Innovation-uptake-model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LightGraphs, Distributions, DataFrames, ProgressMeter, RCall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Random.MersenneTwister(UInt32[0x01332bfa], Random.DSFMT.DSFMT_state(Int32[-1772545288, 1073534108, 1077066014, 1072915095, -2146195133, 1072843413, 301764553, 1073404181, 750472136, 1073628106  …  -1491411563, 1073194977, 716119449, 1072893711, 1632331784, 758890923, 1433693833, -13012230, 382, 0]), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], UInt128[0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000  …  0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000, 0x00000000000000000000000000000000], 1002, 0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Random: seed!\n",
    "seed!(20130810)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Note: This workbook replicates the results from \"Multi-parameter models of innovation diffusion on complex networks\", N. J. McCullen, A.M. Rucklidge, C.S. E. Bale, T. J. Foxon and W.G. Gale (2012). This is a self-didactic attempt*\n",
    "\n",
    "The decision to invest in an innovation is based on its perceived usefulness (*utility*). If the utility exceeds the barrier to adoption (measured by a threshold), the individual adopts the innovation.\n",
    "\n",
    "The utility $u_i$ for the individual $i$ is a combination of personal benefit ($p_i$), direct influence from an individuals peer group and influence from society in general. Hence,\n",
    "\n",
    "$$\n",
    "u_i(t) = \\alpha_ip_i + \\beta_is_i(t) + \\gamma_im(t)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this equation, $s_i$ measures the impact of adoption from the peer group of an individual and $m$ measures the mainstream norm (average adoption among the entire network). Since each individual can attach differing weights to each of these three parameters, i.e., personal benefit, peer group influence and mainstream norm, we can vary the weights $\\alpha_i, \\beta_i, \\gamma_i$ such that $\\alpha_i + \\beta_i + \\gamma_i = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem description is as follows.\n",
    "\n",
    "> Given a particular network, initial set of adopters and parameter\n",
    "values $(\\alpha, \\beta, \\gamma, p, \\theta)$, we ask whether or not the innovation succeeds, that is, do most individuals\n",
    "adopt the innovation. In each case, 5% of\n",
    "the nodes are chosen as seed nodes at random and are set to 1, with the rest initialised at 0. The detailed structure of\n",
    "the network is randomised at each set of parameter values. In order to look at the influence of\n",
    "the parameters on the expected uptake, this calculation is repeated 100 times over a range of parameter\n",
    "values and plotted in the $\\beta$, $\\gamma$ parameter space, with $0 \\leq \\beta \\leq 1$, $0 \\leq \\gamma \\leq 1$ and $\\alpha = 1 - \\beta - \\gamma$. Our dependent variable is the average number of individuals adopted at the end of a predetermined set of time steps.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mutable struct Network\n",
    "    G::LightGraphs.SimpleGraphs.SimpleGraph{Int}\n",
    "    node_status::BitVector\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "error in method definition: function Random.seed! must be explicitly imported to be extended",
     "output_type": "error",
     "traceback": [
      "error in method definition: function Random.seed! must be explicitly imported to be extended",
      "",
      "Stacktrace:",
      " [1] top-level scope at In[4]:1"
     ]
    }
   ],
   "source": [
    "function seed!(N::Network)\n",
    "    seed_set = sample(vertices(N.G), floor(Int, 0.05 * nv(N.G)))\n",
    "    N.node_status[seed_set] = true\n",
    "    \n",
    "    return nothing\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "peer_influence (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function peer_influence(N::Network, node::Int)\n",
    "    return sum([N.node_status[nbr] for nbr in neighbors(N.G, node)])/length(neighbors(N.G, node))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mainstream_norm (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function mainstream_norm(N::Network)\n",
    "    return sum(N.node_status)/nv(N.G)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "evolve! (generic function with 1 method)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function evolve!(N::Network, beta::Float64, gamma::Float64; p = 0.5, theta = 0.25)\n",
    "    for node in shuffle(vertices(N.G))\n",
    "        if N.node_status[node] == false\n",
    "            s, m = peer_influence(N, node), mainstream_norm(N)\n",
    "            if (beta * s + gamma * m + (1 - beta - gamma) * p) > theta\n",
