pfsim.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Demonstration of particle filtering for Gompertz and logistic growth models\n",
    "The code below illustrates how the particle filter (PF) implementation in module gmplgpf.py can be used to model biomass growth. The demo data consists of biomass measured in a shake flask experiment. This notebook is provided as supplement to \"Critical Event Prediction for Shake Flask Cultivation by Sequential Importance Sampling of Gompertz and Logistic Growth Models\",\n",
    "B. Pretzner, R. W. Maschke, C. Haiderer, G. T. John, C. Herwig and P. Sykacek. Correspondence should be addressed to <barbara.pretzner@koerber-pharma.com> and <peter.sykacek@boku.ac.at>\n",
    "\n",
    "(C) P. Sykacek 2021 <peter@sykacek.net>\n",
    "\n",
    "## Installation of gmplgpf.py and dependencies\n",
    "The implementation for PF based inference of logistic and Gompertz growth models (PFLgGrw) is largely self contained and depends only on standard Python 3.x, numpy and scipy. Additional Python modules are however required to run this demo notebook. For details about all dependencies check the requirements.txt file in the github repository https://github.com/psykacek/pf4grwth. This is a conda compatible requirements file which was generated with <i> conda list -e > requirements.txt </i>. To meet the requirements the PF code should run inside a conda environment which was prepared with <i>conda create --name \"type here your envname\" --file requirements.txt</i>. To use the PF for growth models the module gmplgpf.py has to reside in a folder which is in your Python path.\n",
    "\n",
    "## Generic comments about particle filters and their evaluation\n",
    "This demo code investigates PF runs on data where the entire growth profile is available. We use complete data to provide impressions of how the proposed PF copes on a global scale. It is however important to keep in mind that PFs are adaptive inference methods. The proposed approach allows in particular for adaptive innovation rates which allow that the filter adjusts gradually between convergence to stationarity and tracking of non stationary situations. The PF will hence in general only be optimal in a local sense. Evaluating global predictive behavior is motivated by intending to predict when the growth process completes and which final yield we may expect. The visualized global behavior of PF predictive accuracy depends however on the degree of stationarity of the analyzed growth profiles and is hence data dependent.\n",
    "\n",
    "## Data for simulations\n",
    "All data which were used in the publication \"Critical Event Prediction for Shake Flask Cultivation by Sequential Importance Sampling of Gompertz and Logistic Growth Models\", (Pretzner <i>et al.</i> 2021) are available in the folder ./growthprofiles/. The folder contains a description with experimental protocol and duration of measurements in the accompanying signal files (<i>experiment name</i>\\_bm.csv for the biomass data and <i>experiment name</i>\\_o2.csv for the oxygen concentrations). We provide here the calibrated biomass values and oxygen concentration readouts scaled by 10.   \n",
    "\n",
    "## Hyperparameters of the particle filter\n",
    "To reduce simulation time, the evaluation in this script uses a reduced number of only 500 particles. We moreover use the default settings in the PFLgGrw constructor for the (diagonal) Gamma prior distributions over all innovation rates (g: 0.05 and h: 0.5). Further details of the adjustable parameters of the PF and their default values are provided in the source module gmplgpf.py. Parameters which we override are documented below.\n",
    "\n",
    "## Initializing a particle filter for a specific protocol\n",
    "Particle filters (PFs) are sequential Monte Carlo approaches where model parameters represented by a dynamically evolving set of model parameters (the particles). As is pointed out in (Pretzner <i>et al.</i> 2021) inference benefits from starting with a filter that was previously adjusted to a growth profile which was obtained on the same protocol for which we intend predicting biomass development. Despite that PFs are incrementally updated and allow for tracking non stationary model behavior, we find that convergence and initial predictions are greatly aided by starting with parameters which are \"close\" to the situation we expect to find in a new experiment. \n",
    "\n",
    "## Data preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "## particle filter initialisation \n",
    "##\n",
    "## (C) P. Sykacek 2021 <peter@sykacek.net>\n",
    "from IPython import display\n",
    "%matplotlib inline\n",
    "from gmplgpf import PFLgGrw\n",
    "from gmplgpf import NormVals\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.backends.backend_pdf import PdfPages\n",
    "## we turn of all warnings which are a result of\n",
    "## overflows caused by unsuitable particles which \n",
    "## are discarded anyway.\n",
    "##\n",
    "## The motivation for filtering warnings is the intent \n",
    "## to have less flickering graphical output.\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "## Load demo experiments from data description. \n",
