmyffvqpOTZ48GBflQsAAMA/mr2WLFkiixcvliZNmniOPfDAAxIaGiodOnRgkkMAABBYNT/atBUeHp7seNGiRWn2AgAAgRd+dD2vESNGyOXLlz3HLl26JKNGjfKs9QUAABAwzV5TpkyR+++/P9kkh7ly5ZI1a9ZkRBkBAACcCz/VqlWTgwcPyvz582X//v3mmC5o2rlzZ9PvBwAAIGDCz9WrV6VixYqyYsUK6dmzZ8aVCgAAwB/6/OTMmdOrrw8AAEDAd3ju06ePTJgwQa5du5YxJQIAAPCnPj/ff/+9WdX9iy++MP1/cufO7XU/K7kDAICAX9UdAAAgq2BVdwAAYJU09/lJSEgwfX0aNGggd911lwwdOtRMbggAABCQ4Wfs2LHywgsvSJ48eaRkyZIydepU0/kZAAAgIMPP+++/L2+//baZxXnZsmVmVXed6FBrhAAAAAIu/Bw7dsys3u7WvHlzCQoKkt9++y2jygYAAOBc+NF5fXT9rqSTHuqszwAAAAE32svlcsk//vEPCQkJ8RzT2Z579erlNdcP8/wAAICACD9du3ZNduzxxx/3dXkAAAD8I/wwvw8AALBybS8AAICsjPADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArJLD6QIAvlDp0d+cLgIAIIug5gcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBW/CD/Tpk2TsmXLSq5cuaRevXqydevWVB87a9Ysadiwodxyyy1ma968+XUfDwAA4FfhZ9GiRTJo0CAZMWKE7NixQyIiIqRly5Zy6tSpFB+/fv166dSpk0RFRcnmzZuldOnS0qJFC/n1118zvewAACDrcTz8TJo0SXr27CndunWTypUry4wZMyQsLEzmzJmT4uPnz58vTz/9tNSoUUMqVqwos2fPloSEBFm7dm2mlx0AAGQ9joafK1euyPbt203TladA2bKZfa3VSYuLFy/K1atXpWDBgineHxcXJzExMV4bAACwl6Ph58yZMxIfHy/h4eFex3X/xIkTaTrHkCFDpESJEl4BKrFx48ZJ/vz5PZs2kwEAAHs53ux1M8aPHy8LFy6UpUuXms7SKRk2bJicP3/es0VHR2d6OQEAgP9wdFX3woULS/bs2eXkyZNex3W/WLFi133u66+/bsLPV199JdWrV0/1cSEhIWYDAABwvOYnODhYateu7dVZ2d15OTIyMtXnvfrqqzJ69GhZvXq11KlTJ5NKCwAAAoGjNT9Kh7l37drVhJi6devKlClTJDY21oz+Ul26dJGSJUuavjtqwoQJMnz4cFmwYIGZG8jdNyhPnjxmAwAA8Ovw07FjRzl9+rQJNBpkdAi71ui4O0EfO3bMjABzmz59uhkl9ve//93rPDpP0MiRIzO9/AAAIGtxPPyovn37mi21SQ0T+/nnnzOpVAAAIBBl6dFeAAAA6UX4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALCKX4SfadOmSdmyZSVXrlxSr1492bp163Uf//HHH0vFihXN46tVqyarVq3KtLICAICszfHws2jRIhk0aJCMGDFCduzYIREREdKyZUs5depUio/ftGmTdOrUSXr06CE7d+6Udu3amW3v3r2ZXnYAAJD1OB5+Jk2aJD179pRu3bpJ5cqVZcaMGRIWFiZz5sxJ8fFTp06V+++/X5577jmpVKmSjB49WmrVqiVvvfVWppcdAABkPTmcfPErV67I9u3bZdiwYZ5j2bJlk+bNm8vmzZtTfI4e15qixLSmaNmyZSk+Pi4uzmxu58+fN/+PiYmRjBB/KT5DzhuIfPoZxLl8d65Ax3V3BtfdGVx3Z8TEZNh3hsvlytrh58yZMxIfHy/h4eFex3V///79KT7nxIkTKT5ej6dk3LhxMmrUqGTHS5cufVNlx83L3zu/00Ww03iuuyO47s7gugfcdb9w4YLkz58/64afzKC1SolrihISEuSPP/6QQoUKSVBQkAQ6Tcoa9KKjoyVfvnxOF8caXHdncN2dwXV3hm3X3eVymeBTokSJmz6Xo+GncOHCkj17djl58qTXcd0vVqxYis/R4+l5fEhIiNkSK1CggNhG/2HY8I/D33DdncF1dwbX3Rk2Xff8N1nj4xcdnoODg6V27dqydu1ar5oZ3Y+MjEzxOXo88ePVl19+merjAQAA/KrZS5ukunbtKnXq1JG6devKlClTJDY21oz+Ul26dJGSJUuavjuqf//+0rhxY5k4caK0bt1aFi5cKNu2bZOZM2c6/E4AAEBW4Hj46dixo5w+fVqGDx9uOi3XqFFDVq9e7enUfOzYMTMCzK1+/fqyYMECefHFF+WFF16QO+64w4z0qlq1qoPvwn9pk5/OoZS06Q8Zi+vuDK67M7juzuC637ggly/GjAEAAGQRjk9yCAAAkJkIPwAAwCqEHwAAYBXCDwAAsArhJ0Dp1AB33XWX5M2bV4oWLWpWvj9w4IDTxQp406dPl+rVq3smHdP5pz7//HOni2Wd8ePHmxncBwwY