    "                N.node_status[node] = true\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return nothing\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulations on Erdos-Renyi random graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simulate_er (generic function with 2 methods)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simulate_er(n::Int, p::Float64; T = 35, n_realizations = 100)\n",
    "    parameter_space = [(beta, gamma) for beta in linspace(0, 1, 10),\n",
    "                                         gamma in linspace(0, 1, 10)]\n",
    "    \n",
    "    output = DataFrame(r = Int[], avg_degree = Float64[], beta = Float64[], gamma = Float64[], avg_engaged = Float64[])\n",
    "    \n",
    "    @showprogress 1 \"Simulating...\" for (beta, gamma) in parameter_space\n",
    "        for r in 1:n_realizations\n",
    "            g = erdos_renyi(n, p)\n",
    "            ns = falses(nv(g))\n",
    "            N = Network(g, ns)\n",
    "            \n",
    "            seed!(N)\n",
    "\n",
    "            for t in 1:T\n",
    "                evolve!(N, beta, gamma)\n",
    "            end\n",
    "            avg_frac_engaged = sum(N.node_status)/nv(N.G)\n",
    "\n",
    "            push!(output, [r, mean(degree(g)), beta, gamma, avg_frac_engaged])\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return output\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mSimulating...100%|██████████████████████████████████████| Time: 0:00:25\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>r</th><th>avg_degree</th><th>beta</th><th>gamma</th><th>avg_engaged</th></tr></thead><tbody><tr><th>1</th><td>1</td><td>5.064</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>2</th><td>2</td><td>4.876</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>3</th><td>3</td><td>5.028</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>4</th><td>4</td><td>4.988</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>5</th><td>5</td><td>4.82</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>6</th><td>6</td><td>4.872</td><td>0.0</td><td>0.0</td><td>0.998</td></tr><tr><th>7</th><td>7</td><td>5.164</td><td>0.0</td><td>0.0</td><td>0.992</td></tr><tr><th>8</th><td>8</td><td>5.192</td><td>0.0</td><td>0.0</td><td>0.998</td></tr><tr><th>9</th><td>9</td><td>5.152</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>10</th><td>10</td><td>5.104</td><td>0.0</td><td>0.0</td><td>0.996</td></tr><tr><th>11</th><td>11</td><td>5.18</td><td>0.0</td><td>0.0</td><td>0.996</td></tr><tr><th>12</th><td>12</td><td>4.908</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>13</th><td>13</td><td>5.024</td><td>0.0</td><td>0.0</td><td>0.992</td></tr><tr><th>14</th><td>14</td><td>4.864</td><td>0.0</td><td>0.0</td><td>0.996</td></tr><tr><th>15</th><td>15</td><td>5.16</td><td>0.0</td><td>0.0</td><td>0.986</td></tr><tr><th>16</th><td>16</td><td>5.18</td><td>0.0</td><td>0.0</td><td>0.996</td></tr><tr><th>17</th><td>17</td><td>4.984</td><td>0.0</td><td>0.0</td><td>0.992</td></tr><tr><th>18</th><td>18</td><td>5.108</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>19</th><td>19</td><td>5.168</td><td>0.0</td><td>0.0</td><td>0.992</td></tr><tr><th>20</th><td>20</td><td>4.86</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>21</th><td>21</td><td>4.772</td><td>0.0</td><td>0.0</td><td>0.992</td></tr><tr><th>22</th><td>22</td><td>5.048</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>23</th><td>23</td><td>4.936</td><td>0.0</td><td>0.0</td><td>0.986</td></tr><tr><th>24</th><td>24</td><td>5.044</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>25</th><td>25</td><td>5.056</td><td>0.0</td><td>0.0</td><td>0.988</td></tr><tr><th>26</th><td>26</td><td>4.976</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>27</th><td>27</td><td>5.056</td><td>0.0</td><td>0.0</td><td>0.998</td></tr><tr><th>28</th><td>28</td><td>5.028</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>29</th><td>29</td><td>4.92</td><td>0.0</td><td>0.0</td><td>0.99</td></tr><tr><th>30</th><td>30</td><td>4.908</td><td>0.0</td><td>0.0</td><td>0.994</td></tr><tr><th>&vellip;</th><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td></tr></tbody></table>"
      ],
      "text/plain": [
       "10000×5 DataFrames.DataFrame\n",
       "│ Row   │ r   │ avg_degree │ beta │ gamma │ avg_engaged │\n",
       "├───────┼─────┼────────────┼──────┼───────┼─────────────┤\n",
       "│ 1     │ 1   │ 5.064      │ 0.0  │ 0.0   │ 0.994       │\n",
       "│ 2     │ 2   │ 4.876      │ 0.0  │ 0.0   │ 0.994       │\n",
       "│ 3     │ 3   │ 5.028      │ 0.0  │ 0.0   │ 0.994       │\n",
       "│ 4     │ 4   │ 4.988      │ 0.0  │ 0.0   │ 0.99        │\n",
       "│ 5     │ 5   │ 4.82       │ 0.0  │ 0.0   │ 0.994       │\n",
       "│ 6     │ 6   │ 4.872      │ 0.0  │ 0.0   │ 0.998       │\n",
       "│ 7     │ 7   │ 5.164      │ 0.0  │ 0.0   │ 0.992       │\n",
       "│ 8     │ 8   │ 5.192      │ 0.0  │ 0.0   │ 0.998       │\n",