    "## The demo analyses only biomass growth.\n",
    "indir=\"./growthprofiles/\"\n",
    "datadesc=pd.read_csv(indir+\"datadesc.csv\")\n",
    "## make Name the index\n",
    "datadesc.set_index(\"Name\", inplace=True, drop=False)\n",
    "exp4analysis=[\"LB-250ml-1\",\"TB-500ml-3\",\"LB-250ml-2\",\n",
    "              \"TB-500ml-4\"]\n",
    "ifnams=[]\n",
    "## compile description to ifnams:\n",
    "for expnam in exp4analysis:\n",
    "    ifnams.append(indir+datadesc.loc[expnam][\"BMdata\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PF initialization\n",
    "After randomizing the biomass growth curve of the TB-500ml-3 experiment we extract 25% of the data to initialize the particle filter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## select one of the 4 files:\n",
    "ifnam=ifnams[1]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## we cut off after 20 hours.\n",
    "idsel=allx<20\n",
    "allx=allx[idsel]\n",
    "ally=ally[idsel]\n",
    "## \n",
    "if True:\n",
    "    plt.clf()\n",
    "    ## initialising the filter\n",
    "    nwndw=20 ## window size (20 samples in a sliding window constitute X and y)\n",
    "    ## we use 75 evenly spacer time points for predictions\n",
    "    in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "    ## defining the filter\n",
    "    ## the following parametes specify the prior distribution which we use for generating\n",
    "    ## the initial particles\n",
    "    iniw=np.zeros(2)\n",
    "    iniL=5*np.eye(2)\n",
    "    pkmd=2.5\n",
    "    pkprec=1.0\n",
    "    plmd=0.0\n",
    "    plprec=5.0\n",
    "    maxk=np.inf\n",
    "    ## no buffering of past samples\n",
    "    maxinbuff=0\n",
    "    ## note that we use the Gompertz growth model (set dogomp=False for logistic growth)\n",
    "    lpf=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                nprtcls=500, keeprate=0.075, maxinbuff=maxinbuff)\n",
    "\n",
    "    ## for a initialisation we permute the indices randomly.\n",
    "    alldx=np.array(list(range(0, len(allx))))\n",
    "    doreshuffle=True\n",
    "    if doreshuffle:\n",
    "        np.random.shuffle(alldx)\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    ## and reduce the reshuffled data to 25% of the entire time course.\n",
    "    alldx=alldx[0:int(np.ceil(len(alldx)*0.25))]\n",
    "    ## fitting the particle filter \n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        plt.clf()\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpf.addsample(x=cx, y=cy)\n",
    "        nopwnan=lpf.nopwnan\n",
    "        ## get predictions at positions in4pred\n",
    "        if cnt >=20:\n",
    "            x, ymd, yu, yd=lpf.dopred(in4pred)\n",
    "        ## smprange is the slice of samples which we have in the data buffer\n",
    "        smprange=[idx]+smprange[:-1]\n",
    "        trandx=np.array(smprange)\n",
    "        trandx=list(trandx[trandx>=0])\n",
    "        ## plot all samples\n",
    "        pall=plt.plot(allx, ally, 'b.', markersize=3, label='data')\n",
    "        ## plot samples in inference buffer\n",
    "        ptran=plt.plot(allx[trandx], ally[trandx], 'g.', markersize=6, label='train')\n",
    "        ## diagnostic outpit in title: self.nopwnan self.sumpw\n",
    "        ## self.nraccLamb self.nracclambn\n",
    "        nslv=lpf.avprednoise[len(lpf.avprednoise)-1]\n",
    "        if cnt >=20:\n",
    "            ## plot predictions at xpred\n",
    "            pprd=plt.plot(x, ymd, 'r-', label='prediction')\n",
    "            \n",
    "        plt.title(\"Particle filter initialisation (inference on randomly reshuffled data)\")\n",
    "        plt.xlabel(\"time [h]\")\n",
    "        plt.ylabel(\"biomass\")\n",
    "        plt.legend(loc=\"lower right\")\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inferred particle filter\n",
    "The PF which we inferred on one of the terrific broth shake flask experiments is now parameterized. In practice we would pickle the object and load it when needed for monitoring and predicting experiments which use the same recipe.\n",
    "\n",
    "## Monitoring and prediction\n",
    "The initialized PF is capable of adjusting in case biomass growth is non stationary. Such situations may be the result of microbes adapting their metabolism to compensate for changes in their environment (e.g. important resources for one type of metabolism got consumed). For monitoring and prediction we use the PF in its sequential mode of operation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## test predictions on new data (using the same recipe).\n",
    "ifnam=ifnams[3]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## cut off after 20 hours\n",
    "keepdx=allx < 20\n",
    "allx=allx[keepdx]\n",
    "ally=ally[keepdx]\n",
    "## use 75 samples for obtaining global predictions\n",
    "in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "## For assessing predictions, we discare the first 20 samples \n",
    "## and provide time and biomass concentration in the correct \n",
    "## temporal order.\n",
