Fin4 Simulation-2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "import matplotlib.pylab as pl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cadCAD\n",
    "from cadCAD import engine\n",
    "from cadCAD.configuration import Configuration\n",
    "from cadCAD.engine import ExecutionMode, ExecutionContext, Executor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulation_parameters = {\n",
    "    'T': range(20),\n",
    "    'N': 1,\n",
    "    'M': {}\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test of Basic Design"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# general constants\n",
    "\n",
    "TIMESTEP = 'timestep' # access to current timestep with s[TIMESTEP]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_update_name(variable_name):\n",
    "    return \"add_\" + variable_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "USERS = \"users\"\n",
    "PATS = \"pats\"\n",
    "OPATS = \"opats\"\n",
    "CLAIMS = \"claims\"\n",
    "ADD_USERS = get_update_name(USERS)\n",
    "ADD_PATS = get_update_name(PATS)\n",
    "ADD_OPATS = get_update_name(OPATS)\n",
    "ADD_CLAIMS = get_update_name(CLAIMS)\n",
    "WALLET_GAINS = \"wallet_gains\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_conditions = {\n",
    "    USERS: {0:{}}, # users are numerical ids and a dictionary of their current wallet\n",
    "    PATS: [0], # pats are currently simply numerical ids\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## update functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create single user with empty wallet \n",
    "def create_users(params, step, sL, s):\n",
    "    next_user_id = len(s[USERS])\n",
    "    x = {ADD_USERS:[\n",
    "        (next_user_id, {}),\n",
    "         #{random.choice(s[PATS]):random.randint(1,10)}\n",
    "    ]}\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_pat(params, step, sL, s):\n",
    "    next_pat_id = len(s[PATS])\n",
    "    x = {ADD_PATS:[next_pat_id,]}\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def user_actions(params, step, sL, s):\n",
    "    gain = {}\n",
    "    pats = s[PATS]\n",
    "    for user in s[USERS]:\n",
    "        for pat in random.sample(pats, random.randint(0, len(pats))):\n",
    "            gain[(user, pat)] = 1\n",
    "    return {WALLET_GAINS: gain}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## update variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_users(params, step, sL, s, _input):\n",
    "    x = s[USERS].copy()\n",
    "    for new_user_id, wallet in _input[ADD_USERS]:\n",
    "        x[new_user_id] = wallet\n",
    "    return (USERS, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_user_wallets(params, step, sL, s, _input):\n",
    "    x = s[USERS].copy()\n",
    "    changes = _input[WALLET_GAINS]\n",
    "    for (user, pat), gain in changes.items():\n",
    "        x[user][pat] = x[user].get(pat, 0) + gain\n",
    "    return (USERS, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_pat(params, step, sL, s, _input):\n",
    "    x = s[PATS].copy()\n",
    "    x.extend(_input[ADD_PATS])\n",
    "    return (PATS, x)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## test of basic functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "single_proc: [<cadCAD.configuration.Configuration object at 0x7f5cde6f7668>]\n",
      "[<cadCAD.configuration.Configuration object at 0x7f5cde6f7668>]\n",
      "                                                 pats  run  substep  timestep  \\\n",
      "0                                                 [0]    1        0         0   \n",
      "1                                                 [0]    1        1         1   \n",
      "2                                                 [0]    1        2         1   \n",
      "3                                              [0, 1]    1        3         1   \n",
      "4                                              [0, 1]    1        1         2   \n",
      "5                                              [0, 1]    1        2         2   \n",
      "6                                           [0, 1, 2]    1        3         2   \n",
      "7                                           [0, 1, 2]    1        1         3   \n",
      "8                                           [0, 1, 2]    1        2         3   \n",
      "9                                        [0, 1, 2, 3]    1        3         3   \n",
      "10                                       [0, 1, 2, 3]    1        1         4   \n",
      "11                                       [0, 1, 2, 3]    1        2         4   \n",
      "12                                    [0, 1, 2, 3, 4]    1        3         4   \n",
      "13                                    [0, 1, 2, 3, 4]    1        1         5   \n",
      "14                                    [0, 1, 2, 3, 4]    1        2         5   \n",
      "15                                 [0, 1, 2, 3, 4, 5]    1        3         5   \n",
      "16                                 [0, 1, 2, 3, 4, 5]    1        1         6   \n",
      "17                                 [0, 1, 2, 3, 4, 5]    1        2         6   \n",
      "18                              [0, 1, 2, 3, 4, 5, 6]    1        3         6   \n",
      "19                              [0, 1, 2, 3, 4, 5, 6]    1        1         7   \n",
      "20                              [0, 1, 2, 3, 4, 5, 6]    1        2         7   \n",
      "21                           [0, 1, 2, 3, 4, 5, 6, 7]    1        3         7   \n",
      "22                           [0, 1, 2, 3, 4, 5, 6, 7]    1        1         8   \n",