       "│ 9     │ 9   │ 5.152      │ 0.0  │ 0.0   │ 0.994       │\n",
       "│ 10    │ 10  │ 5.104      │ 0.0  │ 0.0   │ 0.996       │\n",
       "│ 11    │ 11  │ 5.18       │ 0.0  │ 0.0   │ 0.996       │\n",
       "⋮\n",
       "│ 9989  │ 89  │ 5.16       │ 1.0  │ 1.0   │ 0.052       │\n",
       "│ 9990  │ 90  │ 5.04       │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9991  │ 91  │ 5.232      │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9992  │ 92  │ 4.968      │ 1.0  │ 1.0   │ 0.054       │\n",
       "│ 9993  │ 93  │ 5.148      │ 1.0  │ 1.0   │ 0.048       │\n",
       "│ 9994  │ 94  │ 4.944      │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9995  │ 95  │ 4.968      │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9996  │ 96  │ 4.92       │ 1.0  │ 1.0   │ 0.052       │\n",
       "│ 9997  │ 97  │ 5.052      │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9998  │ 98  │ 4.66       │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9999  │ 99  │ 5.024      │ 1.0  │ 1.0   │ 0.052       │\n",
       "│ 10000 │ 100 │ 4.932      │ 1.0  │ 1.0   │ 0.052       │"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = simulate_er(500, 0.01)\n",
    "@rput results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RCall.RObject{RCall.VecSxp}\n",
       "# A tibble: 100 x 5\n",
       "# Groups:   beta [?]\n",
       "    beta gamma Degree Avg_Uptake Var_Uptake\n",
       "   <dbl> <dbl>  <dbl>      <dbl>      <dbl>\n",
       " 1    0. 0.      4.97     0.994  0.0000116 \n",
       " 2    0. 0.111   4.97     0.994  0.0000134 \n",
       " 3    0. 0.222   4.97     0.994  0.0000112 \n",
       " 4    0. 0.333   5.01     0.994  0.0000108 \n",
       " 5    0. 0.444   4.98     0.993  0.0000152 \n",
       " 6    0. 0.556   4.99     0.0491 0.00000157\n",
       " 7    0. 0.667   5.01     0.0491 0.00000180\n",
       " 8    0. 0.778   4.99     0.0490 0.00000198\n",
       " 9    0. 0.889   4.99     0.0490 0.00000198\n",
       "10    0. 1.00    4.97     0.0487 0.00000223\n",
       "# ... with 90 more rows\n"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R\"\"\"\n",
    "library(tidyverse)\n",
    "\n",
    "results_summary <- results %>% group_by(beta, gamma) %>% summarize(Degree = mean(avg_degree),\n",
    "                                                                   Avg_Uptake = mean(avg_engaged),\n",
    "                                                                   Var_Uptake = var(avg_engaged)) \n",
    "\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "RCall.RObject{RCall.VecSxp}\n"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R\"\"\"\n",
    "ggplot(data = results_summary, aes(x = gamma, y = beta)) +\n",
    "    geom_point(aes(color = Avg_Uptake)) +\n",
    "    scale_color_gradient(low = \"white\", high = \"black\") +\n",
    "    theme_bw()\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "RCall.RObject{RCall.VecSxp}\n"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: both DataFrames and LightGraphs export \"weights\"; uses of it in module Main must be qualified\n"
     ]
    }
   ],
   "source": [
    "R\"\"\"\n",
    "ggplot(data = results, aes(x = gamma, y = beta)) + \n",
    "    geom_point(aes(color = avg_engaged), position = \"jitter\") +\n",
    "    scale_color_gradient(low = \"grey\", high = \"black\") +\n",
    "    theme_bw()\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulations on Watts-Strogatz graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simulate_ws (generic function with 1 method)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simulate_ws(n::Int, k::Int, p::Float64; T = 35, n_realizations = 100)\n",
    "    parameter_space = [(beta, gamma) for beta in linspace(0, 1, 10),\n",
    "                                         gamma in linspace(0, 1, 10)]\n",
    "    \n",
    "    output = DataFrame(r = Int[], avg_degree = Float64[], beta = Float64[], gamma = Float64[], avg_engaged = Float64[])\n",
    "    \n",
    "    @showprogress 1 \"Simulating...\" for (beta, gamma) in parameter_space\n",
    "        for r in 1:n_realizations\n",
    "            g = watts_strogatz(n, k, p)\n",
    "            ns = falses(nv(g))\n",
    "            N = Network(g, ns)\n",
    "            \n",
    "            seed!(N)\n",
    "\n",
    "            for t in 1:T\n",
    "                evolve!(N, beta, gamma)\n",
    "            end\n",
    "            avg_frac_engaged = sum(N.node_status)/nv(N.G)\n",
    "\n",
    "            push!(output, [r, mean(degree(g)), beta, gamma, avg_frac_engaged])\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return output\n",