4HRRAtrIkSPNdU68VaxY0eliWeHXX3+Vxx9/3KxWEBoaKtWqVTPTviBtCD8BasOGDdKnTx/ZsmWLmQTy6tWr0qJFCzOHEjJOqVKlzBevLtirv4iaNm0qbdu2lR9++MHpolnj+++/l3feeceEUGS8KlWqyPHjxz3bxo0bnS5SwDt79qw0aNBAcubMaf64+vHHH83cd7fccovTRcsyHJ/nBxlD50pKbN68eaYGSL+UGzVq5Fi5Al2bNm289seOHWtqgzSE6pcEMtaff/4pnTt3llmzZsmYMWOcLo4VcuTIkeryQsgYEyZMMGt6zZ0713OsXLlyjpYpq6HmxxLnz583/y9YsKDTRbFGfHy8mYFca9tYfiVzaG2nzvzevHlzp4tijYMHD5qFJm+77TYTPHViWmSs5cuXm1URHnnkEfNHbc2aNU3gR9pR82MBXS9N+z5oNSkzYWe8PXv2mLBz+fJlyZMnjyxdulQqV67sdLECngbNHTt2mGYvZI569eqZWuUKFSqYJq9Ro0ZJw4YNZe/evaa/ITLGkSNHTI2yLg+lKx3oz/wzzzxj1svU5aLw15jh2QK9e/c27cLaFq99UpCxrly5Yv761dq2xYsXy+zZs00fLAJQxomOjjZ/CWv/NndfnyZNmpjlcnS9QGSOc+fOSZkyZWTSpEnSo0cPp4sTsDTk6M/7pk2bPMc0/GgI2rx5s6Nlyypo9gpwffv2lRUrVkhUVBTBJxN/MZUvX15q165tRt1FRETI1KlTnS5WQNO+bKdOnZJatWqZPii6aeB84403zG1tgkTGK1CggNx5551y6NAhp4sS0IoXL57sj6lKlSrR5JgONHsFKK3Q69evn2lyWb9+PZ3hHG52jIuLc7oYAa1Zs2amuTGxbt26mWHXQ4YMkezZsztWNts6nB8+fFieeOIJp4sS0LQLQ9KpS3766SdT64a0IfwEcMfPBQsWyKeffmra3k+cOGGO58+f38wJgYwxbNgwadWqldx6661y4cIF8xlo+FyzZo3TRQto+jOetD9b7ty5zRwo9HPLOM8++6wZ4ahfur/99ptZYVyDZqdOnZwuWkAbOHCg1K9fX1555RXp0KGDbN26VWbOnGk2pA3hJ0BpZzh3v4fEdGjkP/7xD4dKFfi06aVLly6m86cGTe1/osHnvvvuc7pogM/98ssvJuj8/vvvUqRIEbnnnnvMtA56GxlHJ7DVWn39Y+vll182Nfvat01H2yFt6PAMAACsQodnAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8gC/r5558lKChIdu3aJf5i//79cvfdd0uuXLnMauqBQpcn0WutK5anlc6sPmDAAHFC2bJl07WS/bx588yCpNczcuTIgPpMAcIPcAN0iRD9Qhw/frzX8WXLlpnjNtJ1nXQ9LV1wce3atZIVpRRadA0l93IlWcH3338vTz31lNPFAPwa4Qe4QVrDMWHCBDl79qwEiitXrtzwc3U1b13bSRe51AVFA0VwcLAUK1bM70Ot+7PTdbXCwsKcLg7g1wg/wA1q3ry5+VIcN25cupoLtElCmyYS1yK1a9fOrNAcHh5umiB0scJr167Jc889JwULFpRSpUqZRWlTamrSmgkNYrp6+YYNG7zu37t3r1llPk+ePObcTzzxhJw5c8arpqNv376mtqNw4cLSsmXLFN9HQkKCKZOWIyQkxLyn1atXe+7XYLB9+3bzGL2t7zu18+j10oUYQ0NDJSIiQhYvXuy5X4OkLs6oX+B6/x133OF53/rlrmUtXry4eb8ashJfe22WevLJJ81z8+XLJ02bNpXdu3cn+yw++OADc/21JufRRx+VCxcueD4HvX5Tp04170E3bV5M2uyli3jqYp4lS5Y0IaNatWry4YcfSlr99NNP5nz62SU2efJkuf32283t+Ph46dGjh+c6VahQwZQrMffPzdixY6VEiRLmMSk1e02aNMmUUWvlSpcuLU8//bT8+eefycqltZZ6vfXa6s9BdHT0dd/H7NmzpVKlSubxFStWlLfffttz3199VoDTCD/ADcqePbsJLG+++aZZ3fpmrFu3Tn777Tf5+uuvzZeVNiH97W9/k1tuuUW+++476dWrl/zzn/9M9joajgYPHiw7d+6UyMhIadOmjflyVvplrQGgZs2asm3bNhNWTp48KR06dPA6x3vvvWdqN7799luZMWNGiuXTL96JEyfK66+/Lv/+97/Nl+ODDz4oBw8eNPdrs1CVKlVMWfT2s88+m+J59Avw/fffN6/zww8/yMCBA+Xxxx/3hLaXXnpJfvzxR/n8889l3759Mn36dBPK1BtvvCHLly+Xjz76yDStzZ8/3ytEPvLII3Lq1CnzXA1itWrVkmbNmskff/zhVTulX/IrVqwwm76uu+lS36New549e5r3oJuGhaQuX74stWvXlpUrV5pwqU1MGiq3bt2aps/6zjvvlDp16pjyJ6b7jz32mCckatD8+OOPzfUYPny4vPDCC+a9J6bNi3otvvzyS/N+UpItWzZz7fR662etP2vPP/+812MuXrxoQpR+NvpzoD87GgxTo2XVMulz9HPSfwf62en50/JZAY7TVd0BpE/Xrl1dbdu2NbfvvvtuV/fu3c3tpUuXuhL/sxoxYoQrIiLC67mTJ092lSlTxutcuh8fH+85VqFCBVfDhg09+9euXXPlzp3b9eGHH5r9o0ePmtcZP3685zFXr151lSpVyjVhwgSzP3r0aFeLFi28Xjs6Oto878CBA2a/cePGrpo1a/7l+y1RooRr7NixXsfuuusu19NPP+3Z1/ep7zc1ly9fdoWFhbk2bdrkdbxHjx6uTp06mdtt2rRxdevWLcXn9+vXz9W0aVNXQkJCsvu++eYbV758+cxrJHb77be73nnnHXNby6avHxMT47n/ueeec9WrV8+zr9ejf//+XueIiooy1+zs2bOpvrfWrVu7Bg8efN3zJP0Z0LK56eehr7Fv375Un9OnTx9X+/btvX5uwsPDXXFxcV6P058lPX9qPv74Y1ehQoU8+3PnzjWvvWXLFs8xLYce++6771L8OdayL1iwwOu8+vMWGRn5l58V4A+o+QFukvb70b949S/gG6W1JvoXups2UWlTReJaJu1HozUbiWlNhVuOHDlMjYK7HNrkExUVZZq83Js2T7hrQNy0FuN6YmJiTK1UgwYNvI7rfnre86FDh0wNw3333edVJq1tcJend+/esnDhQtM8pbUTmzZt8mrm0dFt2rzzzDPPyBdffOG5T9+rNuXoNUp87qNHj3q9V619yJs3r2dfm2WSXtO/ok1So0ePNp+PNknq66xZs0aOHTuW5nNorYo2qW3ZssXsa82I1lS5Px81bdo089loM56+xsyZM5O9hpZBa+2u56uvvjI1YNpMp+9da6m0dlA/i8Q/O3fddZdnX8uhza8pfb6xsbHmmmqzXOJrPWbMGM+1vt5nBfiDHE4XAMjqGjVqZJqBhg0bZn7pJ6aBxuXSP6L/5+rVq8nOkTNnTq997ROS0jFtDkkrDQPaDKbhLCn90nfTviCZwd3PRJuL9Is4Me1HpLR/0n/+8x9ZtWqVacrRL+0+ffqY5jYNBxpmtFlLv9C1+U77XWmfIT23viftn5NU4mHcN3tN1WuvvWaayLRfjbsvjfaZSk9nce0rpk2SCxYsMNMD6P81+LlpANSmQ21q1ICroUVfV5tAE/urz04Dljaf6rm1iUrD2saNG01w0fLeSMdo9+c4a9YsqVevntd9GtLV9T4rwB8QfgAf0H4jWlvh7nTqpn+1nzhxwgQg92ghX87NozUHGr6UdpDWvi7a0dT9BbRkyRJT26F/2d8o7TysHWq1L0jjxo09x3W/bt26aT5P5cqVTcjR2ovE50lKr1nXrl3N1rBhQ9OvScOPuywdO3Y029///ne5//77TZ8efa96nfV93kzfEq1F0Zqd69H33bZtW9NXSWl40k7M+v7SQzt2a+2Wdp4+cuSIVx8bfQ3tyK6dk90S12Cllf48aPk0RLlrFpP2G3L/7Gi/MPfnqf10tN+PdmhOSmsl9edBy6zvITWpfVYawACnEX4AH9AaAP0i0I6eieloqtOnT8urr75qvgC007H+NaxfDL6gTSM6Qke/pHS0kI6W6t69u7lPa0z0r3P9ctUvWf3S0aYnrVXQkTruv9LTQgOIdsLW0Uga8nQEloa4pJ12r0drL7Q2Qzs56xeyDos/f/68+aLX66FhRzvRalOPNgPGxcWZTrzuL2DtCK61O9qBW7/ItTOw1qBozY7WKmgNiY5+0mutnYq1qU5rmR566CHTHJgWGpy0dkVrTLQpJ6Uvar3eWoOhTXLaIV3LpR3J0xt+Hn74YVMjo9u9995rAkXi19DmQG1O0xFfOkJN5+/R2+lRvnx5U9OonfK1FjC1Tu1aI9avXz/z86sBUgO01kilFm5HjRplmrN0xJyGGv2sNDzpz9+gQYOu+1kB/oA+P4CP6DDvpE0o+sWtQ4A1pOiwbh0RlNpIqButcdJNz63NGTrCxj06yl1bozUZLVq0MAFNm2f0Cyhx/6K00C86/VLT0Vx6Hg1x+lr6JZ0e2ldGRwXpqC+9NvrFqQHF/aWuNS/afFi9enVTo6UBTcOaOzxpsNEgo/1TNKBo85i+F61V09v6nG7dupnwozUp2oSmNRVppZ+NvqYGGa2BSqkfz4svvmhqmrSpU8Otfqlr6EovfT8aSLS/UtIaFB3Zp+FIa020aUn76CSuBUor/bnQIKJNnzoVgobVlIaca/PXkCFDzGgz7culwW/RokWpnlenFNAArSFYfx60Jk9ninZ/jtf7rAB/EKS9np0uBAAAQGYhhgMAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AABAbPL/ACBpR4gswiCDAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " 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 0.233 0.000 0.767 0.000 0.000 0.0\n", "n=4 0.0 0.700 0.078 0.000 0.222 0.000 0.0\n", "n=5 0.0 0.970 