{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Looking at bit collisions in Morgan fingerprints\n",
    "\n",
    "In the group over the past few days we've had a few conversations about bit collisions in Morgan fingerprints. These happen when we fold the fingerprints to be a particular size if two different bits (corresponding to two different atom environments) end up folding onto the same bit.\n",
    "\n",
    "This post is an exploration of how often that happens. I will look at fingerprints with different radii -- 1, 2, and 3 -- folded to a set of different sizes -- 1K, 2K, 4K, 8K.\n",
    "\n",
    "TL;DR version: There are a fair number of collisions at fingerprint sizes below 4K. As expected, higher radii have more collisions. The collisions don't end up making much difference in terms of calculated similarity, but we have observed (not shown here) that it can make a measurable difference in the performance of some machine-learning algorithms.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2024.09.5\n",
      "Fri Feb 28 06:58:42 2025\n"
     ]
    }
   ],
   "source": [
    "from rdkit import Chem\n",
    "import time,random\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "from rdkit.Chem import Draw\n",
    "from rdkit.Chem.Draw import IPythonConsole\n",
    "from rdkit import DataStructs\n",
    "from rdkit.Chem import rdMolProcessing\n",
    "from rdkit.Chem import rdFingerprintGenerator\n",
    "from rdkit import rdBase\n",
    "rdBase.DisableLog('rdApp.*')\n",
    "import rdkit\n",
    "\n",
    "print(rdkit.__version__)\n",
    "import time\n",
    "print(time.asctime())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import chembl_downloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PosixPath('/home/glandrum/.data/chembl/35/chembl_35.sdf.gz')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chembl_downloader.download_sdf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For test data I'll use all compounds from ChEMBL35 that have less than 50 heavy atoms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loop over the molecules and build fingerprints of multiple radii and folded lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done 50000\n",
      "Done 100000\n",
      "Done 150000\n",
      "Done 200000\n",
      "Done 250000\n",
      "Done 350000\n",
      "Done 400000\n",
      "Done 450000\n",
      "Done 500000\n",
      "Done 550000\n",
      "Done 600000\n",
      "Done 650000\n",
      "Done 700000\n",
      "Done 750000\n",
      "Done 800000\n",
      "Done 850000\n",
      "Done 900000\n",
      "Done 950000\n",
      "Done 1000000\n",
      "Done 1050000\n",
      "Done 1100000\n",
      "Done 1150000\n",
      "Done 1200000\n",
      "Done 1250000\n",
      "Done 1300000\n",
      "Done 1350000\n",
      "Done 1400000\n",
      "Done 1450000\n",