    "alldx=np.array(list(range(20, len(allx))))\n",
    "if True:\n",
    "    ## we initialise the input buffer of the filter.\n",
    "    lpf.buffcnt=0\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        plt.clf()\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpf.addsample(x=cx, y=cy)\n",
    "        ## get predictions at positions in4pred\n",
    "        if cnt >=0:\n",
    "            x, ymd, yu, yd=lpf.dopred(in4pred)\n",
    "        ## smprange is the slice of samples which we have in the data buffer\n",
    "        smprange=[idx]+smprange[:-1]\n",
    "        trandx=np.array(smprange)\n",
    "        trandx=list(trandx[trandx>=0])\n",
    "        ## plot all samples\n",
    "        plt.plot(allx, ally, 'b.', markersize=3, label='data')\n",
    "        ## plot samples in inference buffer\n",
    "        plt.plot(allx[trandx], ally[trandx], 'g.', markersize=6, label='train')\n",
    "        if cnt >=0:\n",
    "            ## plot predictions at xpred\n",
    "            plt.plot(x, ymd, 'r-', label='predictions')\n",
    "            \n",
    "        plt.title(\"Particle filter application (sequential use as data arrives)\")\n",
    "        plt.xlabel(\"time [h]\")\n",
    "        plt.ylabel(\"biomass\")\n",
    "        plt.legend(loc=\"lower right\")\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assessment of a-priori predictions with PFs (no prior adaptation to a protocol)\n",
    "The next experiment initializes a new PF and illustrates a simulation without prior adjustment to a recipe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## global predictions on new data withouit intialisations.\n",
    "ifnam=ifnams[0]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## cut off after 10 hours\n",
    "keepdx=allx < 10\n",
    "allx=allx[keepdx]\n",
    "ally=ally[keepdx]\n",
    "## use 75 samples for obtaining global predictions\n",
    "in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "## For assessing a uninitialised particle filter, \n",
    "## we discared thje first 20 samples and provide time \n",
    "## and biomass concentration in the \n",
    "## correct temporal order.\n",
    "alldx=np.array(list(range(20, len(allx))))\n",
    "if True:\n",
    "    ## initialise a new particle filter.\n",
    "    plt.clf()\n",
    "    ## initialising the filter\n",
    "    nwndw=20 ## window size (20 samples in a sliding window constitute X and y)\n",
    "    ## we use 75 evenly spacer time points for predictions\n",
    "    in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "    ## defining the filter\n",
    "    ## the following parametes specify the prior distribution which we use for generating\n",
    "    ## the initial particles\n",
    "    iniw=np.zeros(2)\n",
    "    iniL=5*np.eye(2)\n",
    "    pkmd=2.5\n",
    "    pkprec=1.0\n",
    "    plmd=0.0\n",
    "    plprec=5.0\n",
    "    maxk=np.inf\n",
    "    ## no buffering of past samples\n",
    "    maxinbuff=0\n",
    "    ## note that we use the Gompertz growth model (set dogomp=False for logistic growth)\n",
    "    lpfn=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                nprtcls=500, keeprate=0.075, maxinbuff=maxinbuff)\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        plt.clf()\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpfn.addsample(x=cx, y=cy)\n",
    "        ## get predictions at positions in4pred\n",
    "        if cnt >=20:\n",
    "            x, ymd, yu, yd=lpfn.dopred(in4pred)\n",
    "        ## smprange is the slice of samples which we have in the data buffer\n",
    "        smprange=[idx]+smprange[:-1]\n",
    "        trandx=np.array(smprange)\n",
    "        trandx=list(trandx[trandx>=0])\n",
    "        ## plot all samples\n",
    "        plt.plot(allx, ally, 'b.', markersize=3, label='data')\n",
    "        ## plot samples in inference buffer\n",
    "        plt.plot(allx[trandx], ally[trandx], 'g.', markersize=6, label='train')\n",
    "        if cnt >=20:\n",
    "            ## plot predictions at xpred\n",
    "            plt.plot(x, ymd, 'r-', label='predictions')\n",
    "            \n",
    "        plt.title(\"Immediate particle filter prediction (sequential use of data)\")\n",
    "        plt.xlabel(\"time [h]\")\n",
    "        plt.ylabel(\"biomass\")\n",
    "        plt.legend(loc=\"lower right\")\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0/juoqPFsPsSxHg3aprUZV1vHlFY+xjY6dnFYMjIy/ExySEiKs3OnyFwEoH/+WUSTns6ZA08BrsJB+y1dPYZV6SfCMJwsiw+eImuKnSQL99SWFXK8bPRVwgPdJ3XMuIihjMEjj4j8F0+i887Le7C8dbw87H2+2Xi+ZsR7VZVWBp6Lgu5AgVFzJzMw/RKfdZB0N9OxrJ2H5SCEJDrr1uFJMR1PkRn2VL0KYyTWF64mC9KbyIqjr5Zfi9WXiWtPk+VSWw5mISAASpcWefhhfBUeQ3l8vgvew/jxkQ1DXgyGgxqLeDAYXuCZ4fDbroyx5aKGQ+WNe0MISS62bUPdzDcikyfb+u03a/HuQiVkw/EtZGqVflL2/NPlvnEZ8vvOY0XQZFV2i+VFFIaqBXkRagjuuefQ7t3zJM6C4/Aw1OTPhmpDg2FLfgqxWQtsNx9TvFLI3dhmcYj99MREJTVq1PCwxISQmLFqle0KqL7/HsYA1qBECZHWreW3c2+SG99uJd/vaigHV6Rbzkbpj9BqCTVWxYtLIBbhGAmSBGOO48FfDpNPoNtwvEWu5WUwOWiqs9pifiDmT4y0L8Y4CEkiViK8+e67Ih99ZMcslPr1ZVXdS+SxHy+UGQdbSpHSGia1496F0DTVMhqm+imnKifiTYzDVxCGwzqQz6eB8Z043vMRtsErh2Rgm03htqHhICTB+fdfkQ8+EHn7bduzUFq2FLniCpH27WXqH7Wt2e3bD31Fq6DKlbNW01gkc3AchdSxbbNQ0C2YhzMp50PPBm2Dykn5W+MhmG9qsvVu9qpMhJAYMmsWKqwHi7z/PprO7LWtwdNPy4yaXeSmJ6qLjESzV7zHPv64bTTCVUExPpHcMY7K0FsmzqEG4QPYh8/xuZeuxPwQTK6CbsYyE9qSTiaoTghJBtRAjB1rGwxtNgsrsPbCHvLIHzdIlxca69tjNu/CMRpaFfUJKrdZBRWfFFhVVX7BqipCEqSfxbBhIs+jZvrPPy3vYul5vaXr5Gtl0eoystu0gFqz5pB3cdxxdkc7xi1SuKqKEJKCqBV45RWRl14S2YRQ5dlni4wYIVMLXSBXXOkLeBbqUTibB3sXrIqKfzgCICEk72Rlibz+ukjt2iIPPSTStKlkvjxDzsj6RgbMvzBgNNSzUE9DDYXGLTQmziqpxIMeByHkyNGq7s8+E7nvPis3lLRqJTJhgmU4+p4h8sMPdifvcHELxjASE3ochJAj4/ffRS66yG4jiyC3fPqp3dsbRmPqVJEtW2zvQvtb0LNILmg4CCG5r5ZCM1qpV09k5ky7zkndissuk6lf+6RuXZFLL7U77GnfC41ZaHcNehfJA6uqCCHRo9loe/Sw05Z36CAycKBMXVpV+jQ4tIkaDEWrprRXN0k+6HEQQnLmwAHby9A6J62D0rjGhx+KVK1qpSBXY+EYDK2ecgLg9DKSE3ochJDIaGeL664T+fZbkWuukW87vyEPPlNO2i8VGWUGN9Lco0wymDrQcBBCwqMB7+7d7eFXR46UqdWuDzStdVpLKeqIOGmnSPLDqipCyOFoCloNUGiLqeOPtzLXTq3eLWA0nOy0TrUUYxmpBT0OQkh2tO5Jc39oqnOtoho6VKZ+XyyQU8rdH4O9vFMTGg5CSPbBlC6/3G419cILInfcYfXR0AA4kw8SGg5CSHbmz7c79O3ZIzJxokwtfJE8cqZdW+V05uMIe0Shx0EIsSPbl1xi10NNmyZT150aqJpyguAaAGfzWqIwOE5IqvPllyIXXCBSqZJtQE49NVvVlJMyhAFw4kDDQUgqo6PxXXaZyCmniEyfLlN/qyFnnGFXTzn5pZgyhATDqipCUpVx40Q6dxY580y7J3jZspan4WS0Zc9vUuAeh8/nKwbNguZDi6HHQmyjDIKWQwugxl6VhxDi4osvbKPRooUVCFejoWh1lFZPaTWVGhFCCrqqai90rt/v1/RnDaE2MAzNg7a5GDrRqCf0uoflIYQoX39tJyhs0MA2ICVLWmnQtYpKUU+DMQ0Sk6oqvz2Y+Q7zMd0oeIBzNBiX0WbbmTAs5aDK+Ljeq3IRktJoPZTGNE7Eu9qkSTI1s6z06SOycqVY44Crl8EU6CSmwXEYgTRoHmY3QF/BIPwUtElVaI3r81qzjBCS3yxZItK2rUjlyrgbvxIpXz6Q2VaNBtOgk7gwHDAUByCtpqoGNYURqRe0iS/U14IX4Hs9oUzVxo0bvSgqIcnNpk0i7dqJFC0q3/f/Ss7ocKwMGGB37NPMtkyDTuKuVRWMxxY89L/BbBtoUZCHUd31WQ3MuhDfH4qJSjIyMg4zLISQCOxFuFF78/35p5Ua/d47a2UbC5yZbUk8taqqqDELM18ck/OhpUGboQ2gdDWtqzRwvpXxDULyEQ0f3nijyIwZIm+9JVN3NDtsLHB27CPx5HGgIlXe0jiHMVAfwCh8js+9dCXmh2CCdoCCSldZDu2CuntYHkJSj6eeEnn7bds6dOwoj5xhxzTUYGjHPma3JfHWqmoBJo1CLFeD4cxrtVNvr8pASEqjTW379RPp0sWaapNbx9ugl0HyAlOOEJKMrF6NSuCuIg3RNuXNN2Xq1z4rzKHeRjlUIDNZIckLNByEJBs6zCuqpSQry04rUqxYtqSF9DZIXqHhICTZePBBkZkzRYYPF6ld21qkxsJJWkhvg+QVJjkkJJnQZIU6cl9vhA6vvjqwWI0FDQbJL+hxEJJMcY3rrxdp0sQ2HgYnD5VOCckPaDgISQYOHhTp0UNk/36RDz6weog7BkNzUWmHP2a7JfkFq6oISQaGDLFdijfeEDn+eGvWGfpVm9+yox/JT2g4CEl0fv/d7sl30UV2L3HgbkU1aBDjGyR/YVUVIYleRdW9u0h6utVfQ3y+bB392IqKeAE9DkISmYEDrbHCZdQokWrVslVRafUUW1IRL6DHQUiismyZ3Wfj0kvtXuKAHf1IQUDDQUgiomnebrnF6hWuAXFNKaItqNq3Z0c/4j2sqiIkERk71h47/LXXrBH9HrnKbnKr6NCvhHgJPQ5CEo2tW0XuvFPk9NNFevbMllKEeahIQUCPg5BEQ0dg2rDBTpuepsPdMKUIKVjocRCSSMyZIzJ4sB3f0NQigClFSEFDw0FIonDggMjNN4tUrCjyxBOBxdqSiilFSEHCqipCEoURI0RmzRJ55x17NCbAUf1IUnkcPp+vOjQNWgIthvqG2KY1tBWaZ4R3J0LIYWiPPo1tnHmmSOfO2bwNjupHksnj2A/d5ff758AglMb8bEy/wudfgrabjmXtPCwHIYnPgAEif/8t8umnVloRB21FpcaDralIUngcMAbr1WiYebwuyRKoqlfHIyRp+fNPkeefF+nUSaRZs8BiraZyjAZTi5CkC47D06iFSSPopxCrW2D9fOhLqG6Y7/eEMlUbN270tKyExB1aRaWB8aeeCixyclIxKE6S0nDgYV8Kk4+g2+F5bAtarR5JTSxvgOkr0PhQ+8D6oVCGqqK2KCEkVViwwE5geNttIscdF1jMnFQkaQ0HjEa6MRpj8ND/OHi9GhJoh5mfiEk6vlPByzIRklDoOBvaguqhh7ItdnqKM206SbZWVRrBGw4tgVF4Mcw2x5rtdL6pKc9mr8pESEIxaZLI5Mm2e3HUUdk6+zk5qRjbILHAh4e6Nzv2+dBuUKZDC6GDZvGDUA2dwXGHYJtbMXuzaYG1G7oTy02qttBkZGT4MzMzPSkzIXGD3pfaM1xHZFq6VKRIEWuxGg2Na6i3wWSGJDfgeTtbq/tz850Cb46LAs7AxJfDNq9ioiKEuNFmt3Pn2vENYzTY2Y/EC0w5Qkg8Dgf76KMiJ50k0qVLYDE7+5F4gYaDkHjj44/t1lRqPAofqhRg6nQSL9BwEBJPaH8NNRinnirSsWNgMTv7kXiCSQ4JiSc++MBOPvX++4GxNpzOfpquSqur2JKKxBp6HITEC/vRuLB/f5F69USuuiqwmJ39SLxBw0FIPI0j/uuvIo89hjvz0K3Jzn4kZfpxeAX7cZCkjW3UrStSrJg9yp/LcBASb/04eHUSEg+MHy+ybJnIgw8GjAaHhCXxCg0HIbFGvf5nnhGpXVukQ4fAYg4JS+IVGg5CYo26FppG5957Ay2pFPbbIPEKDQchsUa9jcqVRbp2DSxivw0Sz9BwEBJLfv7ZthJ33ilStGhgMaupSDxDw0FIrL0NHW/jppuyLWY1FYlnaDgIiRWaLl1HYrr1VpHSpQOLWU1F4h0aDkJixYABdr+NPn2yLWY1FYl3aDgIiQV//SXyzjsiPXqIVKwYWMwxN0jSGA6fz9cXKqPDvILh0BzoQq8LR0jS8tprIllZIn37ZlvMMTdIMnkcPfx+/zZM1Vjo61F3CFG98MCwVIemQUugxWp8QmyjDIKWQwugxrn+BYQkGnv2iLz+uki7diInnphtFYPiJJkMhzMEbFtoJIzIfNeycOg44ndh21MxbQ71hmGoE7TNxZDeOaqeEO4mQpKcMWNENm0SueOOwCInvYiiY4kzdTpJBsMxGw/9ycZwTMK8NgE5GOkLMBjroTlmfjsmS6CqQZtdDo3GemUm5sth35Vz9QsISbT0Ii+9JHLaaSKtW2cbb+OHH+yqKkKSZSCnG6CG0Ao84Hfh4X60qa6KCmxfC5NG0E9Bq9SQrHF9XmuWrQ/6vnojKqlRo0a0hyUk/pgyRWTxYvjtI/XCzjZIk7bI1aoqQpLF42gBLYPR2IKH+LWY7wdtjeaL2L4UJh9Bt5s4SbbVIb5yWJ53fG+opgNWVXS1QCEk4Xj5ZZFKlUT+85/DBmnSLh2soiLJZDg09qCeRgNM74X+gEbn9CVsn26Mxhg89D8OsYl6GNVdn6tB66IsEyGJ1+Fv4kSRW24JpBfhIE0kmQ3Hfg1CmJjEQMwOxPRQV9cQaHMpTIZDS7D9i2E2+wzqalpXaQB9q8ZGoiwTIYnFwIG2wejVK7BIPQwGw0myGo7teLA/gKlWU32Bec39rN5EJLSNyHXQudh+nlFbqJfKbIPXL1kBLYeGQXgVIyQJ+fdf+Ohw0jt3FjnmGGsRB2oiyR4c7wjhipcb4BH8hQe/RqgHRPoCtpuRU5Nd48X0jrIMhCQuo0ahsneXyG23hUwtwtgGSTrDocYCkxddn1dHE+MghICDB+2e4i3QxqSRNi5kahGSGilHmkM/QzugfdABKKpWVYSkPNoEdzlqY3sfcq6ZWoSkQozjVUjbD/4GFYf+DxrsVaEISSoG41bRZuRXXRWIa7RvL9KyJfttkOSOcWj1lOaTSsP0AD6OxDxqZwkhEfkDLdc//1zk/vutFlVOXEPR1lSEJLPHoX04imCqLaOegzTJTkkPy0VIcjBkiD01I/wxiSFJBnx2w6YcNvL5amKywTTBVaNRFnpNvRBvi3c4GRkZ/szMzII+LCFHlgW3enWRM8+0u4UTEkPwHJ+t2TcKzOPAwf6AdmvKEOgx6M5YGA1CEopx4+wsuCYozn4bJNVaVbWD5kL/QNsg7RAYnHeKEBIcFD/55EAnDQ4JS1ItOP4ydCW00HTaI4REYu5ckZ9+spMamiy4W7aI1KnDllQkdYLjmvp8EY0GIVHyxhsixYqJdO1qfWS/DZKKHodmxJ2I6qlvMd3rLIyQvJCQ1EXzpOsofx07ihx1FL0NkrIex5PQLqiYyYrriBASzNixIjt2BJrg0tsgqepxHA3v4kJPS0JIMlVT1a8v0lxHCrBjGmo8OLofSTXDMQXVVBfCeOi444SQcGgfozlz7BZV1pA0dqMqZr8lqVhVpQ3R/wfjscc0xWVzXELCeRslSoh06cJ+GyRpibYDYGmoEFTMzKvKeF04QhKKrVtF3n3XHk+8bFn22yCS6h6HdgK8DHreqJ2XhSIkIdGWVDpYE/NSkSQn2p7jz2DSF/rFqK9ZFuk7I6AN0KIw61vrmB6uYWURPiQkQdF+sVpNpQM1ZWRY1VROQJzxDZKqHkdb6AJUT41QYb6NWRaJUWa7SEzH/hoa4RYjJEGZNUtkwQKRnj2toDjTi5BkJuqqKlDONa/ZcSMCQ/AdJv/kukSEJCLDhtlB8c6drY9Mn06SmWib4z4NaZLDaZhqG8NW0AP5cPwW2Od8TNdBd8PYLH24m5kAABkvSURBVM6HfRJS8D3F33tPpFMnkTJlWE1Fkp5oW1WNxUR7M31s1ALLcKfkiTlQTeynAaavQOPDbQjj0hPKVG3cuDGPhyUkf1nyCG6PnTvl54Y3Wp9ZTUVS2nDgQX2KmTbGpDK01iQ8rGKWHTFmbI8dZn4iJunYZ4Uw2w7VAUhUFXXsZkLirJpqodST28c2Y14qkhLkVFV1J4Ron7wAudOp+8znc4/0wDASx2Lyt2bcxXxTY8Q2H+n+CClotOXUaz3nyUc7M+WpSgOl/RU+ueIKu+aqZUu2piIpajjwTFejIaYF1S3QmboYmg69Hum7MAZavdUaqoB59VQeNUPP6n51IOaroJuxbj+mu6FOTNtOEsloqJF4evsw2SNF5bsa18r28bbRKF2aealIchPtmOMfYKIj/o0xi/4DlcN3r/GwbCHhmOMkljj9M3RQppW/7EKrjioyvWw7KfHRO9Z69t0gqTDmeLStqk42QWyHaaY1FCEphRP41pH8Hqw9Tsot3yqXfoqg+Nn2enb2I6lAtP04tCmunSMaYL4ZJt97UyRC4henf8agQSL9Kg0TOekkNE7X1umEpA4RPQ4YiIWY+E1sois+rzafa5rUI4SkDNnSiFRZglcnvDsNGBBIn05IqpBTVRWTGRLiCoZr8FuNx3nN4G2kpwfGFCcklcipVdUfBVUQQuIZNRZOi6kn+u0RuW60SPv2IsccE+uiERLXuaoISVlvQ1tRaUD8k09EztmCP5s3i9xo9xQnJNWg4SAkCm/jF0T0ypUzraY0oeFxx7EJFUlZaDgIieBpnHGGXSOlLak0KC7Ll6Mx+jSRG27A3cPbh6Qm0fbjICRl+2wo2oDK4v43RdLSRLp3j1m5CIk1fGUiJAyHjamRlSUyapTIJZeIVKnC80ZSFnochIRB4xnZeoJPmCDy998MipOUhx4HIRHiGzoNoEHxqlVF2uQ0IjIhyQ0NByFhOvtpfEPjHBarVolMmiTSowf8dDrqJLWh4SAkQme/QHxj+HB7qq2pCElxaDgICRMU185+VoxDg+JqOC6+WKSmpmkjJLWhz01INEHx9etF3niD54oQQI+DkJwYMkSkWjXb4yCE0HAQ4g6K161rK9Ca6vffRb76ym6Cy6A4Id56HD6fbwS0AVoUZr0yCFoOLYAae1UWQnKTk0oVaE01dKjdU5xBcUIKpKpqFBSpwbv6/Sca9YRe97AshESVk0oz4Kqs1lR794qMHCly6aV2/w1CiLfBcb/f/x28iFoRNrkcGo3tdETBmdi2HFQZHxGFJCQ2OakWL3ateA/NqjZuFOnVi/8OQuIkOK6vcGtcn9eaZYcBg9ITylRt1BuZEC9zUrmD4po+/YILeL4JiRPDEWqgZvU+Dl/o9w+FMlQVK1b0uFgk1aqonOy32ZrgLl0q8u23qERFLSrTpxMSN4ZDPYzqrs9o7yjrYlQWksJVVJpeJFtOKuX11+0xxZk+nZC4MhyfQV1N66rmmN/K+AYpSLRqStOKaHqRQCsqRRdoUPzqq0UqVeI/hZCCCo7DGIzFpDVUAfPqXTwKpZuqJ1Qey0SoLbQc2gVxZBxSYKiHocbi4YdFxo8Pim+MHm0bj9tu43+EkBD47EZNiUNGRoY/MzMz1sUgCY7GNrSaSoPigdH9FL0ftD1uqVIis2bpG1DMykhIfoIX+NkaJ86PfTHlCElJwrakmjLFDoyrt0GjQUhImOSQpCSHJTJ0eOUVkWOOEenYscDLREiiQI+DpBQhR/ZzWLFC5PPP7Sa4RYsWeNkISRRoOEhqj+znZvBgOy8Ve4oTEhEaDpLaI/s57NwpMmKEyJVXMi8VITlAw0FSxtvYssVuMBUY2c/NO+/YG7AJLiE5QsNBUiplerlyIYzGwYMiL70k0rjxoRwkhJCwsFUVSSlv47AqKuXTT0WWLRN57z02wSUkCuhxkNT2NrTD37PP2llwO3SISfkISTRoOEjqdvZTpk8X+eknkbvv5tCwhEQJq6pIUlZN9eljzw8aFKGzn/LccyKaqp9ZcD0lKytL1q5dK3v27PH2QESKFSsm1apVk3TN7uwRNBwkaaumFO23EbIVlbJokcgXX9iuSPHiBVrGVEONRmm0g65Vq5bmTIp1cZIWP6peN2/ebJ3v47T61SNYVUWSDrUDGghXW3BYyvRgb6NkSZHevQu0fKmIehrly5en0fAYNcp6nr327Gg4SNKh3oWOHT5hQoTYxurVImPHitx4o8jRRxd4GVMRehrJc55pOEhSxTbq1rWl82pADhsS1uHFF+3pHXcUaBkJSQZoOEjSxTZUYaunFNT/ypAhItdeK1KjRoGVj8QX/fv3l+effz7s+vHjx+NaMsEykg0aDpJ0sY2wHf0cnnjC7i3+qA5KSUhoaDhiZDhQ19YGWgYth+4Psb41tBWaZxTpPZGQqGIbqrDNb5cvFxk+XOSmmwRNfHhGEzUF/hHy5JNPysknnyznn3++LNNsAWDYsGFy+umnS4MGDaRDhw6ya9cu+eGHH+Szzz6Te+65Rxo2bCi///57yO1SuvmWFwJp0O/Q8VARaD5UJ2gbHZP889zst0mTJpgQcogpU/z+li3taY506eL3Fy/u969fz1NYgKDKJ9ff0f+pPqF0mh9kZmb669Wr59+5c6d/69at/hNOOME/YMAA/6ZNmwLbPPTQQ/5BgwZZ89dff71/3LhxgXXhtkuU841nbaZO8kNeehxNoeU4yApoH+bfgy738HgkRd9GNZ4RdowNNwsXirz7rt078NhjC6ScxKMe/0fA9OnT5YorrpASJUpImTJl5LLLLrOWL1q0SM466yypX7++jBkzBh4rXNYQRLtdKuBlB8Cq0BrXZ0QkpVmI7Vqgikq9kXXQ3TAyh/03sL4nJirEMhnMJIeMhXbwe/hh+4zk+IDRDXUwjnvv5SlMACL2+M/HpqrdunWz4hlaBTVq1Cj55ptvQn432u1SAS89jlCNia36KRdzoJowFg0wfQUaH2pHWD8UylBV1PQQJOVRI6E2QDv4Pf64bTQiPmQ0H5VmwUWdNfttpCatWrWSTz75RHbv3o3rZrtM0I4+QOcrV65spUVRT8JBe7rrOodw26UiXhoO9TCquz5XM15FABiCbdAOMz8Rk3S8EVTwsEwkSaqn1EhoKhHHeESsptLq3fvRNkNfOvr2LbDykviicePG0rFjRyvYrcFtrXZSHsebR7NmzeSCCy6QU045JbB9p06dBDEQadSokRUcD7ddSpJfwZJgmWqwFdBxruB43aBttKLZZ+Y1JrLa+RxODI6nbvC7Tp3Dg6VRBcbffdf+4uDBnpeV5F9wnMRvcNyzGAd2vh/ew62YnWRaWI3AssVY1susH4LJVdDNWLYf091QJ/MDCTksnuH00dBBmRyvI8d6cN1Ye4dnZNhNcAkh8d2PAzZgInQSdAL0pFk2xBgNnX8VUi+kAdQcwuOBkNCtazRFug7GlGPPcDf9+ols3Gj3FE/T9xdCSF5hWnUS9zgehRqL9u3t+aiaaP78s8hrr4ncCse3SRPPykdIqkHDQRKqukrRxIU5cuCASK9edn8NbXZFCMk3aDhIXOJ07FMPY/z4XHoainoac9Da+/33RcqW9aychKQiNBwkLg2GxrQ1lqGdvZ2m9FF5Gsqvv4o8+KDIhReKXH21Z2UlJFVhdlwSt1VSGhDXzt65SjuhieeuQmO9okVF3nxTuwp7VlaSWGzB28hr6onmkrZt21rfJYeg4SBx1bHPSY2u6Lx29A47GFMoNBCuY4lrz97q7v6nJNH4cc2P8vT0p62pl4bjgMbDIjBx4kS05kNzPhKAVVUkbrwMzT3o3J9Ok9tc5SoaOdKWuikXXeRJWUnBoMbivNHnyb4D+6RIWhGZ2nWqtKjeIk/7vP/++60e4NpzPD09XUqVKmWlEJk3b541YFN7BNLWrFljjdfdt29f6dnTSo8ntWrVkszMTNmxY4dcfPHFcuaZZ1pp16tWrSqffvqpFNfB7VMMehwkbvppKO5qqlxlRV2wQOSWW2xLwwGaEp5vVn1jGY0D/gPWVD/nlWeeeUZOOOEEy1BoKpFZs2ZZ43M4o/yNGDFCZs+ebRmJQYMGyebNmw/bx2+//Sa9e/e2MuOqF/LRRx/luVyJCD0OEnOc3t9OYDzHhIXBbNhgxzWOOsquomJHv4Snda3WlqfheBz6Ob9p2rSpHHecZkSyUWOhSRAV9TzUSJQvXz7bd3T7hvBYlCZNmsiqVavyvVyJAA0HSew02torXL+k44h/9ZVIpUqelI0ULFotpdVT6mmo0chrNVUoSpYsGZjXFOlTpkyRH3/80Rqvo3Xr1laVVTBFtdGFIQ0vKJppNxWh4SCJixqNc88VVFyLfPGFHWEnSYMai/w0GMFp0t1s3boVDutRltFYunSpzJw5M9+Om4wwxkESc1xpx9PQMcQ//1zknHM8KR9JHrTa6QxcbPXq1bPGEnfTpk0b2b9/v5x22mloW/GwNG/ePEalTAyclOYJQ0ZGho4dHOtikHzoET5qlMjKlQJ33w6GR93BT+uVddhP1EFbRiO/h4kj+c6SJUvk1FNP5ZmN4fn2+Xyz8bzPyI/90+MgBepFOE1vNX2UNmZRo6GDMUXdgkpTiGhwUo2HjuBGo0FIgUPDQfIdxzg4qc8dQ4IWkFYqEe3gp10tnPE1tCFLjs//HTtEunfXYdkEr1Ii8+eLnH8+/3uExAAaDuJZvwzHiwj2MrSTn1YxL15sK6LROHhQ5OOPddxPkdGjbYszfbq2i+R/jpAYwVZVxPNmtWpAtFe4Og2aBSSqaqmsLJGxY7XXllbYipx4osi0aSKtWvE/RkgyexwIxrSBlkHLoftDrFcGmfULILxWkmRDjYh6GatX29OwHobmDFLX5KGHRE46SeT66/FqU9g2IGo8aDQISW7DASOg43QOhi6GNG3df7DMpK8LoOvwKmlJE8O87lV5SGwD5MHVV6Kt+ZxOezombJcuIsccY3/p2WftqigNfmssQ+Ma7A1OSEpUVTWFlqP51wr9AKPxHiaXQ3ZiGBv9PNpvtwmeiW3KQZXxcX2+l2bNGhyBnXpyQse/0IZLHTuK1K9vFjpNtt3TYGksAh7DkoX75fNPD0jWzn1y5t+7ZWmn3bK+yG5p3XibfF95IwIdm1BvtdH+f7g7Y6nRaNdO5JJL7HE0mI2UxDmlSpWyEh+uW7cOVbF95MMPPwy77csvv2wlTdQOhk6q9nfffTdhs+56aTiqQng6BMDrpTSLYhtdls1wwJioN2KlqqxRo8aRlUaNxjXXHNl3Uwi1FZa9OMLRVrXleLbW47ATe6So7N5QBtVPFUUqVBA55RS7x7e2jlJp0yo1HBw7g8QYTbGuqURyQ5UqVSIaDcdwXHvttQHDoanaExkvDUeoEXSCextGsw1eaP1DMRnqdAA8otLoW6yO00BytK9PPWXP6yB6gQ60zkPdPXWrEGo9ccPNmFlYnnshTe56oIic3aa4TP2+mDzSv1DuExeS5OX220XmzcvffWrfHjycI6EJCbWHeLNmzWTu3LkIo52Ehnqj8d5SR3r06CGTJ0+WW2+9VU4//XQrA+7GjRutB/2wYcPwrnOKrFy5Ujp37mz1MNf9uPfbDt7yIjxf1PDcd999MmnSJH3hlRtvvFGfX5ZXcs455+C9qQLaeEwLpGrXzy+++KKVmVf5v//7P5ye2619hkvhrskYhwwZgvBfYavs772nlTnJYzjUe3CPpFMNWncE2+QPOu40x57OkeZ1RTaPsGPUOv3+htyNC67T/6Ih1NnGSJx3gS1C4oFly5bJ8OHDrdQjaiycgZ2KFSsmM2bMsObPwxuOPphPREu+n376SW655Rb5+uuvrTE6br75ZunatasMHqzh28MZOnSoZWDUMOmD/Z9//pGjjz7aMg5qMNRQuNE07iNHjrSOowZGjdrZZ59t5c3S7Lxj0TBEDdc1qC3RFO7qtWh6eD2GJlyM2ciEWlgvZIySxje0wX0RCFFOqRu0DSq05UtIX2P13XZWTvtt0qSJhkSIh0yZ4ve3bGlPVXXq+P01athT/eyg2+gVVKiQPS1d2p7qckLc/PLLLzE/IXjY+qtXrx74PHXqVP/ll1/ur1mzph9v+Nay7du3+2FE/A0aNAgI3oa1DgbAv2/fPmt+69at/pIlSwb2W7euPtr8/iuvvNIPz+WwY+sx4MEc9hlVWP6HH344sLxfv37+gQMHWvusXbt2YDmMhf/xxx+35i+66CJ/hw4d/G+//bZV3mjPN56vmTrJD3nmcWDn++Gq3YrZSZBWGo7AssVY1susH4KJVvS1hZZDu6DuXpWHHFk/DG3kZMa5sXBG5VNvQ192dPAzJ22I9s2zPI7cDMBESAGi1UehPjsp1g+ikYcGrHWwp2i+H4w+VHPaJnj7cIRL4f7FF1/Id999J5999pnAmFiDSql3kzT9OHBSJkInQSdAT5plQ4zR0Hmlt1lfH2L2wjhrTqvVTxq71jYJKjUWThWVGhRtNavNbDVtSK7HByekgFm9erU15oai1UAaQ3BTpkwZa7CmcePGBR7s87VJONDqLSeeMEYHDAvBhYilajWXxkEUraqKlNK9VatWeNkaL7t27ZKdO3daA0mdddZZYcuvhk0HmdJ4yXPPPWdVVWnLroKGKUdISJw0IepBaFqQP/5AAKqabSy0F7iTc0q7YNBYkERBM8a+9dZbVvp0fahrzCIYNQoaB0E1laAKygpKK6hCsmIbpyN4ruN3hEKD29ryU/ev39cmt4o2xdVgtz7w3TRu3Fi6detmjUao8Q39fqNGjcKWX4PvGueoX7++td0dd9wRkya9TKtOQhJqGFdnmRoNNSC5SoVOUpp4SKvubv2U7CzxOK06c1WRqIdxDTU2OCEk9aDhIAUzNjghMUb7TqSCt1EQMMZBCCkQIrUgIol1nmk4CCGeox3sNm/eTONRAEZDz7Oeby9hVRUhxHOqoUne2rVrrTQexFvUaOj59hIaDkKI56Snp1v9I0hywKoqQgghNByEEEK8gx4HIYSQ5O457vP5NLr2xxF+vYI9tBDhecozvJZ4nhLtWqqJ533FlDQceTQ6mfnV5T6Z4XniOeK1xPstEqyqIoQQkitoOAghhNBwRMAat5zkCM8Tz1F+wWspCc9RSsU4CCGE5B1WVRFCCMkVNByEEEJoOHJoajoAWgotgD6BCn7cxTgF56INtAxaDt0f6/LEIzgv1aFp0BJoMdQ31mWKV3Bu0qC50OexLku84sPzB/rQPJP0mmoR6zJFQyp6HF9B9RDbOQ3TX6EHYlyeuAAXbBomg6GLoTrQf7BMpyQ7+6G7cP3ouJzNod48T2FRo7qEF1BEBkL/w/V0CqYNEuV8pZzhwD9oMqQ3vzIT8jb/cOLQFFqOc7MC2of596DLY1ymuAPnZj00x8xvNzd61diWKv6AMdX76hLozViXJY7PURlMWkHD9bPed9CW2JYqOlLOcATRA/oy1oWIE/Tht8b1ea1ZRsLf+LUwaQT9xJN0GC9D90IHeW7CcjykKZRGmiq9N6GSYbeOI5LScODkT4EWhVDgDRrzD2GinseY2JU0rvCFWMa22uFOls9XCpOPoNvxlrjNs/9KYp6bdphswHmZHeuyxDmFocbQ6zhX+gKyE7o/UQqedOCfcH4OF/b1mOjFfR625cPxkIdR3XWatKphnTf/ocQG10+6MRpjcPl8HOvyxCFnQJfhPLXFVMcwLYP5d3Curo1xueLxnluL8+J4rB8miuFISo8jEriA22ByH3QZ/mG7Yl2eOOJn6EScn+OgIpjvBH0W4zLFHTg3PlMnvQTXz4uxLk88gvPyAFQNqmWuo69pNEKep78wWYNL6mSz6Dzol8O3jD+S0uPIgVehotBX9jNAZuIf2Cu2RYo92mAA5+NWzE6CtIXVCCxbHONixevb9HXQQpyveWbZgzhXE2NYJpK43AaNMS9rK6DuMS5PVDDlCCGEkFyRclVVhBBC8gYNByGEEBoOQggh3kGPgxBCCA0HIYQQ76DHQQghhIaDkFymtb7F9bmKprnO7zOIffaH/oT+6/p8d4jtimv/EGgfVCG/y0FIfkCPg6Q6Oh5LwHD4/f510FUeHesl7PuRSBtg/W6oIWaZ7oXELTQcJNV5BjrBvOXrIF+1NCGmrsC0GzQemgCt1J710J0mk+lM6GiznX7/f9BsaDqkYytEQx1s+w20Aurj1Q8kJL9JxZQjhLi53wzs1dCVKt1NPaiRSda3HLpPM5liu5cw39WkDx8K9cLy37C8GeZfg86N4jSrgTkHKg3pyIuaJTWL/x4S79BwEBKZaWbApu14sG/FdIJZvhA6zaRXbwmNM7nPxORCi4YvsO+9mO7FdzdgWslkTCUkrqHhICQy+mB3OOj6fNDcP1rdu8XxWPKw7wO8H0miwBgHSXW2m6qiI8IM4qTxj6udtOtAx44mJGmh4SApDR78mzH53owQOeAId9MFugHfn4+ppqLnWO0kqWFadUIK4kbz+fpjsgOG6vkot1+FSQa23+RtyQjJPfQ4CCkYdkA9nQ6A4XA6AGI23cRRCIk76HEQQgjJFfQ4CCGE0HAQQgjxDnochBBCaDgIIYR4x/8DpLvCicU15mEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## global predictions on new data without intialisations (second LB experiment).\n",
    "ifnam=ifnams[2]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "normby=signals[1:20]\n",
    "normby=normby[np.isfinite(normby)]\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## cut off after 10 hours\n",
    "keepdx=allx < 10\n",
    "allx=allx[keepdx]\n",
    "ally=ally[keepdx]\n",
    "## use 75 samples for obtaining global predictions\n",
    "in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "## For assessing a uninitialised particle filter, \n",
    "## we discared thje first 20 samples and provide time \n",
    "## and biomass concentration in the \n",
    "## correct temporal order.\n",
    "alldx=np.array(list(range(20, len(allx))))\n",
    "if True:\n",
    "    ## initialise a new particle filter.\n",
    "    plt.clf()\n",
    "    ## initialising the filter\n",
    "    nwndw=20 ## window size (20 samples in a sliding window constitute X and y)\n",
    "    ## we use 75 evenly spacer time points for predictions\n",
    "    in4pred=np.linspace(-2, np.amax(allx), 75)\n",
    "    ## defining the filter\n",
    "    ## the following parametes specify the prior distribution which we use for generating\n",
    "    ## the initial particles\n",
    "    iniw=np.zeros(2)\n",
    "    iniL=5*np.eye(2)\n",
    "    pkmd=2.5\n",
    "    pkprec=1.0\n",
    "    plmd=0.0\n",
    "    plprec=5.0\n",
    "    maxk=np.inf\n",
    "    ## no buffering of past samples\n",
    "    maxinbuff=0\n",
    "    ## note that we use the Gompertz growth model (set dogomp=False for logistic growth)\n",