    "end "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mSimulating...100%|██████████████████████████████████████| Time: 0:00:24\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>r</th><th>avg_degree</th><th>beta</th><th>gamma</th><th>avg_engaged</th></tr></thead><tbody><tr><th>1</th><td>1</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>2</th><td>2</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>3</th><td>3</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>4</th><td>4</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>5</th><td>5</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>6</th><td>6</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>7</th><td>7</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>8</th><td>8</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>9</th><td>9</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>10</th><td>10</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>11</th><td>11</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>12</th><td>12</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>13</th><td>13</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>14</th><td>14</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>15</th><td>15</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>16</th><td>16</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>17</th><td>17</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>18</th><td>18</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>19</th><td>19</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>20</th><td>20</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>21</th><td>21</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>22</th><td>22</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>23</th><td>23</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>24</th><td>24</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>25</th><td>25</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>26</th><td>26</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>27</th><td>27</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>28</th><td>28</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>29</th><td>29</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>30</th><td>30</td><td>6.0</td><td>0.0</td><td>0.0</td><td>1.0</td></tr><tr><th>&vellip;</th><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td><td>&vellip;</td></tr></tbody></table>"
      ],
      "text/plain": [
       "10000×5 DataFrames.DataFrame\n",
       "│ Row   │ r   │ avg_degree │ beta │ gamma │ avg_engaged │\n",
       "├───────┼─────┼────────────┼──────┼───────┼─────────────┤\n",
       "│ 1     │ 1   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 2     │ 2   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 3     │ 3   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 4     │ 4   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 5     │ 5   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 6     │ 6   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 7     │ 7   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 8     │ 8   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 9     │ 9   │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 10    │ 10  │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "│ 11    │ 11  │ 6.0        │ 0.0  │ 0.0   │ 1.0         │\n",
       "⋮\n",
       "│ 9989  │ 89  │ 6.0        │ 1.0  │ 1.0   │ 0.048       │\n",
       "│ 9990  │ 90  │ 6.0        │ 1.0  │ 1.0   │ 0.046       │\n",
       "│ 9991  │ 91  │ 6.0        │ 1.0  │ 1.0   │ 0.048       │\n",
       "│ 9992  │ 92  │ 6.0        │ 1.0  │ 1.0   │ 0.044       │\n",
       "│ 9993  │ 93  │ 6.0        │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9994  │ 94  │ 6.0        │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9995  │ 95  │ 6.0        │ 1.0  │ 1.0   │ 0.046       │\n",
       "│ 9996  │ 96  │ 6.0        │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9997  │ 97  │ 6.0        │ 1.0  │ 1.0   │ 0.05        │\n",
       "│ 9998  │ 98  │ 6.0        │ 1.0  │ 1.0   │ 0.048       │\n",
       "│ 9999  │ 99  │ 6.0        │ 1.0  │ 1.0   │ 0.046       │\n",
       "│ 10000 │ 100 │ 6.0        │ 1.0  │ 1.0   │ 0.048       │"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = simulate_ws(500, 6, 0.01)\n",
