Part 3 - A slightly More Complex Agent Based Model.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: A Slightly More Complex Agent Based Model \n",
    "\n",
    "##### Authors: Bill Thompson (biltho@mpi.nl) and Limor Raviv (limor.raviv@mpi.nl) \n",
    "Please let us know if you have any comments, suggestions or questions regarding this notebook. \n",
    "\n",
    "---------------\n",
    "\n",
    "## Summary\n",
    "In this third tutorial, we will build a more complex simulation of agents using the commands in the second notebook, making our agents and their interactions a bit more ecologically valid. \n",
    "\n",
    "The major differences between these models are:\n",
    "1. Instead of having agents with simple binary representaions (either [a] or [i]), agents in this model will have a continuous distribution around their prefered vowel.\n",
    "2. The interactions in this model will be double-sided, so that both agents change their behavior after interacting.\n",
    "3. Agents' personalities will be less rigid, allowing for more interesting changes during interaction: stubborn agents will align a little bit (instead of not at all), while flexible agents will align to a greater extent (but not fully).\n",
    "\n",
    "We will make multiple simulations of interactions under different conditions, and see how this affects the distribution of vowels in the population. \n",
    "\n",
    "\n",
    "-------------- \n",
    "\n",
    "\n",
    "### 1. Setting up the network\n",
    "First, let's create lists containing the possible biases for our agents. In this more complex model, agents have a range of possible vowels they can produce, which is distributed normally around a mean value on a single dimension. In this example, a mean of \"-1\" will correspond to [a] and a mean of \"1\" will corresponf to [i]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the model Parameters\n",
    "\n",
    "vowel_means = [-1., 1.] # set possible inital means for the distributions\n",
    "\n",
    "personalities = ['F', 'S']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function that makes a single agent\n",
    "\n",
    "def make_agent(vowel_mean, personality):\n",
    "    return [vowel_mean, personality]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[-1.0, 'F'],\n",
       " [1.0, 'F'],\n",
       " [-1.0, 'S'],\n",
       " [1.0, 'S'],\n",
       " [1.0, 'F'],\n",
       " [-1.0, 'F'],\n",
       " [1.0, 'F'],\n",
       " [-1.0, 'S']]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a function that makes a population of random agents\n",
    "\n",
    "import random\n",
    "\n",
    "def make_population(N):\n",
    "    \n",
    "    population = []\n",
    "    \n",
    "    for i in range(N):\n",
    "        \n",
    "        m = random.randint(0,1)\n",
    "        \n",
    "        p = random.randint(0,1)\n",
    "        \n",
    "        agent = make_agent(vowel_means[m], personalities[p])\n",
    "        \n",
    "        population.append(agent)\n",
    "\n",
    "    return population\n",
    "\n",
    "\n",
    "# Check that this works by making a population of 8 agents\n",
    "make_population(8)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Introducing more complex interactions\n",
    "So far, this looked similar to our simple model, but now it's time to introduce some new features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because we want our agents to have more complex representations, we also need to write a function that selects a specific vowel from the distribution implied by the agent's mean,  for each interaction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(\"The agent's mean was\", 1.0)\n",
      "(\"The agent's chosen utterance is\", 0.8438989287675807)\n"
     ]
    }
   ],
   "source": [
    "# Create a function that chooses a variant from a distribution centered around the agent's mean vowel\n",
    "\n",
    "from copy import deepcopy \n",
    "from numpy.random import normal\n",
    "import numpy\n",
    "\n",
    "def choose_utterance(agent):   # sample from a normal distribution with SD=0.25 and mean of the teacher\n",
    "    agent_utterance=normal(agent[0],.25)\n",
    "    return agent_utterance\n",
    "\n",
    "# Let's check that this works\n",
    "# You can run this multiple times to see different chosen utterances for different agents\n",
    "\n",
    "pop=make_population(4)\n",
    "vowel = choose_utterance(pop[0])\n",
    "print(\"The agent's mean was\", pop[0][0])\n",
    "print(\"The agent's chosen utterance is\", vowel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this new model, being flexible means that the agent shifts their vowel towards the other agents' utterance (by half of the distance between the mean and the utterance). This just means flexible agents adapt by going half way towards the other agent. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition, stubborn agents are not completey stubborn and are only adapting by a little bit (by 1/10 of the distance between their mean and the other agent's utterance)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to write this function that changes the agents means according to their biased personalities, using simple conditions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.8, 'S']\n",
      "[0.0, 'F']\n"
     ]
    }
   ],
   "source": [
    "# Create a function that shifts the means of a flexible agent\n",
    "\n",
    "def learn(utterance,agent):\n",
    "    if agent[1] == \"F\":\n",
    "        new_mean = (agent[0] + utterance) / 2.\n",
    "    else:\n",
    "        difference = abs(utterance-agent[0])\n",
    "        if utterance > agent[0]:\n",
    "            new_mean = agent[0] + (difference/10.)\n",
    "        else:\n",
    "            new_mean = agent[0] - (difference/10.)\n",
    "    agent[0] = deepcopy(new_mean)\n",
    "\n",
    "\n",
    "# Check that this works\n",
    "\n",
    "# Create two agents with a mean of 1\n",
    "stb_agent = [-1,'S']\n",
    "flex_agent = [-1,'F']\n",
    "\n",
    "# See what happens when each agent learns from an untterance of -1 (the other vowel)\n",
    "learn(1,stb_agent)\n",
    "learn(1,flex_agent)\n",
    "\n",
    "print(stb_agent)\n",
    "print(flex_agent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we want both agents to update their representations after an interaction. This means that instead of having single-sided interactions with a listener and a producer, we now have an exchange of productions between the two agents in which each can learn from each other... "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this, we'll write a new function that updates both agents based on their current utterances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function in which both agents generate utterances and can learn from each other \n",
    "\n",
    "def interact(agent1,agent2): \n",
    "    \n",
    "    agent1_utterance = choose_utterance(agent1)\n",
    "    agent2_utterance = choose_utterance(agent2)\n",
    "    \n",
    "    if agent1[0] == agent2[0]:\n",
    "        pass # do nothing if the two agents have the same distributions \n",
    "    else:\n",
    "        learn(agent2_utterance,agent1)\n",
    "        learn(agent1_utterance, agent2)\n",
    "    #return agent1_utterance, agent2_utterance, agent1, agent2\n",
    "        \n",
    "\n",
    "# Check if it works by uncommenting the \"return\" comment above \n",
    "\n",
    "interact([-1,'F'],[1,'S'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Simulation time!\n",
    "Great! Now we have a double-sided interaction, and we can write a function that chooses random pairs from a populations, and then simulate multiple interactions between different agents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function that chooses two agents from a population\n",