      "23                           [0, 1, 2, 3, 4, 5, 6, 7]    1        2         8   \n",
      "24                        [0, 1, 2, 3, 4, 5, 6, 7, 8]    1        3         8   \n",
      "25                        [0, 1, 2, 3, 4, 5, 6, 7, 8]    1        1         9   \n",
      "26                        [0, 1, 2, 3, 4, 5, 6, 7, 8]    1        2         9   \n",
      "27                     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]    1        3         9   \n",
      "28                     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]    1        1        10   \n",
      "29                     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]    1        2        10   \n",
      "..                                                ...  ...      ...       ...   \n",
      "31                 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]    1        1        11   \n",
      "32                 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]    1        2        11   \n",
      "33             [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]    1        3        11   \n",
      "34             [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]    1        1        12   \n",
      "35             [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]    1        2        12   \n",
      "36         [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]    1        3        12   \n",
      "37         [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]    1        1        13   \n",
      "38         [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]    1        2        13   \n",
      "39     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]    1        3        13   \n",
      "40     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]    1        1        14   \n",
      "41     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]    1        2        14   \n",
      "42  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        14   \n",
      "43  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        15   \n",
      "44  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        15   \n",
      "45  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        15   \n",
      "46  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        16   \n",
      "47  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        16   \n",
      "48  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        16   \n",
      "49  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        17   \n",
      "50  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        17   \n",
      "51  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        17   \n",
      "52  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        18   \n",
      "53  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        18   \n",
      "54  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        18   \n",
      "55  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        19   \n",
      "56  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        19   \n",
      "57  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        19   \n",
      "58  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        1        20   \n",
      "59  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        2        20   \n",
      "60  [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...    1        3        20   \n",
      "\n",
      "                                                users  \n",
      "0                                             {0: {}}  \n",
      "1                                      {0: {}, 1: {}}  \n",
      "2                                      {0: {}, 1: {}}  \n",
      "3                                      {0: {}, 1: {}}  \n",
      "4                               {0: {}, 1: {}, 2: {}}  \n",
      "5                 {0: {1: 1}, 1: {}, 2: {1: 1, 0: 1}}  \n",
      "6                 {0: {1: 1}, 1: {}, 2: {1: 1, 0: 1}}  \n",
      "7          {0: {1: 1}, 1: {}, 2: {1: 1, 0: 1}, 3: {}}  \n",
      "8   {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 1, 0: 1}, ...  \n",
      "9   {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 1, 0: 1}, ...  \n",
      "10  {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 1, 0: 1}, ...  \n",
      "11  {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 2, 0: 2, 2...  \n",
      "12  {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 2, 0: 2, 2...  \n",
      "13  {0: {1: 1}, 1: {2: 1, 0: 1}, 2: {1: 2, 0: 2, 2...  \n",
      "14  {0: {1: 1, 2: 1, 0: 1}, 1: {2: 1, 0: 1}, 2: {1...  \n",
      "15  {0: {1: 1, 2: 1, 0: 1}, 1: {2: 1, 0: 1}, 2: {1...  \n",
      "16  {0: {1: 1, 2: 1, 0: 1}, 1: {2: 1, 0: 1}, 2: {1...  \n",
      "17  {0: {1: 2, 2: 2, 0: 1, 4: 1, 3: 1}, 1: {2: 1, ...  \n",
      "18  {0: {1: 2, 2: 2, 0: 1, 4: 1, 3: 1}, 1: {2: 1, ...  \n",
      "19  {0: {1: 2, 2: 2, 0: 1, 4: 1, 3: 1}, 1: {2: 1, ...  \n",
      "20  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 1, 6: 1, 5: 1}...  \n",
      "21  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 1, 6: 1, 5: 1}...  \n",
      "22  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 1, 6: 1, 5: 1}...  \n",
      "23  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 2, 6: 1, 5: 2}...  \n",
      "24  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 2, 6: 1, 5: 2}...  \n",
      "25  {0: {1: 3, 2: 3, 0: 1, 4: 2, 3: 2, 6: 1, 5: 2}...  \n",
      "26  {0: {1: 4, 2: 4, 0: 2, 4: 3, 3: 3, 6: 2, 5: 3,...  \n",