    "@rput results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RLK2K14ECa6YmYF/2ZU0parsZWvfYIhL0kp3T563IK5A10smlWIFFDQxEo9Sc77KWoUE4qU745DV8baqvR6wpuPsifgbGTGcgYTxqZyIpK0tNxyOIJo71yySw5fT9ZW52AnbrrQF5FXOcZGCXLv3CL5ClvoJ3nGlIqZoUZLFCXid4zp5rTixdvpYPrF1ifTTkMIEJa88WGIdGy8dsUsE6RlJlXkvAE59YjPG618WTRO8SfOITzXrA/HbTfwZBzACr4fKJvxzCUrxYn1zzOqfAQtN5UIJNKVTpi8vA8MRFkip1lIthPvEJJIaPfZ3myKwpaiXqhMN0EotkOa+pFTABjO84cb6AAagixEuX5eUCS0oE9v73l6BXBwEsV48TA5at5AFrfjadi6Wv1byil+YDk/PkUFUj4NyGeD76YdCoYAlb3A/UtEKigNlgekhTeS2f7yfdE59Y3PrEayG2WO8Tn3hPjO9Jrn2tEg2vVMAuMWLZ5mKEIqsmPmF4Mn3qzcBElK6Zdi5hPGpvaAqQ19VXK40pRT3VoguRFo7lo4Rk+ff2nOVddyXVXTG+5CWX0gqX5VLFhPln/gYLDWvMYvCJ3JDm1TVX40QuZYc2GA/ABzZQYUc6DhUYX4GpV14WYEojI3mJmq6u9FM94be/PeW44LrrzjvnxOslL1kiXl2BeQswY1tOKSeSnpzQ+kq9cpOisSWYKUyvxswz+duyzPaEhRvmgICplJaYKEXtEPCcV6S6hAFG4XXOwgsvlbtgBViAVJapStSrTLA8RAEsDVSCefJYE1fD129GwMwQSQ2UT9pQ6Ztp1xLGo9o7YRYv220E4MBaOQPuI7Zk7KhlWWz+lDrI0YDFOyERC3XxRJE5TrwUESmsv3gBW4A167bS1aBpYsL/KAox2KVr0p6ZdiphYwwScyeCVybGQ0F/qiQ8tsgxf/+nVMVcw2NdaJvlzUuMj33sox91gWEXrTxEbmBOTmw7hWafgAPzVp07Hj+79KqZdithYwwSvYUs51GAoUoUsC4wHpenjGk5eS5iIQ+TVDuFcMcdMd6Sgb05Jl4LMdy6SDpwdJd8dz5VHOSKIXxwkjVc1f5WYrxsSufSM9PuJWyMQeIOTeER34EoSNFVYksJ+InKGKuH/+RYIbHVDjFt9HbLLYkXA0azMXRpoDCAKMshqOhJk2pM6qBxlK1aBZVO9RM8M52BhPGoHjANh+tQK+b3tXg6GYjGpxAL2VGgH3bamO+WW+DNb/74xzOxO7HjbIaTWIZ1ppVqj1oxKdKAtbCJOgUKWM2x1rkrZjoDCeNRvZEOTYepEAsYYOyoDyy3ZdW1Y7osH18kPWppwHxeuUo0SCk7kYIKWETKE1u2pIDlvMUtdcy0ewnjUfWdEBGs1nSVWON1gEErZ6Qla5YNgDkw/lNOwAAWXrVKFKj51cTsXEkz5o6U93wEz/mkReClFvM+b8BIzJxm+SxzXtHZc6lovIQkXjJvz3TmzlSk3mRrVJvFlTq1m/I8AttGfVwMsZ2E8ahHYEPqgwXW6rLZBvHDWZ2zhky7JFpoR9IcP7lsqeFa5NIldekaXVVTM1cJTWp/ZmrcWsNlE3NXkLWA5w4Y8+JnFmQPaRacTNp8RHVDwgdpY+Sh8rrzzpB4XbqEz8NARBeOQD7k0wWY5Vtk61zifU8xikwxfsU9YqadSxiP2p/5y0KEroTL55vO6C9mmaxRA8r/WHZIrxZ773srsDy541IbamzppeHLWfL11GCjfEgpNS3xbLYuEudYALVrcqDAyNpPelJA/14csBLIgPGSpYllq5gIqInvTcAWYnmmTl4bAWJRujV7RGKsgFli5lF0SygAaWJ1v3U2ZuyYafcSxqO6Q1NPelIh1gysSDgn9tFMyTNSESNpVVh474MPlvKSgP1ardz4yFWPmNm4niv5Rg5s0NgVkJzNIL810xlIGI+6DTA5kEFQLFKmK18/n5/UtxG08gAh7VSTYzxPOTQ94wIt0ERyDq/6wFh0u01eLM+ahA0mn5PVK4yYtj0VGcPLFi2mLcACAUueIbN33lpoUT1vkZTTu96V/naBCctXM3NeLRXu3dcFRo0oEC82JmzGOw4dmC4x3G8wwHQsoU3fnALIVKhJRSxUYDH+1byErFMlonltGeHGjZ7azY4NeTFgNUyvhThQYL2SEoDXe4ZYD1jOswE7CWRHLELw7lzmFq8x8cpSgZmhX8/yOC2R5iWqxzF+ss7yzEk8MdNLMA8bmCaHSl0dcmKWZVURMfZwmWrEd8vfeyx7eXX3rc83YnklYvUrDCRTM9qaTjWB5wAY2tsFJmJ0ipiLOeg6MeLzjRt5rYU0F2IMWHs+yaxLfTEGzDw6juXdBTRlmJiArDhRh6MflHXfTLuXMB7V3bfelhRwipjE0mFceSE0/P0umhtvvLHZbYpU/B4sVWLalI+8vVifMEO3SjRd4FjeDhIdneneqUCmcc20ewkbY5B0h6a08f1iZPGaZDFWGJVXcIAlLoEslZ2OPO7BPQELjGMDpqqliYCBTib9Ed+BXDPTziWMR3WrRIfX9sACpqrAsEHDbTHCjTf+WLFQRohdNEAvMY97tBkxruWLcze5KqwSPWDrHuS5A+YUlKYCq1YhGiVWiVA+AYf6f2yRWlmmgSYBTNuwAwxoDa1RtXSAuhSv1p88CzaRh7WZK2bavYTxqJs3VlnRmI6YTmjix3AvPpWJsfCKrcqMCIxZW+JBKviCIrbmGTxi+MXySVpte1JT1vMYOxMWz5PT4RLzeemBfJ1MJsh2uLdu+xAZKrKeBgZ2SD47c2R2Cayl02YvV5gmBWyiArYC25hp9xLGow4C6/EKnYQtw9jaRDJFqANULSByu7cVmFCCZUU1A5xwYiCeQTZgdTIbKnLMKc0nYcSSqvjwctXmOQEmDQ/4DEsrKpJGZgPo8lmK072VmKi/QmrFns6JICAcklXAAKfUK7uyurQNNokIYpyy8iprkIQcQD8M34/z6QsXLrxmOfm2jzh3ImHw0hJkhUe7CASWzC1mnE46zzYsqlfF+KrKK0DjxZ0OqAWsmP5i0qY3m5Jh67sRa9Zmiy/u77WiRwLYCkJb0H4wwNobqOBTDz32M/6dcF4g7A4CC1uAolUKWORNFtQ6rrzECF61SC1i9KKaFM5KgTDwxQQsvWsMmyHWHnH/g34d9CsBzyFp6bKapz2EKrG94235+NwPXPiOz6T7kK9ULIvz6KPa3VntN7eVfEbBTvIqOTyrq+cWqe9NnOfMi7VtScwbEBmvpEm8TujFijydcvdI2c9xXbvnBX3tLYqfeigz+9l84o10lNLFKsimCxiDDf6qUiVLWPY66DWKkI/vvrvmGSNfURvzaxUfEG2YNGFO9EDy9fBUqJTBweo6D7JdksIw+yxhn/uhfN59ByZZHLjhQYVVVE3DdcBiBJwBUKLWElcviAP5mVR+r+IDD9gHmHKJChuumqR5XbtLnc4bms72yZnssw1LpD59G3zWeS1wkCKKmObV+mGhI5iKA0umaLxwKKR0xxKr/K50PdIhvcTW83KbrHJiTV9P1MNRrqoOkV3Np820ewlOWPYSH/upz+RXYa69eFuWLLJuH5ghBhJzmdRRcmFWY3o13DrrAibdenLWhZNRcjcjWO278Uv3gLFJAlIOtR8majmjCVUfcFRKepDCz5f5yTEib1t7bqK6eiXG+vyKRumrmuLiYytuYH4p9Q34pTFvPGkdAzM9IMnhAiM5wAnue7z0EdiZqY/ATqM+CGC2Yjt93gcKjLdbzNvw0qlvJiO1Jy9FuOnyuC+Fu6vrZhqrrc2TnIY7qwDRQOIoIznrzE1M/2nClouTQs/H3Hpy05vfx4afpMjlRjISczKzxNiGkYtbmM2SfXmP2IyPr+g5Fh+SL/2viVwN6bnTOL7ubUUr/Joyr3MyCcc47tx3pzj4wal4KbOq9I9keLUKzSs1mePzMAmsRiZr4185p0M88NoATBQ9KpQgXtnnmOkMJIxH9TdWsZbnOj385PedUzixsbxwXlvJgKKlk7mZrlaJxEcDa700vFyHV58YZcYL2DkB5hre6RzDik6AjHWZZYHcBg6rLh0tqhe9KK8ZozcQsI1Vmjk1MKTW2SGlM/5UIbvAWELzIO1AgVke5D1YIgTGp1yStdqw2KAQaxtlZNWLXpTjl4F7ELsImOV3esBPUmGjFoqY8/ikodw8/HvYwILwG1YfeYW+JqkmAlZrLjxMOSKv8CKcV1WtNEPbg3LSBow4hlSKg5nm5M3zBlDvV8+DGaw63sTrUIERJ2b1zVRWgdUyVYERO6jPVtJrQfJYI1WXAHVzsOnXs2m93aRo3Z1j3RnkIH7VCWCiwnNhnZM2rG/6nia4qZByLkT5H+PF3692zSI48ynpfpgBi/HX5f5fgKlkadHA5MP+5k7U4LyAkCfxgakidr6BsdOVVEnFfrFTXYeZgksnLhewa64pTllZnPnDPxygVoksobAwFQDCITvBcuEQJmzHDJhuFNnhOQHWsb3S8FOZykSTxCQwuPXWVMToKWYFFtSCPr7nq8iSOQv8KzjFRQZjm6U7dqLPcNZV4uffcjM/DeMpO0+cjeWBH4Mk5sLDqLW7FViVWIjcemsiVgzHeIW8l8bEWfjAeN8AhW8e0OElz9mx2Ppj1Uw7kB0CM6VMaCnIK272JJ9mXiE3XVVjgOFipJJuppbr4kXQpgfRqGlea8B4j02BiVgJju/m9nAIV8HD10H6fzk8/ucRwOUU/uhfv2n5W8NzzHqctUvIH/menQADd6ijKXV4gwQ8SPIqwEQeWCWWTSFqEaySrEYN18WLF3nZwGEIdpo/88QCEK830uWyzEclwhoXipjW3zXTIo9+4yNXvvu+5e/nf+72K991+5WbbqZwuOfmR7/hvkVbwktMOi7aR1+4K2CebFL2kyCwRlao6zqk/I8D8xYo0E/faGKavEOWnxkUVa1S326qaOtdDCyHsCXs0ReGx90Ov3H7o99UIZXgy+k7XFdA1vAcsxwXbSqX9+yuDeuZfxte7T3q6QOnRgEiCWReVhxCKafRzGyqUcoQvedUPMCpUGLgFV/+JF6JWPMDnU7CZmCXH58KDVy+KhHhwK7KNBmwErMeZ+3OgPV4hVVeLrDGGWPEyJbNkuXRJWFFrLNPh3yvitA069ZWqHmBCl0VO28OAEysnpkQzOWlhF353u+9D0SV+PW3Lw4FrypLzFolFu1SYd50JsBgE6+wChpzZa5HJUatiVQQMPcnP7lvbhPAlHaiDpWTXYPZfPhxYFduCl+ajH5PKjOLQ/H9FcDD/zK5Ff/3T4c/+nP//S0hhdeYJQ46HY/7K2cBjIK4DnQUlxgIXV0ehMrIxqYUyeL125EnZsJIW3hxYB4vWlHrYWZZEjmxf/1W/bClPOXPe0IGcfm6VP8tf/51DedxHAkbsu/diWN1wtKOh4CxPBMGhivwLk9gxCDWdHNbFcYHH2hOm1qC157FaCx13KOpnOJJKpu4ZyYtV25Kf1+YvsPj/lMG9jtL63bd7