    "    lpfn2=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                nprtcls=500, keeprate=0.075, maxinbuff=maxinbuff)\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        plt.clf()\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpfn2.addsample(x=cx, y=cy)\n",
    "        ## get predictions at positions in4pred\n",
    "        if cnt >=20:\n",
    "            x, ymd, yu, yd=lpfn2.dopred(in4pred)\n",
    "        ## smprange is the slice of samples which we have in the data buffer\n",
    "        smprange=[idx]+smprange[:-1]\n",
    "        trandx=np.array(smprange)\n",
    "        trandx=list(trandx[trandx>=0])\n",
    "        ## plot all samples\n",
    "        plt.plot(allx, ally, 'b.', markersize=3, label='data')\n",
    "        ## plot samples in inference buffer\n",
    "        plt.plot(allx[trandx], ally[trandx], 'g.', markersize=6, label='train')\n",
    "        if cnt >=20:\n",
    "            ## plot predictions at xpred\n",
    "            plt.plot(x, ymd, 'r-', label='predictions')\n",
    "            \n",
    "        plt.title(\"Immediate particle filter prediction (sequential use of data)\")\n",
    "        plt.xlabel(\"time [h]\")\n",
    "        plt.ylabel(\"biomass\")\n",
    "        plt.legend(loc=\"lower right\")\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predictive monitoring with particle filters\n",
    "To assess predictive monitoring we compare three modes how the PF can be used.\n",
    "\n",
    "- Application of a naively initialized PF (*unbuffered*).\n",
    "- Application of a PF which was before initialized with a growth experiment that uses the same experimental protocol (*pretrained*).\n",
    "- The PF allows to specify that samples (time and corresponding biomass) are randomly retained after they would normally be discarded. This mode of operation still focuses on most recent observations, but also keeps the estimated growth curve close to earlier samples (*buffered*)\n",
    "\n",
    "To evaluate predictive monitoring we focus on future samples and calculate the mean square errors of all three PF options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## global predictions on new data without intialisations \n",
    "## (second LB experiment). This assessment runs three versions \n",
    "## of the PF - one with and one without retaining earlier \n",
    "## samples for inference and a third PF without buferiung but \n",
    "## pretrained on the same recipe. To assess the global predictive \n",
    "## accuracy over time we subsample indices to obtain SSDs over \n",
    "## test time.\n",
    "ifnam=ifnams[0]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## we cuit off after 20 hours.\n",
    "idsel=allx<10\n",
    "allx=allx[idsel]\n",
    "ally=ally[idsel]\n",
    "## \n",
    "if True:\n",
    "    plt.clf()\n",
    "    ## initialising the filter\n",
    "    nwndw=20 ## window size (20 samples in a sliding window constitute X and y)\n",
    "    ## defining the filter\n",
    "    ## the following parametes specify the prior distribution which we use for generating\n",
    "    ## the initial particles\n",
    "    iniw=np.zeros(2)\n",
    "    iniL=5*np.eye(2)\n",
    "    pkmd=2.5\n",
    "    pkprec=1.0\n",
    "    plmd=0.0\n",
    "    plprec=5.0\n",
    "    maxk=np.inf\n",
    "    ## no buffering of past samples\n",
    "    maxinbuff=0\n",
    "    ## note that we use the Gompertz growth model (set dogomp=False for logistic growth)\n",
    "    lpf5=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                 dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                 nprtcls=500, keeprate=0.075, maxinbuff=maxinbuff)\n",
    "\n",
    "    ## for a initialisation we permute the indices randomly.\n",
    "    alldx=np.array(list(range(0, len(allx))))\n",
    "    doreshuffle=True\n",
    "    if doreshuffle:\n",
    "        np.random.shuffle(alldx)\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    ## and reduce the reshuffled data to 10% of the entire time course.\n",
    "    alldx=alldx[0:int(np.ceil(len(alldx)*0.1))]\n",
    "    ## fitting the particle filter \n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpf5.addsample(x=cx, y=cy)\n",
    "## clear inpit buffer of lpf5\n",
    "lpf5.buffcnt=0\n",
    "## lpf5 is initialised and we switch to evaluation\n",
    "ifnam=ifnams[2]\n",
    "indat=pd.read_csv(ifnam)\n",
    "allx=indat['x']\n",
    "signals=indat['y']\n",
    "## remove the first value which can be done when \n",
    "## directly processing data from the instrument by \n",
    "## storing the first measurement.\n",
    "ally=signals-signals[0]\n",
    "## cut off after 6.5 hours (as after that we have a decay)\n",
    "keepdx=allx < 6.5\n",
    "allx=allx[keepdx]\n",
    "ally=ally[keepdx]\n",
    "## use 100 samples for prediction and evaluiaton\n",
    "id4pred=np.array(list(range(0,len(allx),int(len(allx)/100))))\n",
    "in4pred=allx[id4pred]\n",
    "trg4pred=ally[id4pred]\n",
    "## For assessing a uninitialised particle filter, \n",
    "## we discared thje first 20 samples and provide time \n",