0.022 0.000 0.000 0.008 0.0\n", "n=6 0.0 1.000 0.000 0.000 0.000 0.000 0.0\n" ] } ], "source": [ "count_depths = np.zeros((len(ns), max(ns) + 1))\n", "\n", "for _ in range(n_simulations):\n", " for i, n in enumerate(ns):\n", " f = bf.random_function(n, depth=1)\n", " count_depths[i, f.get_canalizing_depth()] += 1\n", "\n", "count_depths /= n_simulations\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", "out = 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", ");\n", "\n", "print(out.to_string())" ] }, { "cell_type": "markdown", "id": "c08465c6", "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 [@he2016stratification]." ] }, { "cell_type": "markdown", "id": "0f5ae54a", "metadata": {}, "source": [ "## 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 [@kadelka2023collectively] and the normalized input redundancy [@gates2021effective], \n", "change when the degree of the functions changes." ] }, { "cell_type": "code", "execution_count": 4, "id": "3aac0c89", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:34.432659Z", "iopub.status.busy": "2026-03-31T06:05:34.432558Z", "iopub.status.idle": "2026-03-31T06:05:36.317838Z", "shell.execute_reply": "2026-03-31T06:05:36.317611Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_simulations = 100\n", "ns = np.arange(2, 8)\n", "\n", "canalizing_strengths = np.zeros((len(ns), n_simulations))\n", "input_redundancies = np.zeros((len(ns), n_simulations))\n", "\n", "for j in range(n_simulations):\n", " for i, n in enumerate(ns):\n", " f = bf.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": "8dbc040e", "metadata": {}, "source": [ "Both measures decrease with increasing degree, but canalizing strength declines more sharply." ] }, { "cell_type": "markdown", "id": "3715af05", "metadata": {}, "source": [ "### Stratification by canalizing depth\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": "code", "execution_count": 5, "id": "7031c332", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:36.319099Z", "iopub.status.busy": "2026-03-31T06:05:36.319033Z", "iopub.status.idle": "2026-03-31T06:05:40.043921Z", "shell.execute_reply": "2026-03-31T06:05:40.043686Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_simulations = 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, n_simulations))\n", "input_redundancies = np.zeros((len(ns), max_depth + 1, n_simulations))\n", "\n", "for k in range(n_simulations):\n", " for i, n in enumerate(ns):\n", " for depth in np.append(np.arange(n - 1), n):\n", " f = bf.