/y3mxYPg+K0YyuhqzHi7iLgWt9SETq3gCbJPIhOPmJDGTSxPvAHmNRj4rxwwy6yaHUF24PH1gdmyVd5cdck31lJvx0wLg9nYL+RgOU/Y6nCxhj+nciSBdzwPi5ZlHxdAxbvr8QChpPkTS9Dex7GjdiItQxlQWglgtienLTksMqLh4pXSHfNtCYPsxL2xQbm8OoUPh7FpGTrHaAcZRVDRWvISreMeYnc0LpKbHZtnwqYeIuV3PQSz8FUhTmqJmaBPVVLCX5YtmE3m3SuhI0x/DvplyCHF3QLGB94DLxHDCwK8eJTBxQwpzdmeEko6c8DbEGSSCY3/cCJG/RraEq5dNOYKUsf2JXve+TzbwlXQf4zJmFjjHYnqy/o0yv9pErEyCeoaokbsBorYuJUUZaYUa7qY+/cU7yKQjmPOdJEi/LKqiWRwUwv9ssH7G199cV8hV17C+Bc460t6OsAO51sA0wmdIuXq4fmJJCKPmY2OFW2VBGZ1AXS+TecvEPZyuDjFQBReBzPnWLhI9FSwKhlah+lCgT26EYspaCemDfwa82U5Mu0+AnHJIxH9Vav4H8v51CpefvWt4+RCdFBGaf4IlglUqA+ABzLYEnZPN1GViGonzM7UaqmtmKBPU1LJ+WQhPGof4Dn1u9Sbc30DC3rGa9LGI96BDaktmb641rWM16XMB7VPA9D2eqb6Qq0m7i0Z1qt6mCtVnXnzCs+qRYNoE3J8zYVclX7rZgF9ie0eMlGJYxHtU+c6+dcQ3RDhcNHdXiDQqvLAVVr2kA+ImmWvlAG2HHOIoY6monxIWON4vsj5nF0zYHPF2G3gKczy7hrpixfqcXE2ELCeFQHGHMRtbeIp9KPtL7lLH1M3RfnLT9NHAjZXySnI3pSErTT+umNgQDD2skOby9OJoni6QD7U1rGbW4lbIzRuRMOo5wzYGbMSsViYQyYUWKViL51nk2Fw78VmEur2NDOYWvvcZAxCapScaRZpXviqmxaMyV5tpZxm1sJ41FXRjqA1XVGyYFpFa8SGaemV8DKkFTlFQBUf5lXi6vAYi8ieMDwDtRERsqob6Ysz9EybnMrYTzq6uMVBszHFdxkdchDqGp9y5OVsaoy/a1ZMGZgbAOGIu2NLVObagNfCDA2UKmAtTx8M2X5Ki3jNrcSxqN2RjqgmlWRc0pLfyB/TUfXKzBo1CPWKnGa1Hxs1iRqA/M2jM+As7OrovgA92k0e3zTNVOSa7SM29xK2BijcyeSVyM0BMXzPjRfDQx5UWT0Eqf6sPijH6285GAGN38zrhlnFENTqnCVRROoY5MWx4D9WS3jNrcSNsbw70TzYtZdAQa9WH1e9QZr4ak7OAMqahOXSll6c3qO1PlqnSIAACAASURBVHY7iY50NCWQ60DHT5+sOM+6YvXMlOW5WsZtbiWMR93weAX8ZsplaeJtrBGZbfnF2KwpAsYAOPKAzq7xEZcyy3Hbk5fydEz4Oz0zZflzWsZtbiVsjNG5kw6QVRfRAQYOTK4JmE4CQw37mYePflT95L1FzDj1N/YeKjdKqstQNZM7mbRrpiR/Xsu4za2E8ahrbj33E5WCxcAzkwULaJ9Nlz+zG2+BYfEIBBXQgGx/5ojoHiiPVIzF2WzRclAeeslpiXS8wssB9he0pEB8Zvnwct/XLSeP686TkhLGouk7CV0BRcJROVnwoA6wckgrW0qSuiIh+X5iu9KsbBtxNAunR5bG3SNiOVl7uKx3h6NDSvXgCLC/qCUFslkBv3nflX8xTCEMx+y9jspafoVlg7ExGTRNO8SuK1syWw2rfvcpFVWJ1h8XIx0VTkS/YsJqjy/qFMQoAf99OGYieR4JhrR5N8vHoy8MX/LIGIUwFs3cCbM0s69SSvN3NDIbhooBq04kkA1x6ot01RialIYb1MD0BaiXMCleRceidng5wJ6vJQW2mW2/eV9m9q/GKISNMTp3wkA0I0slMNuLRAaL0KloPKVas9wfSyyJimHp8T6Ij1661hNXSx9A7ZOZw9icOtdMOURLCqQS9ug35UhfpGlutqBwtSg2PBUIF6TbHwD2eCXUydrVZKlKDA6wOnxVE81m4xM8kUbHT9KU+cR6klxuQtUrQ0TuxkxZrtWSAqkNS6Qevhkuf/GnuVlgphRJgErp5seeIrJ59eR4VKej8Vr+hby5PSaaGAxe/EShElAa+wm9/4mnkrO/W46embL8JS0pMHuJV77vkTw98YymucmEa7wIGCiljNzD1wcGlRjqcd1q1EJpnJJUVGxcSabDI77GfeLAuBs5Auwvaxm3uZWwMUb3TpRtnbqNn5gk9XRmxw6x9khZrjQinvbnng2JaTwB7YN0TiZ5CLxRrMFmpykP2N/UMm5zK4GOUg8uPP6+flR1Jx0Ly1I0oII1/xGBEa/6GdtovSeTXOffBVbNnXtTIFUyP6aTDZvZLtEBdr2WbQBpCXhw5btux3WaHelWiTM7gZ7p13Q6Q5F3FgaMsNXRerYCJcerriR4Hj4NO0l88CBaH8AjVhozsVm9YLlipiTfrGWITEcCHlz57vsevm7504/adzpWKr4aTMpxYmJYBOR2D7jrQ16BSfUSqxv5W6NqeqYG38/QTzexLNG8glycJlvM+mbK8re0bGCyKmiQtOjv8lWnBMZ6XFYneAldO1Uq46u0AByrR2Cqc8uNSEfRLMTkXezmW+il0QZYmTcsemhAI5eumbL8bS0DXLoS6Ojyl/yft6ys/Bt5vBI2VokaWDM917HDWapirgtbopnNAojxjjv4j57Rk8tR2viuVOkqkSDj+sAiPFHbr9Y3U5YXa1klskHCeNQvdDe3YBJKXsALHB5wYGhIlmhu3dhp4dWIJaUPDDUMWOulUTLIo/VtA5b2zWuVWJ+HjQD7O1rGbW6FjJVrw/EqEQQbcAsYPwSLBXOQuYZW8tLnTAogO7NE9VUepbLSwIDKVKsSa7oyckwpWSBQJVcuXXYxYLeIfiFtXbSxSvy7WkyMLSSUj6WrnSWPGeP7cfLbFHsvyymps+2oFPDPBmKWTGoyE83EKYlXdEa98AJsobJol1vKKSfPV8JzJ3trppdqWb/uugQ8YIULX0eV36bY3q94XAwxpLZmuqBlPeN1CXR05aZQt4rAF77ltyniiXml4lF8scD+vpadAPv8W26+J28h1l6pmN+m2N6v6JewXCW2YSmhKGIX9PEoszjTUUWyGMuOzFDbSqA2jIbapVAYuutWvVJptndZ6Vi5SZx9nWOml2npXnJAAh4sVeI9N5d6sb20dPn8/Q4wv1/F9RgwV/fDXjtwDfdUbCYhVO8MYxSVeIDZ7N/cPcCnnhAjJ6ZToasIoo/GvEloOdIidcqIfysL7AYtJsYWQrbJJexydjqw2cpvU+y0YcERppO2ZmrPWfR7aBhUj9K8+hAnioHAaj/JWBiaf86AWY8fH6BMnkpmy4ZAcMSePNEmFtjLtQyycaXZL+2YU8Z+8ZWK+bPjJXrAeFEBdc6OkaWbzucF+PpZlPTYK83wnZv9FIGUKjYL81IDDpU2HjkArFaJJXQzsH+gJQXiI7A8YWpfz8M4iGZutsEej6h5qQCpSzsBC1640l8C+zg3L7evGMMQutg6arWeM+TVSL4tnhuqxH+oJQXiE+c8YepUG6ukErY6dWdgC9lghzrqCkxM1MWs6kSpS0bhajJS+pl/7GO2pLDKqgHjMMXob8OqnoeRYyKAiRZO8/J9s39MgiE4pyNPmDrN1kV58+bLa8SGhqaCHXVnXmKHyaoSrcsU5ZUESbHkrXiJUVnkN4n5uuUbRC0NK87oaEkmWy45ta6ZsrxSSwrEWVN5wtRpNgfbcmjKcgLX8iE/UwYexeEVdCoxflXtFAJtRoX5KS+RWbmYl4+3yxmGvAFqiUsyHD+s3IoOKNXWwP6JlhTICtUpNwdLleipHmAKGqBGGbtUgFMDw4sDi7juMpQdZNm16IVvDVjEudqKI3vCAlS5KQL4+MT+Auj5yimA/TMtKRCbrTxhavs2LDVgSYanCHDrMhsDcwSDJieUJXroRWQaqJuRhkCz5xUw8YyFZl1rYFHvbc4MTrHoZd0sKefV2sg2p2oTsH+uJQXirKmz3BxMpGvmhsBPmOWVZwIO5g4wgbIc0h6yse3gjCOwupgYdy/WGZ+ifbMFpRUw6cHTt2bA6Knm5pGOW7SM29xKGI9qq0RwC4ePxNZ7UmViS5ZlLR/jVQxfVmCSeQMVMG92hmzfHGCAGlsEq44/7Jxoh+AVMyX5N1rGbW4ljEftAOuZ3uHFgkDrTEZCF1mNGBAYZGDtVx/aM06+G6woLNW+LFCD0TFYqyj8edkm9syU5FVaxm1uJYxHNcDAKTJeGPHqqIL0CptDQh24gqOBo/cFK2C6TPjTFvujGY0Y48XGIXnE8S1kX61l3OZWwnjUztuNJKm+g9iS+XoRE7Nq8xILJYyPViqj9dZ3q5fT215awxd8dgJBpSVbPpEQ89aVogX2b7WM29xK2BjDvxMObGYn3f6USNjnVQoWUIZsH6vq208KWCkGkZuPDGhgTVErbGvlMe5naVoxC+zfaRm3uZWwMYZ/J2RmbmlsqBiVdsgSrgDj8SlZrgDx3UdltWXAoSk2AmV/8AYKn8Dh4pEhduq8mfkL2k+0wF6nZdzmVsLGGP6dEALDS5cxAUyE8zPCoxOmVMVqtVxhpJyfHumov/h6k7aoEDA6NrwylFirQw3MVr9qdZgH7N9rGbe5lTAe1V0yC/KA62QMsCoRiyAo0CkIgeHYFAdGrc+lS9bwXQc92nm+pCcSvBtA6TbsIeAB+w9axm1uJYxHdRel64IBuoA5j1ccHx5YJSvj5HSRRjdIiW0YGvXSJU4MUxViaa2zfHAVRc/XBRbZKsz2xS0tTcwC+49axm1uJYxHXdlFgAFUSpCWd3jxLL0yaK8IdR8jqG69BVaSNIMuxE6kaSNVZj1ekT/NBpZua2A/omXc5lbCxhj+nVjDMuuOqkChdLviQaUrY7/1pRGtDZsuXQL1wJ6b9KRtsoJKvo0OU40DA6M1Zsryn7WM29xKGI868MR5RWk1IAqfmx9q+QuPCFcZmmr2Y9M2iglZa3PCN8XBu/Q8FhDdsAkrRlClFjDCyPqw/6Jl3OZWwsYYvTsRLZeg4hWUloqHceUqL77/TfUW85/ujqSg3n9ogamuryCGvTux+QOoLjXwifldMy3yo1rGbW4lbIyxcic5gzIvUfDiXp8LDJrxg1v4fGA5WpTAbE+WAeuxBDlWCEpXI9CzsLYAjS4wlWc19tUrjpl+TMu4zR17j0ddmarNkdAJr+qEMkh3Ud4PRme8ym8eI2JtCDhaXyIwk6MFxawAPYZEuOpEDmN41kKJ5zXlytPEL71uplu1dOw4JGE86trcemF2yUAxEe6ijsujlwNnBjvfcpSrdWMCZfKugCSil/VEtPZLp2erHdhe3PbSG6vEN2pJgfjM8spN4fH3nf3mYEIOcEXCHi9tzfRmLSmQTRF4+Lqz3xxMyAFabY+Xds30X0kwhE/CufmLsDkYl22+makCT281t8aUQ3uHAeztWlJgm9l25fse+WJsDgbkvtcVe8zbY2oo38x4kOSSsO9NjRe7xsyTqatnB5U1IXm8URDT7Zds0tj6k+qWtKiR3sutGqm2D46+oSoW2Du0pEAqYXVq4VlvDgbdQYvmTtSgmbl7Mg1gStIBh8Ow5sBmc/LzWz+MnH+2xLU64exQ+O7NqRRevdsVaO6H7h9sMhPAu7SkQGzDHv2G+85sczC1ck0YH8/oHYlBi0nSEtFbF9ubFltkOko2mtk0gKxq5psrsFhfkciUs3zjYjn1nkaLVI5SD9aXjDYt6LtDSwrEaW73hLKF7FWDFLYBZtK2Di6oHpQsSlRo2KnRslBQKjyXryxNOmZd/eA/iWv4XjivEn1t+uv0xjeYCX5By7jNrYTxqGtVIgbo8EBVokpjgVnGTUUb74VGLEhgOVo9JCt6I1csogWC322Fs9WumwngfVrGbW4ljEcdacOCE84HQjrAZHZWJ4HRjolsqnbu005szm++XHditUusKdeATTb1qpkAflHLuM2thPGo69vvNfvyI6ADnYgD6ufWaKbVsjFiNHzDCm3SXD9wPYMZm2oQ+juAcSwusXoNl3LXTAC/rGXc5lbCxhi9O+ma13DYmMjV8HHjzCuvb6aHK6F2GSqDBoyZbzLmVjMDeARKy+kqLHz2MIu0ZqZFfkXLuM2thI0xenei+TDr2hPQKpG65meyYjQrsHpGPwTVSJVnV02qPTkCMTOArwCb2ICh2CMstlaxMQZWGFfNtMivahm3uZUwHtWvEteAmdZInUhehmb6Qx3nWBY5p3oufUxsMYQSRmxWpaiQyapGWIZT502WLq/pY5FXzATwYS3jNrcSxqOOVIl9jYEp+wLg8OVZ1kXOsZY0rPy8d2AyYE6T01RaugrSlSNOMUbzXMYC+59axm1uJYxH7e1bvw0wTUxoOkmTMhkl8+LAAKdqF8MFYVzo+AhcKYdO1rphPE0fqGOmJP9Ly7jNrYTxqB4wUzJgnZfqvXVRqnTFKqEiKAUt5yaqxEC2ozXoekeI1tliplZWdx9Ug0i0wssBdqeWcZtbCeNRvVlTIEvKADCeAphmjRfvEQcoRYmeOBu7lfWxxUOwBQzTyhCcpAFth0QPyumAfUzLuM2thI0x/DtRNhXmXSUmAoYxW7sVag6wCYEBXytURa2H5YrmrvepSMxmYwJrpix3axm3uZUwHrU/zU31vXrG76v6aQJdjkyTZ+HU6m/WvERnrPXQ+sAmrhgFBvi7GAJ2Scu4za2EjTH6d+IUlaAUxvTrGrf/nKSYJZRFe7htfaoSAwMAwH73LZVA1N4OBngqwAE6HQB8bF62fID7EkwRI6+YCR7QMm5zK2E8am9HUmNffrodsNAhhmZL54lb+YQELDU5/N18YokQolDljHnmkzqCmg5wi3VZhMphxDmmYuCya6aoZdzmjsnHo+o2DEaAQVfFeDbNKjAo/bGIL4c4qatXJqwhjVHKYL5x+9ovoO2iwk2JUPXmHjhez34XlsBhAutZNzTtiIb1nNWBTIY/48wl1PcMnJyctDbMdJ9yMn9iMGYYLc6caurqWrj39M2a6QwkjEe1q1ecclGUYKHxdBTGy1gNWOHcgKWTEwUsCZ5QefCA8ZhReSBJNW0EpnsLXTOdgYTxqO6CvvRnZpaGruUDTxcUVHBYmmTpozxXqcT4klmnQ0YnXNPpA2MNCFjAwBCDLrBzUMI4MUEIbNmyVEoT2GcpkJGupY71SQt7gKndiiTG0ElOTvpTbfh+LN5jyhZtwnYOI3fMtHsJ41FXFvSJYcEVYD2ofp4SGKCnU/pA5Ximn3wrKBoYM29M6/pOoIeLJ3R4kctRI7VeRM9MZyBhPOoGYESjhXGOrmdBZcfLs8WGsl8sRa3AQn33Sm+IlxUIgcAfqmcJYVN4Op754FfHTGcgYTyqBgbKqlDdDRkkmDSbI0JgMVkZlCWrjubSWX02FqC83QjaHAHOiwpBbG9XAQ6BSk17FEYJWWsH8uh8AsMCQ4c6WxY2uzGadk1kSjorriKUzi2Q129W1+FGOSwIvXqGwezcQAPLrlCXoRKD81AlCjnAFQl7vPQR2Jmp/5ABa42PeZUHa6hAfjNbiXa+N0aRb07ibWEvNa+g2ps+PJlN/CqlmhsB5iQ+VGDM98NZ8M2s3NfjX7x5huDhVBFljuTL4KFKHfnL96qwtRLkYgDTgh27BXJJyuaZNJpIV6n/ZxHeM9POJYxH7T4P42sclArD+pq5Zehm7qbTqW23qYSrhQ2qlyuB8W2oKrD2DAVjRSvrZtq5hPGo/VlTwEY8oGdeTwVtfRjm40HtE8NarWNHfyUKfoO22SKUsgQ8t/pCVAGMshCzE1fNtGsJ41HXnji3gP5Ih04lO3G9VGtaXDjeB9ZXQU2MHak+MKeATTTeaJuxPQDD9+M89hMXvv2h/F5Feyfa8NCM6EJxDS90cnRRAXNVgES6NZVVk33Ta0cZsGiA5SqRdbSrDgul9wuwZtq9BCeMvY7q06/J71W0d6JNzq0oyUFTGGCKWJ8XyxW4bggY34Qec0t88PEmG5gvOsqiplJY/Gu5Ztq9BCeMv/DttvxexXQf6pWKvnlDU6o1mc4KzFkoOxkGdkFz5RlXW9bFkG2tpVqBibwWSnNVsWLC13EuYvewbFm6azQ3rMA8c2DtLYqP/dRn8nsV88no+8OkGvgaZxlXpvNyY3lSRBGj2q41ZHUOXE7CigBt9LX6DpVYPQtDjMqRO3IsrbfPEvbYTz6UPrxXKq7iAhHoU9EnPWLrFzReBbD6S5YS/kqOLjChUo9Ae8mU9fbYhn3uBx+q71V07oTZjYqQKg4OTw+kUvFDgunlmQL1lodtRzBwgZGBWZLIZtQwDVDBjGaUf4XX3rzEpTb85IULF17Te/G2MJ20Yp8Xj6iU7uEAMFryXIxHc32BP/2IZpquOZlobRkH13xI+xvweR16P8w6fqqASGCgFEBULOFNVWIKnUMrQvRJXni0zZEG1g7lCkygwAk/gKdrmWlqhwoMXGBM4+sMYNwKzuXVRq60qurJYRPzpkXJ2QSshdMCaRrEQv7aW2EFtFyjb6ZdSxiPunl9mNR5hc+CcYnABmCADiQHZqhYVK2zpcPKUbmW42WoFxRE/CnIJ9aOmXYuYTzqwJ6/QSjBUXWTCA2Qaq2EBT5Y2AGm3uPgVG3+fOx6LjMUXj1Hf36BBaEEHU4KMEk6Oc5SoyIRMOHqscaIaOQrMGDNYzeLUKIRvhIJq8xJxO+aaecSNsYg6fXDhBGF0mLx8MGGAV7OqyURwJR70TYKyDTKxGrA9Qt6Dpxe5tXhhYULH6qJMtgz0+4lbIxB4s6aCrLUkNIHJixfQwC1CpQHTClBABMmzpkXjGx4l1vXFqQ1jWYkvY+emc5AwnhU/1UebNBI64SJXRUA24lKI24s3RyDGukAbV6qvJAUrx1XBy3WUTpjIT0znYGE8ah+lQiGWJ+XVVVgnWQjwNRsQ97BgiifhnBeEsrUV9GvoWnaqzAdXgcKrNmTlQqhdIGxqIrJuhfTZUlTBNCJ40WClQH2xNHZa4rqTDAqTDbxt943Vyb/kfMaDxgYCj3wcLXrhmfptgEGAYE1Z0DWiiD6Um3hM+0wYEvY1Nk3jPpaGJP5niydY6YzkLAxBkl3tH5uZ0YnLe8EU5XYSdjPMDC33hoZCFi1MRUVB1hEDKCGjDlTgNYesrXP5wwY4OhSs6826maWK2VsXku1AVjGA9WzZ700sMDYgAWmV0SLzqwMazrXTLuXMB7V3wkHakOy6iIAK0RuDK7l7RswYFBj4h/uJWoCJbtcZkrBaQvIsiYf6B2ehSsIXoYgWy+tdcy0cwnjUZ23GxXRUwvJsKKbJdOGqoLZ18u8W6eNZxFoBWYOcbzssqJSPLWkYzUvkafj41BqJKP5k3PlBufCSxSyYU6z5bFF4r5aDDWSSOtptadtBWvw0rFN8PHU5x/YcTHELiWMRz0CG1IfLDDyAMinoMZIfGIsfWFMw0Laf2r9ZqFun/Wii/r++zt1E9TaK9a/oLwDMjkbKuYJW43ZFu2xHM4ZMMcVJHePfxoVT03jhzq27CcQvUA+DJ7NcH+M90f0D4qIMSbj1LU41eRsrFFsI0tbSrRlsdz/IH/nXDgdPV4BlczGTEUmd5KJ075KA0MM5IwDp+LN6agaijhF2Ucr6gcfbF6/AMbK6zly66VlgZmyaB00