{ "cells": [ { "cell_type": "markdown", "id": "Nti1VE8-Dl_5", "metadata": { "id": "Nti1VE8-Dl_5" }, "source": [ "# BoolForge Tutorial #5: Example use cases of the random function generator\n", "\n", "In this tutorial, we will focus on some use cases of the ability to generate a plethora of different types of random Boolean functions.\n", "You will learn how to \n", "- compute the prevalence of canalization, k-canalization and nested canalization for functions of different degree,\n", "- determine the distribution of the canalizing strength as well as the normalized input redundancy for different degrees,\n", "- investigate the correlation between absolute bias and canalization, and\n", "- generate and analyze all dynamically different nested canalizing functions of a given degree.\n", "\n", "To ensure familiarity with these concepts, we highly recommended to first work the previous tutorial." ] }, { "cell_type": "code", "execution_count": 2, "id": "a1a56603", "metadata": {}, "outputs": [], "source": [ "import boolforge\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd" ] }, { "cell_type": "markdown", "id": "788b1861", "metadata": {}, "source": [ "## Prevalence of canalization\n", "\n", "While most 2-input Boolean functions are canalizing, canalization very quickly becomes an elusive property as the degree increases. Using `boolforge.random_function()`, we can easily approximate the probability that an n-input Boolean function has canalizing depth $k$." ] }, { "cell_type": "code", "execution_count": 118, "id": "21a919ec", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " k=0 k=1 k=2 k=3 k=4 k=5 k=6\n", "n=2 0.179 0.000 0.821 0.000 0.00 0.0 0.0\n", "n=3 0.626 0.105 0.000 0.269 0.00 0.0 0.0\n", "n=4 0.952 0.033 0.005 0.000 0.01 0.0 0.0\n", "n=5 1.000 0.000 0.000 0.000 0.00 0.0 0.0\n", "n=6 1.000 0.000 0.000 0.000 0.00 0.0 0.0" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Bgwd79s+fPy+33367uXj58+f3+evdG3mvz88ZqDY9vsln59pXp67PzhXoKm7d4rNzzRy4zmfnCnRPT2nis3NVG0E/x7TaPaqVz87FdXfmurtpRUeZMmUkX758t3yuLBV+ihcvLidPnvQ6pvsaYlKq9VE6Kky3pPQ5GRF+sodk9/k5A5Uvr3/e7Fx3J657SK48PjtXoPPldc8WHOqzcwU6rrsz8mfA96ubL7qsZKl5fiIiIiQqKsrr2Ndff22OAwAA+H3Nz59//ikHDhzwGsquQ9gLFSpkmqa0yerYsWMyf/58c3/v3r3lnXfekRdeeEF69Ogha9askY8//tiMAAOQ+WZEDHC6CFlGX9nldBEA+EPNz5YtW6RWrVpmU9o3R28PHz7c7B8/flyOHj3qeXz58uVN0NHaHp0faOLEiTJ79mwz4gsAAMDva36aNm1qhq6lJqXZm/U527dvz+CSAUiLXYf/98cJAGQVWarPDwAAwK0i/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVRxd2wtA1lbuSqTTRcgyjjhdAAAe1PwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqjoefadOmSbly5SR37txSv3592bx58w0fP2XKFKlYsaKEhIRImTJlZNCgQXLlypVMKy8AAMjaHA0/ixYtksGDB8uIESNk27ZtEh4eLq1atZJTp06l+PjIyEh58cUXzeP37Nkj77//vjnHSy+9lOllBwAAWZOj4WfSpEnSq1cv6d69u1SpUkVmzJghoaGhMmfOnBQfv2HDBmnYsKE8/vjjpraoZcuW0rlz57+sLQIAAHA8/Fy9elW2bt0qLVq0+F9hsmUz+xs3bkzxOQ0aNDDPcYedQ4cOyRdffCEPPvhgqq8TFxcnFy5c8NoAAIC9cjj1wmfOnJH4+HgJCwvzOq77e/fuTfE5WuOjz/vb3/4mLpdLrl+/Lr17975hs9e4ceNk1KhRPi8/AADImhzv8Jwea9eulddee03effdd00fo008/lZUrV8ro0aNTfc6wYcPk/Pnzni0mJiZTywwAAPyLYzU/RYoUkezZs8vJkye9jut+8eLFU3zOK6+8Ik8++aQ89dRTZr969eoSGxsrTz/9tPz73/82zWZJBQcHmw0AAMDRmp9cuXJJnTp1JCoqynMsISHB7EdERKT4nEuXLiULOBqglDaDAQAA+G3Nj9Jh7t26dZO6detKvXr1zBw+WpOjo79U165dpVSpUqbfjmrbtq0ZIVarVi0zJ9CBAwdMbZAed4cgAAAAvw0/nTp1ktOnT8vw4cPlxIkTUrNmTVm1apWnE/TRo0e9anpefvllCQoKMv8/duyYFC1a1ASfsWPHOvguAABAVuJo+FH9+vUzW2odnBPLkSOHmeBQNwAAgIAf7QUAAHCrCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABglRxOFwDwhcqP/eZ0EQAAWQQ1PwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAq9xy+Llw4YIsW7ZM9uzZ45sSAQAA+FP46dixo7zzzjvm9uXLl6Vu3brmWI0aNWTJkiUZUUYAAADnws+3334rjRo1MreXLl0qLpdLzp07J2+99ZaMGTPGdyUDAADwh/Bz/vx5KVSokLm9atUq6dChg4SGhkqbNm1k//79GVFGAAAA58JPmTJlZOPGjRIbG2vCT8uWLc3xs2fPSu7cuX1XMgAAAH9Y2HTgwIHSpUsXyZs3r5QtW1aaNm3qaQ6rXr16RpQRAADAufDzzDPPSL169SQmJkbuv/9+yZbt/yqP7rjjDvr8AACAwAs/Skd46ZaY9vkBAAAIuPATHx8v8+bNk6ioKDl16pQkJCR43b9mzRpflg8AAMDZ8DNgwAATfrSmp1q1ahIUFOTbEgEAAPhT+Fm4cKF8/PHH8uCDD2ZMiQAAAPxpqHuuXLmkQoUKGVMaAAAAfws/Q4YMkalTp5qZnQEAAAK+2Wv9+vUSHR0tX375pVStWlVy5szpdf+nn37qy/IBAAA4G34KFiwoDz/8sG9LAQAA4K/hZ+7cuRlTEgAAAH+d5FCdPn1a9u3bZ25XrFhRihYt6styAQAA+EeHZ13QtEePHlKiRAlp3Lix2UqWLCk9e/aUS5cuZUwpAQAAnAo/gwcPlnXr1snnn38u586dM9tnn31mjulIMAAAgIBq9lqyZIksXrzYs5q70gkPQ0JCpGPHjjJ9+nRflxEAAMC5mh9t2goLC0t2vFixYjR7AQCAwAs/ERERMmLECLly5Yrn2OXLl2XUqFHmPgAAgIBq9tLZnVu1aiWlS5eW8PBwc2znzp2SO3duWb16dUaUEQAAwLnwoyu579+/XxYsWCB79+41xzp37ixdunQx/X4AAAACbp6f0NBQ6dWrl+9LAwAA4A/hZ/ny5dK6dWuzjpfevpGHHnrIV2UDAABwJvy0b99eTpw4YUZ06e3UBAUFSXx8vC/LBwAAkPnhJyEhIcXbAAAAAT/Uff78+RIXF5fs+NWrV819AAAAARV+unfvLufPn092/OLFi+Y+AACAgBrt5XK5TN+epH799VcpUKCAr8oFpEu5K5FOFyHLOOJ0AQAgq4SfWrVqmdCjW/PmzSVHjv89VTs5Hz58WB544IGMKicAAEDmhh/3KK8dO3aYGZ7z5s3ruS9XrlxSrlw56dChg29KBQAA4HT40fW8lIacxx57TIKDgzOqTAAAAP7T4blKlSqm9iepH374QbZs2eKrcgEAAPhH+Onbt6/ExMQkO37s2DFzHwAAQECFn59//llq166dYodovS+9pk2bZprSdFX4+vXry+bNm2/4+HPnzpmQVaJECdP0dvfdd8sXX3yR7tcFAAB2Snf40cBx8uTJZMePHz/uNQIsLRYtWiSDBw82/Ym2bdsm4eHhpjP1qVOnUny8TqR4//33y5EjR2Tx4sWyb98+mTVrlpQqVSq9bwMAAFgq3eGnZcuWMmzYMK+JDrU25qWXXjLBJD0mTZpkVofXyRG1L9GMGTPMivFz5sxJ8fF6/I8//pBly5ZJw4YNTY1RkyZNTGgCAADIkPDz5ptvmj4/ZcuWlfvuu89s5cuXNwufTpw4Mc3n0VqcrVu3SosWLf5XmGzZzP7GjRtTfI6uKB8REWGavcLCwqRatWry2muv3XAxVV2K48KFC14bAACwV7pneNYmpv/85z+yYMEC2blzp4SEhJiam86dO0vOnDnTfJ4zZ86Y0KIhJjHd37t3b4rPOXTokKxZs0a6dOli+vkcOHBAnnnmGbl27ZpnKH5S48aNk1GjRqXzXQIAgECV7vCj8uTJI08//bRkNl1RvlixYjJz5kzJnj271KlTx4wye+ONN1INP9pEp/2K3LTmp0yZMplYagAAkOXDz/79+yU6Otp0TNZAktjw4cPTdI4iRYqYAJO087TuFy9ePMXn6AgvrV3S57lVrlzZNLlpM5rONJ1SB20mZAQAADcdfnR0VZ8+fUx40ZCSeJFTvZ3W8KNBRWtuoqKiPEtnaJDS/X79+qX4HO3kHBkZaR6n/YPUL7/8YkJRSsEHAADglsPPmDFjZOzYsTJ06FC5Vdoc1a1bN6lbt67Uq1dPpkyZIrGxsaYPkeratavpY6T9dpSGrnfeeUcGDBgg/fv3NzVQ2uH52WefveWyAAAAO6Q7/Jw9e1YeffRRn7x4p06d5PTp06a2SJuuatasKatWrfJ0gj569KinhkdpX53Vq1fLoEGDpEaNGiYYaRDyRRADAAB2SHf40eDz1VdfSe/evX1SAG3iSq2Za+3atcmO6VD3TZs2+eS1AQCAfdIdfipUqCCvvPKKCSDVq1dPNrydJigAABBQ4UeHmefNm1fWrVtntsS0wzPhBwAABFT4OXz4cMaUBAAAwB+XtwAAALCq5qdHjx43vD+1RUkBAACy7FD3xHRdrd27d5uV3Zs1a+bLsgEAADgffpYuXZrsmM64rBMQ3nnnnb4qFwAAgP/2+dGJCHW25smTJ/vidAAAAP7f4fngwYNy/fp1X50OAADAP5q9tIYnMZfLJcePH5eVK1eadboAAAACKvxs27bNayV3bfIqWrSoTJw48S9HggEAAGSJ8LN8+XJp3bq1WcoipfW2AAAAAqrPz8MPP2yGsqvs2bPLqVOnMrpcAAAAzoUfbdZyr6SufXwSN3sBAAAEXLNX7969pV27dib06Fa8ePFUHxsfH+/L8gEAAGR++Bk5cqQ89thjcuDAAXnooYdk7ty5UrBgQd+WBAAAwJ9Ge1WqVMlsI0aMkEcffVRCQ0MztmQAAAD+MNRdww8AAEBW5bMZngEAALICwg8AALAK4QcAAFglTeGnUKFCcubMGXNbl7C4ePFiRpcLAADAufBz9epVuXDhgrn9wQcfyJUrVzKmNAAAAP4w2isiIkLat28vderUMTM8P/vssxISEpLiY+fMmePrMgIAAGRu+Pl//+//yeTJk+XgwYNmhufz589T+wMAAAI3/ISFhcn48ePN7fLly8uHH34ohQsXzuiyAQAAOD/J4eHDh31fCgAAAH8e6r5u3Tpp27atVKhQwWy63td3333n+9IBAAA4HX60/0+LFi3M2l7a8dnd+bl58+YSGRnp6/IBAAA42+w1duxYef3112XQoEGeYxqAJk2aJKNHj5bHH3/ctyUEAABwsubn0KFDpskrKW36oj8QAAAIuPBTpkwZiYqKSnb8m2++MfcBAAAEVLPXkCFDTDPXjh07pEGDBubY999/L/PmzZOpU6dmRBkBAACcCz99+vSR4sWLy8SJE+Xjjz82xypXriyLFi2Sdu3a+a5kAAAA/hB+1MMPP2w2AAAAK+b5AQAAyKoIPwAAwCqEHwAAYBXCDwAAsArhBwAAWCXdo73i4+PNnD460eGpU6ckISHB6/41a9b4snwAAADOhp8BAwaY8NOmTRupVq2aBAUF+bZEAAAA/hR+Fi5caCY3fPDBBzOmRAAAAP7U5ydXrlxSoUKFjCkNAACAv4UfXdtL1/ByuVwZUyIAAAB/avZav369REdHy5dffilVq1aVnDlzet3/6aef+rJ8AAAAzoafggULsq4XAACwJ/zMnTs3Y0oCAADgr6u6q9OnT8u+ffvM7YoVK0rRokV9WS4AAAD/6PAcGxsrPXr0kBIlSkjjxo3NVrJkSenZs6dcunQpY0oJAADgVPgZPHiwrFu3Tj7//HM5d+6c2T777DNzTEeCAQAABFSz15IlS2Tx4sXStGlTzzGd8DAkJEQ6duwo06dP93UZAQAAnKv50aatsLCwZMeLFStGsxcAAAi88BMRESEjRoyQK1eueI5dvnxZRo0aZe4DAAAIqGYvnd25VatWUrp0aQkPDzfHdu7cKblz55bVq1dnRBkBAACcCz+6kvv+/ftlwYIFsnfvXnOsc+fO0qVLF9PvBwAAIODm+QkNDZVevXr5vjQAAAD+EH6WL18urVu3Nut46e0beeihh3xVNgAAAGfCT/v27eXEiRNmRJfeTk1QUJDEx8f7snwAAACZH34SEhJSvA0AABDwQ93nz58vcXFxyY5fvXrV3AcAABBQ4ad79+5y/vz5ZMcvXrxo7gMAAAio8ONyuUzfnqR+/fVXKVCggK/KBQAA4Gz4qVWrltSuXdsEn+bNm5vb7k0nO2zUqJG0aNHipgoxbdo0KVeunJkosX79+rJ58+Y0PW/hwoWmPDfqhA0AAHBT8/y4A8aOHTvMDM958+b13JcrVy4TXjp06CDptWjRIrNS/IwZM0zwmTJlijn/vn37zOiy1Bw5ckSee+45E7oAAAB8Hn50PS8dxq4hp2XLllKiRAnxhUmTJpkJE939hTQErVy5UubMmSMvvvhiis/RcuiM0rqe2HfffSfnzp3zSVkAAEDgS1efn+zZs8u//vUvr0VNb4WOENu6datXc1m2bNnM/saNG1N93quvvmpqhXr27PmXr6Ej0y5cuOC1AQAAe2W7mbW9Dh065JMXP3PmjKnFCQsL8zqu+zqpYkrWr18v77//vsyaNStNrzFu3DjTEdu9lSlTxidlBwAAloSfMWPGmL42K1askOPHj2dqrYoOp3/yySdN8ClSpEianjNs2DAzNN+9xcTEZGgZAQBAgC1s+uCDD3rW8Eo85N09BD49y1togNGmtJMnT3od1/3ixYsne/zBgwdNR+e2bdsmm3E6R44cppP0nXfe6fWc4OBgswEAANxU+ImOjvbZldNRYnXq1JGoqCjPaDINM7rfr1+/ZI+vVKmS7Nq1y+vYyy+/bGqEpk6dSpMWAADwffhp0qSJ+JIOc+/WrZvUrVtX6tWrZ4a6x8bGekZ/de3aVUqVKmX67ug8QNrnKLGCBQua/yc9DgAA4JPwo3RouXY63rNnj9mvWrWq9OjR46ZmeO7UqZOcPn1ahg8fbjo516xZU1atWuXpBH306FEzAgwAAMCR8LNlyxYzCWFISIipqXHP1TN27Fj56quvzIzP6aVNXCk1c6m1a9fe8Lnz5s1L9+sBAAB7pTv8DBo0yHR21hFX2slYXb9+XZ566ikZOHCgfPvttxlRTgAAAOdqfhIHH3OSHDnkhRdeMP12AAAA/Fm6O9Pkz5/f9MNJSufPyZcvn6/KBQAA4B/hRzso67ISuiCpBh7ddHV1bfbq3LlzxpQSAADAqWavN99800xmqEPQta+Pypkzp/Tp00fGjx/vq3IBAAD4R/jRiQl1QkGdd0dnXFY6q3JoaGhGlA8AAMD5eX6Uhh33BIMEHwAAELB9frSp65VXXjETGpYrV85seluXmbh27VrGlBIAAMCpmp/+/fvLp59+Kq+//rpERESYYxs3bpSRI0fK77//LtOnT/dV2QAAAJwPP5GRkWZ0V+vWrT3HatSoYRYV1dFehB8AABBQzV7BwcGmqSup8uXLm87QAAAAARV+dA2u0aNHS1xcnOeY3ta1vVJbnwsAACDLNntt375doqKipHTp0hIeHm6O7dy5U65evSrNmzeXRx55xPNY7RsEAACQpcOPDm/v0KGD1zHt7wMAABCQ4Wfu3LkZUxIAAAB/nuTw9OnTsm/fPnO7YsWKUrRoUV+WCwAAwD86PMfGxkqPHj2kRIkS0rhxY7OVLFnSLHZ66dKljCklAACAU+Fn8ODBsm7dOvn888/l3LlzZvvss8/MsSFDhviqXAAAAP7R7LVkyRJZvHixNG3a1HPswQcflJCQEOnYsSOTHAIAgMCq+dGmrbCwsGTHixUrRrMXAAAIvPCj63mNGDFCrly54jl2+fJlGTVqlGetLwAAgIBp9poyZYo88MADySY5zJ07t6xevTojyggAAOBc+Klevbrs379fFixYIHv37jXHdEHTLl26mH4/AAAAARN+rl27JpUqVZIVK1ZIr169Mq5UAAAA/tDnJ2fOnF59fQAAAAK+w3Pfvn1lwoQJcv369YwpEQAAgD/1+fnxxx/Nqu5fffWV6f+TJ08er/tZyR0AAAT8qu4AAABZBau6AwAAq6S5z09CQoLp69OwYUO555575MUXXzSTGwIAAARk+Bk7dqy89NJLkjdvXilVqpRMnTrVdH4GAAAIyPAzf/58effdd80szsuWLTOruutEh1ojBAAAEHDh5+jRo2b1drcWLVpIUFCQ/PbbbxlVNgAAAOfCj87ro+t3JZ30UGd9BgAACLjRXi6XS/75z39KcHCw55jO9ty7d2+vuX6Y5wcAAARE+OnWrVuyY0888YSvywMAAOAf4Yf5fQAAgJVrewEAAGRlhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVvwg/06ZNk3Llyknu3Lmlfv36snnz5lQfO2vWLGnUqJHcdtttZmvRosUNHw8AAOBX4WfRokUyePBgGTFihGzbtk3Cw8OlVatWcurUqRQfv3btWuncubNER0fLxo0bpUyZMtKyZUs5duxYppcdAABkPY6Hn0mTJkmvXr2ke/fuUqVKFZkxY4aEhobKnDlzUnz8ggUL5JlnnpGaNWtKpUqVZPbs2ZKQkCBRUVGZXnYAAJD1OBp+rl69Klu3bjVNV54CZctm9rVWJy0uXbok165dk0KFCqV4f1xcnFy4cMFrAwAA9nI0/Jw5c0bi4+MlLCzM67junzhxIk3nGDp0qJQsWdIrQCU2btw4KVCggGfTZjIAAGAvx5u9bsX48eNl4cKFsnTpUtNZOiXDhg2T8+fPe7aYmJhMLycAAPAfOZx88SJFikj27Nnl5MmTXsd1v3jx4jd87ptvvmnCzzfffCM1atRI9XHBwcFmAwAAcLzmJ1euXFKnTh2vzsruzssRERGpPu/111+X0aNHy6pVq6Ru3bqZVFoAABAIHK35UTrMvVu3bibE1KtXT6ZMmSKxsbFm9Jfq2rWrlCpVyvTdURMmTJDhw4dLZGSkmRvI3Tcob968ZgMAAPDr8NOpUyc5ffq0CTQaZHQIu9bouDtBHz161IwAc5s+fboZJfaPf/zD6zw6T9DIkSMzvfwAACBrcTz8qH79+pkttUkNEzty5EgmlQoAAASiLD3aCwAAIEvW/ASSi3vGO10EAABwA9T8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfgAAgFUIPwAAwCqEHwAAYBXCDwAAsArhBwAAWIXwAwAArEL4AQAAViH8AAAAqxB+AACAVQg/AADAKoQfAABgFcIPAACwCuEHAABYhfADAACsQvgBAABWIfwAAACrEH4AAIBVCD8AAMAqhB8AAGAVwg8AALCKX4SfadOmSbly5SR37txSv3592bx58w0f/8knn0ilSpXM46tXry5ffPFFppUVAABkbY6Hn0WLFsngwYNlxIgRsm3bNgkPD5dWrVrJqVOnUnz8hg0bpHPnztKzZ0/Zvn27tG/f3my7d+/O9LIDAICsx/HwM2nSJOnVq5d0795dqlSpIjNmzJDQ0FCZM2dOio+fOnWqPPDAA/L8889L5cqVZfTo0VK7dm155513Mr3sAAAg68nh5ItfvXpVtm7dKsOGDfMcy5Ytm7Ro0UI2btyY4nP0uNYUJaY1RcuWLUvx8XFxcWZzO3/+vPn/hQsXJCMkxF3KkPMGIl9+Blz3tOO6O4Pr7gyuuzMuZMB3rPucLpcra4efM2fOSHx8vISFhXkd1/29e/em+JwTJ06k+Hg9npJx48bJqFGjkh0vU6bMLZUdt67AFKdLYCeuuzO47s7gugfedb948aIUKFAg64afzKC1SolrihISEuSPP/6QwoULS1BQkAQ6Tcoa9GJiYiR//vxOF8caXHdncN2dwXV3hm3X3eVymeBTsmTJWz6Xo+GnSJEikj17djl58qTXcd0vXrx4is/R4+l5fHBwsNkSK1iwoNhG/2HY8I/D33DdncF1dwbX3Rk2XfcCt1jj4xcdnnPlyiV16tSRqKgor5oZ3Y+IiEjxOXo88ePV119/nerjAQAA/KrZS5ukunXrJnXr1pV69erJlClTJDY21oz+Ul27dpVSpUqZvjtqwIAB0qRJE5k4caK0adNGFi5cKFu2bJGZM2c6/E4AAEBW4Hj46dSpk5w+fVqGDx9uOi3XrFlTVq1a5enUfPToUTMCzK1BgwYSGRkpL7/8srz00kty1113mZFe1apVc/Bd+C9t8tM5lJI2/SFjcd2dwXV3BtfdGVz3mxfk8sWYMQAAgCzC8UkOAQAAMhPhBwAAWIXwAwAArEL4AQAAViH8BCidGuCee+6RfPnySbFixczK9/v27XO6WAFv+vTpUqNGDc+kYzr/1Jdfful0sawzfvx4M4P7wIEDnS5KQBs5cqS5zom3SpUqOV0sKxw7dkyeeOIJs1pBSEiIVK9e3Uz7grQh/ASodevWSd++fWXTpk1mEshr165Jy5YtzRxKyDilS5c2X7y6YK/+ImrWrJm0a9dOfvrpJ6eLZo0ff/xR3nvvPRNCkfGqVq0qx48f92zr1693ukgB7+zZs9KwYUPJmTOn+ePq559/NnPf3XbbbU4XLctwfJ4fZAydKymxefPmmRog/VJu3LixY+UKdG3btvXaHzt2rKkN0hCqXxLIWH/++ad06dJFZs2aJWPGjHG6OFbIkSNHqssLIWNMmDDBrOk1d+5cz7Hy5cs7WqashpofS5w/f978v1ChQk4XxRrx8fFmBnKtbWP5lcyhtZ0683uLFi2cLoo19u/fbxaavOOOO0zw1IlpkbGWL19uVkV49NFHzR+1tWrVMoEfaUfNjwV0vTTt+6DVpMyEnfF27dplws6VK1ckb968snTpUqlSpYrTxQp4GjS3bdtmmr2QOerXr29qlStWrGiavEaNGiWNGjWS3bt3m/6GyBiHDh0yNcq6PJSudKA/888++6xZL1OXi8JfY4ZnC/Tp08e0C2tbvPZJQca6evWq+etXa9sWL14ss2fPNn2wCEAZJyYmxvwlrP3b3H19mjZtapbL0fUCkTnOnTsnZcuWlUmTJknPnj2dLk7A0pCjP+8bNmzwHNPwoyFo48aNjpYtq6DZK8D169dPVqxYIdHR0QSfTPzFVKFCBalTp44ZdRceHi5Tp051ulgBTfuynTp1SmrXrm36oOimgfOtt94yt7UJEhmvYMGCcvfdd8uBAwecLkpAK1GiRLI/pipXrkyTYzrQ7BWgtEKvf//+psll7dq1dIZzuNkxLi7O6WIEtObNm5vmxsS6d+9uhl0PHTpUsmfP7ljZbOtwfvDgQXnyySedLkpA0y4MSacu+eWXX0ytG9KG8BPAHT8jIyPls88+M23vJ06cMMcLFChg5oRAxhg2bJi0bt1abr/9drl48aL5DDR8rl692umiBTT9GU/any1PnjxmDhT6uWWc5557zoxw1C/d3377zawwrkGzc+fOThctoA0aNEgaNGggr732mnTs2FE2b94sM2fONBvShvAToLQznLvfQ2I6NPKf//ynQ6UKfNr00rVrV9P5U4Om9j/R4HP//fc7XTTA53799VcTdH7//XcpWrSo/O1vfzPTOuhtZBydwFZr9fWPrVdffdXU7GvfNh1th7ShwzMAALAKHZ4BAIBVCD8AAMAqhB8AAGAVwg8AALAK4QcAAFiF8AMAAKxC+AEAAFYh/AAAAKsQfoAs6MiRIxIUFCQ7duwQf7F371659957JXfu3GY19UChy5PotdYVy9NKZ1YfOHCgOKFcuXLpWsl+3rx5ZkHSGxk5cmRAfaYA4Qe4CbpEiH4hjh8/3uv4smXLzHEb6bpOup6WLrgYFRUlWVFKoUXXUHIvV5IV/Pjjj/L00087XQzArxF+gJukNRwTJkyQs2fPSqC4evXqTT9XV/PWtZ10kUtdUDRQ5MqVS4oXL+73odb92em6WqGhoU4XB/BrhB/gJrVo0cJ8KY4bNy5dzQXaJKFNE4lrkdq3b29WaA4LCzNNELpY4fXr1+X555+XQoUKSenSpc2itCk1NWnNhAYxXb183bp1Xvfv3r3brDKfN29ec+4nn3xSzpw541XT0a9fP1PbUaRIEWnVqlWK7yMhIcGUScsRHBxs3tOqVas892sw2Lp1q3mM3tb3ndp59HrpQowhISESHh4uixcv9tyvQVIXZ9QvcL3/rrvu8rxv/XLXspYoUcK8Xw1Zia+9Nks99dRT5rn58+eXZs2ayc6dO5N9Fh9++KG5/lqT89hjj8nFixc9n4Nev6lTp5r3oJs2LyZt9tJFPHUxz1KlSpmQUb16dfnoo48krX755RdzPv3sEps8ebLceeed5nZ8fLz07NnTc50qVqxoypWY++dm7NixUrJkSfOYlJq9Jk2aZMqotXJlypSRZ555Rv78889k5dJaS73eem315yAmJuaG72P27NlSuXJl8/hKlSrJu+++67nvrz4rwGmEH+AmZc+e3QSWt99+26xufSvWrFkjv/32m3z77bfmy0qbkP7+97/LbbfdJj/88IP07t1b/vWvfyV7HQ1HQ4YMke3bt0tERIS0bdvWfDkr/bLWAFCrVi3ZsmWLCSsnT56Ujh07ep3jgw8+MLUb33//vcyYMSPF8ukX78SJE+XNN9+U//znP+bL8aGHHpL9+/eb+7VZqGrVqqYsevu5555L8Tz6BTh//nzzOj/99JMMGjRInnjiCU9oe+WVV+Tnn3+WL7/8Uvbs2SPTp083oUy99dZbsnz5cvn4449N09qCBQu8QuSjjz4qp06dMs/VIFa7dm1p3ry5/PHHH161U/olv2LFCrPp67qbLvU96jXs1auXeQ+6aVhI6sqVK1KnTh1ZuXKlCZfaxKShcvPmzWn6rO+++26pW7euKX9iuv/44497QqIGzU8++cRcj+HDh8tLL71k3nti2ryo1+Lrr7827ycl2bJlM9dOr7d+1vqz9sILL3g95tKlSyZE6WejPwf6s6PBMDVaVi2TPkc/J/13oJ+dnj8tnxXgOF3VHUD6dOvWzdWuXTtz+95773X16NHD3F66dKkr8T+rESNGuMLDw72eO3nyZFfZsmW9zqX78fHxnmMVK1Z0NWrUyLN//fp1V548eVwfffSR2T98+LB5nfHjx3sec+3aNVfp0qVdEyZMMPujR492tWzZ0uu1Y2JizPP27dtn9ps0aeKqVavWX77fkiVLusaOHet17J577nE988wznn19n/p+U3PlyhVXaGioa8OGDV7He/bs6ercubO53bZtW1f37t1TfH7//v1dzZo1cyUkJCS777vvvnPlz5/fvEZid955p+u9994zt7Vs+voXLlzw3P/888+76tev79nX6zFgwACvc0RHR5trdvbs2VTfW5s2bVxDhgy54XmS/gxo2dz089DX2LNnT6rP6du3r6tDhw5ePzdhYWGuuLg4r8fpz5KePzWffPKJq3Dhwp79uXPnmtfetGmT55iWQ4/98MMPKf4ca9kjIyO9zqs/bxEREX/5WQH+gJof4BZpvx/9i1f/Ar5ZWmuif6G7aROVNlUkrmXSfjRas5GY1lS45ciRw9QouMuhTT7R0dGmycu9afOEuwbETWsxbuTChQumVqphw4Zex3U/Pe/5wIEDpobh/vvv9yqT1ja4y9OnTx9ZuHChaZ7S2okNGzZ4NfPo6DZt3nn22Wflq6++8tyn71WbcvQaJT734cOHvd6r1j7ky5fPs6/NMkmv6V/RJqnRo0ebz0ebJPV1Vq9eLUePHk3zObRWRZvUNm3aZPa1ZkRrqtyfj5o2bZr5bLQZT19j5syZyV5Dy6C1djfyzTffmBowbabT9661VFo7qJ9F4p+de+65x7Ov5dDm15Q+39jYWHNNtVku8bUeM2aM51rf6LMC/EEOpwsAZHWNGzc2zUDDhg