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": "979b8329", "metadata": {}, "source": [ "### Correlation between canalizing strength and input redundancy\n", "\n", "We can generate all (non-degenerate) \n", "Boolean functions of a certain degree $n$ (only feasible up to $n=4$) and \n", "compare canalizing strength and input redundancy." ] }, { "cell_type": "code", "execution_count": 6, "id": "03d939d0", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:40.045160Z", "iopub.status.busy": "2026-03-31T06:05:40.045084Z", "iopub.status.idle": "2026-03-31T06:05:40.125345Z", "shell.execute_reply": "2026-03-31T06:05:40.125097Z" } }, "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(bf.get_left_side_of_truth_table(2**n)):\n", " f = bf.BooleanFunction(fvec)\n", " strengths[i] = f.get_canalizing_strength()\n", " redundancies[i] = f.get_input_redundancy()\n", " if not allow_degenerate_functions:\n", " degenerate[i] = f.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.tight_layout()\n", "plt.show()\n", "\n", "stats.spearmanr(strengths[which], redundancies[which])" ] }, { "cell_type": "markdown", "id": "5f97c0db", "metadata": {}, "source": [ "Both measures are highly correlated but markedly not the same, \n", "which becomes even more evident when rerunning the analysis for $n=4$ (see @kadelka2026canalization).\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": "9d95ff0e", "metadata": {}, "source": [ "## Correlation between canalization and bias\n", "\n", "All metrics used to assess the sensitivity of Boolean functions \n", "(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": "c65d1d1c", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:40.126521Z", "iopub.status.busy": "2026-03-31T06:05:40.126455Z", "iopub.status.idle": "2026-03-31T06:05:46.082931Z", "shell.execute_reply": "2026-03-31T06:05:46.082708Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = np.arange(2, 6)\n", "n_simulations = 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(n_simulations):\n", " for j, bias in enumerate(bias_values):\n", " f = bf.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] / n_simulations, 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": "67d77d36", "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": "9568abe3", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:46.084108Z", "iopub.status.busy": "2026-03-31T06:05:46.084041Z", "iopub.status.idle": "2026-03-31T06:05:49.006969Z", "shell.execute_reply": "2026-03-31T06:05:49.006769Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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(n_simulations):\n", " for j, bias in enumerate(bias_values):\n", " f = bf.