      "27  {0: {1: 4, 2: 4, 0: 2, 4: 3, 3: 3, 6: 2, 5: 3,...  \n",
      "28  {0: {1: 4, 2: 4, 0: 2, 4: 3, 3: 3, 6: 2, 5: 3,...  \n",
      "29  {0: {1: 5, 2: 5, 0: 3, 4: 4, 3: 3, 6: 3, 5: 4,...  \n",
      "..                                                ...  \n",
      "31  {0: {1: 5, 2: 5, 0: 3, 4: 4, 3: 3, 6: 3, 5: 4,...  \n",
      "32  {0: {1: 5, 2: 5, 0: 4, 4: 4, 3: 3, 6: 3, 5: 4,...  \n",
      "33  {0: {1: 5, 2: 5, 0: 4, 4: 4, 3: 3, 6: 3, 5: 4,...  \n",
      "34  {0: {1: 5, 2: 5, 0: 4, 4: 4, 3: 3, 6: 3, 5: 4,...  \n",
      "35  {0: {1: 6, 2: 5, 0: 4, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "36  {0: {1: 6, 2: 5, 0: 4, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "37  {0: {1: 6, 2: 5, 0: 4, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "38  {0: {1: 6, 2: 5, 0: 5, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "39  {0: {1: 6, 2: 5, 0: 5, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "40  {0: {1: 6, 2: 5, 0: 5, 4: 5, 3: 3, 6: 3, 5: 4,...  \n",
      "41  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "42  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "43  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "44  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "45  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "46  {0: {1: 6, 2: 6, 0: 5, 4: 6, 3: 4, 6: 4, 5: 4,...  \n",
      "47  {0: {1: 7, 2: 7, 0: 6, 4: 7, 3: 5, 6: 5, 5: 5,...  \n",
      "48  {0: {1: 7, 2: 7, 0: 6, 4: 7, 3: 5, 6: 5, 5: 5,...  \n",
      "49  {0: {1: 7, 2: 7, 0: 6, 4: 7, 3: 5, 6: 5, 5: 5,...  \n",
      "50  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "51  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "52  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "53  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "54  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "55  {0: {1: 8, 2: 8, 0: 6, 4: 8, 3: 6, 6: 6, 5: 6,...  \n",
      "56  {0: {1: 9, 2: 9, 0: 6, 4: 9, 3: 7, 6: 7, 5: 7,...  \n",
      "57  {0: {1: 9, 2: 9, 0: 6, 4: 9, 3: 7, 6: 7, 5: 7,...  \n",
      "58  {0: {1: 9, 2: 9, 0: 6, 4: 9, 3: 7, 6: 7, 5: 7,...  \n",
      "59  {0: {1: 9, 2: 10, 0: 7, 4: 10, 3: 8, 6: 8, 5: ...  \n",
      "60  {0: {1: 9, 2: 10, 0: 7, 4: 10, 3: 8, 6: 8, 5: ...  \n",
      "\n",
      "[61 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { \n",
    "            'create_users': create_users,\n",
    "        },\n",
    "        'variables': { \n",
    "            USERS: add_users,\n",
    "        }\n",
    "    },\n",
    "    { \n",
    "        'policies': {\n",
    "            'user_actions': user_actions,\n",
    "        },\n",
    "        'variables': {\n",
    "            USERS: update_user_wallets,\n",
    "        }\n",
    "    },\n",
    "    { \n",
    "        'policies': {\n",
    "            'create_pat': create_pat,\n",
    "        },\n",
    "        'variables': {\n",
    "            PATS: add_pat,\n",
    "        }\n",
    "    },    \n",
    "]\n",
    "\n",
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = executor.execute()\n",
    "\n",
    "df = pd.DataFrame(raw_result)\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial design V0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_conditions = {\n",
    "    USERS: {0:{}}, # users are numerical ids and a dictionary of their current wallet\n",
    "    PATS: [0], # pats are currently simply numerical ids\n",
    "    CLAIMS: {},\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def users_join(params, step, sL, s):\n",
    "    \"\"\"Each step one user joins the system\"\"\"\n",
    "    next_user_id = len(s[USERS])\n",
    "    x = {ADD_USERS:[\n",
    "        (next_user_id, {}),\n",
    "    ]}\n",
    "    return x\n",
    "\n",
    "def claim_pat(params, step, sL, s):\n",
    "    \"\"\"Each step each user creates a random amount of claims for a random selection of PATs\"\"\"\n",
    "    maximum_number_of_actions = 10\n",
    "    new_claims = {}\n",
    "    pats = s[PATS]\n",
    "    for user in s[USERS]:\n",
    "        for pat in random.sample(pats, random.randint(0, min(len(pats), maximum_number_of_actions))):\n",
    "            new_claims[(user, pat)] = 1\n",
    "    return ({ADD_CLAIMS: new_claims})\n",
    "\n",
    "def prove_claim(params, step, sL, s):\n",
    "    \"\"\"Each steps all claims are accepted with a certain probability\"\"\"\n",
    "    acceptance_probability = 1\n",
    "    gains = {}\n",
    "    for (user, pat), gain in s[CLAIMS].items():\n",
    "        if random.random() < acceptance_probability:\n",
    "            gains[(user, pat)] = gain\n",
    "    \n",
    "    return {WALLET_GAINS:gains}\n",
    "\n",
    "def create_new_pats(params, step, sL, s):\n",
    "    \"\"\"Each step one new PAT is added to the system\"\"\"\n",
    "    next_pat_id = len(s[PATS])\n",
    "    x = {ADD_PATS:[next_pat_id,]}\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_users(params, step, sL, s, _input):\n",
    "    x = s[USERS] \n",
    "    \n",
    "    # add new users\n",
    "    for new_user_id, wallet in _input[ADD_USERS]:\n",
    "        x[new_user_id] = wallet\n",
    "    \n",
    "    # update wallet according to proven claims\n",
    "    changes = _input[WALLET_GAINS]\n",
    "    for (user, pat), gain in changes.items():\n",
    "        x[user][pat] = x[user].get(pat, 0) + gain\n",
    "        \n",
    "    return (USERS, x)\n",
    "\n",
    "def update_pats(params, step, sL, s, _input):\n",
    "    x = s[PATS] \n",
    "    x.extend(_input[ADD_PATS])\n",
    "    return (PATS, x)\n",
    "\n",
    "def update_claims(params, step, sL, s, _input):\n",