    "from numpy.random import choice\n",
    "\n",
    "def choose_pair(population):\n",
    "    i = random.randint(0, len(population) - 1) # phyton counts from 0, so pop(8) is an error\n",
    "    j = random.randint(0, len(population) - 1)\n",
    "    \n",
    "    while i == j:\n",
    "        j = random.randint(0, len(population) - 1)\n",
    "        \n",
    "    return population[i], population[j]\n",
    "\n",
    "# Create a function that simulates k interactions in a population of n agents\n",
    "\n",
    "def simulate(n, k):\n",
    "    \n",
    "    initial_population = make_population(n)\n",
    "    population=deepcopy(initial_population)\n",
    "    \n",
    "    for i in range(k):\n",
    "        \n",
    "        agent1, agent2 = choose_pair(population)\n",
    "        \n",
    "        interact(agent1, agent2)\n",
    "    \n",
    "    return initial_population, population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test that our simulation is working by looking at the results. Feel free to change the number of agents and the number of interactions as you please."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('The initial population was', [[-1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'S'], [-1.0, 'F'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [1.0, 'S'], [1.0, 'S'], [1.0, 'F'], [1.0, 'F'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'S']])\n",
      "('The new population is', [[-0.20147229130122885, 'S'], [0.10282243371341192, 'S'], [0.09152519360458244, 'F'], [-0.10843255148833716, 'S'], [-0.04183043955234085, 'S'], [-0.041999523802291425, 'S'], [-0.16613924664284296, 'S'], [0.15939237875670692, 'F'], [-0.05790861011813099, 'F'], [-0.032051980894530166, 'F'], [-0.21454940397801495, 'F'], [0.13640654877246153, 'S'], [0.14290580723644208, 'F'], [0.18454169077445814, 'S'], [-0.046628109441645194, 'F'], [-0.05949678841306871, 'S'], [0.23596500937077494, 'S'], [0.01996936048110598, 'F'], [0.08600221926296601, 'S'], [-0.13985719361470955, 'F'], [-0.1084029771832889, 'F'], [0.17310651291219442, 'S'], [0.009169346634491756, 'S'], [0.018634807416409313, 'F'], [0.017263702453273355, 'F'], [-0.037230574561736104, 'F'], [-0.22973911492166776, 'F'], [-0.15344800868666789, 'S'], [-0.21298489758600378, 'S'], [-0.20819015029134513, 'F'], [-0.0658405937317518, 'F'], [-0.05439436272806135, 'F'], [-0.37222674771969694, 'F'], 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     ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    },
    {
     "data": {
      "image/png": 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q06f/RX8WAPg5XPoHAAtc7COl/v739xUX11GTJz+jO+8coLZt2yo3N9fyfpo3b6GTJ09I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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa498fa6950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run a simulation with 200 agents and 2000 interactions\n",
    "\n",
    "initial_population, new_population = simulate(200,2000)\n",
    "\n",
    "print(\"The initial population was\", initial_population)\n",
    "print(\"The new population is\", new_population)\n",
    "\n",
    "# Plot the agents' initial and final means\n",
    "\n",
    "%matplotlib inline \n",
    "# put plot in the notebook\n",
    "import matplotlib.pyplot as plt # importing a plotting library\n",
    "import seaborn as sns # make the plot look better\n",
    "\n",
    "initial_means = []\n",
    "final_means = []\n",
    "\n",
    "for agent in range(len(initial_population)):\n",
    "    initial_means.append(initial_population[agent][0])\n",
    "    final_means.append(new_population[agent][0])\n",
    "    \n",
    "plt.hist(initial_means, label='initial means')\n",
    "plt.hist(final_means, label='final means')\n",
    "plt.legend(loc='upper center')\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above, the clustering of orange agents (final population) shows convergence, while the spread distribution (blue, initial population) implies divergence.\n",
    "\n",
    "In most simulations, you'll see convergence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But since as you've seen, each simulation yields different outcomes in terms of which variant agents have converged on, we need to run multiple simulations and compute their mean to get a more reliable picture of what's happening. So let's make a function that computes the final means of several simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function to compute the means of the vowels in the population\n",
    "\n",
    "def compute_mean(population):\n",
    "    t=0.\n",
    "    for agent in population:\n",
    "        t += agent[0]\n",
    "    return t/len(population)\n",
    "\n",
    "# Create a function that runs multiuple simulations and returns the final mean of each of them\n",
    "\n",
    "def batch_simulate(n,k,s): #n=pop size, k=no. of interactions, s=no. of simulations\n",
    "    batch_final=[]\n",
    "    for i in range(s):\n",
    "        initial_population, new_population = simulate(n, k)\n",
    "        new_proportion=compute_mean(new_population)\n",
    "        batch_final.append(new_proportion)\n",
    "    return batch_final\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what's going on? Let's run some simulations! This might take a few minutes to complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fa4989d1750>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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a1qvh7QgAUKUY/n7aH3/8ocsvv7zcetOmTXXkyBFTQgEAAABWMFx+r7jiCq1a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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4a7c5fd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run 500 simulations\n",
    "results = batch_simulate(200,2000,500)\n",
    "\n",
    "# Plot the result\n",
    "\n",
    "plt.hist(results, edgecolor = 'white')\n",
    "plt.xlabel('Final Population Mean Vowel')\n",
    "plt.ylabel('Number of Simulations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "What you can see in the histogram above is that there is a nice normal distribution around 0. That is, **in most simulations, the population converges on the mean between the two initial variants**. This result is exactly what we expect given prior studies with similar models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So let's probe this model a bit more by looking at effect of stubborn agents in the population. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we did in the second tutorial, we will see if the number of stubborn agents affects the trend of convergence towards the mean. Since we changed the agents learn in this model, the result might be different this time. Specifically, stubborn agents in the new model are not longer rigid and can align to a new utterance, just to a lesser degree than flexible agents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So let's rewrite the functions defined above so that they created biased populations where we control the number of stubborn agents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modify the function to make populations of N agents with a given number of stubborn agents (st)\n",
    "\n",
    "def make_population_biased(N,st):\n",
    "    \n",
    "    population = []\n",
    "    \n",
    "    for i in range(st):\n",
    "        \n",
    "        m = random.randint(0,1)\n",
    "        \n",
    "        agent = make_agent(vowel_means[m], personalities[1])\n",
    "        \n",
    "        population.append(agent)\n",
    "    \n",
    "    for i in range(N-st):\n",
    "        \n",
    "        m = random.randint(0,1)\n",
    "        \n",
    "        agent = make_agent(vowel_means[m], personalities[0])\n",
    "        \n",
    "        population.append(agent)\n",
    "\n",
    "    return population\n",
    "\n",