      "Done 1500000\n",
      "Done 1550000\n",
      "Done 1600000\n",
      "Done 1650000\n",
      "Done 1700000\n",
      "Done 1750000\n",
      "Done 1800000\n",
      "Done 1850000\n",
      "Done 1900000\n",
      "Done 1950000\n",
      "Done 2000000\n",
      "Done 2050000\n",
      "Done 2100000\n",
      "Done 2150000\n",
      "Done 2200000\n",
      "Done 2250000\n",
      "Done 2300000\n",
      "Done 2350000\n",
      "Done 2400000\n",
      "Done 2450000\n"
     ]
    }
   ],
   "source": [
    "counts=defaultdict(list)\n",
    "\n",
    "rs = (0,1,2,3)\n",
    "sizes= (512,1024,2048,4096,8192)\n",
    "fpgs = []\n",
    "for r in rs:\n",
    "    for sz in sizes:\n",
    "        fpgs.append((r,sz,rdFingerprintGenerator.GetMorganGenerator(radius=r,fpSize=sz)))\n",
    "                    \n",
    "suppl = Chem.MultithreadedSDMolSupplier('/home/glandrum/.data/chembl/35/chembl_35.sdf',numWriterThreads=8)\n",
    "for i,m in enumerate(suppl):\n",
    "    if not m: \n",
    "        continue\n",
    "    if m.GetNumHeavyAtoms() > 50:\n",
    "        continue\n",
    "    for r,sz,fpg in fpgs:\n",
    "        if sz==sizes[0]:\n",
    "            # get the unfolded fingerprint:\n",
    "            counts[(r,-1)].append(len(fpg.GetSparseCountFingerprint(m).GetNonzeroElements()))\n",
    "        counts[(r,sz)].append(fpg.GetFingerprint(m).GetNumOnBits())\n",
    "    if not (i+1)%50000:\n",
    "        print(\"Done {0}\".format(i+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now plot histograms of the numbers of collisions along with the fractions of collisions.\n",
    "\n",
    "The two plots in each row show the same data, the left one uses counts of collisions, the right is the fraction of bits that are collisions. The right plots also include lines showing what fraction of fingerprints have at least that fraction of collisions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import gzip\n",
    "with gzip.open('./results/bit_counts.pkl.gz','wb+') as outf:\n",
    "    pickle.dump(counts,outf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.style.use('tableau-colorblind10')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1600x2000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,20))\n",
    "\n",
    "pidx=1\n",
    "#----------------------------\n",
    "for nbits in (8192,4096,2048,1024,512):\n",
    "    plt.subplot(5,2,pidx)\n",
    "    pidx+=1\n",
    "    ds = []\n",
    "    dps = []\n",
    "    for r in (0,1,2,3):\n",
    "        v1=np.array(counts[r,-1])\n",
    "        v2=np.array(counts[r,nbits])\n",
    "        d = v1-v2\n",
    "        dp=np.array(d,float)\n",
    "        dp/=v1\n",
    "        ds.append(d)\n",
    "        dps.append(dp)\n",
    "    \n",
    "    _=plt.hist(ds,bins=20,log=True,label=(\"r=0\", \"r=1\",\"r=2\",\"r=3\"))\n",