    "    return (CLAIMS, _input[ADD_CLAIMS])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial Design V0\n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { \n",
    "            'users_join': users_join,\n",
    "            'claim_pats': claim_pat,\n",
    "            'prove_claim': prove_claim,\n",
    "            'create_new_pats': create_new_pats\n",
    "        },\n",
    "        'variables': { \n",
    "            USERS: update_users,\n",
    "            PATS: update_pats,\n",
    "            CLAIMS: update_claims, \n",
    "        }\n",
    "    },\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulation_parameters = {\n",
    "    'T': range(100), \n",
    "    'N': 1,\n",
    "    'M': {}\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "single_proc: [<cadCAD.configuration.Configuration object at 0x7f5cb14e4748>]\n",
      "[<cadCAD.configuration.Configuration object at 0x7f5cb14e4748>]\n",
      "{'claims': {(0, 62): 1, (1, 4): 1, (1, 33): 1, (1, 68): 1, (2, 48): 1, (2, 12): 1, (2, 62): 1, (3, 49): 1, (3, 74): 1, (3, 21): 1, (3, 41): 1, (3, 38): 1, (3, 15): 1, (3, 93): 1, (3, 88): 1, (3, 17): 1, (6, 55): 1, (7, 17): 1, (7, 38): 1, (7, 75): 1, (7, 40): 1, (7, 73): 1, (7, 96): 1, (7, 91): 1, (7, 86): 1, (7, 94): 1, (8, 31): 1, (8, 12): 1, (8, 33): 1, (9, 35): 1, (9, 47): 1, (9, 67): 1, (9, 10): 1, (9, 72): 1, (10, 59): 1, (10, 93): 1, (10, 15): 1, (11, 2): 1, (11, 22): 1, (11, 58): 1, (11, 82): 1, (11, 70): 1, (11, 97): 1, (11, 86): 1, (11, 48): 1, (11, 91): 1, (11, 56): 1, (12, 65): 1, (12, 63): 1, (12, 44): 1, (12, 1): 1, (12, 15): 1, (12, 56): 1, (12, 37): 1, (12, 50): 1, (12, 61): 1, (13, 20): 1, (13, 41): 1, (13, 71): 1, (13, 73): 1, (13, 22): 1, (14, 87): 1, (14, 38): 1, (14, 67): 1, (14, 44): 1, (14, 27): 1, (15, 38): 1, (15, 59): 1, (15, 25): 1, (15, 68): 1, (15, 15): 1, (15, 79): 1, (15, 29): 1, (15, 5): 1, (15, 36): 1, (15, 80): 1, (16, 89): 1, (16, 70): 1, (16, 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1, 49: 1, 35: 1, 70: 1, 74: 1, 0: 1, 38: 2, 43: 2, 66: 1, 96: 1, 50: 1, 18: 1, 83: 1}, 96: {42: 1, 63: 1, 68: 1, 51: 1, 31: 2, 56: 1, 30: 1, 24: 1, 2: 1, 15: 1, 71: 1, 38: 1}, 97: {53: 1, 87: 1, 29: 1, 31: 1, 84: 1, 25: 1}, 98: {15: 1, 29: 1, 36: 1, 9: 1, 94: 1, 88: 1}, 99: {}, 100: {}}, 'run': 1, 'substep': 1, 'timestep': 100}\n"
     ]
    }
   ],
   "source": [
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = executor.execute()\n",
    "\n",
    "df = pd.DataFrame(raw_result)\n",
    "#print(df)\n",
    "print(raw_result[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis\n",
    "- Too many different Pats with too little token/activity per PAT\n",
    "- Multiple of same kind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 474, 1: 482, 2: 445, 3: 452, 4: 482, 5: 461, 6: 473, 7: 491, 8: 454, 9: 463, 10: 439, 11: 483, 12: 433, 13: 454, 14: 465, 15: 409, 16: 428, 17: 400, 18: 378, 19: 414, 20: 410, 21: 438, 22: 377, 23: 407, 24: 377, 25: 387, 26: 356, 27: 360, 28: 335, 29: 368, 30: 359, 31: 320, 32: 353, 33: 320, 34: 346, 35: 319, 36: 314, 37: 338, 38: 332, 39: 280, 40: 295, 41: 289, 42: 274, 43: 287, 44: 274, 45: 279, 46: 274, 47: 289, 48: 238, 49: 270, 50: 264, 51: 234, 52: 231, 53: 256, 54: 236, 55: 209, 56: 227, 57: 192, 58: 216, 59: 183, 60: 202, 61: 208, 62: 180, 63: 202, 64: 187, 65: 167, 66: 167, 67: 157, 68: 150, 69: 161, 70: 136, 71: 142, 72: 120, 73: 142, 74: 130, 75: 94, 76: 124, 77: 92, 78: 127, 79: 86, 80: 83, 81: 86, 82: 84, 83: 84, 84: 69, 85: 78, 86: 67, 87: 60, 88: 56, 89: 54, 90: 45, 91: 26, 92: 28, 93: 32, 94: 29, 95: 27, 96: 15, 97: 13, 98: 9, 99: 0, 100: 0}\n"
     ]
    },
    {
     "data": {
      "image/png": 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gt8f26LiXu8zHE9ylwGuS/JDBFWYvZ7An3/KYH1VVD3T3pxj8Mt/HOr3PN1u497kUQmuGL+3wBgbHo88uf333ifrFwOmzf9ptNhnsot8EnKyq9w+tanrsSWa6PXaSPBV4BYMPGe9gcBkPeOy4N/VlPqrquqraU1WzDP79frmq/oqGx3xWkt9L8vSz08CfA/eyXu/zjf6AYRUfSFwB/CeDY5N/t9H9THlsnwQeBP6HwW/tNzM4vvgl4Hvd/TO62jA4c+j7wD3A3Eb3v4Zx/ymDPzfvBo53tytaHzvwEuDb3bjvBa7vlj8f+CawAPwz8ORu+VO6+YVu/fM3egxrHP9lwK1bZczdGO/qbifO5td6vc/9hqokNWizHZaRJPVguEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1KD/Axm9zKeGvmgdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f5cb241af98>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def calculate_total_tokens_per_pat(state):\n",
    "    distribution = {pat:0 for pat in state[PATS]}\n",
    "    for user_wallet in state[USERS].values():\n",
    "        for pat, number_of_tokens in user_wallet.items():\n",
    "            distribution[pat] += number_of_tokens\n",
    "    return distribution\n",
    "\n",
    "print(calculate_total_tokens_per_pat(raw_result[-1]))\n",
    "pl.hist(calculate_total_tokens_per_pat(raw_result[-1]).values(), bins=300)\n",
    "pl.show()\n",
    "\n",
    "pl.scatter(calculate_total_tokens_per_pat(raw_result[-1]).keys(), \n",
    "           calculate_total_tokens_per_pat(raw_result[-1]).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 84, 1: 81, 2: 85, 3: 78, 4: 87, 5: 85, 6: 85, 7: 83, 8: 85, 9: 85, 10: 82, 11: 85, 12: 82, 13: 82, 14: 86, 15: 86, 16: 84, 17: 87, 18: 81, 19: 81, 20: 85, 21: 83, 22: 84, 23: 84, 24: 81, 25: 84, 26: 81, 27: 80, 28: 86, 29: 83, 30: 86, 31: 86, 32: 80, 33: 80, 34: 86, 35: 85, 36: 83, 37: 88, 38: 86, 39: 84, 40: 86, 41: 83, 42: 81, 43: 85, 44: 83, 45: 87, 46: 80, 47: 84, 48: 86, 49: 87, 50: 88, 51: 84, 52: 80, 53: 86, 54: 79, 55: 79, 56: 82, 57: 82, 58: 77, 59: 78, 60: 81, 61: 80, 62: 82, 63: 78, 64: 80, 65: 77, 66: 75, 67: 76, 68: 74, 69: 76, 70: 70, 71: 73, 72: 74, 73: 81, 74: 75, 75: 57, 76: 72, 77: 60, 78: 68, 79: 60, 80: 55, 81: 62, 82: 56, 83: 62, 84: 52, 85: 60, 86: 51, 87: 48, 88: 43, 89: 44, 90: 37, 91: 23, 92: 22, 93: 29, 94: 28, 95: 25, 96: 15, 97: 12, 98: 9, 99: 0, 100: 0}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f5cb2cbc240>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def calculate_active_user_per_pat(state):\n",