0zv/QT00Djcukf0f9z7dq1ZOfImTOn1772CUnpmDaHpJWGAW0G03CWlH7pu2lfkMzg7meizUX6RZyY9iNS2j/pv//9r3zxxRemKUe/tPv27Wua2zQcaJjRZi39QtfmO+13pX2G9Nz6nrR/TlKJh3Hf6jVVb7zxhmki03417r402mcqPZ3Fta+YNklGRkaa6QH0/xr83DQAatOhNjVqwNXQoq+rTaCJ/dVnpwFLm0/13NpEpWFt/fr1JrhoeW+mY7T7c5w1a5bUr1/f6z4N6epGnxXgDwg/gA9ovxGtrXB3OnXTv9pPnDhhApB7tJAv5+bRmgMNX0o7SGtfF+1o6v4CWrJkiant0L/sb5Z2HtYOtdoXpEmTJp7jul+vXr00n6dKlSom5GjtReLzJKXXrFu3bmZr1KiR6dek4cddlk6dOpntH//4hzzwwAOmT4++V73O+j5vpW+J1qJozc6N6Ptu166d6aukNDxpJ2Z9f+mhHbu1dks7Tx86dMirj42+hnZk187JbolrsNJKfx60fBqi3DWLSfsNuX92tF+Y+/PUfjra70c7NCeltZL686Bl1veQmtQ+Kw1ggNMIP4APaA2AfhFoR8/EdDTV6dOn5fXXXzdfANrpWP8a1i8GX9CmER2ho19SOlpIR0v16NHD3Kc1JvrXuX656pesfulo05PWKuhIHfdf6WmhAUQ7YetoJA15OgJLQ1zSTrs3orUXWpuhnZz1C1mHxZ8/f9580ev10LCjnWi1qUebAePi4kwnXvc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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nsim = 1000\n", "ns = np.arange(2,7)\n", "canalizing_depths = np.arange(max(ns)+1)\n", "count_canalizing_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_canalizing_depths[i,f.get_canalizing_depth()] += 1\n", "count_canalizing_depths /= nsim\n", "\n", "fig,ax = plt.subplots()\n", "for i,canalizing_depth in enumerate(canalizing_depths):\n", " ax.bar(ns,count_canalizing_depths[:,i],bottom=np.sum(count_canalizing_depths[:,:i],1),label=str(canalizing_depth))\n", "ax.legend(frameon=False,loc='center',bbox_to_anchor=[0.5,1.1],ncol=8,title='canalizing depth')\n", "ax.set_xticks(ns)\n", "ax.set_xlabel('Number of essential variables')\n", "ax.set_ylabel(f'Proportion of functions')\n", "\n", "pd.DataFrame(count_canalizing_depths,index='n=' + ns.astype(str),columns='k=' + canalizing_depths.astype(str))\n", "\n" ] }, { "cell_type": "markdown", "id": "c74220ca", "metadata": {}, "source": [ "We see that hardly any Boolean function with $n\\geq 5$ inputs is canalizing, let alone nested canalizing. This makes the finding that most Boolean functions in published Boolean gene regulatory network models 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": "code", "execution_count": 119, "id": "ef1b927a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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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 0.00 0.000 0.0\n", "n=3 0.0 0.210 0.000 0.790 0.00 0.000 0.0\n", "n=4 0.0 0.596 0.094 0.000 0.31 0.000 0.0\n", "n=5 0.0 0.950 0.029 0.009 0.00 0.012 0.0\n", "n=6 0.0 1.000 0.000 0.000 0.00 0.000 0.0" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "count_canalizing_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_canalizing_depths[i,f.get_canalizing_depth()] += 1\n", "count_canalizing_depths /= nsim\n", "\n", "fig,ax = plt.subplots()\n", "for i,canalizing_depth in enumerate(canalizing_depths):\n", " ax.bar(ns,count_canalizing_depths[:,i],bottom=np.sum(count_canalizing_depths[:,:i],1),label=str(canalizing_depth))\n", "ax.legend(frameon=False,loc='center',bbox_to_anchor=[0.5,1.1],ncol=8,title='canalizing depth')\n", "ax.set_xticks(ns)\n", "ax.set_xlabel('Number of essential variables')\n", "ax.set_ylabel(f'Proportion of functions')\n", "\n", "pd.DataFrame(count_canalizing_depths,index='n=' + ns.astype(str),columns='k=' + canalizing_depths.astype(str))\n" ] }, { "cell_type": "markdown", "id": "c8738db7", "metadata": {}, "source": [ "This analysis reveals that among Boolean functions of degree $n\\geq 5$, functions with few conditionally canalizing variables are much more abundant than functions with more conditionally canalizing variables, which is mathematically obvious due to the recursive nature of the definition of k-canalization." ] }, { "cell_type": "markdown", "id": "f1d8dda8", "metadata": {}, "source": [ "## Measures of collective canalization for different degree\n", "\n", "Using a similar setup, we can investigate if and how the various