    "\n",
    "\n",
    "# Modify the function so that it calls our biased population \n",
    "\n",
    "def simulate_biased(n, k, st):  #st=no. of stubborn\n",
    "    \n",
    "    initial_population = make_population_biased(n,st)\n",
    "    population=deepcopy(initial_population)\n",
    "    \n",
    "    for i in range(k):\n",
    "        \n",
    "        agent1, agent2 = choose_pair(population)\n",
    "        \n",
    "        interact(agent1, agent2)\n",
    "        \n",
    "    return initial_population, population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that our changes work by simulating one population first. You can change the number of stubborn agents to see how it affects the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('The initial population was', [[-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [1.0, 'S'], [1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'S'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [-1.0, 'F'], [1.0, 'F'], [-1.0, 'F']])\n",
      "('The new population is', [[-0.006545377888789769, 'S'], [0.10900363231614411, 'S'], [0.13952795358856931, 'S'], [0.19640453839701666, 'S'], [-0.21389640248833236, 'S'], [-0.31048066640825817, 'S'], [0.27403755893385334, 'S'], [-0.06516929144611568, 'S'], [0.0996245326165808, 'S'], [0.11823250198857341, 'S'], [-0.2738248340436836, 'S'], [0.2473155619123017, 'S'], [0.33814468299850753, 'S'], [0.11431218978819682, 'S'], [0.28352480686003007, 'S'], [-0.04587802516840195, 'S'], [0.2754859988143461, 'S'], [-0.10003465822482713, 'S'], [0.23571326496439624, 'S'], [-0.17729231018778943, 'S'], [-0.07227727971392271, 'S'], [0.062233782963169754, 'S'], [-0.1388092245959362, 'S'], [0.0697984903411091, 'S'], [0.031748134629156634, 'S'], [0.1312387152431399, 'S'], [-0.1624425214783483, 'S'], [0.06975869338279364, 'S'], [0.057640568038986595, 'S'], [-0.021426845211426054, 'S'], [-0.13970373906938283, 'S'], [-0.043943290230383236, 'S'], [-0.00026090851885109297, 'S'], [0.32220050162040126, 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     ]
    },
    {
     "data": {
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BFQAAAEYiqAIAAMBIBFUAAAAYiaAKAAAAIxFUAQAAYCSCKgAAAIxEUAUAAICR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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa498993e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulate a population with 50 stubborn agents\n",
    "old_pop, new_pop =simulate_biased(200,2000,50)\n",
    "\n",
    "print(\"The initial population was\", old_pop)\n",
    "print(\"The new population is\", new_pop)\n",
    "\n",
    "# Plot the agents' initial and final means\n",
    "\n",
    "initial_means = []\n",
    "final_means = []\n",
    "\n",
    "for agent in range(len(old_pop)):\n",
    "    initial_means.append(old_pop[agent][0])\n",
    "    final_means.append(new_pop[agent][0])\n",
    "    \n",
    "plt.hist(initial_means, label='initial means')\n",
    "plt.hist(final_means, label='final means')\n",
    "plt.legend(loc='upper center')\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because we want to look at the degree of convergence and how it is affected by stubborn agents, we need a measure to capture variance, like the standard deviation (SD). For now, we will write a function that stores the SDs of the final means in multiple simulations. This will give us an idea of how diverged the population was after interacting. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a function to compute the means of the vowels in the population\n",
    "\n",
    "def compute_SD(population):\n",
    "    pop_means=[]\n",
    "    for agent in population:\n",
    "        pop_means.append(deepcopy(agent[0]))\n",
    "    pop_SD= numpy.std(pop_means)\n",
    "    return pop_SD\n",
    "\n",
    "# Rewrite the batch simulation function so that it runs s simulations for each possible proportion of stubborn agents (possible_sts)\n",
    "\n",
    "def batch_simulate_biased(n,k,s): #n-pop size, k=no. of interactions, s=no. of simulations for each bias\n",
    "    \n",
    "    all_results=[]\n",
    "    \n",
    "    possible_sts = [0, int(n / 10.), int(n / 4.), int(n / 2.), int(3*n / 4.), n]\n",
    "    # This time, we'll test 0%, 10%, 25%, 50%, 75% and 100% stubborn agents\n",
    "    \n",
    "    for st in possible_sts:\n",
    "        \n",
    "        print(st)\n",
    "    \n",
    "        current_results = []  # print the progress of the simulations \n",
    "    \n",
    "        for i in range(s):\n",
    "            initial_population, new_population = simulate_biased(n, k, st)\n",
    "            sd = compute_SD(new_population)\n",
    "            current_results.append(sd)\n",
    "        \n",
    "        all_results.append([st,current_results])\n",
    "    \n",
    "    return all_results\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's run a few simulations with different proportions of stubborn agents, and see what happens:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "20\n",
      "50\n",
      "100\n",
      "150\n",
      "200\n"
     ]
    }
   ],
   "source": [
    "# Run 50 simulations of each stubborness proportions in a community of 200 agents \n",
    "results = batch_simulate_biased(200,2000,50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+wuHDBxkyZAQADRs2oXPnLgBMmOBBp05tCA7+nUKFLLhwIZQdO/Zj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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa49893b850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results of the simulations \n",
    "        \n",
    "plt.hist(results[0][1], label='no stubborn agents',edgecolor = 'white')\n",
    "plt.hist(results[1][1], label='20 stubborn agents',edgecolor = 'white')\n",
    "plt.hist(results[2][1], label='50 stubborn agents',edgecolor = 'white')\n",
    "plt.hist(results[3][1], label='100 stubborn agents',edgecolor = 'white')\n",
    "plt.hist(results[4][1], label='150 stubborn agents',edgecolor = 'white')\n",
    "plt.hist(results[5][1], label='200 stubborn agents',edgecolor = 'white')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('SD of Final Vowel Distribution in the Population ')\n",
    "plt.ylabel('Number of Simulations')     \n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, there seems to be no relationship between the degree of variance and the number of stubborn agents in the population, suggesting that all populations converged similarly regardless of how stubborn agents were. Looking at the relatively low SDs, this is presumably because in this new model, 2000 interactions were enough to allow the entire population to converge even if stubborn agents did so slower."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So let's do something more interesting. Let's look at how convergence varies with **population size**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this, we'll rewrite the function so that it simulates different sizes of populations (n) instead of different proportions of stubborn agents. We'll choose n= 10, 150, 250, 350, 450, 550 and 650. (Feel free to change this as you please)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rewrite the batch simulation function so that it runs s simulations for each possible population size (possible_size)\n",
    "\n",
    "def batch_simulate_size(k,s): # k=no. of interactions, s=no. of simulations for each bias\n",
    "    \n",
    "    all_results=[]\n",
    "    \n",
    "    possible_size = [50, 150, 250, 350, 450, 550, 650]\n",
    "        \n",
    "    for n in possible_size:\n",
    "        \n",
    "        print(n)\n",
    "    \n",
    "        current_results = []  # print the progress of the simulations \n",
    "    \n",
    "        for i in range(s):\n",
    "            initial_population, new_population = simulate(n, k)\n",
    "            sd = compute_SD(new_population)\n",