    "    distribution = {pat:0 for pat in state[PATS]}\n",
    "    for user_wallet in state[USERS].values():\n",
    "        for pat, number_of_tokens in user_wallet.items():\n",
    "            distribution[pat] += 1\n",
    "    return distribution\n",
    "\n",
    "print(calculate_active_user_per_pat(raw_result[-1]))\n",
    "pl.hist(calculate_active_user_per_pat(raw_result[-1]).values(), bins=300)\n",
    "pl.show()\n",
    "\n",
    "pl.scatter(calculate_active_user_per_pat(raw_result[-1]).keys(), \n",
    "           calculate_active_user_per_pat(raw_result[-1]).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[86, 85, 82, 85, 87, 84, 84, 84, 81, 81, 82, 83, 83, 85, 81, 84, 82, 79, 86, 82, 83, 84, 85, 89, 82, 81, 86, 79, 85, 83, 91, 83, 79, 82, 82, 82, 84, 83, 84, 84, 81, 76, 91, 82, 83, 84, 83, 86, 86, 74, 80, 85, 84, 82, 81, 81, 80, 79, 84, 82, 83, 80, 80, 75, 77, 81, 79, 77, 82, 83, 82, 77, 63, 71, 71, 70, 65, 66, 69, 60, 53, 59, 56, 66, 60, 51, 52, 52, 44, 49, 40, 32, 26, 31, 25, 16, 12, 6, 6, 0, 0]\n"
     ]
    },
    {
     "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": [
    "def calculate_distributions_of_number_of_tokens(state):\n",
    "    distribution = []\n",
    "    for user_wallet in state[USERS].values():\n",
    "        distribution.append(len(user_wallet))\n",
    "    return distribution\n",
    "\n",
    "print(calculate_distributions_of_number_of_tokens(raw_result[-1]))\n",
    "pl.hist(calculate_distributions_of_number_of_tokens(raw_result[-1]), bins=300)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# New Design (V1)\n",
    "- Req: Concentration/Focus/Emphasis on good PATs\n",
    "- Proposal: List of accepted/good/official PATs (using TCR -> new Token GOV)\n",
    "- Initial Approach, 1 GOV per User (democracy, one vote for each user)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_conditions = {\n",
    "    USERS: {0:{}}, # users are numerical ids and a dictionary of their current wallet\n",
    "    PATS: [0], # pats are currently simply numerical ids\n",
    "    OPATS: [],\n",
    "    CLAIMS: {},\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "def claim_pat_with_opats(params, step, sL, s):\n",
    "    \"\"\"Each step each user creates a random amount of claims for a random selection of PATs\"\"\"\n",
    "    maximum_number_of_actions = 10\n",
    "    probability_on_opat_actions = .9\n",
    "    new_claims = {}\n",
    "    pats = s[PATS]\n",
    "    opats = s[OPATS]\n",
    "\n",
    "    for user in s[USERS]:\n",
    "        number_of_actions = random.randint(0, min(len(pats), maximum_number_of_actions))\n",
    "        opat_actions = min(len(opats), int(number_of_actions*probability_on_opat_actions))\n",
    "        usual_actions = number_of_actions - opat_actions\n",
    "        \n",
    "        for pat in random.sample(opats, opat_actions):\n",
    "            new_claims[(user, pat)] = 1\n",
    "        \n",
    "        for pat in random.sample(pats, random.randint(0, usual_actions)):\n",
    "            new_claims[(user, pat)] = 1\n",
    "    return ({ADD_CLAIMS: new_claims})\n",
    "\n",
    "def propose_opats(params, step, sL, s):\n",
    "    if 5 < s[TIMESTEP] < 20:\n",
    "        proposal_probability = .5\n",
    "    else: \n",
    "        proposal_probability = .01\n",
    "    pats = s[PATS]\n",
    "    opats = s[OPATS]\n",
    "    new_opats = []\n",
    "    if random.random() < proposal_probability:\n",
    "        next_opat = random.choice(pats)\n",
    "        \n",
    "        i = 0\n",
    "        while next_opat in opats:\n",
    "            i += 1\n",
    "            if i >= 10:\n",
    "                break\n",
    "            next_opat = random.choice(pats)\n",
    "        else:\n",
    "            new_opats.append(next_opat)\n",
    "    \n",
    "    return {ADD_OPATS:new_opats}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_opats(params, step, sL, s, _input):\n",
    "    x = s[OPATS]\n",
    "    x.extend(_input[ADD_OPATS])\n",
    "    return (OPATS, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Design V1 with \n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { \n",
    "            'users_join': users_join,\n",
    "            'claim_pats': claim_pat_with_opats,\n",
    "            'prove_claim': prove_claim,\n",
    "            'create_new_pats': create_new_pats,\n",
    "            'propose_opats': propose_opats,\n",
    "        },\n",
    "        'variables': { \n",
    "            USERS: update_users,\n",
    "            PATS: update_pats,\n",
    "            CLAIMS: update_claims, \n",
    "            OPATS: update_opats,\n",
    "        }\n",
    "    },\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulation_parameters = {\n",
    "    'T': range(100), \n",
    "    'N': 1,\n",
    "    'M': {}\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "single_proc: [<cadCAD.configuration.Configuration object at 0x7f5cb1b47f28>]\n",
      "[<cadCAD.configuration.Configuration object at 0x7f5cb1b47f28>]\n",