measures of collective canalization, specifically canalizing strength (Kadelka et al., Advances in Applied Mathematics, 2023) and the normalized input redundancy (Gates et al., PNAS, 2021), change when the degree of the functions changes." ] }, { "cell_type": "code", "execution_count": 120, "id": "970e5586", "metadata": {}, "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", "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", "violinplot_args = {'widths':width,'showmeans':True,'showextrema':False}\n", "fig,ax = plt.subplots()\n", "ax.violinplot(canalizing_strengths.T,positions=ns-width/2,**violinplot_args)\n", "ax.scatter([], [], color='C0', label='canalizing strength')\n", "ax.violinplot(input_redundancies.T,positions=ns+width/2,**violinplot_args)\n", "ax.scatter([], [], color='C1', label='normalized input redundancy')\n", "ax.legend(loc='center',bbox_to_anchor=[0.5,1.05],frameon=False,ncol=2)\n", "ax.set_xlabel('Number of essential variables')\n", "a=ax.set_ylabel('Value')\n" ] }, { "cell_type": "markdown", "id": "7c443612", "metadata": {}, "source": [ "This plot reveals that, on average, both the canalizing strength and the normalized input redundancy decrease as the number of variables increases. However, the dependence of canalizing strength on degree is much stronger.\n", "\n", "If we stratify this analysis by canalizing depth (exact canalizing depth using `EXACT_DEPTH=True` or minimal canalizing depth using the default `EXACT_DEPTH=False`), we can confirm that functions with more conditionally canalizing variables tend to also have higher average collective canalization, irrespective of how it is measured. In other words, the various measures of canalization are all highly correlated." ] }, { "cell_type": "code", "execution_count": null, "id": "c6348491", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nsim = 100\n", "EXACT_DEPTH = False #Default: False\n", "ns = np.arange(2,7)\n", "canalizing_strengths = np.zeros((len(ns),max(ns)+1,nsim))\n", "input_redundancies = np.zeros((len(ns),max(ns)+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", "width = 0.28\n", "violinplot_args = {'widths': width, 'showmeans': True, 'showextrema': False}\n", "fig, ax = plt.subplots(2, 1, figsize=(6, 6), sharex=True)\n", "\n", "base_gap = 1 # gap between groups\n", "intra_gap = 0.3 # gap within group\n", "\n", "max_depth = max(ns)\n", "\n", "for ii, (data, label) in enumerate(zip(\n", " [canalizing_strengths, input_redundancies],\n", " ['canalizing strength', 'normalized input redundancy'])):\n", "\n", " positions = []\n", " values = []\n", " colors_used = []\n", " group_centers = []\n", "\n", " current_x = 0.0\n", " for i, n in enumerate(ns):\n", " valid_depths = np.append(np.arange(n-1), n)\n", " n_viols = len(valid_depths)\n", "\n", " # positions centered on each group's midpoint\n", " offsets = np.linspace(\n", " -(n_viols - 1) * intra_gap / 2,\n", " (n_viols - 1) * intra_gap / 2,\n", " n_viols\n", " )\n", " group_positions = current_x + offsets\n", " positions.extend(group_positions)\n", " group_centers.append(current_x)\n", "\n", " for depth in valid_depths:\n", " values.append(data[i, depth, :])\n", " colors_used.append('C'+str(depth))\n", "\n", " # advance x-position based on total group width\n", " group_width = (n_viols - 1) * intra_gap\n", " current_x += group_width / 2 + base_gap + width + intra_gap\n", "\n", " # plot violins one by one with colors\n", " for vpos, val, c in zip(positions, values, colors_used):\n", " vp = ax[ii].violinplot(val, positions=[vpos], **violinplot_args)\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", " # axis labels\n", " ax[ii].set_ylabel(label)\n", " if ii == 1:\n", " ax[ii].set_xlabel('Number of essential variables (n)')\n", " ax[ii].set_xticks(group_centers)\n", " ax[ii].set_xticklabels(ns)\n", " ax[ii].set_ylim([-0.02,1.02])\n", "\n", "# add