    "            current_results.append(sd)\n",
    "        \n",
    "        all_results.append([n,current_results])\n",
    "    \n",
    "    return all_results\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run some simulations with different population sizes: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "150\n",
      "250\n",
      "350\n",
      "450\n",
      "550\n",
      "650\n"
     ]
    }
   ],
   "source": [
    "# Run 50 simulations of each population size\n",
    "results = batch_simulate_size(2000,50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h1qxpVKhQgTZt2gFw82YUI0aMoX37jup2Zco8e+TslSuX8Pefi4/PdKpXr8Gy\nZYuZN282ixYtK/qdK6Rp0yYxZMgwSW6FEEIIIQojMeERt2IflnQY+bp/P4kaNWoyYcIUDAwMsLKy\npn79hly4cO5vyW00/ft/hKmpWZ72e/fuolWrtrz/fnsAZsyYQ8+enUhIuI2lZaVi3ZeXyynpAF5K\nklshhBBCiEIoX96c2bPnq5cvXDjH+fN/MnHiVACePEklMfEuNjZ2+ba/fPlirieKVahQkYoVLbl8\n+WK+ye2FC+dYs+ZLwsKuoVAocHWtx9SpMzEzKw/AqVMnWblyOfHxcbi61sPa2oYnT54wbZovAPv3\n72Hr1k08eJCMo6MTXl4T1Y/n7dWrM/37f8T333/LjRth2NnZMXXqTN55x4ExYz4lIeE2CxbM4c8/\nzzBtmi9r167k0KEDPH78CCcnF7y9J2NvX7VoDuxrkgvKhBBCCCGKSM+enRg9+hNcXGrTokUrAKKj\no1AoFISEBNG9ewcGD+7Pd98dVLdJSkrC3NwiVz+mpmbcvXs3T/+pqY/x8RlPo0aN2bJlN8uWrSQ+\nPo7NmzcCz+b+TpkygTZt2rFhwzYcHZ3Zu3eXuv3x48fYuDEQb+9JbNy4jTp16jJu3EgeP36sXic4\neB0eHp5s2rQdQ0Mjli//HIB58xZjYVGBceMm4OU1kV9++YkDB/Yxb94iNm/eSfny5ixYMKfIjuXr\nkuRWCCGEEKKIzJu3GH//pYSFXWfFiqXAsykJCoUCe3t7Pv/8Czp16sLixfP53/9+BiA9/Sk6Ojq5\n+tHV1SUjQ5Wn//T0dDw9hzJ48FAsLS3VSXRUVAQABw9+jZOTMx4entjY2PLxx5/i7Oyibv/VV5vx\n8PCkSZPmWFlZ8/HHn1KhQkV++OGQep0PP+xE8+buWFvb0LfvQK5duwKAsbExSqWSMmUMKVPGkDt3\nbqOjo4uFRQUqV7Zi/PhJjBkzvkiP5+uQaQlCCCGEEEWkZk0HAMaO9WbOnJmMGjWO9u070rx5C8qW\nLQtA1arViY2NYd++Pbi5tfz/RDYjVz8qlQp9ff08/ZuZleeDDzqwY8dWbtwIIzo6ivDwMGrXdgUg\nIiIcR0fnXG2cnGrx6FEK8OzCttWrV7BmzZfq+owMFXFxsepla2sb9WtDQ0MyMzPz3dc2bdqxd+8u\nevfugrNzLdzcWtKxY5dXPlZviiS3QgghhBCFkJx8n0uXLuDm1lJdVqVKVTIzM3jyJBVjYxN1Yvuc\nnZ09Z88f1Y2aAAAgAElEQVT+AYC5uQVJSfdy1d+/n0T58uZ5tnXvXiIff+yBg4MjDRu+S+fO3fjt\nt+NcuXIJAKVSSU7OPy/6+ms5MzOLceMmUq9eg1xrGBoaqV9ra79aemhmVp6tW3dz6tRJfvvtONu3\nb+bgwf0EB29FT0/vlfp4E2RaghBCCCFEIdy6dYvp031yJajXrl2hXDlTjI1NCApai5fXyFxtwsKu\nY2tbBQBn51pcuHBeXXfnTgKJiXdxdq6VZ1u//PITJiYm+Psvo2fPvtSu7Up8fJw6obW3r8r161dz\ntbl+/Zr6ta2tHXfv3sHKylr9LyQkiMuXL77i3irUr06cOM6BA/to0qQZEyZMZsOGbcTE3CQyMvwV\n+3oz5MytEEIIITSehWXZl69UQttydHSiZk1H5s+fw5gx47l9O57VqwMYNGgIAM2aubFly0a2b9+C\nm1tLTp06SWjoIQIC1gLQtWtPxo4djrOzCw4OTqxYsYSmTd3yvVOCiYkJd+4kcObMaSpVqsyPPx7m\n2LGf1FMROnfuzvbtW9m6NQR39/f46acjnD//J1ZW1gD06TOARYvmYm1tg4tLbb7+ei8//XSUQYM+\nfqV9NTDQJybmJikpKWRn57By5ReYmZnzzjs1OXz4e/T1DV54V4jiIsmtEEIIITRaZmY27u3eKVQf\nSqUWxsYGpKSkkZX18oczFOQJZVpaWixcuIRlyxYxfPgQDAwM6NWrLz169AHAwcEJPz9/AgPXEBi4\nBkvLysyaNQ8np2cXerm41GLSpKkEBq7h0aNHNGrUGB+f6fluq1Wrtpw/f44ZM6agUICDgzOjR48n\nKGgtmZmZWFpaMneuPwEBSwkKWkfDho1wc2upvmCtdeu2PHhwn8DAtSQnJ2FvX5VFi5apk9+/n5nN\nT7duvVi9OoDY2BjmzvVn6NDhBAQs5f79JOzsquDvvxQjI6N/7eNNU+TknZhR6iQnpxb4MXrizdPW\n1sLU1LDEx0dbW4tFfwQQcf8mANXM7PBpMOatfs9oytiIvPIbG21tLfaEnMlzg/vKNib0GFRfxrAY\nyWdHc70tYxMZGUFWViY1atRUl/n4eOHo6Iyn57ASjOzFno9NUZE5t0IIIYQQpcStW3F4eY3k9Onf\nSUhI4MCB/Zw5c5oWLd4r6dCKjUxLEEIIIYQoJZo3b0HfvgNZuNCPBw+SsbW1Y86cheonkL0NJLkV\nQghRKmhr5/0ysjR//SzEi3h4eOZ6nO/bRpJbIYQQ/3na2lo8jD9I2uMEdZmBkSUmVh0lwRXiLSPJ\nrRBCiFIh7XECT1LicpWZlFAsQoiSIxeUCSGEEEKIUkOSWyGEEEIIUWpIciuEEEIIIUoNSW6FEEII\nIUSpIReUCSGEEELj5Xert4JQKrVy/XyZwtxlY9KkcZiamjFtmq+6bMoUb3799X8oFApycnJQKBT4\n+y+lSZPmAOzcuY2vvtrCkyepvPdeG8aP90FPT++1Y3hTzp79A3Nzc2xtq5R0KC8kya0QQgghNFp+\nt3p7HfGvuF5hbiN35MgPnDz5G+3bd8xVHh0dja/vXOrXb6guK1vWGICffz7Khg2BzJzph6mpGfPm\n+bJ69Qq8vCYVePtv2rhxIwgIWCvJrRBCCCFEYeR3q7c36XVuI5eSksKqVStwdHTOVZ6RkcHt2/E4\nODhhamqWp93u3Tvo06c/TZo0A2DSpGl4e49mxIixGnn2VtNJciuEEEIIUQRWrlzOBx904N69xFzl\nMTE30dLSolKlynnaZGdnc/XqZYYM+URd5uxci4yMDMLDb+Ds7JKnzfHjvxAcvI7o6Gh0dXVp3Lgp\nU6bMQF9fH4DQ0O8IClrL/ftJNG/egpycHOzsquDpOQyAjRsD2b9/D0+fPsXVtS7jx/tQsaIlAG5u\nDZkxYw5btmwkLi4WR0dnZsyYg6VlJXr16gzA2LHD8fQchoeHJ0uWLOR///uZ9HQV9es3YOLEqZib\nWxTNAX1NckGZEEIIIUQhnTlzmvPnzzF48NA8ddHRURgaGuLnN5MuXT5g2LBBnDz5GwCPHz9CpVLl\nSgiVSiUmJuVITLyTp6/4+DhmzJhC9+692bZtD35+Czlz5jTffLMXgPPnz7FwoR8DBw4mKGgL+voG\n/PjjYXX73bu3c+TID8yePZ916zZialqeCRPGkJWVpV4nOHgd48f7EBS0hYcPH7B+/SoA1q/fBMC8\neYvo18+DPXt2cP78nyxbtoqgoM2kpaURELC0CI5m4UhyK4QQQghRCCqVis8/X8CECZPR1dXNUx8T\nE016ejqNGzdl6dIvadKkGZMnj+f69Ws8ffoUIE87HR0dVKqMPH3l5OQwfrwPHTt2wdLSkoYN36V+\n/YZERUUCsH//blq3fp9Onbpia2vHxIlTsLCooG6/bdtmRo4cR506ddX1Dx8+5PffT6jX6dt3AHXr\n1sfevipdu/bg6tUrAJQrVw54NldYX1+fhIQE9PT0qFjREltbO6ZN82XgwMGFO5hFQKYlCCGEEEIU\nQnDwOhwcnGjY8N186z09h9GrVz+MjIwAqFatOtevX+Wbb/YybNhI4FmC/HcZGRnqaQZ/Z21tg46O\nDps2BRMZGUFUVCTR0ZG0a/chABERN+jSpYd6faVSiYODIwBpaWkkJt7F13cqoFCvo1KlExcXo162\nsrJRvzY0NCIzMzPf/ercuRtHj4bSpUs76tatj7t7S9q37/TC41RcJLkVQgghhCiEo0cPk5ycRNu2\n7gBkZDxLVH/++UdCQ38BUCe2z9nZ2RMdHYWJiQm6urrcv5+Era0dAFlZWTx8+IDy5c3zbOvGjTBG\njRqGm5s7rq716Nt3IDt3blPXK5VKICdXm5z/X3w+9cDPzx8bG9tc6xgb/3UJnY6OTr7t/8neviq7\ndn3DiRPH+e2346xdu4ojR0L58st1+TcoJpLcCiGEEEIUwpdfrs11dnP16hWAgpEjxwIwf/5stLS0\nmDJlhnqd8PAwqlevgUKhwNHRmQsXzuHqWg+AS5cuoKOjQ/XqNfJsKzT0O1xd6zFjhp+6LDY2Bnv7\nqgDY21fj+vVr6rrs7Gxu3AijRo13MDIywtTUjKSkezRu3BSAzMxMfH2n0r//oHwvXvs333//LTo6\nurRu3ZaWLVtz+fIlRowYQnJyMqampgXqqyhJciuEEEIIjWdgZKmx23p+p4HnypQxBKByZSsAmjdv\nwaxZ03B1rUetWnUIDf2OixfPM3nyZwB069aTxYsXYG9fFXNzC5YsWUjnzt3yvQ2YsbEJERE3uHr1\nMoaGRnz99V6uXbuClZU1AN2792bs2OHUru1K7dqu7Nmzgzt3bqNQPJuG0KdPf9atW0m5cqbY2tqx\ncWMgly5dwM6uyivtq76+AZGREdSo8Q6pqY/ZtCmYcuXKUalSZUJDD2FhUUE9N7ekSHIrhBBCCI2W\nmZmNiVXH17r37HNKpRbGxgakpKSRlfXyhzMU5gll/+Tu3hJv78mEhARx9+4d7O2rsWRJgDopbt36\nfRISbrN48QIyMjJo2bI1I0aMzbevXr36Eh5+nfHjR6Grq0edOnXx9BzG0aOhALi41MLb24cNG9aT\nkvKQ995rg7NzLbS1n6V8/fp5kJaWxuLF80lNTcXBwZElS75UT5t4ngS/SM+efVi16gtu3Ypn9Ggv\nEhMTmTvXl5SUhzg4OLFw4dKX9vGmKXJyXjSTovRITk4t0jepKBra2lqYmhqW+Phoa2ux6I8AIu7f\nBKCamR0+Dca81e8ZTRkbkVd+Y6OtrcWekDPcin2Ya93KNib0GFT/rRhDbW0tEq4H5rrJfxljayxr\nDi3W/ZfPjuZ6W8bm+Rnd5/N3ATw8etO//0d5npqmKZ6PTVGRW4EJIYQQQpQSly5dxMfHi0uXLnDr\nVjybNgWTmHhXPcf2bSDTEoQQQgghSonu3XuRkHCL6dN9SE19TI0a7/D55wH5Pva3tJLkVgghhBCi\nlFAqlYwZ482YMd4lHUqJkWkJQgghhBCi1JDkVgghhBBClBqS3AohhBBCiFJDklshhBBCCFFqaFRy\nq1Kp6NSpE6dPn1aXxcXF4enpSd26denYsSO//vprCUYohBBCCCE0mcYktyqVCm9vb8LDw3OVjxo1\nigoVKrBnzx46d+7M6NGjSUhIKKEohRBCCCGEJtOIW4FFREQwYcKEPOUnTpwgNjaWnTt3oqenxyef\nfMKJEyfYvXs3o0ePLoFIhRBCCFEStLULdz5OqdTK9fNlCvoUs2PHfmb69EkoFApycnJQKBS0aNEK\nP7+FAEyZ4s2vv/4vV72//1KaNGkOwM6d2/jqqy08eZLKe++1Yfx4H/T09AoUQ3E4e/YPzM3NsbWt\nUtKhvJBGJLenTp2iSZMmeHl5UadOHXX5hQsXcHZ2zjW49evX59y5cyURphBCCCFKgLa2FvtjErn1\n+GmxbK+ykT5dbS0KlOBGR0fSvLk7Pj6fATkA6Orq/q0+Gl/fudSv31BdVrasMQA//3yUDRsCmTnT\nD1NTM+bN82X16hV4eU0qmh0qQuPGjSAgYK0kty/Tr1+/fMsTExOpUKFCrrLy5ctz586d4ghLCCGE\nEBri1uOnRD98UtJhvNDNm1HY21fD1NQ0T11GRga3b8fj4OCU75PCdu/eQZ8+/WnSpBkAkyZNw9t7\nNCNGjNXIs7eaTiOS2xdJS0vL9VcPPPsrSKVSFaifV/0KQhSvl31FVBTjlpX18r+689vO2/6eKejX\nd/9s93evMgbi1eU3Ni8aJy0tBTo6yhfWl6axKejvkTf1Xn3dz05htlUQmj7mLxqXkvidXNBtRkdH\n8e67TfKdPhEdHYOWlhY2NtZ5+s3Ozubq1SsMGzZc3bZOnTpkZGQSFRWOi0utPP0dO/YLgYFruXkz\nCl1dXZo0aca0aTPQ1zcA4PvvDxEYuIakpCTc3FoCOdjZVeHjjz8BIDh4Pfv27ebp06e4utZj4sTJ\nVKxoCUCTJvXx9fVj8+aNxMbG4OTkjK+vH5UqVaZbt44AjB07nI8//oRBg4awaNECjh37CZVKRf36\nDfHxmYaFhUWBjl1Rj69GJ7d6eno8fPgwV5lKpUJfX79A/RgbGxRlWKKIvWh8lm8/S0zCo3zrGjpV\n5M79Jy+sB7C1LItX33pFGtPbpqDH4cYXX/IkJka9XMbWlhrjZH78m/AqY2NmYcjRg1dJzOdzYmFZ\nli59676J0EpMfD5lLzpO0Zd2kPb4r4uTDYwsqeLSp8hiKY7fIRvOR+f7NX1tC2Pupany1FU20sez\nTpU3Hldh/PP3fmF+jxdWQccwNjaGs2dPsWlTMNnZ2XzwwQeMGzcObW1tEhNvYWRkxIIFs/n999+p\nVKkSY8aMwd3dnQcPHqBSpVOtmi2mpobq/kxNy/HkycNcZc+2E8v06T7MmjWLpk2bEh0dzcSJE/nh\nh4MMHjyYP/74g/nz5zBz5kwaNGhAcHAwu3fvZtSoUZiaGrJ582aOHg1l+fLllC9fnuDgYLy9x3Dg\nwAGUSiUAGzasZ+7cuZiZmTF27Fg2bFjH4sWL2bt3D02bNiUgIIBmzZqxY8cOLl48R0hICHp6esya\nNYvVq79g2bJlhR+AQtDo5LZixYp57p5w7969Av9FkJKSpvF/rb6NlEotjI0N8h0fpVKLmIRH3Ih9\nkG9bm4plib3z4vrnXmXs8/uL8W1/z/zb2PxbmycxMTwOj8hV/rYfy6KW39j821mPxIRH3Ip9mG9d\naRqbFx2DF/1+SXucwJOUuJeu+zpxFPSz87rbedHX9JWM9Ln9gjpNHvMX/d5PSUkrkXgKcqwSEm7z\n9OlTFAolfn4LuX37FkuWLCIl5TFeXhO5cuU6T58+pX79RvTt68HPP//I8OEjCAoKwczs2TSFtLRM\nkpNT1X1qa2uTnPwoVxlAcvJjJkyYTOvW7QFwdKxD/foNuXz5GsnJqYSEbKFNm3a0afMhAOPGTeLY\nsWM8fZpBcnIq69cH4uMzlWrVHNX1HTu247vvDtOsmRsAffoMoEYNZwC6dOnBnj07SU5ORaF4NkVC\nS0uXp0+ziYyMRkdHFwMDE4yNjZk6dSYPHz7ME/PLPP/cFBWNTm7r1KnD+vXrUalU6ukJZ86coUGD\nBgXqJysru8BXPYri8ybH53X7lvfMM0VxHORYvhkyNq+mIPtYlMdDU4+tpsb1b0oqGS/IsTI3r8i3\n3x6lbNmyANjbVycjIxM/v5mMGjWeQYOG0qNHX4yMjAAYPLgaV69eYd++PQwbNhKAtLT0XNtTqTLQ\n0dHLE0OlStY0bKhNcHAgkZERREVFEh0dSbt2H5KZmU14eBhduvT4WzsFNWs6kp2dw6NHqdy9e4fP\nPpsCKP62rXRu3rzJu+82+/9tWKnbGxiUISMjI1ccWVk5ZGZm07FjNw4fDqVDh7bUrVsfd/eWtG/f\nqcTfYxqd3DZq1IhKlSoxZcoURo4cyY8//sjFixdZuHBhSYcmhBBCCKH2PLF9zs7OHpVKRUrKQ0xM\nyqkT27/XR0dHYWJigq6uLvfvJ2FrawdAVlYWDx8+oHx58zzbuXEjjFGjhuHm5o6raz369h3Izp3b\n1PXPphbk5GqT8/+LWVlZAPj5+WNjY5trHWNjE/VrHR2dfNv/k719VXbt+oYTJ47z22/HWbt2FUeO\nhPLll+vyb1BMNO6qGYXir78ktLS0WLVqFYmJifTo0YMDBw6wcuVKLC0tSzBCIYQQQoi/nDp1kg4d\nWpOenq4uCwu7jrGxCSYm5Zg/fzYLF/rlahMeHkaVKlVQKBQ4Ojpz4cJftzm9dOkCOjo6VK9eI8+2\nQkO/w9W1HjNm+NG1aw8cHByJjf3rWgd7+2pcv35NvZydnc2NG2EAGBkZYWpqRlLSPaysrLGysqZi\nRUtWrfqCmJibBd7v77//luPHj9GyZWumTfPl889XcOHCOZKTkwvcV1HSuDO3V69ezbVsY2PD5s2b\nSygaIYQQQmiCykYFu5i8OLfl4lIbPT19/P3nMnjwUOLj41i9egUDBgwCoHnzFsyaNQ1X13rUqlWH\n0NDvuHjxPJMnfwZAt249Wbx4Afb2VTE3t2DJkoV07twt39uAGRubEBFxg6tXL2NoaMTXX+/l2rUr\nWFlZA9C9e2/Gjh1O7dqu1K7typ49O7hz57b65GGfPv1Zt24l5cqZYmtrx8aNgVy6dAE7uyqvtK/6\n+gZERkZQo8Y7pKY+ZtOmYMqVK0elSpUJDT2EhUUFypUrV6DjV9Q0LrkVQgghhPi7zMxsutoW7GLy\nfyroxX4FmTdapkwZli79khUrljBs2EeUKWNIly7d6ddvIADu7i3x9p5MSEgQd+/ewd6+GkuWBKhv\nv9W69fskJNxm8eIFZGRk0LJla0aMGJvvtnr16kt4+HXGjx+Frq4ederUxdNzGEePhgLg4lILb28f\nNmxYT0rKQ957rw3OzrXQ1n6W8vXr50FaWhqLF88nNTUVBwdHliz5Uj1t4u/foOenZ88+rFr1Bbdu\nxTN6tBeJiYnMnetLSspDHBycWLhw6Uv7eNMkuRVCCCGExtP0i/2qVLFn6dIvX1jfsWMXOnbs8sL6\nAQMGqc/0/ht9fX1mz16Qp3zIkGf3sL169fL/n7E9qK7z8Oitnr+rpaXF0KHDGTp0eL79Hzt2Ktdy\n+/Ydad++o3r5009H8emno9TLw4ePZvhwzbrlo8bNuRVCCCGEEK/n0qWL+Ph4cenSBW7dimfTpmAS\nE+/SuHHTkg6t2MiZWyGEEEKIUqJ7914kJNxi+nQfUlMfU6PGO3z+eUC+j/0trSS5FUIIIYQoJZRK\nJWPGeDNmjHdJh1JiZFqCEEIIIYQoNSS5FUIIIYQQpYYkt0IIIYQQotSQ5FYIIYQQQpQaktwKIYQQ\nQohS47WS27Nnz3L//n0A9u/fz6effsratWvJyckp0uCEEEIIIYQoiAInt9u3b2fAgAFcv36da9eu\nMXXqVDIyMti4cSMrV658EzEKIYQQ4i2nra1VqH9K5bOUR6l8tfULKiMjgyVL/GnfvhVdurRj7drc\nOdGUKd64uTXE3b2R+ueJE8fV9Tt3bqNbtw9p164FCxf6kZ6eXrgD9oacPfsHMTHRJR3GvyrwfW5D\nQkL47LPPaNKkCUuXLqVGjRoEBwfzv//9D19fX0aP1qxHsAkhhBDiv01bW4uQH64Tk/CoWLZna1mW\nQe1qFugxvcuXL+bPP8+wbNlKnjxJZebMqVSqVJnOnbsBEB0dja/vXOrXb6huU7asMQA//3yUDRsC\nmTnTD1NTM+bN82X16hV4eU0q2h0rAuPGjSAgYC22tlVKOpQXKnByGxcXR6tWrQD49ddfcXd3B6Ba\ntWrcu3evaKMTQgghhABiEh5xI/ZBSYeRr5SUFL799hu++GINDg6OAPTrN5ArVy7RuXM3MjIyuH07\nHgcHp3yfFLZ79w769OlPkybNAJg0aRre3qMZMWIsenp6xbovpUGBk9vy5ctz9+5dtLW1uXr1KhMn\nTgTg2rVrmJubF3mAQgghhBCa7MKFcxgZlaVOHVd12YABg9SvY2JuoqWlRaVKlfO0zc7O5urVywwZ\n8om6zNm5FhkZGYSH38DZ2SVPm+PHfyE4eB3R0dHo6urSuHFTpkyZgb6+PgChod8RFLSW+/eTaN68\nBTk5OdjZVcHTcxgAGzcGsn//Hp4+fYqra13Gj/ehYkVLANzcGjJjxhy2bNlIXFwsjo7OzJgxB0vL\nSvTq1RmAsWOH4+k5DA8PT5YsWcj//vcz6ekq6tdvwMSJUzE3tyiCo/r6CjyppEOHDkycOJGPP/4Y\nS0tLGjVqxKFDh5g+fTodOnR4EzEKIYQQQmisW7fiqVSpEt9//y0DBvSkd+8ubNwYqL7QPjo6CkND\nQ/z8ZtKlywcMGzaIkyd/A+Dx40eoVKpcCaFSqcTEpByJiXfybCs+Po4ZM6bQvXtvtm3bg5/fQs6c\nOc033+wF4Pz5cyxc6MfAgYMJCtqCvr4BP/54WN1+9+7tHDnyA7Nnz2fduo2YmpZnwoQxZGVlqdcJ\nDl7H+PE+BAVt4eHDB6xfvwqA9es3ATBv3iL69fNgz54dnD//J8uWrSIoaDNpaWkEBCwt4qNbcAU+\nczthwgQsLS2JjY1lwIABKJVKkpKS6Nu3r8y3FUIIIcRbJy3tCbGxMRw4sJ9p02aRlHSPRYvmUaZM\nGXr37k9MTDTp6ek0btwUDw9PfvnlRyZPHs+6dSGYmpoCoKurm6tPHR0dVKqMPNvKyclh/HgfOnbs\nAoClpSX16zckKioSgP37d9O69ft06tQVgIkTp3Dq1Al1+23bNjNx4lTq1Kmrru/atT2//36Cpk2b\nA9C37wDq1q0PQNeuPdi7dxcA5cqVA57NFdbX1ychIQE9PT0qVrTE2NiYadN8SUl5WDQHtRAKnNxq\naWnh4eGRq+yfy0IIIYQQbwulUsmTJ0/w9Z1LhQoVAUhIuM3+/bvp3bs/np7D6NWrH0ZGRgBUq1ad\n69ev8s03exk2bCQAKpUqV58ZGRnqaQZ/Z21tg46ODps2BRMZGUFUVCTR0ZG0a/chABERN+jSpUeu\n2J7PA05LSyMx8S6+vlMBhXodlSqduLgY9bKVlY36taGhEZmZmfnud+fO3Th6NJQuXdpRt2593N1b\n0r59p1c+bm9KgZPb7OxsDhw4wNmzZ8nIyMhzb9sFCxYUWXBCCCGEEJqufHlzdHV11YktgK2tHXfv\n/jWt4Hli+5ydnT3R0VGYmJigq6vL/ftJ2NraAZCVlcXDhw8oXz7vtUw3boQxatQw3NzccXWtR9++\nA9m5c5u6XqlUArlzs+ep2vOpB35+/tjY2OZax9jYRP1aR0cn3/b/ZG9flV27vuHEieP89ttx1q5d\nxZEjoXz55br8GxSTAie38+fPZ+vWrdSsWZOyZcu+iZiEEEIIIf4zXFxqo1KpiIuLxdr62VnP6OhI\nLC2fXUA2f/5stLS0mDJlhrpNeHgY1avXQKFQ4OjozIUL53B1rQfApUsX0NHRoXr1Gnm2FRr6Ha6u\n9Zgxw09dFhsbg719VQDs7atx/fo1dV12djY3boRRo8Y7GBkZYWpqRlLSPRo3bgpAZmYmvr5T6d9/\nUL4Xr/2b77//Fh0dXVq3bkvLlq25fPkSI0YMITk5WT3doiQUOLk9cOAA8+fPp1u3bm8iHiGEEEKI\nPGwti++EWkG3ZWNjS5MmzZg3bxYTJkwhKekeW7duYvDgoQA0b96CWbOm4epaj1q16hAa+h0XL55n\n8uTPAOjWrSeLFy/A3r4q5uYWLFmykM6du+V7GzBjYxMiIm5w9eplDA2N+PrrvVy7dgUrK2sAunfv\nzdixw6ld25XatV3Zs2cHd+7cRqF4Ng2hT5/+rFu3knLlTLG1tWPjxkAuXbqAnV2VV9pXfX0DIiMj\nqFHjHVJTH7NpUzDlypWjUqXKhIYewsKignpubkkpcHKrUqlo2LDhy1cUQgghhCgCmZnZDGpXs1B9\nKJVaGBsbkJKSRlbWyx/OUJAHOAD4+s5l2bLFjBo1FH19fXr06E2PHr0BcHdvibf3ZEJCgrh79w72\n9tVYsiRAffut1q3fJyHhNosXLyAjI4OWLVszYsTYfLfTq1dfwsOvM378KHR19ahTpy6ensM4ejQU\nABeXWnh7+7Bhw3pSUh7y3nttcHauhbb2s5SvXz8P0tLSWLx4PqmpqTg4OLJkyZfqaRPPk+AX6dmz\nD6tWfcGtW/GMHu1FYmIic+c+u5DMwcGJhQuXvrSPN63Aya2bmxu//F97dx4XVdn/f/w9DCAo4C4g\n7qZCEYpmi0t2u1WmuZRLGXabllkudd8tmn7N1HI3M0pLy0zMLDVTu8sy7zSr20QzV7JwARdU3ABB\nEZnfH/6YHFmcAzMwDK/n49Ej5zpnznmf6zrn8JnDmcPGjerfv78z8gAAAORitNjMz5Ur2Q5b1rXK\nl6+gMWPGa8yY8XlO79q1u/UJB3np3/9xm2fj5sfHx0evvZb7+005z8ndt2/P/79iu9Y6LSqqj/X+\nXZfgOXgAACAASURBVA8PDw0e/LQGD346z+Vv2vSrzev77++q++/van09ZMizGjLkWevrp58epqef\ndq2nZRkubps1a6bp06frl19+UcOGDXPddMzjwFDamU1//w3yHM44EZYFJrM5V19K9CdQEjxMyvN4\nzOHM49LTk/NAcdm9e5dWrFimsWNfU5UqVbV+/TqdOnXSeo9tWWC4uI2JiVGVKlW0d+9e7d2712aa\nyWSiuEWpF+xfQ4v3faYjKcclSbUCgvVo44c5EReCT81gnVj4gdIT/n7ETPk6dVRtwED6EyhmgRV8\ntOLgCR1Lu5hrWk0/H/WoU90px6Wnp4cWrftDCUmp1rY6Qf56/N4mnAecoFev3kpKOqYxY17ShQtp\natSosWbMeDvPP/vrrgwXtxs2bHBGDsClHEk5rvgzh0s6hltIT0hQ2l/xJR0DgKRjaRd16Hx6sa83\nISlVfyaeK/b1lkVms1nDh/9Lw4f/q6SjlBjDxa109a9j/Pjjj9q/f788PT3VqFEj3Xnnnf//2WoA\nAABAyTBc3J47d06DBg3Snj17FBAQoOzsbKWlpemWW27RwoULFRAQ4IycAAAAwA3lf2d5PqZOnaqL\nFy9q1apV+vXXXxUbG6tVq1YpMzNTM2fOdEZGAAAAwC6Gi9v//ve/evXVVxUaGmptCw0N1dixY7V+\n/XqHhgMAAACMMFzcZmVlqVq13H/ruFq1akpLS3NIKAAAAKAwDBe3t9xyi5YuXZqrfenSpQoLC3NI\nKAAAAKAwDH+h7LnnntOAAQO0Y8cONW/eXCaTSbGxsYqLi9OCBQuckREAAACwi+Ert5GRkVqyZIlC\nQkK0efNmbdq0SbVr19Ynn3yiO++80xkZAQAAALsU6jm3ERERmj17tqOzAAAAAEViV3E7evRojRkz\nRn5+fho9enSB806ePNkhwQAAAACj7Cpujxw5ouzsbOu/AQAAAFdkV3G7ePHiPP99veTk5KInAgAA\nAArJ8BfKwsLCdObMmVztR44cUadOnRwSCgAAACgMu67cLl++XKtXr5YkWSwWPfvss/Ly8rKZ5+TJ\nkwoICHB8QgAAAMBOdhW3HTt21LZt26yvg4KC5OPjYzNP48aN1aNHD8emAwAAAAywq7itVKmSzVMQ\ncp6cAAAAALgSw/fcTp48Oc/CNjMz0+bqLgAAAFDcDP8Rhz179mjs2LHav3+/9fFg19q3b59DggEA\nAABGGb5y+8Ybb8hsNmvs2LHy8vLS//3f/+nxxx+Xp6enZs2a5YyMAAAAgF0MX7ndu3evFi1apIiI\nCK1cuVKNGzfWo48+qqCgIH322We6//77nZETAAAAuCHDV26zs7NVvXp1SVLdunW1f/9+SVKHDh0U\nFxfn2HQAAACAAYaL27p161q/ONagQQPt2rVLkpSamqrMzEzHpgMAAAAMMHxbQlRUlMaMGSNJuvfe\ne9W9e3f5+Pho+/btatasmcMDAgAAAPYyfOW2d+/emjlzpoKCgtSwYUNNnjxZ27ZtU1BQkF577TWH\nB0xKStLTTz+tFi1aqEOHDlq0aJHD1wEAAAD3YPjKrXT1L5bl6Natm7p16+awQNcbOXKkatWqpS++\n+EJ//vmnXnjhBYWEhNhkAAAAACQ7i9vo6Gi7Fzhs2LBCh7leSkqKfv/9d73++uuqU6eO6tSpo7Zt\n2+p///sfxS0AAABysau4XblypV0LM5lMDi1ufXx85OvrqxUrVujf//63EhIStH37dv3rX/9y2DoA\nAADgPuwqbjds2ODsHHny9vbWuHHjNGHCBH388ce6cuWKevXqpV69epVIHgAAALi2Qt1zW5zi4+PV\nvn17DRo0SPv379fEiRPVqlUrde3a1e5lmM2GvzcHJzObPeThYZIkeXmZc41RzjRHrOdG7fasq6zt\nQznba2S77Z3XZDbnOeZXruT+c96wld9xU9jjxZ32a3uO9cLMW9gczu5bZyzfWZnzHAMPU67zQF77\ncV7zFfZcUVxjA+McPSaGi9vQ0FCZTPmfSPft21ekQNf65ZdftHz5cm3atEne3t66+eablZSUpLlz\n5xoqbgMCfB2WCY4x+9PtSkhKzXd6y5sDHbKe/Mb+nS2LdCTluCSpeXB4oZfj7pyx3T41g3X8gwVK\nT0iwtpWvU0eNRjruliZ39eWnv+lUHsdNo0IeL+62Xx/Noy2/bTQyb2GUxr4tzsw1q/tpwdq9Nj8H\n8jrvXz9fnSB/PdeveZHWXRrHBsYYLm7feOMNm+I2KytLhw4d0qpVq/TSSy85NNyePXtUr149eXt7\nW9vCwsL03nvvGVpOSkoGV4VciNnsoYSkVP2ZeC7feWoH+jtkXXmNvdnsoSMpxxV/5rAkqVZAUKGW\n487MZg8FBPga2m4jn7zTExKU9le8TVtZ62OjzGYPnUpK1bHE87mmVQv0K9Qy3anP89v/8jsH2Dtv\nYXIYPXYKux5Hc1bm/LJe/3Mgv/P+9fMVNmdxjQ2MyxkbRzFc3OZ3v2t4eLg+//xzde/evcihctSo\nUUOHDx9WVlaWPD2vRj1w4IBq1aplaDlXrmQrK4sduSxy1NiX1X2oOLe7rPZxSSoLfW5kGx3ZH6Wx\nb0tL5qLmLC3bicJz2Ee/