      "{'claims': {(0, 5): 1, (0, 1): 1, (0, 6): 1, (0, 8): 1, (0, 42): 1, (1, 9): 1, (1, 3): 1, (3, 42): 1, (3, 0): 1, (3, 5): 1, (3, 1): 1, (3, 8): 1, (3, 6): 1, (3, 3): 1, (3, 19): 1, (4, 6): 1, (5, 9): 1, (5, 42): 1, (5, 0): 1, (5, 19): 1, (6, 8): 1, (6, 42): 1, (6, 1): 1, (6, 19): 1, (7, 19): 1, (7, 42): 1, (7, 6): 1, (7, 9): 1, (7, 8): 1, (7, 5): 1, (8, 0): 1, (8, 42): 1, (8, 9): 1, (8, 19): 1, (8, 3): 1, (8, 5): 1, (10, 19): 1, (10, 6): 1, (10, 1): 1, (10, 5): 1, (10, 0): 1, (10, 42): 1, (10, 9): 1, (10, 3): 1, (10, 8): 1, (11, 42): 1, (11, 9): 1, (11, 1): 1, (11, 8): 1, (11, 5): 1, (11, 19): 1, (11, 3): 1, (11, 6): 1, (11, 0): 1, (12, 1): 1, (12, 42): 1, (12, 6): 1, (12, 9): 1, (12, 23): 1, (13, 42): 1, (14, 0): 1, (14, 9): 1, (14, 42): 1, (14, 8): 1, (14, 6): 1, (14, 19): 1, (14, 3): 1, (14, 5): 1, (14, 77): 1, (15, 3): 1, (15, 0): 1, (15, 9): 1, (15, 2): 1, (16, 3): 1, (16, 5): 1, (16, 8): 1, (16, 1): 1, (16, 19): 1, (16, 6): 1, (16, 42): 1, (16, 10): 1, (17, 19): 1, (17, 6): 1, (18, 5): 1, (18, 19): 1, (18, 6): 1, (18, 0): 1, (18, 8): 1, (18, 3): 1, (18, 42): 1, (18, 1): 1, (18, 9): 1, (18, 43): 1, (19, 3): 1, (19, 0): 1, (19, 9): 1, (19, 19): 1, (19, 5): 1, (19, 1): 1, (22, 0): 1, (22, 9): 1, (22, 42): 1, (22, 19): 1, (22, 3): 1, (22, 5): 1, (22, 58): 1, (23, 9): 1, (23, 5): 1, (23, 3): 1, (23, 6): 1, (23, 1): 1, (23, 42): 1, (23, 19): 1, (24, 42): 1, (26, 1): 1, (26, 8): 1, (26, 0): 1, (26, 3): 1, (27, 9): 1, (28, 42): 1, (29, 6): 1, (29, 0): 1, (29, 83): 1, (30, 42): 1, (30, 3): 1, (30, 0): 1, (30, 5): 1, (30, 19): 1, (30, 9): 1, (30, 37): 1, (31, 0): 1, (31, 5): 1, (31, 15): 1, (32, 5): 1, (34, 6): 1, (34, 5): 1, (34, 8): 1, (34, 0): 1, (34, 1): 1, (35, 42): 1, (35, 1): 1, (35, 6): 1, (35, 5): 1, (35, 8): 1, (35, 9): 1, (36, 5): 1, (36, 3): 1, (36, 6): 1, (36, 42): 1, (36, 19): 1, (36, 1): 1, (36, 9): 1, (36, 8): 1, (36, 0): 1, (36, 51): 1, (37, 3): 1, (37, 6): 1, (37, 1): 1, (37, 19): 1, (37, 5): 1, (37, 0): 1, (37, 8): 1, (37, 31): 1, (38, 42): 1, (38, 9): 1, (38, 0): 1, (38, 5): 1, (38, 1): 1, (38, 19): 1, (38, 8): 1, (38, 3): 1, (38, 6): 1, (39, 5): 1, (39, 3): 1, (39, 0): 1, (40, 0): 1, (40, 9): 1, (40, 42): 1, (40, 1): 1, (40, 3): 1, (41, 66): 1, (42, 3): 1, (42, 94): 1, (43, 3): 1, (43, 19): 1, (43, 1): 1, (43, 5): 1, (43, 8): 1, (44, 42): 1, (44, 29): 1, (45, 0): 1, (45, 5): 1, (45, 1): 1, (45, 42): 1, (45, 8): 1, (45, 9): 1, (45, 6): 1, (45, 24): 1, (46, 42): 1, (46, 19): 1, (46, 5): 1, (46, 0): 1, (47, 19): 1, (47, 1): 1, (47, 3): 1, (47, 8): 1, (47, 9): 1, (49, 19): 1, (49, 8): 1, (49, 9): 1, (49, 6): 1, (49, 5): 1, (51, 9): 1, (51, 8): 1, (51, 5): 1, (51, 0): 1, (51, 6): 1, (52, 1): 1, (53, 83): 1, (54, 42): 1, (54, 5): 1, (54, 19): 1, (54, 9): 1, (54, 8): 1, (54, 0): 1, (54, 6): 1, (54, 3): 1, (54, 1): 1, (54, 40): 1, (55, 5): 1, (55, 6): 1, (55, 0): 1, (55, 42): 1, (55, 3): 1, (55, 13): 1, (56, 0): 1, (56, 19): 1, (56, 9): 1, (57, 5): 1, (57, 1): 1, (57, 9): 1, (57, 42): 1, (58, 1): 1, (58, 3): 1, (58, 6): 1, (58, 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52: 1, 0: 4, 85: 1, 91: 1, 98: 1}, 88: {3: 9, 1: 8, 19: 6, 8: 6, 9: 8, 0: 5, 6: 5, 5: 6, 29: 1, 42: 6, 32: 1}, 89: {5: 7, 3: 6, 19: 4, 9: 6, 1: 7, 0: 4, 42: 6, 8: 5, 6: 6, 83: 1, 60: 1, 53: 1, 21: 1}, 90: {3: 4, 42: 6, 5: 3, 8: 5, 6: 4, 9: 3, 46: 1, 1: 2, 19: 3, 0: 1, 26: 1, 37: 1}, 91: {9: 3, 5: 4, 0: 4, 86: 1, 6: 2, 1: 3, 3: 2, 8: 2, 42: 2, 30: 1, 19: 3, 21: 2, 87: 1}, 92: {9: 2, 19: 4, 0: 1, 68: 1, 67: 1, 5: 3, 53: 1, 8: 3, 42: 2, 6: 2, 90: 1, 3: 1, 1: 2, 11: 1, 39: 1}, 93: {0: 3, 1: 2, 6: 3, 3: 5, 8: 3, 9: 3, 42: 4, 5: 4, 19: 2}, 94: {8: 1, 9: 3, 5: 1, 1: 2, 42: 1, 0: 1, 6: 1, 3: 1}, 95: {0: 4, 3: 4, 19: 3, 42: 3, 8: 3, 1: 2, 95: 1, 9: 2, 5: 2, 6: 3, 80: 1}, 96: {0: 2, 19: 2, 14: 1, 5: 1, 1: 1, 3: 1, 9: 1, 42: 1, 6: 1, 8: 1}, 97: {5: 2, 1: 2, 19: 1, 8: 2, 42: 2, 6: 1, 3: 1, 9: 1, 0: 1}, 98: {5: 1, 3: 1, 42: 1, 6: 1, 0: 1, 8: 1, 9: 1, 19: 1}, 99: {}, 100: {}}, 'run': 1, 'substep': 1, 'timestep': 100}\n"
     ]
    }
   ],
   "source": [
    "config = Configuration(initial_state=initial_conditions, #dict containing variable names and initial values\n",
    "                       partial_state_update_blocks=partial_state_update_blocks, #dict containing state update functions\n",
    "                       sim_config=simulation_parameters #dict containing simulation parameters\n",
    "                      )\n",
    "\n",
    "exec_mode = ExecutionMode()\n",
    "exec_context = ExecutionContext(exec_mode.single_proc)\n",
    "executor = Executor(exec_context, [config]) # Pass the configuration object inside an array\n",
    "raw_result, tensor = executor.execute()\n",
    "\n",
    "df = pd.DataFrame(raw_result)\n",
    "#print(df)\n",
    "print(raw_result[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 2377, 1: 2438, 2: 61, 3: 2399, 4: 49, 5: 2433, 6: 2367, 7: 57, 8: 2415, 9: 2315, 10: 54, 11: 44, 12: 52, 13: 48, 14: 34, 15: 41, 16: 34, 17: 45, 18: 38, 19: 2319, 20: 35, 21: 41, 22: 45, 23: 35, 24: 31, 25: 30, 26: 28, 27: 39, 28: 22, 29: 43, 30: 40, 31: 45, 32: 33, 33: 18, 34: 27, 35: 29, 36: 27, 37: 30, 38: 37, 39: 35, 40: 28, 41: 26, 42: 758, 43: 21, 44: 26, 45: 22, 46: 24, 47: 28, 48: 14, 49: 19, 50: 27, 51: 21, 52: 23, 53: 24, 54: 13, 55: 26, 56: 15, 57: 23, 58: 23, 59: 9, 60: 16, 61: 21, 62: 16, 63: 21, 64: 14, 65: 11, 66: 19, 67: 13, 68: 17, 69: 12, 70: 21, 71: 6, 72: 21, 73: 11, 74: 7, 75: 14, 76: 2, 77: 12, 78: 16, 79: 5, 80: 10, 81: 5, 82: 8, 83: 8, 84: 4, 85: 5, 86: 12, 87: 7, 88: 3, 89: 7, 90: 2, 91: 2, 92: 2, 93: 0, 94: 1, 95: 2, 96: 2, 97: 2, 98: 1, 99: 0, 100: 0}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f5cb2568e48>"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "print(calculate_total_tokens_per_pat(raw_result[-1]))\n",
    "pl.hist(calculate_total_tokens_per_pat(raw_result[-1]).values(), bins=300)\n",
    "pl.show()\n",
    "\n",