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] / n_simulations, 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": "e1a4058f", "metadata": {}, "source": [ "## 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 [@kadelka2017influence].\n", "The function `boolforge.hamming_weight_to_ncf_layer_structure(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": "b413bf93", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:49.008117Z", "iopub.status.busy": "2026-03-31T06:05:49.008051Z", "iopub.status.idle": "2026-03-31T06:05:49.023808Z", "shell.execute_reply": "2026-03-31T06:05:49.023614Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Hamming weight Absolute bias Layer structure Average sensitivity Canalizing strength Effective degree\n", "0 1 0.9375 [5] 0.3125 1.0000 1.1250\n", "1 3 0.8125 [3, 2] 0.6875 0.7705 1.3984\n", "2 5 0.6875 [2, 1, 2] 0.9375 0.6369 1.5938\n", "3 7 0.5625 [2, 3] 1.0625 0.5993 1.5833\n", "4 9 0.4375 [1, 1, 3] 1.1875 0.5033 1.7266\n", "5 11 0.3125 [1, 1, 1, 2] 1.3125 0.4657 1.8021\n", "6 13 0.1875 [1, 2, 2] 1.3125 0.4657 1.7708\n", "7 15 0.0625 [1, 4] 1.1875 0.5033 1.6094\n" ] } ], "source": [ "n = 5\n", "all_hamming = np.arange(1, 2 ** (n - 1), 2)\n", "all_abs_bias = 2 * np.abs(all_hamming/2**n - 0.5)\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 = bf.hamming_weight_to_ncf_layer_structure(n, w)\n", " layer_structures.append(layer)\n", " f = bf.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", " \"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": "a6566630", "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 @kadelka2017influence." ] }, { "cell_type": "code", "execution_count": 10, "id": "7e08bfe3", "metadata": { "execution": { "iopub.execute_input": "2026-03-31T06:05:49.024890Z", "iopub.status.busy": "2026-03-31T06:05:49.024822Z", "iopub.status.idle": "2026-03-31T06:05:49.067080Z", "shell.execute_reply": "2026-03-31T06:05:49.066893Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", 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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_weights = np.arange(1, 2 ** (n - 1), 2)\n", " all_abs_bias = 2 * np.abs(all_hamming_weights/2**n - 0.5)\n", " avg_sens = np.zeros(2 ** (n - 2))\n", "\n", " for i, w in enumerate(all_hamming_weights):\n", " layer = bf.hamming_weight_to_ncf_layer_structure(n, w)\n", " f = bf.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": "98a0e913", "metadata": {}, "source": [ "## Summary\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 }