    "    plt.title('%d bits'%nbits)\n",
    "    _=plt.legend()\n",
    "    \n",
    "    plt.subplot(5,2,pidx)\n",
    "    pidx+=1\n",
    "    _=plt.hist(dps,bins=20,log=True,label=(\"r=0\",\"r=1\",\"r=2\",\"r=3\"))\n",
    "    _=plt.legend()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, there are definitely some collisions.\n",
    "\n",
    "Do they make a difference in similarity values? Look at 10K random molecule pairs to find out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(0xF00D)\n",
    "smis = [x.split()[0] for x in file(filen)]\n",
    "ivs=[random.randint(0,len(smis)-1) for x in range(10000)]\n",
    "jvs=[random.randint(0,len(smis)-1) for x in range(10000)]\n",
    "pairs=zip(ivs,jvs)\n",
    "\n",
    "sims=defaultdict(list)\n",
    "for i,j in pairs:\n",
    "    mi = Chem.MolFromSmiles(smis[i])\n",
    "    if not mi:\n",
    "        continue\n",
    "    mj = Chem.MolFromSmiles(smis[j])\n",
    "    if not mj:\n",
    "        continue\n",
    "    for r in 0,1,2,3:\n",
    "        fpi=rdmd.GetMorganFingerprint(mi,r)\n",
    "        for k,v in fpi.GetNonzeroElements().items():\n",
    "            fpi[k]=1\n",
    "        fpj=rdmd.GetMorganFingerprint(mj,r)\n",
    "        for k,v in fpj.GetNonzeroElements().items():\n",
    "            fpj[k]=1\n",
    "        sims[(r,-1)].append(DataStructs.TanimotoSimilarity(fpi,fpj))\n",
    "        for l in 1024,2048,4096,8192:\n",
    "            fpi=rdmd.GetMorganFingerprintAsBitVect(mi,r,l)\n",
    "            fpj=rdmd.GetMorganFingerprintAsBitVect(mj,r,l)\n",
    "            sims[(r,l)].append(DataStructs.TanimotoSimilarity(fpi,fpj))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "-c:12: RuntimeWarning: invalid value encountered in divide\n",
      "-c:17: RuntimeWarning: divide by zero encountered in divide\n",
      "-c:17: RuntimeWarning: invalid value encountered in divide\n",
      "-c:22: RuntimeWarning: divide by zero encountered in divide\n",
      "-c:22: RuntimeWarning: invalid value encountered in divide\n",
      "-c:12: RuntimeWarning: divide by zero encountered in divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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pmTNnaty4cVqwYIHGjh0b73oBAACAhIsoNNfW1urdd9/VJ598oubmZlVVVUmS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\nlZXav3+/vvrqKzU0NGjOnDmSpOLiYn344YfavXu37rrrrk7nHDp0SBM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dLafTqZdeekkD\nBgzQtddeqzfffLPLYydMmKC1a9d22nfPPfeosbFRK1as8B9JBGuaKc8AAABARBmGoQULFigzM1OS\n9PLLL/f4/FjjQUAAAABEXFZWVtDnxkN1AjXNAAAAiLhTZ4uLi4vlcDi63CZPnuz33J6gphkAAACn\nidea5gsuuEBPP/20rrzyyh5dua2tTcePH9fixYvV2Niop556SqmpqerTp0/XkdCnGQAAAMnmvvvu\n0znnnKNly5Zp1apVOvvss7V06dKYxMJMMwAAQILoKr+Ktz7NkRTJmWaSZgAAgASR7PkV5RkAAABA\nDNE9AwAAAAmJ7hkAAAA4TbLnV5RnAAAAADFE0gwAAADYIGkGAAAAbJA0AwAAADZImgEAAAAbJM0A\nAPRipumUYRjdbqbpjHWIQFBaWlpUXl6u7OxsmaapMWPGyOv1xiwe+jQDANCLnVge2ep2i+Tyyegd\nzP6m31+sQt3M/maP4mltbQ34uCFDhmjz5s1qbm7WkiVLNHPmTH300UcB34s+zQAAQNKJn6cnEuRu\nj+DnbRLpKr8yDEPyRPCmHtl+xrKzszV//nytWrVKdXV1OnLkiPr06dPjWxUWFsrj8WjatGldvk+f\nZgAAAPRqzz//vDZs2KCmpiaVlpYqPT29y62kpKTL8w8ePKja2lqNGDEiypGfkBqTuwIAACBpGIah\nBQsWKDMzU5L08ssv9+j848eP64YbbtD3vvc95ebmRiJEW8w0AwAAIOKysrKCOq+9vV033XST0tLS\nVFFREeaoAkfSDAAAgIg7UX9/QnFxsRwOR5fb5MmTO46zLEvl5eX67LPPtHr16qDqoMOF8gwAANAj\npun025XD4UhXc/OhKEaE3mbDhg0BHTdv3jx98MEH2rhxo84666wIR+UfM80AAKBHaHOHaPjoo4/0\n5JNPaseOHRo0aFDHTHRlZWVM4qHlHAAAvVgsWs7R5i5+dZVfmf1N+b7wReyejm841Hy4OWLX74lI\ntpwjaQYAoBcjacapkj2/ok8zAAAAEEMsow0AAICExDLaAABAEuUZ6CzZ8yvKMwAAAIAYImkGACAK\nzP6mDMPodjP7m7EOEYAflGcAABAFhmFIHj8HeBTUz0XKM3CqZM+vKM8AACQku9nXM/28ZxiGnCaz\nswCig2W0AQAx4/vC53f29bjHZj7TF7kFGwDgVMw0AwBsOU3/M8K9bcbX3ww3tcVA/Ljxxhs1ePBg\nmaapCy+8UEuXLo1ZLMw0AwBsNfl8CTXj62+G+0uP7181u11Ldzh0qDk+lgwGAuE0TTVF8P/Rnv4/\n0draqtTUwFLQu+66S7/97W+VlpamDz/8UJdffrkuueQSXX311cGGGzRmmgEAEWOaTr8z1PGoVSdK\nQrrbIpl8AJFw8pfeSG2B/D+RnZ2thx56SKNGjZLD4VBbW1tAsY8YMUJpaWkdr1NTUzVw4MCAzg03\nkmYA6GV6U6mEz9ck/z9uASSL559/Xhs2bFBTU5NKS0uVnp7e5VZSUtLpvPnz56tv374aMWKE7rnn\nHl188cUxiZ/yDADoZRKtVAJA4jMMQwsWLFBmZqYk6eWXXw743Mcff1y/+c1v9Prrr+vaa6/VxRdf\nrEsvvTRSoXaLmWYAAABEXFZWVtDnGoYht9ut6667TpWVlWGMKnBhT5o/+OADzZs3TzNnztTTTz8d\n7ssDAJCQUqVeU3YDBOPU5xiKi4vlcDi63CZPntztNY4fP66+fftGI9zThL08Y/jw4XriiSfU3t6u\nsrIylZeXh/sWAIAwM/ubJzpKIGZOPoDYnaDLblLk96FLxzccaj5MNxBE14YNG2yP+eyzz7Rp0yZN\nmTJFaWlp2rhxo1544QVt3LgxChGeLqCkee7cuVq3bp0GDhyonTt3duz3er368Y9/rLa2Nt16661a\nuHChJOmll17S448/ru9///uRiRoAEFZ2i4z4fQ/xrV1+//v5PPyyhPhkGIaWL1+uefPmybIs5ebm\n6ve//73Gjh0bk3gCSprnzJmj22+/XTfffHPHvra2Nt12223auHGjMjMzNXbsWJWUlCgvL09TpkzR\nlClTVFpaqunTp0cseAAAAPiX7nBE9AHhdIfD9pi9e/f2+LrnnnuuampqgogoMgJKmidMmKD6+vpO\n+7Zt26acnBxlZ2dLksrKylRdXa1PP/1Ua9as0bFjx3TFFVeEO14AAGyZpvNf7e4AsBhPeARd09zY\n2NjpKUiXy6WtW7fq8ssv1+WXXx7QNTweT8e/3W633G53sOEAANDh//eH7k58LqwCIDxqamrCPksd\ndNIcjpWcTk2aAaC3sVualuWWASA2vj4Zu3jx4pCvGXTSnJmZqYaGho7XDQ0NcrlcIQcEAL0Fi4wA\nQPIIuk9zUVGR6urqVF9fr5aWFlVVVZ227KEdj8cTVwXeAAAgDFL895w2+9NzGtFRU1MTtsqGgGaa\nZ8+erddff12ff/65srKy9Itf/EJz5sxRRUWFJk2apLa2NpWXlysvL69HN6c8AwCABESbO8SJk2Ua\nUSvP6G65wuLiYhUXF4ccBAAAABDPwr4iYE94PB66ZgAAAIRJenp6WJo19Fbp6emdXoezi0bMk2YA\nQGcsaQ0gWIcOHYp1CHEl6uUZAIDoYUlrAIg/QXfPCAe6ZwAAACBSot49I1IozwAAAECkhLM8I6Yz\nzQAAAEBvQNIMAAAA2KCmGQAAAAkpnDXNMU+a6dEMIBycptntkr1OkyV7ASAZud3uxHgQEADCpcnn\nk9XNe4aPnscAgNBQ0wwAAADYIGkGAAAAbMS8ppkHAQEAABAJPAgIAOgx03R2+7AkACSicD4ISHkG\nAHTD7N99R47emGj6fE2SrG42AIA/dM8AgG74vvBJHj8H+HsPAJBQmGkGAAAAbJA0AwAAADZi/iAg\n3TMAAAAQCXTPAAAgzvjrTtIbHxwFEgHdMwAAiDP+u5PEb4eSVKnbRN9pmrEOD4gbdM8AACCJtar7\nlN7w+aIZChDXmGkGEFZO039vY2auAAC9ETPNAMKqyefz+4doZq4AAL0RM80AAACADZJmAIgyuiwA\nQO8T0/KMky3naDsHIJn8/y4L3SFxBoBwqKmpCduaIPRpBtArmP39P2AIAMDXhbNPMw8CAugVfF/4\nJI+fA/y9BwBAiKhpBgAAAGyQNAMAgKjytwoh/dwRr0iaASQtulgAsXFyFcLutib6uSMOUdMMIGnR\nxQIAEChmmgEAAAAbJM0AAACADZJmAAAAwEbMFzcJ1yotAAAAwKlqamrCtrhJzJNmVgQEAADxzF+n\nHdN0xjo8+MGKgAAAAFHir9OOz0eXnWRBTTMAAABgg6QZAAAAsEHSDAAAANggaQYAAABskDQDAAAA\nNkiaAfSI2d/stvWSYfAUOYDI8df6jfZviDRazgEJymmaavL5un0/3eHQoebmHl/X94VP8vg5wN97\nfpim819tnQCga/5av514n1/cETkkzUCCavL5/PxokQw/CXUs2P0wlPhhCACIHcozAAAAABskzQAA\nAICNiJRnVFdXa926dWpublZ5ebkmTpwYidsAAAAAURGRpLm0tFSlpaU6fPiwfvazn5E0AwAAoFcL\nuDxj7ty5ysjI0MiRIzvt93q9Gj58uIYNG6Zly5Z1em/JkiW67bbbwhMpAAAAECMBJ81z5syR1+vt\ntK+trU233XabvF6vdu3apcrKSr3//vuyLEsLFy5UcXGxRo8eHfagAQAAgGgKuDxjwoQJqq+v77Rv\n27ZtysnJUXZ2tiSprKxM1dXV2rhxozZt2qTm5mbt3r1bP/jBD8IZMwAAABBVIdU0NzY2Kisrq+O1\ny+XS1q1b9dhjj+n222+3Pd/j8XT82+12y+12hxIOAAAAoJqaGtXU1IT1miElzaEumXtq0gwAAACE\nw9cnYxcvXhzyNUPq05yZmamGhoaO1w0NDXK5XCEHBQAAAMSTkJLmoqIi1dXVqb6+Xi0tLaqqqlJJ\nSUnA53s8nrBPnQPxyGmaMgyj281pmrEOEQCAhFNTUxO2yoaAk+bZs2dr/Pjxqq2tVVZWllasWKHU\n1FRVVFRo0qRJys/P16xZs5SXlxfwzT0eD3XMSApNPp8sqdutyeeLYXQAACQmt9sdtqQ54JrmysrK\nLvcXFxeruLg4LMEAAAAELcX/81aObzjUfLg5igEhkURkRcBAnZxpZrYZAACErF2Sp/u3fR7+qpds\nwtlFI+ZJMwAAABAJJydnY949AwAAAEgGJM0AAACAjZgmzbScA+KPaTr9tscDAKC3CGfLOWqaAXTi\n8zXpRCO87pA4AwB6B2qaAQAAgCgiaQYAAABsUNMMAACAhERNMwAAAGCDmmYAkiSzv0mXCwAAoiCm\nM80AQuP7wtf9krHd7QcAAD3GTDMAAABggwcBAQAAkJB4EBAAAACwwYOAAAAAQBSRNAMAAAA2SJoB\nAAAAGyTNAAAAgA26ZwAAACAh0T0DAAAAsEH3DAAAACCKSJqBOGaaThmG0e0GAEhMdt//TdMZ6xCT\nTkzLMwD45/M1SbL8HEHiDACJyO77v8/H9/9oY6YZScVpmn5/c3eaZqxDBAAAcYiZZiSVJp/P/7yt\nzxe1WAAAQO9ByzkAAAAkJFrOAQAAADZoOQcAAABEEUkzAAAAYIOkGQgDs7//rhwAAKB3o3sG/l97\ndxtS5f3Hcfxjy7YHcSjH0ugYhjeks9StMgKZu3FioLTWuiOKSv7sJmI3iOyZe5DLRQ9WwWQbtcbA\nxW6YstzZXTtrT0w3HQwKas7D1NJBaTsbG5b7/R9Eolue63iu65xzec77BUJe57r5nq+XXF9//c73\nBwcErwelhhA7hHoNAAC4HiPNAAAAgAWKZiAMLGcNAEByY3oGEAaWswYAILkx0gwAAADLvSs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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e57e810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(12,20))\n",
    "\n",
    "pidx=1\n",
    "#----------------------------\n",
    "for nbits in (8192,4096,2048,1024):\n",
    "    subplot(4,1,pidx)\n",
    "    pidx+=1\n",
    "    v1=np.array(sims[1,-1])\n",
    "    v2=np.array(sims[1,nbits])\n",
    "    d1 = v1-v2\n",
    "    d1p=np.array(d1,np.float)\n",
    "    d1p/=v1\n",
    "    v1=np.array(sims[2,-1])\n",
    "    v2=np.array(sims[2,nbits])\n",
    "    d2 = v1-v2\n",
    "    d2p=np.array(d2,np.float)\n",
    "    d2p/=v1\n",
    "    v1=np.array(sims[3,-1])\n",
    "    v2=np.array(sims[3,nbits])\n",
    "    d3 = v1-v2\n",
    "    d3p=np.array(d3,np.float)\n",
    "    d3p/=v1\n",
    "    \n",
    "    _=hist((d1,d2,d3),bins=20,log=True,label=(\"r=1\",\"r=2\",\"r=3\"))\n",
    "    title('%d bits'%nbits)\n",
    "    _=legend()\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The changes in similarity are very minimal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.6"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}