PNkGYOqkmww0MFOM7NQBPoqbzyYGjBfNBx9kD9hkMtC/g56ZzkDCeFR/pAPE+jCjb7Gc4C5MWyV2UrVSwN6i0x92Z502NoQ/iXmJlPBBhwpBtjtUuWbavYTxqP4UAdCmFloM7VOZ18d+w7qOgKVTbULDiyndMaZm+YrSBcb3mThHwDpWXFcxfOhBzuv5Ba0Sx11g/qQpNhCS10WY+hRvpYe5VrIeyq6ZdixhPOqpXpYj27f6KQPc/CQwMKyqiu35G7Qb4OBqo1NmHiM3vceLSpgFtm6mHUvYGINkZQtZA4UFCNMrhJyJxSGTBXtBAUyM1+YM05q8qNshgsImt6l07j7oza3vOJ5dM+1WwsYYJJunuTmKTo8KHGAgkvFyiMAsU1YlykJVcoyssQGpEZPbLC+7UyKI/PvD9QcEzF/Pp0+6K/OCSSoVdKKyaYdmOR8t38unYmIiKXE5HqnKmrxSs81MlQ/Ter4Sb6LMaBUgW8pn39K4xwV9HdkwCccUDSNV5+hbKqABLaa0F8PbQKulMPF42Pc6aDAj4/DetMNGN1gS9jwMfwPy2WnPTLuXsDEGybarVzQYpuoBo89eMuCh0KrE/DoWzgUUDDbKlB9nGkdPAsNVK7mTxlY/TzQbVbz0tG+mnUvYGINkxK13NNDVCN8S6oHk0u+HlfxmZuC292vvJXxUxNaAQWxzGXF6wSTckXPq1vd5ucCCk0g7+L3q0lXl/GgFZsUghiwqIuZHRqwt9ZazzPY5Dc7pxpXRcuzk0LZ96Mjw6hWX16Yq0Q1e0ZX8+CbNotykc0WOylG+SfQ4lPVp4hpGx1GN8q19yueiSuwbUQUMArMq1q0meBYYNzQzc5LIDxqxFlSegXFiVVWXTzDIPMfzCcy1vQnnp71EvfYNmLKwUpGAzZoSXbC2esUb8gBgxdJZvYIwxa4swFLVyPgU7TwDC6AJjQNTHqftOHvp+PowkmkSxLzyIGJ7vCLOggOraVfxiJ0vYKGraEOHeLqGEgSvzcCMKT0/0R2MUiTZqMfMotqRjvbSlnMCbJ3KirsHpj3y8sOAtZm/wIDpX39KZnDYI4dYL5F8Uu2Qds20cwnjUTsd594YoEZVUxE04Gm8gd2tgGlqoFwNgD6vpgIApRTJWKsIMk7XTDuXMB61OzQ18xPX3dMpOTCdIUsXxFRtF5gajNeGNgGapUxIN+nl2RQqxnnohwm7KWDGvvKCQVaJcp63gUJTtUV+DFhn0AI851CUFOwE60igkzrFzxZD30xnIGE86nbrw3gs8FJqYCZbrcYkvGzOdsyCCoECRqBInGdbpGGju8DKlQusb6YzkDAetQ+MWVBm7oVXWHjkA6NCNNu0vIPm7Pmr+8tq6hsT3Mi8lTPUFGDSo+cqYM3YmpnOQMJ4VP0qDyxFdfchy0t0fUVSJpoIRSgp1fxaNvIhUjMzMuMyh9vhJfJWr/MoHWfwMLPUrvZAgXE5wAnue7z0EdiZqY/AKNOwqubxvIp0LHFHLeq2swFWasJzDoy3VugD1hP9zcjr6LgqAjhvz6jRbMlE3nXctz3Qx9GlojQNzoxBbU9MykcmFkKeY4k4TTLSoQILiIXGmtCKzX0E7uGLhJQ4cAWLIQ5bjnoEErd9AHS95cZs3NHPQjTRNRdPWFoilpiiowifdOKPNx0z7VzCeNTR5UbKrmRynRA0LzFSwo/6F+uMJUrHXvKSfTSI/JFYS2RHq6CT4/kA1jNhqEoVAxoaPwl4vW1NTpFOR23ymgfMFjBUeRylCkwAmHRRzh+wZjoDCRtjkGwARhYHbm5u/F5SFt4tgT1gQFaTg005kTEvt7xPjfEpOcLEa9mVHD0znYGE8aj+9nvChK4SQRSVyxqaB2LAtDwtLwksTrI9MjhMqZElhVbt1WEMMb9DDlHpiSAdM52BhPGo/RLG0fnVpUxm0vdVChgoxSxtOk3GvH6BcHkx91IqVTKan+UOTh08MIBZnvZ5gR+J60xyldAAAz1Ltzl8zNimPNT4wHCxDlyPM7qiciJIPAdOhzDcRmAlAfiFr9+2JZmVThGrwBANTU3MqWJlKR9vAepUCYu6fLkj+QTY0Tlm2r2E8ajbzOloWmgUO2n87ERffAUYFaNWGTIXnObSG9NqYgpKh4nc2/RcAfN5BSCH0NN10zg1Idfq7EkhVvrLPX2hEqujEcq2yuCRp63Tsx2/wl84tvcqEV+3kj9H3r0iba8N7gNTIyKWWAeYTDW3HSsdYLSBl518aGze6tLaonUrRCv73i8R326UP/FkoEoUimbwmanbQJaiZ7MDUnWqxKSobRhasrVfWVqYO4tbWR2HGzWvlc4Aot4zMHx/WP7EE/2GPrGMr/zVK/GU1ESzeDUfqTrxN74NMJmsvYqPzGzX83GVtLha0JcRUBz7nj+ZNkc/kDf05c/2uj79xLn92OXPXgfxEqGjOSoZumnWlD9fJrdc6B8U/4/H0kWFDS2Sy9Ecwn66SCPPTA6lhHVfNGBevG0gsmErFk+jgRZTECkqkbjp5WuBseuFi8AaPMDBaVvoHwAABP9JREFUqNo7ZibPIXgMDBhzCB9sz1RqRMFaWO8w2zAGjM9LDKTkpJjO2Fwlk7ihPfByvX9S89986wVjH4xNwyE3f+LR6bBmVsLaROwFGO8ryHJ3AMDwDX1rXiKWpXTMO85VSWdDvFoqEQfKPwyjOCxGK2EN2jTRVO1Z76BtgTmrIUBAFKpI+2hPs04Fjpl2L2E8qrtPR/rUwDgJgWQdGHTHtWTW/AfB9lmO4ghovELqKzH1phZpen+fDgD2XEzMhtxgpt1KGI/qrnEGU4mt1nsSgXDdu0nNmAfzXeSCPo6mM30XgXFRpaizrwr+BsB4/Otm2rGEjTFI3H6YtnHTuMQkAwYZugllKhmHlswCiCpRhbRjtv0o004T78Fhev1wFNqgFfXQzx+wvnkpxIPJgLk5spj9H0Bo24KyX/1kgIE6ZueAvNizFfQky4J3O/7PiKmOumemXUsYj7pxTgds9ix0SB6OVy2cykZ7huJkVg8ZI1o4Z2hLmCaGSPhoBY86qTkbtciJWnPNTLuXMB510xSBbnep8VK2ByIgVDIm6KLHY7J9eRkxPcIL9GzMqBC3+zQMpgpHvWCd9gTxiJ0jYNq8IA4wYQsVwBRb+lAXFBdn+3TIJ5U1ET+TZc9MH+CjgRJYjiE0wF4QYYkdJjDgzhu+ZE8alCJ22qp6qN7jzKmnCPots3hSU9nVK2LoQVhTbLgBIoX6pi2X4r5PTENPYKLy9F0z7V7CeFR7J9WC1Aw1KoyPLCla2+buNhr8Q6z3k7kwdeSDesyAa2/6yLspalRO3n4GvKzKGIcMrMoBrkjY46WPwM5MfQR2GvUR2HYSxqMegQ2pj8DOTH0Edhr1Edh2EsajHoENqY/Azkx9BHYa9RHYdhLGox6BDamPwM5MfQR2GvUR2HYSxqMegQ2pDwjYUYbkzFhlCTvI4wu6xS/s+53XS59ewn4ue5TTStj3DRxlOwn7voGjbCdh3zdwlO0k7PsGjrKdhNMn7SyF3i7xYz9x4dsfWk6+7SOnvPS3feS0l/70hQsXXrP1pZd0t1Eu2156BxJOn7SzjGy7xMu3//RrHvuZU146JzztpRf51ENbXxo+eeE2ymXbS+9AwumTdhZqbpd4kc/e9rkfuPAdnznNpXPC0196+dj60o/9dilhp/rWO5Bw+qSdpdDbJYa0cjAZ7mdPc+mc8PSX/tRDsPWlsUo81bfegYTTJ91NCXvsJx9KH9t9b14+T3/pz/0QbH9pBHYOS9hO2rDP/eBD2QSf3aopYC3gZ0996WzrrS+NwM5hG9ZZCr1d4k9WV207Z2snl86WP4WftyQ77aV3IOGLfL2jfIES9n0DR9lOwr5v4CjbSdj3DRxlOwn7voGjbCdh3zdwlO0k7PsGjrKdhH3fwFG2k7DvG9hOLofH//zN8HAIV8Gjf+17wt94S7gOP0voH3gJ+76BreTKd91+5aabH/3GR658932Pfv3t6d83/h5+5tB93+GZS9j3DWwlCyq452Z49IXhcQuiR/K/36ufj+TQfd/hmUvY9w1sJQXY5cfftxQ1Dex3c+i+7/DMJez7BraSUiVevgou2xL2uzl033d45hL2fQPbyeJ0fP/NV24KX5pbMgHsf+fQfd/gmUvY9w1sK5//uT/4pWhNwr5vYCtZytbiv/+hlrDvGzjKdhL2fQNH2U7Cvm/gKNtJ2PcNHGU7Cfu+gaNsJ/8fgZQTakTeLFgAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "RCall.RObject{RCall.VecSxp}\n"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R\"\"\"\n",
    "ggplot(data = results, aes(x = gamma, y = beta)) + \n",
    "    geom_point(aes(color = avg_engaged), position = \"jitter\") +\n",
    "    scale_color_gradient(low = \"grey\", high = \"black\") +\n",
    "    theme_bw()\n",
    "\n",
    "\"\"\""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.0.2",
   "language": "julia",
   "name": "julia-1.0"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.0.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}