    "pl.scatter(calculate_total_tokens_per_pat(raw_result[-1]).keys(), \n",
    "           calculate_total_tokens_per_pat(raw_result[-1]).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f5cb1945b00>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAGQtJREFUeJzt3X+MHGd9x/HPl/MFLkFwMbmk8TmOjWQ5ICLi9EQDrhBxSE0AEYvSEkSLVUXyH6WFpMjEUf+glZAwMmoCEorkJlDTIuM2sRwLKizkJEKNissZW+Sn6zSQ2GcTH00uIHIqZ+fbP3Y27O3NzM7szOzsPvt+SZZv52Znn9lJvn7mme/zfczdBQAI1+vqbgAAoFoEegAIHIEeAAJHoAeAwBHoASBwBHoACByBHgACR6AHgMAR6AEgcMvqboAkXXLJJb569eq6mwEAA+XIkSO/dPeJTvv1RaBfvXq1pqen624GAAwUM3suy34M3QBA4Aj0ABA4Aj0ABK5joDezb5jZWTN7vGXbcjP7gZmdiP6+ONpuZvY1M3vGzH5qZtdW2XgAQGdZevT/JOkDbdu2Szrk7mslHYpeS9JNktZGf7ZKuqecZgIAutUx68bdf2hmq9s23yzpfdHPuyU9IumOaPu3vLGayY/MbNzMLnf3M2U1uGn/0RntPHhcp+fmtWJ8TNs2rdPm9ZOZ92n93ZvHRmUmzb2ysGi/LPugHlmuP4CGbtMrL2sGb3c/Y2aXRtsnJZ1s2e9UtG1JoDezrWr0+rVq1apcH77/6Izu3PeY5hfOS5Jm5uZ1577HJGlRIE/aR9Ki383NL7y2vbnf9HMv6oEjM6n7tH4eeifL9QfwO2U/jLWYbbFrFbr7LnefcvepiYmO+f6L7Dx4/LX/yZvmF87rtr3HtGHHQ6/19uL22XnweOzv2vfbc/hkx312Hjyeq93d2H90Rht2PKQ127/32rkNu7RrC2Cpbnv0LzSHZMzscklno+2nJF3Rst9KSaeLNDDO6bn5xN81e3dJQTrtva3OZ1hLN+uxukXPNV7S91719QAGVbc9+gOStkQ/b5H0YMv2T0XZN9dJermK8fkV42Opv59fOK8Ri7u5aLy30/slJb4/TzuKoucaL+l7r/p6AIMqS3rlHkn/KWmdmZ0ys1sl7ZB0o5mdkHRj9FqS/l3Ss5KekfSPkv6yikZv27ROY6Mjqfucd1+yz9joiLZtWtfx/WOjI/rEH1zRcZ9tm9bla3hO9FzjxV2/XlwPYFBlybr5RMKvbojZ1yV9umijOmkOW+w8eFwzCUFvMsrESMvM6JRRM3Xl8lqzblaMj8We37D3XFuvP1k3QGfmGcaiqzY1NeXdFjVrH8eWGr27L3306oH/Hz/kcwNQnJkdcfepTvv1RfXKIkLu3YV8bgB6Z+B79AAwrLL26ClqBgCBI9ADQOAI9AAQOAI9AASOQA8AgSPQA0DgCPQAEDgCPQAEjkAPAIEj0ANA4Aj0ABA4Aj0ABI5ADwCBI9ADQOAI9AAQOAI9AASOQA8AgSPQA0DgCPQAEDgCPQAEjkAPAIEj0ANA4Aj0ABA4Aj0ABI5ADwCBI9ADQOAI9AAQOAI9AASuUKA3s9vN7Akze9zM9pjZG8xsjZkdNrMTZrbXzC4oq7EAgPy6DvRmNinpM5Km3P0dkkYk3SLpy5Lucve1kl6SdGsZDQUAdKfo0M0ySWNmtkzShZLOSNoo6f7o97slbS74GQCAAroO9O4+I+krkp5XI8C/LOmIpDl3PxftdkrSZNz7zWyrmU2b2fTs7Gy3zQAAdFBk6OZiSTdLWiNphaSLJN0Us6vHvd/dd7n7lLtPTUxMdNsMAEAHRYZu3i/pZ+4+6+4LkvZJeo+k8WgoR5JWSjpdsI0AgAKKBPrnJV1nZheamUm6QdKTkh6W9LFony2SHizWRABAEUXG6A+r8dD1J5Iei461S9Idkv7GzJ6R9BZJ95XQTgBAl5Z13iWZu39B0hfaNj8r6V1FjgsAKA8zYwEgcAR6AAgcgR4AAkegB4DAEegBIHAEegAIHIEeAAJHoAeAwBHoASBwBHoACByBHgACR6AHgMAR6AEgcAR6AAgcgR4AAkegB4DAEegBIHAEegAIHIEeAAJHoAeAwBHoASBwBHoACByBHgACR6AHgMAR6AEgcAR6AAgcgR4AAkegB4DAEegBIHAEegAIXKFAb2bjZna/mT1tZk+Z2bvNbLmZ/cDMTkR/X1xWYwEA+RXt0X9V0vfd/SpJ75T0lKTtkg65+1pJh6LXAICadB3ozexNkt4r6T5JcvffuvucpJsl7Y522y1pc9FGAgC6V6RH/1ZJs5K+aWZHzexeM7tI0mXufkaSor8vLaGdAIAuFQn0yyRdK+ked18v6TfKMUxjZlvNbNrMpmdnZws0AwCQpkigPyXplLsfjl7fr0bgf8HMLpek6O+zcW92913uPuXuUxMTEwWaAQBI03Wgd/dfSDppZuuiTTdIelLSAUlbom1bJD1YqIUAgEKWFXz/X0v6tpldIOlZSX+hxj8e/2pmt0p6XtKfFPwMAEABhQK9ux+TNBXzqxuKHBcAUB5mxgJA4Aj0ABA4Aj0ABI5ADwCBI9ADQOAI9AAQOAI9AASOQA8AgSPQA0DgCPQAEDgCPQAEjkAPAIEj0ANA4Aj0ABA4Aj0ABI5ADwCBI9ADQOAI9AAQOAI9AASOQA8AgSPQA0DgCPQAEDgCPQAEjkAPAIEj0ANA4Aj0ABA4Aj0ABI5ADwCBI9ADQOAI9AAQOAI9AASucKA3sxEzO2pm341erzGzw2Z2wsz2mtkFxZsJAOhWGT36z0p6quX1lyXd5e5rJb0k6dYSPmMg7D86ow07HtKa7d/Thh0Paf/RmbqbBADFAr2ZrZT0IUn3Rq9N0kZJ90e77Ja0uchnDIr9R2d0577HNDM3L5c0MzevO/c9RrAHULuiPfq7JX1e0qvR67dImnP3c9HrU5ImC37GQNh58LjmF84v2ja/cF47Dx6vqUUA0NB1oDezD0s66+5HWjfH7OoJ799qZtNmNj07O9ttM/rG6bn5XNsBoFeK9Og3SPqImf1c0nfUGLK5W9K4mS2L9lkp6XTcm919l7tPufvUxMREgWb0hxXjY7m2A0CvdB3o3f1Od1/p7qsl3SLpIXf/pKSHJX0s2m2LpAcLt3IAbNu0TmOjI4u2jY2OaNumdTW1CAAalnXeJbc7JH3HzL4o6aik+yr4jFrtPzqjnQeP6/TcvFaMj2nbpnXavL7xKCJpOwDUpZRA7+6PSHok+vlZSe8q47j9qJld03zw2syukaTN6ycJ7AD6ThU9+lql9bbLkJZdQ5AH0I+CCvSdettlILsGwKAJqtZNGbnsnWa3JmXRuMRsWAB9KahAX7S3nWV2a1x2TROzYQH0o6CGblaMj2kmJqhnzWXPMv7eml0T91ndjtdX/WyhqNb2vXlsVGbS3CsLfdlWAIsF1aMvmsue9Y5g8/pJPbp9Y+w04LTjJOn3Ojnt7ZubX9BLryz0ZVsBLBVUoN+8flJf+ujVmhwfk0maHB/Tlz56debeZt7ZrWXNhu33Ojlx7WvVT20FsFRQQzdSsVz2bZvWLcrakdLvCPLun6TfM3mytKNf2gpgqeACfRF5Z7eWNRu26LOFqjTH5WOr0rWpu60AkhHo2+S9IyhjNmxZdwZlap+TkKbutgJIR6CvSFIWTVl1csrK0kk6Ttq4/DhZN8BAIdBXIGmG7vRzL+qBIzOF6+SUNQM47ThJY+4m6dgX/ijzZwCoX1BZN/0iKYtmz+GTpWTXlJWlk3Yc6usD4SDQVyCpN3ze4x9r5s1YKStLJ+041NcHwsHQTQWSsmhGzGKDfbNOTtax7rQsnTxj92nH6XV9fWbeAtUxT+hl9tLU1JRPT0/X3YzSxGWsjI2O6I9/f3LRGH27sdGRTBO88hw/7ZhJx8kzyawMnTJ86mgTMAjM7Ii7T3Xab2h69L2sJZPWG566cnnHOjlJ7006frMH/C8/ej7xmHHnWkavvYzvNevMWwI90J2h6NH3S8+11Zrt30uciDQ2OlKoV97OJP1sx4cKtnipsr7XtO+iqapzAAZZ1h79UDyMrbuWTFyN+6TslRGzXG3t1BuWqsuUKet7zdI+sn2A7g1FoK+zlkxSZcrrr5qIzWrJm5nT6RyqzJQp63tNq/Evke0DFDUUgb7OnPCkXu/DT8/GVtqcTGlrnjsDKX/1zryKfq/N87l97zG9ftnrdPGFozI1Zt42f676HIBhMBQPY+usJZPW602aDRvX1uuvmoidxZo306ZMRb7X9vH9ufkFjY2O6K6PX0NQB0o2FD36onXqi8jb601q68NPz+a6M+jFuRX5Xut8btJpXWAgNEORdVOnqjNTBjUbpa7z6ccMLKBb5NH3iX6pWd9vM0/rqsGfZV1gqf/X8AXyIND3QN016+PGw5u6rXxZVF3PTbJkCpVVHRToFwT6AVGkZn1cz7lVHTNPs55P2XX3kwYqW+8ksvb6gUFBoB8gRWrWd1LHmq+dzqequvvt2u8k+n0NXyAvAn2gssyYbVX22HhVNXC66VmnfReTMW3L8/wg70pijP2jDgT6QOXpfZY9Nl5WT7zquvsm6dHtG5dsz/r8IO9KYp1WGAOqQnploDbseChxbL7qNV/L+uy048T1xKX47KKXXllIPEZcoG8/TlI7k9qXtO5A0va08wHSVJ5eaWZXSPqWpN+T9KqkXe7+VTNbLmmvpNWSfi7pT939pW4/B91J6pX2Il88rcedJ+Mn7hzS3puWXdSu011MlucheVcSS9ou0btHtYrMjD0n6XPu/jZJ10n6tJm9XdJ2SYfcfa2kQ9Fr9Fi3s1bLmDWaZ7w/bTZs6zlkeW/W5xJlzR5Oq0CaZ3tTnpnBVczuZcZwuLru0bv7GUlnop9/bWZPSZqUdLOk90W77Zb0iKQ7CrUSXcmbv1/W2HpaTzxO2h1A8xySZtK2vjfL2H3SuHw3ku6akuoPdVphTMp2DlXk+TN3IGylPIw1s9WS1ks6LOmy6B8BufsZM7u0jM9A9crKcmnNke+Uwy9lr0ffaZ3cLE+bus0uSppZ/OaxUb1h9HVLnjk0VxLLs8JY1vZVkeffqfYQmUKDrXCgN7M3SnpA0m3u/ivrcHva8r6tkrZK0qpVq4o2AyUoM3+82RPPm8OeJKn33F7VM0232UVpY/9JVTeT7qbSvpes7asizz/pvc2ePT39wVaoeqWZjaoR5L/t7vuizS+Y2eXR7y+XdDbuve6+y92n3H1qYmKiSDNQkirq9rc/K+i21nyeqp5NZdW1z7qmbR5Zn6HkWYOgfXueMfeyVjxDf+o6vdIaXffdkl5099tatu+U9L/uvsPMtkta7u6fTzsW6ZX9YRArO/aiCmZda9omXY8saxDkvZZJ+yf9AzeoVVND04s1YzdI+nNJG83sWPTng5J2SLrRzE5IujF6jQFQZ93+bpV5F5LUA65rTdu8q5O1Xqe89f6Trn3aimcYHEWybv5DjX/Y49zQ7XFRrzIqbfZSWVUw07JOOmURVVV1s5vVybK8N0meFc9Yw3ewDMUKUwhXWXchnTJZynjOkFeRu5Wy