legend for depth colors\n", "depth_handles = [\n", " plt.Line2D([0], [0], color='C'+str(d), lw=5, label=f'{d}')\n", " for d in range(max_depth + 1)\n", "]\n", "a=fig.legend(handles=depth_handles, loc='upper center', ncol=7, frameon=False,\n", " title='exact canalizing depth' if EXACT_DEPTH else 'minimal canalizing depth')\n" ] }, { "cell_type": "markdown", "id": "2901dee5", "metadata": { "id": "2901dee5" }, "source": [ "## 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. For example, functions with higher absolute bias are more likely to be canalizing." ] }, { "cell_type": "code", "execution_count": 122, "id": "67a5a393", "metadata": {}, "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", "n_steps = 21\n", "bias_values = np.linspace(0,1,n_steps)\n", "count_canalizing = np.zeros((len(ns),n_steps),dtype=int)\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,\n", " bias=bias,\n", " 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", "xticks = [0,0.25,0.5,0.75,1]\n", "ax.set_xticks(xticks)\n", "ax.set_xticklabels([f'{p} ({round(200*np.abs(p-0.5))}%)' for p in xticks])\n", "ax.set_xlabel('bias (absolute bias)')\n", "ax.set_ylabel('probability canalizing')\n", "a=ax.legend(loc='center',frameon=False,bbox_to_anchor=[0.5,1.05],ncol=6)\n" ] }, { "cell_type": "markdown", "id": "5516d019", "metadata": {}, "source": [ "Similarly, the probability that a function is degenerate (i.e., that it does not depend on all its variables) also increases as the absolute bias increases." ] }, { "cell_type": "code", "execution_count": 123, "id": "3f1a23d8", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = np.arange(2,6)\n", "nsim = 3000\n", "n_steps = 21\n", "bias_values = np.linspace(0,1,n_steps)\n", "count_degenerate = np.zeros((len(ns),n_steps),dtype=int)\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,\n", " bias=bias,\n", " 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", "xticks = [0,0.25,0.5,0.75,1]\n", "ax.set_xticks(xticks)\n", "ax.set_xticklabels([f'{p} ({round(200*np.abs(p-0.5))}%)' for p in xticks])\n", "ax.set_xlabel('bias (absolute bias)')\n", "ax.set_ylabel('probability degenerate')\n", "a=ax.legend(loc='center',frameon=False,bbox_to_anchor=[0.5,1.05],ncol=6)" ] }, { "cell_type": "markdown", "id": "4e7a46d6", "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 dynamics to perturbations. More generally, it determines the dynamical regime of the network (see later tutorials). The ability to generate canalizing functions with a specific canalizing layer structure enables us investigate the link between layer structure and average sensitivity, as well as other properties, such as canalizing strength or effective degree.\n", "\n", "For nested canalizing functions of a given degree $n$, there exists a bijection betweeen their absolute bias and their canalizing layer structure. The function `boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(degree,hamming_weight)` implements this. Iterating over all possible absolute biases (parametrized by the possible Hamming weights), we can thus generate all dynamically different types of n-input nested canalizing functions and investigate their average sensitivity, which we can compute exactly for relatively low degree." ] }, { "cell_type": "code", "execution_count": 124, "id": "336084b7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Hamming weightAbsolute biasLayer structureNumber of layersAverage sensitivityCanalizing strengthEffective degree
010.0625[5]10.31251.01.125
130.1875[3, 2]20.68750.77051.3984
250.3125[2, 1, 2]30.93750.63691.5938
370.4375[2, 3]21.06250.59931.5833
490.5625[1, 1, 3]31.18750.50331.7266
5110.6875[1, 1, 1, 2]41.31250.46571.8021
6130.8125[1, 2, 2]31.31250.46571.7708
7150.9375[1, 4]21.18750.50331.6094
\n", "