    "## and biomass concentration in the \n",
    "## correct temporal order.\n",
    "alldx=np.array(list(range(20, len(allx))))\n",
    "if True:\n",
    "    ## initialise a new particle filter.\n",
    "    plt.clf()\n",
    "    ## initialising the filter\n",
    "    nwndw=20 ## window size (20 samples in a sliding window constitute X and y)\n",
    "    ## defining the filter\n",
    "    ## the following parametes specify the prior distribution which we use for generating\n",
    "    ## the initial particles\n",
    "    iniw=np.zeros(2)\n",
    "    iniL=5*np.eye(2)\n",
    "    pkmd=2.5\n",
    "    pkprec=1.0\n",
    "    plmd=0.0\n",
    "    plprec=5.0\n",
    "    maxk=np.inf\n",
    "    ## buffering of 25 randomly selected past samples\n",
    "    maxinbuff=25\n",
    "    ## note that we use the Gompertz growth model (set dogomp=False for logistic growth)\n",
    "    lpfn3=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                nprtcls=500, keeprate=0.075, maxinbuff=maxinbuff)\n",
    "    ## and comparison without buffering\n",
    "    lpfn4=PFLgGrw(iniw, iniL, pkmd, pkprec, plmd, plprec, maxk=maxk, \n",
    "                dogomp=True, addoffs=True, smpwnd=nwndw, innownd=nwndw, \n",
    "                nprtcls=500, keeprate=0.075, maxinbuff=0)\n",
    "    alldx=list(alldx)\n",
    "    smprange=[-1]*nwndw\n",
    "    ## buffers for ssds and time at prediction\n",
    "    msebf=[]\n",
    "    msenbf=[]\n",
    "    msept=[]\n",
    "    ptm=[]\n",
    "    for cnt, idx in enumerate(alldx):\n",
    "        plt.clf()\n",
    "        ## add sample idx to filter:\n",
    "        cx=[allx[idx]]\n",
    "        cy=ally[idx]\n",
    "        lpfn3.addsample(x=cx.copy(), y=cy.copy())\n",
    "        lpfn4.addsample(x=cx.copy(), y=cy.copy())\n",
    "        lpf5.addsample(x=cx.copy(), y=cy.copy())\n",
    "        ## get predictions at positions in4pred\n",
    "        if cnt >=10 and cnt % 10==0:\n",
    "            ## generate inputs and targets for forward predictions\n",
    "            id4pred=np.array(alldx)\n",
    "            id4pred=id4pred[id4pred>idx]\n",
    "            in4pred=allx[id4pred]\n",
    "            trg4pred=ally[id4pred]\n",
    "            ## time when prediction is made\n",
    "            ptm.append(cx)\n",
    "            xbf, ybf, yu, yd=lpfn3.dopred(in4pred)\n",
    "            msebf.append(np.sum((ybf-trg4pred)**2)/len(ybf))\n",
    "            xnbf, ynbf, yu, yd=lpfn4.dopred(in4pred)\n",
    "            msenbf.append(np.sum((ynbf-trg4pred)**2)/len(ynbf))\n",
    "            xpt, ypt, yu, yd=lpf5.dopred(in4pred)\n",
    "            msept.append(np.sum((ypt-trg4pred)**2)/len(ypt))\n",
    "        ## smprange is the slice of samples which we have in the data buffer\n",
    "        smprange=[idx]+smprange[:-1]\n",
    "        trandx=np.array(smprange)\n",
    "        trandx=list(trandx[trandx>=0])\n",
    "        ## plot all samples\n",
    "        plt.plot(allx, ally, 'b.', markersize=3, label='data')\n",
    "        ## plot samples in inference buffer\n",
    "        plt.plot(allx[trandx], ally[trandx], 'g.', markersize=6, label='train')\n",
    "        if cnt >=10:\n",
    "            ## plot predictions at xpred\n",
    "            plt.plot(xbf, ybf, 'r-', label='buffered')\n",
    "            plt.plot(xnbf, ynbf, 'c-', label='unbuffered')\n",
    "            plt.plot(xpt, ypt, 'm-', label='pretrained')\n",
    "        plt.title(\"Particle filter forward predictions (sequential use of data)\")\n",
    "        plt.xlabel(\"time [h]\")\n",
    "        plt.ylabel(\"biomass\")\n",
    "        plt.legend(loc=\"lower right\")\n",
    "        display.display(plt.gcf())\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## visualisation of MSE of forward predicitons over time\n",
    "plt.clf()\n",
    "plt.plot(ptm, np.log(msebf), 'b-', label='buffered')\n",
    "plt.plot(ptm, np.log(msenbf), 'g-', label='unbuffered')\n",
    "plt.plot(ptm, np.log(msept), 'r-', label='pretrained')\n",
    "plt.title(\"MSEs from forward predictions over prediction time\")\n",
    "plt.xlabel(\"time [h]\")\n",
    "plt.ylabel(\"ln(MSE)\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "Particle filters are sequential inference methods. A PF based estimation of growth curves can in principle be bootstrapped from randomly initialized particles. Our simulations reveal however that initializing PFs by training on biomass profiles which were obtained on identical growth media is beneficial. We observe in the above simulations that a naively initialized PF is particularly challenged with inferring accurate values for the limit biomass parameter when only presented with initial measurements. The simulations suggest that **recipe specific pretraining** of PF growth models is recommended. The initialized filter provides in particular in the first half of the growth process much better predictions. In the second half of the growth experiment the particle filter without buffering provides superior results."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.9"
  },
  "toc-showmarkdowntxt": false
 },
 "nbformat": 4,
 "nbformat_minor": 4
}