7nQG8S4PS1HrBgOvjLuQTj3gOu50itytlFnvf9Du8rAUgR5QfStexWnP2Y/L0+8krd5/nRU0qd5ZDwI9oPpWvGoXl7Mfl6efRVxPvM4ZsMy+rQ+BHqUZ5N5aWWv7xsnzvVQ9Q7XO1bNYuas+BHqUIoTeWhVj0Xm/l6pnqNa5ehYrd9WHrBuUIm/edoji8vDzfi9VzVBtti3LmrlVqWLmNbIh0KMUw95ba/bcZ+bm5fpdjzupeFnS97Jt0zqNjY4s2jY2OpJYyz5PtcuktvTqWUTSuZGTXz2GblCKfspayaOs5wpJPfekVaWSvpekZwVJFS9bq3cmnUNarZ7mil+37z2mnQePF3ou0akdVT4HQToCPUrRL1kreZT5XCFttan2mjHdrm6VpXpn3Dmk9fr/79yrpZx/1u+SnPx6MHSDUgziDMoynysk9dBba8YU+V7yVO+cXziv2/Ye61jtsszKlGnfZS9XrmKVrHgsDo6hVWbly7oqf3aqrJlW7bLMypRp7Yi7o6niexnE6qtF9aJ6JTDQyswCqeuOplNb06pddlOZMm+Fz6x3DWX0xMn8SsYYPYZW2c8V+qUeTru0apd5zj9vhc+0u4bW5wZlPSsZ9syvNPToMbT66blCtz3a1nNIkpbhk+f881T4zHPXUFZPnDz9ZPToMdT6IQukaI+2yDq0ec6/2wqfndpUVk98EDO/eoVAD9SsrBowVeepdzNXIkub0o7bXsnTTImVPMnTT0bWDVCzXqx7W4aqslryrI3bKvSMmiyyZt3QowdqNiiziuN6zNdfNaGdB4/r9r3Huu5Bp80GTnvI3OmuJ2mm7iBXWe0WPXqgZoOa/111uzvNEZCS73ry3CUMwnedhDx6YED0U/ZPU5YsoKrz1ousjZvUtj2HTw5lrj1DN0Af6Ifsn6asWUBV5613miOQllGTVnsoz/6hINADWCRrFlDRZwtZxtBb18xNyrqJO05S2/JWEw0FgR7AIll76kXy1pPuGqafe3HRGHqnNXOTjpM0Fp+0PfRce8boASySdYZpkWcLZY2hJx0nqb7PFzdf3XfPQ3qBHj2ARfL01Lt9tlDWGHra9qS29dPzkF4h0ANYpBczTIuOoTfH5bOugTuMufOtCPQAlqi615t015BlDD0uR75Vp/2LrKQ1qAj0AEpXZP3YqSuXd70G7mTG/VvH/eNq6XSqq9N+ju37X3/VhB5+erZv7iCYGQugVHXNmE2aJZtn9ask7e3vdFfR6f1lYWYsgFrUNWM27/a41a+StK9/e9veY5nf23x/6zq+vVZJoDezD5jZcTN7xsy2V/EZAPpTL2bMjo2OLNqWlguftH9Shk+S5th+3EPkvMfodbAvfYzezEYkfV3SjZJOSfqxmR1w9yfL/iwA/afqapx5s4LSqmPmDdp5evFpx7ht7zH93YEnOj4HKEsVD2PfJekZd39WkszsO5JulkSgB4ZAL1Z6ypsVlHX1q16am1947eeqM4GqGLqZlHSy5fWpaBuAIdCP1TjjtLdzfGxUF184uujnrFrfOzk+pj+7blXqOr5xqqyiWUWP3mK2LRkMM7OtkrZK0qpVqypoBoC6DMrs007t7FQTv1M2Td7snKqqaFbRoz8l6YqW1yslnW7fyd13ufuUu09NTExU0AwAKCbtuUKWO5XWu4ain1dEFYH+x5LWmtkaM7tA0i2SDlTwOQBQqaSMnbs/fo0e3b4x013L5vWTenT7Rt398WuWHKv9uFVV0Sx96Mbdz5nZX0k6KGlE0jfc/YmyPwcAqlZm3Z/2Y2WZfVsWZsYCwIBiZiwAQBKBHgCCR6AHgMAR6AEgcAR6AAhcX2TdmNmspOe6fPslkn5ZYnMGAec8HDjn4VDknK90944zTvsi0BdhZtNZ0otCwjkPB855OPTinBm6AYDAEegBIHAhBPpddTegBpzzcOCch0Pl5zzwY/QAgHQh9OgBACkGOtAPwyLkZnaFmT1sZk+Z2RNm9tlo+3Iz+4GZnYj+vrjutpbJzEbM7KiZfTd6vcbMDkfnuzcqgR0MMxs3s/vN7OnoWr97CK7x7dF/04+b2R4ze0No19nMvmFmZ83s8ZZtsdfVGr4WxbOfmtm1ZbVjYAN9yyLkN0l6u6RPmNnb621VJc5J+py7v03SdZI+HZ3ndkmH3H2tpEPR65B8VtJTLa+/LOmu6HxfknRrLa2qzlclfd/dr5L0TjXOPdhrbGaTkj4jacrd36FGSfNbFN51/idJH2jblnRdb5K0NvqzVdI9ZTViYAO9WhYhd/ffSmouQh4Udz/j7j+Jfv61GgFgUo1z3R3ttlvS5npaWD4zWynpQ5LujV6bpI2S7o92Ce183yTpvZLukyR3/627zyngaxxZJmnMzJZJulDSGQV2nd39h5JebNucdF1vlvQtb/iRpHEzu7yMdgxyoB+6RcjNbLWk9ZIOS7rM3c9IjX8MJF1aX8tKd7ekz0t6NXr9Fklz7n4ueh3atX6rpFlJ34yGq+41s4sU8DV29xlJX5H0vBoB/mVJRxT2dW5Kuq6VxbRBDvSZFiEPhZm9UdIDkm5z91/V3Z6qmNmHJZ119yOtm2N2DelaL5N0raR73H29pN8ooGGaONG49M2S1khaIekiNYYu2oV0nTup7L/zQQ70mRYhD4GZjaoR5L/t7vuizS80b+uiv8/W1b6SbZD0ETP7uRrDcRvV6OGPR7f4UnjX+pSkU+5+OHp9vxqBP9RrLEnvl/Qzd5919wVJ+yS9R2Ff56ak61pZTBvkQD8Ui5BH49P3SXrK3f+h5VcHJG2Jft4i6cFet60K7n6nu69099VqXNOH3P2Tkh6W9LFot2DOV5Lc/ReSTppZc2XoGyQ9qUCvceR5SdeZ2YXRf+PNcw72OrdIuq4HJH0qyr65TtLLzSGewtx9YP9I+qCk/5b0P5L+tu72VHSOf6jG7dtPJR2L/nxQjXHrQ5JORH8vr7utFZz7+yR9N/r5rZL+S9Izkv5N0uvrbl/J53qNpOnoOu+XdHHo11jS30t6WtLjkv5Z0utDu86S9qjxDGJBjR77rUnXVY2hm69H8ewxNTKSSmkHM2MBIHCDPHQDAMiAQA8AgSPQA0DgCPQAEDgCPQAEjkAPAIEj0ANA4Aj0ABC4/wdV5kUllrEUoAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.hist(calculate_active_user_per_pat(raw_result[-1]).values(), bins=300)\n",
    "pl.show()\n",
    "\n",
    "pl.scatter(calculate_active_user_per_pat(raw_result[-1]).keys(), \n",
    "           calculate_active_user_per_pat(raw_result[-1]).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[37, 37, 38, 31, 35, 33, 39, 34, 31, 37, 31, 33, 37, 33, 38, 38, 36, 34, 35, 36, 36, 27, 31, 33, 34, 34, 30, 30, 29, 36, 32, 27, 33, 33, 35, 30, 31, 34, 33, 30, 26, 29, 23, 31, 29, 27, 28, 25, 24, 24, 23, 21, 25, 23, 31, 25, 22, 32, 28, 23, 21, 19, 25, 22, 23, 25, 24, 22, 20, 19, 22, 20, 19, 17, 20, 21, 19, 21, 14, 18, 15, 15, 14, 18, 14, 16, 13, 14, 11, 13, 12, 13, 15, 9, 8, 11, 10, 9, 8, 0, 0]\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(calculate_distributions_of_number_of_tokens(raw_result[-1]))\n",
    "pl.hist(calculate_distributions_of_number_of_tokens(raw_result[-1]), bins=300)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis\n",
    "- It could work??\n",
    "- Vulnerability: Sybil attack\n",
    "- #Req: Introduction of REP as \"Proof-of-work\" for user actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# new policy functions with REP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Design V2 with \n",
    "partial_state_update_blocks = [\n",
    "    { \n",
    "        'policies': { \n",
    "            'users_join': users_join,\n",
    "            'claim_pats': claim_pat_with_opats,\n",
    "            'prove_claim': prove_claim,\n",
    "            'create_new_pats': create_new_pats\n",
    "        },\n",
    "        'variables': { \n",
    "            USERS: update_users,\n",
    "            PATS: update_pats,\n",
    "            CLAIMS: update_claims, \n",
    "        }\n",
    "    },\n",
    "    { \n",
    "        'policies': { \n",
    "            'propose_opats': propose_opats,\n",
    "            'challenge_opats': challenge_opats,\n",
    "            'vote_on_opats': vote_on_opats,\n",
    "        },\n",
    "        'variables': { \n",
    "            'proposals': update_proposals,\n",
    "            'challenges': update_challenges,\n",
    "            OPATS: update_opats,\n",
    "            'failed_proposals': update_failed_proposals,\n",
    "            'failed_challenges': update_failed_challenges,\n",
    "        }\n",
    "    },\n",
    "]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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