iIgI65/ldZT27dvL09NTY8eO1aFDh7Rhwwa99957GjBggEPXAwAAAPfg\nkOL2woULiomJUbVq1RyxOCs/Pz999NFHOnXqlHr37q2pU6fq2WefVe/evR26HgAAALgHh32hzGQy\nafz48Y7IZKNhw4b64IMPHL5cAAAAuJ8if6FMkry8vNS0aVPVrl3bYcEAAAAAoxz2hTIAAACgpBku\nbjMzM/X5559r//79yszMzDV98uTJDgkGAAAAGGW4uB01apS+++47hYWFqVy5cs7IBAAAABSK4eJ2\n48aNmjVrljp16uSMPAAAAEChGX4UWEBAgOrXr++MLAAAAECRGC5un376aU2ePFmJiYnOyAMAAAAU\nmuHbEho3bqxZs2apc+fOeU7ft29fkUMBAAAAhWG4uB07dqzq1aunBx98UOXLl3dGJgAAAKBQDBe3\niYmJWr16terVq+eEOAAAAEDhGb7n9tZbb9Xhw4edkQUAAAAoEsNXbrt3767Ro0fr4YcfVu3ateXl\n5WUzvUePHg4LBwAAABhhuLgdN26cJOn999/PNc1kMlHcAgAAoMQYLm7j4uKckQMAAAAoMsP33AIA\nAACuyq4rt2FhYdq8ebOqVq2q0NBQmUymfOflObcAAAAoKXYVt2+88Yb8/f2t/y6ouAUAAABKil3F\nbc+ePa3/7tWrl9PCAAAAAEVh9z23Z8+eVUxMjFJTUyVJV65c0cyZM9WtWzcNHDhQW7ZscVpIAAAA\nwB52FbeJiYnq1q2bpk+frjNnzki6envCggUL1KBBA9WqVUtDhgzRtm3bnBoWAAAAKIhdtyVER0er\nfv36mjt3rvz8/HTu3DktW7ZM7du311tvvSVJCgkJ0dy5c7VgwQKnBgYAAADyY9eV259//lkjR46U\nn5+f9XVWVpbNH2xo06aNdu7c6ZyUAAAAgB3sKm7Pnj2rkJAQ6+vY2Fh5eHjo9ttvt7ZVrlxZly5d\ncnxCAAAAwE523ZZQpUoVnTx5UsHBwZKuXrkNCwtTxYoVrfPs27dP1apVc05KlDqenvl/bjKb+dsh\nsGUym/PdL7Kysos5DeBa8jqfch4F8mdXcdu2bVvNmzdP06dP14YNG3To0CG98MIL1unp6el69913\n1bp1a6cFRenh6emhRev+UEJSap7TW94cWMyJ4Op8agbrxMIPlJ6QYNNevk4dVRswkAIXZZanp4dW\nJZzSsbSLNu0R1QNKKBHg+uwqbkeOHKmoqCi1bNlSFotF4eHhGjBggCRp6dKleuedd2QymfTss886\nNSxKj4SkVP2ZeC7PabUD/Ys5DUqD9IQEpf0VX9IxAJdzLO2iDp1Pt2kL9vMpoTSA67OruK1Ro4bW\nrFmjn3/+WSaTSa1atZKXl9fVBXh6qmvXrho4cKACA7kiBwAAgJJjV3ErSd7e3rrnnntytffu3duR\neQAAAIBC4450AAAAuA2KWwAAALgNilsAAAC4DbuK22nTpun8+fOSpGPHjslisTg1FAAAAFAYdhW3\nMTExSk29+szSDh066OzZs04NBQAAABSGXU9LCAkJ0bBhwxQWFiaLxaJJkyapXLlyec47efJkhwYE\nAAAA7GVXcTt9+nTNmzdPR48elclk0rFjx6zPuQUAAABchV3FbXh4uKKjoyVJ7du319y5c1W5cmWn\nBgMAAACMsvuPOOTYsGGDJCk+Pl779++Xl5eXGjZsqPr16zs8HAAAAGCE4eI2MzNT//rXv7R+/Xpr\nm8lk0j/+8Q/Nnj1b3t7eDg0IAAAA2Mvwc25nzZqlnTt36p133tHWrVu1ZcsWvf3229q7d6/efvtt\nZ2QEAAAA7GK4uF27dq1ee+01dejQQf7+/qpYsaI6duyoV199VWvWrHFGRgAAAMAuhovbCxcuqEGD\nBrna69evrzNnzjgkFAAAAFAYhovbxo0b65tvvsnV/vXXX/OlMgAAAJQow18oGzp0qJ555hnt27dP\nzZs3l8lkUmxsrL777jvNnDnTGRkBAAAAuxgubu+55x7NmTNH77//vn744QdZLBY1adJEs2fPVufO\nnZ2REQAAALCL4eJWkjp27KiOHTs6OgsAAABQJIbvuQUAAABcFcUtAAAA3AbFLQAAANyG4eI2NjZW\nly9fdkYWAAAAoEgMF7fDhw/X/v37nZElT5mZmXrttdd0++23q02bNnrzzTeLbd0AAAAoXQw/LaFK\nlSpKTU11RpY8TZo0Sb/++qs+/PBDpaWl6fnnn1dISIj69OlTbBkAAABQOhgubu+++24NGTJE7dq1\nU926dVWuXDmb6cOGDXNYuPPnz2vlypX66KOPFB4eLkl64okn9Pvvv1PcAgAAIBfDxe26detUtWpV\n7d69W7t377aZZjKZHFrcbtu2Tf7+/rrtttusbU8++aTDlg8AAAD3Yri43bBhgzNy5CkxMVEhISFa\ntWqV3nvvPV2+fFm9evXS0KFDZTKZii0HAAAASodC/YUySdq6davi4+PVtWtXJSUlqV69evL0LPTi\n8pSenq5Dhw7p888/15QpU3Tq1Cn93//9n8qXL69//vOfdi/HbOaJZ8XJlfo7ryyFyedK21QccrY3\nv+3Oq93DwzkfOMtq31/PGf3rTn1rZF/Nc16Th7y8zHb1yZUr2TfMYbRvz2dnKzOP5QaYimeMPEzK\nd/sL2l57OHo/K+zyCjs2cD5Hj4nhajQtLU2DBg3S77//LpPJpNatW2vGjBlKSEjQwoULFRgY6LBw\nZrNZFy5c0MyZMxUUFCRJOnr0qJYuXWqouA0I8HVYJpQujhr7sroP5bfdf74VrfSEBJu2yi1vy3Ne\nZ2VwV19++ptOJeX+0m6jmx13bs3hbn17NI+2/Lbx+nl9yldX8qEvlZGWZG2rWP1mZWacsWnz9QtS\nvfC+N8xitG/X7U3U94dO5Wof3qKBoeUUVmAFH30en6RjaRdt2mv6+Whg03rFksFeRd1v3W2/R26G\ni9tZs2bJZDLpu+++04MPPihJevHFF/XCCy9o2rRpmjlzpsPC1ahRQ+XKlbMWtpJUv359JSUlFfCu\n3FJSMor8yRP2c6VPxXmNfWHylbV9yGz2UECAb779l56QoLS/4m3afWvXckqWstT3ZrOHTiWl6lji\n+VzTqgX6OXx97tS3+R3XRs4BGWlJSk85Yn3tUyFQFy+csGnLb5nXLju/Yyc/JpOUnW3Jc1pWMY7P\nsbSLOnQ+PVd7UfcTR/9MKGyewowNikfO2DiK4eL2v//9r2bOnKnatWtb2xo2bKhx48bp2WefdVgw\nSWrWrJkuXbqkw4cPq27dupKk+Ph4hYSEGFrOlSvZyspiRy6LHDX2ZXUfcoXtdoUM7qos9K0zttGe\nZRpZb4FfIcm75i1WrrafFDWPq20PHM/wx6kzZ86oevXqudoDAgKUnp77E19R1KtXT+3atdOoUaMU\nFxenH3/8UfPnz9ejjz7q0PUAAADAPRgubm+99VZ9/fXXudqXLFmim2++2SGhrjVjxgzVrVtX/fv3\n1+jRo/XYY4+pf//+Dl8PAAAASj/DtyX861//0hNPPKGdO3cqKytLc+fOVXx8vPbs2aMPPvjA4QH9\n/Pw0ZcoUTZkyxeHLBgAAgHsxfOW2efPm+vTTT+Xr66u6detqx44dCgoK0pIlS3THHXc4IyMAAABg\nl0I9mDY0NFTTp093dBYAAACgSApV3K5fv14LFy7Un3/+KW9vbzVu3FjPPPOMzZ/JBQAAAIqb4dsS\nlixZopEjRyo4OFjDhw/X4MGDVaFCBQ0YMCDPL5oBAAAAxcXwldsPP/zQ+tSCHP/85z/1/vvva86c\nObr//vsdGhAAAACwl+Ert6dOnVLbtm1ztXfq1ElHj+b1xw8BAACA4mG4uL3jjju0bt26XO0//PCD\nIiMjHRIKAAAAKAy7bkuIjo62/js4OFizZ8/W7t271bx5c5nNZu3Zs0dr167VoEGDnBYUAAAAuBG7\nituVK1favA4KCtLu3bu1e/dua1uNGjW0du1aPf/8845NCAAAANjJruJ2w4YNzs4BAAAAFFmhnnMr\nScnJycrMzMzVXrNmzSIFAgAAAArLcHG7ceNGjR49WmfPnrVpt1gsMplM2rdvn8PCAQAAAEYYLm5f\nf/11RURE6NFHH5WPj48zMgEAAACFYri4PXnypObNm6cGDRo4Iw8AAABQaIafc3vnnXdqz549zsgC\nAAAAFInhK7fjx4/Xww8/rB9//FG1a9eWyWSymT5s2DCHhQMAAACMMFzcvvvuu0pOTtaPP/4oX19f\nm2kmk4niFgAAACXGcHG7du1aTZ48WT179nRGHgAAAKDQDN9z6+vrq+bNmzsjCwAAAFAkhovbRx99\nVG+//bYyMjKckQcAAAAoNMO3JcTGxmrr1q365ptvVLVqVXl62i7i+++/d1g4AAAAwAjDxW2LFi3U\nokULZ2QBAAAAisRwccvTEAAAAOCqDBe3q1atKnB6jx49Ch0GKCzfcp7yLff37nwxM8up6/P0tL1d\nPSsr26nrg/u5fh+SJLPZ8NcgyoS8+squY87kkWef0s+AezNc3I4aNSrP9nLlyikoKIjiFiXiwc5V\nddSy2/q6Xrlwbfn1klPW5enpoU/2L9eRlOOSpFoBwXq08cMUuLCbp6eHNq3br1NJqTbtjW4OLKFE\nrsvT00Pnj65VRlqStc3XL0gVQ7re8JjzKV9dZxJW27xXkipWv9kpWQG4BsPFbVxcnM3rK1eu6NCh\nQxo/frz69u3rsGCAERcyL2rb2W3W15Wr1ZPk5bT1HUk5rvgzh522fLi/U0mpOpZ43qatWqBfCaVx\nbRlpSUpPOWLTVrEI7/WpwIcIwJ0V+XczZrNZDRs21OjRo/XWW285IhMAAABQKA678cjDw0MnT550\n1OIAAAAAwxzyhbK0tDR99tlnioiIcEgoAAAAoDAc8oUyT09PRUZGavz48Y7IBAAAABRKkb9QBgAA\nALgKHvYHAAAAt2HXldsBAwbYtTCTyaRFixYVKRAAAABQWHYVtyEhIQVOj42NVWJiogICAhwSCgAA\nACgMu4rbyZMn59melpamKVOmKDExUW3atNGkSZMcGg4AAAAwwvAXynL8/PPPGjt2rFJTUzVx4kT1\n7t3bkbkAAAAAwwwXt+np6ZoyZYo+++wztW7dWpMmTVJwcLAzsgEAAACGGCpuf/nlF40ZM0bnz5/X\nhAkT1KdPH2flAgAAAAyzq7hNT0/XtGnTtGzZMrVq1Uqvv/66goKCnJ0NAAAAMMSu4rZbt246duyY\nateurcjISC1fvjzfeYcNG+awcAAAAIARdhW3FotFwcHBysrK0sqVK/Odz2QyUdwCAACgxNhV3G7Y\nsMHZOQAAAIAi48/vAgAAwG1Q3AIAAMBtUNwCAADAbVDcAgAAwG1Q3AIAAMBtUNwCAADAbZSq4vap\np57S6NGjSzoGAAAAXFSpKW6/+uorbdq0qaRjAAAAwIWViuL2/Pnzmj59uiIiIko6CgAAAFyYXX+h\nrKRNnTpV3bt318mTJ0s6CgAAAFyYy1+5/eWXX7Rt2zY9++yzJR0FAAAALs6li9vMzEyNHz9er776\nqry9vUs6DgAAAFycS9+W8Pbbbys8PFytWrUq0nLMZpeu4d2Oq/S32cMkLy+zzGYPeXiYrO3X/tte\nOcvJ7/2uss2OkrM9eW1XcW6ryWy26fscV65kF1sGZ3CV/aWgHPlNK+6+zy/H9e3F2af29JuRPKaC\nTknGT1cOV9S+deTYXHtev5Y9+2VhxgbFw9Fj4tLF7X/+8x+dPn1akZGRkqTLly9LktatW6ft27fb\nvZyAAF+n5INrq1ndTwvW7pXFInk32KUjKcclSc2Dww0va/6avUo8kSpJqh3oL1Wzne6u+1hJb5dP\nzWAd/2CB0hMSrG3l69RRo5HDSjCV+yhofL/89DedSkq1aase5K/u/SKdHSuXo3m05ZU9r/mcwZ7j\nwuix43HsTJ7tni5QiJX0eeBaOef1hGv2zTpB/nquX3O7l+FK2wPncOniNiYmRllZWdbX06dPlyS9\n+OKLhpaTkpJR6q/0lCau9Kk45wRYrtpxxZ85LEmqFRBkeDmJJ1L1Z+I56+ty1xW37raPmc0eCgjw\nzXO7int80xMSlPZXvE1bae9vVzlG8utHs9lDp5JSdSzxvN3vcZb8+ur6HMXZpwX1QUHHTn5MJik7\n25LntCwX2M+LOuaOHpuEJNvzsWRfxsKMDYpHztg4iksXt8HBwTavK1SoIEmqXbu2oeVcuZKtrCx2\nZDiPu+5jrrpdrpqrtClMP7pK35dkDnvWbSRfgbcl5F3zFitXGfOCGMlYGrYHReMalw8AAAAAB3Dp\nK7fXmzx5cklHAAAAgAvjyi0AAADcBsUtAAAA3AbFLQAAANwGxS0AAADcBsUtAAAA3AbFLQAAANwG\nxS0AAADcBsUtAAAA3AbFLQAAANwGxS0AAADcBsUtAAAA3AbFLQAAANwGxS0AAADcBsUtAAAA3AbF\nLQAAANwGxS0AAADcBsUtAAAA3AbFLQAAANwGxS0AAADcBsUtAAAA3AbFLQAAANwGxS0AAADcBsUt\nAAAA3AbFLQAAANyGZ0kHAEo7s8lDZrPt58SsrOwSSuN4ZrNJsvz92sNkKrkwcBgPD1Ou/TZHfu3A\n9Tw8TNJ15wSzh0kWy98nDWfvT+Z89mV3Og/DGIpboIiC/Wto8b7PdCTluCSpVkCwHm38sFucWE0m\nk1K++UrnYmOtbb61a5VgIjhKleoV9N//xOlUUmquaY1uDiyBRCiNks5maMGavdbXtQP95eEhJVyz\nX7V08v5Us7qfPvzPPpt11gny1+P3NnGL8zCMo7gFHOBIynHFnzlc0jGc4uKJk0r7K76kY8AJTiWl\n6lji+Vzt1QL9SiANSqMr2Rb9deSc9XXORdw/E/9uqx3o7/QcCUmpNutE2cbvngAAAOA2KG4BAADg\nNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2\nKG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYo\nbgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2XL64PXHihEaMGKE77rhD7dq105QpU5SZmVnSsQAA\nAOCCPEs6wI2MGDFClSpV0ieffKJz587plVdekdls1osvvljS0QAAAOBiXPrK7YEDB7Rz505NnjxZ\nDRs2VIsWLTRixAitXbu2pKMBAADABbl0cVu9enXNnz9fVapUsbZZLBalpqaWYCoAAAC4Kpcubv39\n/dWmTRvra4vFopiYGLVq1aoEUwEAAMBVufw9t9eaNm2a4uLitGLFCkPvM5tduoZ3O+7W32aTh2oH\n+ltf1w7018kbvMfLy2zTD1euZDspnXPkZDebTTKZSjhMHkr7Plaa8xd39jzXZ/LIdYx5eBTTjprH\nuqW/j/G/jx37+6nAY8wFjr+CtqXY+r0Qrs+d87q0n5/dkaPPK6WmuJ0+fboWL16s2bNnq2HDhobe\nGxDg66RUKAuC/WtI/rtUrtpxSVKt4HCdPF7we+av2avEE1dvn6kT5K/n+jV3dkyn8Pf31XEX/NnF\nMV1yHNn3aWcP6vKla24zM5nkV7mBvLwr2Mx39Lr3+ZSvruRDXyojLcnaVrH6zQ7LVZC81u3rF6R6\n4X1t5jPaTx7HzuTZ7ukCH4QK2pZTqa779KK8cs/+dLsSkv7e50rz+Rn5KxXF7cSJE7Vs2TJNnz5d\nHTt2NPz+lJQMPpkVo9J8VSo/R1KOK/7MYUlSrYCgG86feCJVfyaes74ubfug2eyhgABfpaZmSJaS\nTpNbaevP65XmY8RRfW8ySeeObdfpo/+7ptFDN932b2Vf+Lspv77KSEtSesoR62ufCoFFzmSv69ct\n/d0vOceOkX4ymaTs7LwPtCwX2M8L2pbMzKxiTmO/63N7eZmVkGR7bs5rPhS/nOPGUVy+uI2Ojtay\nZcv05ptvqlOnToVaxpUr2crKYsdFySmt++CVKxZZXLC4La396Q4c1fcmkynPz03Z2RZlZZe+sb2+\nX4z0U4G3JbjA8VfQtuRXlLuC63Pn90GJ84n7ceniNj4+XnPnztWQIUMUGRmp5ORk67Rq1aqVYDIA\nAAC4Ipcubr///ntlZ2dr7ty5mjt3rqSrT0wwmUzat29fCacDAACAq3Hp4vapp57SU089VdIxAAAA\nUEqU3m81AAAAANehuAUAAIDboLgFAACA26C4BQAAgNuguAUAAIDboLgFAACA26C4BQAAgNuguAUA\nAIDboLgFAACA26C4BQAAgNuguAUAAIDboLgFAACA26C4BQAAgNuguAUAAIDboLgFAACA26C4SiNy\nQAAAIABJREFUBQAAgNuguAUAAIDboLgFAACA26C4BQAAgNuguAUAAIDboLgFAACA26C4BQAAgNug\nuAUAAIDboLgFAACA2/As6QBwNRZlXrEUOIeHySRPD1Mx5SkcD5NJgVXKW1+fLMZ1m00eqh3ob319\n7b9RdCazWWZz0T6XZ2VlG5rfkm2RxZL3ceHhYZJMrn08lBYmk1lms6fk8ff4FnWsUTQeJsYApQ/F\nLWyZTHpn5S4lnkzNd5aRvZupbo0KxRjKuKp+/jpm2aKTHsfVPDhcJ48X37qD/WtI/rtUrtrVlXoH\nBMtsDjNcUCFvPjWDdWLhB0pPSLC2VW55my6dOHnDNkkqX6eOqg0YaGg8zp/N0OpPf89zWp9/3iaf\nCl4GtwJ58fUP1pkj65WRlmRtq1j95hJMhMAKPlpx8ISOpV3MNa2mn49aVnDtnwUomyhukUvKhUs6\nl3op3+lXsgu+susqjqQcV/yZw6oVEFRi64ZzpCckKO2veOtr39q1lJF45IZthWXJtuhCPseERaXj\neCgtMtKSlJ5yxPrap0JgCaaBJB1Lu6hD59PznkhxCxfE7xoAAADgNihuAQAA4DYobgEAAOA2KG4B\nAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEA\nAOA2KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA\n4DYobgEAAOA2KG4BAADgNly+uM3MzNQrr7yili1bqm3btlq4cGFJRwIAAICL8izpADcydepU7d27\nV4sXL9aRI0f08ssvKyQkRJ07dy7paAAAAHAxLn3lNiMjQ8uXL9fYsWMVGhqqjh07avDgwYqJiSnp\naAAAAHBBLl3cxsXF6cqVK2rWrJm1rUWLFtq5c2cJpgIAAICrcuni9tSpU6pUqZI8Pf++e6Jq1aq6\ndOmSzp49W4LJAAAA4Ipc+p7bjIwMeXt727TlvM7MzLR7OWazS9fwLsVixzz+5b1Urlz+u46Hh0l1\ngvzznR5UtbxMpoLXcaN5rp/uV95Tuubzjk85T9UKCJYk1ahQTdLfMxf361oBwfLwMMnTs/TshznH\njNlsynMcytepk6vNJyhIJpOHw9qctczydeoYPieYCtgZy/kUfDzkxcPDpOp5HCOVq1bId12Fmebo\n5VUP8nfY+dRkuvYo+ZuvX5DN63Llq+bKUpQ2ZyzT1y/ommPG9v/2KPB8aJJq+vnkaq7u651n/xU0\nzdHvqennIw+P3FOvP//ndT4vbJu976sT5C8vL7PNOHh6euTKVseB+zQKz9FjYLJYLPbUMyXim2++\n0aRJk7R582ZrW3x8vLp27aotW7YoICCgBNMBAADA1bj0x5XAwECdO3dO2dnZ1rbk5GT5+PhQ2AIA\nACAXly5uw8LC5OnpqR07dljbYmNjFR4eXoKpAAAA4Kpcurj18fFR9+7d9eqrr2rXrl1av369Fi5c\nqMcff7ykowEAAMAFufQ9t5J08eJFvfbaa1q3bp38/f01ePBgRUVFlXQsAAAAuCCXL24BAAAAe7n0\nbQkAAACAERS3AAAAcBsUtwAAAHAbFLcAAABwGxS3AAAAcBulvrjNzMzUK6+8opYtW6pt27ZauHBh\nvvPu3btXffr0UbNmzdS7d2/t2bOnGJOWPUbGJkdsbKw6duxYDOlgZHx++OEH9ejRQ5GRkerevbs2\nbNhQjEnLHiNjs3r1at17771q2rSpHnnkEe3cubMYk5ZNhTm3HTlyRJGRkdq6dWsxJCy7jIzN0KFD\nFRoaqrCwMOv/N27cWIxpyxYjY/PHH3/o0UcfVdOmTfXggw9qy5YtxlZmKeUmTJhg6d69u2Xfvn2W\n7777ztK8eXPLunXrcs2Xnp5uad26tWXatGmW+Ph4y6RJkyytW7e2ZGRklEDqssHesckRFxdnad26\ntaV9+/bFmLLssnd84uLiLOHh4ZaYmBhLQkKCJSYmxnLLLbdY4uLiSiB12WDv2GzdutVy6623Wtas\nWWNJTEy0TJkyxXL77bdb0tPTSyB12WH03GaxWCyDBg2yhIaGWn799ddiSlk2GRmbzp07W9auXWtJ\nTk62/peZmVnMicsOe8cmNTXV0rp1a8u4ceMsCQkJljlz5lhuu+02y+nTp+1eV6kubtPT0y0RERGW\nrVu3WtveffddS1RUVK55P//8c0vHjh1t2jp37mz54osvnJ6zLDIyNhaLxbJ06VJLZGSkpXv37hS3\nxcDI+MyYMcPy5JNP2rQ98cQTljfffNPpOcsiI2Pz9ddfW+bNm2d9nZqaamnSpIll586dxZK1LDJ6\nbrNYLJYvv/zS8sgjj1DcOpmRsbl06ZLl5ptvthw6dKg4I5ZZRsZm0aJFls6dO9u0Pfzww5aNGzfa\nvb5SfVtCXFycrly5ombNmlnbWrRokeev5Xbu3KkWLVrYtDVv3ly//fab03OWRUbGRpI2b96sadOm\n8aeVi4mR8enZs6f+/e9/52pPS0tzasayysjY3HfffRoyZIgk6dKlS/roo49UrVo13XTTTcWWt6wx\nem47e/asZs6cqQkTJsjC30xyKiNjc/DgQZlMJtWqVas4I5ZZRsZm69atat++vU3b559/rrvvvtvu\n9ZXq4vbUqVOqVKmSPD09rW1Vq1bVpUuXdPbsWZt5T548qRo1ati0Va1aVSdOnCiWrGWNkbGRpOjo\naO61LUZGxqdBgwZq0qSJ9fWff/6p//3vf7rrrruKLW9ZYvTYkaRffvlFkZGRevfdd/XKK6/I19e3\nuOKWOUbHZ8qUKerZsycfOIqBkbGJj4+Xn5+fXnrpJbVp00a9e/fWpk2bijtymWFkbBITE1W5cmWN\nGzdObdq0Ub9+/bR9+3ZD6yvVxW1GRoa8vb1t2nJeZ2Zm2rRfvHgxz3mvnw+OYWRsUPwKOz5nzpzR\n8OHD1aJFC3Xo0MGpGcuqwoxNkyZNtHLlSo0YMUIvv/wyXypzIiPj8/PPP+u3337TM888U2z5yjIj\nY3PgwAFdunRJbdu21QcffKB27dpp6NChfNHcSYyMTXp6uhYsWKAaNWpowYIFuu222zRo0CBDFyM9\nbzyL6ypXrlyuTsl5ff2Vi/zm9fHxcW7IMsrI2KD4FWZ8kpOTNXDgQJlMJr311ltOz1hWFWZsqlSp\noipVqig0NFQ7duzQ0qVLFRER4fSsZZG943Pp0iWNHz9er776aq4f6nAOI8fOsGHD9Pjjj8vf31/S\n1Q+Iu3fv1rJlyzRhwoTiCVyGGBkbs9mssLAwDRs2TJIUGhqqn376SV9++aWeeuopu9ZXqq/cBgYG\n6ty5c8rOzra2JScny8fHRwEBAbnmPXXqlE1bcnKyqlevXixZyxojY4PiZ3R8Tpw4of79++vKlSta\nvHixKleuXJxxyxQjY7Nr1y7t3bvXpq1hw4b53r6AorN3fHbu3KnExEQNHz5ckZGRioyMlCQ9+eST\nGj9+fHHHLhOMntdyCtscDRs21MmTJ52esywyMjbVq1dXgwYNbNrq1aun48eP272+Ul3choWFydPT\nUzt27LC2xcbGKjw8PNe8TZs2zfXlsd9++83m5mY4jpGxQfEzMj4ZGRkaPHiwvLy8FBMTo2rVqhVn\n1DLHyNgsX75cM2fOtGnbs2ePGjZs6PScZZW949O0aVN9++23+vLLL7V69WqtXr1akvT6669rxIgR\nxZq5rDBy7IwePVpjxoyxaYuLi1P9+vWdnrMsMjI2zZo1U1xcnE3bgQMHFBISYvf6SnVx6+Pjo+7d\nu+vVV1/Vrl27tH79ei1cuND6jfvk5GRdunRJknTvvfcqNTVVb7zxhuLj4zVp0iSlp6fr/vvvL8lN\ncFtGxgbFz8j4zJs3T0eOHNHkyZOVnZ2t5ORkJScn87QEJzEyNn379tWWLVu0ePFiHT58WHPmzNGu\nXbs0YMCAktwEt2bv+Hh7e6t27do2/0lSjRo1VKVKlZLcBLdl5Njp0KGDVq9erVWrVikhIUHR0dHa\nvn27oqKiSnIT3JaRsenXr5/++OMPRUdHKyEhQW+99ZaOHDmiBx980P4VFvqhZS4iIyPDMmrUKEtk\nZKTl7rvvtnz88cfWaU2aNLF5ju3OnTstPXv2tDRt2tTSp08fy759+0oicplhZGxyrFy5kufcFhN7\nx+e+++6zhIaG5vpv1KhRJRXd7Rk5dn744QdLt27dLE2bNrU8/PDDlh07dpRE5DKlMOc2i8XCc26L\ngZGx+fzzzy2dO3e2REREWHr16mWJjY0tichlhpGx2b59u6Vnz56WiIgIS8+ePS3btm0ztC6TxcKD\n9wAAAOAeSvVtCQAAAMC1KG4BAADgNihuAQAA4DYobgEAAOA2KG4BAADgNihuAQAA4DYobgEAAOA2\nKG4BAADgNihuAQAA4DYoboFCWL16tfr27avIyEhFRkbq4Ycf1rJly2zmiYqKUmhoqPW/8PBwtWnT\nRi+++KKOHj1a5AwbN25U+/bt1bRpU8XExOSa/sUXXyg0NFRhYWE2OUJDQ3XXXXdZ5wkLCytylmuF\nhoZq1apVudozMjLUvHlzTZs2Ld/3du7cWa+++qpD89jj6NGjCg0N1datW/Oc/uuvv9r0X1hYmCIj\nI9WrVy999tlnNvMa7dPt27dr27ZtBc5zbZ+OGjVKAwYMsHv5ecnKytJHH31kfR0dHa0OHToUaZk3\n0r59e0VHRxf6/RkZGVqyZIn19ejRo4vcD9e7fpxzjtu7775bY8eOVUpKikPXdyNRUVEaPXq03fMX\nRx8BpYFnSQcASpvly5fr9ddf17hx49S8eXNZLBb99NNPmjRpkpKTk/Xss89a5+3SpYvGjh0ri8Wi\nS5cuKSEhQW+++ab69u2r5cuXKygoqNA5Zs+erQYNGmjJkiUKCAjIcx6TyaSffvpJ1/+VbZPJJEl6\n4IEHdPfddxc6gxG+vr7q0qWLvvrqK7300ku5pm/fvl2JiYmaNWtWseS5Xk6fFDQ9Z8yys7OVkpKi\n77//XhMnTtSxY8f03HPPSTLep48++qimTJmiFi1a5DvPTz/9JH9/f7ty2mPt2rWaOnWq/vnPf0qS\nBg0apP79+xd5uQVZsWKFfHx8Cv3+Dz74QF988YXTc147ztLVDwL79+/Xyy+/rOTkZM2bN8+p6y+K\n6/tozJgxys7OLuFUQPGjuAUMWrp0qXr37q2ePXta2+rVq6ekpCR9/PHHNsVtuXLlVKVKFevrmjVr\n6oMPPlDXrl01a9asAq9i3khKSoo6dOig4ODgAue7dv3X8/b2VtWqVQudwaiHHnpIK1as0JYtW3TH\nHXfYTFu1apUaNWqk8PDwYstzres/AOSlcuXK1v6qXr26GjZsKG9vb02fPl09evRQvXr1nNKnjl7e\n9QWPr6+vfH19HbqO61WuXLlI77dnfBzl2nGWpMDAQD3++ON66623lJaWJj8/v2LLYsT1feSqOQFn\n47YEwCAPDw/99ttvuX5FOWTIkFy/os6Ln5+fevXqpe+++06XL1/Od75Vq1ape/fuatq0qdq3b6+5\nc+daf3iFhobq2LFjio6OLtJtBStXrlRoaKj1dWhoqFasWKGBAweqadOmatOmjd59913rdIvFovfe\ne0/33Xefbr31VrVo0UJPPvmkEhMT7VpfZGSkGjRooDVr1ti0Z2Zm6ptvvlHv3r2tbUlJSXrhhRfU\npk0bRUZGatCgQfrjjz8kSYsXL9Ydd9xh7Q+LxaI77rhDTz/9tPX9cXFxCg0N1YkTJyRdvXLYpUsX\nNW3aVA888IA+/vhjhxRMffr0kZeXl77++mtJuft048aNeuihh9SsWTO1atVKo0ePVmpqqqSr/W0y\nmTR69GiNHj3aenvE+++/r9atW6tTp05KS0vLdavHlStXNGnSJLVo0UJ33nmnJk6cqMzMTEl532Jx\nbdsXX3yhV155RRaLRWFhYdq6dauio6PVvn17u/pekjXv1KlT1apVKzVr1kxPP/20Tp06lW8/XXtb\nQnR0tAYOHKj58+erXbt2ioiIUFRUlA4cOJDne6Ojo/XOO+/o6NGjCgsL07FjxyRdvao6bdo03XXX\nXYqMjNSzzz6rM2fOWN934sQJPf/882rZsqXuvPNODR06VIcPH77BiObNw8NDJpNJXl5ekqT4+HgN\nHTpUd9xxh2677TaNGDHCmku6ekvBG2+8oX//+99q1qyZ2rVrp/fff986PecWiGvfk1fbtdavX68+\nffooMjJSERER6tWrlzZv3pxvH40aNUpRUVHW99uTeebMmRozZoxatmypFi1a6IUXXlB6enqh+gwo\nKRS3gEGDBw/Wnj17dPfdd2vIkCGaP3++du3aJT8/P9WtW9euZTRu3FgXL17M9wftRx99pHHjxumR\nRx7RmjVr9Pzzz+uDDz7QlClTJF39NXVgYKCeeOIJ/fTTT4XeFpPJlOvX3NOmTdNDDz2k//znP4qK\nitKcOXMUGxsrSVq0aJE+/PBDjR49Wt9++63effddHTp0SFOnTrV7nb169dK3335rLcakqz+0L168\nqAcffFCSdOHCBfXr108nT57UvHnz9Omnn8rX11ePPfaYjh8/rvbt2yslJUW7du2SJO3Zs0cpKSna\ntm2btWDdtGmTwsPDFRgYqGXLlmn69OkaPny4vvrqKz333HOaP3++Zs6cWei+y1G+fHnVqlVLcXFx\nkmz79OzZsxo+fLh69+6tb775Ru+8845iY2OtV+w3b94si8WiMWPGaMyYMdZlrlq1Sh9//LFmz56d\n59W3bdu26cyZM/rss880depUrVu3TjNmzLBOz+vWhWtvRXnllVest6w0a9bMZvqN+j7H2rVrlZKS\noiVLlmjBggXavXu3Zs+ebXe/xcbGatu2bZo/f76WLl2q06dPa8KECXnOO2jQIA0cOFDBwcH66aef\nrLcMbN++XampqVq6dKnef/997dixw9q3GRkZGjBggDw8PLRkyRLFxMSoSpUq6tOnj06ePGl3zitX\nrig2NlaLFy/WPffco3Llyuno0aPq16+ffHx8FBMTow8//FDJycl67LHHdOHCBet7ly5dqooVK+qL\nL77Q888/r3fffVcLFiywTi9onK63Z88ejRgxQt26ddPatWv12WefqWrVqnr55ZeVlZWVZx9duy/a\nm3nRokWqXr26VqxYoRkzZuj777+3uT8bKA0obgGD7r33Xn366afq0KGDfv/9d82aNUu9e/fWfffd\np+3bt9u1jJx7ZHOu4F1vwYIFioqKUr9+/VSnTh1169ZNI0aM0CeffKK0tDRVrVpVHh4eKl++fIG3\nHVgsFjVv3tz6xbfIyEg1b95cSUlJ+b6nZ8+e6tq1q0JCQjRkyBAFBARYt6tevXqaNm2a2rVrp+Dg\nYN1xxx267777tH//fru2W5J69Oih9PR0bdy40dq2evVqdezYURUrVpQkffnllzp//rzmzJmj8PBw\nNWnSRDNnzpSPj4+WLFmikJAQ3XTTTdbC/ueff1a7du108eJF7d69W9LVK6YdO3aUJM2dO1fPPPOM\n7r//ftWqVUudOnXS888/r8WLF9sU2YXl7++vtLS0XO0nTpzQ5cuXFRwcrKCgIEVGRmrevHl67LHH\nJEnVqlWTdPVq/rVFbP/+/dWwYUPdcsstea6vRo0amjJliho2bKh27dpp5MiR+vTTT3Xp0iVJef8K\nP6fN29vbev9ulSpVrFcic9yo73MEBARowoQJql+/vm677TZ16dLF7v1fulo0zpgxQ40bN9Ytt9yi\nvn375vt+X19fVahQQR4eHqpSpYo8PDys/TBx4kTVq1dPLVu2VJcuXazjv3btWqWmpmr69Olq3Lix\nbrrpJr3++uvy8/Mr8DcsFotFDzzwgPV4ufXWWzVw4EA1a9ZMEydOlCR98sknqlChgqZNm6ZGjRop\nIiJCc+bM0enTp7V69Wrrsho0aKBx48apfv366tGjh6KiovTxxx/b3UfXMpvNGjdunKKiohQSEqLQ\n0FBFRUXpzJkzOn36dL59lMPezDfddJOee+451alTR//4xz/UqlUrQ+MKuALuuQUKISIiwnrVLy4u\nThs3btTixYv11FNP6dtvvy2w4JT+Lmrz+iLYmTNnlJycrObNm9u033777crKytKBAwcUERFhV06T\nyaQvv/wyV3uNGjXyfU+DBg1sXvv5+Vlvn7jnnnu0c+dOzZkzRwcPHtTBgwf1119/KTAw0K480tX7\nR9u1a6c1a9aoU6dOOn36tDZv3qz58+db5/nzzz9Vr149VapUydpWrlw5RUREWAvp9u3b6+eff9bQ\noUP1008/qUuXLjp37pz+97//qW7dutqxY4fGjx+vM2fOKCkpSbNmzdKbb75pXZ7FYtHly5d15MgR\nlStXzu78eUlLS8uzD0JDQ/XAAw9oyJAhql69ulq3bq177rlHnTp1KnB5derUKXB6eHi4vL29ra8j\nIiJ0+fJlHTx40Fq4FpY9fS9JtWvXltlstr4OCAgo8Dab61WtWtWmoDf6fil3P1WsWFEXL16UJO3b\nt0/nzp3L9UW9y5cv53v7g3T1mJk/f751PHPuofb0/PvH5Z9//qnw8HCbDwbVqlVT/fr1bfro9ttv\nt1l2ZGSkFixYoHPnzhnaTunqvlSxYkXNnz9fBw4c0OHDh7Vv3z5JVz8o3Ii9mevXr2/zvoCAgHxv\nkwBcFcUtYMCJEyf03nvvaciQIdYffjmPDOrQoYO6du2q2NhYde7cucDl7N69W76+vqpXr16uaTlX\n2K7/9WR2drYsFkuuK203Urt2bUPzX1s0XZ/p/fff17vvvqtevXqpVatWGjhwoNavX6+vvvrK0Doe\nfvhhjRw5UqmpqVqzZo0CAwOtjyfLWV9ev57Nzs62Fhnt27fXhx9+qNOnT+u3336zPrVgy5Ytqlmz\npoKDg9WoUSOdPn1akvTKK6/YrCNHcHCw9b7cwkhPT9fBgwett1Rcb8aMGRo2bJg2bdqkn3/+WS++\n+KJatGhR4K96b/RUgWuLSunvfSOvsZPsK35y2NP3UsH7iT3yy2rE9Vcnr82QnZ2tBg0aaO7cubnm\nKV++fIHLrVmzpmrWrJnvdHv76Np/50yXco9fjoLG6ddff9XgwYN1zz33qEWLFnrwwQeVnp6uYcOG\nFbgtRjMXdVwBV8BtCYAB3t7e+uyzz3J9IUqS9YpZzq+a83PhwgV9+eWXuv/++/P8IVe1alVVq1bN\nep9rjq1bt8rb29twsepI7733noYNG6Zx48apd+/eioiI0MGDBw3/8GvXrp0qVapkLYx79eplM71J\nkyY6ePCgzZeDLl26pN27d+umm26SJDVt2lQVK1bUvHnzVK1aNdWpU0etWrXStm3b9O2331qf21q1\nalVVrVpVCQkJql27tvW/Xbt26c033yzyD+6c5xvfd999uabt3LlTkydPVr169TRgwADNmzdPb7zx\nhrZs2WKzbUbt3bvX5nVsbKx8fX1Vu3Zt64efa2+TOHjwoE1hU9DjxArq+0aNGhU6c3Fr1KiRjh49\nKn9/f+uYBwcHa/r06fk+z9heTZo00c6dO22uNCcnJ+vw4cM2fZRzi0SObdu2qVatWvL395eXl5cs\nFkuuccrPwoULdeedd2rOnDl6/PHHddddd1mvqNqzD9ubGXAHFLeAAZUrV9aTTz6p2bNn680331Rc\nXJwSExP13//+V8OHD9ddd91lczvBpUuXlJycrOTkZB0/flybN2/WU089JUkaOXJkvusZNGiQlixZ\noqVLlyohIUFr1qzRO++8o759+5bo431yvqwSHx+vgwcP6s0339R3331n+L5VDw8Pde/eXTExMdq3\nb58eeughm+ndunVTpUqV9Nxzz2nXrl2Ki4vTCy+8oIyMDPXt29c6X7t27bRs2TLdeeedkq7+2tdi\nsWj9+vU2f5Rg8ODBWrx4sZYsWaLExER99913eu211+Tr62v3lXCLxaLTp08rOTlZp06d0l9//aX5\n8+dr9uzZevrpp/P80FGhQgUtWbJEM2bMUEJCgvbv36///Oc/qlevnvXWlfLlyys+Pt7Qr6qTkpI0\nevRo/fXXX1q3bp2io6M1ePBgeXl5qUaNGgoJCdGiRYt04MABbdu2TW+99ZZNQZtz5XLPnj3W+3Rz\n2Nv3xa1ChQpKSUnRoUOHlJWVdcP5u3fvrkqVKmn48OHauXOn4uPj9fLLL+vHH39U48aN832fPYXi\nI488ogsXLuill17SH3/8oZ07d+q5555T1apV1aVLF+t8sbGxio6O1uHDh7V8+XItXbpUTz75pKSr\nXyotX7683nvvPSUmJurHH38s8Gp+cHCw/vjjD23btk1Hjx7VihUrNGfOHEmyHn8F9ZG9mQF3QHEL\nGDRy5Ei9/vrr2rZtmwYMGKAuXbpoypQpatOmTa5fgX799ddq27at2rZtq06dOmncuHG65ZZb9Pnn\nnxd43+vAgQP10ksvadGiRXrggQf09ttv66mnntIrr7xinccRD/O/3o2+vT1t2jRlZGTo4YcfVlRU\nlP766y9NmDDBel+rkVwPPfSQ9u7dq7vuuivXH7Pw8/PT4sWLVbFiRQ0cOFCPPfaYMjMztXTpUoWE\nhFjna9++vS5fvmy93cDb21stWrSQv7+/brvtNut8AwcO1KhRo7RkyRJ16dJFkydPVr9+/TR+/PgC\nt/36fujTp4/atm2ru+++W3379tWmTZs0derUfH813LBhQ73zzjvasmWLevToof79+8vT09PmkVBP\nPPGEYmJirE9LsOcb9B06dJCnp6d69+6tiRMnqn///nrmmWes06dPn67U1FT16NFD48eP1wsvvGDz\nK/w777xTEREReuSRR/TDDz/YLLugvi/oV/U3kteTOYzo3LmzqlWrpu7du+e6cp0XPz8/xcTEqHLl\nyho8eLD1KQkfffRRrvvKr895IyEhIYqJiVFKSor69eunJ598UoGBgfrkk09sPnx26NCQzUZeAAAA\nuElEQVRB8fHxevDBB/X+++9r9OjR6tOnj6Srhej06dO1b98+6zE+atSofNc5YsQINW3aVEOHDlXP\nnj21fPlyTZ48WT4+PtanhhTUR/ZmBtyBycLNNAAAOFRUVJRq1aqlyZMnl3QUoMzhyi0AAADcBsUt\nAAAA3Aa3JQAAAMBtcOUWAAAAboPiFgAAAG6D4hYAAABug+IWAAAAboPiFgAAAG6D4hYAAABug+IW\nAAAAboPiFgAAAG7j/wG0oseo0XuSvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa498949590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results of the simulations \n",
    "        \n",
    "plt.hist(results[0][1], label='50 agents',edgecolor = 'white')\n",
    "plt.hist(results[1][1], label='150 agents',edgecolor = 'white')\n",
    "plt.hist(results[2][1], label='250 agents',edgecolor = 'white')\n",
    "plt.hist(results[3][1], label='350 agents',edgecolor = 'white')\n",
    "plt.hist(results[4][1], label='450 agents',edgecolor = 'white')\n",
    "plt.hist(results[5][1], label='550 agents',edgecolor = 'white')\n",
    "plt.hist(results[6][1], label='650 agents',edgecolor = 'white')\n",
    "#plt.hist(results[7][1], label='1000 agents',edgecolor = 'white')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('SD of Final Vowel Distribution in the Population ')\n",
    "plt.ylabel('Number of Simulations')     \n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows that population size mediates convergence: given the same number of interactions, smaller populations show lower SDs and therefore higher degrees of convergence. As populations grow, the less converged they are at their final stage. This is reasonable, since bigger populations require more time to reach the same level of connectivity between agents, and have more variance to begin with. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we may predict that given more time to interact, bigger populations will show the same levels of convegrence as smaller populations. We can quickly check this by running a simulation with more interactions (say, 5 times more):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "150\n",
      "250\n",
      "350\n",
      "450\n",
      "550\n",
      "650\n"
     ]
    }
   ],
   "source": [
    "# Run 50 simulations of each population size\n",
    "results = batch_simulate_size(10000,50)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lF+zd+w0KhUK1lLCX1yR69uwDwE8//cDGjWu5fz+FZs1aMHnydIyMqpXqOZWG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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa4989c9f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results of the simulations \n",
    "        \n",
    "plt.hist(results[0][1], label='50 agents',edgecolor = 'white')\n",
    "plt.hist(results[1][1], label='150 agents',edgecolor = 'white')\n",
    "plt.hist(results[2][1], label='250 agents',edgecolor = 'white')\n",
    "plt.hist(results[3][1], label='350 agents',edgecolor = 'white')\n",
    "plt.hist(results[4][1], label='450 agents',edgecolor = 'white')\n",
    "plt.hist(results[5][1], label='550 agents',edgecolor = 'white')\n",
    "plt.hist(results[6][1], label='650 agents',edgecolor = 'white')\n",
    "#plt.hist(results[7][1], label='1000 agents',edgecolor = 'white')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('SD of Final Vowel Distribution in the Population ')\n",
    "plt.ylabel('Number of Simulations')     \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, the results show that with more interactions, there is little to no difference between the different-sized populations, and all eventually reach similar levels of convergence. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wrapping up\n",
    "So you did it! You finished the tutorial and made a model with more complex agents and complex interactions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hopefully, now you feel confident enough to change different parts of the code, or add your own new features. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good luck with your model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bill & Limor"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}