" ], "text/plain": [ " Hamming weight Absolute bias Layer structure Number of layers \\\n", "0 1 0.0625 [5] 1 \n", "1 3 0.1875 [3, 2] 2 \n", "2 5 0.3125 [2, 1, 2] 3 \n", "3 7 0.4375 [2, 3] 2 \n", "4 9 0.5625 [1, 1, 3] 3 \n", "5 11 0.6875 [1, 1, 1, 2] 4 \n", "6 13 0.8125 [1, 2, 2] 3 \n", "7 15 0.9375 [1, 4] 2 \n", "\n", " Average sensitivity Canalizing strength Effective degree \n", "0 0.3125 1.0 1.125 \n", "1 0.6875 0.7705 1.3984 \n", "2 0.9375 0.6369 1.5938 \n", "3 1.0625 0.5993 1.5833 \n", "4 1.1875 0.5033 1.7266 \n", "5 1.3125 0.4657 1.8021 \n", "6 1.3125 0.4657 1.7708 \n", "7 1.1875 0.5033 1.6094 " ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 5\n", "all_possible_hamming_weights = np.arange(1,2**(n-1),2)\n", "all_possible_absolute_biases = all_possible_hamming_weights / 2**(n-1)\n", "n_functions = 2**(n-2)\n", "average_sensitivites=np.zeros(n_functions)\n", "canalizing_strengths=np.zeros(n_functions)\n", "effective_degrees=np.zeros(n_functions)\n", "layer_structures = []\n", "for i,w in enumerate(all_possible_hamming_weights):\n", " layer_structures.append(boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(n,w)[1])\n", " f = boolforge.random_function(n,layer_structure=layer_structures[i])\n", " average_sensitivites[i] = f.get_average_sensitivity(EXACT=True,NORMALIZED=False)\n", " canalizing_strengths[i] = f.get_canalizing_strength()\n", " effective_degrees[i] = f.get_effective_degree()\n", "number_of_layers = list(map(len,layer_structures))\n", "\n", "pd.DataFrame(np.c_[all_possible_hamming_weights,\n", " all_possible_absolute_biases,\n", " list(map(str,layer_structures)),\n", " number_of_layers,\n", " average_sensitivites,\n", " np.round(canalizing_strengths,4),\n", " np.round(effective_degrees,4)],\n", " columns=['Hamming weight',\n", " 'Absolute bias',\n", " 'Layer structure',\n", " 'Number of layers',\n", " 'Average sensitivity',\n", " 'Canalizing strength',\n", " 'Effective degree'])" ] }, { "cell_type": "markdown", "id": "959cf827", "metadata": {}, "source": [ "We notice that nested canalizing functions with higher absolute bias tend to be more sensitive to input changes and also less canalizing. However, the relationship between absolute bias and these other metrics is far from monotonic. Further, we notice that there is a perfect correlation between the average sensitivity of a nested canalizing function and its canalizing strength, and a near perfect correlation between average sensitivity and effective degree.\n", "\n", "To investigate the non-monotonic behavior further, 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": 117, "id": "bcae8513", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ns = np.arange(5,9)\n", "f,ax = plt.subplots()\n", "for n in ns:\n", " all_possible_hamming_weights = np.arange(1,2**(n-1),2)\n", " all_possible_absolute_biases = all_possible_hamming_weights / 2**(n-1)\n", " n_functions = 2**(n-2)\n", " average_sensitivites=np.zeros(n_functions)\n", " layer_structures = []\n", " for i,w in enumerate(all_possible_hamming_weights):\n", " layer_structures.append(boolforge.get_layer_structure_of_an_NCF_given_its_Hamming_weight(n,w)[1])\n", " f = boolforge.random_function(n,layer_structure=layer_structures[i])\n", " average_sensitivites[i] = f.get_average_sensitivity(EXACT=True,NORMALIZED=False)\n", " number_of_layers = list(map(len,layer_structures))\n", " ax.plot(all_possible_absolute_biases,average_sensitivites,'x--',label=f'n={n}')\n", "ax.legend(loc='best',frameon=False)\n", "ax.set_xlabel('Absolute bias of the nested canalizing function')\n", "a=ax.set_ylabel('Average sensitivity')" ] } ], "metadata": { "colab": { "provenance": [ { "file_id": "1uYGafWSuMhd9QxcQkz2tTMTeFsLb_VHA", "timestamp": 1696210918065 } ] }, "kernelspec": { "display_name": "envpy312", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }